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https://planetmath.org/PolynomialEquationOfOddDegree | polynomial equation of odd degree
Theorem.
The equation
$\displaystyle a_{0}x^{n}+a_{1}x^{n-1}+\cdots+a_{n-1}x+a_{n}=0$ (1)
with odd degree $n$ and real coefficients $a_{i}$ ($a_{0}\neq 0$) has at least one real root $x$.
Proof. Denote by $f(x)$ the left hand side of (1). We can write
$f(x)=a_{0}x^{n}[1+g(x)]$
where $\displaystyle g(x):=\frac{a_{1}}{x}\!+\cdots\!+\!\frac{a_{n-1}}{x^{n-1}}\!+\!% \frac{a_{n}}{x^{n}}$. But we have $\displaystyle\lim_{|x|\to\infty}g(x)=0$ because
$\lim_{|x|\to\infty}\frac{a_{i}}{x^{i}}=0$
for all $i=1,\,...,\,n$. Thus there exists an $M>0$ such that
$|g(x)|<1\,\,\mbox{for}\,\,|x|\geqq M.$
Accordingly $1+g(\pm M)>0$ and
$\mbox{sign}f(\pm M)=(\mbox{sign}a_{0})(\mbox{sign}(\pm M))^{n}\cdot 1=(\mbox{% sign}a_{0})(\pm 1)$
since $n$ is odd. Therefore the real polynomial function $f$ has opposite signs in the end points of the interval$[-M,\,M]$. Thus the continuity of $f$ guarantees, according to Bolzano’s theorem, at least one zero $x$ of $f$ in that interval. So (1) has at least one real root $x$.
Title polynomial equation of odd degree PolynomialEquationOfOddDegree 2013-03-22 15:39:19 2013-03-22 15:39:19 pahio (2872) pahio (2872) 7 pahio (2872) Theorem msc 26A15 msc 26A09 msc 12D10 msc 26C05 AlgebraicEquation ExampleOfSolvingACubicEquation | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 22, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9869291186332703, "perplexity": 2739.771329301969}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704799711.94/warc/CC-MAIN-20210126073722-20210126103722-00507.warc.gz"} |
http://scholar.cnki.net/WebPress/brief.aspx?dbcode=SJMF | 作者：Ismaël Soudères 来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.635-685MSP 摘要：We prove the Beilinson--Soul\'e vanishingconjecture formotives attached to the moduli spaces $\mathcal{M}_{0,n}$ of curves of genus$0$ with$n$ marked points. As part of the proof, we also show that thesemotives aremixed Tate. As a consequence of Levine's work, we thus obtain awel...
作者：Kohei Tanaka 来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.779-796MSP 摘要：This paper presents a discrete analog of topological complexityfor finite spaces using purely combinatorial terms. We demonstratethat this coincides with the genuine topological complexity ofthe original finite space. Furthermore, we study therelationship withsimplicial complexit...
作者：Shengkui Ye 来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1195-1204MSP 摘要：Let $M^{r}$ be a connected orientable manifold with the Eulercharacteristic$\chi(M)\not \equiv 0\operatorname{mod}6$. Denote by$\operatorname{SAut}(F_{n})$the unique subgroup of index two in the automorphism group of a freegroup.Then any group action of $\operatorname{SAut}(F_{n}... 作者：Andrew Blumberg , Michael Hill 来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.723-766MSP 摘要：For a genuine'' equivariant commutative ring spectrum$R$,$\pi_0(R)$admits a rich algebraic structure known as a Tambarafunctor. This algebraic structure mirrors the structure on$R$arising from the existence of multiplicative norm maps. Motivated bythe surprising fact that Bo... 作者：Jens Hornbostel 来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1257-1258MSP 摘要：We correct a claim concerningmotivic$S^1$--deloopings. 作者：Bernhard Hanke , Peter Quast 来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.877-895MSP 摘要：$\Gamma\mkern-1.5mu$--structures are weak forms of multiplications on closedoriented manifolds. As wasshown by Hopf the rational cohomologyalgebras ofmanifolds admitting$\Gamma\mkern-1.5mu$--structures are free over odd-degreegenerators.We prove that this condition is also suffi... 作者：Melissa Zhang 来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1147-1194MSP 摘要：For a$2\!$--periodic link$\tilde L$in the thickened annulus and itsquotient link$L$, we exhibit a spectral sequence with\[E^1 \cong \operatorname{AKh}(\tilde L) \otimes_{\mathbb{F}} \mathbb{F}[\theta, \theta^{-1}]\rightrightarrows E^\infty \cong \operatorname{AKh}(L)\otimes_{... 作者：Simon Gritschacher 来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1205-1249MSP 摘要：We study commutative complex$K$--theory, a generalised cohomologytheory built from spaces of ordered commuting tuples in the unitarygroups. We show that the spectrum for commutative complex$K$--theory isstably equivalent to the$k\mkern-1.5mu u$--group ring of$B\mkern-2mu U(1)...
作者：Nancy Guelman , Cristóbal Rivas 来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1067-1076MSP 摘要：Weshow that if $G$ is a solvable group acting on the lineand if there is $T\in G$ having no fixed points, then there is a Radonmeasure $\mu$ on the line quasi-invariant under~$G\!$. In fact, our methodallows for the same conclusion for $G$ inside a class of groups that isclosed u...
作者：Matthew Young 来源：[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.975-1039MSP 摘要：We introduce a relative version of the $2\mskip-1.5mu$--Segal simplicial spacesdefined by Dyckerhoff and Kapranov, and G\'{a}lvez-Carrillo, Kock andTonks. Examples of relative $2\mskip-1.5mu$--Segal spaces include the categorifiedunoriented cyclic nerve, real pseudoholomorphic po... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9414829015731812, "perplexity": 2263.2141355764675}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945222.55/warc/CC-MAIN-20180421125711-20180421145711-00051.warc.gz"} |
http://wire.waynflete.org/edible-opener/ | # Edible opener
Students in Cathy Douglas’s and Lisa Kramer’s Calculus Accelerated classes are in the thick of a unit on the disk method and volumes by rotation.
In today’s “opener” (an exercise used to get the math brain engaged), students were asked to find the volume of a Hostess cupcake by (a) a traditional formula for a truncated cone and (b) “by finding a function that can be rotated about an axis to create the shape, then using calculus to find the volume.” (!) The class compared the two results to see if the volumes were identical.
Students were also asked to determine whether their findings were consistent with the volume listed on the cupcake package. Their results showed about 10 additional cubic centimeters over the package’s listed 45 grams (the gram was originally defined as the mass of one cubic centimeter of water at its maximum density at 4 degrees Celsius). “The creamy spherical filling seemed to be less dense,” says Cathy. “One of my students estimated the cubic centimeters of the creamy filling and found that it accounted for the difference in our volumes and the package’s unit weight.”
Needless to say, the subject matter was consumed at the end of the class… | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.832181990146637, "perplexity": 1215.8727307269412}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247481624.10/warc/CC-MAIN-20190217051250-20190217073250-00572.warc.gz"} |
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A square has a perimeter of 24 inches. What is the area of the square?
1. 36 square inches
2. 144 square inches
3. 12 square inches
4. 28 square inches
A square has a perimeter of 88 feet. What is the area (in square feet) of the square?
1. 121
2. 484
3. 1,936
4. 7,744
What is the area of this rectangle when the measurements are 20 in x 25 in?
1. 450 sq in
2. 400 sq in
3. 90 sq in
4. 500 sq in
The area of the shape shown is half the perimeter. Which could be true?
1. area 9 perimeter 12
2. area 4 perimeter 8
3. area 25 perimeter 50
Mary was making a dog cage for her dog. She wants her dog to have 120 sq. feet of space. Which could be the the width (w) and the length (l) of the cage?
1. w = 40 feet; l = 2 feet
2. w = 4 feet; l = 30 feet
3. w = 60 feet; l = 3 feet
The measurements of the large rectangle are 15 in x 19 in. The measurements of the smaller rectangle are 10 in x 12 in.
What is the area of the shaded part of the larger rectangle?
1. 165 sq in
2. 285 sq in
3. 95 sq in
4. 120 sq in
Frank built a closet with an area of 42 feet. The closet is 7 feet wide. What is the length?
1. 35 feet
2. 7 feet
3. 6 feet
4. 49 feet
What is the area of the square if each side is 5 cm?
1. 5 square centimeters
2. 10 square centimeters
3. 20 square centimeters
4. 25 square centimeters
A rectangular living room measures 12 feet by 10 feet.
A carpet placed on the floor leaves a border 2 feet wide all around it.
What is the area of the border?
1. 80 square feet
2. 72 square feet
3. 40 square feet
4. 120 square feet
A decorative rug in an office building has the dimensions shown. What is the area of the rug?
length - 12 m
width - 6 m
1. $72 m^2$
2. $36 m^2$
3. $18 m^2$
4. $6 m^2$
A square has a length of 34 cm and a width of 34 cm. The area is 1,158 square cm.
1. True
2. False
Length times width gives the
1. area
2. perimeter
3. scale
A rectangle has a length of 56 cm and a width of 12 cm. The area is 634 square cm.
1. True
2. False
A gardener digs a flower bed that is 6 feet long and 3 feet wide. What is the area of the flower bed?
1. 81 square feet
2. 18 square feet
3. 9 square feet
4. 15 square feet
The dimensions of Mark's den are 12 feet by 11 feet. He wants to tile the floor using 1-foot square tiles. How many tiles will he need?
1. 264
2. 46
3. 132
4. 23
Maria knows that her quilt has an area of 24 square inches. She knows that the length is 6 inches. What is the width of her quilt?
1. 5 inches
2. 4 inches
3. 30 inches
4. 18 inches
Mark is wanting to tint a rectangular window. If the window is 4 feet by 2 feet and the cost of tinting is $5.25 per square foot, what would be the cost of tinting the window? 1.$21
2. $33 3.$37
4. \$42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5181089043617249, "perplexity": 3761.7777121789372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646189.21/warc/CC-MAIN-20180319003616-20180319023616-00019.warc.gz"} |
https://pandasthumb.org/archives/2006/12/history-and-cob.html | # History and Cobb County
Many were taken by surprise by the Cobb County School Board’s decision to settle the Selman case, give up their practice of putting evolution “warning labels” in textbooks, and pay $167,000 in fees to the plaintiffs. They had fought this case for four years, and succeeded in getting the Court of Appeals to vacate the district court decision for a retrial. Perhaps the third time Cobb’s sticker got in front of a court would be the charm. Well, the reality was that this was not likely at all. After the case was sent back to the district court for a retrial, the plaintiffs brought on two attorneys from the Kitzmiller case, Eric Rothschild and Richard Katskee. The Court of Appeals had directed the trial court to collect more evidence and clarify the record on a number of points they found insufficiently documented in the record from the first trial. The new legal team petitioned the district court for a new trial and new discovery (“discovery” is the pretrial gathering of documents and evidence that takes place before a trial). Judge Cooper granted this motion, including expert discovery. So, the plaintiffs selected three expert witnesses who had worked on the Kitzmiller case – Ken Miller and Brian Alters, who had both testified in Kitzmiller, and Eugenie Scott of NCSE, who had consulted. Although we now will not have a Kitzmiller sequel in Georgia, the expert witness statements from these witnesses give us some idea of the case that confronted the school board in the retrial. I currently have just uploaded Genie Scott’s expert report (links to expert statements or visit NCSE’s Selman page). (I am waiting for permissions on the other two reports.) It is well known that the Supreme Court tests for constitutionality require judges to examine the history of governmental policies as part of their assessment of whether or not the government’s asserted secular purposes and effects are real, or a sham. Well, Scott’s report shows that there is far more history to “theory not fact” than even I knew until recently. Last year I noted on PT that “theory not fact” goes back to policy passed by the California state Board of Education in 1925 in the midst of the nationwide fundamentalist crusade against evolution. But it turns out that “theory not fact” can be traced back even further, to a 1923 policy pushed in Georgia by William Jennings Bryan himself. Opposition to evolution in Georgia has deep roots. Like those in other southern states, Georgia legislators were enthusiastic over Scopes-type antievolution laws in the 1920s. William Jennings Bryan, in fact, visited Georgia to promote a “theory not fact” bill. In 1923, he urged the Georgia House to pass a bill that would “forbid teachers from teaching evolution as a fact, declaring that they had no right to present it to their pupils as anything other than a theory or hypothesis.” And, as it turns out, “theory not fact” statements were a common feature of antievolution policies both in the 1920s and as part of “creation science” and “intelligent design” policies from the 1960s to the present. The cases in which “theory not fact” language has appeared as part of the challenged creationist policy include Daniel v. Waters (1975), Edwards v. Aguillard (1987), and Kitzmiller v. Dover (2005). It has also appeared in policies or disclaimers in Alabama, Texas, New Mexico, Oklahoma, etc. Read the report for more of the history. Furthermore, Cobb’s theory-not-fact policy did not just occur to someone in Cobb one day as a good idea. Instead, it was just the latest in a long line of antievolution policies in Cobb and Georgia generally: As with the rest of Georgia, evolution education in Cobb County, Georgia, has been a perennial sore spot. A controversy over evolution erupted in Cobb County in 1979 when the Cobb School Board approved on a 7-0 vote a “balanced treatment of evolution” resolution submitted by board member John McClure. The goal of the policy was to teach creation science along with evolution. The district spent$7,600 on instructional materials purchased from two creationist organizations, the Institute for Creation Research and the Creation Research Society. Teachers protested both the policy and the instructional materials, rating them as scientifically and pedagogically substandard, and according to one source, threatened to strike if the policy wasn’t rescinded.
In the mid-1980s, the district became embroiled in a controversy over the alleged teaching of “humanism” as part of a values clarification exercise in the elementary school classes. One of the people who had been central in promoting creationism in the 1980s, Carolyn Sanford, was prominent in this controversy as well. She included evolution education as part of the breakdown of morals in society that she saw as part of a creeping influence of “humanism” in the schools. To try to settle the issue, the Superintendent’s office circulated a memo restricting classroom discussion on a number of topics, including “evolution, abortion, communism, religion, and [values clarification]”. This memo, “Standard Practices to be Observed With Instructional Materials for Selected Curriculum Topics,” was circulated to teachers in December 1984. Although teachers were permitted to supplement the county-approved instructional materials for all other controversial topics, materials used for teaching evolution were restricted to “that selected and purchased through county procedures.” The policy was protested by the president-elect of the citizens group, Georgia Council for Science Education, Paula Eglin, a biology teacher in Cobb County. Because there were at the time no written guidelines for teaching evolution in Cobb County, the restriction on instructional materials were seen as a burden by teachers. The policy remained in place.
In the mid-1990s, evolution returned to Cobb County as a controversial issue, when parents complained about the inclusion of a few pages about the origin of the solar system and Earth in a fourth-grade science book. Parents Jeffrey and Beth Wright objected to the Macmillan / McGraw-Hill book Changing Earth because one chapter, “The Birth of Earth,” included a discussion of different theories about the origin of the solar system, and also mentioned – briefly – the Big Bang. The Wrights were quite clear that their objections to the book were because it conflicted with their biblically based views of creation. To quote from a news story: “We’re not fanatics,” says Beth Wright, “but we believe in creation. If creation isn’t being taught, then nothing should be taught.” The Board of Education, arguing that the topic of the evolution of the earth wasn’t part of the fourth grade curriculum anyway, requested that the publisher reprint the books deleting pages 72–85. The publisher agreed, which generated a considerable amount of discussion in the community, including fiery letters to the editor from both sides of the controversy. During the course of this controversy, reporters uncovered the fact that the official Cobb County policy “Theories of Origin,” Policy IDBD, proscribed the teaching of human evolution in several ways. The policy, originally passed in December of 1979, had undergone a number of revisions, the most recent in August of 1995. This policy would, in a few years, be seen to conflict with the contents of new textbooks.
By the terms of the consent agreement, the board does not have to admit that its “theory not fact” warning label was unconstitutional. But I think that the prospect of the above sort of detailed testimony may have helped convince them that settling was a good idea.
Notes:
Part of the policies ruled unconstitutional in Daniel v. Waters (1975):
Any biology textbook used for teaching in the public schools, which expresses an opinion of, or relates a theory about origins or creation of man and his world shall be prohibited from being used as a textbook in such system unless it specifically states that it is a theory as to the origin and creation of man and his world and is not represented to be scientific fact.
…in Edwards v. Aguillard (1987):
“When creation or evolution is taught, each shall be taught as a theory, rather than as proven scientific fact.”
…in Kitzmiller v. Dover (2005):
“The Theory is not a fact.” | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21037425100803375, "perplexity": 3790.9030327644964}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370511408.40/warc/CC-MAIN-20200410173109-20200410203609-00503.warc.gz"} |
https://apache.googlesource.com/systemds/+/refs/heads/branch-0.11/docs/algorithms-clustering.md | # 3. Clustering
## 3.1. K-Means Clustering
### Description
Given a collection of $n$ records with a pairwise similarity measure, the goal of clustering is to assign a category label to each record so that similar records tend to get the same label. In contrast to multinomial logistic regression, clustering is an unsupervised learning problem with neither category assignments nor label interpretations given in advance. In $k$-means clustering, the records $x_1, x_2, \ldots, x_n$ are numerical feature vectors of $\dim x_i = m$ with the squared Euclidean distance $|x_i - x_{i'}|_2^2$ as the similarity measure. We want to partition $\{x_1, \ldots, x_n\}$ into $k$ clusters $\{S_1, \ldots, S_k\}$ so that the aggregated squared distance from records to their cluster means is minimized:
$$$$\textrm{WCSS},,=,, \sum_{i=1}^n ,\big|x_i - mean(S_j: x_i\in S_j)\big|_2^2 ,,\to,,\min$$$$
The aggregated distance measure in (1) is called the within-cluster sum of squares (WCSS). It can be viewed as a measure of residual variance that remains in the data after the clustering assignment, conceptually similar to the residual sum of squares (RSS) in linear regression. However, unlike for the RSS, the minimization of (1) is an NP-hard problem [AloiseDHP2009].
Rather than searching for the global optimum in (1), a heuristic algorithm called Lloyd’s algorithm is typically used. This iterative algorithm maintains and updates a set of $k$ centroids $\{c_1, \ldots, c_k\}$, one centroid per cluster. It defines each cluster $S_j$ as the set of all records closer to $c_j$ than to any other centroid. Each iteration of the algorithm reduces the WCSS in two steps:
1. Assign each record to the closest centroid, making $mean(S_j)\neq c_j$
2. Reset each centroid to its cluster’s mean: $c_j := mean(S_j)$
After Step 1, the centroids are generally different from the cluster means, so we can compute another “within-cluster sum of squares” based on the centroids:
$$\textrm{WCSS_C},,=,, \sum_{i=1}^n ,\big|x_i - \mathop{\textrm{centroid}}(S_j: x_i\in S_j)\big|_2^2 \label{eqn:WCSS:C}$$
This WCSS_C after Step 1 is less than the means-based WCSS before Step 1 (or equal if convergence achieved), and in Step 2 the WCSS cannot exceed the WCSS_C for the same clustering; hence the WCSS reduction.
Exact convergence is reached when each record becomes closer to its cluster’s mean than to any other cluster’s mean, so there are no more re-assignments and the centroids coincide with the means. In practice, iterations may be stopped when the reduction in WCSS (or in WCSS_C) falls below a minimum threshold, or upon reaching the maximum number of iterations. The initialization of the centroids is also an important part of the algorithm. The smallest WCSS obtained by the algorithm is not the global minimum and varies depending on the initial centroids. We implement multiple parallel runs with different initial centroids and report the best result.
Scoring. Our scoring script evaluates the clustering output by comparing it with a known category assignment. Since cluster labels have no prior correspondence to the categories, we cannot count “correct” and “wrong” cluster assignments. Instead, we quantify them in two ways:
1. Count how many same-category and different-category pairs of records end up in the same cluster or in different clusters;
2. For each category, count the prevalence of its most common cluster; for each cluster, count the prevalence of its most common category.
The number of categories and the number of clusters ($k$) do not have to be equal. A same-category pair of records clustered into the same cluster is viewed as a “true positive,” a different-category pair clustered together is a “false positive,” a same-category pair clustered apart is a “false negative” etc.
### Usage
K-Means:
K-Means Prediction:
### Arguments - K-Means
X: Location to read matrix $X$ with the input data records as rows
C: (default: "C.mtx") Location to store the output matrix with the best available cluster centroids as rows
k: Number of clusters (and centroids)
runs: (default: 10) Number of parallel runs, each run with different initial centroids
maxi: (default: 1000) Maximum number of iterations per run
tol: (default: 0.000001) Tolerance (epsilon) for single-iteration WCSS_C change ratio
samp: (default: 50) Average number of records per centroid in data samples used in the centroid initialization procedure
Y: (default: "Y.mtx") Location to store the one-column matrix $Y$ with the best available mapping of records to clusters (defined by the output centroids)
isY: (default: 0) 0 = do not write matrix $Y$, 1 = write $Y$
fmt: (default: "text") Matrix file output format, such as text, mm, or csv; see read/write functions in SystemML Language Reference for details.
verb: (default: 0) 0 = do not print per-iteration statistics for each run, 1 = print them (the “verbose” option)
### Arguments - K-Means Prediction
X: (default: " ") Location to read matrix $X$ with the input data records as rows, optional when prY input is provided
C: (default: " ") Location to read matrix $C$ with cluster centroids as rows, optional when prY input is provided; NOTE: if both X and C are provided, prY is an output, not input
spY: (default: " ") Location to read a one-column matrix with the externally specified “true” assignment of records (rows) to categories, optional for prediction without scoring
prY: (default: " ") Location to read (or write, if X and C are present) a column-vector with the predicted assignment of rows to clusters; NOTE: No prior correspondence is assumed between the predicted cluster labels and the externally specified categories
fmt: (default: "text") Matrix file output format for prY, such as text, mm, or csv; see read/write functions in SystemML Language Reference for details.
0: (default: " ") Location to write the output statistics defined in Table 6, by default print them to the standard output
### Examples
K-Means:
K-Means Prediction:
To predict Y given X and C:
To compare “actual” labels spY with “predicted” labels given X and C:
To compare “actual” labels spY with given “predicted” labels prY:
### Details
Our clustering script proceeds in 3 stages: centroid initialization, parallel $k$-means iterations, and the best-available output generation. Centroids are initialized at random from the input records (the rows of $X$), biased towards being chosen far apart from each other. The initialization method is based on the k-means++ heuristic from [ArthurVassilvitskii2007], with one important difference: to reduce the number of passes through $X$, we take a small sample of $X$ and run the k-means++ heuristic over this sample. Here is, conceptually, our centroid initialization algorithm for one clustering run:
The sampling of $X$ and the selection of centroids are performed independently and in parallel for each run of the $k$-means algorithm. When we sample the rows of $X$, rather than tossing a random coin for each row, we compute the number of rows to skip until the next sampled row as $\lceil \log(u) / \log(1 - p) \rceil$ where $u\in (0, 1)$ is uniformly random. This time-saving trick works because
$$Prob[k-1 < \log_{1-p}(u) < k] ,,=,, p(1-p)^{k-1} ,,=,, Prob[\textrm{skip k-1 rows}]$$
However, it requires us to estimate the maximum sample size, which we set near $ks + 10\sqrt{ks}$ to make it generous enough.
Once we selected the initial centroid sets, we start the $k$-means iterations independently in parallel for all clustering runs. The number of clustering runs is given as the runs input parameter. Each iteration of each clustering run performs the following steps:
• Compute the centroid-dependent part of squared Euclidean distances from all records (rows of $X$) to each of the $k$ centroids using matrix product.
• Take the minimum of the above for each record.
• Update the current within-cluster sum of squares (WCSS) value, with centroids substituted instead of the means for efficiency.
• Check the convergence criterion: $$\textrm{WCSS}{\mathrm{old}} - \textrm{WCSS}{\mathrm{new}} < {\varepsilon}\cdot\textrm{WCSS}_{\mathrm{new}}$$ as well as the number of iterations limit.
• Find the closest centroid for each record, sharing equally any records with multiple closest centroids.
• Compute the number of records closest to each centroid, checking for “runaway” centroids with no records left (in which case the run fails).
• Compute the new centroids by averaging the records in their clusters.
When a termination condition is satisfied, we store the centroids and the WCSS value and exit this run. A run has to satisfy the WCSS convergence criterion to be considered successful. Upon the termination of all runs, we select the smallest WCSS value among the successful runs, and write out this run’s centroids. If requested, we also compute the cluster assignment of all records in $X$, using integers from 1 to $k$ as the cluster labels. The scoring script can then be used to compare the cluster assignment with an externally specified category assignment.
### Returns
We output the $k$ centroids for the best available clustering, i. e. whose WCSS is the smallest of all successful runs. The centroids are written as the rows of the $k,{\times},m$-matrix into the output file whose path/name was provided as the C input argument. If the input parameter isY was set to 1, we also output the one-column matrix with the cluster assignment for all the records. This assignment is written into the file whose path/name was provided as the Y input argument. The best WCSS value, as well as some information about the performance of the other runs, is printed during the script execution. The scoring script Kmeans-predict.dml prints all its results in a self-explanatory manner, as defined in Table 6. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.3634803593158722, "perplexity": 1998.6469680318448}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710533.96/warc/CC-MAIN-20221128135348-20221128165348-00276.warc.gz"} |
https://worldwidescience.org/topicpages/g/generalized+conformational+energy.html | #### Sample records for generalized conformational energy
1. General Conformity
Science.gov (United States)
The General Conformity requirements ensure that the actions taken by federal agencies in nonattainment and maintenance areas do not interfere with a state’s plans to meet national standards for air quality.
2. Conformal General Relativity
CERN Document Server
Pervushin, V
2001-01-01
The inflation-free solution of problems of the modern cosmology (horizon, cosmic initial data, Planck era, arrow of time, singularity,homogeneity, and so on) is considered in the conformal-invariant unified theory given in the space with geometry of similarity where we can measure only the conformal-invariant ratio of all quantities. Conformal General Relativity is defined as the $SU_c(3)\\times SU(2)\\times U(1)$-Standard Model where the dimensional parameter in the Higgs potential is replaced by a dilaton scalar field described by the negative Penrose-Chernikov-Tagirov action. Spontaneous SU(2) symmetry breaking is made on the level of the conformal-invariant angle of the dilaton-Higgs mixing, and it allows us to keep the structure of Einstein's theory with the equivalence principle. We show that the lowest order of the linearized equations of motion solves the problems mentioned above and describes the Cold Universe Scenario with the constant temperature T and z-history of all masses with respect to an obser...
3. 40 CFR 52.2133 - General conformity.
Science.gov (United States)
2010-07-01
... 40 Protection of Environment 4 2010-07-01 2010-07-01 false General conformity. 52.2133 Section 52...) APPROVAL AND PROMULGATION OF IMPLEMENTATION PLANS (CONTINUED) South Carolina § 52.2133 General conformity. The General Conformity regulations adopted into the South Carolina State Implementation Plan...
4. 40 CFR 52.938 - General conformity.
Science.gov (United States)
2010-07-01
... 40 Protection of Environment 3 2010-07-01 2010-07-01 false General conformity. 52.938 Section 52...) APPROVAL AND PROMULGATION OF IMPLEMENTATION PLANS Kentucky § 52.938 General conformity. The General Conformity regulations were submitted on November 10, 1995, and adopted into the Kentucky...
5. Conformal Gravity: Dark Matter and Dark Energy
Directory of Open Access Journals (Sweden)
Robert K. Nesbet
2013-01-01
Full Text Available This short review examines recent progress in understanding dark matter, dark energy, and galactic halos using theory that departs minimally from standard particle physics and cosmology. Strict conformal symmetry (local Weyl scaling covariance, postulated for all elementary massless fields, retains standard fermion and gauge boson theory but modifies Einstein–Hilbert general relativity and the Higgs scalar field model, with no new physical fields. Subgalactic phenomenology is retained. Without invoking dark matter, conformal gravity and a conformal Higgs model fit empirical data on galactic rotational velocities, galactic halos, and Hubble expansion including dark energy.
6. Conformal methods in general relativity
CERN Document Server
Valiente Kroon, Juan A
2016-01-01
This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this the perfect reference companion on the topic.
7. Conformal collider physics: Energy and charge correlations
CERN Document Server
Hofman, Diego M
2008-01-01
We study observables in a conformal field theory which are very closely related to the ones used to describe hadronic events at colliders. We focus on the correlation functions of the energies deposited on calorimeters placed at a large distance from the collision. We consider initial states produced by an operator insertion and we study some general properties of the energy correlation functions for conformal field theories. We argue that the small angle singularities of energy correlation functions are controlled by the twist of non-local light-ray operators with a definite spin. We relate the charge two point function to a particular moment of the parton distribution functions appearing in deep inelastic scattering. The one point energy correlation functions are characterized by a few numbers. For ${\\cal N}=1$ superconformal theories the one point function for states created by the R-current or the stress tensor are determined by the two parameters $a$ and $c$ characterizing the conformal anomaly. Demandin...
8. Conformal general relativity contains the quantum
CERN Document Server
Bonal, R; Cardenas, R
2000-01-01
Based on the de Broglie-Bohm relativistic quantum theory of motion we show that the conformal formulation of general relativity, being linked with a Weyl-integrable geometry, may implicitly contain the quantum effects of matter. In this context the Mach's principle is discussed.
9. Generalized Orbifold Construction for Conformal Nets
CERN Document Server
Bischoff, Marcel
2016-01-01
Let $\\mathcal{B}$ be a conformal net. We give the notion of a proper action of a finite hypergroup acting by vacuum preserving unital completely positive (so-called stochastic) maps, which generalizes the proper actions of finite groups. Taking fixed points under such an action gives a finite index subnet $\\mathcal{B}^K$ of $\\mathcal{B}$, which generalizes the $G$-orbifold. Conversely, we show that if $\\mathcal{A}\\subset \\mathcal{B}$ is a finite inclusion of conformal nets, then $\\mathcal{A}$ is a generalized orbifold $\\mathcal{A}=\\mathcal{B}^K$ of the conformal net $\\mathcal{B}$ by a unique finite hypergroup $K$. There is a Galois correspondence between intermediate nets $\\mathcal{B}^K\\subset \\mathcal{A} \\subset \\mathcal{B}$ and subhypergroups $L\\subset K$ given by $\\mathcal{A}=\\mathcal{B}^L$. In this case, the fixed point of $\\mathcal{B}^K\\subset \\mathcal{A}$ is the generalized orbifold by the hypergroup of double cosets $L\\backslash K/ L$. If $\\mathcal{A}\\subset \\mathcal{B}$ is an finite index inclusion of...
10. Willmore energy estimates in conformal Berger spheres
Energy Technology Data Exchange (ETDEWEB)
Barros, Manuel, E-mail: [email protected] [Departamento de Geometria y Topologia, Facultad de Ciencias Universidad de Granada, 1807 Granada (Spain); Ferrandez, Angel, E-mail: [email protected] [Departamento de Matematicas, Universidad de Murcia Campus de Espinardo, 30100 Murcia (Spain)
2011-07-15
Highlights: > The Willmore energy is computed in a wide class of surfaces. > Isoperimetric inequalities for the Willmore energy of Hopf tori are obtained. > The best possible lower bound is achieved on isoareal Hopf tori. - Abstract: We obtain isoperimetric inequalities for the Willmore energy of Hopf tori in a wide class of conformal structures on the three sphere. This class includes, on the one hand, the family of conformal Berger spheres and, on the other hand, a one parameter family of Lorentzian conformal structures. This allows us to give the best possible lower bound of Willmore energies concerning isoareal Hopf tori.
11. Slice Energy and Conformal Frames in Theories of Gravitation
CERN Document Server
Cotsakis, S
2004-01-01
We examine and compare the behaviour of the scalar field slice energy in different classes of theories of gravity, in particular higher-order and scalar-tensor theories. We find a universal formula for the energy and compare the resulting conservation laws with those known in general relativity. This leads to a comparison between the inflaton, the dilaton and other forms of scalar fields present in these generalized theories. It also shows that all such conformally-related, generalized theories of gravitation allow for the energy on a slice to be invariably defined and its fundamental properties be insensitive to conformal transformations.
12. On gravitational energy in conformal teleparallel gravity
Science.gov (United States)
da Silva, J. G.; Ulhoa, S. C.
2017-07-01
The paper deals with the definition of gravitational energy in conformal teleparallel gravity. The total energy is defined by means of the field equations which allow a local conservation law. Then such an expression is analyzed for a homogeneous and isotropic Universe. This model is implemented by the Friedmann-Robertson-Walker (FRW) line element. The energy of the Universe in the absence of matter is identified with the dark energy, however it can be expanded for curved models defining such an energy as the difference between the total energy and the energy of the perfect fluid which is the matter field in the FRW model.
13. Simple Space-Time Symmetries: Generalizing Conformal Field Theory
CERN Document Server
Mack, G; Mack, Gerhard; Riese, Mathias de
2004-01-01
We study simple space-time symmetry groups G which act on a space-time manifold M=G/H which admits a G-invariant global causal structure. We classify pairs (G,M) which share the following additional properties of conformal field theory: 1) The stability subgroup H of a point in M is the identity component of a parabolic subgroup of G, implying factorization H=MAN, where M generalizes Lorentz transformations, A dilatations, and N special conformal transformations. 2) special conformal transformations in N act trivially on tangent vectors to the space-time manifold M. The allowed simple Lie groups G are the universal coverings of SU(m,m), SO(2,D), Sp(l,R), SO*(4n) and E_7(-25) and H are particular maximal parabolic subgroups. All these groups G admit positive energy representations. It will also be shown that the classical conformal groups SO(2,D) are the only allowed groups which possess a time reflection automorphism; in all other cases space-time has an intrinsic chiral structure.
14. 75 FR 17253 - Revisions to the General Conformity Regulations
Science.gov (United States)
2010-04-05
... Protection Agency 40 CFR Parts 51 and 93 Revisions to the General Conformity Regulations; Final Rule #0;#0... PROTECTION AGENCY 40 CFR Parts 51 and 93 RIN 2060-AH93 Revisions to the General Conformity Regulations AGENCY... or Federal implementation plan (SIP, TIP, or FIP) for attaining clean air (General...
15. General Information for Transportation and Conformity
Science.gov (United States)
Transportation conformity is required by the Clean Air Act section 176(c) (42 U.S.C. 7506(c)) to ensure that federal funding and approval are given to highway and transit projects that are consistent with SIP.
16. On Useful Conformal Tranformations In General Relativity
CERN Document Server
Carneiro, D F; De Lima, A G; Shapiro, I L
2004-01-01
Local conformal transformations are known as a useful tool in various applications of the gravitational theory, especially in cosmology. We describe some new aspects of these transformations, in particular using them for derivation of Einstein equations for the cosmological and Schwarzschild metrics. Furthermore, the conformal transformation is applied for the dimensional reduction of the Gauss-Bonnet topological invariant in $d=4$ to the spaces of lower dimensions.
17. On useful conformal tranformations in general relativity
Science.gov (United States)
Carneiro, D. F.; Freiras, E. A.; Gonçalves, B.; de Lima, A. G.; Shapiro, I.
2004-12-01
Local conformal transformations are known as a useful tool in various applications of the gravitational theory, especially in cosmology. We describe some new aspects of these transformations, in particular using them for derivation of Einstein equations for the cosmological and Schwarzschild metrics. Furthermore, the conformal transformation is applied for the dimensional reduction of the Gauss-Bonnet topological invariant in $d=4$ to the spaces of lower dimensions.
18. Energy of knots and conformal geometry
CERN Document Server
O'Hara, Jun
2003-01-01
Energy of knots is a theory that was introduced to create a "canonical configuration" of a knot - a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a "canonical configuration" of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments. Contents: In Search of the "Optima
19. Conformal Invariance and Conserved Quantities of General Holonomic Systems
Institute of Scientific and Technical Information of China (English)
CAI Jian-Le
2008-01-01
Conformal invarianee and conserved quantities of general holonomic systems are studied. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators are described.The definition of conformal invariance and determining equation for the system are provided.The conformal factor expression is deduced from conformal invariance and Lie symmetry.The necessary and sufficient condition,that conformal invariance of the system would be Lie symmetry,is obtained under the infinitesimal one-parameter transformation group. The corresponding conserved quantity is derived with the aid of a structure equation.Lastly,an example is given to demonstrate the application of the result.
20. Basic Information About the General Conformity Rule
Science.gov (United States)
These regulations ensure that federal activities or actions don't cause new violations to the NAAQS and ensure that NAAQS attainment is not delayed. This page has general information about how and where these regulations apply.
1. Conformational Nonequilibrium Enzyme Kinetics: Generalized Michaelis-Menten Equation.
Science.gov (United States)
Piephoff, D Evan; Wu, Jianlan; Cao, Jianshu
2017-08-03
In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. On the basis of a discrete kinetic network model, we use an integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction. The traditional Michaelis-Menten (MM) rate equation is extended to a generalized form, which includes non-MM corrections induced by conformational population currents within combined cyclic kinetic loops. When conformational detailed balance is satisfied, the turnover rate reduces to the MM functional form, explaining its general validity. For the first time, a one-to-one correspondence is established between non-MM terms and combined cyclic loops with unbalanced conformational currents. Cooperativity resulting from nonequilibrium conformational dynamics can be achieved in enzymatic reactions, and we provide a novel, rigorous means of predicting and characterizing such behavior. Our generalized MM equation affords a systematic approach for exploring cNESS enzyme kinetics.
2. PDB ligand conformational energies calculated quantum-mechanically.
Science.gov (United States)
Sitzmann, Markus; Weidlich, Iwona E; Filippov, Igor V; Liao, Chenzhong; Peach, Megan L; Ihlenfeldt, Wolf-Dietrich; Karki, Rajeshri G; Borodina, Yulia V; Cachau, Raul E; Nicklaus, Marc C
2012-03-26
(RSCC). We repeated these calculations with the solvent model IEFPCM, which yielded energy differences that were generally somewhat lower than the corresponding vacuum results but did not produce a qualitatively different picture. Torsional sampling around the crystal conformation at the molecular mechanics level using the MMFF94s force field typically led to an increase in energy. © 2012 American Chemical Society
3. Energy flow in non-equilibrium conformal field theory
Science.gov (United States)
Bernard, Denis; Doyon, Benjamin
2012-09-01
We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.
4. Generalized Wilson-Fisher critical points from the conformal OPE
CERN Document Server
Gliozzi, Ferdinando; Petkou, Anastasios C; Wen, Congkao
2016-01-01
We study possible smooth deformations of Generalized Free Conformal Field Theories in arbitrary dimensions by exploiting the singularity structure of the conformal blocks dictated by the null states. We derive in this way, at the first non trivial order in the $\\epsilon$-expansion, the anomalous dimensions of an infinite class of scalar local operators, without using the equations of motion. In the cases where other computational methods apply, the results agree.
5. Conformal anomaly of generalized form factors and finite loop integrals
CERN Document Server
Chicherin, Dmitry
2017-01-01
We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an $\\ell-$loop integral is a 2nd-order differential equation whose right-hand side is an $(\\ell-1)-$loop integral. We show several examples, in particular the four-dimensional scalar double box.
6. 76 FR 77182 - Approval and Promulgation of Air Quality Implementation Plans; Virginia; General Conformity...
Science.gov (United States)
2011-12-12
... Conformity Requirements for Federal Agencies Applicable to Federal Actions AGENCY: Environmental Protection... adopted by Virginia for the purpose of incorporating Federal general conformity requirements revisions... approving Virginia's general conformity SIP revision and if that provision may be severed from the...
7. 76 FR 77150 - Approval and Promulgation of Air Quality Implementation Plans; Virginia; General Conformity...
Science.gov (United States)
2011-12-12
... Conformity Requirements for Federal Agencies Applicable to Federal Actions AGENCY: Environmental Protection... regulation adopted by Virginia to incorporate revisions to Federal general conformity requirements... state general conformity requirements rule for Federal agencies applicable to Federal actions...
8. Singular conformally invariant trilinear forms and generalized Rankin Cohen operators
CERN Document Server
Jean-Louis, Clerc
2011-01-01
The most singular residues of the standard meromorphic family of trilinear conformally invariant forms on $\\mathcal C^\\infty_c(\\mathbb R^d)$ are computed. Their expression involves covariant bidifferential operators (generalized Rankin Cohen operators), for which new formul\\ae \\ are obtained. The main tool is a Bernstein-Sato identity for the kernel of the forms.
9. A phenomenological relationship between molecular geometry change and conformational energy change
Science.gov (United States)
Bodi, Andras; Bjornsson, Ragnar; Arnason, Ingvar
2010-08-01
A linear correlation is established between the change in the axial/equatorial conformational energy difference and the change in the molecular geometry transformation during conformational inversion in substituted six-membered ring systems, namely in the 1-substituted cyclohexane/silacyclohexane, cyclohexane/ N-substituted piperidine and 1-substituted silacyclohexane/ P-substituted phosphorinane compound families, and for the analogous gauche/anti conformational isomerism in 1-substituted propanes/1-silapropanes. The nuclear repulsion energy parameterizes the molecular geometry, and changes in the conformational energy between the related compound families are linearly correlated with the changes in the nuclear repulsion energy difference based on DFT (B3LYP, M06-2X), G3B3, and CBS-QB3 calculations. This correlation reproduces the sometimes remarkable contrast between the conformational behavior of analogous compounds, e.g., the lack of a general equatorial preference in silacyclohexanes.
10. Vacuum energy sequestering and conformal symmetry
Science.gov (United States)
Ben-Dayan, Ido; Richter, Robert; Ruehle, Fabian; Westphal, Alexander
2016-05-01
In a series of recent papers Kaloper and Padilla proposed a mechanism to sequester standard model vacuum contributions to the cosmological constant. We study the consequences of embedding their proposal into a fully local quantum theory. In the original work, the bare cosmological constant Λ and a scaling parameter λ are introduced as global fields. We find that in the local case the resulting Lagrangian is that of a spontaneously broken conformal field theory where λ plays the role of the dilaton. A vanishing or a small cosmological constant is thus a consequence of the underlying conformal field theory structure.
11. Conformal Gravity with the most general ELKO Matter
OpenAIRE
Fabbri, Luca
2011-01-01
Recently we have constructed the conformal gravity with metric and torsion, finding the gravitational field equations that give the conservation laws and trace condition; in the present paper we apply this theory to the case of ELKO matter field, proving that their spin and energy densities once the matter field equations are considered imply the validity of the conservation laws and trace condition mentioned above.
12. Conformally-modified gravity and vacuum energy
CERN Document Server
Henke, Christian
2016-01-01
The paper deals with a modified theory of gravity and the cosmological consequences. Instead of concerning the field equations directly, we modify a conformally-related and equivalent equation, such that a spontaneous symmetry breaking at Planck scale occurs in the trace equation. As the consequence the cosmological constant problem is solved.
13. Anisotropic scaling and generalized conformal invariance at Lifshitz points
Science.gov (United States)
Henkel, Malte; Pleimling, Michel
2002-08-01
A new variant of the Wolff cluster algorithm is proposed for simulating systems with competing interactions. This method is used in a high-precision study of the Lifshitz point of the 3D ANNNI model. At the Lifshitz point, several critical exponents are found and the anisotropic scaling of the correlators is verified. The functional form of the two-point correlators is shown to be consistent with the predictions of generalized conformal invariance.
14. Prosocial Conformity: Prosocial Norms Generalize Across Behavior and Empathy.
Science.gov (United States)
Nook, Erik C; Ong, Desmond C; Morelli, Sylvia A; Mitchell, Jason P; Zaki, Jamil
2016-08-01
Generosity is contagious: People imitate others' prosocial behaviors. However, research on such prosocial conformity focuses on cases in which people merely reproduce others' positive actions. Hence, we know little about the breadth of prosocial conformity. Can prosocial conformity cross behavior types or even jump from behavior to affect? Five studies address these questions. In Studies 1 to 3, participants decided how much to donate to charities before learning that others donated generously or stingily. Participants who observed generous donations donated more than those who observed stingy donations (Studies 1 and 2). Crucially, this generalized across behaviors: Participants who observed generous donations later wrote more supportive notes to another participant (Study 3). In Studies 4 and 5, participants observed empathic or non-empathic group responses to vignettes. Group empathy ratings not only shifted participants' own empathic feelings (Study 4), but they also influenced participants' donations to a homeless shelter (Study 5). These findings reveal the remarkable breadth of prosocial conformity. © 2016 by the Society for Personality and Social Psychology, Inc.
15. 78 FR 57335 - Approval and Promulgation of Implementation Plans; State of Missouri; Conformity of General...
Science.gov (United States)
2013-09-18
... AGENCY 40 CFR Part 52 Approval and Promulgation of Implementation Plans; State of Missouri; Conformity of... conformity rule in its entirety to bring it into compliance with the Federal general conformity rule which was updated in the Federal Register on April 5, 2010. General conformity regulations prohibit...
16. Energy flux positivity and unitarity in conformal field theories
NARCIS (Netherlands)
Kulaxizi, M.; Parnachev, A.
2011-01-01
We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop lightlike poles. The re
17. Gauge formulation of general relativity using conformal and spin symmetries.
Science.gov (United States)
Wang, Charles H-T
2008-05-28
The gauge symmetry inherent in Maxwell's electromagnetics has a profound impact on modern physics. Following the successful quantization of electromagnetics and other higher order gauge field theories, the gauge principle has been applied in various forms to quantize gravity. A notable development in this direction is loop quantum gravity based on the spin-gauge treatment. This paper considers a further incorporation of the conformal gauge symmetry in canonical general relativity. This is a new conformal decomposition in that it is applied to simplify recently formulated parameter-free construction of spin-gauge variables for gravity. The resulting framework preserves many main features of the existing canonical framework for loop quantum gravity regarding the spin network representation and Thiemann's regularization. However, the Barbero-Immirzi parameter is converted into the conformal factor as a canonical variable. It behaves like a scalar field but is somehow non-dynamical since the Hamiltonian constraint does not depend on its momentum. The essential steps of the mathematical derivation of this parameter-free framework for the spin-gauge variables of gravity are spelled out. The implications for the loop quantum gravity programme are briefly discussed.
18. Enhanced conformational sampling technique provides an energy landscape view of large-scale protein conformational transitions.
Science.gov (United States)
Shao, Qiang
2016-10-26
Large-scale conformational changes in proteins are important for their functions. Tracking the conformational change in real time at the level of a single protein molecule, however, remains a great challenge. In this article, we present a novel in silico approach with the combination of normal mode analysis and integrated-tempering-sampling molecular simulation (NMA-ITS) to give quantitative data for exploring the conformational transition pathway in multi-dimensional energy landscapes starting only from the knowledge of the two endpoint structures of the protein. The open-to-closed transitions of three proteins, including nCaM, AdK, and HIV-1 PR, were investigated using NMA-ITS simulations. The three proteins have varied structural flexibilities and domain communications in their respective conformational changes. The transition state structure in the conformational change of nCaM and the associated free-energy barrier are in agreement with those measured in a standard explicit-solvent REMD simulation. The experimentally measured transition intermediate structures of the intrinsically flexible AdK are captured by the conformational transition pathway measured here. The dominant transition pathways between the closed and fully open states of HIV-1 PR are very similar to those observed in recent REMD simulations. Finally, the evaluated relaxation times of the conformational transitions of three proteins are roughly at the same level as reported experimental data. Therefore, the NMA-ITS method is applicable for a variety of cases, providing both qualitative and quantitative insights into the conformational changes associated with the real functions of proteins.
19. Generalized conformal realizations of Kac-Moody algebras
Science.gov (United States)
Palmkvist, Jakob
2009-01-01
We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n =1, this reduces to the well known Kantor-Koecher-Tits construction. Our generalization utilizes a new relation between different generalized Jordan triple systems, together with their known connections to Jordan and Lie algebras. Applied to the Jordan algebra of Hermitian 3×3 matrices over the division algebras R, C, H, O, the construction gives the exceptional Lie algebras f4, e6, e7, e8 for n =2. Moreover, we obtain their infinite-dimensional extensions for n ≥3. In the case of 2×2 matrices, the resulting Lie algebras are of the form so(p +n,q+n) and the concomitant nonlinear realization generalizes the conformal transformations in a spacetime of signature (p,q).
20. Anisotropic scaling and generalized conformal invariance at Lifshitz points
CERN Document Server
Pleimling, M; Pleimling, Michel; Henkel, Malte
2001-01-01
The behaviour of the 3D axial next-nearest neighbour Ising (ANNNI) model at the uniaxial Lifshitz point is studied using Monte Carlo techniques. A new variant of the Wolff cluster algorithm permits the analysis of systems far larger than in previous studies. The Lifshitz point critical exponents are $\\alpha=0.18(2)$, $\\beta=0.238(5)$ and $\\gamma=1.36(3)$. Data for the spin-spin correlation function are shown to be consistent with the explicit scaling function derived from the assumption of local scale invariance, which is a generalization of conformal invariance to the anisotropic scaling {\\em at} the Lifshitz point.
1. Conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems
Institute of Scientific and Technical Information of China (English)
Li Yuan-Cheng; Xia Li-Li; Wang Xiao-Ming
2009-01-01
This paper studies conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems. The definition and the determining equation of conformal invariance for mechanico-electrical systems are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry under the infinitesimal singleparameter transformation group. The generalized Hojman conserved quantities from the conformal invariance of the system are given. An example is given to illustrate the application of the result.
2. General Relativity and Energy
Science.gov (United States)
Jackson, A. T.
1973-01-01
Reviews theoretical and experimental fundamentals of Einstein's theory of general relativity. Indicates that recent development of the theory of the continually expanding universe may lead to revision of the space-time continuum of the finite and unbounded universe. (CC)
3. Wormholes admitting conformal Killing vectors and supported by generalized Chaplygin gas
Energy Technology Data Exchange (ETDEWEB)
Kuhfittig, Peter K.F. [Milwaukee School of Engineering, Department of Mathematics, Milwaukee, WI (United States)
2015-08-15
When Morris and Thorne first proposed that traversable wormholes may be actual physical objects, they concentrated on the geometry by specifying the shape and redshift functions. This mathematical approach necessarily raises questions regarding the determination of the required stress-energy tensor. This paper discusses a natural way to obtain a complete wormhole solution by assuming that the wormhole (1) is supported by generalized Chaplygin gas and (2) admits conformal Killing vectors. (orig.)
4. Conformal symmetry wormholes and the null energy condition
CERN Document Server
Kuhfittig, Peter K F
2016-01-01
In this paper we seek a relationship between the assumption of conformal symmetry and the exotic matter needed to hold a wormhole open. By starting with a Morris-Thorne wormhole having a constant energy density, it is shown that the conformal factor provides the extra degree of freedom sufficient to account for the exotic matter. The same holds for Morris-Thorne wormholes in a noncommutative-geometry setting. Applied to thin shells, there would exist a radius that results in a wormhole with positive surface density and negative surface pressure and which violates the null energy condition on the thin shell.
5. Slice Energy in Higher Order Gravity Theories and Conformal Transformations
CERN Document Server
Cotsakis, S
2004-01-01
We show that there is a generic transport of energy between the scalar field generated by the conformal transformation of higher order gravity theories and the matter component. We give precise relations of this exchange and show that, unless we are in a stationary spacetime, slice energy is not generically conserved. These results translate into statements about the relative behaviour of ordinary matter, dark matter and dark energy in the context of higher order gravity.
6. Conformal invariance, dark energy, and CMB non-gaussianity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Department of Physics, CERN, Theory Division CH-1211 Geneva 23 (Switzerland); Mazur, Pawel O. [Department of Physics and Astronomy, University of South Carolina Columbia SC 29208 (United States); Mottola, Emil, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Theoretical Division, MS B285 Los Alamos National Laboratory Los Alamos, NM 87545 (United States)
2012-09-01
In addition to simple scale invariance, a universe dominated by dark energy naturally gives rise to correlation functions possessing full conformal invariance. This is due to the mathematical isomorphism between the conformal group of certain three dimensional slices of de Sitter space and the de Sitter isometry group SO(4,1). In the standard homogeneous, isotropic cosmological model in which primordial density perturbations are generated during a long vacuum energy dominated de Sitter phase, the embedding of flat spatial R{sup 3} sections in de Sitter space induces a conformal invariant perturbation spectrum and definite prediction for the shape of the non-Gaussian CMB bispectrum. In the case in which the density fluctuations are generated instead on the de Sitter horizon, conformal invariance of the S{sup 2} horizon embedding implies a different but also quite definite prediction for the angular correlations of CMB non-Gaussianity on the sky. Each of these forms for the bispectrum is intrinsic to the symmetries of de Sitter space, and in that sense, independent of specific model assumptions. Each is different from the predictions of single field slow roll inflation models, which rely on the breaking of de Sitter invariance. We propose a quantum origin for the CMB fluctuations in the scalar gravitational sector from the conformal anomaly that could give rise to these non-Gaussianities without a slow roll inflaton field, and argue that conformal invariance also leads to the expectation for the relation n{sub S}−1 = n{sub T} between the spectral indices of the scalar and tensor power spectrum. Confirmation of this prediction or detection of non-Gaussian correlations in the CMB of one of the bispectral shape functions predicted by conformal invariance can be used both to establish the physical origins of primordial density fluctuations, and distinguish between different dynamical models of cosmological vacuum dark energy.
7. Conformal invariance and particle aspects in general relativity
CERN Document Server
Salehi, H; Darabi, F
2000-01-01
We study the breakdown of conformal symmetry in a conformally invariantgravitational model. The symmetry breaking is introduced by defining apreferred conformal frame in terms of the large scale characteristics of theuniverse. In this context we show that a local change of the preferredconformal frame results in a Hamilton-Jacobi equation describing a particlewith adjustable mass. In this equation the dynamical characteristics of theparticle substantially depends on the applied conformal factor and localgeometry. Relevant interpretations of the results are also discussed.
8. Conformally invariant gauge conditions in electromagnetism and general relativity
Energy Technology Data Exchange (ETDEWEB)
Esposito, Giampiero; Stornaiolo, Cosimo
2000-06-01
The construction of conformally invariant gauge conditions for Maxwell and Einstein theories on a manifold M is found to involve two basic ingredients. First, covariant derivatives of a linear gauge (e.g. Lorenz or de Donder), completely contracted with the tensor field representing the metric on the vector bundle of the theory. Second, the addition of a compensating term, obtained by covariant differentiation of a suitable tensor field built from the geometric data of the problem. The existence theorem for such a gauge in gravitational theory is here proved when the manifold M is endowed with a m-dimensional positive-definite metric g. An application to a generally covariant integral formulation of the Einstein equations is also outlined.
9. 40 CFR 51.858 - Criteria for determining conformity of general Federal actions.
Science.gov (United States)
2010-07-01
... 40 Protection of Environment 2 2010-07-01 2010-07-01 false Criteria for determining conformity of... Determining Conformity of General Federal Actions to State or Federal Implementation Plans § 51.858 Criteria for determining conformity of general Federal actions. Link to an amendment published at 75 FR...
10. 40 CFR 51.859 - Procedures for conformity determinations of general Federal actions.
Science.gov (United States)
2010-07-01
... 40 Protection of Environment 2 2010-07-01 2010-07-01 false Procedures for conformity... IMPLEMENTATION PLANS Determining Conformity of General Federal Actions to State or Federal Implementation Plans § 51.859 Procedures for conformity determinations of general Federal actions. Link to an...
11. Investigation on the low energy conformational surface of tabun to probe the role of its different conformers on biological activity
Science.gov (United States)
Paukku, Yuliya; Michalkova, Andrea; Majumdar, D.; Leszczynski, Jerzy
2006-05-01
Conformational studies have been carried out on the two different enantiomers of tabun at the density functional and second order Møller-Plesset perturbation levels of theory to generate low energy potential energy surfaces in the gas phase as well as in aqueous environment. The structures of the low energy conformers together with their molecular electrostatic potential surfaces have been compared with those of the non-aged acetylcholinesterase-tabun complex to locate the active conformer of this molecule.
12. Accurate calculation of conformational free energy differences in explicit water: the confinement-solvation free energy approach.
Science.gov (United States)
Esque, Jeremy; Cecchini, Marco
2015-04-23
The calculation of the free energy of conformation is key to understanding the function of biomolecules and has attracted significant interest in recent years. Here, we present an improvement of the confinement method that was designed for use in the context of explicit solvent MD simulations. The development involves an additional step in which the solvation free energy of the harmonically restrained conformers is accurately determined by multistage free energy perturbation simulations. As a test-case application, the newly introduced confinement/solvation free energy (CSF) approach was used to compute differences in free energy between conformers of the alanine dipeptide in explicit water. The results are in excellent agreement with reference calculations based on both converged molecular dynamics and umbrella sampling. To illustrate the general applicability of the method, conformational equilibria of met-enkephalin (5 aa) and deca-alanine (10 aa) in solution were also analyzed. In both cases, smoothly converged free-energy results were obtained in agreement with equilibrium sampling or literature calculations. These results demonstrate that the CSF method may provide conformational free-energy differences of biomolecules with small statistical errors (below 0.5 kcal/mol) and at a moderate computational cost even with a full representation of the solvent.
13. Conformal invariance and conserved quantities of general holonomic systems in phase space
Institute of Scientific and Technical Information of China (English)
Xia Li-Li; Cai Jian-Le; Li Yuan-Cheng
2009-01-01
This paper studies the conformed invariance and conserved quantities of general holonomic systems in phase space.The definition and the determining equation of conformed invariance for general holonomic systems in phase space are provided.The conformal factor expression is deduced from conformeal invariance and Lie symmetry.The relationship between the conformed invaxiance and the Lie symmetry is discussed,and the necessary and sufficient condition that the conformal invaxiance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced.The conserved quantities of the system axe given.An example is given to illustrate the application of the result.
14. An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity
CERN Document Server
Curry, Sean
2014-01-01
The following are expanded lecture notes for the course of eight one hour lectures given by the second author at the 2014 summer school Asymptotic Analysis in General Relativity held in Grenoble by the Institut Fourier. The first four lectures deal with conformal geometry and the conformal tractor calculus, taking as primary motivation the search for conformally invariant tensors and diffrerential operators. The final four lectures apply the conformal tractor calculus to the study of conformally compactified geometries, motivated by the conformal treatment of infinity in general relativity.
15. Hawking-Hayward quasi-local energy under conformal transformations
CERN Document Server
Prain, Angus; Faraoni, Valerio; Lapierre-Léonard, Marianne
2015-01-01
We derive a formula describing the transformation of the Hawking-Hayward quasi-local energy under a conformal rescaling of the spacetime metric. A known formula for the transformation of the Misner-Sharp-Hernandez mass is recovered as a special case.
16. Generalized BRST symmetry for arbitrary spin conformal field theory
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker, E-mail: [email protected] [Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016 (India); Mandal, Bhabani Prasad, E-mail: [email protected] [Department of Physics, Banaras Hindu University, Varanasi 221005 (India)
2015-05-11
We develop the finite field-dependent BRST (FFBRST) transformation for arbitrary spin-s conformal field theories. We discuss the novel features of the FFBRST transformation in these systems. To illustrate the results we consider the spin-1 and spin-2 conformal field theories in two examples. Within the formalism we found that FFBRST transformation connects the generating functionals of spin-1 and spin-2 conformal field theories in linear and non-linear gauges. Further, the conformal field theories in the framework of FFBRST transformation are also analyzed in Batalin–Vilkovisky (BV) formulation to establish the results.
17. Wormhole supported by dark energy admitting conformal motion
Science.gov (United States)
Bhar, Piyali; Rahaman, Farook; Manna, Tuhina; Banerjee, Ayan
2016-12-01
In this article, we study the possibility of sustaining static and spherically symmetric traversable wormhole geometries admitting conformal motion in Einstein gravity, which presents a more systematic approach to search a relation between matter and geometry. In wormhole physics, the presence of exotic matter is a fundamental ingredient and we show that this exotic source can be dark energy type which support the existence of wormhole spacetimes. In this work we model a wormhole supported by dark energy which admits conformal motion. We also discuss the possibility of the detection of wormholes in the outer regions of galactic halos by means of gravitational lensing. Studies of the total gravitational energy for the exotic matter inside a static wormhole configuration are also performed.
18. Wormhole supported by dark energy admitting conformal motion
Energy Technology Data Exchange (ETDEWEB)
Bhar, Piyali [Government General Degree College, Singur, Department of Mathematics, Hooghly, West Bengal (India); Rahaman, Farook; Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Manna, Tuhina [St. Xavier' s College, Department of Mathematics and Statistics (Commerce Evening), Kolkata, West Bengal (India)
2016-12-15
In this article, we study the possibility of sustaining static and spherically symmetric traversable wormhole geometries admitting conformal motion in Einstein gravity, which presents a more systematic approach to search a relation between matter and geometry. In wormhole physics, the presence of exotic matter is a fundamental ingredient and we show that this exotic source can be dark energy type which support the existence of wormhole spacetimes. In this work we model a wormhole supported by dark energy which admits conformal motion. We also discuss the possibility of the detection of wormholes in the outer regions of galactic halos by means of gravitational lensing. Studies of the total gravitational energy for the exotic matter inside a static wormhole configuration are also performed. (orig.)
19. A robust force field based method for calculating conformational energies of charged drug-like molecules
DEFF Research Database (Denmark)
Pøhlsgaard, Jacob; Harpsøe, Kasper; Jørgensen, Flemming Steen
2012-01-01
The binding affinity of a drug like molecule depends among other things on the availability of the bioactive conformation. If the bioactive conformation has a significantly higher energy than the global minimum energy conformation, the molecule is unlikely to bind to its target. Determination of ...... compounds generated by conformational analysis with modified electrostatics are good approximations of the conformational distributions predicted by experimental data and in simulated annealing performed in explicit solvent.......The binding affinity of a drug like molecule depends among other things on the availability of the bioactive conformation. If the bioactive conformation has a significantly higher energy than the global minimum energy conformation, the molecule is unlikely to bind to its target. Determination...... of the global minimum energy conformation and calculation of conformational penalties of binding are prerequisites for prediction of reliable binding affinities. Here, we present a simple and computationally efficient procedure to estimate the global energy minimum for a wide variety of structurally diverse...
20. 40 CFR 1033.201 - General requirements for obtaining a certificate of conformity.
Science.gov (United States)
2010-07-01
... certificate of conformity. 1033.201 Section 1033.201 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY....201 General requirements for obtaining a certificate of conformity. Certification is the process by... certificate of conformity for freshly manufactured locomotives. Anyone meeting the definition...
1. 77 FR 47621 - Appalachian Gateway Project; Notice of Availability of Draft General Conformity Analysis
Science.gov (United States)
2012-08-09
... Conformity Analysis In accordance with the National Environmental Policy Act of 1969, the Clean Air Act and... prepared this draft General Conformity Determination (GCD) for the Appalachian Gateway Project (Project) to... the Project will achieve conformity in Pennsylvania with the use of Pennsylvania Department...
2. 40 CFR 93.158 - Criteria for determining conformity of general Federal actions.
Science.gov (United States)
2010-07-01
... 40 Protection of Environment 20 2010-07-01 2010-07-01 false Criteria for determining conformity of... (CONTINUED) AIR PROGRAMS (CONTINUED) DETERMINING CONFORMITY OF FEDERAL ACTIONS TO STATE OR FEDERAL IMPLEMENTATION PLANS Determining Conformity of General Federal Actions to State or Federal Implementation...
3. 40 CFR 93.159 - Procedures for conformity determinations of general Federal actions.
Science.gov (United States)
2010-07-01
... 40 Protection of Environment 20 2010-07-01 2010-07-01 false Procedures for conformity... PROTECTION AGENCY (CONTINUED) AIR PROGRAMS (CONTINUED) DETERMINING CONFORMITY OF FEDERAL ACTIONS TO STATE OR FEDERAL IMPLEMENTATION PLANS Determining Conformity of General Federal Actions to State or...
4. The energy profiles of atomic conformational transition intermediates of adenylate kinase.
Science.gov (United States)
Feng, Yaping; Yang, Lei; Kloczkowski, Andrzej; Jernigan, Robert L
2009-11-15
The elastic network interpolation (ENI) (Kim et al., Biophys J 2002;83:1620-1630) is a computationally efficient and physically realistic method to generate conformational transition intermediates between two forms of a given protein. However it can be asked whether these calculated conformations provide good representatives for these intermediates. In this study, we use ENI to generate conformational transition intermediates between the open form and the closed form of adenylate kinase (AK). Based on C(alpha)-only intermediates, we construct atomic intermediates by grafting all the atoms of known AK structures onto the C(alpha) atoms and then perform CHARMM energy minimization to remove steric conflicts and optimize these intermediate structures. We compare the energy profiles for all intermediates from both the CHARMM force-field and from knowledge-based energy functions. We find that the CHARMM energies can successfully capture the two energy minima representing the open AK and closed AK forms, while the energies computed from the knowledge-based energy functions can detect the local energy minimum representing the closed AK form and show some general features of the transition pathway with a somewhat similar energy profile as the CHARMM energies. The combinatorial extension structural alignment (Shindyalov et al., 1998;11:739-747) and the k-means clustering algorithm are then used to show that known PDB structures closely resemble computed intermediates along the transition pathway.
5. Energy Flux Positivity and Unitarity in Conformal Field Theories
Science.gov (United States)
Kulaxizi, Manuela; Parnachev, Andrei
2011-01-01
We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop lightlike poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-free is equivalent to the condition of positivity of energy flux.
6. Energy flux positivity and unitarity in conformal field theories.
Science.gov (United States)
Kulaxizi, Manuela; Parnachev, Andrei
2011-01-07
We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop lightlike poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-free is equivalent to the condition of positivity of energy flux.
7. Generally covariant vs. gauge structure for conformal field theories
Energy Technology Data Exchange (ETDEWEB)
Campigotto, M., E-mail: [email protected] [Dipartimento di Fisica, University of Torino, Via P. Giuria 1, 10125, Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Via P. Giuria 1, 10125, Torino (Italy); Fatibene, L. [Dipartimento di Matematica, University of Torino, Via C. Alberto 10, 10123, Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Via P. Giuria 1, 10125, Torino (Italy)
2015-11-15
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group. -- Highlights: •Both a natural and a gauge natural structure for conformal gravity are defined. •Global properties and natural lift of spacetime transformations are described. •The possible definitions of physical state are considered and discussed. •The gauge natural theory has less physical states than the corresponding natural one. •The dynamics forces to prefer the gauge natural structure over the natural one.
8. Conformation of antifreeze glycoproteins as determined from conformational energy calculations and fully assigned proton NMR spectra
Energy Technology Data Exchange (ETDEWEB)
Bush, C.A.; Rao, B.N.N.
1986-05-01
The /sup 1/H NMR spectra of AFGP's ranging in molecular weight from 2600 to 30,000 Daltons isolated from several different species of polar fish have been measured. The spectrum of AFGP 1-4 from Pagothenia borchgrevinki with an average of 30 repeating subunits has a single resonance for each proton of the glycotripeptide repeating unit, (ala-(gal-(..beta..-1..-->..3) galNAc-(..cap alpha..--O-)thr-ala)/sub n/. Its /sup 1/H NMR spectrum including resonances of the amide protons has been completely assigned. Coupling constants and nuclear Overhauser enhancements (n.O.e.) between protons on distant residues imply conformational order. The 2600 dalton molecular weight glycopeptides (AFGP-8) have pro in place of ala at certain specific points in the sequence and AFGP-8R of Eleginus gracilis has arg in place of one thr. The resonances of pro and arg were assigned by decoupling. The resonances of the carboxy and amino terminals have distinct chemical shifts and were assigned in AFGP-8 of Boreogadus saida by titration. n.O.e. between ..cap alpha..--protons and amide protons of the adjacent residue (sequential n.O.e.) were used in assignments of additional resonances and to assign the distinctive resonances of thr followed by pro. Conformational energy calculations on the repeating glycotripeptide subunit of AFGP show that the ..cap alpha..--glucosidic linkage has a fixed conformation while the ..beta..--linkage is less rigid. A conformational model for AFGP 1-4, which is based on the calculations has the peptide in an extended left-handed helix with three residues per turn similar to polyproline II. The model is consistent with CD data, amide proton coupling constants, temperature dependence of amide proton chemical shifts.
9. CALCULATION OF CONFORMATIONAL ENTROPY AND FREE ENERGY OF POLYSILANE CHAIN
Institute of Scientific and Technical Information of China (English)
Meng-bo Luo; Ying-cai Chen; Jian-hua Huang; Jian-min Xu
2001-01-01
The conformational entropy S and free energy F were calculated by exact enumeration of polysilane chain up to 23 segments with excluded volume (EV) and long-range van der Waals (VW) interaction. A nonlinear relation between SEV+VW and chain length n was found though SEV was found to vary linearly with n. We found that the second-order transition temperature of polysilane chain with VW interaction increases with the increase of chain length, while that of polysilane chain without VW interaction is chain length independent. Moreover, the free energies FEV+VW and FEV are both linearly related with n, and FEV+VW＜FEV for all temperatures.
10. Assignment of Side-Chain Conformation Using Adiabatic Energy Mapping, Free Energy Perturbation, and Molecular Dynamic Simulations
DEFF Research Database (Denmark)
Frimurer, Thomas M.; Günther, Peter H.; Sørensen, Morten Dahl
1999-01-01
adiabatic mapping, conformational change, essentialdynamics, free energy simulations, Kunitz type inhibitor *ga3(VI)......adiabatic mapping, conformational change, essentialdynamics, free energy simulations, Kunitz type inhibitor *ga3(VI)...
11. 75 FR 20591 - AES Sparrows Point LNG, LLC and Mid-Atlantic Express, LLC; Notice of Final General Conformity...
Science.gov (United States)
2010-04-20
... Energy Regulatory Commission AES Sparrows Point LNG, LLC and Mid-Atlantic Express, LLC; Notice of Final General Conformity Determination for Pennsylvania for the Proposed Sparrows Point LNG Terminal and... liquefied natural gas (LNG) import terminal and natural gas pipeline proposed by AES Sparrows Point LNG,...
12. Stable phantom-energy wormholes admitting conformal motions
CERN Document Server
Kuhfittig, Peter K F
2016-01-01
It has been argued that wormholes are as good a prediction of Einstein's theory as black holes but the theoretical construction requires a reverse strategy, specifying the desired geometric properties of the wormhole and leaving open the determination of the stress-energy tensor. We begin by confirming an earlier result by the author showing that a complete wormhole solution can be obtained by adopting the equation of state $p=\\omega\\rho$ and assuming that the wormhole admits a one-parameter group of conformal motions. The main purpose of this paper is to use the assumption of conformal symmetry to show that the wormhole is stable to linearized radial perturbations whenever $-1.5<\\omega <-1$.
13. Stable phantom-energy wormholes admitting conformal motions
Science.gov (United States)
Kuhfittig, Peter K. F.
It has been argued that wormholes are as good a prediction of Einstein’s theory as black holes but the theoretical construction requires a reverse strategy, specifying the desired geometric properties of the wormhole and leaving open the determination of the stress-energy tensor. We begin by confirming an earlier result by the author showing that a complete wormhole solution can be obtained by adopting the equation of state p = ωρ and assuming that the wormhole admits a one-parameter group of conformal motions. The main purpose of this paper is to use the assumption of conformal symmetry to show that the wormhole is stable to linearized radial perturbations whenever ‑ 1.5 < ω < ‑1.
14. [Conformal radiotherapy of prostatic cancer: a general review].
Science.gov (United States)
Chauvet, B; Oozeer, R; Bey, P; Pontvert, D; Bolla, M
1999-01-01
Recent progress in radiotherapeutic management of localized prostate cancer is reviewed. Clinical aspects--including dose-effect beyond 70 Gy, relative role of conformal radiation therapy techniques and of early hormonal treatment--are discussed as well as technical components--including patient immobilization, organ motion, prostate contouring, beam arrangement, 3-D treatment planning and portal imaging. The local control and biological relapse-free survival rates appear to be improved by high dose conformal radiotherapy from 20 to 30% for patients with intermediate and high risk of relapse. A benefit of overall survival is expected but not yet demonstrated. Late reactions, especially the rectal toxicity, remain moderate despite the dose escalation. However, conformal radiotherapy demands a high precision at all steps of the procedure.
15. Conformational energy calculations and proton nuclear overhauser enhancements reveal a unique conformation for blood group A oligosaccharides
Energy Technology Data Exchange (ETDEWEB)
Bush, C.A.; Yan, Z.Y.; Rao, B.N.N.
1986-10-01
The H NMR spectra of a series of blood group A active oligosaccharides containing from four to ten sugar residues have been completely assigned, and quantitative nuclear Overhauser enhancements (NOE) have been measured between protons separated by known distances within the pyranoside ring. The observation of NOE between anomeric protons and those of the aglycon sugar as well as small effects between protons of distant rings suggests that the oligosaccharides have well-defined conformations. Conformational energy calculations were carried out on a trisaccharide, Fuc( -1 2)(GalNAc( -1 3))-GalUS -O-me, which models the nonreducing terminal fragments of the blood group A oligosaccharides. The results of calculations with three different potential energy functions which have been widely used in peptides and carbohydrates gave several minimum energy conformations. In NOE calculations from conformational models, the rotational correlation time was adjusted to fit T1's and intra-ring NOE. Comparison of calculated maps of NOE as a function of glycosidic dihedral angles showed that only a small region of conformational space was consistent with experimental data on a blood group A tetrasaccharide alditol. This conformation occurs at an energy minimum in all three energy calculations. Temperature dependence of the NOE implies that the oligosaccharides adopt single rigid conformations which do not change with temperature.
16. Predictive Sampling of Rare Conformational Events in Aqueous Solution: Designing a Generalized Orthogonal Space Tempering Method.
Science.gov (United States)
Lu, Chao; Li, Xubin; Wu, Dongsheng; Zheng, Lianqing; Yang, Wei
2016-01-12
In aqueous solution, solute conformational transitions are governed by intimate interplays of the fluctuations of solute-solute, solute-water, and water-water interactions. To promote molecular fluctuations to enhance sampling of essential conformational changes, a common strategy is to construct an expanded Hamiltonian through a series of Hamiltonian perturbations and thereby broaden the distribution of certain interactions of focus. Due to a lack of active sampling of configuration response to Hamiltonian transitions, it is challenging for common expanded Hamiltonian methods to robustly explore solvent mediated rare conformational events. The orthogonal space sampling (OSS) scheme, as exemplified by the orthogonal space random walk and orthogonal space tempering methods, provides a general framework for synchronous acceleration of slow configuration responses. To more effectively sample conformational transitions in aqueous solution, in this work, we devised a generalized orthogonal space tempering (gOST) algorithm. Specifically, in the Hamiltonian perturbation part, a solvent-accessible-surface-area-dependent term is introduced to implicitly perturb near-solute water-water fluctuations; more importantly in the orthogonal space response part, the generalized force order parameter is generalized as a two-dimension order parameter set, in which essential solute-solvent and solute-solute components are separately treated. The gOST algorithm is evaluated through a molecular dynamics simulation study on the explicitly solvated deca-alanine (Ala10) peptide. On the basis of a fully automated sampling protocol, the gOST simulation enabled repetitive folding and unfolding of the solvated peptide within a single continuous trajectory and allowed for detailed constructions of Ala10 folding/unfolding free energy surfaces. The gOST result reveals that solvent cooperative fluctuations play a pivotal role in Ala10 folding/unfolding transitions. In addition, our assessment
17. Positive Energy Conditions in 4D Conformal Field Theory
CERN Document Server
Farnsworth, Kara; Prilepina, Valentina
2015-01-01
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality $\\langle T^{00} \\rangle \\ge -C/L^4$, where $L$ is the size of the smearing region, and $C$ is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the "conformal collider" constraints of Hofman and Maldacena. We speculate that there may be theories that violate the Hofman-Maldacena bounds, but satisfy our bounds. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarka...
18. Positive energy conditions in 4D conformal field theory
Science.gov (United States)
Farnsworth, Kara; Luty, Markus A.; Prilepina, Valentina
2016-10-01
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality ≥ - C/L 4, where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the "conformal collider" constraints of Hofman and Maldacena. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.
19. Theoretical study of the conformation and energy of supercoiled DNA
Energy Technology Data Exchange (ETDEWEB)
Hunt, N. G. [Lawrence Berkeley Lab., CA (United States). Structural Biology Div.; California Univ., Berkeley, CA (United States). Dept. of Physics
1992-01-01
The two sugar-phosphate backbones of the DNA molecule wind about each other in helical paths. For circular DNA molecules, or for linear pieces of DNA with the ends anchored, the two strands have a well-defined linking number, Lk. If Lk differs from the equilibrium linking number Lk{sub 0}, the molecule is supercoiled. The linking difference {Delta}Lk = Lk-Lk{sub 0} is partitioned between torsional deformation of the DNA, or twist ({Delta}Tw), and a winding of the DNA axis about itself known as writhe (Wr). In this dissertation, the conformation and energy of supercoiled DNA are examined by treating DNA as an elastic cylinder. Finite-length and entropic effects are ignored, and all extensive quantities are treated as linear densities. Two classes of conformation are considered: the plectonemic or interwound form, in which the axis of the DNA double helix winds about itself in a double superhelix, and the toroidal shape in which the axis is wrapped around a torus. Minimum energy conformation are found. For biologically relevant values of specific linking differences, the plectonemic DNA, the superhelical pitch angle {alpha} is in the range 45{degree} < {alpha} {le} 90{degree}. For low values of specific linking difference {vert_bar}{sigma}{vert_bar} ({sigma} = {Delta}Lk/Lk{sub 0}), most linking difference is in writhe. As {vert_bar}{sigma}{vert_bar} increases, a greater proportion of linking difference is in twist. Interaction between DNA strands is treated first as a hard-body excluded volume and then as a screened electrostatic repulsion. Ionic strength is found to have a large effect, resulting in significantly greater torsional stress in supercoiled DNA at low ionic strength.
20. Binary cluster collision dynamics and minimum energy conformations
Energy Technology Data Exchange (ETDEWEB)
2013-10-15
The collision dynamics of one Ag or Cu atom impinging on a Au{sub 12} cluster is investigated by means of DFT molecular dynamics. Our results show that the experimentally confirmed 2D to 3D transition of Au{sub 12}→Au{sub 13} is mostly preserved by the resulting planar Au{sub 12}Ag and Au{sub 12}Cu minimum energy clusters, which is quite remarkable in view of the excess energy, well larger than the 2D–3D potential barrier height. The process is accompanied by a large s−d hybridization and charge transfer from Au to Ag or Cu. The dynamics of the collision process mainly yields fusion of projectile and target, however scattering and cluster fragmentation also occur for large energies and large impact parameters. While Ag projectiles favor fragmentation, Cu favors scattering due to its smaller mass. The projectile size does not play a major role in favoring the fragmentation or scattering channels. By comparing our collision results with those obtained by an unbiased minimum energy search of 4483 Au{sub 12}Ag and 4483 Au{sub 12}Cu configurations obtained phenomenologically, we find that there is an extra bonus: without increase of computer time collisions yield the planar lower energy structures that are not feasible to obtain using semi-classical potentials. In fact, we conclude that phenomenological potentials do not even provide adequate seeds for the search of global energy minima for planar structures. Since the fabrication of nanoclusters is mainly achieved by synthesis or laser ablation, the set of local minima configurations we provide here, and their distribution as a function of energy, are more relevant than the global minimum to analyze experimental results obtained at finite temperatures, and is consistent with the dynamical coexistence of 2D and 3D liquid Au clusters conformations obtained previously.
1. Exclusion Statistics in Conformal Field Theory -- generalized fermions and spinons for level-1 WZW theories
OpenAIRE
1998-01-01
We systematically study the exclusion statistics for quasi-particles for Conformal Field Theory spectra by employing a method based on recursion relations for truncated spectra. Our examples include generalized fermions in c
2. General Conformity Training Module 2.5: Proactive Role for Federal Agencies
Science.gov (United States)
Module 2.5 explains how taking a proactive role will allow a federal agency to more effectively participate in newly promulgated programs under the General Conformity Regulations, such as the emission reduction credits and the emission budgets programs.
3. Conformational disorder in energy transfer: beyond Förster theory.
Science.gov (United States)
Nelson, Tammie; Fernandez-Alberti, Sebastian; Roitberg, Adrian E; Tretiak, Sergei
2013-06-21
Energy transfer in donor-acceptor chromophore pairs, where the absorption of each species is well separated while donor emission and acceptor absorption overlap, can be understood through a Förster resonance energy transfer model. The picture is more complex for organic conjugated polymers, where the total absorption spectrum can be described as a sum of the individual contributions from each subunit (chromophore), whose absorption is not well separated. Although excitations in these systems tend to be well localized, traditional donors and acceptors cannot be defined and energy transfer can occur through various pathways where each subunit (chromophore) is capable of playing either role. In addition, fast torsional motions between individual monomers can break conjugation and lead to reordering of excited state energy levels. Fast torsional fluctuations occur on the same timescale as electronic transitions leading to multiple trivial unavoided crossings between excited states during dynamics. We use the non-adiabatic excited state molecular dynamics (NA-ESMD) approach to simulate energy transfer between two poly-phenylene vinylene (PPV) oligomers composed of 3-rings and 4-rings, respectively, separated by varying distances. The change in the spatial localization of the transient electronic transition density, initially localized on the donors, is used to determine the transfer rate. Our analysis shows that evolution of the intramolecular transition density can be decomposed into contributions from multiple transfer pathways. Here we present a detailed analysis of ensemble dynamics as well as a few representative trajectories which demonstrate the intertwined role of electronic and conformational processes. Our study reveals the complex nature of energy transfer in organic conjugated polymer systems and emphasizes the caution that must be taken in performing such an analysis when a single simple unidirectional pathway is unlikely.
4. Enhanced conformational sampling to visualize a free-energy landscape of protein complex formation.
Science.gov (United States)
Iida, Shinji; Nakamura, Haruki; Higo, Junichi
2016-06-15
We introduce various, recently developed, generalized ensemble methods, which are useful to sample various molecular configurations emerging in the process of protein-protein or protein-ligand binding. The methods introduced here are those that have been or will be applied to biomolecular binding, where the biomolecules are treated as flexible molecules expressed by an all-atom model in an explicit solvent. Sampling produces an ensemble of conformations (snapshots) that are thermodynamically probable at room temperature. Then, projection of those conformations to an abstract low-dimensional space generates a free-energy landscape. As an example, we show a landscape of homo-dimer formation of an endothelin-1-like molecule computed using a generalized ensemble method. The lowest free-energy cluster at room temperature coincided precisely with the experimentally determined complex structure. Two minor clusters were also found in the landscape, which were largely different from the native complex form. Although those clusters were isolated at room temperature, with rising temperature a pathway emerged linking the lowest and second-lowest free-energy clusters, and a further temperature increment connected all the clusters. This exemplifies that the generalized ensemble method is a powerful tool for computing the free-energy landscape, by which one can discuss the thermodynamic stability of clusters and the temperature dependence of the cluster networks.
5. Generalized Wick theorems in conformal field theory and the Borcherds identity
CERN Document Server
Takagi, Taichiro
2016-01-01
As the missing counterpart of the well-known generalized Wick theorem for interacting fields in two dimensional conformal field theory, we present a new formula for the operator product expansion of a normally ordered operator and a single operator on its right hand. Quite similar to the original Wick theorem for the opposite order operator product, it expresses the contraction i.e. the singular part of the operator product expansion as a contour integral of only two terms, each of which is a product of a contraction and a single operator. We discuss the relationship between these formulas and the Borcherds identity satisfied by the quantum fields associated with the theory of vertex algebras. A derivation of these formulas by an analytic method is also presented. The validity of our new formula is illustrated by a few examples including the Sugawara construction of the energy momentum tensor for the quantized currents of affine Lie algebras.
6. Comparative structural and vibrational study of the four lowest energy conformers of serotonin
Science.gov (United States)
2017-02-01
A computational investigation of all possible lowest energy conformers of serotonin was carried out at the B3LYP/6-311 ++G** level. Out of the 14 possible lowest energy conformers, the first 4 conformers were investigated thoroughly for the optimized geometries, fundamental frequencies, the potential energy distributions, APT and natural charges, natural bond orbital (NBO) analysis, MEP, Contour map, total density array, HOMO, LUMO energies. The second third and fourth conformers are energetically at higher temperatures of 78, 94 and 312 K respectively with respect to the first one. Bond angles and bond lengths do not show significant variations while the dihedral angles vary significantly in going from one conformer to the other. Some of the vibrational modes of the indole moiety are conformation dependent to some extent whereas most of the normal modes of vibration of amino-ethyl side chain vary significantly in going from one conformer to conformer. The MEP for the four conformers suggested that the sites of the maximum positive and negative ESP change on changing the conformation. The charges at some atomic sites also change significantly from conformer to conformer.
7. A Calculus for Conformal Hypersurfaces and new higher Willmore energy functionals
CERN Document Server
Gover, A Rod
2016-01-01
The invariant theory for conformal hypersurfaces is studied by treating these as the conformal infinity of a conformally compact manifold: For a given conformal hypersurface embedding, a distinguished ambient metric is found (within its conformal class) by solving a singular version of the Yamabe problem. Using existence results for asymptotic solutions to this problem, we develop the details of how to proliferate conformal hypersurface invariants. In addition we show how to compute the the solution's asymptotics. We also develop a calculus of conformal hypersurface invariant differential operators and in particular, describe how to compute extrinsically coupled analogues of conformal Laplacian powers. Our methods also enable the study of integrated conformal hypersurface invariants and their functional variations. As a main application we develop new higher dimensional analogues of the Willmore energy for embedded surfaces. This complements recent progress on the existence and construction of such functional...
8. Numerical conformal mapping via a boundary integral equation with the adjoint generalized Neumann kernel
OpenAIRE
Nasser, Mohamed M. S.; Murid, Ali H. M.; Sangawi, Ali W. K.
2013-01-01
This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral equation is derived by reformulating the conformal mapping as an adjoint Riemann-Hilbert problem. From the adjoint Riemann-Hilbert problem, we derive a boundary integral equation with the adjoint generalized Neumann kernel for the derivative of the boundary...
9. Rotational Spectroscopy of the Lowest Energy Conformer of 2-Cyanobutane.
Science.gov (United States)
Müller, Holger S P; Zingsheim, Oliver; Wehres, Nadine; Grabow, Jens-Uwe; Lewen, Frank; Schlemmer, Stephan
2017-09-28
Isopropyl cyanide was recently detected in space as the first branched alkyl compound. Its abundance with respect to n-propyl cyanide in the Galactic center source Sagittarius B2(N2) is about 0.4. Astrochemical model calculations suggest that for the heavier homologue butyl cyanide the branched isomers dominate over the unbranched n-butyl cyanide and that 2-cyanobutane is the most abundant isomer. We have studied the rotational spectrum of 2-cyanobutane between 2 and 24 GHz using Fourier transform microwave spectroscopy and between 36 and 402 GHz employing (sub)millimeter absorption spectroscopy. Transitions of the lowest energy conformer were identified easily. Its rotational spectrum is very rich, and the quantum numbers J and Ka reach values of 111 and 73, respectively. This wealth of data yielded rotational and centrifugal distortion parameters up to tenth order, diagonal and one off-diagonal (14)N nuclear quadrupole coupling parameters, and one nuclear spin-rotation coupling parameter. We have also carried out quantum chemical calculations in part to facilitate the assignments. The molecule 2-cyanobutane was not found in the present ALMA data of Sagittarius B2(N2), but it may be found in the more sensitive data that have been completed very recently in the ALMA Cycle 4.
10. Triangulating Nucleic Acid Conformations Using Multicolor Surface Energy Transfer.
Science.gov (United States)
Riskowski, Ryan A; Armstrong, Rachel E; Greenbaum, Nancy L; Strouse, Geoffrey F
2016-02-23
Optical ruler methods employing multiple fluorescent labels offer great potential for correlating distances among several sites, but are generally limited to interlabel distances under 10 nm and suffer from complications due to spectral overlap. Here we demonstrate a multicolor surface energy transfer (McSET) technique able to triangulate multiple points on a biopolymer, allowing for analysis of global structure in complex biomolecules. McSET couples the competitive energy transfer pathways of Förster Resonance Energy Transfer (FRET) with gold-nanoparticle mediated Surface Energy Transfer (SET) in order to correlate systematically labeled points on the structure at distances greater than 10 nm and with reduced spectral overlap. To demonstrate the McSET method, the structures of a linear B-DNA and a more complex folded RNA ribozyme were analyzed within the McSET mathematical framework. The improved multicolor optical ruler method takes advantage of the broad spectral range and distances achievable when using a gold nanoparticle as the lowest energy acceptor. The ability to report distance information simultaneously across multiple length scales, short-range (10-50 Å), mid-range (50-150 Å), and long-range (150-350 Å), distinguishes this approach from other multicolor energy transfer methods.
11. Stalking Higher Energy Conformers on the Potential Energy Surface of Charged Species.
Science.gov (United States)
Brites, Vincent; Cimas, Alvaro; Spezia, Riccardo; Sieffert, Nicolas; Lisy, James M; Gaigeot, Marie-Pierre
2015-03-10
Combined theoretical DFT-MD and RRKM methodologies and experimental spectroscopic infrared predissociation (IRPD) strategies to map potential energy surfaces (PES) of complex ionic clusters are presented, providing lowest and high energy conformers, thresholds to isomerization, and cluster formation pathways. We believe this association not only represents a significant advance in the field of mapping minima and transition states on the PES but also directly measures dynamical pathways for the formation of structural conformers and isomers. Pathways are unraveled over picosecond (DFT-MD) and microsecond (RRKM) time scales while changing the amount of internal energy is experimentally achieved by changing the loss channel for the IRPD measurements, thus directly probing different kinetic and isomerization pathways. Demonstration is provided for Li(+)(H2O)3,4 ionic clusters. Nonstatistical formation of these ionic clusters by both direct and cascade processes, involving isomerization processes that can lead to trapping of high energy conformers along the paths due to evaporative cooling, has been unraveled.
12. General Randic matrix and general Randi'c energy
Directory of Open Access Journals (Sweden)
Ran Gu;
2014-09-01
Full Text Available Let $G$ be a simple graph with vertex set $V(G = {v_1, v_2,ldots , v_n}$ and $d_i$ the degree of its vertex $v_i$, $i = 1, 2, cdots, n$. Inspired by the Randi'c matrix and the general Randi'c index of a graph, we introduce the concept of general Randi'c matrix $textbf{R}_alpha$ of $G$, which is defined by $(textbf{R}_alpha_{i,j}=(d_id_j^alpha$ if $v_i$ and $v_j$ are adjacent, and zero otherwise. Similarly, the general Randi'{c} eigenvalues are the eigenvalues of the general Randi'{c} matrix, the greatest general Randi'{c} eigenvalue is the general Randi'{c} spectral radius of $G$, and the general Randi'{c} energy is the sum of the absolute values of the general Randi'{c} eigenvalues. In this paper, we prove some properties of the general Randi'c matrix and obtain lower and upper bounds for general Randi'{c} energy, also, we get some lower bounds for general Randi'{c} spectral radius of a connected graph. Moreover, we give a new sharp upper bound for the general Randi'{c} energy when $alpha=-1/2$.[2mm] noindent{bf Keywords:} general Randi'c matrix, general Randi'c energy, eigenvalues, spectral radius.
13. Energy levels and quantum states of [Leu]enkephalin conformations based on theoretical and experimental investigations
Energy Technology Data Exchange (ETDEWEB)
Abdali, Salim; Jensen, Morten O; Bohr, Henrik [Quantum Protein Centre (QUP), Department of Physics, Bldg. 309, Technical University of Denmark, DK-2800 Kgs. Lyngby (Denmark)
2003-05-14
This paper describes a theoretical and experimental study of [Leu]enkephalin conformations with respect to the quantum states of the atomic structure of the peptide. Results from vibrational absorption measurements and quantum calculations are used to outline a quantum picture and to assign vibrational modes to the different conformations. The energy landscape of the conformations is reported as a function of a Hamming distance in Ramachandran space. Molecular dynamics simulations reveal a pronounced stability of the so-called single-bend low-energy conformation, which supports the derived quantum picture of this peptide.
14. Energy levels and quantum states of [Leu]enkephalin conformations based on theoretical and experimental investigations
DEFF Research Database (Denmark)
Abdali, Salim; Jensen, Morten Østergaard; Bohr, Henrik
2003-01-01
This paper describes a theoretical and experimental study of [Leu]enkephalin conformations with respect to the quantum estates of the atomic structure of the peptide. Results from vibrational absorption measurements and quantum calculations are used to outline a quantum picture and to assign...... vibrational modes to the different conformations. The energy landscape of the conformations is reported as a function of a Hamming distance in Ramachandran space. Molecular dynamics simulations reveal a pronounced stability of the so-called single-bend low-energy conformation, which supports the derived...... quantum picture of this peptide....
15. Conformal transformations and conformal invariance in gravitation
CERN Document Server
Dabrowski, Mariusz P; Blaschke, David B
2008-01-01
Conformal transformations are frequently used tools in order to study relations between various theories of gravity and Einstein relativity. Because of that, in this paper we discuss the rules of conformal transformations for geometric quantities in general relativity. In particular, we discuss the conformal transformations of the matter energy-momentum tensor. We thoroughly discuss the latter and show the subtlety of the conservation law (i.e., the geometrical Bianchi identity) imposed in one of the conformal frames in reference to the other. The subtlety refers to the fact that conformal transformation creates'' an extra matter term composed of the conformal factor which enters the conservation law. In an extreme case of the flat original spacetime the matter is created'' due to work done by the conformal transformation to bend the spacetime which was originally flat. We also discuss how to construct the conformally invariant gravity which, in the simplest version, is a special case of the Brans-Dicke t...
16. Peptoid conformational free energy landscapes from implicit-solvent molecular simulations in AMBER.
Science.gov (United States)
Voelz, Vincent A; Dill, Ken A; Chorny, Ilya
2011-01-01
To test the accuracy of existing AMBER force field models in predicting peptoid conformation and dynamics, we simulated a set of model peptoid molecules recently examined by Butterfoss et al. (JACS 2009, 131, 16798-16807) using QM methods as well as three peptoid sequences with experimentally determined structures. We found that AMBER force fields, when used with a Generalized Born/Surface Area (GBSA) implicit solvation model, could accurately reproduce the peptoid torsional landscape as well as the major conformers of known peptoid structures. Enhanced sampling by replica exchange molecular dynamics (REMD) using temperatures from 300 to 800 K was used to sample over cis-trans isomerization barriers. Compared to (Nrch)5 and cyclo-octasarcosyl, the free energy of N-(2-nitro-3-hydroxyl phenyl)glycine-N-(phenyl)glycine has the most "foldable" free energy landscape, due to deep trans-amide minima dictated by N-aryl sidechains. For peptoids with (S)-N (1-phenylethyl) (Nspe) side chains, we observe a discrepancy in backbone dihedral propensities between molecular simulations and QM calculations, which may be due to force field effects or the inability to capture n --> n* interactions. For these residues, an empirical phi-angle biasing potential can "rescue" the backbone propensities seen in QM. This approach can serve as a general strategy for addressing force fields without resorting to a complete reparameterization. Overall, this study demonstrates the utility of implicit-solvent REMD simulations for efficient sampling to predict peptoid conformational landscapes, providing a potential tool for first-principles design of sequences with specific folding properties.
17. Free Energy-Based Conformational Search Algorithm Using the Movable Type Sampling Method.
Science.gov (United States)
Pan, Li-Li; Zheng, Zheng; Wang, Ting; Merz, Kenneth M
2015-12-08
In this article, we extend the movable type (MT) sampling method to molecular conformational searches (MT-CS) on the free energy surface of the molecule in question. Differing from traditional systematic and stochastic searching algorithms, this method uses Boltzmann energy information to facilitate the selection of the best conformations. The generated ensembles provided good coverage of the available conformational space including available crystal structures. Furthermore, our approach directly provides the solvation free energies and the relative gas and aqueous phase free energies for all generated conformers. The method is validated by a thorough analysis of thrombin ligands as well as against structures extracted from both the Protein Data Bank (PDB) and the Cambridge Structural Database (CSD). An in-depth comparison between OMEGA and MT-CS is presented to illustrate the differences between the two conformational searching strategies, i.e., energy-based versus free energy-based searching. These studies demonstrate that our MT-based ligand conformational search algorithm is a powerful approach to delineate the conformational ensembles of molecular species on free energy surfaces.
18. 78 FR 57267 - Approval and Promulgation of Implementation Plans; State of Missouri; Conformity of General...
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2013-09-18
... (44 U.S.C. 3501 et seq.); is certified as not having a significant economic impact on a substantial... revision amends rule 10 CSR 10-6.300 Conformity of General Federal Actions to State Implementation Plans... affect the stringency of the SIP or adversely impact air quality. II. Have the requirements for approval...
19. On a Generalization of GKO Coset Construction of Conformal Field Theories
CERN Document Server
Kumar, Dushyant
2015-01-01
We introduce a generalization of Goddard-Kent-Olive (GKO) coset construction of two dimensional conformal field theories based on a choice of a scaled affine subalgebra $\\hat{\\mathfrak{h}}^s$ of a given affine Lie algebra $\\hat{\\mathfrak{h}}$. We study some aspects of the construction through the example of Ising CFT as a generalized GKO coset of $\\text{su(2)}_1$ with a scaling factor $s=2$.
20. Elucidation of the conformational free energy landscape in H.pylori LuxS and its implications to catalysis
Directory of Open Access Journals (Sweden)
Bhattacharyya Moitrayee
2010-08-01
Full Text Available Abstract Background One of the major challenges in understanding enzyme catalysis is to identify the different conformations and their populations at detailed molecular level in response to ligand binding/environment. A detail description of the ligand induced conformational changes provides meaningful insights into the mechanism of action of enzymes and thus its function. Results In this study, we have explored the ligand induced conformational changes in H.pylori LuxS and the associated mechanistic features. LuxS, a dimeric protein, produces the precursor (4,5-dihydroxy-2,3-pentanedione for autoinducer-2 production which is a signalling molecule for bacterial quorum sensing. We have performed molecular dynamics simulations on H.pylori LuxS in its various ligand bound forms and analyzed the simulation trajectories using various techniques including the structure network analysis, free energy evaluation and water dynamics at the active site. The results bring out the mechanistic details such as co-operativity and asymmetry between the two subunits, subtle changes in the conformation as a response to the binding of active and inactive forms of ligands and the population distribution of different conformations in equilibrium. These investigations have enabled us to probe the free energy landscape and identify the corresponding conformations in terms of network parameters. In addition, we have also elucidated the variations in the dynamics of water co-ordination to the Zn2+ ion in LuxS and its relation to the rigidity at the active sites. Conclusions In this article, we provide details of a novel method for the identification of conformational changes in the different ligand bound states of the protein, evaluation of ligand-induced free energy changes and the biological relevance of our results in the context of LuxS structure-function. The methodology outlined here is highly generalized to illuminate the linkage between structure and function in
1. Experimental conformational energy maps of proteins and peptides.
Science.gov (United States)
Balaji, Govardhan A; Nagendra, H G; Balaji, Vitukudi N; Rao, Shashidhar N
2017-06-01
We have presented an extensive analysis of the peptide backbone dihedral angles in the PDB structures and computed experimental Ramachandran plots for their distributions seen under a various constraints on X-ray resolution, representativeness at different sequence identity percentages, and hydrogen bonding distances. These experimental distributions have been converted into isoenergy contour plots using the approach employed previously by F. M. Pohl. This has led to the identification of energetically favored minima in the Ramachandran (ϕ, ψ) plots in which global minima are predominantly observed either in the right-handed α-helical or the polyproline II regions. Further, we have identified low energy pathways for transitions between various minima in the (ϕ,ψ) plots. We have compared and presented the experimental plots with published theoretical plots obtained from both molecular mechanics and quantum mechanical approaches. In addition, we have developed and employed a root mean square deviation (RMSD) metric for isoenergy contours in various ranges, as a measure (in kcal.mol(-1) ) to compare any two plots and determine the extent of correlation and similarity between their isoenergy contours. In general, we observe a greater degree of compatibility with experimental plots for energy maps obtained from molecular mechanics methods compared to most quantum mechanical methods. The experimental energy plots we have investigated could be helpful in refining protein structures obtained from X-ray, NMR, and electron microscopy and in refining force field parameters to enable simulations of peptide and protein structures that have higher degree of consistency with experiments. Proteins 2017; 85:979-1001. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
2. Protein Conformational Change Based on a Two-dimensional Generalized Langevin Equation
Institute of Scientific and Technical Information of China (English)
Ying-xi Wang; Shuang-mu Linguang; Nan-rong Zhao; Yi-jing Yan
2011-01-01
A two-dimensional generalized Langevin equation is proposed to describe the protein conformational change,compatible to the electron transfer process governed by atomic packing density model.We assume a fractional Gaussian noise and a white noise through bond and through space coordinates respectively,and introduce the coupling effect coming from both fluctuations and equilibrium variances.The general expressions for autocorrelation functions of distance fluctuation and fluorescence lifetime variation are derived,based on which the exact conformational change dynamics can be evaluated with the aid of numerical Laplace inversion technique.We explicitly elaborate the short time and long time approximations.The relationship between the two-dimensional description and the one-dimensional theory is also discussed.
3. NIR Laser Radiation Induced Conformational Changes and Tunneling Lifetimes of High-Energy Conformers of Amino Acids in Low-Temperature Matrices
Science.gov (United States)
Bazso, Gabor; Najbauer, Eszter E.; Magyarfalvi, Gabor; Tarczay, Gyorgy
2013-06-01
We review our recent results on combined matrix isolation FT-IR and NIR laser irradiation studies on glycine alanine, and cysteine. The OH and the NH stretching overtones of the low-energy conformers of these amino acids deposited in Ar, Kr, Xe, and N_{2} matrices were irradiated. At the expense of the irradiated conformer, other conformers were enriched and new, high-energy, formerly unobserved conformers were formed in the matrices. This enabled the separation and unambiguous assignment of the vibrational transitions of the different conformers. The main conversion paths and their efficiencies are described qualitatively showing that there are significant differences in different matrices. It was shown that the high-energy conformer decays in the matrix by H-atom tunneling. The lifetimes of the high-energy conformers in different matrices were measured. Based on our results we conclude that some theoretically predicted low-energy conformers of amino acids are likely even absent in low-energy matrices due to fast H-atom tunneling. G. Bazso, G. Magyarfalvi, G. Tarczay J. Mol. Struct. 1025 (Light-Induced Processes in Cryogenic Matrices Special Issue) 33-42 (2012). G. Bazso, G. Magyarfalvi, G. Tarczay J. Phys. Chem. A 116 (43) 10539-10547 (2012). G. Bazso, E. E. Najbauer, G. Magyarfalvi, G. Tarczay J. Phys. Chem. A in press, DOI: 10.1021/jp400196b. E. E. Najbauer, G. Bazso, G. Magyarfalvi, G. Tarczay in preparation.
4. Conformal generally covariant quantum field theory. The scalar field and its Wick products
Energy Technology Data Exchange (ETDEWEB)
Pinamonti, N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2008-06-15
In this paper we generalize the construction of generally covariant quantum theories given in [R. Brunetti, K. Fredenhagen, R. Verch, Commun. Math. Phys. 237, 31 (2003)] to encompass the conformal covariant case. After introducing the abstract framework, we discuss the massless conformally coupled Klein Gordon field theory, showing that its quantization corresponds to a functor between two certain categories. At the abstract level, the ordinary fields, could be thought as natural transformations in the sense of category theory. We show that, the Wick monomials without derivatives (Wick powers), can be interpreted as fields in this generalized sense, provided a non trivial choice of the renormalization constants is given. A careful analysis shows that the transformation law of Wick powers is characterized by a weight, and it turns out that the sum of fields with different weights breaks the conformal covariance. At this point there is a difference between the previously given picture due to the presence of a bigger group of covariance. It is furthermore shown that the construction does not depend upon the scale {mu} appearing in the Hadamard parametrix, used to regularize the fields. Finally, we briefly discuss some further examples of more involved fields. (orig.)
5. Solar energy education. Renewable energy activities for general science
Energy Technology Data Exchange (ETDEWEB)
1985-01-01
Renewable energy topics are integrated with the study of general science. The literature is provided in the form of a teaching manual and includes such topics as passive solar homes, siting a home for solar energy, and wind power for the home. Other energy topics are explored through library research activities. (BCS)
6. Characterization of low-energy conformational domains for Met-enkephalin.
Science.gov (United States)
Perez, J J; Villar, H O; Loew, G H
1992-04-01
An extensive exploration of the conformational hypersurface of Met-enkephalin has been carried out, in order to characterize different low-energy conformational domains accessible to this pentapeptide. The search strategy used consisted of two steps. First, systematic nested rotations were performed using the ECEPP potential. Ninety-two low-energy structures were found and minimized using the CHARMm potential. High and low-temperature molecular dynamics trajectories were then computed for the lowest energy structures in an interative fashion until no lower energy conformers could be found. The same search strategy was used in these studies simulating three different environments, a distance-dependent dielectric epsilon = r, and two constant dielectrics epsilon = 10 and epsilon = 80. The lowest energy structure found in a distance-dependent dielectric is a Gly-Gly beta-II'-type turn. All other structures found for epsilon = r within 10 kcal/mol of this lowest energy structure are also bends. In the more polar environments, the density of conformational states is significantly larger compared to the apolar media. Moreover, fewer hydrogen bonds are formed in the more polar environments, which increases the flexibility of the peptide and results in less structured conformers. Comparisons are made with previous calculations and experimental results.
7. Assessing Energy-Dependent Protein Conformational Changes in the TonB System.
Science.gov (United States)
Larsen, Ray A
2017-01-01
Changes in conformation can alter a protein's vulnerability to proteolysis. Thus, in vivo differential proteinase sensitivity provides a means for identifying conformational changes that mark discrete states in the activity cycle of a protein. The ability to detect a specific conformational state allows for experiments to address specific protein-protein interactions and other physiological components that potentially contribute to the function of the protein. This chapter presents the application of this technique to the TonB-dependent energy transduction system of Gram-negative bacteria, a strategy that has refined our understanding of how the TonB protein is coupled to the ion electrochemical gradient of the cytoplasmic membrane.
8. Conformational Control of Energy Transfer: A Mechanism for Biocompatible Nanocrystal-Based Sensors
OpenAIRE
Kay, Euan R; Lee, Jungmin; Nocera, Daniel; Bawendi, Moungi G
2012-01-01
Fold-up fluorophore: A new paradigm for designing self-referencing fluorescent nanosensors is demonstrated by interfacing a pH-triggered molecular conformational switch with quantum dots. Analytedependent, large-amplitude conformational motion controls the distance between the nanocrystal energy donor and an organic FRET acceptor. The result is a fluorescence signal capable of reporting pH values from individual endosomes in living cells.
9. Scalar vacuum structure in general relativity and alternative theories. Conformal continuations
CERN Document Server
Bronnikov, K A
2001-01-01
We discuss the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field $\\phi$ in general relativity (GR), scalar-tensor theories (STT) and high-order gravity ($L=f(R)$) in various dimensions. In GR, for fields with arbitrary potentials $V(\\phi)$, not necessarily positive-definite, it is shown that the list of all possible types of space-time causal structure in the models under consideration is the same as the one for $\\phi = const$. In particular, there are no regular black holes with any asymptotics. These features are extended to STT and $f(R)$ theories, connected with GR by conformal mappings, unless there is a conformal continuation, i.e., a case when a singularity in a solution of GR maps to a regular surface in an alternative theory, and the solution is continued through such a surface. This effect is exemplified by exact solutions in GR with a massless conformal scalar field, considered as a special STT. Necessary conditions for the existence of a conf...
10. The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
Science.gov (United States)
Gliozzi, Ferdinando; Guerrieri, Andrea L.; Petkou, Anastasios C.; Wen, Congkao
2017-04-01
We describe in detail the method used in our previous work arXiv:1611.10344 https://arxiv.org/abs/1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the ɛ-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O( N)-invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.
11. Octonionic M-theory and /D=11 generalized conformal and superconformal algebras
Science.gov (United States)
Lukierski, Jerzy; Toppan, Francesco
2003-08-01
Following [Phys. Lett. B 539 (2002) 266] we further apply the octonionic structure to supersymmetric D=11 M-theory. We consider the octonionic 2n+1×2n+1 Dirac matrices describing the sequence of Clifford algebras with signatures (9+n,n) (n=0,1,2,…) and derive the identities following from the octonionic multiplication table. The case n=1 (4×4 octonion-valued matrices) is used for the description of the D=11 octonionic M-superalgebra with 52 real bosonic charges; the n=2 case (8×8 octonion-valued matrices) for the D=11 conformal M-algebra with 232 real bosonic charges. The octonionic structure is described explicitly for n=1 by the relations between the 528 Abelian O(10,1) tensorial charges Zμ, Zμν, Zμ…μ5 of the M-superalgebra. For n=2 we obtain 2080 real non-Abelian bosonic tensorial charges Zμν, Zμ1μ2μ3, Zμ1…μ6 which, suitably constrained describe the generalized D=11 octonionic conformal algebra. Further, we consider the supersymmetric extension of this octonionic conformal algebra which can be described as D=11 octonionic superconformal algebra with a total number of 64 real fermionic and 239 real bosonic generators.
12. Generalized dark energy interactions with multiple fluids
CERN Document Server
van de Bruck, Carsten; Mimoso, José P; Nunes, Nelson J
2016-01-01
In the search for an explanation for the current acceleration of the Universe, scalar fields are the most simple and useful tools to build models of dark energy. This field, however, must in principle couple with the rest of the world and not necessarily in the same way to different particles or fluids. We provide the most complete dynamical system analysis to date, consisting of a canonical scalar field conformally and disformally coupled to both dust and radiation. We perform a detailed study of the existence and stability conditions of the systems and comment on constraints imposed on the disformal coupling from Big-Bang Nucleosynthesis and given current limits on the variation of the fine-structure constant.
13. Generalized dark energy interactions with multiple fluids
Science.gov (United States)
van de Bruck, Carsten; Mifsud, Jurgen; Mimoso, José P.; Nunes, Nelson J.
2016-11-01
In the search for an explanation for the current acceleration of the Universe, scalar fields are the most simple and useful tools to build models of dark energy. This field, however, must in principle couple with the rest of the world and not necessarily in the same way to different particles or fluids. We provide the most complete dynamical system analysis to date, consisting of a canonical scalar field conformally and disformally coupled to both dust and radiation. We perform a detailed study of the existence and stability conditions of the systems and comment on constraints imposed on the disformal coupling from Big-Bang Nucleosynthesis and given current limits on the variation of the fine-structure constant.
14. Anisotropic Generalized Ghost Pilgrim Dark Energy Model in General Relativity
Science.gov (United States)
Santhi, M. Vijaya; Rao, V. U. M.; Aditya, Y.
2017-02-01
A spatially homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type- I Universe filled with matter and generalized ghost pilgrim dark energy (GGPDE) has been studied in general theory of relativity. To obtain determinate solution of the field equations we have used scalar expansion proportional to the shear scalar which leads to a relation between the metric potentials. Some well-known cosmological parameters (equation of state (EoS) parameter ( ω Λ), deceleration parameter ( q) and squared speed of sound {vs2}) and planes (ω _{Λ }-dot {ω }_{Λ } and statefinder) are constructed for obtained model. The discussion and significance of these parameters is totally done through pilgrim dark energy parameter ( β) and cosmic time ( t).
15. Simple implementation of general dark energy models
Energy Technology Data Exchange (ETDEWEB)
Bloomfield, Jolyon K. [MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Ave #37241, Cambridge, MA, 02139 (United States); Pearson, Jonathan A., E-mail: [email protected], E-mail: [email protected] [Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE (United Kingdom)
2014-03-01
We present a formalism for the numerical implementation of general theories of dark energy, combining the computational simplicity of the equation of state for perturbations approach with the generality of the effective field theory approach. An effective fluid description is employed, based on a general action describing single-scalar field models. The formalism is developed from first principles, and constructed keeping the goal of a simple implementation into CAMB in mind. Benefits of this approach include its straightforward implementation, the generality of the underlying theory, the fact that the evolved variables are physical quantities, and that model-independent phenomenological descriptions may be straightforwardly investigated. We hope this formulation will provide a powerful tool for the comparison of theoretical models of dark energy with observational data.
16. Potential Energy Surface-Based Automatic Deduction of Conformational Transition Networks and Its Application on Quantum Mechanical Landscapes of d-Glucose Conformers.
Science.gov (United States)
Satoh, Hiroko; Oda, Tomohiro; Nakakoji, Kumiyo; Uno, Takeaki; Tanaka, Hiroaki; Iwata, Satoru; Ohno, Koichi
2016-11-08
This paper describes our approach that is built upon the potential energy surface (PES)-based conformational analysis. This approach automatically deduces a conformational transition network, called a conformational reaction route map (r-map), by using the Scaled Hypersphere Search of the Anharmonic Downward Distortion Following method (SHS-ADDF). The PES-based conformational search has been achieved by using large ADDF, which makes it possible to trace only low transition state (TS) barriers while restraining bond lengths and structures with high free energy. It automatically performs sampling the minima and TS structures by simply taking into account the mathematical feature of PES without requiring any a priori specification of variable internal coordinates. An obtained r-map is composed of equilibrium (EQ) conformers connected by reaction routes via TS conformers, where all of the reaction routes are already confirmed during the process of the deduction using the intrinsic reaction coordinate (IRC) method. The postcalculation analysis of the deduced r-map is interactively carried out using the RMapViewer software we have developed. This paper presents computational details of the PES-based conformational analysis and its application to d-glucose. The calculations have been performed for an isolated glucose molecule in the gas phase at the RHF/6-31G level. The obtained conformational r-map for α-d-glucose is composed of 201 EQ and 435 TS conformers and that for β-d-glucose is composed of 202 EQ and 371 TS conformers. For the postcalculation analysis of the conformational r-maps by using the RMapViewer software program we have found multiple minimum energy paths (MEPs) between global minima of (1)C4 and (4)C1 chair conformations. The analysis using RMapViewer allows us to confirm the thermodynamic and kinetic predominance of (4)C1 conformations; that is, the potential energy of the global minimum of (4)C1 is lower than that of (1)C4 (thermodynamic predominance
17. The first experimental observation of the higher-energy trans conformer of trifluoroacetic acid
Science.gov (United States)
Apóstolo, R. F. G.; Bazsó, Gábor; Bento, R. R. F.; Tarczay, G.; Fausto, R.
2016-12-01
We report here the first experimental observation of the higher-energy conformer of trifluoroacetic acid (trans-TFA). The new conformer was generated by selective narrowband near-infrared vibrational excitation of the lower-energy cis-TFA conformer isolated in cryogenic matrices (Ar, Kr, N2) and shown to spontaneously decay to this latter form in the various matrix media, by tunneling. The decay rates in the different matrices were measured and compared with those of the trans conformers of other carboxylic acids in similar experimental conditions. The experimental studies received support from quantum chemistry calculations undertaken at various levels of approximation, which allowed a detailed characterization of the relevant regions of the potential energy surface of the molecule and the detailed assignment of the infrared spectra of the two conformers in the various matrices. Noteworthly, in contrast to cis-TFA that has its trifluoromethyl group eclipsed with the Cdbnd O bond of the carboxylic moiety, trans-TFA has the trifluoromethyl group eclipsed with the Csbnd O bond. This unusual structure of trans-TFA results from the fact that the relative orientation of the CF3 and COOH groups in this geometry facilitates the establishment of an intramolecular hydrogen-bond-like interaction between the OH group and the closely located in-plane fluorine atom of the CF3 moiety.
18. Conformity to the surviving sepsis campaign international guidelines among physicians in a general intensive care unit in Nairobi.
Science.gov (United States)
Mung'ayi, V; Karuga, R
2010-08-01
There are emerging therapies for managing septic critically-ill patients. There is little data from the developing world on their usage. To determine the conformity rate for resuscitation and management bundles for septic patients amongst physicians in a general intensive care unit. Cross sectional observational study. The general intensive care unit, Aga Khan University Hospital,Nairobi. Admitting physicians from all specialties in the general intensive care unit. The physicians had high conformity rates of 92% and 96% for the fluid resuscitation and use of va so pressors respectively for the initial resuscitation bundle. They had moderate conformity rates for blood cultures prior to administering antibiotics (57%) and administration of antibiotics within first hour of recognition of septic shock (54%). There was high conformity rate to the glucose control policy (81%), use of protective lung strategy in acute lung injury/Acute respiratory distress syndrome, venous thromboembolism prophylaxis (100%) and stress ulcer prophylaxis (100%) in the management bundle. Conformity was moderate for use of sedation, analgesia and muscle relaxant policy (69%), continuous renal replacement therapies (54%) and low for steroid policy (35%), administration ofdrotrecogin alfa (0%) and selective digestive decontamination (15%). There is varying conformity to the international sepsis guidelines among physicians caring for patients in our general ICU. Since increased conformity would improve survival and reduce morbidity, there is need for sustained education and guideline based performance improvement.
19. 40 CFR 1039.201 - What are the general requirements for obtaining a certificate of conformity?
Science.gov (United States)
2010-07-01
... obtaining a certificate of conformity? 1039.201 Section 1039.201 Protection of Environment ENVIRONMENTAL... obtaining a certificate of conformity? (a) You must send us a separate application for a certificate of conformity for each engine family. A certificate of conformity is valid from the indicated effective...
20. 40 CFR 1042.201 - General requirements for obtaining a certificate of conformity.
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2010-07-01
... certificate of conformity. 1042.201 Section 1042.201 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY... of conformity. (a) You must send us a separate application for a certificate of conformity for each engine family. A certificate of conformity is valid starting with the indicated effective date, but it...
1. 40 CFR 1048.201 - What are the general requirements for obtaining a certificate of conformity?
Science.gov (United States)
2010-07-01
... obtaining a certificate of conformity? 1048.201 Section 1048.201 Protection of Environment ENVIRONMENTAL... certificate of conformity? (a) You must send us a separate application for a certificate of conformity for each engine family. A certificate of conformity is valid starting with the indicated effective...
2. 40 CFR 1045.201 - What are the general requirements for obtaining a certificate of conformity?
Science.gov (United States)
2010-07-01
... obtaining a certificate of conformity? 1045.201 Section 1045.201 Protection of Environment ENVIRONMENTAL... obtaining a certificate of conformity? Engine manufacturers must certify their engines with respect to the... conformity: (a) You must send us a separate application for a certificate of conformity for each...
3. Conformational search by potential energy annealing: Algorithm and application to cyclosporin A
Science.gov (United States)
van Schaik, René C.; van Gunsteren, Wilfred F.; Berendsen, Herman J. C.
1992-04-01
A major problem in modelling (biological) macromolecules is the search for low-energy conformations. The complexity of a conformational search problem increases exponentially with the number of degrees of freedom which means that a systematic search can only be performed for very small structures. Here we introduce a new method (PEACS) which has a far better performance than conventional search methods. To show the advantages of PEACS we applied it to the refinement of Cyclosporin A and compared the results with normal molecular dynamics (MD) refinement. The structures obtained with PEACS were lower in energy and agreed with the NMR parameters much better than those obtained with MD. From the results it is further clear that PEACS samples a much larger part of the available conformational space than MD does.
4. A New Conformal Theory of Semi-Classical Quantum General Relativity
Directory of Open Access Journals (Sweden)
Suhendro I.
2007-10-01
Full Text Available We consider a new four-dimensional formulation of semi-classical quantum general relativity in which the classical space-time manifold, whose intrinsic geometric properties give rise to the effects of gravitation, is allowed to evolve microscopically by means of a conformal function which is assumed to depend on some quantum mechanical wave function. As a result, the theory presented here produces a unified field theory of gravitation and (microscopic electromagnetism in a somewhat simple, effective manner. In the process, it is seen that electromagnetism is actually an emergent quantum field originating in some kind of stochastic smooth extension (evolution of the gravitational field in the general theory of relativity.
5. Dynamic energy landscapes of riboswitches help interpret conformational rearrangements and function.
Directory of Open Access Journals (Sweden)
Giulio Quarta
Full Text Available Riboswitches are RNAs that modulate gene expression by ligand-induced conformational changes. However, the way in which sequence dictates alternative folding pathways of gene regulation remains unclear. In this study, we compute energy landscapes, which describe the accessible secondary structures for a range of sequence lengths, to analyze the transcriptional process as a given sequence elongates to full length. In line with experimental evidence, we find that most riboswitch landscapes can be characterized by three broad classes as a function of sequence length in terms of the distribution and barrier type of the conformational clusters: low-barrier landscape with an ensemble of different conformations in equilibrium before encountering a substrate; barrier-free landscape in which a direct, dominant "downhill" pathway to the minimum free energy structure is apparent; and a barrier-dominated landscape with two isolated conformational states, each associated with a different biological function. Sharing concepts with the "new view" of protein folding energy landscapes, we term the three sequence ranges above as the sensing, downhill folding, and functional windows, respectively. We find that these energy landscape patterns are conserved in various riboswitch classes, though the order of the windows may vary. In fact, the order of the three windows suggests either kinetic or thermodynamic control of ligand binding. These findings help understand riboswitch structure/function relationships and open new avenues to riboswitch design.
6. Conformational energy range of ligands in protein crystal structures: The difficult quest for accurate understanding.
Science.gov (United States)
Peach, Megan L; Cachau, Raul E; Nicklaus, Marc C
2017-02-24
In this review, we address a fundamental question: What is the range of conformational energies seen in ligands in protein-ligand crystal structures? This value is important biophysically, for better understanding the protein-ligand binding process; and practically, for providing a parameter to be used in many computational drug design methods such as docking and pharmacophore searches. We synthesize a selection of previously reported conflicting results from computational studies of this issue and conclude that high ligand conformational energies really are present in some crystal structures. The main source of disagreement between different analyses appears to be due to divergent treatments of electrostatics and solvation. At the same time, however, for many ligands, a high conformational energy is in error, due to either crystal structure inaccuracies or incorrect determination of the reference state. Aside from simple chemistry mistakes, we argue that crystal structure error may mainly be because of the heuristic weighting of ligand stereochemical restraints relative to the fit of the structure to the electron density. This problem cannot be fixed with improvements to electron density fitting or with simple ligand geometry checks, though better metrics are needed for evaluating ligand and binding site chemistry in addition to geometry during structure refinement. The ultimate solution for accurately determining ligand conformational energies lies in ultrahigh-resolution crystal structures that can be refined without restraints.
7. Calculation of relative free energies for ligand-protein binding, solvation, and conformational transitions using the GROMOS software.
Science.gov (United States)
Riniker, Sereina; Christ, Clara D; Hansen, Halvor S; Hünenberger, Philippe H; Oostenbrink, Chris; Steiner, Denise; van Gunsteren, Wilfred F
2011-11-24
The calculation of the relative free energies of ligand-protein binding, of solvation for different compounds, and of different conformational states of a polypeptide is of considerable interest in the design or selection of potential enzyme inhibitors. Since such processes in aqueous solution generally comprise energetic and entropic contributions from many molecular configurations, adequate sampling of the relevant parts of configurational space is required and can be achieved through molecular dynamics simulations. Various techniques to obtain converged ensemble averages and their implementation in the GROMOS software for biomolecular simulation are discussed, and examples of their application to biomolecules in aqueous solution are given.
8. Four-Node Generalized Conforming Membrane Elements with Drilling DOFs Using Quadrilateral Area Coordinate Methods
Directory of Open Access Journals (Sweden)
Xiao-Ming Chen
2015-01-01
Full Text Available Two 4-node generalized conforming quadrilateral membrane elements with drilling DOF, named QAC4θ and QAC4θM, were successfully developed. Two kinds of quadrilateral area coordinates are used together in the assumed displacement fields of the new elements, so that the related formulations are quite straightforward and will keep the order of the Cartesian coordinates unchangeable while the mesh is distorted. The drilling DOF is defined as the additional rigid rotation at the element nodes to avoid improper constraint. Both elements can pass the strict patch test and exhibit better performance than other similar models. In particular, they are both free of trapezoidal locking in MacNeal’s beam test and insensitive to various mesh distortions.
9. A general approach to visualize protein binding and DNA conformation without protein labelling.
Science.gov (United States)
Song, Dan; Graham, Thomas G W; Loparo, Joseph J
2016-01-01
Single-molecule manipulation methods, such as magnetic tweezers and flow stretching, generally use the measurement of changes in DNA extension as a proxy for examining interactions between a DNA-binding protein and its substrate. These approaches are unable to directly measure protein-DNA association without fluorescently labelling the protein, which can be challenging. Here we address this limitation by developing a new approach that visualizes unlabelled protein binding on DNA with changes in DNA conformation in a relatively high-throughput manner. Protein binding to DNA molecules sparsely labelled with Cy3 results in an increase in fluorescence intensity due to protein-induced fluorescence enhancement (PIFE), whereas DNA length is monitored under flow of buffer through a microfluidic flow cell. Given that our assay uses unlabelled protein, it is not limited to the low protein concentrations normally required for single-molecule fluorescence imaging and should be broadly applicable to studying protein-DNA interactions.
10. 77 FR 59100 - Approval and Promulgation of Implementation Plans; Alabama: General and Transportation Conformity...
Science.gov (United States)
2012-09-26
... Transportation Conformity & New Source Review Prevention of Significant Deterioration for Fine Particulate Matter... transportation conformity regulations. EPA is approving portions of Alabama's May 2, 2011, SIP revision because... transportation conformity regulations into the SIP. Alabama's May 2, 2011, SIP revision includes changes to...
11. Parallel cascade selection molecular dynamics for efficient conformational sampling and free energy calculation of proteins
Science.gov (United States)
Kitao, Akio; Harada, Ryuhei; Nishihara, Yasutaka; Tran, Duy Phuoc
2016-12-01
Parallel Cascade Selection Molecular Dynamics (PaCS-MD) was proposed as an efficient conformational sampling method to investigate conformational transition pathway of proteins. In PaCS-MD, cycles of (i) selection of initial structures for multiple independent MD simulations and (ii) conformational sampling by independent MD simulations are repeated until the convergence of the sampling. The selection is conducted so that protein conformation gradually approaches a target. The selection of snapshots is a key to enhance conformational changes by increasing the probability of rare event occurrence. Since the procedure of PaCS-MD is simple, no modification of MD programs is required; the selections of initial structures and the restart of the next cycle in the MD simulations can be handled with relatively simple scripts with straightforward implementation. Trajectories generated by PaCS-MD were further analyzed by the Markov state model (MSM), which enables calculation of free energy landscape. The combination of PaCS-MD and MSM is reported in this work.
12. Mapping transiently formed and sparsely populated conformations on a complex energy landscape
Science.gov (United States)
Wang, Yong; Papaleo, Elena; Lindorff-Larsen, Kresten
2016-01-01
Determining the structures, kinetics, thermodynamics and mechanisms that underlie conformational exchange processes in proteins remains extremely difficult. Only in favourable cases is it possible to provide atomic-level descriptions of sparsely populated and transiently formed alternative conformations. Here we benchmark the ability of enhanced-sampling molecular dynamics simulations to determine the free energy landscape of the L99A cavity mutant of T4 lysozyme. We find that the simulations capture key properties previously measured by NMR relaxation dispersion methods including the structure of a minor conformation, the kinetics and thermodynamics of conformational exchange, and the effect of mutations. We discover a new tunnel that involves the transient exposure towards the solvent of an internal cavity, and show it to be relevant for ligand escape. Together, our results provide a comprehensive view of the structural landscape of a protein, and point forward to studies of conformational exchange in systems that are less characterized experimentally. DOI: http://dx.doi.org/10.7554/eLife.17505.001 PMID:27552057
13. Toward accurate prediction of pKa values for internal protein residues: the importance of conformational relaxation and desolvation energy.
Science.gov (United States)
Wallace, Jason A; Wang, Yuhang; Shi, Chuanyin; Pastoor, Kevin J; Nguyen, Bao-Linh; Xia, Kai; Shen, Jana K
2011-12-01
Proton uptake or release controls many important biological processes, such as energy transduction, virus replication, and catalysis. Accurate pK(a) prediction informs about proton pathways, thereby revealing detailed acid-base mechanisms. Physics-based methods in the framework of molecular dynamics simulations not only offer pK(a) predictions but also inform about the physical origins of pK(a) shifts and provide details of ionization-induced conformational relaxation and large-scale transitions. One such method is the recently developed continuous constant pH molecular dynamics (CPHMD) method, which has been shown to be an accurate and robust pK(a) prediction tool for naturally occurring titratable residues. To further examine the accuracy and limitations of CPHMD, we blindly predicted the pK(a) values for 87 titratable residues introduced in various hydrophobic regions of staphylococcal nuclease and variants. The predictions gave a root-mean-square deviation of 1.69 pK units from experiment, and there were only two pK(a)'s with errors greater than 3.5 pK units. Analysis of the conformational fluctuation of titrating side-chains in the context of the errors of calculated pK(a) values indicate that explicit treatment of conformational flexibility and the associated dielectric relaxation gives CPHMD a distinct advantage. Analysis of the sources of errors suggests that more accurate pK(a) predictions can be obtained for the most deeply buried residues by improving the accuracy in calculating desolvation energies. Furthermore, it is found that the generalized Born implicit-solvent model underlying the current CPHMD implementation slightly distorts the local conformational environment such that the inclusion of an explicit-solvent representation may offer improvement of accuracy.
14. Teaching Energy to a General Audience
Science.gov (United States)
2010-02-01
A new, interdisciplinary course entitled Energy!'' has been developed by faculty in the physics and chemistry departments to meet the university's science and technology general education requirement. This course now enrolls over 400 students each semester in a single lecture where faculty from both departments co-teach throughout the term. Topics include the fundamentals of energy, fossil fuels, global climate change, nuclear energy, and renewable energy sources. The students represent an impressive range of majors (science, engineering, business, humanities, etc.) and comprise freshmen to seniors. To effectively teach this diverse audience and increase classroom engagement, in-class clickers'' are used with guided questions to teach concepts, which are then explicitly reinforced with online LON-CAPAfootnotetextFree open-source distributed learning content management and assessment system (www.lon-capa.org) homework. This online system enables immediate feedback in a structured manner, where students can practice randomized versions of problems for homework, quizzes, and exams. The course is already in high demand after only two semesters, in part because it is particularly relevant to students given the challenging energy and climate issues facing the nation and world. )
15. General solar energy information user study
Energy Technology Data Exchange (ETDEWEB)
Belew, W.W.; Wood, B.L.; Marle, T.L.; Reinhardt, C.L.
1981-03-01
This report describes the results of a series of telephone interviews with groups of users of information on general solar energy. These results, part of a larger study on many different solar technologies, identify types of information each group needed and the best ways to get information to each group. The report is 1 of 10 discussing study results. The overall study provides baseline data about information needs in the solar community. An earlier study identified the information user groups in the solar community and the priority (to accelerate solar energy commercialization) of getting information to each group. In the current study only high-priority groups were examined. Results from 13 groups of respondents are analyzed in this report: Loan Officers, Real Estate Appraisers, Tax Assessors, Insurers, Lawyers, Utility Representatives, Public Interest Group Representatives, Information and Agricultural Representatives, Public Interest Group Representatives, Information and Agricultural Specialists at State Cooperative Extension Service Offices, and State Energy Office Representatives. The data will be used as input to the determination of information products and services the Solar Energy Research Institute, the Solar Energy Information Data Bank Network, and the entire information outreach community should be preparing and disseminating.
16. Elucidating molecular motion through structural and dynamic filters of energy-minimized conformer ensembles.
Science.gov (United States)
Emani, Prashant S; Bardaro, Michael F; Huang, Wei; Aragon, Sergio; Varani, Gabriele; Drobny, Gary P
2014-02-20
Complex RNA structures are constructed from helical segments connected by flexible loops that move spontaneously and in response to binding of small molecule ligands and proteins. Understanding the conformational variability of RNA requires the characterization of the coupled time evolution of interconnected flexible domains. To elucidate the collective molecular motions and explore the conformational landscape of the HIV-1 TAR RNA, we describe a new methodology that utilizes energy-minimized structures generated by the program "Fragment Assembly of RNA with Full-Atom Refinement (FARFAR)". We apply structural filters in the form of experimental residual dipolar couplings (RDCs) to select a subset of discrete energy-minimized conformers and carry out principal component analyses (PCA) to corroborate the choice of the filtered subset. We use this subset of structures to calculate solution T1 and T(1ρ) relaxation times for (13)C spins in multiple residues in different domains of the molecule using two simulation protocols that we previously published. We match the experimental T1 times to within 2% and the T(1ρ) times to within less than 10% for helical residues. These results introduce a protocol to construct viable dynamic trajectories for RNA molecules that accord well with experimental NMR data and support the notion that the motions of the helical portions of this small RNA can be described by a relatively small number of discrete conformations exchanging over time scales longer than 1 μs.
17. The effect of tensile stress on the conformational free energy landscape of disulfide bonds.
Directory of Open Access Journals (Sweden)
Full Text Available Disulfide bridges are no longer considered to merely stabilize protein structure, but are increasingly recognized to play a functional role in many regulatory biomolecular processes. Recent studies have uncovered that the redox activity of native disulfides depends on their C-C-S-S dihedrals, χ2 and χ'2. Moreover, the interplay of chemical reactivity and mechanical stress of disulfide switches has been recently elucidated using force-clamp spectroscopy and computer simulation. The χ2 and χ'2 angles have been found to change from conformations that are open to nucleophilic attack to sterically hindered, so-called closed states upon exerting tensile stress. In view of the growing evidence of the importance of C-C-S-S dihedrals in tuning the reactivity of disulfides, here we present a systematic study of the conformational diversity of disulfides as a function of tensile stress. With the help of force-clamp metadynamics simulations, we show that tensile stress brings about a large stabilization of the closed conformers, thereby giving rise to drastic changes in the conformational free energy landscape of disulfides. Statistical analysis shows that native TDi, DO and interchain Ig protein disulfides prefer open conformations, whereas the intrachain disulfide bridges in Ig proteins favor closed conformations. Correlating mechanical stress with the distance between the two a-carbons of the disulfide moiety reveals that the strain of intrachain Ig protein disulfides corresponds to a mechanical activation of about 100 pN. Such mechanical activation leads to a severalfold increase of the rate of the elementary redox S(N2 reaction step. All these findings constitute a step forward towards achieving a full understanding of functional disulfides.
18. FEARCF a multidimensional free energy method for investigating conformational landscapes and chemical reaction mechanisms
Institute of Scientific and Technical Information of China (English)
NAIDOO Kevin J.
2012-01-01
The development and implementation of a computational method able to produce free energies in multiple dimensions,descriptively named the free energies from adaptive reaction coordinate forces (FEARCF) method is described in this paper.While the method can be used to calculate free energies of association,conformation and reactivity here it is shown in the context of chemical reaction landscapes.A reaction free energy surface for the Claisen rearrangement of chorismate to prephenate is used as an illustration of the method's efficient convergence.FEARCF simulations are shown to achieve fiat histograms for complex multidimensional free energy volumes.The sampling efficiency by which it produces multidimensional free energies is demonstrated on the complex puckering of a pyranose ring,that is described by a three dimensional W(θ1,θ2,θ3) potential of mean force.
19. Millimeter and submillimeter wave spectroscopy of higher energy conformers of 1,2-propanediol
Science.gov (United States)
Zakharenko, O.; Bossa, J.-B.; Lewen, F.; Schlemmer, S.; Müller, H. S. P.
2017-03-01
We have performed a study of the millimeter/submillimeter wave spectrum of four higher energy conformers of 1,2-propanediol. The present analysis of rotational transitions carried out in the frequency range 38-400 GHz represents a significant extension of previous microwave work. The new data were combined with previously-measured microwave transitions and fitted using a Watson's S-reduced Hamiltonian. The final fits were within experimental accuracy, and included spectroscopic parameters up to sixth order of angular momentum, for the ground states of the four higher energy conformers following previously studied ones: g‧Ga, gG‧g‧, aGg‧ and g‧Gg. The present analysis provides reliable frequency predictions for astrophysical detection of 1,2-propanediol by radio telescope arrays at millimeter wavelengths.
20. Transportation Conformity
Science.gov (United States)
This section provides information on: current laws, regulations and guidance, policy and technical guidance, project-level conformity, general information, contacts and training, adequacy review of SIP submissions
1. Energy flow in the cryptophyte PE545 antenna is directed by bilin pigment conformation.
Science.gov (United States)
Curutchet, Carles; Novoderezhkin, Vladimir I; Kongsted, Jacob; Muñoz-Losa, Aurora; van Grondelle, Rienk; Scholes, Gregory D; Mennucci, Benedetta
2013-04-25
Structure-based calculations are combined with quantitative modeling of spectra and energy transfer dynamics to detemine the energy transfer scheme of the PE545 principal light-harvesting antenna of the cryptomonad Rhodomonas CS24. We use a recently developed quantum-mechanics/molecular mechanics (QM/MM) method that allows us to account for pigment-protein interactions at atomic detail in site energies, transition dipole moments, and electronic couplings. In addition, conformational flexibility of the pigment-protein complex is accounted for through molecular dynamics (MD) simulations. We find that conformational disorder largely smoothes the large energetic differences predicted from the crystal structure between the pseudosymmetric pairs PEB50/61C-PEB50/61D and PEB82C-PEB82D. Moreover, we find that, in contrast to chlorophyll-based photosynthetic complexes, pigment composition and conformation play a major role in defining the energy ladder in the PE545 complex, rather than specific pigment-protein interactions. This is explained by the remarkable conformational flexibility of the eight bilin pigments in PE545, characterized by a quasi-linear arrangement of four pyrrole units. The MD-QM/MM site energies allow us to reproduce the main features of the spectra, and minor adjustments of the energies of the three red-most pigments DBV19A, DBV19B, and PEB82D allow us to model the spectra of PE545 with a similar quality compared to our original model (model E from Novoderezhkin et al. Biophys. J.2010, 99, 344), which was extracted from the spectral and kinetic fit. Moreover, the fit of the transient absorption kinetics is even better in the new structure-based model. The largest difference between our previous and present results is that the MD-QM/MM calculations predict a much smaller gap between the PEB50/61C and PEB50/61D sites, in better accord with chemical intuition. We conclude that the current adjusted MD-QM/MM energies are more reliable in order to explore the
2. The generalized Erlangen program and setting a geometry for four- dimensional conformal fields
Energy Technology Data Exchange (ETDEWEB)
Neeman, Y. [Tel Aviv Univ. (Israel). Sackler Faculty of Exact Sciences]|[Texas Univ., Austin, TX (United States). Center for Particle Physics; Hehl, F.W.; Mielke, E.W. [Koeln Univ. (Germany). Inst. fuer Theoretische Physik
1993-10-22
This is the text of a talk at the International Symposium on Mathematical Physics towards the XXI Century held in March 1993 at Beersheva, Israel. In the first part we attempt to summarize XXth Century Physics, in the light of Kelvins 1900 speech Dark Clouds over XIXth Century Physics. Contrary to what is usually said, Kelvin predicted that the clouds (relativity and quantum mechanics) would revolutionize physics and that one hundred years might be needed to harmonize them with classical physics. Quantum Gravity can be considered as a leftover from Kelvins program -- so are the problems with the interpretation of quantum mechanics. At the end of the XXth Century, the Standard Model is the new panoramic synthesis, drawn in gauge-geometric lines -- realizing the Erlangen program beyond F. Kleins expectations. The hierarchy problem and the smallness of the cosmological constant are our clouds, generations and the Higgs sector are to us what radioactivity was in 1900. In the second part we describe Metric-Affine spacetimes. We construct the Noether machinery and provide expressions for the conserved energy and hypermomentum. Superimposing conformal invariance over the affine structure induces the Virasoro-like infinite constraining algebra of diffeomorphisms, applied with constant parameters and opening the possibility of a 4DCFT, similar to 2DCFT.
3. Elucidating Hyperconjugation from Electronegativity to Predict Drug Conformational Energy in a High Throughput Manner.
Science.gov (United States)
Liu, Zhaomin; Pottel, Joshua; Shahamat, Moeed; Tomberg, Anna; Labute, Paul; Moitessier, Nicolas
2016-04-25
Computational chemists use structure-based drug design and molecular dynamics of drug/protein complexes which require an accurate description of the conformational space of drugs. Organic chemists use qualitative chemical principles such as the effect of electronegativity on hyperconjugation, the impact of steric clashes on stereochemical outcome of reactions, and the consequence of resonance on the shape of molecules to rationalize experimental observations. While computational chemists speak about electron densities and molecular orbitals, organic chemists speak about partial charges and localized molecular orbitals. Attempts to reconcile these two parallel approaches such as programs for natural bond orbitals and intrinsic atomic orbitals computing Lewis structures-like orbitals and reaction mechanism have appeared. In the past, we have shown that encoding and quantifying chemistry knowledge and qualitative principles can lead to predictive methods. In the same vein, we thought to understand the conformational behaviors of molecules and to encode this knowledge back into a molecular mechanics tool computing conformational potential energy and to develop an alternative to atom types and training of force fields on large sets of molecules. Herein, we describe a conceptually new approach to model torsion energies based on fundamental chemistry principles. To demonstrate our approach, torsional energy parameters were derived on-the-fly from atomic properties. When the torsional energy terms implemented in GAFF, Parm@Frosst, and MMFF94 were substituted by our method, the accuracy of these force fields to reproduce MP2-derived torsional energy profiles and their transferability to a variety of functional groups and drug fragments were overall improved. In addition, our method did not rely on atom types and consequently did not suffer from poor automated atom type assignments.
4. A Low Energy Consumption DOA Estimation Approach for Conformal Array in Ultra-Wideband
Directory of Open Access Journals (Sweden)
Liangtian Wan
2013-12-01
Full Text Available Most direction-of-arrival (DOA estimation approaches for conformal array suffer from high computational complexity, which cause high energy loss for the direction finding system. Thus, a low energy consumption DOA estimation algorithm for conformal array antenna is proposed in this paper. The arbitrary baseline direction finding algorithm is extended to estimate DOA for a conformal array in ultra-wideband. The rotation comparison method is adopted to solve the ambiguity of direction finding. The virtual baseline approach is used to construct the virtual elements. Theoretically, the virtual elements can be extended in the space flexibility. Four elements (both actual and virtual elements can be used to obtain a group of solutions. The space angle estimation can be obtained by using sub-array divided technique and matrix inversion method. The stability of the proposed algorithm can be guaranteed by averaging the angles obtained by different sub-arrays. Finally, the simulation results verify the effectiveness of the proposed method with high DOA estimation accuracy and relatively low computational complexity.
5. Conformational Explosion: Understanding the Complexity of the Para-Dialkylbenzene Potential Energy Surfaces
Science.gov (United States)
Mishra, Piyush; Hewett, Daniel M.; Zwier, Timothy S.
2017-06-01
This talk focuses on the single-conformation spectroscopy of small-chain para-dialkylbenzenes. This work builds on previous studies from our group on long-chain n-alkylbenzenes that identified the first folded structure in octylbenzene. The dialkylbenzenes are representative of a class of molecules that are common components of coal and aviation fuel and are known to be present in vehicle exhaust. We bring the molecules para-diethylbenzene, para-dipropylbenzene and para-dibutylbenzene into the gas phase and cool the molecules in a supersonic expansion. The jet-cooled molecules are then interrogated using laser-induced fluorescence excitation, fluorescence dip IR spectroscopy (FDIRS) and dispersed fluorescence. The LIF spectra in the S_{0}-S_{1} origin region show dramatic increases in the number of resolved transitions with increasing length of alkyl chains, reflecting an explosion in the number of unique low-energy conformations formed when two independent alkyl chains are present. Since the barriers to isomerization of the alkyl chain are similar in size, this results in an 'egg carton' shape to the potential energy surface. We use a combination of electronic frequency shift and alkyl CH stretch infrared spectra to generate a consistent set of conformational assignments.
6. Coarse-grained free energy functions for studying protein conformational changes: a double-well network model.
Science.gov (United States)
Chu, Jhih-Wei; Voth, Gregory A
2007-12-01
In this work, a double-well network model (DWNM) is presented for generating a coarse-grained free energy function that can be used to study the transition between reference conformational states of a protein molecule. Compared to earlier work that uses a single, multidimensional double-well potential to connect two conformational states, the DWNM uses a set of interconnected double-well potentials for this purpose. The DWNM free energy function has multiple intermediate states and saddle points, and is hence a "rough" free energy landscape. In this implementation of the DWNM, the free energy function is reduced to an elastic-network model representation near the two reference states. The effects of free energy function roughness on the reaction pathways of protein conformational change is demonstrated by applying the DWNM to the conformational changes of two protein systems: the coil-to-helix transition of the DB-loop in G-actin and the open-to-closed transition of adenylate kinase. In both systems, the rough free energy function of the DWNM leads to the identification of distinct minimum free energy paths connecting two conformational states. These results indicate that while the elastic-network model captures the low-frequency vibrational motions of a protein, the roughness in the free energy function introduced by the DWNM can be used to characterize the transition mechanism between protein conformations.
7. 77 FR 64183 - Notice of Availability of a Final General Conformity Determination for the California High-Speed...
Science.gov (United States)
2012-10-18
... California High-Speed Train System Merced to Fresno Section AGENCY: Federal Railroad Administration (FRA... Section of the California High-Speed Train (HST) System on September 18, 2012. FRA is the lead Federal... General Conformity requirements. The California High Speed Rail Authority (Authority), as the...
8. The Relationship between Alcohol Use and Peer Pressure Susceptibility, Peer Popularity and General Conformity in Northern Irish School Children
Science.gov (United States)
McKay, Michael T.; Cole, Jon C.
2012-01-01
This cross-sectional study investigated the bivariate and more fully controlled (with socio-demographic measures) relationship between self-reported drinking behaviour and peer pressure susceptibility, desire for peer popularity and general conformity in a sample of 11-16-year-old school children in Northern Ireland. Self-reported drinking…
9. The Relationship between Alcohol Use and Peer Pressure Susceptibility, Peer Popularity and General Conformity in Northern Irish School Children
Science.gov (United States)
McKay, Michael T.; Cole, Jon C.
2012-01-01
This cross-sectional study investigated the bivariate and more fully controlled (with socio-demographic measures) relationship between self-reported drinking behaviour and peer pressure susceptibility, desire for peer popularity and general conformity in a sample of 11-16-year-old school children in Northern Ireland. Self-reported drinking…
10. Semiexperimental equilibrium structure of the lower energy conformer of glycidol by the mixed estimation method.
Science.gov (United States)
Demaison, Jean; Craig, Norman C; Conrad, Andrew R; Tubergen, Michael J; Rudolph, Heinz Dieter
2012-09-13
Rotational constants were determined for (18)O-substituted isotopologues of the lower energy conformer of glycidol, which has an intramolecular inner hydrogen bond from the hydroxyl group to the oxirane ring oxygen. Rotational constants were previously determined for the (13)C and the OD species. These rotational constants have been corrected with the rovibrational constants calculated from an ab initio cubic force field. The derived semiexperimental equilibrium rotational constants have been supplemented by carefully chosen structural parameters, including those for hydrogen atoms, from medium level ab initio calculations. The combined data have been used in a weighted least-squares fit to determine an equilibrium structure for the glycidol H-bond inner conformer. This work shows that the mixed estimation method allows us to determine a complete and reliable equilibrium structure for large molecules, even when the rotational constants of a number of isotopologues are unavailable.
11. Cation-π Interactions in Serotonin: Conformational, Electronic Distribution, and Energy Decomposition Analysis.
Science.gov (United States)
Pratuangdejkul, Jaturong; Jaudon, Pascale; Ducrocq, Claire; Nosoongnoen, Wichit; Guerin, Georges-Alexandre; Conti, Marc; Loric, Sylvain; Launay, Jean-Marie; Manivet, Philippe
2006-05-01
An adiabatic conformational analysis of serotonin (5-hydroxytryptamine, 5-HT) using quantum chemistry led to six stable conformers that can be either +gauche (Gp), -gauche (Gm), and anti (At) depending upon the value taken by ethylamine side chain and 5-hydroxyl group dihedral angles φ1, φ2, and φ4, respectively. Further vibrational frequency analysis of the GmGp, GmGm, and GmAt conformers with the 5-hydroxyl group in the anti position revealed an additional red-shifted N-H stretch mode band in GmGp and GmGm that is absent in GmAt. This band corresponds to the 5-HT side-chain N-H bond involved in an intramolecular nonbonded interaction with the 5-hydroxy indole ring. The influence of this nonbonded interaction on the electronic distribution was assessed by analysis of the spin-spin coupling constants of GmGp and GmGm that show a marked increase for C2-C3 and C8-C9 bonds in GmGm and GmGp, respectively, with a decrease of their double bond character and an increase of their length. The Atoms in Molecules (AIM), Natural Bond Orbital (NBO), and fluorescence and CD spectra (TDDFT method) analyses confirmed the existence in GmGp and GmGm of a through-space charge-transfer between the HOMO and the HOMO-1 π-orbital of the indole ring and the LUMO σ* N-H antibonding orbital of the ammonium group. The strength of the cation-π interaction was determined by calculating binding energies of the NH4(+)/5-hydroxyindole complexes extracted from stable conformers. The energy decomposition analysis indicated that cationic-π interactions in the GmGp and GmGm conformers are governed by the electrostatic term with significant contributions from polarization and charge transfer. The lower stability of the GmGm over the GmGp comes from a higher exchange repulsion and a weaker polarization contributions. Our results provide insight into the nature of intramolecular forces that influence the conformational properties of 5-HT.
12. Narrowband NIR-Induced In Situ Generation of the High-Energy Trans Conformer of Trichloroacetic Acid Isolated in Solid Nitrogen and its Spontaneous Decay by Tunneling to the Low-Energy Cis Conformer
Directory of Open Access Journals (Sweden)
R. F. G. Apóstolo
2015-12-01
Full Text Available The monomeric form of trichloroacetic acid (CCl3COOH; TCA was isolated in a cryogenic nitrogen matrix (15 K and the higher energy trans conformer (O=C–O–H dihedral: 180° was generated in situ by narrowband near-infrared selective excitation the 1st OH stretching overtone of the low-energy cis conformer (O=C–O–H dihedral: 0°. The spontaneous decay, by tunneling, of the generated high-energy conformer into the cis form was then evaluated and compared with those observed previously for the trans conformers of acetic and formic acids in identical experimental conditions. The much faster decay of the high-energy conformer of TCA compared to both formic and acetic acids (by ~35 and ca. 25 times, respectively was found to correlate well with the lower energy barrier for the trans→cis isomerization in the studied compound. The experimental studies received support from quantum chemistry calculations undertaken at the DFT(B3LYP/cc-pVDZ level of approximation, which allowed a detailed characterization of the potential energy surface of the molecule and the detailed assignment of the infrared spectra of the two conformers.
13. Connecting free energy surfaces in implicit and explicit solvent: an efficient method to compute conformational and solvation free energies.
Science.gov (United States)
Deng, Nanjie; Zhang, Bin W; Levy, Ronald M
2015-06-09
The ability to accurately model solvent effects on free energy surfaces is important for understanding many biophysical processes including protein folding and misfolding, allosteric transitions, and protein–ligand binding. Although all-atom simulations in explicit solvent can provide an accurate model for biomolecules in solution, explicit solvent simulations are hampered by the slow equilibration on rugged landscapes containing multiple basins separated by barriers. In many cases, implicit solvent models can be used to significantly speed up the conformational sampling; however, implicit solvent simulations do not fully capture the effects of a molecular solvent, and this can lead to loss of accuracy in the estimated free energies. Here we introduce a new approach to compute free energy changes in which the molecular details of explicit solvent simulations are retained while also taking advantage of the speed of the implicit solvent simulations. In this approach, the slow equilibration in explicit solvent, due to the long waiting times before barrier crossing, is avoided by using a thermodynamic cycle which connects the free energy basins in implicit solvent and explicit solvent using a localized decoupling scheme. We test this method by computing conformational free energy differences and solvation free energies of the model system alanine dipeptide in water. The free energy changes between basins in explicit solvent calculated using fully explicit solvent paths agree with the corresponding free energy differences obtained using the implicit/explicit thermodynamic cycle to within 0.3 kcal/mol out of ∼3 kcal/mol at only ∼8% of the computational cost. We note that WHAM methods can be used to further improve the efficiency and accuracy of the implicit/explicit thermodynamic cycle.
14. Conformal "Thin-Sandwich" Data for the Initail-Value Problem of General Relativity
CERN Document Server
York, J W
1999-01-01
The initial-value problem is posed by giving a conformal three-metric on each of two nearby spacelike hypersurfaces, their proper-time separation up to a multiplier to be determined, and the mean (extrinsic) curvature of one slice. The resulting equations have the {\\it same} elliptic form as does the one-hypersurface formulation. The metrical roots of this form are revealed by a conformal thin sandwich'' viewpoint coupled with the transformation properties of the lapse function.
15. Experimental and computational study of crystalline formic acid composed of the higher-energy conformer.
Science.gov (United States)
Hakala, Mikko; Marushkevich, Kseniya; Khriachtchev, Leonid; Hämäläinen, Keijo; Räsänen, Markku
2011-02-07
Crystalline formic acid (FA) is studied experimentally and by first-principles simulations in order to identify a bulk solid structure composed of the higher-energy (cis) conformer. In the experiments, deuterated FA (HCOOD) was deposited in a Ne matrix and transformed to the cis conformer by vibrational excitation of the ground state (trans) form. Evaporation of the Ne host above 13 K prepared FA in a bulk solid state mainly composed of cis-FA. Infrared absorption spectroscopy at 4.3 K shows that the obtained solid differs from that composed of trans-FA molecules and that the state persists up to the annealing temperature of at least 110 K. The first-principles simulations reveal various energetically stable periodic chain structures containing cis-FA conformers. These chain structures contain either purely cis or both cis and trans forms. The vibrational frequencies of the calculated structures were compared to the experiment and a tentative assignment is given for a novel solid composed of cis-FA.
16. Visualizing potential energy curves and conformations on ultra high-resolution display walls.
Science.gov (United States)
Kirschner, Karl N; Reith, Dirk; Jato, Oliver; Hinkenjann, André
2015-11-01
In this contribution, we examine how visualization on an ultra high-resolution display wall can augment force-field research in the field of molecular modeling. Accurate force fields are essential for producing reliable simulations, and subsequently important for several fields of applications (e.g. rational drug design and biomolecular modeling). We discuss how using HORNET, a recently constructed specific ultra high-resolution tiled display wall, enhances the visual analytics that are necessary for conformational-based interpretation of the raw data from molecular calculations. Simultaneously viewing multiple potential energy graphs and conformation overlays leads to an enhanced way of evaluating force fields and in their optimization. Consequently, we have integrated visual analytics into our existing Wolf2Pack workflow. We applied this workflow component to analyze how major AMBER force fields (Parm14SB, Gaff, Lipid14, Glycam06j) perform at reproducing the quantum mechanics relative energies and geometries of saturated hydrocarbons. Included in this comparison are the 1996 OPLS force field and our newly developed ExTrM force field. While we focus on atomistic force fields the ideas presented herein are generalizable to other research areas, particularly those that involve numerous representations of large data amounts and whose simultaneous visualization enhances the analysis.
17. Energy management and conservation at General Motors
Energy Technology Data Exchange (ETDEWEB)
Kelly, R.L.
1982-07-01
An energy conservation plan on a corporate level, some results and potential benefits, two areas for future savings and a national energy policy, as revealed at the 1982 National Industrial Electric Conference are described. Phases of the program are Administrative Controls, Engineering Solutions, and Financial Controls. Heating, ventilation and air conditioning, the largest energy users in the corporation, comprise 27.6% of the total energy used. Suggested engineering solutions cover product specifications, process changes, heat recovery applications, materials conservation, improved equipment control, and facility changes. Computerized Facility Monitoring and Control Systems (FMC) automatically start and stop energy consuming equipment for maximum conservation. Conservation centers around energy accountability- knowing where, how much, and how wisely it is being used, and its cost.
18. Conformal field theory
CERN Document Server
Ketov, Sergei V
1995-01-01
Conformal field theory is an elegant and powerful theory in the field of high energy physics and statistics. In fact, it can be said to be one of the greatest achievements in the development of this field. Presented in two dimensions, this book is designed for students who already have a basic knowledge of quantum mechanics, field theory and general relativity. The main idea used throughout the book is that conformal symmetry causes both classical and quantum integrability. Instead of concentrating on the numerous applications of the theory, the author puts forward a discussion of the general
19. A coarse-grained generalized second law for holographic conformal field theories
Science.gov (United States)
Bunting, William; Fu, Zicao; Marolf, Donald
2016-03-01
We consider the universal sector of a d\\gt 2 dimensional large-N strongly interacting holographic CFT on a black hole spacetime background B. When our CFT d is coupled to dynamical Einstein-Hilbert gravity with Newton constant G d , the combined system can be shown to satisfy a version of the thermodynamic generalized second law (GSL) at leading order in G d . The quantity {S}{CFT}+\\frac{A({H}B,{perturbed})}{4{G}d} is non-decreasing, where A({H}B,{perturbed}) is the (time-dependent) area of the new event horizon in the coupled theory. Our S CFT is the notion of (coarse-grained) CFT entropy outside the black hole given by causal holographic information—a quantity in turn defined in the AdS{}d+1 dual by the renormalized area {A}{ren}({H}{{bulk}}) of a corresponding bulk causal horizon. A corollary is that the fine-grained GSL must hold for finite processes taken as a whole, though local decreases of the fine-grained generalized entropy are not obviously forbidden. Another corollary, given by setting {G}d=0, states that no finite process taken as a whole can increase the renormalized free energy F={E}{out}-{{TS}}{CFT}-{{Ω }}J, with T,{{Ω }} constants set by {H}B. This latter corollary constitutes a 2nd law for appropriate non-compact AdS event horizons.
20. The effect of beam energy on the quality of IMRT plans for prostate conformal radiotherapy.
Science.gov (United States)
de Boer, Steven F; Kumek, Yunus; Jaggernauth, Wainwright; Podgorsak, Matthew B
2007-04-01
Three dimensional conformal radiation therapy (3DCRT) for prostate cancer is most commonly delivered with high-energy photons, typically in the range of 10-21 MV. With the advent of Intensity Modulated Radiation Therapy (IMRT), an increase in the number of monitor units (MU) relative to 3DCRT has lead to a concern about secondary malignancies. This risk becomes more relevant at higher photon energies where there is a greater neutron contribution. Subsequently, the majority of IMRT prostate treatments being delivered today are with 6-10 MV photons where neutron production is negligible. However, the absolute risk is small [Hall, E. J. Intensity Modulated Radiation Therapy, Protons, and the Risk of Second Cancers. Int J Radiat Oncol Bio Phys 65, 1-7 (2006); Kry, F. S., Salehpour, M., Followill, D. S., Stovall, M., Kuban, D. A., White, R. A., and Rosen, I. I. The Calculated Risk of Fatal Secondary Malignancies From Intensity Modulated Radiation Therapy. Int J Radiat Oncol Bio Phys 62, 1195-1203 (2005).] and therefore it has been suggested that the use of an 18MV IMRT may achieve better target coverage and normal tissue sparing such that this benefit outweighs the risks. This paper investigates whether 18MV IMRT offer better target coverage and normal tissue sparing. Computed Tomography (CT) image sets of ten prostate cancer patients were acquired and two separate IMRT plans were created for each patient. One plan used 6 MV beams, and the other used 18 MV, both in a coplanar, non-opposed beam geometry. Beam arrangements and optimization constraints were the same for all plans. This work includes a comparison and discussion of the total integral dose, neutron dose conformity index, and total number of MU for plans generated with both energies.
1. A reoptimized GROMOS force field for hexopyranose-based carbohydrates accounting for the relative free energies of ring conformers, anomers, epimers, hydroxymethyl rotamers, and glycosidic linkage conformers.
Science.gov (United States)
Hansen, Halvor S; Hünenberger, Philippe H
2011-04-30
This article presents a reoptimization of the GROMOS 53A6 force field for hexopyranose-based carbohydrates (nearly equivalent to 45A4 for pure carbohydrate systems) into a new version 56A(CARBO) (nearly equivalent to 53A6 for non-carbohydrate systems). This reoptimization was found necessary to repair a number of shortcomings of the 53A6 (45A4) parameter set and to extend the scope of the force field to properties that had not been included previously into the parameterization procedure. The new 56A(CARBO) force field is characterized by: (i) the formulation of systematic build-up rules for the automatic generation of force-field topologies over a large class of compounds including (but not restricted to) unfunctionalized polyhexopyranoses with arbritrary connectivities; (ii) the systematic use of enhanced sampling methods for inclusion of experimental thermodynamic data concerning slow or unphysical processes into the parameterization procedure; and (iii) an extensive validation against available experimental data in solution and, to a limited extent, theoretical (quantum-mechanical) data in the gas phase. At present, the 56A(CARBO) force field is restricted to compounds of the elements C, O, and H presenting single bonds only, no oxygen functions other than alcohol, ether, hemiacetal, or acetal, and no cyclic segments other than six-membered rings (separated by at least one intermediate atom). After calibration, this force field is shown to reproduce well the relative free energies of ring conformers, anomers, epimers, hydroxymethyl rotamers, and glycosidic linkage conformers. As a result, the 56A(CARBO) force field should be suitable for: (i) the characterization of the dynamics of pyranose ring conformational transitions (in simulations on the microsecond timescale); (ii) the investigation of systems where alternative ring conformations become significantly populated; (iii) the investigation of anomerization or epimerization in terms of free-energy differences
2. Energy management and conservation at General Motors
Energy Technology Data Exchange (ETDEWEB)
Kelly, R.L.
1982-07-01
An energy conservation plan on a corporate level, some of the results and potential benefits, two specific areas for future savings and a national energy policy are described. It is from a paper presented during the 1982 National Industrial Electric Conference, sponsored by The Electrification Council and held in Lexington, Ky. The formal energy conservation program has evolved into three phases: Phase I - Administrative Controls; Phase II - Engineering Solutions; Phase III - Financial Controls. All GM plants worldwide have completed a Five Year Energy Conservation Plan for the period 1981 through 1985. A summary of the Plans from 217 locations reveals that the potential exists to save another 39.1 billion Btu by 1985 at a cost of /572 million. The payback for such projects averages three years.
3. LEAR (Low Energy Antiproton Ring), general view.
CERN Multimedia
1990-01-01
When the Antiproton Project was launched in the late 1970s, it was recognized that in addition to the primary purpose of high-energy proton-antiproton collisions in the SPS, there was interesting physics to be done with low-energy antiprotons. In 1982, LEAR was ready to receive antiprotons from the Antiproton Accumulator (AA), via the PS. A year later, delivery of antiprotons to the experiments began, at momenta as low as 100 MeV/c (kinetic energy 5.3 MeV), in an "Ultra-Slow Extraction" mode, dispensing some E9 antiprotons over times counted in hours. For such an achievement, stochastic and electron cooling had to be brought to high levels of perfection.
4. The Activation of c-Src Tyrosine Kinase: Conformational Transition Pathway and Free Energy Landscape.
Science.gov (United States)
Fajer, Mikolai; Meng, Yilin; Roux, Benoît
2016-10-28
Tyrosine kinases are important cellular signaling allosteric enzymes that regulate cell growth, proliferation, metabolism, differentiation, and migration. Their activity must be tightly controlled, and malfunction can lead to a variety of diseases, particularly cancer. The nonreceptor tyrosine kinase c-Src, a prototypical model system and a representative member of the Src-family, functions as complex multidomain allosteric molecular switches comprising SH2 and SH3 domains modulating the activity of the catalytic domain. The broad picture of self-inhibition of c-Src via the SH2 and SH3 regulatory domains is well characterized from a structural point of view, but a detailed molecular mechanism understanding is nonetheless still lacking. Here, we use advanced computational methods based on all-atom molecular dynamics simulations with explicit solvent to advance our understanding of kinase activation. To elucidate the mechanism of regulation and self-inhibition, we have computed the pathway and the free energy landscapes for the "inactive-to-active" conformational transition of c-Src for different configurations of the SH2 and SH3 domains. Using the isolated c-Src catalytic domain as a baseline for comparison, it is observed that the SH2 and SH3 domains, depending upon their bound orientation, promote either the inactive or active state of the catalytic domain. The regulatory structural information from the SH2-SH3 tandem is allosterically transmitted via the N-terminal linker of the catalytic domain. Analysis of the conformational transition pathways also illustrates the importance of the conserved tryptophan 260 in activating c-Src, and reveals a series of concerted events during the activation process.
5. Computing conformational free energy differences in explicit solvent: An efficient thermodynamic cycle using an auxiliary potential and a free energy functional constructed from the end points.
Science.gov (United States)
Harris, Robert C; Deng, Nanjie; Levy, Ronald M; Ishizuka, Ryosuke; Matubayasi, Nobuyuki
2016-12-23
Many biomolecules undergo conformational changes associated with allostery or ligand binding. Observing these changes in computer simulations is difficult if their timescales are long. These calculations can be accelerated by observing the transition on an auxiliary free energy surface with a simpler Hamiltonian and connecting this free energy surface to the target free energy surface with free energy calculations. Here, we show that the free energy legs of the cycle can be replaced with energy representation (ER) density functional approximations. We compute: (1) The conformational free energy changes for alanine dipeptide transitioning from the right-handed free energy basin to the left-handed basin and (2) the free energy difference between the open and closed conformations of β-cyclodextrin, a "host" molecule that serves as a model for molecular recognition in host-guest binding. β-cyclodextrin contains 147 atoms compared to 22 atoms for alanine dipeptide, making β-cyclodextrin a large molecule for which to compute solvation free energies by free energy perturbation or integration methods and the largest system for which the ER method has been compared to exact free energy methods. The ER method replaced the 28 simulations to compute each coupling free energy with two endpoint simulations, reducing the computational time for the alanine dipeptide calculation by about 70% and for the β-cyclodextrin by > 95%. The method works even when the distribution of conformations on the auxiliary free energy surface differs substantially from that on the target free energy surface, although some degree of overlap between the two surfaces is required. © 2016 Wiley Periodicals, Inc.
6. Integrated Hamiltonian sampling: a simple and versatile method for free energy simulations and conformational sampling.
Science.gov (United States)
Mori, Toshifumi; Hamers, Robert J; Pedersen, Joel A; Cui, Qiang
2014-07-17
Motivated by specific applications and the recent work of Gao and co-workers on integrated tempering sampling (ITS), we have developed a novel sampling approach referred to as integrated Hamiltonian sampling (IHS). IHS is straightforward to implement and complementary to existing methods for free energy simulation and enhanced configurational sampling. The method carries out sampling using an effective Hamiltonian constructed by integrating the Boltzmann distributions of a series of Hamiltonians. By judiciously selecting the weights of the different Hamiltonians, one achieves rapid transitions among the energy landscapes that underlie different Hamiltonians and therefore an efficient sampling of important regions of the conformational space. Along this line, IHS shares similar motivations as the enveloping distribution sampling (EDS) approach of van Gunsteren and co-workers, although the ways that distributions of different Hamiltonians are integrated are rather different in IHS and EDS. Specifically, we report efficient ways for determining the weights using a combination of histogram flattening and weighted histogram analysis approaches, which make it straightforward to include many end-state and intermediate Hamiltonians in IHS so as to enhance its flexibility. Using several relatively simple condensed phase examples, we illustrate the implementation and application of IHS as well as potential developments for the near future. The relation of IHS to several related sampling methods such as Hamiltonian replica exchange molecular dynamics and λ-dynamics is also briefly discussed.
7. Universal geometrical factor of protein conformations as a consequence of energy minimization
CERN Document Server
Wu, Ming-Chya; Ma, Wen-Jong; Kouza, Maksim; Hu, Chin-Kun; 10.1209/0295-5075/96/68005
2012-01-01
The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein conformation as a consequence of energy minimization in protein folding. Folding simulations of 10 polypeptides with chain length ranging from 183 to 548 residues manifest that the dimensionless ratio (V/(A)) of the van der Waals volume V to the surface area A and average atomic radius of the folded structures, calculated with atomic radii setting used in SMMP [Eisenmenger F., et. al., Comput. Phys. Commun., 138 (2001) 192], approach 0.49 quickly during the course of energy minimization. A large scale analysis of protein structures show that the ratio for real and well-designed proteins is universal and equal to 0.491\\pm0.005. The fractional composition of hydrophobic and hydrophilic residues does not affect the ratio substantially. The ratio also holds for intrinsically disorde...
8. Octonionic M-theory and D=11 Generalized Conformal and Superconformal Algebras
CERN Document Server
Lukierski, J
2003-01-01
Following [1] we further apply the octonionic structure to supersymmetric D=11 $M$-theory. We consider the octonionic $2^{n+1} \\times 2^{n+1}$ Dirac matrices describing the sequence of Clifford algebras with signatures ($9+n,n$) ($n=0,1,2, ...$) and derive the identities following from the octonionic multiplication table. The case $n=1$ ($4\\times 4$ octonion-valued matrices) is used for the description of the D=11 octonionic $M$-superalgebra with 52 real bosonic charges; the $n=2$ case ($8 \\times 8$ octonion-valued matrices) for the D=11 conformal $M$-algebra with 232 real bosonic charges. The octonionic structure is described explicitly for $n=1$ by the relations between the 512 Abelian O(10,1) tensorial charges $Z_\\mu$, $Z_{\\mu\ 9. The clinical potential of high energy, intensity and energy modulated electron beams optimized by simulated annealing for conformal radiation therapy Science.gov (United States) Salter, Bill Jean, Jr. Purpose. The advent of new, so called IVth Generation, external beam radiation therapy treatment machines (e.g. Scanditronix' MM50 Racetrack Microtron) has raised the question of how the capabilities of these new machines might be exploited to produce extremely conformal dose distributions. Such machines possess the ability to produce electron energies as high as 50 MeV and, due to their scanned beam delivery of electron treatments, to modulate intensity and even energy, within a broad field. Materials and methods. Two patients with 'challenging' tumor geometries were selected from the patient archives of the Cancer Therapy and Research Center (CTRC), in San Antonio Texas. The treatment scheme that was tested allowed for twelve, energy and intensity modulated beams, equi-spaced about the patient-only intensity was modulated for the photon treatment. The elementary beams, incident from any of the twelve allowed directions, were assumed parallel, and the elementary electron beams were modeled by elementary beam data. The optimal arrangement of elementary beam energies and/or intensities was optimized by Szu-Hartley Fast Simulated Annealing Optimization. Optimized treatment plans were determined for each patient using both the high energy, intensity and energy modulated electron (HIEME) modality, and the 6 MV photon modality. The 'quality' of rival plans were scored using three different, popular objective functions which included Root Mean Square (RMS), Maximize Dose Subject to Dose and Volume Limitations (MDVL - Morrill et. al.), and Probability of Uncomplicated Tumor Control (PUTC) methods. The scores of the two optimized treatments (i.e. HIEME and intensity modulated photons) were compared to the score of the conventional plan with which the patient was actually treated. Results. The first patient evaluated presented a deeply located target volume, partially surrounding the spinal cord. A healthy right kidney was immediately adjacent to the tumor volume, separated 10. Paul Scherrer Institute Scientific Report 1998. Volume V: General Energy Energy Technology Data Exchange (ETDEWEB) Daum, C.; Leuenberger, J. [eds. 1999-08-01 In view of its mission to contribute towards the development of a globally more sustainable energy supply system, the General Energy Department is focusing on four topical areas: advancing technologies for the use of renewable energies; investigating options for chemical and electrochemical energy storage on various time scales; developing highly efficient converters for the low emission use of fossil and renewable fuels, including both combustion devices and fuel cells; analyzing the consequences of energy use, and advancing scenarios for the development of the energy supply system. Progress in 1998 in these topical areas is described in this report. A list of scientific publications in 1998 is also provided. (author) figs., tabs., refs. 11. Combined experimental powder X-ray diffraction and DFT data to obtain the lowest energy molecular conformation of friedelin Energy Technology Data Exchange (ETDEWEB) Oliveira, Djalma Menezes de; Mussel, Wagner da Nova; Duarte, Lucienir Pains; Silva, Gracia Divina de Fatima; Duarte, Helio Anderson; Gomes, Elionai Cassiana de Lima [Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG (Brazil). Dept. de Quimica; Guimaraes, Luciana [Universidade Federal de Sao Joao Del-Rei (UFSJ), MG (Brazil). Dept. de Ciencias Naturais; Vieira Filho, Sidney A., E-mail: [email protected] [Universidade Federal de Ouro Preto (UFOP), MG (Brazil). Dept. de Farmacia 2012-07-01 Friedelin molecular conformers were obtained by Density Functional Theory (DFT) and by ab initio structure determination from powder X-ray diffraction. Their conformers with the five rings in chair-chair-chair-boat-boat, and with all rings in chair, are energy degenerated in gas-phase according to DFT results. The powder diffraction data reveals that rings A, B and C of friedelin are in chair, and rings D and E in boat-boat, conformation. The high correlation values among powder diffraction data, DFT and reported single crystal data indicate that the use of conventional X-ray diffractometer can be applied in routine laboratory analysis in the absence of a single-crystal diffractometer. (author) 12. Combined experimental powder X-ray diffraction and DFT data to obtain the lowest energy molecular conformation of friedelin Directory of Open Access Journals (Sweden) Djalma Menezes de Oliveira 2012-01-01 Full Text Available Friedelin molecular conformers were obtained by Density Functional Theory (DFT and by ab initio structure determination from powder X-ray diffraction. Their conformers with the five rings in chair-chair-chair-boat-boat, and with all rings in chair, are energy degenerated in gas-phase according to DFT results. The powder diffraction data reveals that rings A, B and C of friedelin are in chair, and rings D and E in boat-boat, conformation. The high correlation values among powder diffraction data, DFT and reported single-crystal data indicate that the use of conventional X-ray diffractometer can be applied in routine laboratory analysis in the absence of a single-crystal diffractometer. 13. Generalized ghost dark energy in Brans-Dicke theory CERN Document Server Sheykhi, A; Yosefi, Y 2013-01-01 It was argued that the vacuum energy of the Veneziano ghost field of QCD, in a time-dependent background, can be written in the general form,$H + O(H^2)$, where$H$is the Hubble parameter. Based on this, a phenomenological dark energy model whose energy density is of the form$\\rho=\\alpha H+\\beta H^{2}$was recently proposed to explain the dark energy dominated universe. In this paper, we investigate this generalized ghost dark energy model in the setup of Brans-Dicke cosmology. We study the cosmological implications of this model. In particular, we obtain the equation of state and the deceleration parameters and a differential equation governing the evolution of this dark energy model. It is shown that the equation of state parameter of the new ghost dark energy can cross the phantom line ($w_D=-1$) provided the parameters of the model are chosen suitably. 14. Commercial Building Partnership General Merchandise Energy Savings Overview Energy Technology Data Exchange (ETDEWEB) None 2013-03-01 The Commercial Building Partnership (CBP) paired selected commercial building owners and operators with representatives of DOE, national laboratories and private sector exports to explore energy efficiency measures across general merchandise commercial buildings. 15. General Merchandise 50% Energy Savings Technical Support Document Energy Technology Data Exchange (ETDEWEB) Hale, E.; Leach, M.; Hirsch, A.; Torcellini, P. 2009-09-01 This report documents technical analysis for medium-box general merchandise stores aimed at providing design guidance that achieves whole-building energy savings of at least 50% over ASHRAE Standard 90.1-2004. 16. Chinese hotel general managers' perspectives on energy-saving practices Science.gov (United States) Zhu, Yidan As hotels' concern about sustainability and budget-control is growing steadily, energy-saving issues have become one of the important management concerns hospitality industry face. By executing proper energy-saving practices, previous scholars believed that hotel operation costs can decrease dramatically. Moreover, they believed that conducting energy-saving practices may eventually help the hotel to gain other benefits such as an improved reputation and stronger competitive advantage. The energy-saving issue also has become a critical management problem for the hotel industry in China. Previous research has not investigated energy-saving in China's hotel segment. To achieve a better understanding of the importance of energy-saving, this document attempts to present some insights into China's energy-saving practices in the tourist accommodations sector. Results of the study show the Chinese general managers' attitudes toward energy-saving issues and the differences among the diverse hotel managers who responded to the study. Study results indicate that in China, most of the hotels' energy bills decrease due to the implementation of energy-saving equipments. General managers of hotels in operation for a shorter period of time are typically responsible for making decisions about energy-saving issues; older hotels are used to choosing corporate level concerning to this issue. Larger Chinese hotels generally have official energy-saving usage training sessions for employees, but smaller Chinese hotels sometimes overlook the importance of employee training. The study also found that for the Chinese hospitality industry, energy-saving practices related to electricity are the most efficient and common way to save energy, but older hotels also should pay attention to other ways of saving energy such as water conservation or heating/cooling system. 17. Conformal Infinity Directory of Open Access Journals (Sweden) Frauendiener Jörg 2000-08-01 Full Text Available The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, conformal infinity'' is related with almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved out of physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation and how it lends itself very naturally to solve radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection. 18. Conformal Infinity Science.gov (United States) Frauendiener, Jörg 2004-12-01 The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related to almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved from physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation, and how it lends itself very naturally to the solution of radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection. 19. Conformal Infinity Directory of Open Access Journals (Sweden) Frauendiener Jörg 2004-01-01 Full Text Available The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, 'conformal infinity' is related to almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved from physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation, and how it lends itself very naturally to the solution of radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection. 20. Full QM Calculation of RNA Energy Using Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps Method. Science.gov (United States) Jin, Xinsheng; Zhang, John Z H; He, Xiao 2017-03-30 In this study, the electrostatically embedded generalized molecular fractionation with conjugate caps (concaps) method (EE-GMFCC) was employed for efficient linear-scaling quantum mechanical (QM) calculation of total energies of RNAs. In the EE-GMFCC approach, the total energy of RNA is calculated by taking a proper combination of the QM energy of each nucleotide-centric fragment with large caps or small caps (termed EE-GMFCC-LC and EE-GMFCC-SC, respectively) deducted by the energies of concaps. The two-body QM interaction energy between non-neighboring ribonucleotides which are spatially in close contact are also taken into account for the energy calculation. Numerical studies were carried out to calculate the total energies of a number of RNAs using the EE-GMFCC-LC and EE-GMFCC-SC methods at levels of the Hartree-Fock (HF) method, density functional theory (DFT), and second-order many-body perturbation theory (MP2), respectively. The results show that the efficiency of the EE-GMFCC-SC method is about 3 times faster than the EE-GMFCC-LC method with minimal accuracy sacrifice. The EE-GMFCC-SC method is also applied for relative energy calculations of 20 different conformers of two RNA systems using HF and DFT, respectively. Both single-point and relative energy calculations demonstrate that the EE-GMFCC method has deviations from the full system results of only a few kcal/mol. 1. Determination of the electron-detachment energies of 2'-deoxyguanosine 5'-monophosphate anion: influence of the conformation. Science.gov (United States) Rubio, Mercedes; Roca-Sanjuán, Daniel; Serrano-Andrés, Luis; Merchán, Manuela 2009-02-26 The vertical electron-detachment energies (VDEs) of the singly charged 2'-deoxyguanosine 5'-monophosphate anion (dGMP-) are determined by using the multiconfigurational second-order perturbation CASPT2 method at the MP2 ground-state equilibrium geometry of relevant conformers. The origin of the unique low-energy band in the gas phase photoelectron spectrum of dGMP-, with maximum at around 5.05 eV, is unambiguously assigned to electron detachment from the highest occupied molecular orbital of pi-character belonging to guanine fragment of a syn conformation. The presence of a short H-bond linking the 2-amino and phosphate groups, the guanine moiety acting as proton donor, is precisely responsible for the pronounced decrease of the computed VDE with respect to that obtained in other conformations. As a whole, the present research supports the nucleobase as the site with the lowest ionization potential in negatively charged (deprotonated) nucleotides at the most stable conformations as well as for B-DNA-like type arrangements, in agreement with experimental evidence. 2. Control systems are General Motors' biggest energy saver Energy Technology Data Exchange (ETDEWEB) 1979-06-01 In 1978, General Motors Corp. used almost 3% less energy than it did in 1972, even though production had increased about 25%. Most of the savings are the result of improved technology and design changes in buildings, equipment, and processes. Computerized energy management control systems are now in operation or being installed in 78 GM buildings. 3. Development of the Model of the Generalized Quintom Dark Energy Institute of Scientific and Technical Information of China (English) WANG Wei; GUI Yuan-Xing; SHAO Ying 2006-01-01 @@ We consider a generalized quintom (GQ) dark energy modelfor changing the equal weight of the negative-kinetic scalar field (phantom) and the normal scalar field (quintessence) in quintom dark energy. Though the phantomdominated scaling solution is a stable late-time attractor, the early evolution of GQ is different from that of the quintom model and the adjustability of the dark energy state equation in the model is improved. 4. Available Potential Energy and the Maintenance of the General Circulation OpenAIRE Lorenz, Edward N. 2011-01-01 The available potential energy of the atmosphere may be defined as the difference between the total potential energy and the minimum total potential energy which could result from any adiabatic redistribution of mass. It vanishes if the density stratification is horizontal and statically stable everywhere, and is positive otherwise. It is measured approximately by a weighted vertical average of the horizontal variance of temperature. In magnitude it is generally about ten times the total kine... 5. Dissecting CFT Correlators and String Amplitudes. Conformal Blocks and On-Shell Recursion for General Tensor Fields Energy Technology Data Exchange (ETDEWEB) Hansen, Tobias 2015-07-15 This thesis covers two main topics: the tensorial structure of quantum field theory correlators in general spacetime dimensions and a method for computing string theory scattering amplitudes directly in target space. In the first part tensor structures in generic bosonic CFT correlators and scattering amplitudes are studied. To this end arbitrary irreducible tensor representations of SO(d) (traceless mixed-symmetry tensors) are encoded in group invariant polynomials, by contracting with sets of commuting and anticommuting polarization vectors which implement the index symmetries of the tensors. The tensor structures appearing in CFT{sub d} correlators can then be inferred by studying these polynomials in a d + 2 dimensional embedding space. It is shown with an example how these correlators can be used to compute general conformal blocks describing the exchange of mixed-symmetry tensors in four-point functions, which are crucial for advancing the conformal bootstrap program to correlators of operators with spin. Bosonic string theory lends itself as an ideal example for applying the same methods to scattering amplitudes, due to its particle spectrum of arbitrary mixed-symmetry tensors. This allows in principle the definition of on-shell recursion relations for string theory amplitudes. A further chapter introduces a different target space definition of string scattering amplitudes. As in the case of on-shell recursion relations, the amplitudes are expressed in terms of their residues via BCFW shifts. The new idea here is that the residues are determined by use of the monodromy relations for open string theory, avoiding the infinite sums over the spectrum arising in on-shell recursion relations. Several checks of the method are presented, including a derivation of the Koba-Nielsen amplitude in the bosonic string. It is argued that this method provides a target space definition of the complete S-matrix of string theory at tree-level in a at background in terms of a 6. A coarse-grained generalized second law for holographic conformal field theories CERN Document Server Bunting, William; Marolf, Donald 2015-01-01 We consider the universal sector of a$d$-dimensional large-$N$strongly-interacting holographic CFT on a black hole spacetime background$B$. When our CFT$_d$is coupled to dynamical Einstein-Hilbert gravity with Newton constant$G_{d}$, the combined system can be shown to satisfy a version of the thermodynamic Generalized Second Law (GSL) at leading order in$G_{d}$. The quantity$S_{CFT} + \\frac{A(H_{B, \\text{perturbed}})}{4G_{d}}$is non-decreasing, where$A(H_{B, \\text{perturbed}})$is the (time-dependent) area of the new event horizon in the coupled theory. Our$S_{CFT}$is the notion of (coarse-grained) CFT entropy outside the black hole given by causal holographic information -- a quantity in turn defined in the AdS$_{d+1}$dual by the renormalized area$A_{ren}(H_{\\rm bulk})$of a corresponding bulk causal horizon. A corollary is that the fine-grained GSL must hold for finite processes taken as a whole, though local decreases of the fine-grained generalized entropy are not obviously forbidden. Anothe... 7. 76 FR 11437 - Application To Export Electric Energy; Societe Generale Energy Corp. Science.gov (United States) 2011-03-02 ... Application To Export Electric Energy; Societe Generale Energy Corp. AGENCY: Office of Electricity Delivery.... (SGEC) has applied for authority to transmit electric energy from the United States to Canada pursuant... application from the SGEC for authority to transmit electric energy from the United States to Canada as... 8. Finding low-energy conformations of lattice protein models by quantum annealing CERN Document Server Perdomo-Ortiz, Alejandro; Drew-Brook, Marshall; Rose, Geordie; Aspuru-Guzik, Alán 2012-01-01 Lattice protein folding models are a cornerstone of computational biophysics. Although these models are a coarse grained representation, they provide useful insight into the energy landscape of natural proteins. Finding low-energy three-dimensional structures is an intractable problem even in the simplest model, the Hydrophobic-Polar (HP) model. Exhaustive search of all possible global minima is limited to sequences in the tens of amino acids. Description of protein-like properties are more accurately described by generalized models, such as the one proposed by Miyazawa and Jernigan (MJ), which explicitly take into account the unique interactions among all 20 amino acids. There is theoretical and experimental evidence of the advantage of solving classical optimization problems using quantum annealing over its classical analogue (simulated annealing). In this report, we present a benchmark implementation of quantum annealing for a biophysical problem (six different experiments up to 81 superconducting quantum ... 9. General relativistic models for rotating magnetized neutron stars in conformally flat space-time Science.gov (United States) Pili, A. G.; Bucciantini, N.; Del Zanna, L. 2017-09-01 The extraordinary energetic activity of magnetars is usually explained in terms of dissipation of a huge internal magnetic field of the order of 1015-16 G. How such a strong magnetic field can originate during the formation of a neutron star (NS) is still subject of active research. An important role can be played by fast rotation: if magnetars are born as millisecond rotators dynamo mechanisms may efficiently amplify the magnetic field inherited from the progenitor star during the collapse. In this case, the combination of rapid rotation and strong magnetic field determine the right physical condition not only for the development of a powerful jet-driven explosion, manifesting as a gamma-ray burst, but also for a copious gravitational waves emission. Strong magnetic fields are indeed able to induce substantial quadrupolar deformations in the star. In this paper, we analyse the joint effect of rotation and magnetization on the structure of a polytropic and axisymmetric NS, within the ideal magneto-hydrodynamic regime. We will consider either purely toroidal or purely poloidal magnetic field geometries. Through the sampling of a large parameter space, we generalize previous results in literature, inferring new quantitative relations that allow for a parametrization of the induced deformation, that takes into account also the effects due to the stellar compactness and the current distribution. Finally, in the case of purely poloidal field, we also discuss how different prescription on the surface charge distribution (a gauge freedom) modify the properties of the surrounding electrosphere and its physical implications. 10. Kerr-Taub-NUT General Frame, Energy, and Momentum in Teleparallel Equivalent of General Relativity Directory of Open Access Journals (Sweden) Gamal G. L. Nashed 2012-01-01 Full Text Available A new exact solution describing a general stationary and axisymmetric object of the gravitational field in the framework of teleparallel equivalent of general relativity (TEGR is derived. The solution is characterized by three parameters “the gravitational mass M, the rotation a, and the NUT L.” The vierbein field is axially symmetric, and the associated metric gives the Kerr-Taub-NUT spacetime. Calculation of the total energy using two different methods, the gravitational energy momentum and the Riemannian connection 1-form Γα̃β, is carried out. It is shown that the two methods give the same results of energy and momentum. The value of energy is shown to depend on the mass M and the NUT parameter L. If L is vanishing, then the total energy reduced to the energy of Kerr black hole. 11. How Do DFT-DCP, DFT-NL, and DFT-D3 Compare for the Description of London-Dispersion Effects in Conformers and General Thermochemistry? Science.gov (United States) Goerigk, Lars 2014-03-11 The dispersion-core-potential corrected B3LYP-DCP method (Torres and DiLabio J. Phys. Chem. Lett. 2012, 3, 1738) is for the first time thoroughly assessed and compared with the B3LYP-NL (Hujo and Grimme J. Chem. Theory Comput. 2011, 7, 3866) and B3LYP-D3 (Grimme et al. J. Comput. Chem. 2011, 32, 1456) methods for a broad range of chemical problems that particularly shed light on intramolecular London-dispersion effects in conformers and general thermochemistry. The analysis is based on a compilation of 473 reference cases, the majority of which are taken from the GMTKN30 database (Goerigk and Grimme J. Chem. Theory Comput. 2010, 6, 107; 2011, 7, 291). The results confirm previous findings that B3LYP-DCP indeed predicts very good binding energies for noncovalently bound complexes, particularly with small basis sets. However, problems are identified for the description of intramolecular effects in some conformers and chemical reactions, for which B3LYP-DCP sometimes gives results similar or worse than uncorrected B3LYP. Surprisingly large errors for total atomization energies reveal an unwanted influence of the DCPs on the short-range electronic structure of the investigated systems. However, a recently modified carbon potential for B3LYP-DCP (DiLabio et al. Theor. Chem. Acc. 2013, 132, 1389) was additionally tested that seems to solve most of those problems and provides improved results. An overall comparison between all tested methods shows that B3LYP-NL is the most robust and accurate approach, closely followed by B3LYP-D3. This is also true when small basis sets of double-ζ quality are applied for which those methods have not been parametrized. However, binding energies of noncovalently bound complexes can be more strongly influenced by basis-set superposition-error effects than for B3LYP-DCP. Finally, it is noted that the DFT-D3 and DFT-NL schemes are readily applicable to a large range of chemical elements and they are therefore particularly recommended for 12. How universal are hydrogen bond correlations? A density functional study of intramolecular hydrogen bonding in low-energy conformers of α-amino acids Science.gov (United States) Ramaniah, Lavanya M.; Kamal, C.; Kshirsagar, Rohidas J.; Chakrabarti, Aparna; Banerjee, Arup 2013-10-01 Hydrogen bonding is one of the most important and ubiquitous interactions present in Nature. Several studies have attempted to characterise and understand the nature of this very basic interaction. These include both experimental and theoretical investigations of different types of chemical compounds, as well as systems subjected to high pressure. The O-H..O bond is of course the best studied hydrogen bond, and most studies have concentrated on intermolecular hydrogen bonding in solids and liquids. In this paper, we analyse and characterise normal hydrogen bonding of the general type, D-H...A, in intramolecular hydrogen bonding interactions. Using a first-principles density functional theory approach, we investigate low energy conformers of the twenty α-amino acids. Within these conformers, several different types of intramolecular hydrogen bonds are identified. The hydrogen bond within a given conformer occurs between two molecular groups, either both within the backbone itself, or one in the backbone and one in the side chain. In a few conformers, more than one (type of) hydrogen bond is seen to occur. Interestingly, the strength of the hydrogen bonds in the amino acids spans quite a large range, from weak to strong. The signature of hydrogen bonding in these molecules, as reflected in their theoretical vibrational spectra, is analysed. With the new first-principles data from 51 hydrogen bonds, various parameters relating to the hydrogen bond, such as hydrogen bond length, hydrogen bond angle, bond length and vibrational frequencies are studied. Interestingly, the correlation between these parameters in these bonds is found to be in consonance with those obtained in earlier experimental studies of normal hydrogen bonds on vastly different systems. Our study provides some of the most detailed first-principles support, and the first involving vibrational frequencies, for the universality of hydrogen bond correlations in materials. 13. Paul Scherrer Institute Scientific Report 1999. Volume V: General Energy Energy Technology Data Exchange (ETDEWEB) Daum, Christina; Leuenberger, Jakob [eds. 2000-07-01 Strengthening of international collaborations represented a strategic goal of the General Energy Research Department for 1999. For the Fifth Framework Program of the European Union, we participated in consortia and in the successful preparation of several proposals. National networks with partners from academia and Industry have been formed in two topical areas of central interest in the context of sustainability, i.e. 'Ecoefficient energy use and material cycles' and 'Sustainable transportation' on the other hand. Research at PSI comprises all aspects of human energy use, with the ultimate goal of promoting development towards a sustainable energy supply system. In the General Energy Research Department, technologies are being advanced for the utilization of renewable energy sources, low-loss energy storage, efficient conversion, and low emission energy use. Experimental and model-based assessment of these emissions forms the basis of a comprehensive assessment of economic, ecological and environmental consequences, for both present and future energy supply systems. The research program of the department is centered around 1) development, use, and characterisation of catalysts for energy technologies in many different fields, like e.g. the partial oxidation of methanol for hydrogen production, the processing of methane by catalytic combustion and reforming; 2) use of concentrated solar radiation to induce chemical conversions, thereby producing energy carriers; 3) development of efficient, less polluting combustion engines and burners by advancing the detailed understanding of reaction mechanisms and combustion pathways; 4) research and development of low temperature polymer electrolyte fuel cells, novel batteries and capacitors, with applications envisaged for electric vehicles, photovoltaics and on-site load leveling; 5) experimental and model based research concerning transportation and chemistry of atmospheric trace gases related to 14. Extended Theories of Gravity with Generalized Energy Conditions CERN Document Server Mimoso, José P; Capozziello, Salvatore 2014-01-01 We address the problem of the energy conditions in modified gravity taking into account the additional degrees of freedom related to scalar fields and curvature invariants. The latter are usually interpreted as generalized {\\it geometrical fluids} that differ in meaning with respect to the matter fluids generally considered as sources of the field equations. In extended gravity theories the curvature terms are encapsulated in a tensor$H^{ab}$and a coupling$g(\\Psi^i)$that can be recast as effective Einstein field equations, with corrections to the energy-momentum tensor of matter. The formal validity of standard energy inequalities does not assure basic requirements such as the attractive nature of gravity, so we argue that the energy conditions have to be considered in a wider sense. 15. Cosmological constraints on the generalized holographic dark energy CERN Document Server Lu, Jianbo; Wu, Yabo; Wang, Tianqiang 2012-01-01 We use the Markov ChainMonte Carlo method to investigate global constraints on the generalized holographic (GH) dark energy with flat and non-flat universe from the current observed data: the Union2 dataset of type supernovae Ia (SNIa), high-redshift Gamma-Ray Bursts (GRBs), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. The most stringent constraints on the GH model parameter are obtained. In addition, it is found that the equation of state for this generalized holographic dark energy can cross over the phantom boundary wde =-1. 16. High energy collisions of particles inside ergosphere: general approach CERN Document Server Zaslavskii, O B 2013-01-01 We show that recent observation made in Grib and Pavlov, arXiv:1301.0698 for the Kerr black hole is valid in the general case of rotating axially symmetric metric. Namely, collision of two particles in the ergosphere leads to indefinite growth of the energy in the centre of mass frame, provided the angular momentum of one of two particles is negative and increases without limit for a fixed energy at infinity. General approach enabled us to elucidate, why the role of the ergosphere in this process is crucial. 17. Paul Scherrer Institut Scientific Report 2003. Volume V: General Energy Energy Technology Data Exchange (ETDEWEB) Wokaun, Alexander; Daum, Christina (eds.) 2004-03-01 Research at PSI comprises all aspects of human energy use, with the ultimate goal of promoting development towards a sustainable energy supply system. In the General Energy Research Department, technologies are being advanced for the utilization of renewable energy sources, low-loss energy storage, efficient conversion, and low emission energy use. Experimental and model-based assessment of these emissions forms the basis of a comprehensive assessment of economic, ecological and environmental consequences, for both present and future energy supply systems. The research program of the department is centered around 1) development, use, and characterisation of catalysts for energy technologies in many different fields, like e.g. the partial oxidation of methanol for hydrogen production, the processing of methane by catalytic combustion and reforming; 2) use of concentrated solar radiation to induce chemical conversions, thereby producing energy carriers; 3) development of efficient, less polluting combustion engines and burners by advancing the detailed understanding of reaction mechanisms and combustion pathways; 4) research and development of low temperature polymer electrolyte fuel cells, novel batteries and capacitors, with applications envisaged for electric vehicles, photovoltaics and on-site load leveling; 5) experimental and model based research concerning transportation and chemistry of atmospheric trace gases related to anthropogenic energy transformations. Progress in 2000 in these topical areas is described in this report. A list of scientific publications in 2002 is also provided. 18. Paul Scherrer Institut Scientific Report 2001. Volume V: General Energy Energy Technology Data Exchange (ETDEWEB) Wokaun, Alexander; Daum, Christina (eds.) 2002-03-01 Research at PSI comprises all aspects of human energy use, with the ultimate goal of promoting development towards a sustainable energy supply system. In the General Energy Research Department, technologies are being advanced for the utilization of renewable energy sources, low-loss energy storage, efficient conversion, and low emission energy use. Experimental and model-based assessment of these emissions forms the basis of a comprehensive assessment of economic, ecological and environmental consequences, for both present and future energy supply systems. The research program of the department is centered around 1) development, use, and characterisation of catalysts for energy technologies in many different fields, like e.g. the partial oxidation of methanol for hydrogen production, the processing of methane by catalytic combustion and reforming; 2) use of concentrated solar radiation to induce chemical conversions, thereby producing energy carriers; 3) development of efficient, less polluting combustion engines and burners by advancing the detailed understanding of reaction mechanisms and combustion pathways; 4) research and development of low temperature polymer electrolyte fuel cells, novel batteries and capacitors, with applications envisaged for electric vehicles, photovoltaics and on-site load leveling; 5) experimental and model based research concerning transportation and chemistry of atmospheric trace gases related to anthropogenic energy transformations. Progress in 2000 in these topical areas is described in this report. A list of scientific publications in 2001 is also provided. 19. Paul Scherrer Institute Scientific Report 2000. Volume V: General Energy Energy Technology Data Exchange (ETDEWEB) Daum, Christina; Leuenberger, Jakob [eds. 2001-03-01 Research at PSI comprises all aspects of human energy use, with the ultimate goal of promoting development towards a sustainable energy supply system. In the General Energy Research Department, technologies are being advanced for the utilization of renewable energy sources, low-loss energy storage, efficient conversion, and low emission energy use. Experimental and model-based assessment of these emissions forms the basis of a comprehensive assessment of economic, ecological and environmental consequences, for both present and future energy supply systems. The research program of the department is centered around (1) development, use, and characterisation of catalysts for energy technologies in many different fields, like e.g. the partial oxidation of methanol for hydrogen production, the processing of methane by catalytic combustion and reforming; (2) use of concentrated solar radiation to induce chemical conversions, thereby producing energy carriers; (3) development of efficient, less polluting combustion engines and burners by advancing the detailed understanding of reaction mechanisms and combustion pathways; (4) research and development of low temperature polymer electrolyte fuel cells, novel batteries and capacitors, with applications envisaged for electric vehicles, photovoltaics and on-site load leveling; (5) experimental and model based research concerning transportation and chemistry of atmospheric trace gases related to anthropogenic energy transformations. Progress in 2000 in these topical areas is described in this report. A list of scientific publications in 2000 is also provided. 20. General business model patterns for Local Energy Management concepts Directory of Open Access Journals (Sweden) Emanuele eFacchinetti 2016-03-01 Full Text Available The transition towards a more sustainable global energy system, significantly relying on renewable energies and decentralized energy systems, requires a deep reorganization of the energy sector. The way how energy services are generated, delivered and traded is expected to be very different in the coming years. Business model innovation is recognized as a key driver for the successful implementation of the energy turnaround. This work contributes to this topic by introducing a heuristic methodology easing the identification of general business model patterns best suited for Local Energy Management concepts such as Energy Hubs. A conceptual framework characterizing the Local Energy Management business model solution space is developed. Three reference business model patterns providing orientation across the defined solution space are identified, analyzed and compared. Through a market review a number of successfully implemented innovative business models have been analyzed and allocated within the defined solution space. The outcomes of this work offer to potential stakeholders a starting point and guidelines for the business model innovation process, as well as insights for policy makers on challenges and opportunities related to Local Energy Management concepts. 1. Paul Scherrer Institut Scientific Report 2004. Volume V: General Energy Energy Technology Data Exchange (ETDEWEB) Wokaun, Alexander; Daum, Christina (eds.) 2005-03-01 Research at PSI comprises all aspects of human energy use, with the ultimate goal of promoting development towards a sustainable energy supply system. In the General Energy Research Department, technologies are being advanced for the utilization of renewable energy sources, low-loss energy storage, efficient conversion, and low emission energy use. Experimental and model-based assessment of these emissions forms the basis of a comprehensive assessment of economic, ecological and environmental consequences, for both present and future energy supply systems. The research program of the department is centered around 1) development, use, and characterisation of catalysts for energy technologies in many different fields, like e.g. the partial oxidation of methanol for hydrogen production, the processing of methane by catalytic combustion and reforming; 2) use of concentrated solar radiation to induce chemical conversions, thereby producing energy carriers; 3) development of efficient, less polluting combustion engines and burners by advancing the detailed understanding of reaction mechanisms and combustion pathways; 4) research and development of low temperature polymer electrolyte fuel cells, novel batteries and capacitors, with applications envisaged for electric vehicles, photovoltaics and on-site load leveling; 5) experimental and model based research concerning transportation and chemistry of atmospheric trace gases related to anthropogenic energy transformations. Progress in 2000 in these topical areas is described in this report. A list of scientific publications in 2002 is also provided. 2. Paul Scherrer Institut Scientific Report 2002. Volume V: General Energy Energy Technology Data Exchange (ETDEWEB) Wokaun, Alexander; Daum, Christina (eds.) 2003-03-01 Research at PSI comprises all aspects of human energy use, with the ultimate goal of promoting development towards a sustainable energy supply system. In the General Energy Research Department, technologies are being advanced for the utilization of renewable energy sources, low-loss energy storage, efficient conversion, and low emission energy use. Experimental and model-based assessment of these emissions forms the basis of a comprehensive assessment of economic, ecological and environmental consequences, for both present and future energy supply systems. The research program of the department is centered around 1) development, use, and characterisation of catalysts for energy technologies in many different fields, like e.g. the partial oxidation of methanol for hydrogen production, the processing of methane by catalytic combustion and reforming; 2) use of concentrated solar radiation to induce chemical conversions, thereby producing energy carriers; 3) development of efficient, less polluting combustion engines and burners by advancing the detailed understanding of reaction mechanisms and combustion pathways; 4) research and development of low temperature polymer electrolyte fuel cells, novel batteries and capacitors, with applications envisaged for electric vehicles, photovoltaics and on-site load leveling; 5) experimental and model based research concerning transportation and chemistry of atmospheric trace gases related to anthropogenic energy transformations. Progress in 2000 in these topical areas is described in this report. A list of scientific publications in 2002 is also provided. 3. Paul Scherrer Institute Scientific Report 2000. Volume V: General Energy Energy Technology Data Exchange (ETDEWEB) Daum, Christina; Leuenberger, Jakob [eds. 2001-07-01 Research at PSI comprises all aspects of human energy use, with the ultimate goal of promoting development towards a sustainable energy supply system. In the General Energy Research Department, technologies are being advanced for the utilization of renewable energy sources, low-loss energy storage, efficient conversion, and low emission energy use. Experimental and model-based assessment of these emissions forms the basis of a comprehensive assessment of economic, ecological and environmental consequences, for both present and future energy supply systems. The research program of the department is centered around 1) development, use, and characterisation of catalysts for energy technologies in many different fields, like e.g. the partial oxidation of methanol for hydrogen production, the processing of methane by catalytic combustion and reforming; 2) use of concentrated solar radiation to induce chemical conversions, thereby producing energy carriers; 3) development of efficient, less polluting combustion engines and burners by advancing the detailed understanding of reaction mechanisms and combustion pathways; 4) research and development of low temperature polymer electrolyte fuel cells, novel batteries and capacitors, with applications envisaged for electric vehicles, photovoltaics and on-site load leveling; 5) experimental and model based research concerning transportation and chemistry of atmospheric trace gases related to anthropogenic energy transformations. Progress in 2000 in these topical areas is described in this report. A list of scientific publications in 2000 is also provided. 4. Generalized Lorentz invariance with an invariant energy scale CERN Document Server Magueijo, J; Magueijo, Joao; Smolin, Lee 2003-01-01 The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a non-linear action of the Lorentz transformations on momentum space. Several examples are discussed in which the speed of light varies with energy and elementary particles have a maximum momenta and/or energy. Energy and momentum conservation are suitably generalized and a proposal is made for how the new transformation laws apply to composite systems. We then use these results to explain the ultra high energy cosmic ray anomaly and we find a form of the theory that explains the anomaly, and leads also to a maximum momentum and a speed of light that diverges with energy. We finally propose that the spatial coordinates be identified as the generators of translation in Minkowski spacetime. In some examples this leads to a commutative geometry, but with an energy dependent Planck constant. 5. Exploring transition pathway and free-energy profile of large-scale protein conformational change by combining normal mode analysis and umbrella sampling molecular dynamics. Science.gov (United States) Wang, Jinan; Shao, Qiang; Xu, Zhijian; Liu, Yingtao; Yang, Zhuo; Cossins, Benjamin P; Jiang, Hualiang; Chen, Kaixian; Shi, Jiye; Zhu, Weiliang 2014-01-09 Large-scale conformational changes of proteins are usually associated with the binding of ligands. Because the conformational changes are often related to the biological functions of proteins, understanding the molecular mechanisms of these motions and the effects of ligand binding becomes very necessary. In the present study, we use the combination of normal-mode analysis and umbrella sampling molecular dynamics simulation to delineate the atomically detailed conformational transition pathways and the associated free-energy landscapes for three well-known protein systems, viz., adenylate kinase (AdK), calmodulin (CaM), and p38α kinase in the absence and presence of respective ligands. For each protein under study, the transient conformations along the conformational transition pathway and thermodynamic observables are in agreement with experimentally and computationally determined ones. The calculated free-energy profiles reveal that AdK and CaM are intrinsically flexible in structures without obvious energy barrier, and their ligand binding shifts the equilibrium from the ligand-free to ligand-bound conformation (population shift mechanism). In contrast, the ligand binding to p38α leads to a large change in free-energy barrier (ΔΔG ≈ 7 kcal/mol), promoting the transition from DFG-in to DFG-out conformation (induced fit mechanism). Moreover, the effect of the protonation of D168 on the conformational change of p38α is also studied, which reduces the free-energy difference between the two functional states of p38α and thus further facilitates the conformational interconversion. Therefore, the present study suggests that the detailed mechanism of ligand binding and the associated conformational transition is not uniform for all kinds of proteins but correlated to their respective biological functions. 6. Conformational selection through electrostatics: Free energy simulations of GTP and GDP binding to archaeal initiation factor 2. Science.gov (United States) Satpati, Priyadarshi; Simonson, Thomas 2012-05-01 Archaeal Initiation Factor 2 is a GTPase involved in protein biosynthesis. In its GTP-bound, "ON" conformation, it binds an initiator tRNA and carries it to the ribosome. In its GDP-bound, "OFF" conformation, it dissociates from tRNA. To understand the specific binding of GTP and GDP and their dependence on the conformational state, molecular dynamics free energy simulations were performed. The ON state specificity was predicted to be weak, with a GTP/GDP binding free energy difference of -1 kcal/mol, favoring GTP. The OFF state specificity is larger, 4 kcal/mol, favoring GDP. The overall effects result from a competition among many interactions in several complexes. To interpret them, we use a simpler, dielectric continuum model. Several effects are robust with respect to the model details. Both nucleotides have a net negative charge, so that removing them from solvent into the binding pocket carries a desolvation penalty, which is large for the ON state, and strongly disfavors GTP binding compared to GDP. Short-range interactions between the additional GTP phosphate group and ionized sidechains in the binding pocket offset most, but not all of the desolvation penalty; more distant groups also contribute significantly, and the switch 1 loop only slightly. The desolvation penalty is lower for the more open, wetter OFF state, and the GTP/GDP difference much smaller. Short-range interactions in the binding pocket and with more distant groups again make a significant contribution. Overall, the simulations help explain how conformational selection is achieved with a single phosphate group. Copyright © 2012 Wiley Periodicals, Inc. 7. The quantum mechanics based on a general kinetic energy CERN Document Server Wei, Yuchuan 2016-01-01 In this paper, we introduce the Schrodinger equation with a general kinetic energy operator. The conservation law is proved and the probability continuity equation is deducted in a general sense. Examples with a Hermitian kinetic energy operator include the standard Schrodinger equation, the relativistic Schrodinger equation, the fractional Schrodinger equation, the Dirac equation, and the deformed Schrodinger equation. We reveal that the Klein-Gordon equation has a hidden non-Hermitian kinetic energy operator. The probability continuity equation with sources indicates that there exists a different way of probability transportation, which is probability teleportation. An average formula is deducted from the relativistic Schrodinger equation, the Dirac equation, and the K-G equation. 8. Generalized energy conditions in Extended Theories of Gravity CERN Document Server Capozziello, Salvatore; Mimoso, José P 2014-01-01 Theories of physics can be considered viable if the initial value problem and the energy conditions are formulated self-consistently. The former allow a uniquely determined dynamical evolution of the system, and the latter guarantee that causality is preserved and that "plausible" physical sources have been considered. In this work, we consider the further degrees of freedom related to curvature invariants and scalar fields in Extended Theories of Gravity (ETG). These new degrees of freedom can be recast as effective perfect fluids that carry different meanings with respect to the standard matter fluids generally adopted as sources of the field equations. It is thus somewhat misleading to apply the standard general relativistic energy conditions to this effective energy-momentum, as the latter contains the matter content and a geometrical quantity, which arises from the ETG considered. Here, we explore this subtlety, extending on previous work, in particular, to cases with the contracted Bianchi identities wi... 9. Generalized Ensemble Sampling of Enzyme Reaction Free Energy Pathways Science.gov (United States) Wu, Dongsheng; Fajer, Mikolai I.; Cao, Liaoran; Cheng, Xiaolin; Yang, Wei 2016-01-01 Free energy path sampling plays an essential role in computational understanding of chemical reactions, particularly those occurring in enzymatic environments. Among a variety of molecular dynamics simulation approaches, the generalized ensemble sampling strategy is uniquely attractive for the fact that it not only can enhance the sampling of rare chemical events but also can naturally ensure consistent exploration of environmental degrees of freedom. In this review, we plan to provide a tutorial-like tour on an emerging topic: generalized ensemble sampling of enzyme reaction free energy path. The discussion is largely focused on our own studies, particularly ones based on the metadynamics free energy sampling method and the on-the-path random walk path sampling method. We hope that this mini presentation will provide interested practitioners some meaningful guidance for future algorithm formulation and application study. PMID:27498634 10. Generalized trends in the formation energies of perovskite oxides DEFF Research Database (Denmark) Zeng, Zhenhua; Calle-Vallejo, Federico; Mogensen, Mogens Bjerg 2013-01-01 Generalized trends in the formation energies of several families of perovskite oxides (ABO3) and plausible explanations to their existence are provided in this study through a combination of DFT calculations, solid-state physics analyses and simple physical/chemical descriptors. The studied...... systematically on the oxidation state of the A-site cation; and (IV) the trends in formation energies of perovskites with elements from different periods at the B site depend on the oxidation state of A-site cations. Since the energetics of perovskites is shown to be the superposition of the individual...... contributions of their constituent oxides, the trends can be rationalized in terms of A–O and B–O interactions in the ionic crystal. These findings reveal the existence of general systematic trends in the formation energies of perovskites and provide further insight into the role of ion–ion interactions... 11. Cosmological General Relativity With Scale Factor and Dark Energy CERN Document Server Oliveira, Firmin J 2014-01-01 In this paper the four-dimensional space-velocity Cosmological General Relativity of Carmeli is developed by a general solution to the Einstein field equations. The metric is given in the Tolman form and the vacuum mass density is included in the energy-momentum tensor. The scale factor redshift equation is obtained, forming the basis for deriving the various redshift-distance relations of cosmological analysis. A linear equation of state dependent on the scale factor is assumed to account for the effects of an evolving dark energy in the expansion of the universe. Modeling simulations are provided for a few combinations of mass density, vacuum density and state parameter values over a sample of high redshift SNe Ia data. Also, the Carmeli cosmological model is derived as a special case of the general solution. 12. General-equilibrium approach to energy/environmental economic analysis Energy Technology Data Exchange (ETDEWEB) Groncki, P J 1978-08-01 This paper presents a brief critique of the use of fixed-coefficient input-output models for use in energy/environmental modeling systems, a shortcoming of input-output models that has been often been noted. Then, given the existence of aggregate, general-equilibrium, variable-coefficient growth models, a methodology is presented for using this information to adjust a recent disaggregated input-output table. This methodology takes into account all of the general-equilibrium aspects of the aggregate model in making the changes in the disaggregate model. The use of various weighting schemes and the implicit technological change biases they embody are examined. The methodology is being tested on historical tables for the United States, and preliminary results are discussed. This methodology's ability to fully capture the general-equilibrium nature of the economy should enhance the usefulness of input-output models in energy/environmental modeling systems. 13. A big bounce, slow-roll inflation and dark energy from conformal gravity CERN Document Server Gegenberg, Jack; Seahra, Sanjeev S 2016-01-01 We examine the cosmological sector of a gauge theory of gravity based on the SO(4,2) conformal group of Minkowski space. We allow for conventional matter coupled to the spacetime metric as well as matter coupled to the field that gauges special conformal transformations. An effective cosmological constant is generated dynamically via solution of the equations of motion, and this allows us to recover the late time acceleration of the universe. Furthermore, gravitational fields sourced by ordinary cosmological matter (i.e. dust and radiation) are significantly weakened in the very early universe, which has the effect of replacing the big bang with a big bounce. Finally, we find that this bounce is followed by a period of nearly-exponential slow roll inflation that can last long enough to explain the large scale homogeneity of the cosmic microwave background. 14. Extracting black-hole's rotational energy: the generalized Penrose process CERN Document Server Lasota, J -P; Abramowicz, M; Tchekhovskoy, A; Narayan, R 2014-01-01 In the case involving particles the necessary and sufficient condition for the Penrose process to extract energy from a rotating black hole is absorption of particles with negative energies and angular momenta. No torque at the black hole horizon occurs. In this article we consider the case of arbitrary fields or matter described by an unspecified, general energy-momentum tensor and show that the necessary and sufficient condition for extraction of black-hole's rotational energy is analogous to that in mechanical Penrose process: absorption of negative energy and negative angular momentum. We also show that a necessary condition for the Penrose process to occur is for the Noether current (the conserved energy-momentum density vector) to be spacelike or past-directed (timelike or null) on some part of the horizon. In the particle case our general criterion for the occurrence of a Penrose process reproduces the standard result. In the case of relativistic jet-producing "magnetically arrested disks" we show that... 15. High Energy Physics Signatures from Inflation and Conformal Symmetry of de Sitter CERN Document Server Kehagias, Alex 2015-01-01 During inflation, the geometry of spacetime is described by a (quasi-)de Sitter phase. Inflationary observables are determined by the underlying (softly broken) de Sitter isometry group SO(1, 4) which acts like a conformal group on R^3: when the fluctuations are on super-Hubble scales, the correlators of the scalar fields are constrained by conformal invariance. Heavy fields with mass m larger than the Hubble rate H correspond to operators with imaginary dimensions in the dual Euclidean three-dimensional conformal field theory. By making use of the dS/CFT correspondence we show that, besides the Boltzmann suppression expected from the thermal properties of de Sitter space, the generic effect of heavy fields in the inflationary correlators of the light fields is to introduce power-law suppressed corrections of the form O(H^2/m^2). This can be seen, for instance, at the level of the four-point correlator for which we provide the correction due to a massive scalar field exchange. 16. Superspace conformal field theory Energy Technology Data Exchange (ETDEWEB) Quella, Thomas [Koeln Univ. (Germany). Inst. fuer Theoretische Physik; Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2013-07-15 Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory. 17. Energy-Dependent Fission Q Values Generalized for All Actinides Energy Technology Data Exchange (ETDEWEB) Vogt, R 2008-09-25 We generalize Madland's parameterization of the energy release in fission to obtain the dependence of the fission Q values on incident neutron energy, E{sub n}, for all major and minor actinides. These Q(E{sub n}) parameterizations are included in the ENDL2008 release. This paper describes calculations of energy-dependent fission Q values based on parameterizations of the prompt energy release in fission [1], developed by Madland [1] to describe the prompt energy release in neutron-induced fission of {sup 235}U, {sup 238}U, and {sup 239}Pu. The energy release is then related to the energy deposited during fission so that experimentally measurable quantities can be used to obtain the Q values. A discussion of these specific parameterizations and their implementation in the processing code for Monte Carlo neutron transport, MCFGEN, [2] is described in Ref. [3]. We extend this model to describe Q(E) for all actinides, major and minor, in the Evaluated Nuclear Data Library (ENDL) 2008 release, ENDL2008. 18. Generalized Energy-Dependent Q Values for Fission Energy Technology Data Exchange (ETDEWEB) Vogt, R 2010-03-31 We extend Madland's parameterization of the energy release in fission to obtain the dependence of the fission Q value for major and minor actinides on the incident neutron energies in the range 0 {le} E{sub n} {le} 20 MeV. Our parameterization is based on the actinide evaluations recommended for the ENDF/B-VII.1 release. This paper describes the calculation of energydependent fission Q values based on the calculation of the prompt energy release in fission by Madland. This calculation was adopted for use in the LLNL ENDL database and then generalized to obtain the prompt fission energy release for all actinides. Here the calculation is further generalized to the total energy release in fission. There are several stages in a fission event, depending on the time scale. Neutrons and gammas may be emitted at any time during the fission event.While our discussion here is focussed on compound nucleus creation by an incident neutron, similar parameterizations could be obtained for incident gammas or spontaneous fission. 19. Oscillatory Universe, dark energy equation of state and general relativity CERN Document Server Ghosh, Partha Pratim; Usmani, A A; Mukhopadhyay, Utpal 2012-01-01 The concept of oscillatory Universe appears to be realistic and buried in the dynamic dark energy equation of state. We explore its evolutionary history under the frame work of general relativity. We observe that oscillations do not go unnoticed with such an equation of state and that their effects persist later on in cosmic evolution. The classical' general relativity seems to retain the past history of oscillatory Universe in the form of increasing scale factor as the classical thermodynamics retains this history in the form of increasing cosmological entropy. 20. Disulphide trapping of an in vivo energy-dependent conformation of Escherichia coli TonB protein. Science.gov (United States) Ghosh, Joydeep; Postle, Kathleen 2005-01-01 In Escherichia coli, the TonB system transduces the protonmotive force (pmf) of the cytoplasmic membrane to support a variety of transport events across the outer membrane. Cytoplasmic membrane proteins ExbB and ExbD appear to harvest pmf and transduce it to TonB. Experimental evidence suggests that TonB shuttles to the outer membrane, apparently to deliver conformationally stored potential energy to outer membrane transporters. In the most recent model, discharged TonB is then recycled to the cytoplasmic membrane to be re-energized by the energy coupling proteins, ExbB/D. It has been suggested that the carboxy-terminal 75 amino acids of active TonB could be represented by the rigid, strand-exchanged, dimeric crystal structure of the corresponding fragment. In contrast, recent genetic studies of alanine substitutions have suggested instead that in vivo the carboxy-terminus of intact TonB is dynamic and flexible. The biochemical studies presented here confirm and extend those results by demonstrating that individual cys substitution at aromatic residues in one monomeric subunit can form spontaneous dimers in vivo with the identical residue in the other monomeric subunit. Two energized TonBs appear to form a single cluster of 8-10 aromatic amino acids, including those found at opposite ends of the crystal structure. The aromatic cluster requires both the amino-terminal energy coupling domain of TonB, and ExbB/D (and cross-talk analogues TolQ/R) for in vivo formation. The large aromatic cluster is detected in cytoplasmic membrane-, but not outer membrane-associated TonB. Consistent with those observations, the aromatic cluster can form in the first half of the energy transduction cycle, before release of conformationally stored potential energy to ligand-loaded outer membrane transporters. The model that emerges is one in which, after input of pmf mediated through ExbB/D and the TonB transmembrane domain, the TonB carboxy-terminus can form a meta-stable high-energy 1. Limits of the energy-momentum tensor in general relativity CERN Document Server Paiva, F M; Hall, G S; MacCallum, M A H; Paiva, Filipe M.; Reboucas, Marcelo J.; Hall, Graham S.; Callum, Malcolm A.H. Mac 1998-01-01 A limiting diagram for the Segre classification of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch's work on limits of space-times is also extended. The same argument also justifies part of the procedure for classification of a given spacetime using Cartan scalars. 2. The Generalized Conversion Factor in Einstein's Mass-Energy Equation Directory of Open Access Journals (Sweden) Sharma A. 2008-07-01 Full Text Available Einstein’s September 1905 paper is origin of light energy-mass inter conversion equa- tion ( L = mc 2 and Einstein speculated E = mc 2 from it by simply replacing L by E . From its critical analysis it follows that L = mc 2 is only true under special or ideal conditions. Under general cases the result is L / mc 2 ( E / mc 2 . Conse- quently an alternate equation E = Ac 2 M has been suggested, which implies that energy emitted on annihilation of mass can be equal, less and more than predicted by E = mc 2 . The total kinetic energy of fission fragments of U 235 or Pu 239 is found experimentally 20–60 MeV less than Q -value predicted by mc 2 . The mass of parti- cle Ds (2317 discovered at SLAC, is more than current estimates. In many reactions including chemical reactions E = mc 2 is not confirmed yet, but regarded as true. It implies the conversion factor than c 2 is possible. These phenomena can be explained with help of generalized mass-energy equation E = Ac 2 M . 3. The Generalized Conversion Factor in Einstein's Mass-Energy Equation Directory of Open Access Journals (Sweden) Ajay Sharma 2008-07-01 Full Text Available Einstein's September 1905 paper is origin of light energy-mass inter conversion equation ($L = Delta mc^{2}$and Einstein speculated$E = Delta mc^{2}$from it by simply replacing$L$by$E$. From its critical analysis it follows that$L = Delta mc^{2}$is only true under special or ideal conditions. Under general cases the result is$L propto Delta mc^{2}$($E propto Delta mc^{2}$. Consequently an alternate equation$Delta E = A ub c^{2}Delta M$has been suggested, which implies that energy emitted on annihilation of mass can be equal, less and more than predicted by$Delta E = Delta mc^{2}$. The total kinetic energy of fission fragments of U-235 or Pu-239 is found experimentally 20-60 MeV less than Q-value predicted by$Delta mc^{2}$. The mass of particle Ds (2317 discovered at SLAC, is more than current estimates. In many reactions including chemical reactions$E = Delta mc^{2}$is not confirmed yet, but regarded as true. It implies the conversion factor than$c^{2}$is possible. These phenomena can be explained with help of generalized mass-energy equation$Delta E = A ub c^{2}Delta M$. 4. Generalized trends in the formation energies of perovskite oxides. Science.gov (United States) Zeng, ZhenHua; Calle-Vallejo, Federico; Mogensen, Mogens B; Rossmeisl, Jan 2013-05-28 Generalized trends in the formation energies of several families of perovskite oxides (ABO3) and plausible explanations to their existence are provided in this study through a combination of DFT calculations, solid-state physics analyses and simple physical/chemical descriptors. The studied elements at the A site of perovskites comprise rare-earth, alkaline-earth and alkaline metals, whereas 3d and 5d metals were studied at the B site. We also include ReO3-type compounds, which have the same crystal structure of cubic ABO3 perovskites except without A-site elements. From the observations we extract the following four conclusions for the perovskites studied in the present paper: for a given cation at the B site, (I) perovskites with cations of identical oxidation state at the A site possess close formation energies; and (II) perovskites with cations of different oxidation states at the A site usually have quite different but ordered formation energies. On the other hand, for a given A-site cation, (III) the formation energies of perovskites vary linearly with respect to the atomic number of the elements at the B site within the same period of the periodic table, and the slopes depend systematically on the oxidation state of the A-site cation; and (IV) the trends in formation energies of perovskites with elements from different periods at the B site depend on the oxidation state of A-site cations. Since the energetics of perovskites is shown to be the superposition of the individual contributions of their constituent oxides, the trends can be rationalized in terms of A-O and B-O interactions in the ionic crystal. These findings reveal the existence of general systematic trends in the formation energies of perovskites and provide further insight into the role of ion-ion interactions in the properties of ternary compounds. 5. GENERALIZED ENERGY CONSERVATION AND UNSTABLE PERTURBATION PROPERTY IN BAROTROPIC VORTEX Institute of Scientific and Technical Information of China (English) HUANG Hong; ZHANG Ming 2006-01-01 Based on a barotropic vortex model, generalized energy-conserving equation was derived and two necessary conditions of basic flow destabilization are gained. These conditions correspond to generalized barotropic instability and super speed instability. They are instabilities of vortex and gravity inertial wave respectively. In order to relate to practical situation, a barotropic vortex was analyzed, the basic flow of which is similar to lower level basic wind field of tropical cyclones and the maximum wind radius of which is 500 km.The results show that generalized barotropic instability depending upon the radial gradient of relative vorticity can appear in this vortex. It can be concluded that unstable vortex Rossby wave may appear in barotropic vortex. 6. A general end point free energy calculation method based on microscopic configurational space coarse-graining CERN Document Server Tian, Pu 2015-01-01 Free energy is arguably the most important thermodynamic property for physical systems. Despite the fact that free energy is a state function, presently available rigorous methodologies, such as those based on thermodynamic integration (TI) or non-equilibrium work (NEW) analysis, involve energetic calculations on path(s) connecting the starting and the end macrostates. Meanwhile, presently widely utilized approximate end-point free energy methods lack rigorous treatment of conformational variation within end macrostates, and are consequently not sufficiently reliable. Here we present an alternative and rigorous end point free energy calculation formulation based on microscopic configurational space coarse graining, where the configurational space of a high dimensional system is divided into a large number of sufficiently fine and uniform elements, which were termed conformers. It was found that change of free energy is essentially decided by change of the number of conformers, with an error term that accounts... 7. New potentials for conformal mechanics CERN Document Server Papadopoulos, G 2012-01-01 We show that V=\\alpha x^2+\\beta x^{-2} arises as a potential of 1-dimensional conformal theories. This class of conformal models includes the DFF model \\alpha=0 and the harmonic oscillator \\beta=0. The construction is based on a different embedding of the conformal symmetry group into the time re-parameterizations from that of the DFF model and its generalizations. Depending on the range of the couplings$\\alpha, \\beta$, these models can have a ground state and a well-defined energy spectrum, and exhibit either a$SL(2,\\bR)$or a SO(3) conformal symmetry. The latter group can also be embedded in Diff(S^1). We also present several generalizations of these models which include the Calogero models with harmonic oscillator couplings and non-linear models with suitable metric and potential couplings. In addition, we give the conditions on the couplings for a class of gaugetheories to admit a SL(2,\\bR) or SO(3) conformal symmetry. We present examples of such systems with general gauge groups and global symmetries t... 8. A generalized recipe to construct elementary or multi-step reaction paths via a stochastic formulation: Application to the conformational change in noble gas clusters Energy Technology Data Exchange (ETDEWEB) Talukder, Srijeeta; Sen, Shrabani [Department of Chemistry, University of Calcutta, 92 A P C Road, Kolkata 700 009 (India); Sharma, Rahul [Department of Chemistry, St. Xavier’s College, 30 Mother Teresa Sarani, Kolkata 700 016 (India); Banik, Suman K., E-mail: [email protected] [Department of Chemistry, Bose Institute, 93/1 A P C Road, Kolkata 700 009 (India); Chaudhury, Pinaki, E-mail: [email protected] [Department of Chemistry, University of Calcutta, 92 A P C Road, Kolkata 700 009 (India) 2014-03-18 Highlights: • We demonstrate a general strategy to map out reaction paths irrespective of the number of kinetic steps involved. • The objective function proposed does not need the information of gradient norm and eigenvalue of Hessian matrix explicitly. • A stochastic optimizer Simulated Annealing is used in searching reaction path. • The strategy is applied in mapping out the path for conformational changes in pure Ar clusters and Ar{sub N}Xe mixed clusters. - abstract: In this paper we demonstrate a general strategy to map out reaction paths irrespective of the number of kinetic steps required to bring about the change. i.e., whether the transformation takes place in a single step or in multiple steps with the appearance of intermediates. The objective function proposed is unique and works equally well for a concerted or a multiple step pathway. As the objective function proposed does not explicitly involves the calculation of the gradient of the potential energy function or the eigenvalues of the Hessian Matrix during the iterative process, the calculation is computationally economical. To map out the reaction path, we cast the entire problem as one of optimization and the solution is done with the use of the stochastic optimizer Simulated Annealing. The formalism is tested on Argon clusters (Ar{sub N}) and Argon clusters singly doped with Xenon (Ar{sub N-1}Xe). The size of the systems for which the method is applied ranges from N=7-25, where N is the total number of atoms in the cluster. We also test the results obtained by us by comparing with an established gradient only method. Moreover to demonstrate that our strategy can overcome the standard problems of drag method, we apply our strategy to a two dimensional LEPS + harmonic oscillator Potential to locate the TS, in which standard drag method has been seen to encounter problems. 9. Conformational characteristics of dimeric subunits of RNA from energy minimization studies. Mixed sugar-puckered ApG, ApU, CpG, and CpU. Science.gov (United States) Thiyagarajan, P; Ponnuswamy, P K 1981-09-01 Following the procedure described in the preceding article, the low energy conformations located for the four dimeric subunits of RNA, ApG, ApU, CpG, and CpU are presented. The A-RNA type and Watson-Crick type helical conformations and a number of different kinds of loop promoting ones were identified as low energy in all the units. The 3E-3E and 3E-2E pucker sequences are found to be more or less equally preferred; the 2E-2E sequence is occasionally preferred, while the 2E-3E is highly prohibited in all the units. A conformation similar to the one observed in the drug-dinucleoside monophosphate complex crystals becomes a low energy case only for the CpG unit. The low energy conformations obtained for the four model units were used to assess the stability of the conformational states of the dinucleotide segments in the four crystal models of the tRNAPhe molecule. Information on the occurrence of the less preferred sugar-pucker sequences in the various loop regions in the tRNAPhe molecule has been obtained. A detailed comparison of the conformational characteristics of DNA and RNA subunits at the dimeric level is presented on the basis of the results. 10. Generalized Ghost Dark Energy with Non-Linear Interaction CERN Document Server Ebrahimi, E; Mehrabi, A; Movahed, S M S 2016-01-01 In this paper we investigate ghost dark energy model in the presence of non-linear interaction between dark energy and dark matter. The functional form of dark energy density in the generalized ghost dark energy (GGDE) model is$\\rho_D\\equiv f(H, H^2)$with coefficient of$H^2$represented by$\\zeta$and the model contains three free parameters as$\\Omega_D, \\zeta$and$b^2$(the coupling coefficient of interactions). We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state, deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model. To compare the interacting GGDE model with observational data sets, we use more recent observational outcomes, namely SNIa, gamma-ray bursts, baryonic acoustic oscillation and the most relevant CMB parameters including, the position of acoustic peaks, shift parameters and redshift to recombination. For GGDE with the first non-linear interaction, the j... 11. Wang-Landau molecular dynamics technique to search for low-energy conformational space of proteins CERN Document Server Nagasima, Takehiro; Mitsui, Takashi; Nishikawa, Ken-Ichi 2007-01-01 Multicanonical molecular dynamics (MD) is a powerful technique for sampling conformations on rugged potential surfaces such as protein. However, it is notoriously difficult to estimate the multicanonical temperature effectively. Wang and Landau developed a convenient method for estimating the density of states based on a multicanonical Monte Carlo method. In their method, the density of states is calculated autonomously during a simulation. In this paper we develop a set of techniques to effectively apply the Wang-Landau method to MD simulations. In the multicanonical MD, the estimation of the derivative of the density of states is critical. In order to estimate it accurately, we devise two original improvements. First, the correction for the density of states is made smooth by using the Gaussian distribution obtained by a short canonical simulation. Second, an approximation is applied to the derivative, which is based on the Gaussian distribution and the multiple weighted histogram technique. A test of this ... 12. 18 CFR 153.21 - Conformity with requirements. Science.gov (United States) 2010-04-01 ... 18 Conservation of Power and Water Resources 1 2010-04-01 2010-04-01 false Conformity with requirements. 153.21 Section 153.21 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY... Requirements § 153.21 Conformity with requirements. (a) General Rule. Applications under subparts B and C... 13. Conformational Dynamics and Binding Free Energies of Inhibitors of BACE-1: From the Perspective of Protonation Equilibria. Directory of Open Access Journals (Sweden) M Olivia Kim 2015-10-01 Full Text Available BACE-1 is the β-secretase responsible for the initial amyloidogenesis in Alzheimer's disease, catalyzing hydrolytic cleavage of substrate in a pH-sensitive manner. The catalytic mechanism of BACE-1 requires water-mediated proton transfer from aspartyl dyad to the substrate, as well as structural flexibility in the flap region. Thus, the coupling of protonation and conformational equilibria is essential to a full in silico characterization of BACE-1. In this work, we perform constant pH replica exchange molecular dynamics simulations on both apo BACE-1 and five BACE-1-inhibitor complexes to examine the effect of pH on dynamics and inhibitor binding properties of BACE-1. In our simulations, we find that solution pH controls the conformational flexibility of apo BACE-1, whereas bound inhibitors largely limit the motions of the holo enzyme at all levels of pH. The microscopic pKa values of titratable residues in BACE-1 including its aspartyl dyad are computed and compared between apo and inhibitor-bound states. Changes in protonation between the apo and holo forms suggest a thermodynamic linkage between binding of inhibitors and protons localized at the dyad. Utilizing our recently developed computational protocol applying the binding polynomial formalism to the constant pH molecular dynamics (CpHMD framework, we are able to obtain the pH-dependent binding free energy profiles for various BACE-1-inhibitor complexes. Our results highlight the importance of correctly addressing the binding-induced protonation changes in protein-ligand systems where binding accompanies a net proton transfer. This work comprises the first application of our CpHMD-based free energy computational method to protein-ligand complexes and illustrates the value of CpHMD as an all-purpose tool for obtaining pH-dependent dynamics and binding free energies of biological systems. 14. Generalized holographic Ricci dark energy and generalized second law of thermodynamics in Bianchi Type I universe CERN Document Server Li, En-Kun; Geng, Jin-Ling; Duan, Peng-Fei 2016-01-01 Generalized second law of thermodynamics in the Bianchi type I universe with the generalized holographic Ricci dark energy model is studied in this paper. The behavior of dark energy's equation of state parameter indicates that it is matter-like in the early time of the universe but phantom-like in the future. By analysing the evolution of the deviations of state parameter and the total pressure of the universe, we find that for an anisotropic Bianchi type I universe, it transits from a high anisotropy stage to a more homogeneous stage in the near past. Using the normal entropy given by Gibbs' law of thermodynamics, it is proved that the generalized second law of thermodynamics does not always satisfied throughout the history of the universe when we assume the universe is enclosed by the generalized Ricci scalar radius$R_{gr}. It becomes invalid in the near past to the future, and the formation of the galaxies will be helpful in explaining such phenomenon, for that the galaxies's formation is an entropy inc... 15. Energy density and spatial curvature in general relativity Energy Technology Data Exchange (ETDEWEB) Frankel, T.; Galloway, G.J. 1981-04-01 Positive energy density tends to limit the size of space. This effect is studied within several contexts. We obtain sufficient conditions (which involve the energy density in a crucial way) for the compactness of spatial hypersurfaces in space-time. We then obtain some results concerning static or, more generally, stationary space-times. The Schwarzchild solution puts an upper bound on the size of a static spherically symmetric fluid with density bounded from below. We derive a result of roughly the same nature which, however, requires no symmetry and allows for rotation. Also, we show that static or rotating universes with L = 0 require that the density along some spatial geodesic must fall off rapidly with distance from a point. 16. Dissipative generalized Chaplygin gas as phantom dark energy Energy Technology Data Exchange (ETDEWEB) Cruz, Norman [Departamento de Fisica, Facultad de Ciencia, Universidad de Santiago, Casilla 307, Santiago (Chile)]. E-mail: [email protected]; Lepe, Samuel [Instituto de Fisica, Facultad de Ciencias Basicas y Matematicas, Pontificia Universidad Catolica de Valparaiso, Avenida Brasil 2950, Valparaiso (Chile)]. E-mail: [email protected]; Pena, Francisco [Departamento de Ciencias Fisicas, Facultad de Ingenieria, Ciencias y Administracion, Universidad de la Frontera, Avda. Francisco Salazar 01145, Casilla 54-D, Temuco (Chile)]. E-mail: [email protected] 2007-03-15 The generalized Chaplygin gas, characterized by the equation of state p=-A/{rho}{sup {alpha}}, has been considered as a model for dark energy due to its dark-energy-like evolution at late times. When dissipative processes are taken into account, within the framework of the standard Eckart theory of relativistic irreversible thermodynamics, cosmological analytical solutions are found. Using the truncated causal version of the Israel-Stewart formalism, a suitable model was constructed which crosses the w=-1 barrier. The future-singularities encountered in both approaches are of a new type, and not included in the classification presented by Nojiri and Odintsov [S. Nojiri, S.D. Odintsov, Phys. Rev. D 72 (2005) 023003]. 17. Energies and 2'-Hydroxyl Group Orientations of RNA Backbone Conformations. Benchmark CCSD(T)/CBS Database, Electronic Analysis, and Assessment of DFT Methods and MD Simulations. Science.gov (United States) Mládek, Arnošt; Banáš, Pavel; Jurečka, Petr; Otyepka, Michal; Zgarbová, Marie; Šponer, Jiří 2014-01-14 Sugar-phosphate backbone is an electronically complex molecular segment imparting RNA molecules high flexibility and architectonic heterogeneity necessary for their biological functions. The structural variability of RNA molecules is amplified by the presence of the 2'-hydroxyl group, capable of forming multitude of intra- and intermolecular interactions. Bioinformatics studies based on X-ray structure database revealed that RNA backbone samples at least 46 substates known as rotameric families. The present study provides a comprehensive analysis of RNA backbone conformational preferences and 2'-hydroxyl group orientations. First, we create a benchmark database of estimated CCSD(T)/CBS relative energies of all rotameric families and test performance of dispersion-corrected DFT-D3 methods and molecular mechanics in vacuum and in continuum solvent. The performance of the DFT-D3 methods is in general quite satisfactory. The B-LYP-D3 method provides the best trade-off between accuracy and computational demands. B3-LYP-D3 slightly outperforms the new PW6B95-D3 and MPW1B95-D3 and is the second most accurate density functional of the study. The best agreement with CCSD(T)/CBS is provided by DSD-B-LYP-D3 double-hybrid functional, although its large-scale applications may be limited by high computational costs. Molecular mechanics does not reproduce the fine energy differences between the RNA backbone substates. We also demonstrate that the differences in the magnitude of the hyperconjugation effect do not correlate with the energy ranking of the backbone conformations. Further, we investigated the 2'-hydroxyl group orientation preferences. For all families, we conducted a QM and MM hydroxyl group rigid scan in gas phase and solvent. We then carried out set of explicit solvent MD simulations of folded RNAs and analyze 2'-hydroxyl group orientations of different backbone families in MD. The solvent energy profiles determined primarily by the sugar pucker match well with the 18. Generalized average local ionization energy and its representations in terms of Dyson and energy orbitals. Science.gov (United States) Kohut, Sviataslau V; Cuevas-Saavedra, Rogelio; Staroverov, Viktor N 2016-08-21 Ryabinkin and Staroverov [J. Chem. Phys. 141, 084107 (2014)] extended the concept of average local ionization energy (ALIE) to correlated wavefunctions by defining the generalized ALIE as Ī(r)=-∑jλj|fj(r)|(2)/ρ(r), where λj are the eigenvalues of the generalized Fock operator and fj(r) are the corresponding eigenfunctions (energy orbitals). Here we show that one can equivalently express the generalized ALIE as Ī(r)=∑kIk|dk(r)|(2)/ρ(r), where Ik are single-electron removal energies and dk(r) are the corresponding Dyson orbitals. The two expressions for Ī(r) emphasize different physical interpretations of this quantity; their equivalence enables one to calculate the ALIE at any level of ab initio theory without generating the computationally expensive Dyson orbitals. 19. Towards understanding the free and receptor bound conformation of neuropeptide Y by fluorescence resonance energy transfer studies. Science.gov (United States) Haack, Michael; Beck-Sickinger, Annette G 2009-06-01 Despite a considerable sequence identity of the three mammalian hormones of the neuropeptide Y family, namely neuropeptide Y, peptide YY and pancreatic polypeptide, their structure in solution is described to be different. A so-called pancreatic polypeptide-fold has been identified for pancreatic polypeptide, whereas the structure of the N-terminal segment of neuropeptide Y is unknown. This element is important for the binding of neuropeptide Y to two of its relevant receptors, Y(1) and Y(5), but not to the Y(2) receptor subtype. In this study now, three doubly fluorescent-labeled analogs of neuropeptide Y have been synthesized that still bind to the Y(5) receptor with high affinity to investigate the conformation in solution and, for the first time, to probe the conformational changes upon binding of the ligand to its receptor in cell membrane preparations. The results obtained from the fluorescence resonance energy transfer investigations clearly show considerable differences in transfer efficiency that depend both on the solvent as well as on the peptide concentration. However, the studies do not support a pancreatic polypeptide-like folding of neuropeptide Y in the presence of membranes that express the human Y(5) receptor subtype. 20. Some invariant solutions for non-conformal perfect fluid plates in 5-flat form in general relativity Indian Academy of Sciences (India) Mukesh Kumar; Y K Gupta 2010-06-01 A set of six invariant solutions for non-conformal perfect fluid plates in 5-flat form is obtained using one-parametric Lie group of transformations. Out of the six solutions so obtained, three are in implicit form while the remaining three could be expressed explicitly. Each solution describes an accelerating fluid distribution and is new as far as authors are aware. 1. Gravitational Energy-Momentum and Conservation of Energy-Momentum in General Relativity Science.gov (United States) Wu, Zhao-Yan 2016-06-01 Based on a general variational principle, Einstein-Hilbert action and sound facts from geometry, it is shown that the long existing pseudotensor, non-localizability problem of gravitational energy-momentum is a result of mistaking different geometrical, physical objects as one and the same. It is also pointed out that in a curved spacetime, the sum vector of matter energy-momentum over a finite hyper-surface can not be defined. In curvilinear coordinate systems conservation of matter energy-momentum is not the continuity equations for its components. Conservation of matter energy-momentum is the vanishing of the covariant divergence of its density-flux tensor field. Introducing gravitational energy-momentum to save the law of conservation of energy-momentum is unnecessary and improper. After reasonably defining “change of a particle's energy-momentum”, we show that gravitational field does not exchange energy-momentum with particles. And it does not exchange energy-momentum with matter fields either. Therefore, the gravitational field does not carry energy-momentum, it is not a force field and gravity is not a natural force. 2. Conformational Transitions Science.gov (United States) Czerminski, Ryszard; Roitberg, Adrian; Choi, Chyung; Ulitsky, Alexander; Elber, Ron 1991-10-01 on the number of the direct paths between the minima. The influence on the distribution of the barriers and the minima energies is less significant. Calculation of reaction paths in large molecular systems requires new computational techniques. We employed our newly developed reaction path algorithm (SPW) for the study of the B to Z transition in DNA. The SPW (Self Penalty Walk) algorithm is explained in detail. A complex reaction coordinate (the B to Z transition in DNA) is calculated and analyzed. The calculated reaction path is for six basepairs DNA (including all 376 atoms). The path consists of 180° flips of two basepairs from the B DNA conformation to the Z DNA conformation. 3. Anisotropic conjugated polymer chain conformation tailors the energy migration in nanofibers CERN Document Server Camposeo, Andrea; Moffa, Maria; Fasano, Vito; Altamura, Davide; Giannini, Cinzia; Pisignano, Dario; Scholes, Gregory D 2016-01-01 Conjugated polymers are complex multi-chromophore systems, with emission properties strongly dependent on the electronic energy transfer through active sub-units. Although the packing of the conjugated chains in the solid state is known to be a key factor to tailor the electronic energy transfer and the resulting optical properties, most of the current solution-based processing methods do not allow for effectively controlling the molecular order, thus making the full unveiling of energy transfer mechanisms very complex. Here we report on conjugated polymer fibers with tailored internal molecular order, leading to a significant enhancement of the emission quantum yield. Steady state and femtosecond time-resolved polarized spectroscopies evidence that excitation is directed toward those chromophores oriented along the fiber axis, on a typical timescale of picoseconds. These aligned and more extended chromophores, resulting from the high stretching rate and electric field applied during the fiber spinning proces... 4. Rotational Spectroscopy of the Low Energy Conformer of 2-METHYLBUTYRONITRILE and Search for it Toward Sagittarius B2(N2) Science.gov (United States) Müller, Holger S. P.; Wehres, Nadine; Zingsheim, Oliver; Lewen, Frank; Schlemmer, Stephan; Grabow, Jens-Uwe; Garrod, Robin T.; Belloche, Arnaud; Menten, Karl M. 2017-06-01 Quite recently, some of us detected iso-propyl cyanide as the first branched alkyl molecule in space. The identification was made in an ALMA Cycle 0 and 1 molecular line survey of Sagittarius B2(N) at 3 mm. The branched isomer was only slightly less abundant than its straight-chain isomer with a ratio of about 2:5. While initial chemical models favored the branched isomer somewhat, more recent models are able to reproduce the observed ratio. Moreover, the models predicted that among the next longer butyl cyanides (BuCNs) 2-methylbutyronitrile (2-MBN) should be more abundant than both n-BuCN and 3-MBN by factors of around 2, with t-BuCN being almost negligible. With the rotational spectra of t- and n-BuCN studied, we investigated those of 2-MBN and 3-MBN betwen ˜40 and ˜400 GHz by conventional absorption spectroscopy and by chirped-pulse and resonator Fourier transform microwave (FTMW) spectroscopy. The analyses were guided by quantum-chemical calculations. A. Belloche, R. T. Garrod, H. S. P. Müller, and K. M. Menten, Science 345 1584. R. T. Garrod, A. Belloche, H. S. P. Müller, and K. M. Menten, Astron. Astrophys., in press; doi: 10.1051/0004-6361/201630254. With the rotational spectra of t- and n-BuCN studied, we investigated those of 2-MBN and 3-MBN betwen ˜40 and ˜400 GHz by conventional absorption spectroscopy and by chirped-pulse and resonator Fourier transform microwave (FTMW) spectroscopy. The analyses were guided by quantum-chemical calculations. Here we report the analysis of the low-energy conformer of 2-MBN and a search for it in our current ALMA data. Two additional conformers are higher by ˜250 and ˜280 cm^{-1}. The low-energy conformer displays a very rich rotational spectrum because of its great asymmetry (κ ≈ 0.14) and large a- and b-dipole moment components. Accurate ^{14}N quadrupole coupling parameters were obtained from the FTMW spectral recordings. 5. EL JUICIO DE APARIENCIA DE BUEN DERECHO FRENTE A LA IMPARCIALIDAD DEL JUEZ QUE DECRETA MEDIDAS CAUTELARES INNOMINADAS CONFORME EL CODIGO GENERAL DEL PROCESO EN COLOMBIA OpenAIRE Laguado Serrano, Cristian Eduardo; Vargas Buitrago, Jordan Aquiles 2015-01-01 La presente tesis denominada “El juicio de apariencia de buen derecho frente a la imparcialidad del juez que decreta medidas cautelares innominadas conforme el código general del proceso en Colombia”, plantea que a través la reforma del código de procedimiento civil buscando lograr un código general del proceso, al implementar las denominadas medidas cautelares innominadas se establecieron una serie de requisitos que a simple vista son claros y precisos; no obstante, al llevar ... 6. Predicting free energy contributions to the conformational stability of folded proteins from the residue sequence with radial basis function networks Energy Technology Data Exchange (ETDEWEB) Casadio, R.; Fariselli, P.; Vivarelli, F. [Univ. of Bologna (Italy); Compiani, M. [Univ. of Camerino (Italy) 1995-12-31 Radial basis function neural networks are trained on a data base comprising 38 globular proteins of well resolved crystallographic structure and the corresponding free energy contributions to the overall protein stability (as computed partially from crystallographic analysis and partially with multiple regression from experimental thermodynamic data by Ponnuswamy and Gromiha (1994)). Starting from the residue sequence and using as input code the percentage of each residue and the total residue number of the protein, it is found with a cross-validation method that neural networks can optimally predict the free energy contributions due to hydrogen bonds, hydrophobic interactions and the unfolded state. Terms due to electrostatic and disulfide bonding free energies are poorly predicted. This is so also when other input codes, including the percentage of secondary structure type of the protein and/or residue-pair information are used. Furthermore, trained on the computed and/or experimental {Delta}G values of the data base, neural networks predict a conformational stability ranging from about 10 to 20 kcal mol{sup -1} rather independently of the residue sequence, with an average error per protein of about 9 kcal mol{sup -1}. 7. Predicting free energy contributions to the conformational stability of folded proteins from the residue sequence with radial basis function networks. Science.gov (United States) Casadio, R; Compiani, M; Fariselli, P; Vivarelli, F 1995-01-01 Radial basis function neural networks are trained on a data base comprising 38 globular proteins of well resolved crystallographic structure and the corresponding free energy contributions to the overall protein stability (as computed partially from chrystallographic analysis and partially with multiple regression from experimental thermodynamic data by Ponnuswamy and Gromiha (1994)). Starting from the residue sequence and using as input code the percentage of each residue and the total residue number of the protein, it is found with a cross-validation method that neural networks can optimally predict the free energy contributions due to hydrogen bonds, hydrophobic interactions and the unfolded state. Terms due to electrostatic and disulfide bonding free energies are poorly predicted. This is so also when other input codes, including the percentage of secondary structure type of the protein and/or residue-pair information are used. Furthermore, trained on the computed and/or experimental delta G values of the data base, neural networks predict a conformational stability ranging from about 10 to 20 kcal mol-1 rather independently of the residue sequence, with an average error per protein of about 9 kcal mol-1. 8. Supergravitational conformal Galileons Science.gov (United States) Deen, Rehan; Ovrut, Burt 2017-08-01 The worldvolume actions of 3+1 dimensional bosonic branes embedded in a five-dimensional bulk space can lead to important effective field theories, such as the DBI conformal Galileons, and may, when the Null Energy Condition is violated, play an essential role in cosmological theories of the early universe. These include Galileon Genesis and "bouncing" cosmology, where a pre-Big Bang contracting phase bounces smoothly to the presently observed expanding universe. Perhaps the most natural arena for such branes to arise is within the context of superstring and M -theory vacua. Here, not only are branes required for the consistency of the theory, but, in many cases, the exact spectrum of particle physics occurs at low energy. However, such theories have the additional constraint that they must be N = 1 supersymmetric. This motivates us to compute the worldvolume actions of N = 1 supersymmetric three-branes, first in flat superspace and then to generalize them to N = 1 supergravitation. In this paper, for simplicity, we begin the process, not within the context of a superstring vacuum but, rather, for the conformal Galileons arising on a co-dimension one brane embedded in a maximally symmetric AdS 5 bulk space. We proceed to N = 1 supersymmetrize the associated worldvolume theory and then generalize the results to N = 1 supergravity, opening the door to possible new cosmological scenarios 9. Conformal piezoelectric energy harvesting and storage from motions of the heart, lung, and diaphragm. Science.gov (United States) Dagdeviren, Canan; Yang, Byung Duk; Su, Yewang; Tran, Phat L; Joe, Pauline; Anderson, Eric; Xia, Jing; Doraiswamy, Vijay; Dehdashti, Behrooz; Feng, Xue; Lu, Bingwei; Poston, Robert; Khalpey, Zain; Ghaffari, Roozbeh; Huang, Yonggang; Slepian, Marvin J; Rogers, John A 2014-02-01 Here, we report advanced materials and devices that enable high-efficiency mechanical-to-electrical energy conversion from the natural contractile and relaxation motions of the heart, lung, and diaphragm, demonstrated in several different animal models, each of which has organs with sizes that approach human scales. A cointegrated collection of such energy-harvesting elements with rectifiers and microbatteries provides an entire flexible system, capable of viable integration with the beating heart via medical sutures and operation with efficiencies of ∼2%. Additional experiments, computational models, and results in multilayer configurations capture the key behaviors, illuminate essential design aspects, and offer sufficient power outputs for operation of pacemakers, with or without battery assist. 10. Probing bulk defect energy bands using generalized charge pumping method Science.gov (United States) Masuduzzaman, Muhammad; Weir, Bonnie; Alam, Muhammad Ashraful 2012-04-01 The multifrequency charge pumping (CP) technique has long been used to probe the density of defects at the substrate-oxide interface, as well as in the bulk of the oxide of MOS transistors. However, profiling the energy levels of the defects has been more difficult due to the narrow scanning range of the voltage of a typical CP signal, and the uncertainty associated with the defect capture cross-section. In this paper, we discuss a generalized CP method that can identify defect energy bands within a bulk oxide, without requiring separate characterization of the defect capture cross-section. We use the new technique to characterize defects in both fresh and stressed samples of various dielectric compositions. By quantifying the way defects are generated as a function of time, we gain insight into the nature of defect generation in a particular gate dielectric. We also discuss the relative merits of voltage, time, and other variables of CP to probe bulk defect density, and compare the technique with related characterization approaches. 11. Laplacian-based generalized gradient approximations for the exchange energy CERN Document Server Cancio, Antonio C 2013-01-01 It is well known that in the gradient expansion approximation to density functional theory (DFT) the gradient and Laplacian of the density make interchangeable contributions to the exchange correlation (XC) energy. This is an arbitrary "gauge" freedom for building DFT models, normally used to eliminate the Laplacian from the generalized gradient approximation (GGA) level of DFT development. We explore the implications of keeping the Laplacian at this level of DFT, to develop a model that fits the known behavior of the XC hole, which can only be described as a system average in conventional GGA. We generate a family of exchange models that obey the same constraints as conventional GGA's, but which in addition have a finite-valued potential at the atomic nucleus unlike GGA's. These are tested against exact densities and exchange potentials for small atoms, and for constraints chosen to reproduce the SOGGA and the APBE variants of the GGA. The model reliably reproduces exchange energies of closed shell atoms, on... 12. Incidence angle modifiers. A general approach for energy calculations Energy Technology Data Exchange (ETDEWEB) Carvalho, Maria Joao; Horta, Pedro; Mendes, Joao Farinha [INETI - Inst. Nacional de Engenharia Tecnologia, Inovacao, IP, Lisboa (Portugal); Collares Pereira, Manuel; Carbajal, Wildor Maldonado [AO SOL, Energias Renovaveis, S.A., Samora Correia (Portugal) 2008-07-01 The calculation of the energy (power) delivered by a given solar collector, requires special care in the consideration of the way it handles the incoming solar radiation. Some collectors, e.g. flat plate types, are easy to characterize from an optical point of view, given their rotational symmetry with respect to the incident angle on the entrance aperture. This in contrast with collectors possessing a 2D (or cylindrical) symmetry, such as collectors using evacuated tubes or CPC collectors, requiring the incident radiation to be decomposed and treated in two orthogonal planes. Analyses of incidence angle modifier (IAM) along these lines were done in the past for parabolic through, evacuated tube (ETC) or compound parabolic concentrator (CPC) collectors. The present paper addresses a general approach to IAM calculation, treating in a general, equivalent and systematic way all collector types. This approach will allow the proper handling of the solar radiation available to each collector type, subdivided in its different components, folding that with the optical effects present in the solar collector and enabling more accurate comparisons between different collector types, in terms of long term performance calculation. (orig.) 13. Feasibility of using intermediate x-ray energies for highly conformal extracranial radiotherapy Energy Technology Data Exchange (ETDEWEB) Dong, Peng; Yu, Victoria; Nguyen, Dan; Demarco, John; Low, Daniel A.; Sheng, Ke, E-mail: [email protected] [Department of Radiation Oncology, University of California Los Angeles, California 90095 (United States); Woods, Kaley; Boucher, Salime [RadiaBeam Technologies, Santa Monica, California 90404 (United States) 2014-04-15 Purpose: To investigate the feasibility of using intermediate energy 2 MV x-rays for extracranial robotic intensity modulated radiation therapy. Methods: Two megavolts flattening filter free x-rays were simulated using the Monte Carlo code MCNP (v4c). A convolution/superposition dose calculation program was tuned to match the Monte Carlo calculation. The modeled 2 MV x-rays and actual 6 MV flattened x-rays from existing Varian Linacs were used in integrated beam orientation and fluence optimization for a head and neck, a liver, a lung, and a partial breast treatment. A column generation algorithm was used for the intensity modulation and beam orientation optimization. Identical optimization parameters were applied in three different planning modes for each site: 2, 6 MV, and dual energy 2/6 MV. Results: Excellent agreement was observed between the convolution/superposition and the Monte Carlo calculated percent depth dose profiles. For the patient plans, overall, the 2/6 MV x-ray plans had the best dosimetry followed by 2 MV only and 6 MV only plans. Between the two single energy plans, the PTV coverage was equivalent but 2 MV x-rays improved organs-at-risk sparing. For the head and neck case, the 2MV plan reduced lips, mandible, tongue, oral cavity, brain, larynx, left and right parotid gland mean doses by 14%, 8%, 4%, 14%, 24%, 6%, 30% and 16%, respectively. For the liver case, the 2 MV plan reduced the liver and body mean doses by 17% and 18%, respectively. For the lung case, lung V20, V10, and V5 were reduced by 13%, 25%, and 30%, respectively. V10 of heart with 2 MV plan was reduced by 59%. For the partial breast treatment, the 2 MV plan reduced the mean dose to the ipsilateral and contralateral lungs by 27% and 47%, respectively. The mean body dose was reduced by 16%. Conclusions: The authors showed the feasibility of using flattening filter free 2 MV x-rays for extracranial treatments as evidenced by equivalent or superior dosimetry compared to 6 MV plans 14. Near-IR laser generation of a high-energy conformer of L-alanine and the mechanism of its decay in a low-temperature nitrogen matrix. Science.gov (United States) Nunes, Cláudio M; Lapinski, Leszek; Fausto, Rui; Reva, Igor 2013-03-28 Monomers of L-alanine (ALA) were isolated in cryogenic nitrogen matrices at 14 K. Two conformers were identified for the compound trapped from the gas-phase into the solid nitrogen environment. The potential energy surface (PES) of ALA was theoretically calculated at the MP2 and QCISD levels. Twelve minima were located on this PES. Seven low-energy conformers fall within the 0-10 kJ mol(-1) range and should be appreciably populated in the equilibrium gas phase prior to deposition. Observation of only two forms in the matrices is explained in terms of calculated barriers to conformational rearrangements. All conformers with the O=C-O-H moiety in the cis orientation are separated by low barriers and collapse to the most stable form I during deposition of the matrix onto the low-temperature substrate. The second observed form II has the O=C-O-H group in the trans orientation. The remaining trans forms have very high relative energies (between 24 and 30 kJ mol(-1)) and are not populated. The high-energy trans form VI, that differs from I only by rotation of the OH group, was found to be separated from other conformers by barriers that are high enough to open a perspective for its stabilization in a matrix. The form VI was photoproduced in situ by narrow-band near-infrared irradiation of the samples at 6935-6910 cm(-1), where the first overtone of the OH stretching vibration in form I appears. The photogenerated form VI decays in N2 matrices back to conformer I with a characteristic decay time of ∼15 min. The mechanism of the VI → I relaxation is rationalized in terms of the proton tunneling. 15. Conformational unfolding in the N-terminal region of ribonuclease A detected by nonradiative energy transfer. Science.gov (United States) McWherter, C A; Haas, E; Leed, A R; Scheraga, H A 1986-04-22 Unfolding in the N-terminal region of RNase A was studied by the nonradiative energy-transfer technique. RNase A was labeled with a nonfluorescent acceptor (2,4-dinitrophenyl) on the alpha-amino group and a fluorescent donor (ethylenediamine monoamide of 2-naphthoxyacetic acid) on a carboxyl group in the vicinity of residue 50 (75% at Glu-49 and 25% at Asp-53). The distribution of donor labeling sites does not affect the results of this study since they are close in both the sequence and the three-dimensional structure. The sites of labeling were determined by peptide mapping. The derivatives possessed full enzymatic activity and underwent reversible thermal transitions. However, there were some quantitative differences in the thermodynamic parameters. When the carboxyl groups were masked, there was a 5 degrees C lowering of the melting temperature at pH 2 and 4, and no significant change in delta H(Tm). Labeling of the alpha-amino group had no effect on the melting temperature or delta H(Tm) at pH 2 but did result in a dramatic decrease in delta H(Tm) of the unfolding reaction at pH 4. The melting temperature did not change appreciably at pH 4, indicating that an enthalpy/entropy compensation had occurred. The efficiencies of energy transfer determined with both fluorescence intensity and lifetime measurements were in reasonably good agreement. The transfer efficiency dropped from about 60% under folding conditions to roughly 20% when the derivatives were unfolded with disulfide bonds intact and was further reduced to 5% when the disulfide bonds were reduced. The interprobe separation distance was estimated to be 35 +/- 2 A under folding conditions. The contribution to the interprobe distance resulting from the finite size of the probes was treated by using simple geometric considerations and a rotational isomeric state model of the donor probe linkage. With this model, the estimated average interprobe distance of 36 A is in excellent agreement with the 16. Conformal Nets II: Conformal Blocks Science.gov (United States) Bartels, Arthur; Douglas, Christopher L.; Henriques, André 2017-03-01 Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net. 17. Conformal Nets II: Conformal Blocks Science.gov (United States) Bartels, Arthur; Douglas, Christopher L.; Henriques, André 2017-08-01 Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net. 18. Energy loss of ions in a magnetized plasma: conformity between linear response and binary collision treatments. Science.gov (United States) Nersisyan, H B; Zwicknagel, G; Toepffer, C 2003-02-01 The energy loss of a heavy ion moving in a magnetized electron plasma is considered within the linear response (LR) and binary collision (BC) treatments with the purpose to look for a connection between these two models. These two complementary approaches yield close results if no magnetic field is present, but there develop discrepancies with growing magnetic field at ion velocities that are lower than, or comparable with, the thermal velocity of the electrons. We show that this is a peculiarity of the Coulomb interaction which requires cutoff procedures to account for its singularity at the origin and its infinite range. The cutoff procedures in the LR and BC treatments are different as the order of integrations in velocity and in ordinary (Fourier) spaces is reversed in both treatments. While BC involves a velocity average of Coulomb logarithms, there appear in LR Coulomb logarithms of velocity averaged cutoffs. The discrepancies between LR and BC vanish, except for small contributions of collective modes, for smoothened potentials that require no cutoffs. This is shown explicitly with the help of an improved BC in which the velocity transfer is treated up to second order in the interaction in Fourier space. 19. Exact solutions of the general equilibrium shape equations in a general power model of free energy for DNA structures Science.gov (United States) Yavari, Morteza 2014-02-01 The aim of this paper is to generalize the results of the Feoli's formalism (A. Feoli et al., Nucl. Phys. B 705, 577 (2005)) for DNA structures. The exact solutions of the general equilibrium shape equations for a general power model of free energy are investigated using the Feoli's formalism. The free energy of B- to Z-DNA transition is also calculated in this formalism. 20. On conformally related -waves Indian Academy of Sciences (India) Varsha Daftardar-Gejji 2001-05-01 Brinkmann [1] has shown that conformally related distinct Ricci flat solutions are -waves. Brinkmann's result has been generalized to include the conformally invariant source terms. It has been shown that [4] ifg_{ik}$and$\\overline{g}_{ik}$($=^{-2}g_{ik}$, : a scalar function), are distinct metrics having the same Einstein tensor,$G_{ik}=\\overline{G}_{ik}$, then both represent (generalized)$pp$-waves and$_{i}$is a null convariantly constant vector of$g_{ik}$. Thus$pp$-waves are the only candidates which yield conformally related nontrivial solutions of$G_{ik}=T_{ik}=\\overline{G}_{ik}$, with$T_{ik}$being conformally invariant source. In this paper the functional form of the conformal factor for the conformally related$pp$-waves/generalized$pp$-waves has been obtained. It has been shown that the most general$pp$-wave, conformally related to${\\rm d}s^{2}=-2{\\rm d}u[{\\rm d}v-m{\\rm d}y+H{\\rm d}u]+P^{-2}[{\\rm d}y^{2}+{\\rm d}z^{2}]$, turns out to the$(au+b)^{-2}{\\rm d}s^{2}$, where , are constants. Only in the special case when$m=0$,$H=1$, and$P=P(y,z)$, the conformal factor is$(au+b)^{-2}$or$(a(u+v)+b)^{-2}$. 1. Conformal Relativity: Theory and Observations CERN Document Server Pervushin, V; Zorin, A 2005-01-01 Theoretical and observational arguments are listed in favor of a new principle of relativity of units of measurements as the basis of a conformal-invariant unification of General Relativity and Standard Model by replacement of all masses with a scalar (dilaton) field. The relative units mean conformal observables: the coordinate distance, conformal time, running masses, and constant temperature. They reveal to us a motion of a universe along its hypersurface in the field space of events like a motion of a relativistic particle in the Minkowski space, where the postulate of the vacuum as a state with minimal energy leads to arrow of the geometric time. In relative units, the unified theory describes the Cold Universe Scenario, where the role of the conformal dark energy is played by a free minimal coupling scalar field in agreement with the most recent distance-redshift data from type Ia supernovae. In this Scenario, the evolution of the Universe begins with the effect of intensive creation of primordial W-Z-b... 2. A generalized model for estimating the energy density of invertebrates Science.gov (United States) James, Daniel A.; Csargo, Isak J.; Von Eschen, Aaron; Thul, Megan D.; Baker, James M.; Hayer, Cari-Ann; Howell, Jessica; Krause, Jacob; Letvin, Alex; Chipps, Steven R. 2012-01-01 Invertebrate energy density (ED) values are traditionally measured using bomb calorimetry. However, many researchers rely on a few published literature sources to obtain ED values because of time and sampling constraints on measuring ED with bomb calorimetry. Literature values often do not account for spatial or temporal variability associated with invertebrate ED. Thus, these values can be unreliable for use in models and other ecological applications. We evaluated the generality of the relationship between invertebrate ED and proportion of dry-to-wet mass (pDM). We then developed and tested a regression model to predict ED from pDM based on a taxonomically, spatially, and temporally diverse sample of invertebrates representing 28 orders in aquatic (freshwater, estuarine, and marine) and terrestrial (temperate and arid) habitats from 4 continents and 2 oceans. Samples included invertebrates collected in all seasons over the last 19 y. Evaluation of these data revealed a significant relationship between ED and pDM (r2 = 0.96, p calorimetry approaches. This model should prove useful for a wide range of ecological studies because it is unaffected by taxonomic, seasonal, or spatial variability. 3. DFT Conformation and Energies of Amylose Fragments at Atomic Resolution Part I: Syn Forms of Alpha-Maltotetraose Science.gov (United States) DFT optimization studies of ninety syn '-maltotetraose (DP-4) amylose fragments have been carried out at the B3LYP/6-311++G** level of theory. The DP-4 fragments studied include V-helix, tightly bent conformations, a boat, and a 1C4 conformer. The standard hydroxymethyl rotamers (gg, gt, tg) were ... 4. DFT studies of the conformation and relative energies of alpha-maltotetraose (DP-4): An amylose fragment at atomic resolution Science.gov (United States) DFT optimization studies of more than one hundred conformations of a-maltotetraose have been carried out at the B3LYP/6-311++G** level of theory. The DP-4 fragments of predominately 4C1 chair residues include tightly bent forms, helix, band-flips, kinks, boat, and some 1C4 conformers. The three do... 5. The Augmenting Effects of Desolvation and Conformational Energy Terms on the Predictions of Docking Programs against mPGES-1. Directory of Open Access Journals (Sweden) Ashish Gupta Full Text Available In this study we introduce a rescoring method to improve the accuracy of docking programs against mPGES-1. The rescoring method developed is a result of extensive computational study in which different scoring functions and molecular descriptors were combined to develop consensus and rescoring methods. 127 mPGES-1 inhibitors were collected from literature and were segregated into training and external test sets. Docking of the 27 training set compounds was carried out using default settings in AutoDock Vina, AutoDock, DOCK6 and GOLD programs. The programs showed low to moderate correlation with the experimental activities. In order to introduce the contributions of desolvation penalty and conformation energy of the inhibitors various molecular descriptors were calculated. Later, rescoring method was developed as empirical sum of normalised values of docking scores, LogP and Nrotb. The results clearly indicated that LogP and Nrotb recuperate the predictions of these docking programs. Further the efficiency of the rescoring method was validated using 100 test set compounds. The accurate prediction of binding affinities for analogues of the same compounds is a major challenge for many of the existing docking programs; in the present study the high correlation obtained for experimental and predicted pIC50 values for the test set compounds validates the efficiency of the scoring method. 6. The Augmenting Effects of Desolvation and Conformational Energy Terms on the Predictions of Docking Programs against mPGES-1 Science.gov (United States) Gupta, Ashish; Chaudhary, Neha; Kakularam, Kumar Reddy; Pallu, Reddanna; Polamarasetty, Aparoy 2015-01-01 In this study we introduce a rescoring method to improve the accuracy of docking programs against mPGES-1. The rescoring method developed is a result of extensive computational study in which different scoring functions and molecular descriptors were combined to develop consensus and rescoring methods. 127 mPGES-1 inhibitors were collected from literature and were segregated into training and external test sets. Docking of the 27 training set compounds was carried out using default settings in AutoDock Vina, AutoDock, DOCK6 and GOLD programs. The programs showed low to moderate correlation with the experimental activities. In order to introduce the contributions of desolvation penalty and conformation energy of the inhibitors various molecular descriptors were calculated. Later, rescoring method was developed as empirical sum of normalised values of docking scores, LogP and Nrotb. The results clearly indicated that LogP and Nrotb recuperate the predictions of these docking programs. Further the efficiency of the rescoring method was validated using 100 test set compounds. The accurate prediction of binding affinities for analogues of the same compounds is a major challenge for many of the existing docking programs; in the present study the high correlation obtained for experimental and predicted pIC50 values for the test set compounds validates the efficiency of the scoring method. PMID:26305898 7. Decipher the mechanisms of protein conformational changes induced by nucleotide binding through free-energy landscape analysis: ATP binding to Hsp70. Directory of Open Access Journals (Sweden) Adrien Nicolaï Full Text Available ATP regulates the function of many proteins in the cell by transducing its binding and hydrolysis energies into protein conformational changes by mechanisms which are challenging to identify at the atomic scale. Based on molecular dynamics (MD simulations, a method is proposed to analyze the structural changes induced by ATP binding to a protein by computing the effective free-energy landscape (FEL of a subset of its coordinates along its amino-acid sequence. The method is applied to characterize the mechanism by which the binding of ATP to the nucleotide-binding domain (NBD of Hsp70 propagates a signal to its substrate-binding domain (SBD. Unbiased MD simulations were performed for Hsp70-DnaK chaperone in nucleotide-free, ADP-bound and ATP-bound states. The simulations revealed that the SBD does not interact with the NBD for DnaK in its nucleotide-free and ADP-bound states whereas the docking of the SBD was found in the ATP-bound state. The docked state induced by ATP binding found in MD is an intermediate state between the initial nucleotide-free and final ATP-bound states of Hsp70. The analysis of the FEL projected along the amino-acid sequence permitted to identify a subset of 27 protein internal coordinates corresponding to a network of 91 key residues involved in the conformational change induced by ATP binding. Among the 91 residues, 26 are identified for the first time, whereas the others were shown relevant for the allosteric communication of Hsp70 s in several experiments and bioinformatics analysis. The FEL analysis revealed also the origin of the ATP-induced structural modifications of the SBD recently measured by Electron Paramagnetic Resonance. The pathway between the nucleotide-free and the intermediate state of DnaK was extracted by applying principal component analysis to the subset of internal coordinates describing the transition. The methodology proposed is general and could be applied to analyze allosteric communication in 8. Conformal house DEFF Research Database (Denmark) Ryttov, Thomas Aaby; Sannino, Francesco 2010-01-01 fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions...... at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms... 9. Annual report 2005 General Direction of the Energy and raw materials; Rapport annuel 2005 Direction Generale de L'Energie et des Matieres Premieres Energy Technology Data Exchange (ETDEWEB) NONE 2005-07-01 This 2005 annual report of the DGEMP (General Direction of the Energy and the raw Materials), takes stock on the energy bill and accounting of the France. The first part presents the electric power, natural gas and raw materials market in France. The second part is devoted to the diversification of the energy resources with a special attention to the renewable energies and the nuclear energy. The third part discusses the energy and raw materials prices and the last part presents the international cooperation in the energy domain. (A.L.B.) 10. 77 FR 4203 - Energy Conservation Program: Test Procedures for General Service Fluorescent Lamps, General... Science.gov (United States) 2012-01-27 ... Fluorescent Lamps, General Service Incandescent Lamps, and Incandescent Reflector Lamps AGENCY: Office of... the test procedures for general service fluorescent lamps (GSFLs), general service incandescent lamps (GSILs), and incandescent reflector lamps (IRLs). That proposed rulemaking serves as the basis for... 11. Molecular Mechanism and Energy Basis of Conformational Diversity of Antibody SPE7 Revealed by Molecular Dynamics Simulation and Principal Component Analysis Science.gov (United States) Chen, Jianzhong; Wang, Jinan; Zhu, Weiliang 2016-11-01 More and more researchers are interested in and focused on how a limited repertoire of antibodies can bind and correspondingly protect against an almost limitless diversity of invading antigens. In this work, a series of 200-ns molecular dynamics (MD) simulations followed by principal component (PC) analysis and free energy calculations were performed to probe potential mechanism of conformational diversity of antibody SPE7. The results show that the motion direction of loops H3 and L3 is different relative to each other, implying that a big structural difference exists between these two loops. The calculated energy landscapes suggest that the changes in the backbone angles ψ and φ of H-Y101 and H-Y105 provide significant contributions to the conformational diversity of SPE7. The dihedral angle analyses based on MD trajectories show that the side-chain conformational changes of several key residues H-W33, H-Y105, L-Y34 and L-W93 around binding site of SPE7 play a key role in the conformational diversity of SPE7, which gives a reasonable explanation for potential mechanism of cross-reactivity of single antibody toward multiple antigens. 12. GM energy management: organization and results. [General Motors Energy Technology Data Exchange (ETDEWEB) DeKoker, N. 1975-01-01 Energy conservation is not new to industry. The effective and efficient use of labor and materials including energy has been an important tool in cost control for many years. Today, an even greater emphasis must be placed on conserving energy while at the same time stimulating the longer term development of existing as well as new energy resources. Energy conservation in manufacturing can involve product material and/or finish specification changes, process changes or elimination, improved control of equipment, the installation of heat recovery devices and the consolidation of operations. GM's organization to meet these energy management challenges and some of the specific measures taken to improve the efficiency of manufacturing operations are presented. 13. Conformational sampling techniques. Science.gov (United States) Hatfield, Marcus P D; Lovas, Sándor 2014-01-01 The potential energy hyper-surface of a protein relates the potential energy of the protein to its conformational space. This surface is useful in determining the native conformation of a protein or in examining a statistical-mechanical ensemble of structures (canonical ensemble). In determining the potential energy hyper-surface of a protein three aspects must be considered; reducing the degrees of freedom, a method to determine the energy of each conformation and a method to sample the conformational space. For reducing the degrees of freedom the choice of solvent, coarse graining, constraining degrees of freedom and periodic boundary conditions are discussed. The use of quantum mechanics versus molecular mechanics and the choice of force fields are also discussed, as well as the sampling of the conformational space through deterministic and heuristic approaches. Deterministic methods include knowledge-based statistical methods, rotamer libraries, homology modeling, the build-up method, self-consistent electrostatic field, deformation methods, tree-based elimination and eigenvector following routines. The heuristic methods include Monte Carlo chain growing, energy minimizations, metropolis monte carlo and molecular dynamics. In addition, various methods to enhance the conformational search including the deformation or smoothing of the surface, scaling of system parameters, and multi copy searching are also discussed. 14. A conformal model of gravitons CERN Document Server Donoghue, John F 2016-01-01 In the description of general covariance, the vierbein and the Lorentz connection can be treated as independent fundamental fields. With the usual gauge Lagrangian, the Lorentz connection is characterized by an asymptotically free running coupling. When running from high energy, the coupling gets large at a scale which can be called the Planck mass. If the Lorentz connection is confined at that scale, the low energy theory can have the Einstein Lagrangian induced at low energy through dimensional transmutation. However, in general there will be new divergences in such a theory and the Lagrangian basis should be expanded. I construct a conformally invariant model with a larger basis size which potentially may have the same property. 15. 76 FR 56661 - Energy Conservation Program: Test Procedures for General Service Fluorescent Lamps, General... Science.gov (United States) 2011-09-14 ... energy efficiency, energy use, or estimated annual operating cost of a covered product during a... test procedures and offer the public an opportunity to present oral and written comments on them. (42 U...''), 10 CFR 430.23 (Test procedures for the measurement of energy and water consumption''), 10 CFR... 16. Vacuum polarization energy for general backgrounds in one space dimension Science.gov (United States) Weigel, H. 2017-03-01 For field theories in one time and one space dimensions we propose an efficient method to compute the vacuum polarization energy of static field configurations that do not allow a decomposition into symmetric and anti-symmetric channels. The method also applies to scenarios in which the masses of the quantum fluctuations at positive and negative spatial infinity are different. As an example we compute the vacuum polarization energy of the kink soliton in the ϕ6 model. We link the dependence of this energy on the position of the soliton to the different masses. 17. Vertical Ionization Energies of α-L-Amino Acids as a Function of Their Conformation: an Ab Initio Study Directory of Open Access Journals (Sweden) Georges Dive 2004-11-01 Full Text Available Abstract: Vertical ionization energies (IE as a function of the conformation are determined at the quantum chemistry level for eighteen α-L-amino acids. Geometry optimization of the neutrals are performed within the Density Functional Theory (DFT framework using the hybrid method B3LYP and the 6-31G**(5d basis set. Few comparisons are made with wave-function-based ab initio correlated methods like MP2, QCISD or CCSD. For each amino acid, several conformations are considered that lie in the range 10-15 kJ/mol by reference to the more stable one. Their IE are calculated using the Outer-Valence-Green's-Functions (OVGF method at the neutrals' geometry. Few comparisons are made with MP2 and QCISD IE. It turns out that the OVGF results are satisfactory but an uncertainty relative to the most stable conformer at the B3LYP level persists. Moreover, the value of the IE can largely depend on the conformation due to the fact that the ionized molecular orbitals (MO can change a lot as a function of the nuclear structure. 18. Energy conservation: Policies, programs, and general studies. Citations from the NTIS data base Science.gov (United States) Hundemann, A. S. 1980-08-01 National policies, programs, and general studies or ways to conserve energy are presented. Topic areas cover such subjects as electric load management, effects of price and taxation on energy conservation, public attitudes and behavior toward energy saving, energy savings through reduction in hot water consumption, and telecommunications substitutability for travel. 19. General engineering ethics and multiple stress of atomic energy engineering Energy Technology Data Exchange (ETDEWEB) Takeda, Kunihiko [Shibaura Inst. of Tech., Tokyo (Japan) 1999-08-01 The factors, by which the modern engineering ethics has been profoundly affected, were classified to three categories, namely mental blow, the destruction of human function and environment damage. The role of atomic energy engineering in the ethic field has been shown in the first place. It is pointed out that it has brought about the mental blow by the elucidation of universal truth and discipline and the functional disorder by the power supply. However, the direct effect of radiation to the human kinds is only a part of the stresses comparing to the accumulation of the social stress which should be taken into account of by the possibility of disaster and the suspicion of the atomic energy politics. An increase in the multiple stresses as well as the restriction of criticism will place obstacles on the promotion of atomic energy. (author) 20. DGP cosmological model with generalized Ricci dark energy Energy Technology Data Exchange (ETDEWEB) Aguilera, Yeremy [Universidad de Santiago, Departamento de Matematicas y Ciencia de la Computacion, Santiago (Chile); Avelino, Arturo [Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States); Cruz, Norman [Universidad de Santiago, Departamento de Fisica, Facultad de Ciencia, Santiago (Chile); Lepe, Samuel [Pontificia Universidad Catolica de Valparaiso, Facultad de Ciencias, Instituto de Fisica, Valparaiso (Chile); Pena, Francisco [Universidad de La Frontera, Departamento de Ciencias Fisicas, Facultad de Ingenieria y Ciencias, Temuco (Chile) 2014-11-15 The brane-world model proposed by Dvali, Gabadadze and Porrati (DGP) leads to an accelerated universe without cosmological constant or other form of dark energy for the positive branch (element of = +1). For the negative branch (element of = -1) we have investigated the behavior of a model with an holographic Ricci-like dark energy and dark matter, where the IR cutoff takes the form αH{sup 2} + βH, H being the Hubble parameter and α, β positive constants of the model. We perform an analytical study of the model in the late-time dark energy dominated epoch, where we obtain a solution for r{sub c}H(z), where r{sub c} is the leakage scale of gravity into the bulk, and conditions for the negative branch on the holographic parameters α and β, in order to hold the conditions of weak energy and accelerated universe. On the other hand, we compare the model versus the late-time cosmological data using the latest type Ia supernova sample of the Joint Light-curve Analysis (JLA), in order to constrain the holographic parameters in the negative branch, as well as r{sub c}H{sub 0} in the positive branch, where H{sub 0} is the Hubble constant. We find that the model has a good fit to the data and that the most likely values for (r{sub c}H{sub 0}, α, β) lie in the permitted region found from an analytical solution in a dark energy dominated universe. We give a justification to use a holographic cutoff in 4D for the dark energy in the 5-dimensional DGP model. Finally, using the Bayesian Information Criterion we find that this model is disfavored compared with the flat ΛCDM model. (orig.) 1. Stress-energy-momentum of affine-metric gravity generalized Komar superpotential CERN Document Server Giachetta, G 1995-01-01 In case of the Einstein's gravitation theory and its first order Palatini reformulation, the stress-energy-momentum of gravity has been proved to reduce to the Komar superpotential. We generalize this result to the affine-metric theory of gravity in case of general connections and arbitrary Lagrangian densities invariant under general covariant transformations. In this case, the stress-energy-momentum of gravity comes to the generalized Komar superpotential depending on a Lagrangian density in a precise way. 2. Quantum massive conformal gravity Energy Technology Data Exchange (ETDEWEB) Faria, F.F. [Universidade Estadual do Piaui, Centro de Ciencias da Natureza, Teresina, PI (Brazil) 2016-04-15 We first find the linear approximation of the second plus fourth order derivative massive conformal gravity action. Then we reduce the linearized action to separated second order derivative terms, which allows us to quantize the theory by using the standard first order canonical quantization method. It is shown that quantum massive conformal gravity is renormalizable but has ghost states. A possible decoupling of these ghost states at high energies is discussed. (orig.) 3. Workers’ Conformism Directory of Open Access Journals (Sweden) Nikolay Ivantchev 2013-10-01 Full Text Available Conformism was studied among 46 workers with different kinds of occupations by means of two modified scales measuring conformity by Santor, Messervey, and Kusumakar (2000 – scale for perceived peer pressure and scale for conformism in antisocial situations. The hypothesis of the study that workers’ conformism is expressed in a medium degree was confirmed partly. More than a half of the workers conform in a medium degree for taking risk, and for the use of alcohol and drugs, and for sexual relationships. More than a half of the respondents conform in a small degree for anti-social activities (like a theft. The workers were more inclined to conform for risk taking (10.9%, then – for the use of alcohol, drugs and for sexual relationships (8.7%, and in the lowest degree – for anti-social activities (6.5%. The workers who were inclined for the use of alcohol and drugs tended also to conform for anti-social activities. 4. A CONFORMATIONAL ELASTICITY THEORY Institute of Scientific and Technical Information of China (English) 1998-01-01 A new statistical theory based on the rotational isomeric state model describing the chain conformational free energy has been proposed. This theory can be used to predict different tensions of rubber elongation for chemically different polymers, and the energy term during the elongation of natural rubber coincides with the experimental one. 5. DNA – A General Energy System Simulation Tool DEFF Research Database (Denmark) Elmegaard, Brian; Houbak, Niels 2005-01-01 operation. The program decides at runtime to apply the DAE solver if the system contains differential equations. This makes it easy to extend an existing steady state model to simulate dynamic operation of the plant. The use of the program is illustrated by examples of gas turbine models. The paper also......The paper reviews the development of the energy system simulation tool DNA (Dynamic Network Analysis). DNA has been developed since 1989 to be able to handle models of any kind of energy system based on the control volume approach, usually systems of lumped parameter components. DNA has proven...... to be a useful tool in the analysis and optimization of several types of thermal systems: Steam turbines, gas turbines, fuels cells, gasification, refrigeration and heat pumps for both conventional fossil fuels and different types of biomass. DNA is applicable for models of both steady state and dynamic... 6. Energy, momentum, and center of mass in general relativity CERN Document Server Wang, Mu-Tao 2016-01-01 These notions in the title are of fundamental importance in any branch of physics. However, there have been great difficulties in finding physically acceptable definitions of them in general relativity since Einstein's time. I shall explain these difficulties and progresses that have been made. In particular, I shall introduce new definitions of center of mass and angular momentum at both the quasi-local and total levels, which are derived from first principles in general relativity and by the method of geometric analysis. With these new definitions, the classical formula p=mv is shown to be consistent with Einstein's field equation for the first time. This paper is based on joint work [14][15] with Po-Ning Chen and Shing-Tung Yau. 7. Conformationally averaged vertical detachment energy of finite size NO3(-)·nH2O clusters: a route connecting few to many. Science.gov (United States) Pathak, Arup Kumar; Samanta, Alok Kumar; Maity, Dilip Kumar 2011-04-07 We report conformationally averaged VDEs (VDE(w)(n)) for different sizes of NO(3)(-)·nH(2)O clusters calculated by using uncorrelated HF, correlated hybrid density functional (B3LYP, BHHLYP) and correlated ab intio (MP2 and CCSD(T)) theory. It is observed that the VDE(w)(n) at the B3LYP/6-311++G(d,p), B3LYP/Aug-cc-Pvtz and CCSD(T)/6-311++G(d,p) levels is very close to the experimentally measured VDE. It is shown that the use of calculated results of the conformationally averaged VDE for small-sized solvated negatively-charged clusters and a microscopic theory-based general expression for the same provides a route to obtain the VDE for a wide range of cluster sizes, including bulk. 8. High energy light scattering in the generalized eikonal approximation. Science.gov (United States) Chen, T W 1989-10-01 The generalized eikonal approximation method is applied to the study of light scattering by a dielectric medium. In this method, the propagation of light inside the medium is assumed to be rectilinear, as in the usual eikonal method, but with a parameterized propagator which is used to include the edge effect and ray optics behavior at the limit of very short wavelengths. The resulting formulas for the intensity and extinction efficiency factor are compared numerically and shown to agree excellently with the exact results for a homogeneous dielectric sphere. 9. A Generalization of Electromagnetic Fluctuation-Induced Casimir Energy Directory of Open Access Journals (Sweden) Yi Zheng 2015-01-01 Full Text Available Intermolecular forces responsible for adhesion and cohesion can be classified according to their origins; interactions between charges, ions, random dipole—random dipole (Keesom, random dipole—induced dipole (Debye are due to electrostatic effects; covalent bonding, London dispersion forces between fluctuating dipoles, and Lewis acid-base interactions are due to quantum mechanical effects; pressure and osmotic forces are of entropic origin. Of all these interactions, the London dispersion interaction is universal and exists between all types of atoms as well as macroscopic objects. The dispersion force between macroscopic objects is called Casimir/van der Waals force. It results from alteration of the quantum and thermal fluctuations of the electrodynamic field due to the presence of interfaces and plays a significant role in the interaction between macroscopic objects at micrometer and nanometer length scales. This paper discusses how fluctuational electrodynamics can be used to determine the Casimir energy/pressure between planar multilayer objects. Though it is confirmation of the famous work of Dzyaloshinskii, Lifshitz, and Pitaevskii (DLP, we have solved the problem without having to use methods from quantum field theory that DLP resorted to. Because of this new approach, we have been able to clarify the contributions of propagating and evanescent waves to Casimir energy/pressure in dissipative media. 10. A Generalized Framework for Energy Conservation in Wireless Sensor Network Directory of Open Access Journals (Sweden) V. S. Anita Sofia 2011-01-01 Full Text Available A Wireless Sensor Networks (WSN consists of spatially distributed autonomous sensors to cooperatively monitor physical or environmental conditions, such as temperature, sound, vibration, pressure, motion or pollutants. WSN contains a large number of nodes with a limited energy supply. A wireless sensor network consists of nodes that can communicate with each other via wireless links. Sensors are be remotely deployed in large numbers and operates autonomously in unattended environments. One way to support efficient communication between sensors is to organize the network into several groups, called clusters, with each cluster electing one node as the head of cluster To support scalability, nodes are often grouped into disjoint and mostly non-overlapping clusters. This paper deals about the frame work for energy conservation of a Wireless sensor network. The frame work is developed such a way that the nodes are to be clustered, electing the cluster head, performing intra cluster transmission and from the cluster head the information is transmitted to the base station. 11. 40 CFR 93.154 - Conformity analysis. Science.gov (United States) 2010-07-01 ... 40 Protection of Environment 20 2010-07-01 2010-07-01 false Conformity analysis. 93.154 Section 93...) DETERMINING CONFORMITY OF FEDERAL ACTIONS TO STATE OR FEDERAL IMPLEMENTATION PLANS Determining Conformity of General Federal Actions to State or Federal Implementation Plans § 93.154 Conformity analysis. Any... 12. Students' Misunderstandings about the Energy Conservation Principle: A General View to Studies in Literature Science.gov (United States) Tatar, Erdal; Oktay, Munir 2007-01-01 This paper serves to review previously reported studies on students' misunderstandings about the energy conservation principle (the first law of thermodynamics). Generally, studies in literature highlighted students' misunderstandings about the energy conservation principle stem from preliminaries about energy concept in daily life. Since prior… 13. Paul Scherrer Institut Scientific Report 2001. Volume V: General Energy Energy Technology Data Exchange (ETDEWEB) Wokaun, A.; Daum, C. (eds.) 2002-03-01 Major advances in 'Energy and Materials Cycles' have been achieved in the removal of heavy metals from the solid residues of municipal waste incineration. It has been conclusively shown that the oxidation/reduction conditions established during the thermal treatment of filter ash have a decisive influence on the evaporation of groups of heavy metals. With respect to biomass gasification, studies have been carried out with respect to the best way of extracting pure hydrogen from the low calorific value gas that is typically obtained from a biomass gasifier. The overarching goal of the laboratory 'High Temperature Solar Technology' is the use of solar energy for the production of solar fuels, or for the reduction of CO{sub 2} emissions in large scale industrial processes that are conventionally carried out with the use of fossil fuels. In a short-term project targeted at the solar production of lime, highly encouraging results (98% degree of calcination, adjustable reactivity of the lime) have been obtained in a 10 kW prototype reactor. Hybrid processes, in which the calorific value of fossil fuels is upgraded by solar energy, represent the medium-term strategy. In this context, the successful operation of the SYNMET reactor, in which zinc oxide is reacted with methane to produce zinc and synthesis gas, represents an important milestone. The physical sciences group has come up with a novel scheme in which sulfides, rather than oxides, are used as starting materials. Copper sulfide Cu{sub 2}S has been identified as a promising raw material, from which metallic copper would be produced in a solar reduction step. For the use of a catalytic combustor upstream of the main burning chamber of the gas turbine, it is crucial to know the stream wise distance over the catalyst where homogeneous ignition is initiated. The combustion-group working at this concept has made great advances in matching the observed ignition distances with theory. In addition, the 14. Paul Scherrer Institut Scientific Report 2001. Volume V: General Energy Energy Technology Data Exchange (ETDEWEB) Wokaun, A.; Daum, C. (eds.) 2002-03-01 Major advances in 'Energy and Materials Cycles' have been achieved in the removal of heavy metals from the solid residues of municipal waste incineration. It has been conclusively shown that the oxidation/reduction conditions established during the thermal treatment of filter ash have a decisive influence on the evaporation of groups of heavy metals. With respect to biomass gasification, studies have been carried out with respect to the best way of extracting pure hydrogen from the low calorific value gas that is typically obtained from a biomass gasifier. The overarching goal of the laboratory 'High Temperature Solar Technology' is the use of solar energy for the production of solar fuels, or for the reduction of CO{sub 2} emissions in large scale industrial processes that are conventionally carried out with the use of fossil fuels. In a short-term project targeted at the solar production of lime, highly encouraging results (98% degree of calcination, adjustable reactivity of the lime) have been obtained in a 10 kW prototype reactor. Hybrid processes, in which the calorific value of fossil fuels is upgraded by solar energy, represent the medium-term strategy. In this context, the successful operation of the SYNMET reactor, in which zinc oxide is reacted with methane to produce zinc and synthesis gas, represents an important milestone. The physical sciences group has come up with a novel scheme in which sulfides, rather than oxides, are used as starting materials. Copper sulfide Cu{sub 2}S has been identified as a promising raw material, from which metallic copper would be produced in a solar reduction step. For the use of a catalytic combustor upstream of the main burning chamber of the gas turbine, it is crucial to know the stream wise distance over the catalyst where homogeneous ignition is initiated. The combustion-group working at this concept has made great advances in matching the observed ignition distances with theory. In addition, the 15. Frequent Questions about General Conformity Science.gov (United States) These regulations ensure that federal activities or actions don't cause new violations to the NAAQS and ensure that NAAQS attainment is not delayed. This page has information about other agency representatives or stakeholders 16. 群体工作中用势艺术之探讨%Discussion on Art of Conforming to General Drift During Mass Sports Work Institute of Scientific and Technical Information of China (English) 2013-01-01 Based on the successful examples of conforming to general drift in Chinese history ,this article focus on the reality of jiangsu mass sports .From leadership and methodology perspective , the author discuss mass sports in nowadays ,in order to improve ability and level of mass sports worker to know things ,analyze this situation and solve problems .% 本文源于对江苏群体工作的现实关注，从领导学和方法论的视角出发，在探究中国历史中“用势艺术”成功范例的基础上，试图对当今群体工作作相应的梳理与探讨，以期提高广大群体工作者看待事物、分析情况、解决问题的能力和层次。 17. Charged Dilaton, Energy, Momentum and Angular-Momentum in Teleparallel Theory Equivalent to General Relativity CERN Document Server Nashed, Gamal Gergess Lamee 2008-01-01 We apply the energy-momentum tensor to calculate energy, momentum and angular-momentum of two different tetrad fields. This tensor is coordinate independent of the gravitational field established in the Hamiltonian structure of the teleparallel equivalent of general relativity (TEGR). The spacetime of these tetrad fields is the charged dilaton. Our results show that the energy associated with one of these tetrad fields is consistent, while the other one does not show this consistency. Therefore, we use the regularized expression of the gravitational energy-momentum tensor of the TEGR. We investigate the energy within the external event horizon using the definition of the gravitational energy-momentum. 18. Non-linear Realizations of Conformal Symmetry and Effective Field Theory for the Pseudo-Conformal Universe CERN Document Server Hinterbichler, Kurt; Khoury, Justin 2012-01-01 The pseudo-conformal scenario is an alternative to inflation in which the early universe is described by an approximate conformal field theory on flat, Minkowski space. Some fields acquire a time-dependent expectation value, which breaks the flat space so(4,2) conformal algebra to its so(4,1) de Sitter subalgebra. As a result, weight-0 fields acquire a scale invariant spectrum of perturbations. The scenario is very general, and its essential features are determined by the symmetry breaking pattern, irrespective of the details of the underlying microphysics. In this paper, we apply the well-known coset technique to derive the most general effective lagrangian describing the Goldstone field and matter fields, consistent with the assumed symmetries. The resulting action captures the low energy dynamics of any pseudo-conformal realization, including the U(1)-invariant quartic model and the Galilean Genesis scenario. We also derive this lagrangian using an alternative method of curvature invariants, consisting of ... 19. M(o)ller Energy Complexes of Monopoles and Textures in General Relativity and Teleparallel Gravity Institute of Scientific and Technical Information of China (English) Melis Aygün; Ihsan Yllmaz 2007-01-01 The energy problem of monopole and texture spacetimes is investigated in the context of two different approaches of gravity such as general relativity and teleparallel gravity.In this connection,firstly the energies for monopoles and textures are evaluated by using the Moiler energy-momentum prescription in different approximations.It is obtained that energy distributions of M?ller definition give the same results for these topological defects (monopole and texture)in general relativity(GR)and teleparallel gravity(TG).The results strengthen the importance of the M?ller energy-momentum definitions in giyen spacetimes and the viewpoint of Lessner that M(o)ller energy-momentum complex is a powerful concept for energy and momentum. 20. Nuclear matter symmetry energy from generalized polarizabilities: dependences on momentum, isospin, density and temperature CERN Document Server Braghin, F L 2004-01-01 Symmetry energy terms from macroscopic mass formulae are investigated as generalized polarizabilities of nuclear matter. Besides the neutron-proton (n-p) symmetry energy the spin dependent symmetry energies and a scalar one are also defined. They depend on the nuclear densities ($\\rho$), neutron-proton asymmetry ($b$), temperature ($T$) and exchanged energy and momentum ($q$). Based on a standard expression for the generalized polarizabilities, a differential equation is proposed to constrain the dependence of the symmetry energy on the n-p asymmetry and on the density. Some solutions are discussed. The q-dependence (zero frequence) of the symmetry energy coefficients with Skyrme-type forces is investigated in the four channels of the particle-hole interaction. Spin dependent symmetry energies are also investigated indicating much stronger differences in behavior with$qfor each Skyrme force than the results for the neutron-proton one. 1. Annual report 2001. General direction of energy and raw materials; Rapport annuel 2001. Direction generale de l'energie et des matieres premieres Energy Technology Data Exchange (ETDEWEB) NONE 2001-07-01 This report summarizes the 2001 activity of the French general direction of energy and raw materials (DGEMP) of the ministry of finances and industry: 1 - security of energy supplies: a recurrent problem; 2001, a transition year for nuclear energy worldwide; petroleum refining in font of the 2005 dead-line; the OPEC and the upset of the oil market; the pluri-annual planning of power production investments; renewable energies: a reconfirmed priority; 2 - the opening of markets: the opening of French electricity and gas markets; the international development of Electricite de France (EdF) and of Gaz de France (GdF); electricity and gas industries: first branch agreements; 3 - the present-day topics: 2001, the year of objective contracts; AREVA, the future to be prepared; the new IRSN; the agreements on climate and the energy policy; the mastery of domestic energy consumptions; the safety of hydroelectric dams; Technip-Coflexip: the birth of a para-petroleum industry giant; the cleansing of the mining activity in French Guyana; the future of workmen of Lorraine basin coal mines; 4 - 2001 at a glance: highlights; main legislative and regulatory texts; 5 - DGEMP: November 2001 reorganization and new organization chart; energy and raw materials publications; www.industrie.gouv.fr/energie. (J.S.) 2. Conformational analysis of six- and twelve-membered ring compounds by molecular dynamics DEFF Research Database (Denmark) Christensen, I T; Jørgensen, Flemming Steen 1997-01-01 A molecular dynamics (MD)-based conformational analysis has been performed on a number of cycloalkanes in order to demonstrate the reliability and generality of MD as a tool for conformational analysis. MD simulations on cyclohexane and a series of methyl-substituted cyclohexanes were performed...... provided 19 out of the 20 most stable conformations found in the MM2 force field. Finally, the general performance of the MD method for conformational analysis is discussed........ A series of methyl-substituted 1,3-dioxanes were investigated at 1000 K, and the number of chair-chair interconversions could be quantitatively correlated to the experimentally determined ring inversion barrier. Similarly, the distribution of sampled minimum-energy conformations correlated with the energy... 3. Office of Inspector General audit report on the U.S. Department of Energys aircraft activities Energy Technology Data Exchange (ETDEWEB) NONE 1999-01-01 On October 19, 1998, the Office of Inspector General (OIG) was asked to undertake a review of the Department of Energys aircraft activities. It was also requested that they report back within 90 days. The OIG has gathered information concerning the number of aircraft, the level of utilization, and the cost of the Departments aircraft operations. They have also briefly summarized four issues that, in their judgment, may require management attention. 4. Variations in energy spectra and water-to-material stopping-power ratios in three-dimensional conformal and intensity-modulated photon fields. Science.gov (United States) Jang, Si Young; Liu, H Helen; Mohan, Radhe; Siebers, Jeffrey V 2007-04-01 Because of complex dose distributions and dose gradients that are created in three-dimensional conformal radiotherapy (3D-CRT) and intensity-modulated radiation therapy (IMRT), photon- and electron-energy spectra might change significantly with spatial locations and doses. This study examined variations in photon- and electron-energy spectra in 3D-CRT and IMRT photon fields. The effects of spectral variations on water-to-material stopping-power ratios used in Monte Carlo treatment planning systems and the responses of energy-dependent dosimeters, such as thermoluminescent dosimeters (TLDs) and radiographic films were further studied. The EGSnrc Monte Carlo code was used to simulate megavoltage 3D-CRT and IMRT photon fields. The photon- and electron-energy spectra were calculated in 3D water phantoms and anthropomorphic phantoms based on the fluence scored in voxel grids. We then obtained the water-to-material stopping-power ratios in the local voxels using the Spencer-Attix cavity theory. Changes in the responses of films and TLDs were estimated based on the calculated local energy spectra and published data on the dosimeter energy dependency. Results showed that the photon-energy spectra strongly depended on spatial positions and doses in both the 3D-CRT and IMRT fields. The relative fraction of low-energy photons (stopping-power ratio over the range of calculated dose for both 3D-CRT and IMRT was negligible (< 1.0%) for ICRU tissue, cortical bone, and soft bone and less than 3.6% for dry air and lung. Because of spectral softening at low doses, radiographic films in the phantoms could over-respond to dose by more than 30%, whereas the over-response of TLDs was less than 10%. Thus, spatial variations of the photon- and electron-energy spectra should be considered as important factors in 3D-CRT and IMRT dosimetry. 5. Pontential energies and potential-energy tensors for subsystems: general properties CERN Document Server Caimmi, R 2016-01-01 With regard to generic two-component systems, the theory of first variations of global quantities is reviewed and explicit expressions are inferred for subsystem potential energies and potential-energy tensors. Performing a conceptual experiment, a physical interpretation of subsystem potential energies and potential-energy tensors is discussed. Subsystem tidal radii are defined by requiring an unbound component in absence of the other one. To this respect, a few guidance examples are presented as: (i) an embedding and an embedded homogeneous sphere; (ii) an embedding and an embedded truncated, singular isothermal sphere where related centres are sufficiently distant; (iii) a homogeneous sphere and a Roche system i.e. a mass point surrounded by a vanishing atmosphere. The results are discussed and compared with the findings of earlier investigations. 6. An Analysis of Metaphors Used by Students to Describe Energy in an Interdisciplinary General Science Course Science.gov (United States) Lancor, Rachael 2015-01-01 The meaning of the term energy varies widely in scientific and colloquial discourse. Teasing apart the different connotations of the term can be especially challenging for non-science majors. In this study, undergraduate students taking an interdisciplinary, general science course (n?=?49) were asked to explain the role of energy in five contexts:… 7. Wormhole geometries in fourth-order conformal Weyl gravity Science.gov (United States) Varieschi, Gabriele U.; Ault, Kellie L. 2016-04-01 We present an analysis of the classic wormhole geometries based on conformal Weyl gravity, rather than standard general relativity. The main characteristics of the resulting traversable wormholes remains the same as in the seminal study by Morris and Thorne, namely, that effective super-luminal motion is a viable consequence of the metric. Improving on previous work on the subject, we show that for particular choices of the shape and redshift functions the wormhole metric in the context of conformal gravity does not violate the main energy conditions at or near the wormhole throat. Some exotic matter might still be needed at the junction between our solutions and flat spacetime, but we demonstrate that the averaged null energy condition (as evaluated along radial null geodesics) is satisfied for a particular set of wormhole geometries. Therefore, if fourth-order conformal Weyl gravity is a correct extension of general relativity, traversable wormholes might become a realistic solution for interstellar travel. 8. Stress-energy tensor correlators in N-dimensional hot flat spaces via the generalized zeta-function method Science.gov (United States) Cho, H. T.; Hu, B. L. 2012-09-01 We calculate the expectation values of the stress-energy bitensor defined at two different spacetime points x, x‧ of a massless, minimally coupled scalar field with respect to a quantum state at finite temperature T in a flat N-dimensional spacetime by means of the generalized zeta-function method. These correlators, also known as the noise kernels, give the fluctuations of energy and momentum density of a quantum field which are essential for the investigation of the physical effects of negative energy density in certain spacetimes or quantum states. They also act as the sources of the Einstein-Langevin equations in stochastic gravity which one can solve for the dynamics of metric fluctuations as in spacetime foams. In terms of constitutions these correlators are one rung above (in the sense of the correlation—BBGKY or Schwinger-Dyson—hierarchies) the mean (vacuum and thermal expectation) values of the stress-energy tensor which drive the semiclassical Einstein equation in semiclassical gravity. The low- and the high-temperature expansions of these correlators are also given here: at low temperatures, the leading order temperature dependence goes like TN while at high temperatures they have a T2 dependence with the subleading terms exponentially suppressed by e-T. We also discuss the singular behavior of the correlators in the x‧ → x coincident limit as was done before for massless conformal quantum fields. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. 9. Spacetime Conformal Fluctuations and Quantum Dephasing Science.gov (United States) Bonifacio, Paolo M. 2009-06-01 Any quantum system interacting with a complex environment undergoes decoherence. Empty space is filled with vacuum energy due to matter fields in their ground state and represents an underlying environment that any quantum particle has to cope with. In particular quantum gravity vacuum fluctuations should represent a universal source of decoherence. To study this problem we employ a stochastic approach that models spacetime fluctuations close to the Planck scale by means of a classical, randomly fluctuating metric (random gravity framework). We enrich the classical scheme for metric perturbations over a curved background by also including matter fields and metric conformal fluctuations. We show in general that a conformally modulated metric induces dephasing as a result of an effective nonlinear newtonian potential obtained in the appropriate nonrelativistic limit of a minimally coupled Klein-Gordon field. The special case of vacuum fluctuations is considered and a quantitative estimate of the expected effect deduced. Secondly we address the question of how conformal fluctuations could physically arise. By applying the random gravity framework we first show that standard GR seems to forbid spontaneous conformal metric modulations. Finally we argue that a different result follows within scalar-tensor theories of gravity such as e.g. Brans-Dicke theory. In this case a conformal modulation of the metric arises naturally as a result of the fluctuations in the Brans-Dicke field and quantum dephasing of a test particle is expected to occur. For large negative values of the coupling parameter the conformal fluctuations may also contribute to alleviate the well known problem of the large zero point energy due to quantum matter fields. 10. Gravitational radiation fields in teleparallel equivalent of general relativity and their energies Institute of Scientific and Technical Information of China (English) Gamal G.L. Nashed 2010-01-01 We derive two new retarded solutions in the teleparallel theory equivalent to general relativity (TEGR). One of these solutions gives a divergent energy. Therefore, we use the regularized expression of the gravitational energy-momentum tensor, which is a coordinate dependent. A detailed analysis of the loss of the mass of Bondi space-time is carried out using the flux of the gravitational energy-momentum. 11. Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity Institute of Scientific and Technical Information of China (English) Gamal G.L.Nashed 2012-01-01 A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity (TEGR).A spacetime which is not asymptotically flat is derived.The energy conditions of this spacetime are studied.It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy.The singularities of this solution are discussed. 12. Molecular mechanics conformational analysis of tylosin Science.gov (United States) Ivanov, Petko M. 1998-01-01 The conformations of the 16-membered macrolide antibiotic tylosin were studied with molecular mechanics (AMBER∗ force field) including modelling of the effect of the solvent on the conformational preferences (GB/SA). A Monte Carlo conformational search procedure was used for finding the most probable low-energy conformations. The present study provides complementary data to recently reported analysis of the conformations of tylosin based on NMR techniques. A search for the low-energy conformations of protynolide, a 16-membered lactone containing the same aglycone as tylosin, was also carried out, and the results were compared with the observed conformation in the crystal as well as with the most probable conformations of the macrocyclic ring of tylosin. The dependence of the results on force field was also studied by utilizing the MM3 force field. Some particular conformations were computed with the semiempirical molecular orbital methods AM1 and PM3. 13. On Energy and Momentum of the Friedman and Some More General Universes CERN Document Server Garecki, Janusz 2016-01-01 Recently some authors concluded that the energy and momentum of the Fiedman universes, flat and closed, are equal to zero locally and globally (flat universes) or only globally (closed universes). The similar conclusion was also done for more general only homogeneous universes (Kasner and Bianchi type I). Such conclusions originated from coordinate dependent calculations performed only in comoving Cartesian coordinates by using the so-called {\\it energy-momentum complexes}. By using new coordinate independent expressions on energy and momentum one can show that the Friedman and more general universes {\\it needn't be energetic nonentity}. 14. Energy Savings Forecast of Solid-State Lighting in General Illumination Applications Energy Technology Data Exchange (ETDEWEB) none, 2014-08-29 With declining production costs and increasing technical capabilities, LED adoption has recently gained momentum in general illumination applications. This is a positive development for our energy infrastructure, as LEDs use significantly less electricity per lumen produced than many traditional lighting technologies. The U.S. Department of Energy’s Energy Savings Forecast of Solid-State Lighting in General Illumination Applications examines the expected market penetration and resulting energy savings of light-emitting diode, or LED, lamps and luminaires from today through 2030. 15. Ligand-induced conformational changes: Improved predictions of ligand binding conformations and affinities DEFF Research Database (Denmark) Frimurer, T.M.; Peters, Günther H.J.; Iversen, L.F. 2003-01-01 A computational docking strategy using multiple conformations of the target protein is discussed and evaluated. A series of low molecular weight, competitive, nonpeptide protein tyrosine phosphatase inhibitors are considered for which the x-ray crystallographic structures in complex with protein...... tyrosine phosphatase 1 B (PTP1B) are known. To obtain a quantitative measure of the impact of conformational changes induced by the inhibitors, these were docked to the active site region of various structures of PTP1B using the docking program FlexX. Firstly, the inhibitors were docked to a PTP1B crystal...... predicted binding energy and a correct docking mode. Thirdly, to improve the predictability of the docking procedure in the general case, where only a single target protein structure is known, we evaluate an approach which takes possible protein side-chain conformational changes into account. Here, side... 16. Free Energy and the Generalized Optimality Equations for Sequential Decision Making CERN Document Server Ortega, Pedro A 2012-01-01 The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be axiomatically derived. Here we apply the free energy principle to general decision trees that include both adversarial and stochastic environments. We derive generalized sequential optimality equations that not only include the Bellman optimality equations as a limit case, but also lead to well-known decision-rules such as Expectimax, Minimax and Expectiminimax. We show how these decision-rules can be derived from a single free energy principle that assigns a resource parameter to each node in the decision tree. These resource parameters express a concrete computational cost that can be measured as the amount of samples that are needed from the distribution that belongs to each node. The free energy principle therefore provides the normative basis for generalized optimality equations t... 17. Generalized Scaling of Urban Heat Island Effect and Its Applications for Energy Consumption and Renewable Energy Directory of Open Access Journals (Sweden) T.-W. Lee 2014-01-01 Full Text Available In previous work from this laboratory, it has been found that the urban heat island intensity (UHI can be scaled with the urban length scale and the wind speed, through the time-dependent energy balance. The heating of the urban surfaces during the daytime sets the initial temperature, and this overheating is dissipated during the night-time through mean convection motion over the urban surface. This may appear to be in contrast to the classical work by Oke (1973. However, in this work, we show that if the population density is used in converting the population data into urbanized area, then a good agreement with the current theory is found. An additional parameter is the “urban flow parameter,” which depends on the urban building characteristics and affects the horizontal convection of heat due to wind. This scaling can be used to estimate the UHI intensity in any cities and therefore predict the required energy consumption during summer months. In addition, all urbanized surfaces are expected to exhibit this scaling, so that increase in the surface temperature in large energy-consumption or energy-producing facilities (e.g., solar electric or thermal power plants can be estimated. 18. Conformal Coating of Three-Dimensional Nanostructures via Atomic Layer Deposition for Development of Advanced Energy Storage Devices and Plasmonic Transparent Conductors Science.gov (United States) Malek, Gary A. Due to the prodigious amount of electrical energy consumed throughout the world, there exists a great demand for new and improved methods of generating electrical energy in a clean and renewable manner as well as finding more effective ways to store it. This enormous task is of great interest to scientists and engineers, and much headway is being made by utilizing three-dimensional (3D) nanostructured materials. This work explores the application of two types of 3D nanostructured materials toward fabrication of advanced electrical energy storage and conversion devices. The first nanostructured material consists of vertically aligned carbon nanofibers. This three-dimensional structure is opaque, electrically conducting, and contains active sites along the outside of each fiber that are conducive to chemical reactions. Therefore, they make the perfect 3D conducting nanostructured substrate for advanced energy storage devices. In this work, the details for transforming vertically aligned carbon nanofiber arrays into core-shell structures via atomic layer deposition as well as into a mesoporous manganese oxide coated supercapacitor electrode are given. Another unique type of three-dimensional nanostructured substrate is nanotextured glass, which is transparent but non-conducting. Therefore, it can be converted to a 3D transparent conductor for possible application in photovoltaics if it can be conformally coated with a conducting material. This work details that transformation as well as the addition of plasmonic gold nanoparticles to complete the transition to a 3D plasmonic transparent conductor. 19. Spherically symmetric conformal gravity and "gravitational bubbles" CERN Document Server Berezin, V A; Eroshenko, Yu N 2016-01-01 The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equation are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the "gravitational bubbles", which is compact and with zero Weyl tensor. The second class is more general, with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly the same features of non-vacuum solu... 20. Generalization of radiative jet energy loss to non-zero magnetic mass Energy Technology Data Exchange (ETDEWEB) Djordjevic, Magdalena, E-mail: [email protected] [Institute of Physics Belgrade, University of Belgrade (Serbia); Djordjevic, Marko [Faculty of Biology, University of Belgrade (Serbia) 2012-03-19 Reliable predictions for jet quenching in ultra-relativistic heavy ion collisions require accurate computation of radiative energy loss. While all available energy loss formalisms assume zero magnetic mass - in accordance with the one-loop perturbative calculations - different non-perturbative approaches report a non-zero magnetic mass at RHIC and LHC. We here generalize a recently developed energy loss formalism in a realistic finite size QCD medium, to consistently include a possibility for existence of non-zero magnetic screening. We also present how the inclusion of finite magnetic mass changes the energy loss results. Our analysis suggests a fundamental constraint on magnetic to electric mass ratio. 1. Recursion Relations for Conformal Blocks CERN Document Server Penedones, João; Yamazaki, Masahito 2016-09-12 In the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension\\Delta$of the exchanged operator. In particular, we argue, using representation theory of parabolic Verma modules, that in odd spacetime dimension the singularities are only simple poles. We discuss how to use this information to write recursion relations that determine the conformal blocks. We first recover the recursion relation introduced in 1307.6856 for conformal blocks of external scalar operators. We then generalize this recursion relation for the conformal blocks associated to the four point function of three scalar and one vector operator. Finally we specialize to the case in which the vector operator is a conserved current. 2. NEW PRINCIPLES OF POWER AND ENERGY RATE OF INCREMENTAL RATE TYPE FOR GENERALIZED CONTINUUM FIELD THEORIES Institute of Scientific and Technical Information of China (English) 戴天民 2001-01-01 The aim of this paper is to establish new principles of power and energy rate of incremental type in generalized continuum mechanics. By combining new principles of virtual velocity and virtual angular velocity as well as of virtual stress and virtual couple stress with cross terms of incremental rate type a new principle of power and energy rate of incremental rate type with cross terms for micropolar continuum field theories is presented and from it all corresponding equations of motion and boundary conditions as well as power and energy rate equations of incremental rate type for micropolar and nonlocal micropolar continua with the help of generalized Piola's theorems in all and without any additional requirement are derived. Complete results for micromorphic continua could be similarly derived. The derived results in the present paper are believed to be new. They could be used to establish corresponding finite element methods of incremental rate type for generalized continuum mechanics. 3. Generalized energy balance and reciprocity relations for thin-film optics Energy Technology Data Exchange (ETDEWEB) Dupertuis, M.A.; Proctor, M. [Institut de Micro- et Optoelectronique, Lausanne (Switzerland); Acklin, B. [AT& T Bell Labs., Holmdel, NJ (United States) 1994-03-01 Energy balance and reciprocity relations are studied for harmonic inhomogeneous plane waves that are incident upon a stack of continuous absorbing dielectric media that are macroscopically characterized by their electric and magnetic permittivities and their conductivities. New cross terms between parallel electric and parallel magnetic modes are identified in the fully generalized Poynting vector. The symmetry and the relations between the general Fresnel coefficients are investigated in the context of energy balance at the interface. The contributions of the so-called mixed Poynting vector are discussed in detail. In particular a new transfer matrix is introduced for energy fluxes in thin-film optics based on the Poynting and mixed Poynting vectors. Finally, the study of reciprocity relations leads to a generalization of a theorem of reversibility for conducting and dielectric media. 16 refs. 4. Energy-Momentum of the Friedmann Models in General Relativity and Teleparallel Theory of Gravity CERN Document Server Sharif, M 2008-01-01 This paper is devoted to the evaluation of the energy-momentum density components for the Friedmann models. For this purpose, we have used M${\\o}$ller's pseudotensor prescription in General Relativity and a certain energy-momentum density developed from his teleparallel formulation. It is shown that the energy density of the closed Friedmann universe vanishes on the spherical shell at the radius$\\rho=2\\sqrt{3}$. This coincides with the earlier results available in the literature. We also discuss the energy of the flat and open models. A comparison shows a partial consistency between the M${\\o}ller's pseudotensor for General Relativity and teleparallel theory. Further, it is shown that the results are independent of the free dimensionless coupling constant of the teleparallel gravity. 5. General Relativistic Energy Conditions The Hubble expansion in the epoch of galaxy formation CERN Document Server Visser, M 1997-01-01 The energy conditions of Einstein gravity (classical general relativity) are designed to extract as much information as possible from classical general relativity without enforcing a particular equation of state for the stress-energy. This systematic avoidance of the need to specify a particular equation of state is particularly useful in a cosmological setting --- since the equation of state for the cosmological fluid in a Friedmann-Robertson-Walker type universe is extremely uncertain. I shall show that the energy conditions provide simple and robust bounds on the behaviour of both the density and look-back time as a function of red-shift. I shall show that current observations suggest that the so-called strong energy condition (SEC) is violated sometime between the epoch of galaxy formation and the present. This implies that no possible combination of normal'' matter is capable of fitting the observational data. 6. Fake Conformal Symmetry in Unimodular Gravity CERN Document Server Oda, Ichiro 2016-01-01 We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It is shown that the Noether currents for both Weyl symmetry and global scale symmetry, identically vanish as in the conformally invariant scalar-tensor gravity. We clearly explain why in the class of conformally invariant gravitational theories, the Noether currents vanish by starting with the conformally invariant scalar-tensor gravity. Moreover, we comment on both classical and quantum-mechanical equivalences among Einstein's general relativity, the conformally invariant scalar-tensor gravity and the Weyl-transverse (WTDiff) gravity. Finally, we discuss the Weyl current in the conformally invariant scalar action and see that it is also vanishing. 7. Fake conformal symmetry in unimodular gravity Science.gov (United States) Oda, Ichiro 2016-08-01 We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It is shown that the Noether currents for both Weyl symmetry and global scale symmetry vanish exactly as in conformally invariant scalar-tensor gravity. We clearly explain why in the class of conformally invariant gravitational theories, the Noether currents vanish by starting with conformally invariant scalar-tensor gravity. Moreover, we comment on both classical and quantum-mechanical equivalences in Einstein's general relativity, conformally invariant scalar-tensor gravity, and the Weyl-transverse gravity. Finally, we discuss the Weyl current in the conformally invariant scalar action and see that it is also vanishing. 8. Proving the Achronal Averaged Null Energy Condition from the Generalized Second Law CERN Document Server Wall, Aron C 2009-01-01 A null line is a complete achronal null geodesic. It is proven that for any quantum fields minimally coupled to semiclassical Einstein gravity, the averaged null energy condition (ANEC) on null lines is a consequence of the generalized second law of thermodynamics for causal horizons. Auxiliary assumptions include CPT and the existence of a suitable renormalization scheme for the generalized entropy. Although the ANEC can be violated on general geodesics in curved spacetimes, as long as the ANEC holds on null lines there exist theorems showing that semiclassical gravity should satisfy positivity of energy, topological censorship, and should not admit closed timelike curves. It is pointed out that these theorems fail once the linearized graviton field is quantized, because then the renormalized shear squared term in the Raychaudhuri equation can be negative. A "shear-inclusive" generalization of the ANEC is proposed to remedy this, and is proven under an additional assumption about perturbations to horizons in... 9. CONTINUOUS-ENERGY MONTE CARLO METHODS FOR CALCULATING GENERALIZED RESPONSE SENSITIVITIES USING TSUNAMI-3D Energy Technology Data Exchange (ETDEWEB) Perfetti, Christopher M [ORNL; Rearden, Bradley T [ORNL 2014-01-01 This work introduces a new approach for calculating sensitivity coefficients for generalized neutronic responses to nuclear data uncertainties using continuous-energy Monte Carlo methods. The approach presented in this paper, known as the GEAR-MC method, allows for the calculation of generalized sensitivity coefficients for multiple responses in a single Monte Carlo calculation with no nuclear data perturbations or knowledge of nuclear covariance data. The theory behind the GEAR-MC method is presented here, and proof of principle is demonstrated by using the GEAR-MC method to calculate sensitivity coefficients for responses in several 3D, continuous-energy Monte Carlo applications. 10. Energy Savings Forecast of Solid-State Lighting in General Illumination Applications Energy Technology Data Exchange (ETDEWEB) Penning, Julie [Navigant Consulting Inc., Washington, DC (United States); Stober, Kelsey [Navigant Consulting Inc., Washington, DC (United States); Taylor, Victor [Navigant Consulting Inc., Washington, DC (United States); Yamada, Mary [Navigant Consulting Inc., Washington, DC (United States) 2016-09-01 The DOE report, Energy Savings Forecast of Solid-State Lighting in General Illumination Applications, is a biannual report which models the adoption of LEDs in the U.S. general-lighting market, along with associated energy savings, based on the full potential DOE has determined to be technically feasible over time. This version of the report uses an updated 2016 U.S. lighting-market model that is more finely calibrated and granular than previous models, and extends the forecast period to 2035 from the 2030 limit that was used in previous editions. 11. General Navier–Stokes-like momentum and mass-energy equations Energy Technology Data Exchange (ETDEWEB) Monreal, Jorge, E-mail: [email protected] 2015-03-15 A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors. 12. 40 CFR 51.854 - Conformity analysis. Science.gov (United States) 2010-07-01 ... 40 Protection of Environment 2 2010-07-01 2010-07-01 false Conformity analysis. 51.854 Section 51... FOR PREPARATION, ADOPTION, AND SUBMITTAL OF IMPLEMENTATION PLANS Determining Conformity of General Federal Actions to State or Federal Implementation Plans § 51.854 Conformity analysis. Link to... 13. Hybridization of General Cargo Ships to meet the Required Energy Efficiency Design Index OpenAIRE Øverleir, Magnus Anders 2015-01-01 In this thesis a hybrid propulsion system is proposed for a general cargo ship with the aim to meet the required Energy Efficiency Design Index (EEDI). The study has investigated how a hybrid propulsion system will influence the ship s EEDI value and fuel economy. The central problem is the coming challenge for the general cargo segment meeting the required efficiency value. Especially small vessels (3 000-15 000 DWT) with high speed will have troubles complying with the stricter regulations.... 14. A general theory of evolution based on energy efficiency: its implications for diseases. Science.gov (United States) Yun, Anthony J; Lee, Patrick Y; Doux, John D; Conley, Buford R 2006-01-01 We propose a general theory of evolution based on energy efficiency. Life represents an emergent property of energy. The earth receives energy from cosmic sources such as the sun. Biologic life can be characterized by the conversion of available energy into complex systems. Direct energy converters such as photosynthetic microorganisms and plants transform light energy into high-energy phosphate bonds that fuel biochemical work. Indirect converters such as herbivores and carnivores predominantly feed off the food chain supplied by these direct converters. Improving energy efficiency confers competitive advantage in the contest among organisms for energy. We introduce a term, return on energy (ROE), as a measure of energy efficiency. We define ROE as a ratio of the amount of energy acquired by a system to the amount of energy consumed to generate that gain. Life-death cycling represents a tactic to sample the environment for innovations that allow increases in ROE to develop over generations rather than an individual lifespan. However, the variation-selection strategem of Darwinian evolution may define a particular tactic rather than an overarching biological paradigm. A theory of evolution based on competition for energy and driven by improvements in ROE both encompasses prior notions of evolution and portends post-Darwinian mechanisms. Such processes may involve the exchange of non-genetic traits that improve ROE, as exemplified by cognitive adaptations or memes. Under these circumstances, indefinite persistence may become favored over life-death cycling, as increases in ROE may then occur more efficiently within a single lifespan rather than over multiple generations. The key to this transition may involve novel methods to address the promotion of health and cognitive plasticity. We describe the implications of this theory for human diseases. 15. Conformational plasticity and dynamics in the generic protein folding catalyst SlyD unraveled by single-molecule FRET. Science.gov (United States) Kahra, Dana; Kovermann, Michael; Löw, Christian; Hirschfeld, Verena; Haupt, Caroline; Balbach, Jochen; Hübner, Christian Gerhard 2011-08-26 The relation between conformational dynamics and chemistry in enzyme catalysis recently has received increasing attention. While, in the past, the mechanochemical coupling was mainly attributed to molecular motors, nowadays, it seems that this linkage is far more general. Single-molecule fluorescence methods are perfectly suited to directly evidence conformational flexibility and dynamics. By labeling the enzyme SlyD, a member of peptidyl-prolyl cis-trans isomerases of the FK506 binding protein type with an inserted chaperone domain, with donor and acceptor fluorophores for single-molecule fluorescence resonance energy transfer, we directly monitor conformational flexibility and conformational dynamics between the chaperone domain and the FK506 binding protein domain. We find a broad distribution of distances between the labels with two main maxima, which we attribute to an open conformation and to a closed conformation of the enzyme. Correlation analysis demonstrates that the conformations exchange on a rate in the 100 Hz range. With the aid from Monte Carlo simulations, we show that there must be conformational flexibility beyond the two main conformational states. Interestingly, neither the conformational distribution nor the dynamics is significantly altered upon binding of substrates or other known binding partners. Based on these experimental findings, we propose a model where the conformational dynamics is used to search the conformation enabling the chemical step, which also explains the remarkable substrate promiscuity connected with a high efficiency of this class of peptidyl-prolyl cis-trans isomerases. 16. Thermal corrections to the Casimir energy in a general weak gravitational field Science.gov (United States) Nazari, Borzoo 2016-12-01 We calculate finite temperature corrections to the energy of the Casimir effect of a two conducting parallel plates in a general weak gravitational field. After solving the Klein-Gordon equation inside the apparatus, mode frequencies inside the apparatus are obtained in terms of the parameters of the weak background. Using Matsubara’s approach to quantum statistical mechanics gravity-induced thermal corrections of the energy density are obtained. Well-known weak static and stationary gravitational fields are analyzed and it is found that in the low temperature limit the energy of the system increases compared to that in the zero temperature case. 17. The Generalized Energy Equation and Instability in the Two-layer Barotropic Vortex Institute of Scientific and Technical Information of China (English) 2007-01-01 The linear two-layer barotropic primitive equations in cylindrical coordinates are used to derive a generalized energy equation, which is subsequently applied to explain the instability of the spiral wave in the model. In the two-layer model, there are not only the generalized barotropic instability and the super highspeed instability, but also some other new instabilities, which fall into the range of the Kelvin-Helmholtz instability and the generalized baroclinic instability, when the upper and lower basic flows are different.They are perhaps the mechanisms of the generation of spiral cloud bands in tropical cyclones as well. 18. How to be smart and energy efficient: a general discussion on thermochromic windows. Science.gov (United States) Long, Linshuang; Ye, Hong 2014-09-19 A window is a unique element in a building because of its simultaneous properties of being "opaque" to inclement weather yet transparent to the observer. However, these unique features make the window an element that can reduce the energy efficiency of buildings. A thermochromic window is a type of smart window whose solar radiation properties vary with temperature. It is thought that the solar radiation gain of a room can be intelligently regulated through the use of thermochromic windows, resulting in lower energy consumption than with standard windows. Materials scientists have made many efforts to improve the performance of thermochromic materials. Despite these efforts, fundamental problems continue to confront us. How should a "smart" window behave? Is a "smart" window really the best candidate for energy-efficient applications? What is the relationship between smartness and energy performance? To answer these questions, a general discussion of smartness and energy performance is provided. 19. An Analysis of Metaphors Used by Students to Describe Energy in an Interdisciplinary General Science Course Science.gov (United States) Lancor, Rachael 2015-04-01 The meaning of the term energy varies widely in scientific and colloquial discourse. Teasing apart the different connotations of the term can be especially challenging for non-science majors. In this study, undergraduate students taking an interdisciplinary, general science course (n = 49) were asked to explain the role of energy in five contexts: radiation, transportation, generating electricity, earthquakes, and the big bang theory. The responses were qualitatively analyzed under the framework of conceptual metaphor theory. This study presents evidence that non-science major students spontaneously use metaphorical language that is consistent with the conceptual metaphors of energy previously identified in the discourse of students in introductory physics, biology, and chemistry courses. Furthermore, most students used multiple coherent metaphors to explain the role of energy in these complex topics. This demonstrates that these conceptual metaphors for energy have broader applicability than just traditional scientific contexts. Implications for this work as a formative assessment tool in instruction will also be discussed. 20. Generalizing the McClelland bounds for total {pi}-electron energy Energy Technology Data Exchange (ETDEWEB) Gutman, I. [Univ. of Kragujevac (Czechoslovakia). Faculty of Science; Indulal, G. [St. Aloysius Coll., Edathua, Alappuzha (India). Dept. of Mathematics; Todeschini, R. [Univ. of Milano (Italy). Dept. of Environmental Science 2008-05-15 In 1971 McClelland obtained lower and upper bounds for the total {pi}-electron energy. We now formulate the generalized version of these bounds, applicable to the energy-like expression E{sub X}={sigma}{sub i=1}{sup n} vertical stroke x{sub i}-x vertical stroke, where x{sub 1},x{sub 2},.., x{sub n} are any real numbers, and x is their arithmetic mean. In particular, if x{sub 1},x{sub 2},..,x{sub n} are the eigenvalues of the adjacency, Laplacian, or distance matrix of some graph G, then E{sub X} is the graph energy, Laplacian energy, or distance energy, respectively, of G. (orig.) 1. Conformation-mediated Förster resonance energy transfer (FRET) in blue-emitting polyvinylpyrrolidone (PVP)-passivated zinc oxide (ZnO) nanoparticles. Science.gov (United States) Kurt, Hasan; Alpaslan, Ece; Yildiz, Burçin; Taralp, Alpay; Ow-Yang, Cleva W 2017-02-15 Homopolymers, such as polyvinylpyrrolidone (PVP), are commonly used to passivate the surface of blue-light emitting ZnO nanoparticles during colloid nucleation and growth. However, although PVP is known to auto-fluoresce at 400nm, which is near the absorption edge of ZnO, the impact of PVP adsorption characteristics on the surface of ZnO and the surface-related photophysics of PVP-capped ZnO nanoparticles is not well understood. To investigate, we have synthesized ZnO nanoparticles in solvents containing PVP of 3 concentrations-0.5, 0.7, and 0.11gmL(-1). Using time-domain NMR, we show that the adsorbed polymer conformation differs with polymer concentration-head-to-tail under low concentration (e.g., 0.05gmL(-1)) and looping, then train-like, with increasing concentration (e.g., 0.07gmL(-1) and 0.11gmL(-1), respectively). When the surface-adsorbed PVP is entrained, the surface states of ZnO are passivated and radiative emission from surface trap states is suppressed, allowing emission to be dominated by exciton transitions in the UV (ca. 310nm). Moreover, the reduced proximity between the PVP molecule and the ZnO gives rise to increased efficiency of energy transfer between the exciton emission of ZnO and the HOMO-LUMO absorption of PVP (ca. 400nm). As a result, light emission in the blue is enhanced in the PVP-capped ZnO nanoparticles. We thus show that the emission properties of ZnO can be tuned by controlling the adsorbed PVP conformation on the ZnO surface via the PVP concentration in the ZnO precipitation medium. 2. Intramolecular ex vivo Fluorescence Resonance Energy Transfer (FRET of Dihydropyridine Receptor (DHPR β1a Subunit Reveals Conformational Change Induced by RYR1 in Mouse Skeletal Myotubes. Directory of Open Access Journals (Sweden) Dipankar Bhattacharya Full Text Available The dihydropyridine receptor (DHPR β1a subunit is essential for skeletal muscle excitation-contraction coupling, but the structural organization of β1a as part of the macromolecular DHPR-ryanodine receptor type I (RyR1 complex is still debatable. We used fluorescence resonance energy transfer (FRET to probe proximity relationships within the β1a subunit in cultured skeletal myotubes lacking or expressing RyR1. The fluorescein biarsenical reagent FlAsH was used as the FRET acceptor, which exhibits fluorescence upon binding to specific tetracysteine motifs, and enhanced cyan fluorescent protein (CFP was used as the FRET donor. Ten β1a reporter constructs were generated by inserting the CCPGCC FlAsH binding motif into five positions probing the five domains of β1a with either carboxyl or amino terminal fused CFP. FRET efficiency was largest when CCPGCC was positioned next to CFP, and significant intramolecular FRET was observed for all constructs suggesting that in situ the β1a subunit has a relatively compact conformation in which the carboxyl and amino termini are not extended. Comparison of the FRET efficiency in wild type to that in dyspedic (lacking RyR1 myotubes revealed that in only one construct (H458 CCPGCC β1a -CFP FRET efficiency was specifically altered by the presence of RyR1. The present study reveals that the C-terminal of the β1a subunit changes conformation in the presence of RyR1 consistent with an interaction between the C-terminal of β1a and RyR1 in resting myotubes. 3. Fluorescence Resonance Energy Transfer-based Structural Analysis of the Dihydropyridine Receptor α1S Subunit Reveals Conformational Differences Induced by Binding of the β1a Subunit* Science.gov (United States) Mahalingam, Mohana; Perez, Claudio F.; Fessenden, James D. 2016-01-01 The skeletal muscle dihydropyridine receptor α1S subunit plays a key role in skeletal muscle excitation-contraction coupling by sensing membrane voltage changes and then triggering intracellular calcium release. The cytoplasmic loops connecting four homologous α1S structural domains have diverse functions, but their structural arrangement is poorly understood. Here, we used a novel FRET-based method to characterize the relative proximity of these intracellular loops in α1S subunits expressed in intact cells. In dysgenic myotubes, energy transfer was observed from an N-terminal-fused YFP to a FRET acceptor, ReAsH (resorufin arsenical hairpin binder), targeted to each α1S intracellular loop, with the highest FRET efficiencies measured to the α1S II-III loop and C-terminal tail. However, in HEK-293T cells, FRET efficiencies from the α1S N terminus to the II-III and III-IV loops and the C-terminal tail were significantly lower, thus suggesting that these loop structures are influenced by the cellular microenvironment. The addition of the β1a dihydropyridine receptor subunit enhanced FRET to the II-III loop, thus indicating that β1a binding directly affects II-III loop conformation. This specific structural change required the C-terminal 36 amino acids of β1a, which are essential to support EC coupling. Direct FRET measurements between α1S and β1a confirmed that both wild type and truncated β1a bind similarly to α1S. These results provide new insights into the role of muscle-specific proteins on the structural arrangement of α1S intracellular loops and point to a new conformational effect of the β1a subunit in supporting skeletal muscle excitation-contraction coupling. PMID:27129199 4. Fluorescence Resonance Energy Transfer-based Structural Analysis of the Dihydropyridine Receptor α1S Subunit Reveals Conformational Differences Induced by Binding of the β1a Subunit. Science.gov (United States) Mahalingam, Mohana; Perez, Claudio F; Fessenden, James D 2016-06-24 The skeletal muscle dihydropyridine receptor α1S subunit plays a key role in skeletal muscle excitation-contraction coupling by sensing membrane voltage changes and then triggering intracellular calcium release. The cytoplasmic loops connecting four homologous α1S structural domains have diverse functions, but their structural arrangement is poorly understood. Here, we used a novel FRET-based method to characterize the relative proximity of these intracellular loops in α1S subunits expressed in intact cells. In dysgenic myotubes, energy transfer was observed from an N-terminal-fused YFP to a FRET acceptor, ReAsH (resorufin arsenical hairpin binder), targeted to each α1S intracellular loop, with the highest FRET efficiencies measured to the α1S II-III loop and C-terminal tail. However, in HEK-293T cells, FRET efficiencies from the α1S N terminus to the II-III and III-IV loops and the C-terminal tail were significantly lower, thus suggesting that these loop structures are influenced by the cellular microenvironment. The addition of the β1a dihydropyridine receptor subunit enhanced FRET to the II-III loop, thus indicating that β1a binding directly affects II-III loop conformation. This specific structural change required the C-terminal 36 amino acids of β1a, which are essential to support EC coupling. Direct FRET measurements between α1S and β1a confirmed that both wild type and truncated β1a bind similarly to α1S These results provide new insights into the role of muscle-specific proteins on the structural arrangement of α1S intracellular loops and point to a new conformational effect of the β1a subunit in supporting skeletal muscle excitation-contraction coupling. © 2016 by The American Society for Biochemistry and Molecular Biology, Inc. 5. Wormhole geometries in fourth-order conformal Weyl gravity CERN Document Server Varieschi, Gabriele U 2015-01-01 We present an analysis of the classic wormhole geometries based on conformal Weyl gravity, rather than standard general relativity. The main characteristics of the resulting traversable wormholes remain the same as in the seminal study by Morris and Thorne, namely, that effective super-luminal motion is a viable consequence of the metric. Improving on previous work on the subject, we show that for particular choices of the shape and redshift functions, the wormhole metric in the context of conformal gravity does not violate the main energy conditions, as was the case of the original solutions. In particular, the resulting geometry does not require the use of exotic matter at or near the wormhole throat. Therefore, if fourth-order conformal Weyl gravity is a correct extension of general relativity, traversable wormholes might become a realistic solution for interstellar travel. 6. Conformal Gravity and the Alcubierre Warp Drive Metric CERN Document Server Varieschi, Gabriele U 2012-01-01 We present an analysis of the classic Alcubierre metric based on conformal gravity, rather than standard general relativity. The main characteristics of the resulting warp drive remain the same as in the original study by Alcubierre, namely that effective super-luminal motion is a viable outcome of the metric. We show that for particular choices of the shaping function, the Alcubierre metric in the context of conformal gravity does not violate the weak energy condition, as was the case of the original solution. In particular, the resulting warp drive does not require the use of exotic matter. Therefore, if conformal gravity is a correct extension of general relativity, super-luminal motion via an Alcubierre metric might be a realistic solution, thus allowing faster-than-light interstellar travel. 7. Helix 3 acts as a conformational hinge in Class A GPCR activation: An analysis of interhelical interaction energies in crystal structures. Science.gov (United States) Lans, Isaias; Dalton, James A R; Giraldo, Jesús 2015-12-01 A collection of crystal structures of rhodopsin, β2-adrenergic and adenosine A2A receptors in active, intermediate and inactive states were selected for structural and energetic analyses to identify the changes involved in the activation/deactivation of Class A GPCRs. A set of helix interactions exclusive to either inactive or active/intermediate states were identified. The analysis of these interactions distinguished some local conformational changes involved in receptor activation, in particular, a packing between the intracellular domains of transmembrane helices H3 and H7 and a separation between those of H2 and H6. Also, differential movements of the extracellular and intracellular domains of these helices are apparent. Moreover, a segment of residues in helix H3, including residues L/I3.40 to L3.43, is identified as a key component of the activation mechanism, acting as a conformational hinge between extracellular and intracellular regions. Remarkably, the influence on the activation process of some glutamic and aspartic acidic residues and, as a consequence, the influence of variations on local pH is highlighted. Structural hypotheses that arose from the analysis of rhodopsin, β2-adrenergic and adenosine A2A receptors were tested on the active and inactive M2 muscarinic acetylcholine receptor structures and further discussed in the context of the new mechanistic insights provided by the recently determined active and inactive crystal structures of the μ-opioid receptor. Overall, the structural and energetic analyses of the interhelical interactions present in this collection of Class A GPCRs suggests the existence of a common general activation mechanism featuring a chemical space useful for drug discovery exploration. 8. Energy Conservation: Policies, Programs, and General Studies. 1979-July, 1980 (Citations from the NTIS Data Base). Science.gov (United States) Hundemann, Audrey S. The 135 abstracts presented pertain to national policies, programs, and general strategies for conserving energy. In addition to the abstract, each citation lists the title, author, sponsoring agency, subject categories, number of pages, date, descriptors, identifiers, and ordering information for each document. Topics covered in this compilation… 9. Energy density in general relativity a possible role of cosmological constant CERN Document Server Ray, S; Ray, Saibal; Bhadra, Sumana 2004-01-01 We consider a static spherically symmetric charged anisotropic fluid source of finite physical radius (\\sim 10^{-16} cm) by introducing a scalar variable \\Lambda dependent on the radial coordinate r under general relativity. From the solution sets a possible role of the cosmological constant is investigated which indicates the dependency of energy density of electron on the variable \\Lambda. 10. Non-existence of global solutions to generalized dissipative Klein-Gordon equations with positive energy Directory of Open Access Journals (Sweden) Maxim Olegovich Korpusov 2012-07-01 Full Text Available In this article the initial-boundary-value problem for generalized dissipative high-order equation of Klein-Gordon type is considered. We continue our study of nonlinear hyperbolic equations and systems with arbitrary positive energy. The modified concavity method by Levine is used for proving blow-up of solutions. 11. Deriving Internal Energy by Virtue of Generalized Feynman-Hellmann Theorem for Mixed States Institute of Scientific and Technical Information of China (English) FAN Hong-Yi; JIANG Zhong-Hua 2005-01-01 We show how to directly use the generalized Feynman-Hellmann theorem, which is suitable for mixed state ensemble average, to derive the internal energy of Hamiltonian systems. A concrete example, which is a two coupled harminic oscillators, is used for elucidating our approach. 12. Conformal supermultiplets without superpartners CERN Document Server Jarvis, Peter 2011-01-01 We consider polynomial deformations of Lie superalgebras and their representations. For the class A(n-1,0) ~ sl(n/1), we identify families of superalgebras of quadratic and cubic type, consistent with Jacobi identities. For such deformed superalgebras we point out the possibility of zero step supermultiplets, carried on a single, irreducible representation of the even (Lie) subalgebra. For the conformal group SU(2,2) in 1+3-dimensional spacetime, such irreducible (unitary) representations correspond to standard conformal fields (j_1,j_2;d), where (j_1,j_2) is the spin and d the conformal dimension; in the massless class j_1 j_2=0, and d=j_1+j_2+1. We show that these repesentations are zero step supermultiplets for the superalgebra SU_(2)(2,2/1), the quadratic deformation of conformal supersymmetry SU(2,2/1). We propose to elevate SU_(2)(2,2/1) to a symmetry of the S-matrix. Under this scenario, low-energy standard model matter fields (leptons, quarks, Higgs scalars and gauge fields) descended from such confor... 13. P-loop conformation governed crizotinib resistance in G2032R-mutated ROS1 tyrosine kinase: clues from free energy landscape. Directory of Open Access Journals (Sweden) Huiyong Sun 2014-07-01 Full Text Available Tyrosine kinases are regarded as excellent targets for chemical drug therapy of carcinomas. However, under strong purifying selection, drug resistance usually occurs in the cancer cells within a short term. Many cases of drug resistance have been found to be associated with secondary mutations in drug target, which lead to the attenuated drug-target interactions. For example, recently, an acquired secondary mutation, G2032R, has been detected in the drug target, ROS1 tyrosine kinase, from a crizotinib-resistant patient, who responded poorly to crizotinib within a very short therapeutic term. It was supposed that the mutation was located at the solvent front and might hinder the drug binding. However, a different fact could be uncovered by the simulations reported in this study. Here, free energy surfaces were characterized by the drug-target distance and the phosphate-binding loop (P-loop conformational change of the crizotinib-ROS1 complex through advanced molecular dynamics techniques, and it was revealed that the more rigid P-loop region in the G2032R-mutated ROS1 was primarily responsible for the crizotinib resistance, which on one hand, impaired the binding of crizotinib directly, and on the other hand, shortened the residence time induced by the flattened free energy surface. Therefore, both of the binding affinity and the drug residence time should be emphasized in rational drug design to overcome the kinase resistance. 14. P-loop conformation governed crizotinib resistance in G2032R-mutated ROS1 tyrosine kinase: clues from free energy landscape. Science.gov (United States) Sun, Huiyong; Li, Youyong; Tian, Sheng; Wang, Junmei; Hou, Tingjun 2014-07-01 Tyrosine kinases are regarded as excellent targets for chemical drug therapy of carcinomas. However, under strong purifying selection, drug resistance usually occurs in the cancer cells within a short term. Many cases of drug resistance have been found to be associated with secondary mutations in drug target, which lead to the attenuated drug-target interactions. For example, recently, an acquired secondary mutation, G2032R, has been detected in the drug target, ROS1 tyrosine kinase, from a crizotinib-resistant patient, who responded poorly to crizotinib within a very short therapeutic term. It was supposed that the mutation was located at the solvent front and might hinder the drug binding. However, a different fact could be uncovered by the simulations reported in this study. Here, free energy surfaces were characterized by the drug-target distance and the phosphate-binding loop (P-loop) conformational change of the crizotinib-ROS1 complex through advanced molecular dynamics techniques, and it was revealed that the more rigid P-loop region in the G2032R-mutated ROS1 was primarily responsible for the crizotinib resistance, which on one hand, impaired the binding of crizotinib directly, and on the other hand, shortened the residence time induced by the flattened free energy surface. Therefore, both of the binding affinity and the drug residence time should be emphasized in rational drug design to overcome the kinase resistance. 15. Spacetime Conformal Fluctuations and Quantum Dephasing CERN Document Server Bonifacio, Paolo M Any quantum system interacting with a complex environment undergoes decoherence. Empty space is filled with vacuum energy due to matter fields in their ground state and represents an underlying environment that any quantum particle has to cope with. In particular quantum gravity vacuum fluctuations should represent a universal source of decoherence. To study this problem we employ a stochastic approach that models spacetime fluctuations close to the Planck scale by means of a classical, randomly fluctuating metric (random gravity framework). We enrich the classical scheme for metric perturbations over a curved background by also including matter fields and metric conformal fluctuations. We show in general that a conformally modulated metric induces dephasing as a result of an effective nonlinear newtonian potential obtained in the appropriate nonrelativistic limit of a minimally coupled Klein-Gordon field. The special case of vacuum fluctuations is considered and a quantitative estimate of the expected effect... 16. A chord error conforming tool path B-spline fitting method for NC machining based on energy minimization and LSPIA Directory of Open Access Journals (Sweden) Shanshan He 2015-10-01 Full Text Available Piecewise linear (G01-based tool paths generated by CAM systems lack G1 and G2 continuity. The discontinuity causes vibration and unnecessary hesitation during machining. To ensure efficient high-speed machining, a method to improve the continuity of the tool paths is required, such as B-spline fitting that approximates G01 paths with B-spline curves. Conventional B-spline fitting approaches cannot be directly used for tool path B-spline fitting, because they have shortages such as numerical instability, lack of chord error constraint, and lack of assurance of a usable result. Progressive and Iterative Approximation for Least Squares (LSPIA is an efficient method for data fitting that solves the numerical instability problem. However, it does not consider chord errors and needs more work to ensure ironclad results for commercial applications. In this paper, we use LSPIA method incorporating Energy term (ELSPIA to avoid the numerical instability, and lower chord errors by using stretching energy term. We implement several algorithm improvements, including (1 an improved technique for initial control point determination over Dominant Point Method, (2 an algorithm that updates foot point parameters as needed, (3 analysis of the degrees of freedom of control points to insert new control points only when needed, (4 chord error refinement using a similar ELSPIA method with the above enhancements. The proposed approach can generate a shape-preserving B-spline curve. Experiments with data analysis and machining tests are presented for verification of quality and efficiency. Comparisons with other known solutions are included to evaluate the worthiness of the proposed solution. 17. Energy distributions of Bianchi type-VI h Universe in general relativity and teleparallel gravity Science.gov (United States) Özkurt, Şeref; Aygün, Sezg&idot; n. 2017-04-01 In this paper, we have investigated the energy and momentum density distributions for the inhomogeneous generalizations of homogeneous Bianchi type-VI h metric with Einstein, Bergmann-Thomson, Landau-Lifshitz, Papapetrou, Tolman and Møller prescriptions in general relativity (GR) and teleparallel gravity (TG). We have found exactly the same results for Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum distributions in Bianchi type-VI h metric for different gravitation theories. The energy-momentum distributions of the Bianchi type- VI h metric are found to be zero for h = -1 in GR and TG. However, our results agree with Tripathy et al, Tryon, Rosen and Aygün et al. 18. Cloud-radiative effects on implied oceanic energy transport as simulated by atmospheric general circulation models Science.gov (United States) Gleckler, P. J.; Randall, D. A.; Boer, G.; Colman, R.; Dix, M.; Galin, V.; Helfand, M.; Kiehl, J.; Kitoh, A.; Lau, W. 1995-01-01 This paper summarizes the ocean surface net energy flux simulated by fifteen atmospheric general circulation models constrained by realistically-varying sea surface temperatures and sea ice as part of the Atmospheric Model Intercomparison Project. In general, the simulated energy fluxes are within the very large observational uncertainties. However, the annual mean oceanic meridional heat transport that would be required to balance the simulated surface fluxes is shown to be critically sensitive to the radiative effects of clouds, to the extent that even the sign of the Southern Hemisphere ocean heat transport can be affected by the errors in simulated cloud-radiation interactions. It is suggested that improved treatment of cloud radiative effects should help in the development of coupled atmosphere-ocean general circulation models. 19. Generalization of radiative jet energy loss to non-zero magnetic mass CERN Document Server Djordjevic, Magdalena 2011-01-01 Reliable predictions for jet quenching in ultra-relativistic heavy ion collisions require accurate computation of radiative energy loss. With this goal, an energy loss formalism in a realistic finite size dynamical QCD medium was recently developed. While this formalism assumes zero magnetic mass - in accordance with the one-loop perturbative calculations - different non-perturbative approaches report a non-zero magnetic mass at RHIC and LHC. We here generalize the energy loss to consistently include a possibility for existence of non-zero magnetic screening. We also present how the inclusion of finite magnetic mass changes the energy loss results. Our analysis indicates a fundamental constraint on magnetic to electric mass ratio. 20. Moller Energy-Momentum Complex in General Relativity for Higher Dimensional Universes Institute of Scientific and Technical Information of China (English) M. Aygün; S. Aygün; (I). Yilmaz; H. Baysal; (I). Tarhan 2007-01-01 Using the Moller energy-momentum definition in general relativity (GR) we calculate the total energy-momentum distribution associated with (n + 2)-dimensional homogeneous and isotropic model of the universe. It is found that total energy of Moller is vanishing in (n+ 2) dimensions everywhere but n-momentum components of Moller in (n + 2) dimensions are different from zero. Also, we evaluate the static Einstein Universe, FRW universe and de Sitter universe in four dimensions by using (n + 2)-type metric, then calculate the Moller energy-momentum distribution of these spacetimes. However, our results are consistent with the results of Banerjee and Sen, Xulu, Radinschi, Vargas, Cooperstock-Israelit, A ygin et al., Rosen, and Johri et al. in four dimensions. 1. Conformal Patterson-Walker metrics CERN Document Server Hammerl, Matthias; Šilhan, Josef; Taghavi-Chabert, Arman; Žádník, Vojtěch 2016-01-01 The classical Patterson-Walker construction of a split-signature (pseudo-)Riemannian structure from a given torsion-free affine connection is generalized to a construction of a split-signature conformal structure from a given projective class of connections. A characterization of the induced structures is obtained. We achieve a complete description of Einstein metrics in the conformal class formed by the Patterson-Walker metric. Finally, we describe all symmetries of the conformal Patterson-Walker metric. In both cases we obtain descriptions in terms of geometric data on the original structure. 2. Controlling the Conformational Energy of a Phenyl Group by Tuning the Strength of a Nonclassical CH···O Hydrogen Bond: The Case of 5-Phenyl-1,3-dioxane. Science.gov (United States) Bailey, William F; Lambert, Kyle M; Stempel, Zachary D; Wiberg, Kenneth B; Mercado, Brandon Q 2016-12-16 Anancomeric 5-phenyl-1,3-dioxanes provide a unique opportunity to study factors that control conformation. Whereas one might expect an axial phenyl group at C(5) of 1,3-dioxane to adopt a conformation similar to that in axial phenylcyclohexane, a series of studies including X-ray crystallography, NOE measurements, and DFT calculations demonstrate that the phenyl prefers to lie over the dioxane ring in order to position an ortho-hydrogen to participate in a stabilizing, nonclassical CH···O hydrogen bond with a ring oxygen of the dioxane. Acid-catalyzed equilibration of a series of anancomeric 2-tert-butyl-5-aryl-1,3-dioxane isomers demonstrates that remote substituents on the phenyl ring affect the conformational energy of a 5-aryl-1,3-dioxane: electron-withdrawing substituents decrease the conformational energy of the aryl group, while electron-donating substituents increase the conformational energy of the group. This effect is correlated in a very linear way to Hammett substituent parameters. In short, the strength of the CH···O hydrogen bond may be tuned in a predictable way in response to the electron-withdrawing or electron-donating ability of substituents positioned remotely on the aryl ring. This effect may be profound: a 3,5-bis-CF3 phenyl group at C(5) in 1,3-dioxane displays a pronounced preference for the axial orientation. The results are relevant to broader conformational issues involving heterocyclic systems bearing aryl substituents. 3. Conformational changes in glycine tri- and hexapeptide DEFF Research Database (Denmark) Yakubovich, Alexander V.; Solov'yov, Ilia; Solov'yov, Andrey V. 2006-01-01 conformations and calculated the energy barriers for transitions between them. Using a thermodynamic approach, we have estimated the times of the characteristic transitions between these conformations. The results of our calculations have been compared with those obtained by other theoretical methods...... also investigated the influence of the secondary structure of polypeptide chains on the formation of the potential energy landscape. This analysis has been performed for the sheet and the helix conformations of chains of six amino acids.... 4. Strategies to Save 50% Site Energy in Grocery and General Merchandise Stores Energy Technology Data Exchange (ETDEWEB) Hirsch, A.; Hale, E.; Leach, M. 2011-03-01 This paper summarizes the methodology and main results of two recently published Technical Support Documents. These reports explore the feasibility of designing general merchandise and grocery stores that use half the energy of a minimally code-compliant building, as measured on a whole-building basis. We used an optimization algorithm to trace out a minimum cost curve and identify designs that satisfy the 50% energy savings goal. We started from baseline building energy use and progressed to more energy-efficient designs by sequentially adding energy design measures (EDMs). Certain EDMs figured prominently in reaching the 50% energy savings goal for both building types: (1) reduced lighting power density; (2) optimized area fraction and construction of view glass or skylights, or both, as part of a daylighting system tuned to 46.5 fc (500 lux); (3) reduced infiltration with a main entrance vestibule or an envelope air barrier, or both; and (4) energy recovery ventilators, especially in humid and cold climates. In grocery stores, the most effective EDM, which was chosen for all climates, was replacing baseline medium-temperature refrigerated cases with high-efficiency models that have doors. 5. Paul Scherrer Institut annual report 1996. Annex V: PSI general energy technology newsletter 1996 Energy Technology Data Exchange (ETDEWEB) Daum, C.; Leuenberger, J. [eds. 1997-06-01 Surveying the results of General Energy Research in 1996, three major trends can be identified. First, in areas where research results have reached an advanced stage, decisive steps have been taken to promote a transfer towards industrial realization; examples include biomass gasification, advanced battery concepts, and combustion research. Second, in projects with longer term orientation, several options are being evaluated by exploratory studies, e.g. in solar chemistry and reaction analysis. Third, in line with the strategic planning of our institute, the development and characterization of materials for energy research has received increased attention. (author) figs., tabs., refs. 6. Generalized Chou-Yang Model and Meson-Proton Elastic Scattering at High Energies Science.gov (United States) Saleem, Mohammad; Aleem, Fazal-E.; Rashid, Haris The various characteristics of meson-proton elastic scattering at high energies are explained by using the generalized Chou-Yang model which takes into consideration the anisotropic scattering of objects constituting pions(kaons) and protons. A new parametrization of the proton form factor consistent with the recent experimental data is proposed. It is then shown that all the data for meson-proton elastic scattering at 200 and 250 GeV/c are in agreement with theoretical computations. The physical picture of generalized Chou-Yang model which is based on multiple scattering theory is given in detail. 7. Generalized Chou-Yang model and meson-proton elastic scattering at high energies Energy Technology Data Exchange (ETDEWEB) Saleem, M.; Aleem, F.E.; Rashid, H. 1989-01-01 The various characteristics of meson-proton elastic scattering at high energies are explained by using the generalized Chou-Yang model which takes into consideration the anisotropic scattering of objects constituting pions(kaons) and protons. A new parametrization of the proton form factor consistent with the recent experimental data is proposed. It is then shown that all the data for meson-proton elastic scattering at 200 and 250 GeV/c are in agreement with theoretical computations. The physical picture of generalized Chou-Yang model which is based on multiple scattering theory is given in detail. 8. Escherichia coli Phosphoenolpyruvate Dependent Phosphotransferase System. NMR Studies of the Conformation of HPr and P-HPr and the Mechanism of Energy Coupling NARCIS (Netherlands) Dooijewaard, G.; Roossien, F.F.; Robillard, G.T. 1979-01-01 1H and 31P nuclear magnetic resonance investigations of the phosphoprotein intermediate P-HPr and the parent molecule HPr of the E. coli phosphoenolpyruvate dependent phosphotransferase system (PTS) show that HPr can exist in two conformations. These conformations influence the protonation state of 9. DFT Conformation and Energies of Amylose Fragments at Atomic Resolution Part 2: “Band-flip” and “Kink” Forms of Alpha-Maltotetraose Science.gov (United States) In Part 2 of this series of DFT optimization studies of '-maltotetraose, we present results at the B3LYP/6-311++G** level of theory for conformations denoted “band-flips” and “kinks”. Recent experimental X-ray studies have found examples of amylose fragments with conformations distorted from the us... 10. Gas-phase hydrogen/deuterium exchange of 5'- and 3'-mononucleotides in a quadrupole ion trap: exploring the role of conformation and system energy. Science.gov (United States) Chipuk, Joseph E; Brodbelt, Jennifer S 2007-04-01 Gas-phase hydrogen/deuterium (H/D) exchange reactions for deprotonated 2'-deoxy-5'-monophosphate and 2'-deoxy-3'-monophosphate nucleotides with D(2)O were performed in a quadrupole ion trap mass spectrometer. To augment these experiments, molecular modeling was also conducted to identify likely deprotonation sites and potential gas-phase conformations of the anions. A majority of the 5'-monophosphates exchanged extensively with several of the compounds completely incorporating deuterium in place of their labile hydrogen atoms. In contrast, most of the 3'-monophosphate isomers exchanged relatively few hydrogen atoms, even though the rate of the first two exchanges was greater than observed for the 5'-monophosphates. Mononucleotides that failed to incorporate more than two deuterium atoms under default reaction conditions were often found to exchange more extensively when reactions were performed under higher energy conditions. Integration of the experimental and theoretical results supports the use of a relay exchange mechanism and suggests that the exchange behavior depends highly on the identity and orientation of the nucleobase and the position and flexibility of the deprotonated phosphate moiety. These observations also highlight the importance of the distance between the various participating groups in addition to their gas-phase acidity and basicity. 11. Palatini wormholes and energy conditions from the prism of General Relativity CERN Document Server Bejarano, C; Olmo, Gonzalo J; Rubiera-Garcia, D 2016-01-01 Wormholes are hypothetical shortcuts in spacetime that in General Relativity unavoidably violate all of the pointwise energy conditions. In this paper, we consider several wormhole spacetimes that, as opposed to the standard \\emph{designer} procedure frequently employed in the literature, arise directly from gravitational actions including additional terms resulting from contractions of the Ricci tensor with the metric, and which are formulated assuming independence between metric and connection (Palatini approach). We reinterpret such wormhole solutions under the prism of General Relativity and study the matter sources that thread them. We discuss the size of violation of the energy conditions in different cases, and how this is related to the same spacetimes when viewed from the modified gravity side. 12. Fluorescence resonance energy transfer biosensors that detect Ran conformational changes and a Ran x GDP-importin-beta -RanBP1 complex in vitro and in intact cells. Science.gov (United States) Plafker, Kendra; Macara, Ian G 2002-08-16 The Ran GTPase plays a central role in nucleocytoplasmic transport. Association of Ran x GTP with transport carriers (karyopherins) triggers the loading/unloading of export or import cargo, respectively. The C-terminal tail of Ran x GTP is deployed in an extended conformation when associated with a Ran binding domain or importins. To monitor tail orientation, a Ran-GFP fusion was labeled with the fluorophore Alexa546. Fluorescence resonance energy transfer (FRET) occurs efficiently between the green fluorescent protein (GFP) and Alexa546 for Ran x GDP and Ran x GTP, suggesting that the tail is tethered in both states. However, Ran x GTP complexes with importin-beta, RanBP1, and Crm1 all show reduced FRET consistent with tail extension. Displacement of the C-terminal tail of Ran by karyopherins may be a general mechanism to facilitate RanBP1 binding. A Ran x GDP-RanBP1-importin-beta complex also displayed a low FRET signal. To detect this complex in vivo, a bipartite biosensor consisting of Ran-Alexa546 plus GST-GFP-RanBP1, was co-injected into the cytoplasm of cells. The Ran redistributed predominantly to the nucleus, and RanBP1 remained cytoplasmic. Nonetheless, a robust cytoplasmic FRET signal was detectable, which suggests that a significant fraction of cytoplasmic Ran.GDP may exist in a ternary complex with RanBP1 and importins. 13. Deformed Potential Energy of 263Db in a Generalized Liquid Drop Model Institute of Scientific and Technical Information of China (English) 陈宝秋; 马中玉; 赵耀林 2003-01-01 The macroscopic deformed potential energy for super-heavy nuclei 263 Db,which governs the entrance and alpha decay channels,is determined within a generalized liquid drop model(GLDM).A quasi-molecular shape is as sumed in the GLDM,which includes volume-,surface-,and Coulomb-energies,proximity effects,mass asymmetry,and an accurate nuclear radius.The microscopic single particle energies are derived from a shell model in an axially deformed Woods-Saxon potential with a quasi-molecular shape.The shell correction is calculated by the Strutinsky method.The total deformed potential energy of a nucleus can be calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction.The theory is applied to predict the deformed potential energy of the experiment 22Ne + 241Am → 263Db* → 259Db + 4n,which was performed on the Heavy Ion Accelerator in Lanzhou.It is found that the neck in the quasi-molecular shape is responsible for the deep valley of the fusion barrier due to the shell corrections.In the cold fusion path,the double-hump fusion barrier is predicted by the shell correction and complete fusion events may occur. 14. Stereoelectronic effects dictate molecular conformation and biological function of heterocyclic amides. Science.gov (United States) Reid, Robert C; Yau, Mei-Kwan; Singh, Ranee; Lim, Junxian; Fairlie, David P 2014-08-27 Heterocycles adjacent to amides can have important influences on molecular conformation due to stereoelectronic effects exerted by the heteroatom. This was shown for imidazole- and thiazole-amides by comparing low energy conformations (ab initio MP2 and DFT calculations), charge distribution, dipole moments, and known crystal structures which support a general principle. Switching a heteroatom from nitrogen to sulfur altered the amide conformation, producing different three-dimensional electrostatic surfaces. Differences were attributed to different dipole and orbital alignments and spectacularly translated into opposing agonist vs antagonist functions in modulating a G-protein coupled receptor for inflammatory protein complement C3a on human macrophages. Influences of the heteroatom were confirmed by locking the amide conformation using fused bicyclic rings. These findings show that stereoelectronic effects of heterocycles modulate molecular conformation and can impart strikingly different biological properties. 15. Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity CERN Document Server Satin, Seema; Hu, Bei Lok 2016-01-01 For a conformally-coupled scalar field we obtain the conformally-related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally-related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally-related spacetime is known. For example, from the Minkowski solution of Martin and Verdaguer, those of the Einstein-Langevin equations in conformally-flat spacetimes, especially for spatially-flat Friedmann-Robertson-Walker models, can be readily obtained. 16. Conformally related Einstein-Langevin equations for metric fluctuations in stochastic gravity Science.gov (United States) Satin, Seema; Cho, H. T.; Hu, Bei Lok 2016-09-01 For a conformally coupled scalar field we obtain the conformally related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally related spacetime is known. For example, from the Minkowski solution of Martín and Verdaguer, those of the Einstein-Langevin equations in conformally flat spacetimes, especially for spatially flat Friedmann-Robertson-Walker models, can be readily obtained. 17. Cosmological isotropic matter-energy generalizations of Schwarzschild and Kerr metrics CERN Document Server Arik, Metin 2016-01-01 We present a time dependent isotropic fluid solution around a Schwarzschild black hole. We offer the solutions and discuss the effects on the field equations and the horizon. We derive the energy density, pressure and the equation of state parameter. In the second part, we generalize the rotating black hole solution to an expanding universe. We derive from the proposed metric the special solutions of the field equations for the dust approximation and the dark energy solution. We show that the presence of a rotating black hole does not modify the scale factorb(t)=t^{2/3}$law for dust, nor$b(t)=e^{\\lambda\\hspace{1mm}t}$and$p=-\\rho$for dark energy. 18. Energy and angular momentum of general 4-dimensional stationary axi-symmetric spacetime in teleparallel geometry CERN Document Server Nashed, Gamal Gergess Lamee 2008-01-01 We derive an exact general axi-symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation. The solution is characterized by four parameters$M$(mass),$Q$(charge),$a$(rotation) and$L$(NUT). We then, calculate the total exterior energy using the energy-momentum complex given by M{\\o}ller in the framework of Weitzenb$\\ddot{o}$ck geometry. We show that the energy contained in a sphere is shared by its interior as well as exterior. We also calculate the components of the spatial momentum to evaluate the angular momentum distribution. We show that the only non-vanishing components of the angular momentum is in the Z direction. 19. Intercomparison and interpretation of surface energy fluxes in atmospheric general circulation models Science.gov (United States) Randall, D. A.; Cess, R. D.; Blanchet, J. P.; Boer, G. J.; Dazlich, D. A.; Del Genio, A. D.; Deque, M.; Dymnikov, V.; Galin, V.; Ghan, S. J. 1992-01-01 Responses of the surface energy budgets and hydrologic cycles of 19 atmospheric general circulation models to an imposed, globally uniform sea surface temperature perturbation of 4 K were analyzed. The responses of the simulated surface energy budgets are extremely diverse and are closely linked to the responses of the simulated hydrologic cycles. The response of the net surface energy flux is not controlled by cloud effects; instead, it is determined primarily by the response of the latent heat flux. The prescribed warming of the oceans leads to major increases in the atmospheric water vapor content and the rates of evaporation and precipitation. The increased water vapor amount drastically increases the downwelling IR radiation at the earth's surface, but the amount of the change varies dramatically from one model to another. 20. Modeling conformational ensembles of slow functional motions in Pin1-WW. Directory of Open Access Journals (Sweden) Faruck Morcos Full Text Available Protein-protein interactions are often mediated by flexible loops that experience conformational dynamics on the microsecond to millisecond time scales. NMR relaxation studies can map these dynamics. However, defining the network of inter-converting conformers that underlie the relaxation data remains generally challenging. Here, we combine NMR relaxation experiments with simulation to visualize networks of inter-converting conformers. We demonstrate our approach with the apo Pin1-WW domain, for which NMR has revealed conformational dynamics of a flexible loop in the millisecond range. We sample and cluster the free energy landscape using Markov State Models (MSM with major and minor exchange states with high correlation with the NMR relaxation data and low NOE violations. These MSM are hierarchical ensembles of slowly interconverting, metastable macrostates and rapidly interconverting microstates. We found a low population state that consists primarily of holo-like conformations and is a "hub" visited by most pathways between macrostates. These results suggest that conformational equilibria between holo-like and alternative conformers pre-exist in the intrinsic dynamics of apo Pin1-WW. Analysis using MutInf, a mutual information method for quantifying correlated motions, reveals that WW dynamics not only play a role in substrate recognition, but also may help couple the substrate binding site on the WW domain to the one on the catalytic domain. Our work represents an important step towards building networks of inter-converting conformational states and is generally applicable. 1. f(R in Holographic and Agegraphic Dark Energy Models and the Generalized Uncertainty Principle Directory of Open Access Journals (Sweden) Barun Majumder 2013-01-01 Full Text Available We studied a unified approach with the holographic, new agegraphic, and f(R dark energy model to construct the form of f(R which in general is responsible for the curvature driven explanation of the very early inflation along with presently observed late time acceleration. We considered the generalized uncertainty principle in our approach which incorporated the corrections in the entropy-area relation and thereby modified the energy densities for the cosmological dark energy models considered. We found that holographic and new agegraphic f(R gravity models can behave like phantom or quintessence models in the spatially flat FRW universe. We also found a distinct term in the form of f(R which goes as R 3 / 2 due to the consideration of the GUP modified energy densities. Although the presence of this term in the action can be important in explaining the early inflationary scenario, Capozziello et al. recently showed that f(R ~ R 3 / 2 leads to an accelerated expansion, that is, a negative value for the deceleration parameter q which fits well with SNeIa and WMAP data. 2. Implications of conformal invariance in momentum space Energy Technology Data Exchange (ETDEWEB) Bzowski, Adam [Institute for Theoretical Physics,K.U. Leuven, Celestijnenlaan 200D, 3000 Leuven (Belgium); McFadden, Paul [Perimeter Institute for Theoretical Physics,31 Caroline St. N. Waterloo, N2L 2Y5 Ontario (Canada); Skenderis, Kostas [Mathematical Sciences, University of Southampton,Highfield, SO17 1BJ Southampton (United Kingdom) 2014-03-25 We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a novel and very effective decomposition of tensor correlators which reduces their computation to that of a number of scalar form factors. For example, the most general 3-point function of a conserved and traceless stress-energy tensor is determined by only five form factors. Dilatations and special conformal Ward identities then impose additional conditions on these form factors. The special conformal Ward identities become a set of first and second order differential equations, whose general solution is given in terms of integrals involving a product of three Bessel functions (‘triple-K integrals’). All in all, the correlators are completely determined up to a number of constants, in agreement with well-known position space results. In odd dimensions 3-point functions are finite without renormalisation while in even dimensions non-trivial renormalisation in required. In this paper we restrict ourselves to odd dimensions. A comprehensive analysis of renormalisation will be discussed elsewhere. This paper contains two parts that can be read independently of each other. In the first part, we explain the method that leads to the solution for the correlators in terms of triple-K integrals while the second part contains a self-contained presentation of all results. Readers interested only in results may directly consult the second part of the paper. 3. Conformal Coating of Cobalt-Nickel Layered Double Hydroxides Nanoflakes on Carbon Fibers for High-performance Electrochemical Energy Storage Supercapacitor Devices KAUST Repository Warsi, Muhammad Farooq 2014-07-01 High specific capacitance coupled with the ease of large scale production is two desirable characteristics of a potential pseudo-supercapacitor material. In the current study, the uniform and conformal coating of nickel-cobalt layered double hydroxides (CoNi0.5LDH,) nanoflakes on fibrous carbon (FC) cloth has been achieved through cost-effective and scalable chemical precipitation method, followed by a simple heat treatment step. The conformally coated CoNi0.5LDH/FC electrode showed 1.5 times greater specific capacitance compared to the electrodes prepared by conventional non-conformal (drop casting) method of depositing CoNi0.5LDH powder on the carbon microfibers (1938 Fg-1 vs 1292 Fg-1). Further comparison of conformally and non-conformally coated CoNi0.5LDH electrodes showed the rate capability of 79%: 43% capacity retention at 50 Ag-1 and cycling stability 4.6%: 27.9% loss after 3000 cycles respectively. The superior performance of the conformally coated CoNi0.5LDH is mainly due to the reduced internal resistance and fast ionic mobility between electrodes as compared to non-conformally coated electrodes which is evidenced by EIS and CV studies. © 2014 Elsevier Ltd. 4. Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space Institute of Scientific and Technical Information of China (English) 2010-01-01 The conformal geometry of regular hypersurfaces in the conformal space is studied.We classify all the conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in the conformal space up to conformal equivalence. 5. Deformed Potential Energy of Super Heavy Element Z = 120 in a Generalized Liquid Drop Model Institute of Scientific and Technical Information of China (English) CHEN Bao-Qiu; MA Zhong-Yu; ZHU Zhi-Yuan; SONG Hong-Qiu; ZHAO Yao-Lin 2005-01-01 @@ The macroscopic deformed potential energy for super-heavy elements Z = 120 is determined within a generalized liquid drop model (GLDM). The shell correction is calculated with the Strutinsky method and the microscopic single particle energies are derived from the shell model in an axially deformed Woods-Saxon potential with the same quasi-molecular shape. The total potential energy of a nucleus is calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is adopted to describe the deformed potential energies in a set of cold reactions. The neck in the quasi-molecular shape is responsible to the deep valley of the fusion barrier due to shell corrections. In the cold fusion path, the doublehump fusion barrier is predicted by the shell correction and complete fusion events may occur. The results show that some of projectile-target combinations in the entrance channel, such as 50Ca+252Fm→ 302120* and 58Fe+244pu→ 302120*, favour the fusion reaction, which can be considered as candidates for the synthesis of super heavy nuclei Z = 120 and the former might be the best cold fusion reaction to produce the nucleus 302120among them. 6. Conformal invariant saturation CERN Document Server Navelet, H 2002-01-01 We show that, in onium-onium scattering at (very) high energy, a transition to saturation happens due to quantum fluctuations of QCD dipoles. This transition starts when the order alpha^2 correction of the dipole loop is compensated by its faster energy evolution, leading to a negative interference with the tree level amplitude. After a derivation of the the one-loop dipole contribution using conformal invariance of the elastic 4-gluon amplitude in high energy QCD, we obtain an exact expression of the saturation line in the plane (Y,L) where Y is the total rapidity and L, the logarithm of the onium scale ratio. It shows universal features implying the Balitskyi - Fadin - Kuraev - Lipatov (BFKL) evolution kernel and the square of the QCD triple Pomeron vertex. For large L, only the higher BFKL Eigenvalue contributes, leading to a saturation depending on leading log perturbative QCD characteristics. For initial onium scales of same order, however, it involves an unlimited summation over all conformal BFKL Eigen... 7. Hot Conformal Gauge Theories CERN Document Server Mojaza, Matin; Sannino, Francesco 2010-01-01 We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged in such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Due to large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors and matter representation. We show that the reduced free energy changes sign, at the second, fifth and sixth order in the coupling, when decreasing the number of flavors from the upper end of the conformal window. If the change in sign is interpreted as signal of an instability of the system then we infer a critical number of flavors. Surprisingly this number, if computed to the order g^2, agrees with previous predictions for the lower boundary o... 8. Impacts of the EISA 2007 Energy Efficiency Standard on General Service Lamps Energy Technology Data Exchange (ETDEWEB) Kantner, Colleen L. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Alstone, Andrea L. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Ganeshalingam, Mohan [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Gerke, Brian F. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Hosbach, Robert [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States) 2017-01-20 The Energy Policy and Conservation Act of 1975, as amended by the Energy Independence and Security Act of 2007 (EISA 2007), requires that, effective beginning January 1, 2020, the Secretary of Energy shall prohibit the sale of any general service lamp (GSL) that does not meet a minimum efficacy standard of 45 lumens per watt. This is referred to as the EISA 2007 backstop. The U.S. Department of Energy recently revised the definition of the term GSL to include certain lamps that were either previously excluded or not explicitly mentioned in the EISA 2007 definition. For this subset of GSLs, we assess the impacts of the EISA 2007 backstop on national energy consumption, carbon dioxide emissions, and consumer expenditures. To estimate these impacts, we projected the energy use, purchase price, and operating cost of representative lamps purchased during a 30-year analysis period, 2020-2049, for cases in which the EISA 2007 backstop does and does not take effect; the impacts of the backstop are then given by the difference between the two cases. In developing the projection model, we also performed the most comprehensive assessment to date of usage patterns and lifetime distributions for the analyzed lamp types in the United States. There is substantial uncertainty in the estimated impacts, which arises from uncertainty in the speed and extent of the market conversion to solid state lighting technology that would occur in the absence of the EISA 2007 backstop. In our central estimate we find that the EISA 2007 backstop results in significant energy savings of 27 quads and consumer net present value of$120 billion (at a seven percent discount rate) for lamps shipped between 2020 and 2049, and carbon dioxide emissions reduction of 540 million metric tons by 2030 for those GSLs not explicitly included in the EISA 2007 definition of a GSL.
9. Impact of the EISA 2007 Energy Efficiency Standard on General Service Lamps
Energy Technology Data Exchange (ETDEWEB)
Kantner, Colleen L.S. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Alstone, Andrea L. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Ganeshalingam, Mohan [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Gerke, Brian F. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Hosbach, Robert [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2017-06-20
The Energy Policy and Conservation Act of 1975, as amended by the Energy Independence and Security Act of 2007 (EISA 2007), requires that, effective beginning January 1, 2020, the Secretary of Energy shall prohibit the sale of any general service lamp (GSL) that does not meet a minimum efficacy standard of 45 lumens per watt. This is referred to as the EISA 2007 backstop. The U.S. Department of Energy recently revised the definition of the term GSL to include certain lamps that were either previously excluded or not explicitly mentioned in the EISA 2007 definition. For this subset of GSLs, we assess the impacts of the EISA 2007 backstop on national energy consumption, carbon dioxide emissions, and consumer expenditures. To estimate these impacts, we projected the energy use, purchase price, and operating cost of representative lamps purchased during a 30-year analysis period, 2020-2049, for cases in which the EISA 2007 backstop does and does not take effect; the impacts of the backstop are then given by the difference between the two cases. In developing the projection model, we also performed the most comprehensive assessment to date of usage patterns and lifetime distributions for the analyzed lamp types in the United States. There is substantial uncertainty in the estimated impacts, which arises from uncertainty in the speed and extent of the market conversion to solid state lighting technology that would occur in the absence of the EISA 2007 backstop. In our central estimate we find that the EISA 2007 backstop results in significant energy savings of 27 quads and consumer net present value of $120 billion (at a seven percent discount rate) for lamps shipped between 2020 and 2049, and carbon dioxide emissions reduction of 540 million metric tons by 2030 for those GSLs not explicitly included in the EISA 2007 definition of a GSL. 10. Nonlocal gravity: Conformally flat spacetimes CERN Document Server Bini, Donato 2016-01-01 The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity in two-dimensional spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein's field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of nonlocal gravity. 11. Generalization of classical mechanics for nuclear motions on nonadiabatically coupled potential energy surfaces in chemical reactions. Science.gov (United States) Takatsuka, Kazuo 2007-10-18 Classical trajectory study of nuclear motion on the Born-Oppenheimer potential energy surfaces is now one of the standard methods of chemical dynamics. In particular, this approach is inevitable in the studies of large molecular systems. However, as soon as more than a single potential energy surface is involved due to nonadiabatic coupling, such a naive application of classical mechanics loses its theoretical foundation. This is a classic and fundamental issue in the foundation of chemistry. To cope with this problem, we propose a generalization of classical mechanics that provides a path even in cases where multiple potential energy surfaces are involved in a single event and the Born-Oppenheimer approximation breaks down. This generalization is made by diagonalization of the matrix representation of nuclear forces in nonadiabatic dynamics, which is derived from a mixed quantum-classical representation of the electron-nucleus entangled Hamiltonian [Takatsuka, K. J. Chem. Phys. 2006, 124, 064111]. A manifestation of quantum fluctuation on a classical subsystem that directly contacts with a quantum subsystem is discussed. We also show that the Hamiltonian thus represented gives a theoretical foundation to examine the validity of the so-called semiclassical Ehrenfest theory (or mean-field theory) for electron quantum wavepacket dynamics, and indeed, it is pointed out that the electronic Hamiltonian to be used in this theory should be slightly modified. 12. High energy conformers of M(+)(APE)(H2O)(0-1)Ar(0-1) clusters revealed by combined IR-PD and DFT-MD anharmonic vibrational spectroscopy. Science.gov (United States) Brites, V; Nicely, A L; Sieffert, N; Gaigeot, M-P; Lisy, J M 2014-07-14 IR-PD vibrational spectroscopy and DFT-based molecular dynamics simulations are combined in order to unravel the structures of M(+)(APE)(H2O)0-1 ionic clusters (M = Na, K), where APE (2-amino-1-phenyl ethanol) is commonly used as an analogue for the noradrenaline neurotransmitter. The strength of the synergy between experiments and simulations presented here is that DFT-MD provides anharmonic vibrational spectra that unambiguously help assign the ionic clusters structures. Depending on the interacting cation, we have found that the lowest energy conformers of K(+)(APE)(H2O)0-1 clusters are formed, while the lowest energy conformers of Na(+)(APE)(H2O)0-1 clusters can only be observed through water loss channel (i.e. without argon tagged to the clusters). Trapping of higher energy conformers is observed when the argon loss channel is recorded in the experiment. This has been rationalized by transition state energies. The dynamical anharmonic vibrational spectra unambiguously provide the prominent OH stretch due to the OH···NH2 H-bond, within 10 cm(-1) of the experiment, hence reproducing the 240-300 cm(-1) red-shift (depending on the interacting cation) from bare neutral APE. When this H-bond is not present, the dynamical anharmonic spectra provide the water O-H stretches as well as the rotational motion of the water molecule at finite temperature, as observed in the experiment. 13. Spatial separation of molecular conformers and clusters. Science.gov (United States) Horke, Daniel; Trippel, Sebastian; Chang, Yuan-Pin; Stern, Stephan; Mullins, Terry; Kierspel, Thomas; Küpper, Jochen 2014-01-09 Gas-phase molecular physics and physical chemistry experiments commonly use supersonic expansions through pulsed valves for the production of cold molecular beams. However, these beams often contain multiple conformers and clusters, even at low rotational temperatures. We present an experimental methodology that allows the spatial separation of these constituent parts of a molecular beam expansion. Using an electric deflector the beam is separated by its mass-to-dipole moment ratio, analogous to a bender or an electric sector mass spectrometer spatially dispersing charged molecules on the basis of their mass-to-charge ratio. This deflector exploits the Stark effect in an inhomogeneous electric field and allows the separation of individual species of polar neutral molecules and clusters. It furthermore allows the selection of the coldest part of a molecular beam, as low-energy rotational quantum states generally experience the largest deflection. Different structural isomers (conformers) of a species can be separated due to the different arrangement of functional groups, which leads to distinct dipole moments. These are exploited by the electrostatic deflector for the production of a conformationally pure sample from a molecular beam. Similarly, specific cluster stoichiometries can be selected, as the mass and dipole moment of a given cluster depends on the degree of solvation around the parent molecule. This allows experiments on specific cluster sizes and structures, enabling the systematic study of solvation of neutral molecules. 14. RECOVERY AND ENERGY SAVINGS OF ALUMINUM CAN BEVERAGE CONSUMED IN GENERAL AND VOCATIONAL TECHNICAL HIGH SCHOOLS Directory of Open Access Journals (Sweden) Mert ZORAĞA 2012-01-01 Full Text Available In commitments of Kyoto protocol principles, 100% recyclable features aluminum is one of most current metal. In this protocol, Turkey is not contractor to develop policies to prevent climate change to apply, to take measures to increase energy efficiency and savings, to limit greenhouse gas emissions. Aluminum production from used aluminum requires 95% less energy than production from raw material and recycled aluminum put in the production reduces flue gases pollutant emissions at rate of 99%. Between 2004-2005 and 2009-2010 academic year education is estimated that every one of 5 and 10 students were consumed average 1 aluminum can beverage each day to take into account habits of general and vocational high school students. In case of recovery of 50% this cans will save approximately 4.7 and 13.1 million kWh electrical energy, in the case of 75% recovery will save between 7.2 and 19.9 million kWh electrical energy, in the case of 100% will save the 9.4 and 25 million kWh electrical energy than the same amount of aluminum in the primary method (from ore in our country. In the same conditions is estimated that realization of an efficient recycling project will provide between 5.2 and 20 million kWh of electrical energy savings in the 2010 -2011 academic year education. In this study, anymore it turned into a habit of recovery of packaging waste application in most countries as the name “Blue Angels Project” to place in our country has been trying to bring clarity to issues. 15. On the generalized eigenvalue method for energies and matrix elements in lattice field theory CERN Document Server Blossier, Benoit; von Hippel, Georg; Mendes, Tereza; Sommer, Rainer 2009-01-01 We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as$\\exp(-(E_{N+1}-E_n) t)$. The gap$E_{N+1}-E_n$can be made large by increasing the number$N$of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order$1/m_b$in HQET. 16. Energy and momentum of general spherically symmetric frames on the regularizing teleparallelism Institute of Scientific and Technical Information of China (English) Gamal G. L. Nashed 2012-01-01 In the context of the covariant teleparallel framework,we use the 2-form translational momentum to compute the total energy of two general spherically symmetric frames.The first one is characterized by an arbitrary function H(γ),which preserves the spherical symmetry and reproduces all the previous solutions,while the other one is characterized by a parameter ξ which ensures the vanishing of the axial of trace of the torsion.We calculate the total energy by using two procedures,i.e.,when the Weitzenb?ck connection Γαβ is trivial,and show how H(r) and ξ play the role of an inertia that leads the total energy to be unphysical.Therefore,we take into account Γαβ and show that although the spacetimes we use contain an arbitrary function and one parameter,they have no effect on the form of the total energy and momentum as it should be. 17. A generalized free energy perturbation theory accounting for end states with differing configuration space volume. Science.gov (United States) Ullmann, R Thomas; Ullmann, G Matthias 2011-01-27 We present a generalized free energy perturbation theory that is inspired by Monte Carlo techniques and based on a microstate description of a transformation between two states of a physical system. It is shown that the present free energy perturbation theory stated by the Zwanzig equation follows as a special case of our theory. Our method uses a stochastic mapping of the end states that associates a given microstate from one ensemble with a microstate from the adjacent ensemble according to a probability distribution. In contrast, previous free energy perturbation methods use a static, deterministic mapping that associates fixed pairs of microstates from the two ensembles. The advantages of our approach are that end states of differing configuration space volume can be treated easily also in the case of discrete configuration spaces and that the method does not require the potentially cumbersome search for an optimal deterministic mapping. The application of our theory is illustrated by some example problems. We discuss practical applications for which our findings could be relevant and point out perspectives for further development of the free energy perturbation theory. 18. Quasi-Local Energy-Momentum and Angular Momentum in General Relativity Directory of Open Access Journals (Sweden) Szabados László B. 2009-06-01 Full Text Available The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential applications of the quasi-local concepts and specific constructions are briefly mentioned.This review is based on talks given at the Erwin Schrödinger Institute, Vienna in July 1997, at the Universität Tübingen in May 1998, and at the National Center for Theoretical Sciences in Hsinchu, Taiwan and at the National Central University, Chungli, Taiwan, in July 2000. 19. Energy distributions of Bianchi type-$VI_{h}$Universe in general relativity and teleparallel gravity Indian Academy of Sciences (India) SEREF ÖZKURT; SEZGIN AYGÜN 2017-04-01 In this paper, we have investigated the energy and momentum density distributions for the inhomogeneous generalizations of homogeneous Bianchi type-$VI_{h}$metric with Einstein, Bergmann–Thomson, Landau–Lifshitz,Papapetrou, Tolman and M$\\phi$ller prescriptions in general relativity (GR) and teleparallel gravity (TG). We have found exactly the same results for Einstein, Bergmann–Thomson and Landau–Lifshitz energy–momentum distributions in Bianchi type-$VI_{h}$metric for different gravitation theories. The energy–momentum distributions of the Bianchi type-$VI_{h}$metric are found to be zero for$h$= −1 in GR and TG. However, our results agree with Tripathy et al, Tryon, Rosen and Aygün et al. 20. Quartet-metric general relativity: scalar graviton, dark matter, and dark energy Energy Technology Data Exchange (ETDEWEB) Pirogov, Yury F. [SRC Institute for High Energy Physics of NRC Kurchatov Institute, Protvino (Russian Federation) 2016-04-15 General relativity extended through a dynamical scalar quartet is proposed as a theory of the scalar-vector-tensor gravity, generically describing the unified gravitational dark matter (DM) and dark energy (DE). The implementation in the weak-field limit of the Higgs mechanism for the extended gravity, with a redefinition of metric field, is exposed in a generally covariant form. Under a natural restriction on the parameters, the redefined theory possesses in the linearized approximation a residual transverse-diffeomorphism invariance, and consistently comprises the massless tensor graviton and a massive scalar one as a DM particle. The number of adjustable parameters in the full nonlinear theory and a partial decoupling of the latter from its weak-field limit noticeably extend the perspectives for the unified description of the gravity DM and DE in the various phenomena at the different scales. (orig.) 1. Generalized Analysis of a Distributed Energy Efficient Algorithm for Change Detection CERN Document Server Banerjee, Taposh 2009-01-01 An energy efficient distributed Change Detection scheme based on Page's CUSUM algorithm was presented in \\cite{icassp}. In this paper we consider a nonparametric version of this algorithm. In the algorithm in \\cite{icassp}, each sensor runs CUSUM and transmits only when the CUSUM is above some threshold. The transmissions from the sensors are fused at the physical layer. The channel is modeled as a Multiple Access Channel (MAC) corrupted with noise. The fusion center performs another CUSUM to detect the change. In this paper, we generalize the algorithm to also include nonparametric CUSUM and provide a unified analysis. 2. On the stability of the dark energy based on generalized uncertainty principle CERN Document Server Pasqua, Antonio; Khomenko, Iuliia 2013-01-01 The new agegraphic Dark Energy (NADE) model (based on generalized uncertainty principle) interacting with Dark Matter (DM) is considered in this study via power-law form of the scale factor$a(t)$. The equation of state (EoS) parameter$\\omega_{G}$is observed to have a phantom-like behaviour. The stability of this model is investigated through the squared speed of sound$v_{s}^{2}$: it is found that$v_{s}^{2}$always stays at negative level, which indicates instability of the considered model. 3. Generalized Least Energy of Separation for Desalination and Other Chemical Separation Processes Directory of Open Access Journals (Sweden) Karan H. Mistry 2013-05-01 Full Text Available Increasing global demand for fresh water is driving the development and implementation of a wide variety of seawater desalination technologies driven by different combinations of heat, work, and chemical energy. This paper develops a consistent basis for comparing the energy consumption of such technologies using Second Law efficiency. The Second Law efficiency for a chemical separation process is defined in terms of the useful exergy output, which is the minimum least work of separation required to extract a unit of product from a feed stream of a given composition. For a desalination process, this is the minimum least work of separation for producing one kilogram of product water from feed of a given salinity. While definitions in terms of work and heat input have been proposed before, this work generalizes the Second Law efficiency to allow for systems that operate on a combination of energy inputs, including fuel. The generalized equation is then evaluated through a parametric study considering work input, heat inputs at various temperatures, and various chemical fuel inputs. Further, since most modern, large-scale desalination plants operate in cogeneration schemes, a methodology for correctly evaluating Second Law efficiency for the desalination plant based on primary energy inputs is demonstrated. It is shown that, from a strictly energetic point of view and based on currently available technology, cogeneration using electricity to power a reverse osmosis system is energetically superior to thermal systems such as multiple effect distillation and multistage flash distillation, despite the very low grade heat input normally applied in those systems. 4. The sensitivity of BAO dark energy constraints to general isocurvature perturbations Energy Technology Data Exchange (ETDEWEB) Kasanda, S. Muya; Zunckel, C.; Moodley, K. [School of Mathematical Sciences, University of KwaZulu-Natal, University Road, Durban, 4041 (South Africa); Bassett, B.A.; Okouma, P., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Dept. of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town (South Africa) 2012-07-01 Baryon Acoustic Oscillation (BAO) surveys will be a leading method for addressing the dark energy challenge in the next decade. We explore in detail the effect of allowing for small amplitude admixtures of general isocurvature perturbations in addition to the dominant adiabatic mode. We find that non-adiabatic initial conditions leave the sound speed unchanged but instead excite different harmonics. These harmonics couple differently to Silk damping, altering the form and evolution of acoustic waves in the baryon-photon fluid prior to decoupling. This modifies not only the scale on which the sound waves imprint onto the baryon distribution, which is used as the standard ruler in BAO surveys, but also the shape, width and height of the BAO peak. We discuss these effects in detail and show how more general initial conditions impact our interpretation of cosmological data in dark energy studies. We find that the inclusion of these additional isocurvature modes leads to a decrease in the Dark Energy Task Force figure of merit (FoM) by 46% i.e., FoM{sub ISO} = 0.54 × FoM{sub AD} and 53% for the BOSS and ADEPT experiments respectively when considered in conjunction with PLANK data. We also show that the incorrect assumption of adiabaticity has the potential to bias our estimates of the dark energy parameters by 2.7σ (2.2σ) for a single correlated isocurvature mode (CDM isocurvature), and up to 4.9σ (5.7σ) for three correlated isocurvature modes in the case of the BOSS (ADEPT) experiment. We find that the use of the large scale structure data in conjunction with CMB data improves our ability to measure the contributions of different modes to the initial conditions by as much as 95% for certain modes in the fully correlated case. 5. Logarithmic conformal field theory Science.gov (United States) Gainutdinov, Azat; Ridout, David; Runkel, Ingo 2013-12-01 Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more 6. Non-conformable, partial and conformable transposition DEFF Research Database (Denmark) König, Thomas; Mäder, Lars Kai 2013-01-01 Although member states are obliged to transpose directives into domestic law in a conformable manner and receive considerable time for their transposition activities, we identify three levels of transposition outcomes for EU directives: conformable, partially conformable and non-conformable....... Compared with existing transposition models, which do not distinguish between different transposition outcomes, we examine the factors influencing each transposition process by means of a competing risk analysis. We find that preference-related factors, in particular the disagreement of a member state...... and the Commission regarding a directive’s outcome, play a much more strategic role than has to date acknowledged in the transposition literature. Whereas disagreement of a member state delays conformable transposition, it speeds up non-conformable transposition. Disagreement of the Commission only prolongs... 7. Conformational landscape of an amyloid intra-cellular domain and Landau-Ginzburg-Wilson paradigm in protein dynamics Science.gov (United States) Dai, Jin; Niemi, Antti J.; He, Jianfeng 2016-07-01 The Landau-Ginzburg-Wilson paradigm is proposed as a framework, to investigate the conformational landscape of intrinsically unstructured proteins. A universal Cα-trace Landau free energy is deduced from general symmetry considerations, with the ensuing all-atom structure modeled using publicly available reconstruction programs Pulchra and Scwrl. As an example, the conformational stability of an amyloid precursor protein intra-cellular domain (AICD) is inspected; the reference conformation is the crystallographic structure with code 3DXC in Protein Data Bank (PDB) that describes a heterodimer of AICD and a nuclear multi-domain adaptor protein Fe65. Those conformations of AICD that correspond to local or near-local minima of the Landau free energy are identified. For this, the response of the original 3DXC conformation to variations in the ambient temperature is investigated, using the Glauber algorithm. The conclusion is that in isolation the AICD conformation in 3DXC must be unstable. A family of degenerate conformations that minimise the Landau free energy is identified, and it is proposed that the native state of an isolated AICD is a superposition of these conformations. The results are fully in line with the presumed intrinsically unstructured character of isolated AICD and should provide a basis for a systematic analysis of AICD structure in future NMR experiments. 8. Conformational landscape of an amyloid intra-cellular domain and Landau-Ginzburg-Wilson paradigm in protein dynamics. Science.gov (United States) Dai, Jin; Niemi, Antti J; He, Jianfeng 2016-07-28 The Landau-Ginzburg-Wilson paradigm is proposed as a framework, to investigate the conformational landscape of intrinsically unstructured proteins. A universal Cα-trace Landau free energy is deduced from general symmetry considerations, with the ensuing all-atom structure modeled using publicly available reconstruction programs Pulchra and Scwrl. As an example, the conformational stability of an amyloid precursor protein intra-cellular domain (AICD) is inspected; the reference conformation is the crystallographic structure with code 3DXC in Protein Data Bank (PDB) that describes a heterodimer of AICD and a nuclear multi-domain adaptor protein Fe65. Those conformations of AICD that correspond to local or near-local minima of the Landau free energy are identified. For this, the response of the original 3DXC conformation to variations in the ambient temperature is investigated, using the Glauber algorithm. The conclusion is that in isolation the AICD conformation in 3DXC must be unstable. A family of degenerate conformations that minimise the Landau free energy is identified, and it is proposed that the native state of an isolated AICD is a superposition of these conformations. The results are fully in line with the presumed intrinsically unstructured character of isolated AICD and should provide a basis for a systematic analysis of AICD structure in future NMR experiments. 9. Cavity as a source of conformational fluctuation and high-energy state: High-pressure NMR study of a cavity-enlarged mutant of T4 lysozyme CERN Document Server Maeno, Akihiro; Hirata, Fumio; Otten, Renee; Dahlquist, Frederick W; Yokoyama, Shigeyuki; Akasaka, Kazuyuki; Mulder, Frans A A; Kitahara, Ryo 2014-01-01 Although the structure, function, conformational dynamics, and controlled thermodynamics of proteins are manifested by their corresponding amino acid sequences, the natural rules for molecular design and their corresponding interplay remain obscure. In this study, we focused on the role of internal cavities of proteins in conformational dynamics. We investigated the pressure-induced responses from the cavity-enlarged L99A mutant of T4 lysozyme, using high-pressure NMR spectroscopy. The signal intensities of the methyl groups in the 1H/13C HSQC spectra, particularly those around the enlarged cavity, decreased with the increasing pressure, and disappeared at 200 MPa, without the appearance of new resonances, thus indicating the presence of heterogeneous conformations around the cavity within the ground state ensemble. Above 200 MPa, the signal intensities of more than 20 methyl groups gradually decreased with the increasing pressure, without the appearance of new resonances. Interestingly, these residues closel... 10. Dissipation, generalized free energy, and a self-consistent nonequilibrium thermodynamics of chemically driven open subsystems. Science.gov (United States) Ge, Hao; Qian, Hong 2013-06-01 Nonequilibrium thermodynamics of a system situated in a sustained environment with influx and efflux is usually treated as a subsystem in a larger, closed "universe." A question remains with regard to what the minimally required description for the surrounding of such an open driven system is so that its nonequilibrium thermodynamics can be established solely based on the internal stochastic kinetics. We provide a solution to this problem using insights from studies of molecular motors in a chemical nonequilibrium steady state (NESS) with sustained external drive through a regenerating system or in a quasisteady state (QSS) with an excess amount of adenosine triphosphate (ATP), adenosine diphosphate (ADP), and inorganic phosphate (Pi). We introduce the key notion of minimal work that is needed, W(min), for the external regenerating system to sustain a NESS (e.g., maintaining constant concentrations of ATP, ADP and Pi for a molecular motor). Using a Markov (master-equation) description of a motor protein, we illustrate that the NESS and QSS have identical kinetics as well as the second law in terms of the same positive entropy production rate. The heat dissipation of a NESS without mechanical output is exactly the W(min). This provides a justification for introducing an ideal external regenerating system and yields a free-energy balance equation between the net free-energy input F(in) and total dissipation F(dis) in an NESS: F(in) consists of chemical input minus mechanical output; F(dis) consists of dissipative heat, i.e. the amount of useful energy becoming heat, which also equals the NESS entropy production. Furthermore, we show that for nonstationary systems, the F(dis) and F(in) correspond to the entropy production rate and housekeeping heat in stochastic thermodynamics and identify a relative entropy H as a generalized free energy. We reach a new formulation of Markovian nonequilibrium thermodynamics based on only the internal kinetic equation without further 11. Impact of Dust on Mars Surface Albedo and Energy Flux with LMD General Circulation Model Science.gov (United States) Singh, D.; Flanner, M.; Millour, E.; Martinez, G. 2015-12-01 Mars, just like Earth experience different seasons because of its axial tilt (about 25°). This causes growth and retreat of snow cover (primarily CO2) in Martian Polar regions. The perennial caps are the only place on the planet where condensed H2O is available at surface. On Mars, as much as 30% atmospheric CO2 deposits in each hemisphere depending upon the season. This leads to a significant variation on planet's surface albedo and hence effecting the amount of solar flux absorbed or reflected at the surface. General Circulation Model (GCM) of Laboratoire de Météorologie Dynamique (LMD) currently uses observationally derived surface albedo from Thermal Emission Spectrometer (TES) instrument for the polar caps. These TES albedo values do not have any inter-annual variability, and are independent of presence of any dust/impurity on surface. Presence of dust or other surface impurities can significantly reduce the surface albedo especially during and right after a dust storm. This change will also be evident in the surface energy flux interactions. Our work focuses on combining earth based Snow, Ice, and Aerosol Radiation (SNICAR) model with current state of GCM to incorporate the impact of dust on Martian surface albedo, and hence the energy flux. Inter-annual variability of surface albedo and planet's top of atmosphere (TOA) energy budget along with their correlation with currently available mission data will be presented. 12. Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential Energy Technology Data Exchange (ETDEWEB) Carmona-Espíndola, Javier, E-mail: [email protected] [Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México D. F. 09340, México (Mexico); Gázquez, José L., E-mail: [email protected] [Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México D. F. 09340, México (Mexico); Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México D. F. 07360, México (Mexico); Vela, Alberto [Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México D. F. 07360, México (Mexico); Trickey, S. B. [Quantum Theory Project, Department of Physics and Department of Chemistry, University of Florida, P.O. Box 118435, Gainesville, Florida 32611-8435 (United States) 2015-02-07 A new non-empirical exchange energy functional of the generalized gradient approximation (GGA) type, which gives an exchange potential with the correct asymptotic behavior, is developed and explored. In combination with the Perdew-Burke-Ernzerhof (PBE) correlation energy functional, the new CAP-PBE (CAP stands for correct asymptotic potential) exchange-correlation functional gives heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies on standard test sets that are fully competitive with those obtained from other GGA-type functionals that do not have the correct asymptotic exchange potential behavior. Distinct from them, the new functional provides important improvements in quantities dependent upon response functions, e.g., static and dynamic polarizabilities and hyperpolarizabilities. CAP combined with the Lee-Yang-Parr correlation functional gives roughly equivalent results. Consideration of the computed dynamical polarizabilities in the context of the broad spectrum of other properties considered tips the balance to the non-empirical CAP-PBE combination. Intriguingly, these improvements arise primarily from improvements in the highest occupied and lowest unoccupied molecular orbitals, and not from shifts in the associated eigenvalues. Those eigenvalues do not change dramatically with respect to eigenvalues from other GGA-type functionals that do not provide the correct asymptotic behavior of the potential. Unexpected behavior of the potential at intermediate distances from the nucleus explains this unexpected result and indicates a clear route for improvement. 13. The Energy-Momentum Tensor for a Dissipative Fluid in General Relativity CERN Document Server Pimentel, Oscar M; Lora-Clavijo, F D 2016-01-01 Considering the growing interest of the astrophysicist community in the study of dissipative fluids with the aim of getting a more realistic description of the universe, we present in this paper a physical analysis of the energy-momentum tensor of a viscous fluid with heat flux. We introduce the general form of this tensor and, using the approximation of small velocity gradients, we relate the stresses of the fluid with the viscosity coefficients, the shear tensor and the expansion factor. Exploiting these relations, we can write the stresses in terms of the extrinsic curvature of the normal surface to the 4-velocity vector of the fluid, and we can also establish a connection between the perfect fluid and the symmetries of the spacetime. On the other hand, we calculate the energy conditions for a dissipative fluid through contractions of the energy-momentum tensor with the 4-velocity vector of an arbitrary observer. This method is interesting because it allows us to compute the conditions in a reasonable easy... 14. Charged Axially Symmetric Solution and Energy in Teleparallel Theory Equivalent to General Relativity CERN Document Server Nashed, Gamal Gergess Lamee 2007-01-01 An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity (TEGR). The associated metric has the structure function$G(\\xi)=1-{\\xi}^2-2mA{\\xi}^3-q^2A^2{\\xi}^4$. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorisable form$(1-{\\xi}^2)(1+r_{+}A\\xi)(1+r_{-}A\\xi)$with$r_{\\pm}$as the horizons of Reissner-Nordstr$\\ddot{o}$m space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner-Nordstr$\\ddot{o}$m black hole. In Calculating the energy content of this tetrad field using the gravitational energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the gravitational energy-moment... 15. Generalized Extreme Value Distribution Models for the Assessment of Seasonal Wind Energy Potential of Debuncha, Cameroon Directory of Open Access Journals (Sweden) Nkongho Ayuketang Arreyndip 2016-01-01 Full Text Available The method of generalized extreme value family of distributions (Weibull, Gumbel, and Frechet is employed for the first time to assess the wind energy potential of Debuncha, South-West Cameroon, and to study the variation of energy over the seasons on this site. The 29-year (1983–2013 average daily wind speed data over Debuncha due to missing values in the years 1992 and 1994 is gotten from NASA satellite data through the RETScreen software tool provided by CANMET Canada. The data is partitioned into min-monthly, mean-monthly, and max-monthly data and fitted using maximum likelihood method to the two-parameter Weibull, Gumbel, and Frechet distributions for the purpose of determining the best fit to be used for assessing the wind energy potential on this site. The respective shape and scale parameters are estimated. By making use of the P values of the Kolmogorov-Smirnov statistic (K-S and the standard error (s.e analysis, the results show that the Frechet distribution best fits the min-monthly, mean-monthly, and max-monthly data compared to the Weibull and Gumbel distributions. Wind speed distributions and wind power densities of both the wet and dry seasons are compared. The results show that the wind power density of the wet season was higher than in the dry season. The wind speeds at this site seem quite low; maximum wind speeds are listed as between 3.1 and 4.2 m/s, which is below the cut-in wind speed of many modern turbines (6–10 m/s. However, we recommend the installation of low cut-in wind turbines like the Savonius or Aircon (10 KW for stand-alone low energy need. 16. The conformal approach to asymptotic analysis CERN Document Server Nicolas, Jean-Philippe 2015-01-01 This essay was written as an extended version of a talk given at a conference in Strasbourg on "Riemann, Einstein and geometry", organized by Athanase Papadopoulos in September 2014. Its aim is to present Roger Penrose's approach to asymptotic analysis in general relativity, which is based on conformal geometric techniques, focusing on historical and recent aspects of two specialized topics~: conformal scattering and peeling. 17. Asymptotic symmetry algebra of conformal gravity CERN Document Server Irakleidou, M 2016-01-01 We compute asymptotic symmetry algebras of conformal gravity. Due to more general boundary conditions allowed in conformal gravity in comparison to those in Einstein gravity, we can classify the corresponding algebras. The highest algebra for non-trivial boundary conditions is five dimensional and it leads to global geon solution with non-vanishing charges. 18. An extension theorem for conformal gauge singularities CERN Document Server Tod, Paul 2007-01-01 We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem. 19. Using Graphs of Gibbs Energy versus Temperature in General Chemistry Discussions of Phase Changes and Colligative Properties Science.gov (United States) Hanson, Robert M.; Riley, Patrick; Schwinefus, Jeff; Fischer, Paul J. 2008-01-01 The use of qualitative graphs of Gibbs energy versus temperature is described in the context of chemical demonstrations involving phase changes and colligative properties at the general chemistry level. (Contains 5 figures and 1 note.) 20. Measuring the mechanical properties of molecular conformers Science.gov (United States) Jarvis, S. P.; Taylor, S.; Baran, J. D.; Champness, N. R.; Larsson, J. A.; Moriarty, P. 2015-09-01 Scanning probe-actuated single molecule manipulation has proven to be an exceptionally powerful tool for the systematic atomic-scale interrogation of molecular adsorbates. To date, however, the extent to which molecular conformation affects the force required to push or pull a single molecule has not been explored. Here we probe the mechanochemical response of two tetra(4-bromophenyl)porphyrin conformers using non-contact atomic force microscopy where we find a large difference between the lateral forces required for manipulation. Remarkably, despite sharing very similar adsorption characteristics, variations in the potential energy surface are capable of prohibiting probe-induced positioning of one conformer, while simultaneously permitting manipulation of the alternative conformational form. Our results are interpreted in the context of dispersion-corrected density functional theory calculations which reveal significant differences in the diffusion barriers for each conformer. These results demonstrate that conformational variation significantly modifies the mechanical response of even simple porpyhrins, potentially affecting many other flexible molecules. 1. Fast adaptive principal component extraction based on a generalized energy function Institute of Scientific and Technical Information of China (English) 欧阳缮; 保铮; 廖桂生 2003-01-01 By introducing an arbitrary diagonal matrix, a generalized energy function (GEF) is proposed for searching for the optimum weights of a two layer linear neural network. From the GEF, we derive a recur- sive least squares (RLS) algorithm to extract in parallel multiple principal components of the input covari-ance matrix without designing an asymmetrical circuit. The local stability of the GEF algorithm at the equilibrium is analytically verified. Simulation resultsshow that the GEF algorithm for parallel multiple principal components extraction exhibits the fast convergence and has the improved robustness resis- tance tothe eigenvalue spread of the input covariance matrix as compared to the well-known lateral inhi- bition model (APEX) and least mean square error reconstruction(LMSER) algorithms. 2. Effect of vacancy defects on generalized stacking fault energy of fcc metals. Science.gov (United States) Asadi, Ebrahim; Zaeem, Mohsen Asle; Moitra, Amitava; Tschopp, Mark A 2014-03-19 Molecular dynamics (MD) and density functional theory (DFT) studies were performed to investigate the influence of vacancy defects on generalized stacking fault (GSF) energy of fcc metals. MEAM and EAM potentials were used for MD simulations, and DFT calculations were performed to test the accuracy of different common parameter sets for MEAM and EAM potentials in predicting GSF with different fractions of vacancy defects. Vacancy defects were placed at the stacking fault plane or at nearby atomic layers. The effect of vacancy defects at the stacking fault plane and the plane directly underneath of it was dominant compared to the effect of vacancies at other adjacent planes. The effects of vacancy fraction, the distance between vacancies, and lateral relaxation of atoms on the GSF curves with vacancy defects were investigated. A very similar variation of normalized SFEs with respect to vacancy fractions were observed for Ni and Cu. MEAM potentials qualitatively captured the effect of vacancies on GSF. 3. Derrida's Generalized Random Energy models; 4, Continuous state branching and coalescents CERN Document Server Bovier, A 2003-01-01 In this paper we conclude our analysis of Derrida's Generalized Random Energy Models (GREM) by identifying the thermodynamic limit with a one-parameter family of probability measures related to a continuous state branching process introduced by Neveu. Using a construction introduced by Bertoin and Le Gall in terms of a coherent family of subordinators related to Neveu's branching process, we show how the Gibbs geometry of the limiting Gibbs measure is given in terms of the genealogy of this process via a deterministic time-change. This construction is fully universal in that all different models (characterized by the covariance of the underlying Gaussian process) differ only through that time change, which in turn is expressed in terms of Parisi's overlap distribution. The proof uses strongly the Ghirlanda-Guerra identities that impose the structure of Neveu's process as the only possible asymptotic random mechanism. 4. Generalized ghost pilgrim dark energy in F(T,TG) cosmology Science.gov (United States) Sharif, M.; Nazir, Kanwal 2016-07-01 This paper is devoted to study the generalized ghost pilgrim dark energy (PDE) model in F(T,TG) gravity with flat Friedmann-Robertson-Walker (FRW) universe. In this scenario, we reconstruct F(T,TG) models and evaluate the corresponding equation of state (EoS) parameter for different choices of the scale factors. We assume power-law scale factor, scale factor for unification of two phases, intermediate and bouncing scale factor. We study the behavior of reconstructed models and EoS parameters graphically. It is found that all the reconstructed models show decreasing behavior for PDE parameter u = -2. On the other hand, the EoS parameter indicates transition from dust-like matter to phantom era for all choices of the scale factor except intermediate for which this is less than - 1. We conclude that all the results are in agreement with PDE phenomenon. 5. Axial symmetry and conformal Killing vectors CERN Document Server Mars, M; Mars, Marc; Senovilla, Jose M.M. 1993-01-01 Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in conformally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, we prove that in axisymmetric spacetimes with another symmetry (such as stationary and axisymmetric or cylindrically symmetric spacetimes) and a conformal symmetry, the commutator of the axial Killing vector with the two others mush vanish or else the symmetry is larger than that originally considered. The results are completely general and do not depend on Einstein's equations or any particular matter content. 6. Einstein and the conservation of energy-momentum in general relativity CERN Document Server Weinstein, Galina 2013-01-01 The main purpose of the present paper is to show that a correction of one mistake was crucial for Einstein's pathway to the first version of the 1915 general theory of relativity, but also might have played a role in obtaining the final version of Einstein's 1915 field equations. In 1914 Einstein wrote the equations for conservation of energy-momentum for matter, and established a connection between these equations and the components of the gravitational field. He showed that a material point in gravitational fields moves on a geodesic line in space-time, the equation of which is written in terms of the Christoffel symbols. By November 4, 1915, Einstein found it advantageous to use for the components of the gravitational field, not the previous equation, but the Christoffel symbols. He corrected the 1914 equations of conservation of energy-momentum for matter. Einstein had already basically possessed the field equations in 1912 together with his mathematician friend Marcel Grossman, but because he had not rec... 7. On the optimization of the generalized coplanar Hohmann impulsive transfer adopting energy change concept Energy Technology Data Exchange (ETDEWEB) Kamel, Osman M. [Cairo Univ., Astronomy and Space Sciences Dept., Giza (Egypt); Soliman, Adel S. [National Research Center, Theoretical Physics Dept., Dokki, Giza (Egypt) 2005-02-15 We considered the problem of transferring the rocket's orbit to higher energy orbit, using minimum fuel cost, as a problem in change of energy, since this is most convenient. For the generalized Hohmann case (the departure; the transferring and the destination orbits are ellipses), we adopt the first configuration only, when the apogee of transfer orbit, and the apogee of destination orbit are coincident. Firstly, we assign the {delta}v{sub A}, {delta}v{sub B} increments in velocity at points A,B (the position of peri-apse and apo-apse impulses respectively), as functions of the eccentricity of the transfer orbit, e{sub T}. Subsequently, we apply the optimum condition leading to the derivation of the quartic equation in e{sub T}, and showed how to deduce ({delta}v{sub A}+{delta}v{sub B}){sub Min}. A numerical example is presented, in which we determined the four roots of the quartic equation, by a numerical Mathematica Version 2.2. We selected the adequate consistent root, only one in this case, and evaluated ({delta}v{sub A}+{delta}v{sub B}){sub Min} for the two orbits of the couple Earth and Mars. This article is a new approach and leads to new discoveries involved in the problem, consequently adds new insight and avoids complexities of previous procedures. (Author) 8. Lectures on Conformal Field Theory CERN Document Server Qualls, Joshua D 2015-01-01 These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students, these lecture notes have been prepared for a more general audience. They are intended as an introduction to conformal field theories in various dimensions, with applications related to topics of particular interest: topics include the conformal bootstrap program, boundary conformal field theory, and applications related to the AdS/CFT correspondence. We assume the reader to be familiar with quantum mechanics at the graduate level and to have some basic knowledge of quantum field theory. Familiarity with string theory is not a prerequisite for this lectures, although it can only help. 9. Renyi entropy and conformal defects Energy Technology Data Exchange (ETDEWEB) Bianchi, Lorenzo [Humboldt-Univ. Berlin (Germany). Inst. fuer Physik; Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Meineri, Marco [Scuola Normale Superiore, Pisa (Italy); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Istituto Nazionale di Fisica Nucleare, Pisa (Italy); Myers, Robert C. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Smolkin, Michael [California Univ., Berkely, CA (United States). Center for Theoretical Physics and Department of Physics 2016-04-18 We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy. 10. Calculation of positron binding energies using the generalized any particle propagator theory Energy Technology Data Exchange (ETDEWEB) Romero, Jonathan; Charry, Jorge A. [Department of Chemistry, Universidad Nacional de Colombia, Av. Cra. 30 #45-03, Bogotá (Colombia); Flores-Moreno, Roberto [Departamento de Química, Universidad de Guadalajara, Blvd. Marcelino García Barragán 1421, Guadalajara Jal., C. P. 44430 (Mexico); Varella, Márcio T. do N. [Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970 São Paulo, SP (Brazil); Reyes, Andrés, E-mail: [email protected] [Department of Chemistry, Universidad Nacional de Colombia, Av. Cra. 30 #45-03, Bogotá (Colombia); Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970 São Paulo, SP (Brazil) 2014-09-21 We recently extended the electron propagator theory to any type of quantum species based in the framework of the Any-Particle Molecular Orbital (APMO) approach [J. Romero, E. Posada, R. Flores-Moreno, and A. Reyes, J. Chem. Phys. 137, 074105 (2012)]. The generalized any particle molecular orbital propagator theory (APMO/PT) was implemented in its quasiparticle second order version in the LOWDIN code and was applied to calculate nuclear quantum effects in electron binding energies and proton binding energies in molecular systems [M. Díaz-Tinoco, J. Romero, J. V. Ortiz, A. Reyes, and R. Flores-Moreno, J. Chem. Phys. 138, 194108 (2013)]. In this work, we present the derivation of third order quasiparticle APMO/PT methods and we apply them to calculate positron binding energies (PBEs) of atoms and molecules. We calculated the PBEs of anions and some diatomic molecules using the second order, third order, and renormalized third order quasiparticle APMO/PT approaches and compared our results with those previously calculated employing configuration interaction (CI), explicitly correlated and quantum Montecarlo methodologies. We found that renormalized APMO/PT methods can achieve accuracies of ∼0.35 eV for anionic systems, compared to Full-CI results, and provide a quantitative description of positron binding to anionic and highly polar species. Third order APMO/PT approaches display considerable potential to study positron binding to large molecules because of the fifth power scaling with respect to the number of basis sets. In this regard, we present additional PBE calculations of some small polar organic molecules, amino acids and DNA nucleobases. We complement our numerical assessment with formal and numerical analyses of the treatment of electron-positron correlation within the quasiparticle propagator approach. 11. Calculation of positron binding energies using the generalized any particle propagator theory Science.gov (United States) Romero, Jonathan; Charry, Jorge A.; Flores-Moreno, Roberto; Varella, Márcio T. do N.; Reyes, Andrés 2014-09-01 We recently extended the electron propagator theory to any type of quantum species based in the framework of the Any-Particle Molecular Orbital (APMO) approach [J. Romero, E. Posada, R. Flores-Moreno, and A. Reyes, J. Chem. Phys. 137, 074105 (2012)]. The generalized any particle molecular orbital propagator theory (APMO/PT) was implemented in its quasiparticle second order version in the LOWDIN code and was applied to calculate nuclear quantum effects in electron binding energies and proton binding energies in molecular systems [M. Díaz-Tinoco, J. Romero, J. V. Ortiz, A. Reyes, and R. Flores-Moreno, J. Chem. Phys. 138, 194108 (2013)]. In this work, we present the derivation of third order quasiparticle APMO/PT methods and we apply them to calculate positron binding energies (PBEs) of atoms and molecules. We calculated the PBEs of anions and some diatomic molecules using the second order, third order, and renormalized third order quasiparticle APMO/PT approaches and compared our results with those previously calculated employing configuration interaction (CI), explicitly correlated and quantum Montecarlo methodologies. We found that renormalized APMO/PT methods can achieve accuracies of ˜0.35 eV for anionic systems, compared to Full-CI results, and provide a quantitative description of positron binding to anionic and highly polar species. Third order APMO/PT approaches display considerable potential to study positron binding to large molecules because of the fifth power scaling with respect to the number of basis sets. In this regard, we present additional PBE calculations of some small polar organic molecules, amino acids and DNA nucleobases. We complement our numerical assessment with formal and numerical analyses of the treatment of electron-positron correlation within the quasiparticle propagator approach. 12. Energy Conversions in the Atmosphere on the Scale of the General Circulation OpenAIRE Mieghem, Jacques Van 2011-01-01 From the equations of balance established for the different forms of energy (potential, kinetic and internal energies), the energy fluxes, the rates of energy production and conversion are deduced. Provided weighted mean values are considered the zonally averaged value of the kinetic energy may be decomposed into kinetic energy of the mean motion and the mean kinetic energy of the large-scale eddies. The corresponding equations of balance are established. The axial symmetry with respect to th... 13. 76 FR 50204 - Decision and Order Granting a Waiver to Fujitsu General Limited From the Department of Energy... Science.gov (United States) 2011-08-12 ... No. CAC-033, which grants Fujitsu General Limited (Fujitsu) a waiver from the existing DOE test... Energy. Decision and Order In the Matter of: Fujitsu General Limited (Fujitsu) (Case No. CAC- 033... petition for waiver filed by Fujitsu (Case No. CAC-033) is hereby granted as set forth in the... 14. Energy, momentum and angular momentum in the dyadosphere of a charged spacetime in teleparallel equivalent of general relativity Institute of Scientific and Technical Information of China (English) Gamal G.L.Nashed 2012-01-01 We apply the energy momentum and angular momentum tensor to a tetrad field,with two unknown functions of radial coordinate,in the framework of a teleparallel equivalent of general relativity (TEGR).The definition of the gravitational energy is used to investigate the energy within the external event horizon of the dyadosphere region for the Reissner-Nordstr(o)m black hole.We also calculate the spatial momentum and angular momentum. 15. Viscous conformal gauge theories DEFF Research Database (Denmark) Toniato, Arianna; Sannino, Francesco; Rischke, Dirk H. 2017-01-01 We present the conformal behavior of the shear viscosity-to-entropy density ratio and the fermion-number diffusion coefficient within the perturbative regime of the conformal window for gauge-fermion theories.......We present the conformal behavior of the shear viscosity-to-entropy density ratio and the fermion-number diffusion coefficient within the perturbative regime of the conformal window for gauge-fermion theories.... 16. Conformal gravity and "gravitational bubbles" CERN Document Server Berezin, V A; Eroshenko, Yu N 2015-01-01 We describe the general structure of the spherically symmetric solutions in the Weyl conformal gravity. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions, consisting of two classes, is found. The first one contains the solutions with constant two-dimensional curvature scalar, and the representatives are the famous Robertson--Walker metrics. We called one of them the "gravitational bubbles", which is compact and with zero Weyl tensor. These "gravitational bubbles" are the pure vacuum curved space-times (without any material sources, including the cosmological constant), which are absolutely impossible in General Relativity. This phenomenon makes it easier to create the universe from "nothing". The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family, which can be conformally covered by the thee-para... 17. Implications of conformal symmetry in quantum mechanics Science.gov (United States) Okazaki, Tadashi 2017-09-01 In conformal quantum mechanics with the vacuum of a real scaling dimension and with a complete orthonormal set of energy eigenstates, which is preferable under the unitary evolution, the dilatation expectation value between energy eigenstates monotonically decreases along the flow from the UV to the IR. In such conformal quantum mechanics, there exist bounds on scaling dimensions of the physical states and the gauge operators. 18. Representation of target-bound drugs by computed conformers: implications for conformational libraries Directory of Open Access Journals (Sweden) Goede Andrean 2006-06-01 Full Text Available Abstract Background The increasing number of known protein structures provides valuable information about pharmaceutical targets. Drug binding sites are identifiable and suitable lead compounds can be proposed. The flexibility of ligands is a critical point for the selection of potential drugs. Since computed 3D structures of millions of compounds are available, the knowledge of their binding conformations would be a great benefit for the development of efficient screening methods. Results Integration of two public databases allowed superposition of conformers for 193 approved drugs with 5507 crystallised target-bound counterparts. The generation of 9600 drug conformers using an atomic force field was carried out to obtain an optimal coverage of the conformational space. Bioactive conformations are best described by a conformational ensemble: half of all drugs exhibit multiple active states, distributed over the entire range of the reachable energy and conformational space. A number of up to 100 conformers per drug enabled us to reproduce the bound states within a similarity threshold of 1.0 Å in 70% of all cases. This fraction rises to about 90% for smaller or average sized drugs. Conclusion Single drugs adopt multiple bioactive conformations if they interact with different target proteins. Due to the structural diversity of binding sites they adopt conformations that are distributed over a broad conformational space and wide energy range. Since the majority of drugs is well represented by a predefined low number of conformers (up to 100 this procedure is a valuable method to compare compounds by three-dimensional features or for fast similarity searches starting with pharmacophores. The underlying 9600 generated drug conformers are downloadable from the Super Drug Web site 1. All superpositions are visualised at the same source. Additional conformers (110,000 of 2400 classified WHO-drugs are also available. 19. Five-dimensional teleparallel theory equivalent to general relativity, the axially symmetric solution,energy and spatial momentum Institute of Scientific and Technical Information of China (English) Gamal G.L. Nashed 2011-01-01 A theory of (4+1)-dimensional gravity is developed on the basis of the teleparallel theory equivalent to general relativity.The fundamental gravitational field variables are the five-dimensional vector fields (pentad),defined globally on a manifold M,and gravity is attributed to the torsion.The Lagrangian density is quadratic in the torsion tensor.We then give the exact five-dimensional solution.The solution is a generalization of the familiar Schwarzschild and Kerr solutions of the four-dimensional teleparallel equivalent of general relativity.We also use the definition of the gravitational energy to calculate the energy and the spatial momentum. 20. Conformational and Vibrational Studies of Triclosan Science.gov (United States) Özişik, Haci; Bayari, S. Haman; Saǧlam, Semran 2010-01-01 The conformational equilibrium of triclosan (5-chloro-2-(2, 4-dichlorophenoxy) phenol) have been calculated using density functional theory (DFTe/B3LYP/6-311++G(d, p)) method. Four different geometries were found to correspond to energy minimum conformations. The IR spectrum of triclosan was measured in the 4000-400 cm-1 region. We calculated the harmonic frequencies and intensities of the most stable conformers in order to assist in the assignment of the vibrational bands in the experimental spectrum. The fundamental vibrational modes were characterized depending on their total energy distribution (TED%) using scaled quantum mechanical (SQM) force field method. 1. Hot Conformal Gauge Theories DEFF Research Database (Denmark) Mojaza, Matin; Pica, Claudio; Sannino, Francesco 2010-01-01 We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged in s.......e. they are independent on the specific matter representation.......We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged...... in such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Due to large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors and matter representation. We... 2. Conformal mapping for multiple terminals Science.gov (United States) Wang, Weimin; Ma, Wenying; Wang, Qiang; Ren, Hao 2016-11-01 Conformal mapping is an important mathematical tool that can be used to solve various physical and engineering problems in many fields, including electrostatics, fluid mechanics, classical mechanics, and transformation optics. It is an accurate and convenient way to solve problems involving two terminals. However, when faced with problems involving three or more terminals, which are more common in practical applications, existing conformal mapping methods apply assumptions or approximations. A general exact method does not exist for a structure with an arbitrary number of terminals. This study presents a conformal mapping method for multiple terminals. Through an accurate analysis of boundary conditions, additional terminals or boundaries are folded into the inner part of a mapped region. The method is applied to several typical situations, and the calculation process is described for two examples of an electrostatic actuator with three electrodes and of a light beam splitter with three ports. Compared with previously reported results, the solutions for the two examples based on our method are more precise and general. The proposed method is helpful in promoting the application of conformal mapping in analysis of practical problems. 3. A general method to derive tissue parameters for Monte Carlo dose calculation with multi-energy CT Science.gov (United States) Lalonde, Arthur; Bouchard, Hugo 2016-11-01 To develop a general method for human tissue characterization with dual- and multi-energy CT and evaluate its performance in determining elemental compositions and quantities relevant to radiotherapy Monte Carlo dose calculation. Ideal materials to describe human tissue are obtained applying principal component analysis on elemental weight and density data available in literature. The theory is adapted to elemental composition for solving tissue information from CT data. A novel stoichiometric calibration method is integrated to the technique to make it suitable for a clinical environment. The performance of the method is compared with two techniques known in literature using theoretical CT data. In determining elemental weights with dual-energy CT, the method is shown to be systematically superior to the water-lipid-protein material decomposition and comparable to the parameterization technique. In determining proton stopping powers and energy absorption coefficients with dual-energy CT, the method generally shows better accuracy and unbiased results. The generality of the method is demonstrated simulating multi-energy CT data to show the potential to extract more information with multiple energies. The method proposed in this paper shows good performance to determine elemental compositions from dual-energy CT data and physical quantities relevant to radiotherapy dose calculation. The method is particularly suitable for Monte Carlo calculations and shows promise in using more than two energies to characterize human tissue with CT. 4. A general method to derive tissue parameters for Monte Carlo dose calculation with multi-energy CT. Science.gov (United States) Lalonde, Arthur; Bouchard, Hugo 2016-11-21 To develop a general method for human tissue characterization with dual- and multi-energy CT and evaluate its performance in determining elemental compositions and quantities relevant to radiotherapy Monte Carlo dose calculation. Ideal materials to describe human tissue are obtained applying principal component analysis on elemental weight and density data available in literature. The theory is adapted to elemental composition for solving tissue information from CT data. A novel stoichiometric calibration method is integrated to the technique to make it suitable for a clinical environment. The performance of the method is compared with two techniques known in literature using theoretical CT data. In determining elemental weights with dual-energy CT, the method is shown to be systematically superior to the water-lipid-protein material decomposition and comparable to the parameterization technique. In determining proton stopping powers and energy absorption coefficients with dual-energy CT, the method generally shows better accuracy and unbiased results. The generality of the method is demonstrated simulating multi-energy CT data to show the potential to extract more information with multiple energies. The method proposed in this paper shows good performance to determine elemental compositions from dual-energy CT data and physical quantities relevant to radiotherapy dose calculation. The method is particularly suitable for Monte Carlo calculations and shows promise in using more than two energies to characterize human tissue with CT. 5. Econometrically calibrated computable general equilibrium models: Applications to the analysis of energy and climate politics Science.gov (United States) Schu, Kathryn L. Economy-energy-environment models are the mainstay of economic assessments of policies to reduce carbon dioxide (CO2) emissions, yet their empirical basis is often criticized as being weak. This thesis addresses these limitations by constructing econometrically calibrated models in two policy areas. The first is a 35-sector computable general equilibrium (CGE) model of the U.S. economy which analyzes the uncertain impacts of CO2 emission abatement. Econometric modeling of sectors' nested constant elasticity of substitution (CES) cost functions based on a 45-year price-quantity dataset yields estimates of capital-labor-energy-material input substitution elasticities and biases of technical change that are incorporated into the CGE model. I use the estimated standard errors and variance-covariance matrices to construct the joint distribution of the parameters of the economy's supply side, which I sample to perform Monte Carlo baseline and counterfactual runs of the model. The resulting probabilistic abatement cost estimates highlight the importance of the uncertainty in baseline emissions growth. The second model is an equilibrium simulation of the market for new vehicles which I use to assess the response of vehicle prices, sales and mileage to CO2 taxes and increased corporate average fuel economy (CAFE) standards. I specify an econometric model of a representative consumer's vehicle preferences using a nested CES expenditure function which incorporates mileage and other characteristics in addition to prices, and develop a novel calibration algorithm to link this structure to vehicle model supplies by manufacturers engaged in Bertrand competition. CO2 taxes' effects on gasoline prices reduce vehicle sales and manufacturers' profits if vehicles' mileage is fixed, but these losses shrink once mileage can be adjusted. Accelerated CAFE standards induce manufacturers to pay fines for noncompliance rather than incur the higher costs of radical mileage improvements 6. Generalized hard-core dimer model approach to low-energy Heisenberg frustrated antiferromagnets: General properties and application to the kagome antiferromagnet Science.gov (United States) Schwandt, David; Mambrini, Matthieu; Poilblanc, Didier 2010-06-01 We propose a general nonperturbative scheme that quantitatively maps the low-energy sector of spin-1/2 frustrated Heisenberg antiferromagnets to effective generalized quantum dimer models. We develop the formal lattice-independent frame and establish some important results on (i) the locality of the generated Hamiltonians, (ii) how full resummations can be performed in this renormalization scheme. The method is then applied to the much debated kagome antiferromagnet for which a fully resummed effective Hamiltonian—shown to capture the essential properties and provide deep insights on the microscopic model [D. Poilblanc, M. Mambrini, and D. Schwandt, Phys. Rev. B 81, 180402(R) (2010)]—is derived. 7. Phenomenology of dark energy: general features of large-scale perturbations Science.gov (United States) Pèrenon, Louis; Piazza, Federico; Marinoni, Christian; Hui, Lam 2015-11-01 We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to ΛCDM at intermediate redshifts (0.5 lesssim z lesssim 1), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by ΛCDM. (3) The gravitational slip parameter η—the ratio of the space part of the metric perturbation to the time part—is bounded from above. For Brans-Dicke-type theories η is at most unity. For more general theories, η can exceed unity at intermediate redshifts, but not more than about 1.5 if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data. 8. BayeSED: A General Approach to Fitting the Spectral Energy Distribution of Galaxies Science.gov (United States) Han, Yunkun; Han, Zhanwen 2014-11-01 We present a newly developed version of BayeSED, a general Bayesian approach to the spectral energy distribution (SED) fitting of galaxies. The new BayeSED code has been systematically tested on a mock sample of galaxies. The comparison between the estimated and input values of the parameters shows that BayeSED can recover the physical parameters of galaxies reasonably well. We then applied BayeSED to interpret the SEDs of a large Ks -selected sample of galaxies in the COSMOS/UltraVISTA field with stellar population synthesis models. Using the new BayeSED code, a Bayesian model comparison of stellar population synthesis models has been performed for the first time. We found that the 2003 model by Bruzual & Charlot, statistically speaking, has greater Bayesian evidence than the 2005 model by Maraston for the Ks -selected sample. In addition, while setting the stellar metallicity as a free parameter obviously increases the Bayesian evidence of both models, varying the initial mass function has a notable effect only on the Maraston model. Meanwhile, the physical parameters estimated with BayeSED are found to be generally consistent with those obtained using the popular grid-based FAST code, while the former parameters exhibit more natural distributions. Based on the estimated physical parameters of the galaxies in the sample, we qualitatively classified the galaxies in the sample into five populations that may represent galaxies at different evolution stages or in different environments. We conclude that BayeSED could be a reliable and powerful tool for investigating the formation and evolution of galaxies from the rich multi-wavelength observations currently available. A binary version of the BayeSED code parallelized with Message Passing Interface is publicly available at https://bitbucket.org/hanyk/bayesed. 9. Simple, yet powerful methodologies for conformational sampling of proteins. Science.gov (United States) Harada, Ryuhei; Takano, Yu; Baba, Takeshi; Shigeta, Yasuteru 2015-03-07 Several biological functions, such as molecular recognition, enzyme catalysis, signal transduction, allosteric regulation, and protein folding, are strongly related to conformational transitions of proteins. These conformational transitions are generally induced as slow dynamics upon collective motions, including biologically relevant large-amplitude fluctuations of proteins. Although molecular dynamics (MD) simulation has become a powerful tool for extracting conformational transitions of proteins, it might still be difficult to reach time scales of the biological functions because the accessible time scales of MD simulations are far from biological time scales, even if straightforward conventional MD (CMD) simulations using massively parallel computers are employed. Thus, it is desirable to develop efficient methods to achieve canonical ensembles with low computational costs. From this perspective, we review several enhanced conformational sampling techniques of biomolecules developed by us. In our methods, multiple independent short-time MD simulations are employed instead of single straightforward long-time CMD simulations. Our basic strategy is as follows: (i) selection of initial seeds (initial structures) for the conformational sampling in restarting MD simulations. Here, the seeds should be selected as candidates with high potential to transit. (ii) Resampling from the selected seeds by initializing velocities in restarting short-time MD simulations. A cycle of these simple protocols might drastically promote the conformational transitions of biomolecules. (iii) Once reactive trajectories extracted from the cycles of short-time MD simulations are obtained, a free energy profile is evaluated by means of umbrella sampling (US) techniques with the weighted histogram analysis method (WHAM) as a post-processing technique. For the selection of the initial seeds, we proposed four different choices: (1) Parallel CaScade molecular dynamics (PaCS-MD), (2) Fluctuation 10. CO2, energy and economy interactions: A multisectoral, dynamic, computable general equilibrium model for Korea Science.gov (United States) Kang, Yoonyoung While vast resources have been invested in the development of computational models for cost-benefit analysis for the "whole world" or for the largest economies (e.g. United States, Japan, Germany), the remainder have been thrown together into one model for the "rest of the world." This study presents a multi-sectoral, dynamic, computable general equilibrium (CGE) model for Korea. This research evaluates the impacts of controlling COsb2 emissions using a multisectoral CGE model. This CGE economy-energy-environment model analyzes and quantifies the interactions between COsb2, energy and economy. This study examines interactions and influences of key environmental policy components: applied economic instruments, emission targets, and environmental tax revenue recycling methods. The most cost-effective economic instrument is the carbon tax. The economic effects discussed include impacts on main macroeconomic variables (in particular, economic growth), sectoral production, and the energy market. This study considers several aspects of various COsb2 control policies, such as the basic variables in the economy: capital stock and net foreign debt. The results indicate emissions might be stabilized in Korea at the expense of economic growth and with dramatic sectoral allocation effects. Carbon dioxide emissions stabilization could be achieved to the tune of a 600 trillion won loss over a 20 year period (1990-2010). The average annual real GDP would decrease by 2.10% over the simulation period compared to the 5.87% increase in the Business-as-Usual. This model satisfies an immediate need for a policy simulation model for Korea and provides the basic framework for similar economies. It is critical to keep the central economic question at the forefront of any discussion regarding environmental protection. How much will reform cost, and what does the economy stand to gain and lose? Without this model, the policy makers might resort to hesitation or even blind speculation. With 11. 40 CFR 51.857 - Frequency of conformity determinations. Science.gov (United States) 2010-07-01 ... 40 Protection of Environment 2 2010-07-01 2010-07-01 false Frequency of conformity determinations... Conformity of General Federal Actions to State or Federal Implementation Plans § 51.857 Frequency of conformity determinations. Link to an amendment published at 75 FR 17272, April 5, 2010. (a) The... 12. 40 CFR 93.157 - Frequency of conformity determinations. Science.gov (United States) 2010-07-01 ... 40 Protection of Environment 20 2010-07-01 2010-07-01 false Frequency of conformity determinations... PROGRAMS (CONTINUED) DETERMINING CONFORMITY OF FEDERAL ACTIONS TO STATE OR FEDERAL IMPLEMENTATION PLANS Determining Conformity of General Federal Actions to State or Federal Implementation Plans § 93.157... 13. 40 CFR 86.407-78 - Certificate of conformity required. Science.gov (United States) 2010-07-01 ... 40 Protection of Environment 18 2010-07-01 2010-07-01 false Certificate of conformity required. 86... Regulations for 1978 and Later New Motorcycles, General Provisions § 86.407-78 Certificate of conformity... conformity issued pursuant to this subpart, except as specified in paragraph (b) of this section,... 14. Conserved Quantities and Conformal Mechanico-Electrical Systems Institute of Scientific and Technical Information of China (English) FU Jing-Li; WANG Xian-Jun; XIE Feng-Ping 2008-01-01 The conformal mechanico-electrical systems are presented by infinitesimal point transformations of time and generalized coordinates. The necessary and sufficient conditions that the conformal mechanico-electrical systems possess Lie symmetry are given. The Noether conserved quantities of the conformal mechanico-electrical systems are obtained from Lie symmetries. 15. Entanglement Temperature in Non-conformal Cases CERN Document Server He, Song; Wu, Jun-Bao 2013-01-01 Potential reconstruction can be used to find various analytical asymptotical AdS solutions in Einstein dilation system generally. We have generated two simple solutions without physical singularity called zero temperature solutions. We also proposed a numerical way to obtain black hole solution in Einstein dilaton system with special dilaton potential. By using this method, we obtain the corresponding black hole solutions numerically and investigate the thermal stability of the black hole by comparing the free energy of thermal gas and the corresponding black hole. In two groups of non-conformal gravity solutions obtained in this paper, we find that the two thermal gas solutions are more unstable than black hole solutions respectively. Finally, we consider black hole solutions as a thermal state of zero temperature solutions to check that the first thermal dynamical law exists in entanglement system from holographic point of view. 16. Phenomenology of dark energy: general features of large-scale perturbations CERN Document Server Perenon, Louis; Marinoni, Christian; Hui, Lam 2015-01-01 We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to$\\Lambda$CDM at intermediate redshifts ($0.5 \\lesssim z \\lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by$\\Lambda$CDM. (3) The gravitational sli... 17. BayeSED: A General Approach to Fitting the Spectral Energy Distribution of Galaxies CERN Document Server Han, Yunkun 2014-01-01 We present a newly developed version of BayeSED, a general Bayesian approach to the spectral energy distribution (SED) fitting of galaxies. The new BayeSED code has been systematically tested on a mock sample of galaxies. The comparison between estimated and inputted value of the parameters show that BayeSED can recover the physical parameters of galaxies reasonably well. We then applied BayeSED to interpret the SEDs of a large Ks-selected sample of galaxies in the COSMOS/UltraVISTA field with stellar population synthesis models. With the new BayeSED code, a Bayesian model comparison of stellar population synthesis models has been done for the first time. We found that the model by Bruzual & Charlot (2003), statistically speaking, has larger Bayesian evidence than the model by Maraston (2005) for the Ks-selected sample. Besides, while setting the stellar metallicity as a free parameter obviously increases the Bayesian evidence of both models, varying the IMF has a notable effect only on the Maraston (2005... 18. Consumer protection issues in energy: a guide for attorneys general. Insulation, solar, automobile device, home devices Energy Technology Data Exchange (ETDEWEB) Cohen, Harry I.; Hulse, William S.; Jones, Robert R.; Langer, Robert M.; Petrucelli, Paul J.; Schroeder, Robert J. 1979-11-01 The guide attempts to bring together two important and current issues: energy and consumer protection. Perhaps the most basic consumer-protection issue in the energy area is assuring adequate supplies at adequate prices. It is anticipated, though, that consumers will want to consider new ways to lower enegy consumption and cost, and will thus be susceptible to fraudulent energy claims. Information is prepared on insulation, solar, energy-saving devices for the home, and energy-saving devices for the automobile. 19. Office of Inspector General audit report on the U.S. Department of Energys consolidated financial statements for fiscal year 1998 Energy Technology Data Exchange (ETDEWEB) NONE 1999-02-01 The Department prepared the Fiscal Year 1998 Accountability Report to combine critical financial and program performance information in a single report. The Departments consolidated financial statements and the related audit reports are included as major components of the Accountability Report. The Office of Inspector General audited the Departments consolidated financial statements as of and for the years ended September 30, 1998 and 1997. In the opinion of the Office of Inspector General, except for the environmental liabilities lines items in Fiscal year 1998, these financial statements present fairly, in all material respects, the financial position of the Department as of September 30, 1998 and 1997, and its consolidated net cost, changes in net position, budgetary resources, financing activities, and custodial activities for the years then ended in conformity with Federal accounting standards. In accordance with Government Auditing Standards, the Office of Inspector General issued a separate report on the Department internal controls. This report discusses needed improvements to the environmental liabilities estimating process and the reporting of performance measure information. 20. Expansion Formulation of General Relativity: the Gauge Functions for Energy-Momentum Tensor Science.gov (United States) Beloushko, Konstantin; Karbanovski, Valeri At present the one of the GR (General Relativity) basic problem remains a definition of the gravitation field (GF) energy. We shall analyze this content. As well known, the energy-momentum tensor'' (EMT) of GF was introduced by Einstein [1] with purpose of the SRT (Special Relativity Theory) generalization. It supposed also, that EMT of matter satisfy to the condition begin{equation} ⪉bel{GrindEQ__1_1_} T^{ik} _{;i} =0 (a semicolon denotes a covariant differentiation with respect to coordinates). In absence of GF the equation (ref{GrindEQ__1_1_}) reduces to a corresponding SRT expression begin{equation} ⪉bel{GrindEQ__1_2_} T^{ik} _{,i} =0 (a comma denotes a differentiation with respect to coordinates of space-time). Obviously, the conservation law'' (ref{GrindEQ__1_2_}) is not broken by transformation begin{equation} ⪉bel{GrindEQ__1_3_} T^{ik} to tilde{T}^{ik} =T^{ik} +h^{ikl} _{,l} , where for h(ikl) takes place a constrain begin{equation} ⪉bel{GrindEQ__1_4_} h^{ikl} =-h^{ilk} Later the given property has been used for a construction pseudo-tensor'' tau (ik) of pure'' GF [2, S 96] begin{equation} ⪉bel{GrindEQ__1_5_} -gleft(frac{c^{4} }{8pi G} left(R^{ik} -frac{1}{2} g^{ik} Rright)+tau ^{ik} right)=h^{ikl} _{,l} However such definition was a consequence of non-covariant transition from a reference system with condition g(ik) _{,l} =0 to an arbitrary frame. Therefore the Landau-Lifshitz pseudo-tensor has no physical contents and considered problem remains actual. The non-covariant character'' of GF energy was the reason for criticism of GR as Einstein's contemporaries [3, 4], as and during the subsequent period (see, for example, [5]). In [6] were analyzed the grounds of given problem, which are connected with a formulation indefiniteness of the conservation law'' in curved space-time. In [7] contends, that the gravitational energy in EMT can be separated only artificially'' by a choice of the certain coordinate system. In [8] is concluded 1. On functional representations of the conformal algebra Science.gov (United States) Rosten, Oliver J. 2017-07-01 Starting with conformally covariant correlation functions, a sequence of functional representations of the conformal algebra is constructed. A key step is the introduction of representations which involve an auxiliary functional. It is observed that these functionals are not arbitrary but rather must satisfy a pair of consistency equations corresponding to dilatation and special conformal invariance. In a particular representation, the former corresponds to the canonical form of the exact renormalization group equation specialized to a fixed point whereas the latter is new. This provides a concrete understanding of how conformal invariance is realized as a property of the Wilsonian effective action and the relationship to action-free formulations of conformal field theory. Subsequently, it is argued that the conformal Ward Identities serve to define a particular representation of the energy-momentum tensor. Consistency of this construction implies Polchinski's conditions for improving the energy-momentum tensor of a conformal field theory such that it is traceless. In the Wilsonian approach, the exactly marginal, redundant field which generates lines of physically equivalent fixed points is identified as the trace of the energy-momentum tensor. 2. Conformational elasticity theory of chain molecules Institute of Scientific and Technical Information of China (English) YANG; Xiaozhen 2001-01-01 This paper develops a conformational elasticity theory of chain molecules, which is based on three key points: (ⅰ) the molecular model is the rotational isomeric state (RIS) model; (ⅱ) the conformational distribution function of a chain molecule is described by a function of two variables, the end-to-end distance of a chain conformation and the energy of the conformation; (ⅲ) the rule of changes in the chain conformational states during deformation is that a number of chain conformations would vanish. The ideal deformation behavior calculated by the theory shows that the change in chain conformations is physically able to make the upward curvature of the stress-strain curve at the large-scale deformation of natural rubber. With the theory, different deformation behaviors between polymers with different chemical structures can be described, the energy term of the stress in the deformations can be predicted, and for natural rubber the fraction of the energy term is around 13%, coinciding with the experimental results. 3. Conformal theory of galactic halos CERN Document Server Nesbet, R K 2011-01-01 Current cosmological theory describes an isolated galaxy as an observable central galaxy, surrounded by a large spherical halo attributed to dark matter. Galaxy formation by condensation of mass-energy out of a primordial uniform background is shown here to leave a scar, observed as a centripetal gravitational field halo in anomalous galactic rotation and in gravitational lensing. Conformal theory accounts for the otherwise counterintuitive centripetal effect. 4. Energy Science.gov (United States) 2003-01-01 Canada, Britain, and Spain. We found that the energy industry is not in crisis ; however, U.S. government policies, laws, dollars, and even public...CEIMAT (Centro de Investagaciones Energeticas , Medioambeintales y Tecnologicas) Research and development Page 3 of 28ENERGY 8/10/04http://www.ndu.edu...meet an emerging national crisis (war), emergency (natural disaster), or major impact event (Y2K). Certain resources are generally critical to the 5. Evolution of holographic dark energy with interaction term$Q \\propto H\\rho_{\\rm de}$and generalized second law Indian Academy of Sciences (India) Praseetha P; Mathew Titus K 2016-03-01 A flat FLRW Universe with dark matter and dark energy, which are interacting witheach other, is considered. The dark energy is represented by the holographic dark energy model and the interaction term is taken as proportional to the dark energy density. We have studied the cosmological evolution and analysed the validity of the generalized second law of thermodynamics (GSL) under thermal equilibrium conditions and non-equilibrium conditions. We have found thatthe GSL is completely valid at the apparent horizon but violated at the event horizon under thermal equilibrium condition. Under thermal non-equilibrium condition, for the GSL to be valid, we found out that the temperature of the dark energy must be greater than the temperature of the apparent horizon if the dark energy behaves as a quintessence fluid. 6. Temperature effects on the generalized planar fault energies and twinnabilities of Al, Ni and Cu: First principles calculations KAUST Repository Liu, Lili 2014-06-01 Based on the quasiharmonic approach from first-principles phonon calculations, the volume versus temperature relations for Al, Ni and Cu are obtained. Using the equilibrium volumes at temperature T, the temperature dependences of generalized planar fault energies have also been calculated by first-principles calculations. It is found that the generalized planar fault energies reduce slightly with increasing temperature. Based on the calculated generalized planar fault energies, the twinnabilities of Al, Ni and Cu are discussed with the three typical criteria for crack tip twinning, grain boundary twinning and inherent twinning at different temperatures. The twinnabilities of Al, Ni and Cu also decrease slightly with increasing temperature. Ni and Cu have the inherent twinnabilities. But, Al does not exhibit inherent twinnability. These results are in agreement with the previous theoretical studies at 0 K and experimental observations at ambient temperature. © 2014 Elsevier B.V. All rights reserved. 7. Radiation Analysis and Characteristics of Conformal Reflectarray Antennas Directory of Open Access Journals (Sweden) Payam Nayeri 2012-01-01 Full Text Available This paper investigates the feasibility of designing reflectarray antennas on conformal surfaces. A generalized analysis approach is presented that can be applied to compute the radiation performance of conformal reflectarray antennas. Using this approach, radiation characteristics of conformal reflectarray antennas on singly curved platforms are studied and the performances of these designs are compared with planar designs. It is demonstrated that a conformal reflectarray antenna can be a suitable choice for applications requiring high-gain antennas on curved platforms. 8. A study of the kinetic energy generation with general circulation models Science.gov (United States) Chen, T.-C.; Lee, Y.-H. 1983-01-01 The history data of winter simulation by the GLAS climate model and the NCAR community climate model are used to examine the generation of atmospheric kinetic energy. The contrast between the geographic distributions of the generation of kinetic energy and divergence of kinetic energy flux shows that kinetic energy is generated in the upstream side of jets, transported to the downstream side and destroyed there. The contributions from the time-mean and transient modes to the counterbalance between generation of kinetic energy and divergence of kinetic energy flux are also investigated. It is observed that the kinetic energy generated by the time-mean mode is essentially redistributed by the time-mean flow, while that generated by the transient flow is mainly responsible for the maintenance of the kinetic energy of the entire atmospheric flow. 9. Conformant Planning via Symbolic Model Checking CERN Document Server Cimatti, A; 10.1613/jair.774 2011-01-01 We tackle the problem of planning in nondeterministic domains, by presenting a new approach to conformant planning. Conformant planning is the problem of finding a sequence of actions that is guaranteed to achieve the goal despite the nondeterminism of the domain. Our approach is based on the representation of the planning domain as a finite state automaton. We use Symbolic Model Checking techniques, in particular Binary Decision Diagrams, to compactly represent and efficiently search the automaton. In this paper we make the following contributions. First, we present a general planning algorithm for conformant planning, which applies to fully nondeterministic domains, with uncertainty in the initial condition and in action effects. The algorithm is based on a breadth-first, backward search, and returns conformant plans of minimal length, if a solution to the planning problem exists, otherwise it terminates concluding that the problem admits no conformant solution. Second, we provide a symbolic representation ... 10. A geodesic model in conformal superspace CERN Document Server Gomes, Henrique de A 2016-01-01 In this paper, I look for the most general geometrodynamical symmetries compatible with spatial relational principles. I argue that they lead either to a completely static Universe, or one embodying spatial conformal diffeomorphisms. Demanding locality for an action compatible with these principles severely limits its form, both for the gravitational part as well as all matter couplings. The simplest and most natural choice for pure gravity has two propagating physical degrees of freedom (and no refoliation-invariance). The system has a geometric interpretation as a geodesic model in infinite dimensional conformal superspace. Conformal superspace is a stratified manifold, with different strata corresponding to different isometry groups. Choosing space to be (homeomorphic to)$S^3$, conformal superspace has a preferred stratum with maximal stabilizer group. This stratum consists of a single point -- corresponding to the conformal geometry of the round 3-sphere. This is the most homogeneous non-degenerate geome... 11. Transitive conformal holonomy groups CERN Document Server Alt, Jesse 2011-01-01 For$(M,[g])$a conformal manifold of signature$(p,q)$and dimension at least three, the conformal holonomy group$\\mathrm{Hol}(M,[g]) \\subset O(p+1,q+1)$is an invariant induced by the canonical Cartan geometry of$(M,[g])$. We give a description of all possible connected conformal holonomy groups which act transitively on the M\\"obius sphere$S^{p,q}$, the homogeneous model space for conformal structures of signature$(p,q)$. The main part of this description is a list of all such groups which also act irreducibly on$\\R^{p+1,q+1}$. For the rest, we show that they must be compact and act decomposably on$\\R^{p+1,q+1}$, in particular, by known facts about conformal holonomy the conformal class$[g]$must contain a metric which is locally isometric to a so-called special Einstein product. 12. LINEAR GENERAL EQUILIBRIUM MODEL OF ENERGY DEMAND AND CO2 EMISSIONS GENERATED BY THE ANDALUSIAN PRODUCTIVE SYSTEM Directory of Open Access Journals (Sweden) Manuel Alejandro Cardenete 2012-01-01 Full Text Available In this study we apply a multiplier decomposition methodology of a linear general equilibrium model based on the regional social accounting matrix to the Andalusian economy. The aim of this methodology is to separate the size of the different effects in terms of energy expenditure and total emissions generated by the whole productive system to satisfy the final demand of each branch of the Andalusian economy and the direct emissions generated to produce energy for each subsystem. 13. Stress-energy distribution for a cylindrical artificial gravity field via the Darmois-Israel junction conditions of general relativity Science.gov (United States) Istrate, Nicolae; Lindner, John 2014-03-01 We design an Earth-like artificial gravity field using the Darmois-Israel junction conditions of general relativity to connect the flat spacetime outside an infinitesimally thin cylinder to the curved spacetime inside. In the calculation of extrinsic curvature, our construction exploits Earth's weak gravity, which implies similar inside and outside curvatures, to approximate the unit normal inside by the negative unit normal outside. The stress-energy distribution on the cylinder's sides includes negative energy density. 14. Conformal dynamical equivalence and applications Science.gov (United States) Spyrou, N. K. 2011-02-01 The "Conformal Dynamical Equivalence" (CDE) approach is briefly reviewed, and some of its applications, at various astrophysical levels (Sun, Solar System, Stars, Galaxies, Clusters of Galaxies, Universe as a whole), are presented. According to the CDE approach, in both the Newtonian and general-relativistic theories of gravity, the isentropic hydrodynamic flows in the interior of a bounded gravitating perfect-fluid source are dynamically equivalent to geodesic motions in a virtual, fully defined fluid source. Equivalently, the equations of hydrodynamic motion in the former source are functionally similar to those of the geodesic motions in the latter, physically, fully defined source. The CDE approach is followed for the dynamical description of the motions in the fluid source. After an observational introduction, taking into account all the internal physical characteristics of the corresponding perfect-fluid source, and based on the property of the isentropic hydrodynamic flows (quite reasonable for an isolated physical system), we examine a number of issues, namely, (i) the classical Newtonian explanation of the celebrated Pioneer-Anomaly effect in the Solar System, (ii) the possibility of both the attractive gravity and the repulsive gravity in a non-quantum Newtonian framework, (iii) the evaluation of the masses - theoretical, dynamical, and missing - and of the linear dimensions of non-magnetized and magnetized large-scale cosmological structures, (iv) the explanation of the flat-rotation curves of disc galaxies, (v) possible formation mechanisms of winds and jets, and (vi) a brief presentation of a conventional approach - toy model to the dynamics of the Universe, characterized by the dominant collisional dark matter (with its subdominant luminous baryonic "contamination"), correctly interpreting the cosmological observational data without the need of the notions dark energy, cosmological constant, and universal accelerating expansion. 15. On Functional Representations of the Conformal Algebra CERN Document Server Rosten, Oliver J 2014-01-01 Starting with conformally covariant correlation functions, a sequence of functional representations of the conformal algebra is constructed. A key step is the introduction of representations which involve an auxiliary functional. It is observed that these functionals are not arbitrary but rather must satisfy a pair of consistency equations; one such is identified, in a particular representation, as an Exact Renormalization Group equation specialized to a fixed-point. Therefore, the associated functional is identified with the Wilsonian Effective Action and this creates a concrete link between action-free formulations of Conformal Field Theory and the cutoff-regularized path integral approach. Following this, the energy-momentum tensor is investigated, from which it becomes apparent that the conformal Ward Identities serve to define a particular representation of the energy-momentum tensor. It follows, essentially trivially, that if the Schwinger functional exists and is non-vanishing then theories exhibiting ... 16. Radical covalent organic frameworks: a general strategy to immobilize open-accessible polyradicals for high-performance capacitive energy storage. Science.gov (United States) Xu, Fei; Xu, Hong; Chen, Xiong; Wu, Dingcai; Wu, Yang; Liu, Hao; Gu, Cheng; Fu, Ruowen; Jiang, Donglin 2015-06-01 Ordered π-columns and open nanochannels found in covalent organic frameworks (COFs) could render them able to store electric energy. However, the synthetic difficulty in achieving redox-active skeletons has thus far restricted their potential for energy storage. A general strategy is presented for converting a conventional COF into an outstanding platform for energy storage through post-synthetic functionalization with organic radicals. The radical frameworks with openly accessible polyradicals immobilized on the pore walls undergo rapid and reversible redox reactions, leading to capacitive energy storage with high capacitance, high-rate kinetics, and robust cycle stability. The results suggest that channel-wall functional engineering with redox-active species will be a facile and versatile strategy to explore COFs for energy storage. 17. The Optimal Price Ratio of Typical Energy Sources in Beijing Based on the Computable General Equilibrium Model Directory of Open Access Journals (Sweden) Yongxiu He 2014-04-01 Full Text Available In Beijing, China, the rational consumption of energy is affected by the insufficient linkage mechanism of the energy pricing system, the unreasonable price ratio and other issues. This paper combines the characteristics of Beijing’s energy market, putting forward the society-economy equilibrium indicator R maximization taking into consideration the mitigation cost to determine a reasonable price ratio range. Based on the computable general equilibrium (CGE model, and dividing four kinds of energy sources into three groups, the impact of price fluctuations of electricity and natural gas on the Gross Domestic Product (GDP, Consumer Price Index (CPI, energy consumption and CO2 and SO2 emissions can be simulated for various scenarios. On this basis, the integrated effects of electricity and natural gas price shocks on the Beijing economy and environment can be calculated. The results show that relative to the coal prices, the electricity and natural gas prices in Beijing are currently below reasonable levels; the solution to these unreasonable energy price ratios should begin by improving the energy pricing mechanism, through means such as the establishment of a sound dynamic adjustment mechanism between regulated prices and market prices. This provides a new idea for exploring the rationality of energy price ratios in imperfect competitive energy markets. 18. Conformal higher-order viscoelastic fluid mechanics CERN Document Server Fukuma, Masafumi 2012-01-01 We present a generally covariant formulation of conformal higher-order viscoelastic fluid mechanics with strain allowed to take arbitrarily large values. We give a general prescription to determine the dynamics of a relativistic viscoelastic fluid in a way consistent with the hypothesis of local thermodynamic equilibrium and the second law of thermodynamics. We then elaborately study the transient time scales at which the strain almost relaxes and becomes proportional to the gradients of velocity. We particularly show that a conformal second-order fluid with all possible parameters in the constitutive equations can be obtained without breaking the hypothesis of local thermodynamic equilibrium, if the conformal fluid is defined as the long time limit of a conformal second-order viscoelastic system. We also discuss how local thermodynamic equilibrium could be understood in the context of the fluid/gravity correspondence. 19. Conformal higher-order viscoelastic fluid mechanics Science.gov (United States) Fukuma, Masafumi; Sakatani, Yuho 2012-06-01 We present a generally covariant formulation of conformal higher-order viscoelastic fluid mechanics with strain allowed to take arbitrarily large values. We give a general prescription to determine the dynamics of a relativistic viscoelastic fluid in a way consistent with the hypothesis of local thermodynamic equilibrium and the second law of thermodynamics. We then elaborately study the transient time scales at which the strain almost relaxes and becomes proportional to the gradients of velocity. We particularly show that a conformal second-order fluid with all possible parameters in the constitutive equations can be obtained without breaking the hypothesis of local thermodynamic equilibrium, if the conformal fluid is defined as the long time limit of a conformal second-order viscoelastic system. We also discuss how local thermodynamic equilibrium could be understood in the context of the fluid/gravity correspondence. 20. Conformal field theory on the plane CERN Document Server Ribault, Sylvain 2014-01-01 We provide an introduction to conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry. We describe the mathematical structures which appear in such theories, from the Virasoro algebra and its representations, to the BPZ equations and their solutions. As examples, we study a number of models: Liouville theory, (generalized) minimal models, free bosonic theories, the$H_3^+$model, and the$SU_2$and$\\widetilde{SL}_2(\\mathbb{R})$WZW models. 1. 75 FR 62141 - In the Matter of Certain Energy Drink Products; Notice of Issuance of a Corrected General... Science.gov (United States) 2010-10-07 ... From the Federal Register Online via the Government Publishing Office INTERNATIONAL TRADE COMMISSION In the Matter of Certain Energy Drink Products; Notice of Issuance of a Corrected General Exclusion Order AGENCY: U.S. International Trade Commission. ACTION: Notice. SUMMARY: Notice is hereby... 2. Generalized Chou-Yang model for p(antip)p and. lambda. (anti. lambda. )p elastic scattering at high energies Energy Technology Data Exchange (ETDEWEB) Saleem, M.; Fazal-E-Aleem; Azhar, I.A. 1988-06-01 The various characteristics of pp and antipp elastic scattering at high energies are explained by using the generalized Chou-Yang model which takes into consideration the anisotropic scattering of objects constituting colliding particles. The model is also used to extract the form factor and radius of the ..lambda.. particle. 3. Identification of general linear relationships between activation energies and enthalpy changes for dissociation reactions at surfaces. Science.gov (United States) Michaelides, Angelos; Liu, Z-P; Zhang, C J; Alavi, Ali; King, David A; Hu, P 2003-04-02 The activation energy to reaction is a key quantity that controls catalytic activity. Having used ab inito calculations to determine an extensive and broad ranging set of activation energies and enthalpy changes for surface-catalyzed reactions, we show that linear relationships exist between dissociation activation energies and enthalpy changes. Known in the literature as empirical Brønsted-Evans-Polanyi (BEP) relationships, we identify and discuss the physical origin of their presence in heterogeneous catalysis. The key implication is that merely from knowledge of adsorption energies the barriers to catalytic elementary reaction steps can be estimated. 4. [Dosimetric evaluation of conformal radiotherapy: conformity factor]. Science.gov (United States) Oozeer, R; Chauvet, B; Garcia, R; Berger, C; Felix-Faure, C; Reboul, F 2000-01-01 The aim of three-dimensional conformal therapy (3DCRT) is to treat the Planning Target Volume (PTV) to the prescribed dose while reducing doses to normal tissues and critical structures, in order to increase local control and reduce toxicity. The evaluation tools used for optimizing treatment techniques are three-dimensional visualization of dose distributions, dose-volume histograms, tumor control probabilities (TCP) and normal tissue complication probabilities (NTCP). These tools, however, do not fully quantify the conformity of dose distributions to the PTV. Specific tools were introduced to measure this conformity for a given dose level. We have extended those definitions to different dose levels, using a conformity index (CI). CI is based on the relative volumes of PTV and outside the PTV receiving more than a given dose. This parameter has been evaluated by a clinical study including 82 patients treated for lung cancer and 82 patients treated for prostate cancer. The CI was low for lung dosimetric studies (0.35 at the prescribed dose 66 Gy) due to build-up around the GTV and to spinal cord sparing. For prostate dosimetric studies, the CI was higher (0.57 at the prescribed dose 70 Gy). The CI has been used to compare treatment plans for lung 3DCRT (2 vs 3 beams) and prostate 3DCRT (4 vs 7 beams). The variation of CI with dose can be used to optimize dose prescription. 5. Conformational stability of calreticulin DEFF Research Database (Denmark) Jørgensen, C.S.; Trandum, C.; Larsen, N. 2005-01-01 The conformational stability of calreticulin was investigated. Apparent unfolding temperatures (T-m) increased from 31 degrees C at pH 5 to 51 degrees C at pH 9, but electrophoretic analysis revealed that calreticulin oligomerized instead of unfolding. Structural analyses showed that the single C......-terminal a-helix was of major importance to the conformational stability of calreticulin.... 6. The simulated features of heliospheric cosmic-ray modulation with a time-dependent drift model. III - General energy dependence Science.gov (United States) Potgieter, M. S.; Le Roux, J. A. 1992-01-01 The time-dependent cosmic-ray transport equation is solved numerically in an axially symmetric heliosphere. Gradient and curvature drifts are incorporated, together with an emulated wavy neutral sheet. This model is used to simulate heliospheric cosmic-ray modulation for the period 1985-1989 during which drifts are considered to be important. The general energy dependence of the modulation of Galactic protons is studied as predicted by the model for the energy range 1 MeV to 10 GeV. The corresponding instantaneous radial and latitudinal gradients are calculated, and it is found that, whereas the latitudinal gradients follow the trends in the waviness of the neutral sheet to a large extent for all energies, the radial gradients below about 200 MeV deviate from this general pattern. In particular, these gradients increase when the waviness decreases for the simulated period 1985-1987.3, after which they again follow the neutral sheet by increasing rapidly. 7. N = 4 l-conformal Galilei superalgebra Science.gov (United States) Galajinsky, Anton; Masterov, Ivan 2017-08-01 An N = 4 supersymmetric extension of the l-conformal Galilei algebra is constructed. This is achieved by combining generators of spatial symmetries from the l-conformal Galilei algebra and those underlying the most general superconformal group in one dimension D (2 , 1 ; α). The value of the group parameter α is fixed from the requirement that the resulting superalgebra is finite-dimensional. The analysis reveals α = -1/2 thus reducing D (2 , 1 ; α) to OSp (4 | 2). 8. Effective Conformal Descriptions of Black Hole Entropy Directory of Open Access Journals (Sweden) Steven Carlip 2011-07-01 Full Text Available It is no longer considered surprising that black holes have temperatures and entropies. What remains surprising, though, is the universality of these thermodynamic properties: their exceptionally simple and general form, and the fact that they can be derived from many very different descriptions of the underlying microscopic degrees of freedom. I review the proposal that this universality arises from an approximate conformal symmetry, which permits an effective “conformal dual” description that is largely independent of the microscopic details. 9. Conformally Invariant Spinorial Equations in Six Dimensions CERN Document Server Batista, Carlos 2016-01-01 This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for some of these equations are established. Moreover, in the course of the article, some useful identities involving the curvature of the spinorial connection are attained and a digression about harmonic forms and more general massless fields is made. 10. Conformal Killing Vectors Of Plane Symmetric Four Dimensional Lorentzian Manifolds CERN Document Server Khan, Suhail; Bokhari, Ashfaque H; Khan, Gulzar Ali; Mathematics, Department of; Peshawar, University of; Pakhtoonkhwa, Peshawar Khyber; Pakistan.,; Petroleum, King Fahd University of; Minerals,; 31261, Dhahran; Arabia, Saudi 2015-01-01 In this paper, we investigate conformal Killing's vectors (CKVs) admitted by some plane symmetric spacetimes. Ten conformal Killing's equations and their general forms of CKVs are derived along with their conformal factor. The existence of conformal Killing's symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. Considering the cases of time-like and inheriting CKVs, we obtain spacetimes admitting plane conformal symmetry. Integrability conditions are solved completely for some known non-conformally flat and conformally flat classes of plane symmetric spacetimes. A special vacuum plane symmetric spacetime is obtained, and it is shown that for such a metric CKVs are just the homothetic vectors (HVs). Among all the examples considered, there exists only one case with a six dimensional algebra of special CKVs admitting one proper CKV. In all other examples of non-conformally flat metrics, no proper ... 11. Generative models of conformational dynamics. Science.gov (United States) Langmead, Christopher James 2014-01-01 Atomistic simulations of the conformational dynamics of proteins can be performed using either Molecular Dynamics or Monte Carlo procedures. The ensembles of three-dimensional structures produced during simulation can be analyzed in a number of ways to elucidate the thermodynamic and kinetic properties of the system. The goal of this chapter is to review both traditional and emerging methods for learning generative models from atomistic simulation data. Here, the term 'generative' refers to a model of the joint probability distribution over the behaviors of the constituent atoms. In the context of molecular modeling, generative models reveal the correlation structure between the atoms, and may be used to predict how the system will respond to structural perturbations. We begin by discussing traditional methods, which produce multivariate Gaussian models. We then discuss GAMELAN (GRAPHICAL MODELS OF ENERGY LANDSCAPES), which produces generative models of complex, non-Gaussian conformational dynamics (e.g., allostery, binding, folding, etc.) from long timescale simulation data. 12. Geothermal energy: Technology and general studies. Citations from the NTIS data base Science.gov (United States) Hundemann, A. S. 1980-09-01 This bibliography contains 311 citations of Government-sponsored research on geothermal energy conversion, power plants, heat extraction, and space heating. Studies on fluid flow, heat transfer, rock fracturing, environmental impacts, pressure, and reservoir engineering are included. Reports on economics, legislation, technology assessment, comparative evaluation with other energy sources, Government policies, and planning are also cited. 13. Eikonalization of Conformal Blocks CERN Document Server Fitzpatrick, A Liam; Walters, Matthew T; Wang, Junpu 2015-01-01 Classical field configurations such as the Coulomb potential and Schwarzschild solution are built from the$t$-channel exchange of many light degrees of freedom. We study the CFT analog of this phenomenon, which we term the eikonalization' of conformal blocks. We show that when an operator$T$appears in the OPE$\\mathcal{O}(x) \\mathcal{O}(0)$, then the large spin$\\ell$Fock space states$[TT \\cdots T]_{\\ell}$also appear in this OPE with a computable coefficient. The sum over the exchange of these Fock space states in an$\\langle \\mathcal{O} \\mathcal{O} \\mathcal{O} \\mathcal{O} \\rangle$correlator build the classical `$T$field' in the dual AdS description. In some limits the sum of all Fock space exchanges can be represented as the exponential of a single$T$exchange in the 4-pt correlator of$\\mathcal{O}$. Our results should be useful for systematizing$1/\\ell$perturbation theory in general CFTs and simplifying the computation of large spin OPE coefficients. As examples we obtain the leading$\\log \\ell\$...
14. Energy care. The tool for structured attention for energy efficiency. For profit and non-profit organizations conform ISO 14001(2004); Energiezorg. Het middel voor structurele aandacht voor energie-efficiency. Voor profit- en non-profitorganisaties conform ISO14001:2004
Energy Technology Data Exchange (ETDEWEB)
NONE
2006-06-15
An energy care ('energiezorg' in Dutch) system has been developed by means of which profit and non-profit organizations can continuously control the consumption of energy and improve the energy efficiency within their organization. [Dutch] Steeds meer organisaties en bedrijven nemen maatregelen om energie te besparen of de energie-efficiency te verbeteren. Dit levert zowel financiele als milieuwinst op. Helaas zijn de effecten van de inspanningen vaak maar tijdelijk. Zodra de aandacht voor het onderwerp wegebt, neemt het energiegebruik weer toe. Daarom heeft SenterNovem een systeem voor structurele aandacht ontwikkeld. Dit zorgt ervoor dat energiegebruik binnen de onderneming of organisatie de aandacht krijgt die het verdient en dat de aandacht nooit verslapt. Dat blijkt ook uit de ervaringen van veel bedrijven en instellingen. Zij constateren dat invoering van Energiezorg niet alleen bijdraagt aan een blijvende verlaging van het energiegebruik, maar zelfs ook extra energiebesparing oplevert van gemiddeld 3 procent. Dit geldt voor zowel profit- als non-profitorganisaties. Het instrument Energiezorg is geschikt voor kleine, middelgrote en grote organisaties en bedrijven.
15. Boundary terms of conformal anomaly
Directory of Open Access Journals (Sweden)
Sergey N. Solodukhin
2016-01-01
Full Text Available We analyze the structure of the boundary terms in the conformal anomaly integrated over a manifold with boundaries. We suggest that the anomalies of type B, polynomial in the Weyl tensor, are accompanied with the respective boundary terms of the Gibbons–Hawking type. Their form is dictated by the requirement that they produce a variation which compensates the normal derivatives of the metric variation on the boundary in order to have a well-defined variational procedure. This suggestion agrees with recent findings in four dimensions for free fields of various spins. We generalize this consideration to six dimensions and derive explicitly the respective boundary terms. We point out that the integrated conformal anomaly in odd dimensions is non-vanishing due to the boundary terms. These terms are specified in three and five dimensions.
16. Boundary terms of conformal anomaly
Energy Technology Data Exchange (ETDEWEB)
Solodukhin, Sergey N., E-mail: [email protected]
2016-01-10
We analyze the structure of the boundary terms in the conformal anomaly integrated over a manifold with boundaries. We suggest that the anomalies of type B, polynomial in the Weyl tensor, are accompanied with the respective boundary terms of the Gibbons–Hawking type. Their form is dictated by the requirement that they produce a variation which compensates the normal derivatives of the metric variation on the boundary in order to have a well-defined variational procedure. This suggestion agrees with recent findings in four dimensions for free fields of various spins. We generalize this consideration to six dimensions and derive explicitly the respective boundary terms. We point out that the integrated conformal anomaly in odd dimensions is non-vanishing due to the boundary terms. These terms are specified in three and five dimensions.
17. The impact of a stimulus to energy efficiency on the economy and the environment: A regional computable general equilibrium analysis
Energy Technology Data Exchange (ETDEWEB)
Hanley, Nick D. [Department of Economics, University of Stirling, Stirling FK9 4LA (United Kingdom); McGregor, Peter G.; Swales, J. Kim [Fraser of Allander Institute, CPPR and Department of Economics, University of Strathclyde, Sir William Duncan Building, 130 Rottenrow, Glasgow G4 0GE (United Kingdom); Turner, Karen [Fraser of Allander Institute and Department of Economics, University of Strathclyde, Sir William Duncan Building, 130 Rottenrow, Glasgow G4 0GE (United Kingdom)
2006-02-01
Sustainable development is a key objective of UK national and regional policies. Improvements in resource productivity have been suggested as both a measure of progress towards sustainable development and as a means of achieving sustainability. Making 'more with less' intuitively seems to be good for the environment, and this is the presumption of current UK policy. However, in a system-wide context, improvements in energy efficiency lower the cost of energy in efficiency units and may even stimulate the consumption and production of energy measured in physical units, and increase pollution. Simulations of a computable general equilibrium model of Scotland suggest that an across the board stimulus to energy efficiency there would actually stimulate energy production and consumption and lead to a deterioration in environmental indicators. The implication is that policies directed at stimulating energy efficiency are not, in themselves, sufficient to secure environmental improvements: this may require the use of complementary energy policies designed to moderate incentives to increased energy consumption. (author)
18. 75 FR 22586 - Energy Conservation Program for Consumer Products: Notice of Petition for Waiver of General...
Science.gov (United States)
2010-04-29
... asterisks, or wild cards, denote color or other features that do not affect energy performance.) DOE notes...****, ZFGP21HZ****. The asterisks, or wild cards, denote color or other features that do not affect...
19. A general scheme for the estimation of oxygen binding energies on binary transition metal surface alloys
DEFF Research Database (Denmark)
Greeley, Jeffrey Philip; Nørskov, Jens Kehlet
2005-01-01
A simple scheme for the estimation of oxygen binding energies on transition metal surface alloys is presented. It is shown that a d-band center model of the alloy surfaces is a convenient and appropriate basis for this scheme; variations in chemical composition, strain effects, and ligand effects...... for the estimation of oxygen binding energies on a wide variety of transition metal alloys. (c) 2005 Elsevier B.V. All rights reserved....
20. EC declaration of conformity.
Science.gov (United States)
Donawa, M E
1996-05-01
The CE-marking procedure requires that manufacturers draw up a written declaration of conformity before placing their products on the market. However, some companies do not realize that this is a requirement for all devices. Also, there is no detailed information concerning the contents and format of the EC declaration of conformity in the medical device Directives or in EC guidance documentation. This article will discuss some important aspects of the EC declaration of conformity and some of the guidance that is available on its contents and format. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8763025403022766, "perplexity": 3118.585857077437}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812913.37/warc/CC-MAIN-20180220070423-20180220090423-00683.warc.gz"} |
http://mathhelpforum.com/math-topics/168492-drawing-displacement-time-wave.html | # Thread: Drawing a displacement/time wave
1. ## Drawing a displacement/time wave
1. The problem statement, all variables and given/known data
Hi
I need help on how to draw Displacement/time waves. I am considering this question:
If a wave is travelling from left to right, draw a diagram of what the wave would look like 10ms later. The amplitude is 0.02 and wavelength is 0.2 m respectively.
2. Relevant equations
Speed = distance/time
3. The attempt at a solution
I can clearly work out the distance which is 0.3m. But I am not sure of the amplitude, shape and wavelength. Can someone please comment?
2. I find it strange that you don't have the speed of the wave but managed to get the distance covered within 10 ms...
What you basically need to draw is a sine curve starting at the distance covered on the x axis, going towards the left.
The wavelength is measured on the x-axis and consists of a complete cycle of the sine graph.
The amplitude indicates the maximum and minimum points of the graph. Here, the maximum is 0.02 m and the minimum is -0.02 m.
3. Sorry. the speed wasn't included in the question (Thats by me). So, what happens if the furthest point on the sine curve is 0.3m?
4. Yes, as the wavelength is 0.2 m, it means you'll have a cycle and a half drawn.
The resulting graph will be quite similar to the graph of y = 0.02sin(x) between 0 and 0.3 m, with two maxima at 0.5 and 2.5 m and a minimum at 1.5.
5. Thanks. That makes more sense. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9409170746803284, "perplexity": 411.2771159572267}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689752.21/warc/CC-MAIN-20170923160736-20170923180736-00303.warc.gz"} |
https://www.physicsforums.com/threads/velocity-profile.652866/ | # Velocity Profile
1. Nov 17, 2012
### CrazyNeutrino
What is a velocity profile in fluid mechanics? Why do they give you a ratio between the fluids velocity and a random reference velocity and why is it equal to a completely arbitrary function?
Does the ratio equal a function because it is an experimental fact?
2. Nov 17, 2012
### Staff: Mentor
Can you give a specific example of what is troubling you? It is difficult to understand your question otherwise. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9070075750350952, "perplexity": 817.6366196862674}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171271.48/warc/CC-MAIN-20170219104611-00637-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://studyadda.com/notes/neet/chemistry/chemical-arithmetic/limiting-reagent-or-reactant/6359 | # JEE Main & Advanced Chemistry Chemical Arithmetic Limiting reagent or reactant
## Limiting reagent or reactant
Category : JEE Main & Advanced
### Limiting reagent or reactant
In many situations, an excess of one or more substance is available for chemical reaction. Some of these excess substances will therefore be left over when the reaction is complete; the reaction stops immediately as soon as one of the reactant is totally consumed.
The substance that is totally consumed in a reaction is called limiting reagent because it determines or limits the amount of product. The other reactant present in excess are called as excess reagents.
Let us consider a chemical reaction which is initiated by passing a spark through a reaction vessel containing 10 mole of H2 and 7 mole of O2.
$2\underset{{}}{\mathop{\,{{H}_{2}}\,}}\,(g)\,\,+\,\,\underset{{}}{\mathop{{{O}_{2}}\,}}\,(g)\,\xrightarrow{{}}\,\,2\,\,\underset{{}}{\mathop{{{H}_{2}}O}}\,\,(v)$
Moles before reaction 10 7 0 Moles after reaction 0 2 10
The reaction stops only after consumption of 5 moles of O2 as no further amount of H2 is left to react with unreacted O2. Thus H2 is a limiting reagent in this reaction.
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https://www.gamedev.net/forums/topic/160989-chunked-lod-more-about-it/ | #### Archived
This topic is now archived and is closed to further replies.
# chunked lod.. more about it
This topic is 5584 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
As simple as the theory is, I just can''t get it working in my application. I''m so frustrated that sometimes I want to give up on the program. But as always I come back to it, but I still can''t get it to work. I have everything working from the LOD algorithm to the patching of different levels. The part I''m stuck on is rendering it. I''m using a recursive solution because that''s what the paper suggested. But nothing I do seems to work! First off, it subdivides all the way down to the highest level of detail block everywhere- meaning the screen space error test is always failing until it just renders the highest level block available. Second, my framerate is dropping in the 20''s, when even rendering the terrain normally (without recursion and all the checking) on the highest level is detail gives between 40-50. I''m sure that Chunked LOD helps the framerate or it wouldn''t have caught the interest of people as it has! Something is just wrong in my code- which I will post when I get home in a little bit. I just really want to hear other people''s ideas or pseudocode for the rendering part. There''s not too much information on Chunked LOD yet. Another question I had is when calculating K in the equation [max_error/D * K]. I can''t get acrobat reader working on this computer (their new version seems to have a lot of bugs), so I can''t look up the exact equation of K right now, but when I looked at tulrich''s source code the K equation looked a little different than in his paper(like he didn''t multiply the denominator by 2). Can someone verify the equation of K? Thanks!
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Well, I can''t post my code yet actually because I''m rewriting a lot of my Terrain class for optimization and also to make a tree hierarchy of the patches. This will make the recursive drawing a lot simpler. Maybe it will work?
How many people use Chunked LOD? I''m really getting the impression that no one uses it because no one responds to posts like this. Not that I mind that much, I''m just starting to debate if it''s really worth my time.
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Hi,
Chunked LOD should work well for terrain so don''t give up on it yet. From reading your post I''d say there is going to be a bug or mistake somewhere in the code. I say this based on the fact that it appears you are always rendering the highest detail LOD.
I''ve not done Chunked LOD yet, (although I have made a chunk terrain engine) but I would look at the space error metric, possibly the value you have is too low, or the equation is inccorect.
However if that is not the case how about approaching this from a different angle. The aim at the moment I would say is to ensure that the chunk LOD is working, so replace your space error metric with a simple distance to chunk origin test. I.e for each visable chunk get the distance from the camera to the chunk. Then depedning on how many levels of LOD you have, set it so that the further away a chunk is the higher the LOD used (less polygons). This way at least it will show whether the LOD system is working. It should be an easy visual check with wireframe mode, further away chunks having less polys. Don''t bother trying to make this ''work'' or look good, its just the easiest way I can think of testing most of the chunk lod terrain to ensure that code is working.
If it doesn''t work, then you know the problem is somewhere in the LOD/patching/chunks. If it does work, then the problem should be within the screen base error metric code.
Don''t know if this will help. But at the moment it looks like you need to pin down where the problem is.
As to the vertue of Chunked LOD algorithm this post might be of interest if you''ve not seen it already
http://www.gamedev.net/community/forums/topic.asp?topic_id=156531
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I don''t know what you are doing wrong but chunked LOD should be faster than brute force in all cases (except when >90% of terrain is in view).
This will be a bit OT : There is one point that always botherd me in most QT based algoritems. They all need to recurse down to leaf level. What''s the point of that. GMM was created for the purpose to use less CPU & more GPU. But is it realy so? It sure is better then ROAM but in the end you are rendering a few nodes at full LOD (1000 tris/call) but there are a lot of calls (for nodes far away) that render only a few tris (<16). This is bad in 2 ways. First you need to recures down to the leafs [you don''t actualy need to use recursion] so you waste a lot of time just getting there then you render a node with 8 tris. Now that is just a waste of time. So in my engine I combined GMM and Adaptive QT. This works like a charm. All calls to render a node now have the same amount of tris. And recursion stops when node size on screen is under some treshold. For nodes near camera recursion goes all the way down to level 0 LOD while for nodes far away it goes only to level 4 or so. Combined with iterative tree tansvelsal it gives much better results than any of other algoritems I implemented from papers found on the net. And I''ve tried quite a lot .
You should never let your fears become the boundaries of your dreams.
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Darkwing: From what I understand from the Chunked lod paper, that''s exactly what it does. Thanks though..
Thanks for the reply noisecrime. I''ve tested the different levels to make sure they are ok but I guess I haven''t tested a simple distance LOD algorithm yet. I will do that as soon as I get home and post the results. I had seen that thread a little while back but I forgot about it, I''ll scan through it and see if has any information, thanks!
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Sorry for taking so long to do it, I'm writing a Perlin Noise tutorial that's starting to become more interesting (and less frustrating :D ).
Well, I did as you said noisecrime and tested the distance LOD. It worked, so I am sure that the error is in the screen space error metric code.
But I got it EXACTLY like it is off the Chunked LOD paper. This is my code:
void RenderNode(D3DXVECTOR3 view, int level, lodchunk* node) {double screen_error; if(level != 4) { float x1 = node->midx - view.x; float y1 = node->midy - view.y; float z1 = node->midz - view.z; double dist = sqrt(x1*x1 + y1*y1 + z1+z1); dist -= XTerrain/LODController->GetSubFactor(level)/2.0f; //just kind of a spherical distance, this would be the radius screen_error = node->maximum_geo_err/dist * k; } else screen_error = 1.0; if(screen_error < 2.0) { LODController->RenderLodChunk(level, node); } else { RenderNode(view, level+1, node->sib1); RenderNode(view, level+1, node->sib2); RenderNode(view, level+1, node->sib3); RenderNode(view, level+1, node->sib4); }}and k is set as :double k = 1280/ (2*tan(D3DX_PI/3.0/2.0));I actually used D3DX_PI/6.0 but that reflects the original equation better.
Any blatant errors?
[edited by - okonomiyaki on June 7, 2003 4:35:13 PM]
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Well I can''t see any obvious errors, but then i''ve never implemented this, and there are a few unknown varibles that make it difficult to know what values you should be getting.
I''ll state the obvious though. Its the code within the if(level != 4) statement that must be the cause of the problem. That is if as you say every cunk is rendered at the lowest LOD (highest poly). It means that the if statemnet is always making screen_error >= 2.0 forcing the recursion down until level == 4.
I would monitor the values produced within the if statement, simply dump them out to a log file, or even dry run through some values yourself since you should know the value of all the varibles. Double check that it works as expected.
Sorry I can''t be of more help.
BTW how did you test the LOD? I would hope that it was just some code to replace the RenderNode function code - just to ensure that running down to that handler worked.
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Yeah, I simply replaced some of the code in the RenderNode function to see if the distance was in a certain range, then render the appropriate level.
Yeah, my values are totally screwed up, but I don''t know why. I don''t know which equation is wrong. I wish someone would at least verify the equation of K. But thanks a lot for the help noisecrime! I appreciate the interest, and I''ll just keep debugging it. Thanks for the help though.
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Sorry i couldn't have been of more help, however i'm interested in this area becuase at some point i'd want to try implementing it. So i checked out the paper you mentioned in the original email and worked through some of the code.
I'm not sure but i'd question the second line of code below
double dist = sqrt(x1*x1 + y1*y1 + z1+z1);
dist -= XTerrain/LODController->GetSubFactor(level)/2.0f;
I can't see any reason for that line. In the paper 'dist' is calacualted as you have in the first line. So try ditching that second line.
Looking at it, the second line appears more like the calculation for the LOD geo-error per level. That is if the chunk has a master error metric of say 16 units, then higher levels of LOD should have half the error value - so level 1 = 16 level 2 = 8 etc. I would have thought these values would have been precalaculated and stored with each level of LOD for the chunk, but i guess they could be worked out dynamically. In which case your second line above the variable should note be 'dist' but a temporary variable level_geo_error. If so then this value should be used in
screen_error = level_geo_error/dist * k;
Definaiton of K
double k = 1280/ (2*tan(D3DX_PI/3.0/2.0));
in the paper it is
k = viewportwidth/2*tan(horizontal FOV/2.0)
So this means your FOV is 120 degrees - which to me is rather large, but there may be a good reason for it. Anyway it shouldn't be the cause of your problems.
[edited by - noisecrime on June 9, 2003 8:50:54 PM]
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o.k. Now i''ve been thinking about chunk LOD some more i''d like to ask how do you calcualte each chunks maximum geometric error?
Its something that doesn''t appear to be described in any detail in that paper, and I don''t remember it being discussed in any others.
I had almost asumed that perhaps you''d use the bounding box for a chunk comparing it against each LOD level. You''d be comparing the highest hieght of each LOD level to the maximum LOD (most polys) and using the difference as the error metric. But i''m not sure tat makes much sense.
Further more i''m confused by the paper as he say''s
''For simplicity''s sake, I assign the same E to all the meshes at a particular level in the chunk tree.''
where E = Maximum geometric error
This seams counter productive to me, as each child chunk could well have an error greater or less than an other.
Furthermore his equaition for calculating the error for specific LOD levels, is simply to divide the parent level by two, which again I would have assumed to be inaccruate.
Whether the inaccrucies of either these two points actually contribute to the performance of the algorithm i''m not sure.
Anyone care to explain?
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https://networks.skewed.de/net/yahoo_song | # Netzschleuder network catalogue, repository and centrifuge
Problems with this dataset? Open an issue.
You may also take a look at the source code.
The network in this dataset can be loaded directly from graph-tool with:
import graph_tool.all as gt
g = gt.collection.ns["yahoo_song"]
# yahoo_song — Yahoo song ratings (2011)
Description
A bipartite network of users and songs they rated, as used in the 2011 KDD Cup and extracted from Yahoo! Music. Edge weights denote a rating scaled from 0 to 100. More information about this data set is available at http://konect.cc/networks/yahoo-song1
1. Description obtained from the ICON project.
Tags
Economic Preferences Timestamps Weighted
Citation
Upstream URL OK
http://konect.cc/networks/yahoo-song
Networks
Tip: hover your mouse over a table header to obtain a legend.
Name Nodes Edges $\left<k\right>$ $\sigma_k$ $\lambda_h$ $\tau$ $r$ $c$ $\oslash$ $S$ Kind Mode NPs EPs gt GraphML GML csv
yahoo_song 1,625,951 256,804,235 315.88 2364.80 4238.65 3.03 -0.11 0.00 6 1.00 Undirected Bipartite weight time 890.4 MiB 1.493 GiB 1.234 GiB 1.420 GiB
Ridiculograms | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5870009064674377, "perplexity": 8344.768826082372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711232.54/warc/CC-MAIN-20221208014204-20221208044204-00344.warc.gz"} |
https://www.dataquest.io/blog/learning-curves-machine-learning/ | # Tutorial: Learning Curves for Machine Learning in Python
January 3, 2018
When building machine learning models, we want to keep error as low as possible. That’s a key skill for anyone aiming to learn Python for data science. Two major sources of error are bias and variance. If we managed to reduce these two, then we could build more accurate models.
But how do we diagnose bias and variance in the first place? And what actions should we take once we’ve detected something?
In this post, we’ll learn how to answer both these questions using learning curves. We’ll work with a real world data set and try to predict the electrical energy output of a power plant.
Some familiarity with scikit-learn and machine learning theory is assumed. If you don’t frown when I say cross-validation or supervised learning, then you’re good to go. If you’re new to machine learning and have never tried scikit, a good place to start is this blog post.
We begin with a brief introduction to bias and variance.
## The bias-variance trade-off
In supervised learning, we assume there’s a real relationship between feature(s) and target and estimate this unknown relationship with a model. Provided the assumption is true, there really is a model, which we’ll call $f$, which describes perfectly the relationship between features and target.
In practice, $f$ is almost always completely unknown, and we try to estimate it with a model $\hat{f}$ (notice the slight difference in notation between $f$ and $\hat{f}$). We use a certain training set and get a certain $\hat{f}$. If we use a different training set, we are very likely to get a different $\hat{f}$. As we keep changing training sets, we get different outputs for $\hat{f}$. The amount by which $\hat{f}$ varies as we change training sets is called variance.
To estimate the true $f$, we use different methods, like linear regression or random forests. Linear regression, for instance, assumes linearity between features and target. For most real-life scenarios, however, the true relationship between features and target is complicated and far from linear. Simplifying assumptions give bias to a model. The more erroneous the assumptions with respect to the true relationship, the higher the bias, and vice-versa.
Generally, a model $\hat{f}$ will have some error when tested on some test data. It can be shown mathematically that both bias and variance can only add to a model’s error. We want a low error, so we need to keep both bias and variance at their minimum. However, that’s not quite possible. There’s a trade-off between bias and variance.
A low-biased method fits training data very well. If we change training sets, we’ll get significantly different models $\hat{f}$.
You can see that a low-biased method captures most of the differences (even the minor ones) between the different training sets. $\hat{f}$ varies a lot as we change training sets, and this indicates high variance.
The less biased a method, the greater its ability to fit data well. The greater this ability, the higher the variance. Hence, the lower the bias, the greater the variance.
The reverse also holds: the greater the bias, the lower the variance. A high-bias method builds simplistic models that generally don’t fit well training data. As we change training sets, the models $\hat{f}$ we get from a high-bias algorithm are, generally, not very different from one another.
If $\hat{f}$ doesn’t change too much as we change training sets, the variance is low, which proves our point: the greater the bias, the lower the variance.
Mathematically, it’s clear why we want low bias and low variance. As mentioned above, bias and variance can only add to a model’s error. From a more intuitive perspective though, we want low bias to avoid building a model that’s too simple. In most cases, a simple model performs poorly on training data, and it’s extremely likely to repeat the poor performance on test data.
Similarly, we want low variance to avoid building an overly complex model. Such a model fits almost perfectly all the data points in the training set. Training data, however, generally contains noise and is only a sample from a much larger population. An overly complex model captures that noise. And when tested on out-of-sample data, the performance is usually poor. That’s because the model learns the sample training data too well. It knows a lot about something and little about anything else.
In practice, however, we need to accept a trade-off. We can’t have both low bias and low variance, so we want to aim for something in the middle.
We’ll try to build some practical intuition for this trade-off as we generate and interpret learning curves below.
## Learning curves – the basic idea
Let’s say we have some data and split it into a training set and validation set. We take one single instance (that’s right, one!) from the training set and use it to estimate a model. Then we measure the model’s error on the validation set and on that single training instance. The error on the training instance will be 0, since it’s quite easy to perfectly fit a single data point. The error on the validation set, however, will be very large.
That’s because the model is built around a single instance, and it almost certainly won’t be able to generalize accurately on data that hasn’t seen before. Now let’s say that instead of one training instance, we take ten and repeat the error measurements. Then we take fifty, one hundred, five hundred, until we use our entire training set. The error scores will vary more or less as we change the training set. We thus have two error scores to monitor: one for the validation set, and one for the training sets. If we plot the evolution of the two error scores as training sets change, we end up with two curves. These are called learning curves. In a nutshell, a learning curve shows how error changes as the training set size increases.
The diagram below should help you visualize the process described so far. On the training set column you can see that we constantly increase the size of the training sets. This causes a slight change in our models $\hat{f}$. In the first row, where n = 1 (n is the number of training instances), the model fits perfectly that single training data point. However, the very same model fits really bad a validation set of 20 different data points. So the model’s error is 0 on the training set, but much higher on the validation set. As we increase the training set size, the model cannot fit perfectly anymore the training set. So the training error becomes larger. However, the model is trained on more data, so it manages to fit better the validation set. Thus, the validation error decreases. To remind you, the validation set stays the same across all three cases. If we plotted the error scores for each training size, we’d get two learning curves looking similarly to these: Learning curves give us an opportunity to diagnose bias and variance in supervised learning models. We’ll see how that’s possible in what follows.
## Introducing the data
The learning curves plotted above are idealized for teaching purposes. In practice, however, they usually look significantly different. So let’s move the discussion in a practical setting by using some real-world data. We’ll try to build regression models that predict the hourly electrical energy output of a power plant. The data we use come from Turkish researchers Pınar Tüfekci and Heysem Kaya, and can be downloaded from here. As the data is stored in a .xlsx file, we use pandas’ read_excel() function to read it in:
import pandas as pd
print(electricity.info())
electricity.head(3)
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 9568 entries, 0 to 9567
Data columns (total 5 columns):
AT 9568 non-null float64
V 9568 non-null float64
AP 9568 non-null float64
RH 9568 non-null float64
PE 9568 non-null float64
dtypes: float64(5)
memory usage: 373.8 KB
None
AT V AP RH PE
0 14.96 41.76 1024.07 73.17 463.26
1 25.18 62.96 1020.04 59.08 444.37
2 5.11 39.40 1012.16 92.14 488.56
Let’s quickly decipher each column name:
Abbreviation Full name
AT Ambiental Temperature
V Exhaust Vacuum
AP Ambiental Pressure
RH Relative Humidity
PE Electrical Energy Output
The PE column is the target variable, and it describes the net hourly electrical energy output. All the other variables are potential features, and the values for each are actually hourly averages (not net values, like for PE). The electricity is generated by gas turbines, steam turbines, and heat recovery steam generators. According to the documentation of the data set, the vacuum level has an effect on steam turbines, while the other three variables affect the gas turbines. Consequently, we’ll use all of the feature columns in our regression models. At this step we’d normally put aside a test set, explore the training data thoroughly, remove any outliers, measure correlations, etc. For teaching purposes, however, we’ll assume that’s already done and jump straight to generate some learning curves. Before we start that, it’s worth noticing that there are no missing values. Also, the numbers are unscaled, but we’ll avoid using models that have problems with unscaled data.
## Deciding upon the training set sizes
Let’s first decide what training set sizes we want to use for generating the learning curves. The minimum value is 1. The maximum is given by the number of instances in the training set. Our training set has 9568 instances, so the maximum value is 9568. However, we haven’t yet put aside a validation set. We’ll do that using an 80:20 ratio, ending up with a training set of 7654 instances (80%), and a validation set of 1914 instances (20%). Given that our training set will have 7654 instances, the maximum value we can use to generate our learning curves is 7654. For our case, here, we use these six sizes:
train_sizes = [1, 100, 500, 2000, 5000, 7654]
An important thing to be aware of is that for each specified size a new model is trained. If you’re using cross-validation, which we’ll do in this post, k models will be trained for each training size (where k is given by the number of folds used for cross-validation). To save code running time, it’s good practice to limit yourself to 5-10 training sizes.
## The learning_curve() function from scikit-learn
We’ll use the learning_curve() function from the scikit-learn library to generate a learning curve for a regression model. There’s no need on our part to put aside a validation set because learning_curve() will take care of that. In the code cell below, we:
• Do the required imports from sklearn.
• Declare the features and the target.
• Use learning_curve() to generate the data needed to plot a learning curve. The function returns a tuple containing three elements: the training set sizes, and the error scores on both the validation sets and the training sets. Inside the function, we use the following parameters:
• estimator — indicates the learning algorithm we use to estimate the true model;
• X — the data containing the features;
• y — the data containing the target;
• train_sizes — specifies the training set sizes to be used;
• cv — determines the cross-validation splitting strategy (we’ll discuss this immediately);
• scoring — indicates the error metric to use; the intention is to use the mean squared error (MSE) metric, but that’s not a possible parameter for scoring; we’ll use the nearest proxy, negative MSE, and we’ll just have to flip signs later on.
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import learning_curve
features = ['AT', 'V', 'AP', 'RH']
target = 'PE'
train_sizes, train_scores, validation_scores = learning_curve(
estimator = LinearRegression(),
X = electricity[features],
y = electricity[target], train_sizes = train_sizes, cv = 5,
scoring = 'neg_mean_squared_error')
We already know what’s in train_sizes. Let’s inspect the other two variables to see what learning_curve() returned:
print('Training scores:\n\n', train_scores)
print('\n', '-' * 70) # separator to make the output easy to read
print('\nValidation scores:\n\n', validation_scores)
Training scores:
[[ -0. -0. -0. -0. -0. ] [-19.71230701 -18.31492642 -18.31492642 -18.31492642 -18.31492642] [-18.14420459 -19.63885072 -19.63885072 -19.63885072 -19.63885072] [-21.53603444 -20.18568787 -19.98317419 -19.98317419 -19.98317419] [-20.47708899 -19.93364211 -20.56091569 -20.4150839 -20.4150839 ] [-20.98565335 -20.63006094 -21.04384703 -20.63526811 -20.52955609]] --------------------------------------------------------------------Validation scores:
[[-619.30514723 -379.81090366 -374.4107861 370.03037109 -373.30597982]
[ -21.80224219 -23.01103419 20.81350389 -22.88459236 -23.44955492]
[ -19.96005238 -21.2771561 19.75136596 -21.4325615 -21.89067652]
[ -19.92863783 21.35440062 19.62974239 -21.38631648 -21.811031 ]
[ -19.88806264 -21.3183303 19.68228562 -21.35019525 -21.75949097]
[ -19.9046791 21.33448781 19.67831137 -21.31935146 -21.73778949]]
Since we specified six training set sizes, you might have expected six values for each kind of score. Instead, we got six rows for each, and every row has five error scores. This happens because learning_curve() runs a k-fold cross-validation under the hood, where the value of k is given by what we specify for the cv parameter. In our case, cv = 5, so there will be five splits. For each split, an estimator is trained for every training set size specified. Each column in the two arrays above designates a split, and each row corresponds to a test size. Below is a table for the training error scores to help you understand the process better:
Training set size (index) Split1 Split2 Split3 Split4 Split5
1 0 0 0 0 0
100 -19.71230701 -18.31492642 -18.31492642 -18.31492642 -18.31492642
500 -18.14420459 -19.63885072 -19.63885072 -19.63885072 -19.63885072
2000 -21.53603444 -20.18568787 -19.98317419 -19.98317419 -19.98317419
5000 -20.47708899 -19.93364211 -20.56091569 -20.4150839 -20.4150839
7654 -20.98565335 -20.63006094 -21.04384703 -20.63526811 -20.52955609
To plot the learning curves, we need only a single error score per training set size, not 5. For this reason, in the next code cell we take the mean value of each row and also flip the signs of the error scores (as discussed above).
train_scores_mean = -train_scores.mean(axis = 1)
validation_scores_mean = -validation_scores.mean(axis = )
print('Mean training scores\n\n', pd.Series(train_scores_mean, index = train_sizes))
print('\n', '-' * 20) # separator
print('\nMean validation scores\n\n',pd.Series(validation_scores_mean, index = train_sizes))
Mean training scores
1 -0.000000
100 18.594403
500 19.339921
2000 20.334249
5000 20.360363
7654 20.764877
dtype: float64
--------------------
Mean validation scores
1 423.372638
100 22.392186
500 20.862362
2000 20.822026
5000 20.799673
7654 20.794924
dtype: float64
Now we have all the data we need to plot the learning curves. Before doing the plotting, however, we need to stop and make an important observation. You might have noticed that some error scores on the training sets are the same. For the row corresponding to training set size of 1, this is expected, but what about other rows? With the exception of the last row, we have a lot of identical values. For instance, take the second row where we have identical values from the second split onward. Why is that so? This is caused by not randomizing the training data for each split. Let’s walk through a single example with the aid of the diagram below. When the training size is 500 the first 500 instances in the training set are selected.
For the first split, these 500 instances will be taken from the second chunk. From the second split onward, these 500 instances will be taken from the first chunk. Because we don’t randomize the training set, the 500 instances used for training are the same for the second split onward. This explains the identical values from the second split onward for the 500 training instances case. An identical reasoning applies to the 100 instances case, and a similar reasoning applies to the other cases. To stop this behavior, we need to set the shuffle parameter to True in the learning_curve() function. This will randomize the indices for the training data for each split. We haven’t randomized above for two reasons:
• The data comes pre-shuffled five times (as mentioned in the documentation) so there’s no need to randomize anymore.
• I wanted to make you aware about this quirk in case you stumble upon it in practice.
Finally, let’s do the plotting.
## Learning curves – high bias and low variance
We plot the learning curves using a regular matplotlib workflow:
import matplotlib.pyplot as plt
plt.style.use('seaborn')
plt.plot(train_sizes, train_scores_mean, label = 'Training error')
plt.plot(train_sizes, validation_scores_mean, label = 'Validation error')
plt.ylabel('MSE', fontsize = 14)
plt.xlabel('Training set size', fontsize = 14)
plt.title('Learning curves for a linear regression model', fontsize = 18, y = 1.03)
plt.legend()
plt.ylim(0,40)
(0, 40)
There’s a lot of information we can extract from this plot. Let’s proceed granularly. When the training set size is 1, we can see that the MSE for the training set is 0. This is normal behavior, since the model has no problem fitting perfectly a single data point. So when tested upon the same data point, the prediction is perfect. But when tested on the validation set (which has 1914 instances), the MSE rockets up to roughly 423.4. This relatively high value is the reason we restrict the y-axis range between 0 and 40. This enables us to read most MSE values with precision. Such a high value is expected, since it’s extremely unlikely that a model trained on a single data point can generalize accurately to 1914 new instances it hasn’t seen in training. When the training set size increases to 100, the training MSE increases sharply, while the validation MSE decreases likewise.
The linear regression model doesn’t predict all 100 training points perfectly, so the training MSE is greater than 0. However, the model performs much better now on the validation set because it’s estimated with more data. From 500 training data points onward, the validation MSE stays roughly the same. This tells us something extremely important: adding more training data points won’t lead to significantly better models. So instead of wasting time (and possibly money) with collecting more data, we need to try something else, like switching to an algorithm that can build more complex models.
To avoid a misconception here, it’s important to notice that what really won’t help is adding more instances (rows) to the training data. Adding more features, however, is a different thing and is very likely to help because it will increase the complexity of our current model. Let’s now move to diagnosing bias and variance. The main indicator of a bias problem is a high validation error. In our case, the validation MSE stagnates at a value of approximately 20. But how good is that? We’d benefit from some domain knowledge (perhaps physics or engineering in this case) to answer this, but let’s give it a try.
Technically, that value of 20 has MW$^2$ (megawatts squared) as units (the units get squared as well when we compute the MSE). But the values in our target column are in MW (according to the documentation). Taking the square root of 20 MW$^2$ results in approximately 4.5 MW. Each target value represents net hourly electrical energy output. So for each hour our model is off by 4.5 MW on average. According to this Quora answer, 4.5 MW is equivalent to the heat power produced by 4500 handheld hair dryers. And this would add up if we tried to predict the total energy output for one day or a longer period. We can conclude that the an MSE of 20 MW$^2$ is quite large. So our model has a bias problem.
But is it a low bias problem or a high bias problem? To find the answer, we need to look at the training error. If the training error is very low, it means that the training data is fitted very well by the estimated model. If the model fits the training data very well, it means it has low bias with respect to that set of data. If the training error is high, it means that the training data is not fitted well enough by the estimated model. If the model fails to fit the training data well, it means it has high bias with respect to that set of data.
In our particular case, the training MSE plateaus at a value of roughly 20 MW$^2$. As we’ve already established, this is a high error score. Because the validation MSE is high, and the training MSE is high as well, our model has a high bias problem. Now let’s move with diagnosing eventual variance problems. Estimating variance can be done in at least two ways:
• By examining the gap between the validation learning curve and training learning curve.
• By examining the training error: its value and its evolution as the training set sizes increase.
A narrow gap indicates low variance. Generally, the more narrow the gap, the lower the variance. The opposite is also true: the wider the gap, the greater the variance. Let’s now explain why this is the case. As we’ve discussed earlier, if the variance is high, then the model fits training data too well. When training data is fitted too well, the model will have trouble generalizing on data that hasn’t seen in training. When such a model is tested on its training set, and then on a validation set, the training error will be low and the validation error will generally be high. As we change training set sizes, this pattern continues, and the differences between training and validation errors will determine that gap between the two learning curves.
The relationship between the training and validation error, and the gap can be summarized this way: $gap = validation\ error – training\ error$ So the bigger the difference between the two errors, the bigger the gap. The bigger the gap, the bigger the variance. In our case, the gap is very narrow, so we can safely conclude that the variance is low. High training MSE scores are also a quick way to detect low variance. If the variance of a learning algorithm is low, then the algorithm will come up with simplistic and similar models as we change the training sets. Because the models are overly simplified, they cannot even fit the training data well (they underfit the data). So we should expect high training MSEs. Hence, high training MSEs can be used as indicators of low variance.
In our case, the training MSE plateaus at around 20, and we’ve already concluded that’s a high value. So besides the narrow gap, we now have another confirmation that we have a low variance problem. So far, we can conclude that:
• Our learning algorithm suffers from high bias and low variance, underfitting the training data.
• Adding more instances (rows) to the training data is hugely unlikely to lead to better models under the current learning algorithm.
One solution at this point is to change to a more complex learning algorithm. This should decrease the bias and increase the variance. A mistake would be to try to increase the number of training instances. Generally, these other two fixes also work when dealing with a high bias and low variance problem:
• Training the current learning algorithm on more features (to avoid collecting new data, you can generate easily polynomial features). This should lower the bias by increasing the model’s complexity.
• Decreasing the regularization of the current learning algorithm, if that’s the case. In a nutshell, regularization prevents the algorithm from fitting the training data too well. If we decrease regularization, the model will fit training data better, and, as a consequence, the variance will increase and the bias will decrease.
## Learning curves – low bias and high variance
Let’s see how an unregularized Random Forest regressor fares here. We’ll generate the learning curves using the same workflow as above. This time we’ll bundle everything into a function so we can use it for later. For comparison, we’ll also display the learning curves for the linear regression model above.
### Bundling our previous work into a function ###
def learning_curves(estimator, data, features, target, train_sizes, cv):
train_sizes, train_scores, validation_scores = learning_curve(
estimator, data[features], data[target], train_sizes =
train_sizes,
cv = cv, scoring = 'neg_mean_squared_error')
train_scores_mean = -train_scores.mean(axis = 1)
validation_scores_mean = -validation_scores.mean(axis = 1)
plt.plot(train_sizes, train_scores_mean, label = 'Training error')
plt.plot(train_sizes, validation_scores_mean, label = 'Validation error')
plt.ylabel('MSE', fontsize = 14)
plt.xlabel('Training set size', fontsize = 14)
title = 'Learning curves for a ' + str(estimator).split('(')[0] + ' model'
plt.title(title, fontsize = 18, y = 1.03)
plt.legend()
plt.ylim(0,40)
### Plotting the two learning curves ###
from sklearn.ensemble import RandomForestRegressor
plt.figure(figsize = (16,5))
for model, i in [(RandomForestRegressor(), 1), (LinearRegression(),2)]:
plt.subplot(1,2,i)
learning_curves(model, electricity, features, target, train_sizes, 5)
Now let’s try to apply what we’ve just learned. It’d be a good idea to pause reading at this point and try to interpret the new learning curves yourself. Looking at the validation curve, we can see that we’ve managed to decrease bias. There still is some significant bias, but not that much as before. Looking at the training curve, we can deduce that this time there’s a low bias problem.
The new gap between the two learning curves suggests a substantial increase in variance. The low training MSEs corroborate this diagnosis of high variance. The large gap and the low training error also indicates an overfitting problem. Overfitting happens when the model performs well on the training set, but far poorer on the test (or validation) set. One more important observation we can make here is that adding new training instances is very likely to lead to better models. The validation curve doesn’t plateau at the maximum training set size used. It still has potential to decrease and converge toward the training curve, similar to the convergence we see in the linear regression case. So far, we can conclude that:
• Our learning algorithm (random forests) suffers from high variance and quite a low bias, overfitting the training data.
• Adding more training instances is very likely to lead to better models under the current learning algorithm.
At this point, here are a couple of things we could do to improve our model:
• Adding more training instances.
• Increase the regularization for our current learning algorithm. This should decrease the variance and increase the bias.
• Reducing the numbers of features in the training data we currently use. The algorithm will still fit the training data very well, but due to the decreased number of features, it will build less complex models. This should increase the bias and decrease the variance.
In our case, we don’t have any other readily available data. We could go into the power plant and take some measurements, but we’ll save this for another post (just kidding). Let’s rather try to regularize our random forests algorithm. One way to do that is to adjust the maximum number of leaf nodes in each decision tree. This can be done by using the max_leaf_nodes parameter of RandomForestRegressor(). It’s not necessarily for you to understand this regularization technique. For our purpose here, what you need to focus on is the effect of this regularization on the learning curves.
learning_curves(RandomForestRegressor(max_leaf_nodes = 350), electricity, features, target, train_sizes, 5)
Not bad! The gap is now more narrow, so there’s less variance. The bias seems to have increased just a bit, which is what we wanted. But our work is far from over! The validation MSE still shows a lot of potential to decrease. Some steps you can take toward this goal include:
• Adding more training instances.
• Adding more features.
• Feature selection.
• Hyperparameter optimization.
## The ideal learning curves and the irreducible error
Learning curves constitute a great tool to do a quick check on our models at every point in our machine learning workflow. But how do we know when to stop? How do we recognize the perfect learning curves? For our regression case before, you might think that the perfect scenario is when both curves converge toward an MSE of 0. That’s a perfect scenario, indeed, but, unfortunately, it’s not possible. Neither in practice, neither in theory. And this is because of something called irreducible error. When we build a model to map the relationship between the features $X$ and the target $Y$, we assume that there is such a relationship in the first place.
Provided the assumption is true, there is a true model $f$ that describes perfectly the relationship between $X$ and $Y$, like so:
$$Y = f(X) + irreducible\ error \tag{1}$$
But why is there an error?! Haven’t we just said that $f$ describes the relationship between X and Y perfectly?! There’s an error there because $Y$ is not only a function of our limited number of features $X$. There could be many other features that influence the value of $Y$. Features we don’t have. It might also be the case that $X$ contains measurement errors. So, besides $X$, $Y$ is also a function of $irreducible\ error$. Now let’s explain why this error is irreducible. When we estimate $f(X)$ with a model $\hat{f}(X)$, we introduce another kind of error, called reducible error:
$$f(X) = \hat{f}(X) + reducible\ error \tag{2}$$
Replacing $f(X)$ in $(1)$ we get:
$$Y = \hat{f}(X) + reducible\ error + irreducible\ error \tag{3}$$
Error that is reducible can be reduced by building better models. Looking at equation $(2)$ we can see that if the $reducible\ error$ is 0, our estimated model $\hat{f}(X)$ is equal to the true model $f(X)$.
However, from $(3)$ we can see that $irreducible\ error$ remains in the equation even if $reducible\ error$ is 0. From here we deduce that no matter how good our model estimate is, generally there still is some error we cannot reduce. And that’s why this error is considered irreducible. This tells us that that in practice the best possible learning curves we can see are those which converge to the value of some irreducible error, not toward some ideal error value (for MSE, the ideal error score is 0; we’ll see immediately that other error metrics have different ideal error values).
In practice, the exact value of the irreducible error is almost always unknown. We also assume that the irreducible error is independent of $X$. This means that we cannot use $X$ to find the true irreducible error. Expressing the same thing in the more precise language of mathematics, there’s no function $g$ to map $X$ to the true value of the irreducible error:
$$irreducible\ error \neq g(X)$$
So there’s no way to know the true value of the irreducible error based on the data we have. In practice, a good workaround is to try to lower the error score as much as possible, while keeping in mind that the limit is given by some irreducible error.
## What about classification?
So far, we’ve learned about learning curves in a regression setting. For classification tasks, the workflow is almost identical. The main difference is that we’ll have to choose another error metric – one that is suitable for evaluating the performance of a classifier. Let’s see an example:
Unlike what we’ve seen so far, notice that the learning curve for the training error is above the one for the validation error. This is because the score used, accuracy, describes how good the model is. The higher the accuracy, the better. The MSE, on the other side, describes how bad a model is. The lower the MSE, the better. This has implications for the irreducible error as well. For error metrics that describe how bad a model is, the irreducible error gives a lower bound: you cannot get lower than that. For error metrics that describe how good a model is, the irreducible error gives an upper bound: you cannot get higher than that. As a side note here, in more technical writings the term Bayes error rate is what’s usually used to refer to the best possible error score of a classifier. The concept is analogous to the irreducible error.
## Next steps
Learning curves constitute a great tool to diagnose bias and variance in any supervised learning algorithm. We’ve learned how to generate them using scikit-learn and matplotlib, and how to use them to diagnose bias and variance in our models. To reinforce what you’ve learned, these are some next steps to consider:
• Generate learning curves for a regression task using a different data set.
• Generate learning curves for a classification task.
• Generate learning curves for a supervised learning task by coding everything from scratch (don’t use learning_curve() from scikit-learn). Using cross-validation is optional.
• Compare learning curves obtained without cross-validating with curves obtained using cross-validation. The two kinds of curves should be for the same learning algorithm.
Tags
advanced, bias, classification, curves, energy, Learn Python, learning curves, Machine Learning, power, python, Scikit-Learn, tutorial, Tutorials, variance
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# Q: Persuasive Paper Part 1: A Problem Exists
Choose one in 55 topics below.Using your thesis statement and research, present the problem that needs to be addressed with your proposed solution. Note: Your solution, advantages, and challenges, will be in Parts 2 and 3. Write a three to four (3-4) page paper in which you: 1. Provide an appropriate title and an interesting opening paragraph to appeal to your stated audience (appeal with logic, ethics, or emotion). 2. Include a defensible, relevant thesis statement in the first paragraph. (Revised from Assignment 2) 3. Describe the history and status of the issue and provide an overview of the problem(s) that need to be addressed. This should be one or two (1or 2) paragraphs. 4. Explain the first problem (economic, social, political, environmental, complexity, inequity, ethical/moral, etc.) and provide support for your claims. This should be one or two (1 or 2) paragraphs. 5. Explain the second problem (economic, social, political, environmental, complexity, inequity, ethical/moral, etc.). and provide support for your claims. This should be one or two (1 or 2) paragraphs. 6. Explain the third problem (economic, social, political, environmental, complexity, inequity, ethical/moral, etc.) and provide support for your claims. This should be one or two (1 or 2) paragraphs. 7. Provide a concluding paragraph that summarizes the stated problems and promises a solution. 8. Develop a coherently structured paper with an introduction, body, and conclusion. 9. Use effective transitional words, phrases, and sentences throughout the paper. 10. Support claims with at least three (3) quality, relevant references. Use credible, academic sources available through Strayer University’s Resource Center.Topics 1) Should regulations be changed regarding the hydraulic fracturing of shale to produce natural gas? 2) Should taxes on people making over $250,000 a year be changed? 3) Should affirmative action laws be changed? 4) Should Transportation Security (TSA) regulations be changed? 5) Should regulations for stem cell research and use be changed? 6) Should regulations for home schools be changed? 7) Should funding for the U.S. space program be changed? 8) Should changes be made to the Food and Drug Administration (FDA)? 9) Should changes be made to the regulations for foods that are served in public schools? 10) Should changes be made to regulations for mental health drugs for minors? 11) Should regulations be changed regarding genetically altering plants and/or animals? 12) Should the Family and Medical Leave Act be changed? 13) Should changes be made to the U.S. immigration policy? 14) Should taxes on alcohol and tobacco be increased to help pay for rising medical costs? 15) Should regulations regarding the use of cell phones while driving be standardized? 16) Should recycling regulations be standardized across all regions and states? 17) Should the U.S. develop more energy sources such as ENG 215 – Appendices ©2012 Strayer University. All Rights Reserved. This document contains Strayer University Confidential and Proprietary information and may not be copied, further distributed, or otherwise disclosed in whole or in part, without the expressed written permission of Strayer University. ENG 215 Student Version 1122 (1118 2-7-2012) Final Page 40 of 41 solar power and wind energy? 18) Should the instant replay used in the NFL be applied to other sports? 19) Should regulations regarding payment of college athletes be changed? 20) Should minors who commit violent crimes be tried as adults? 21) Should regulations regarding public employee unions’ right to strike be changed? 22) Should child welfare regulations be changed? 23) Should changes be made to the No Child Left Behind Act? 24) Should English be made the official language of the United States? 25) Should DUI (driving under the influence) laws be changed? 26) Should the U.S. build more nuclear power plants for an energy source? 27) Should employers with 401K plans for employees be required to have an “opt out” policy rather than an “opt in” policy? 28) Should sex offender registration laws be changed? 29) Should laws governing student laws be changed? 30) Should laws governing credit card companies be changed? 31) Should laws governing nursing homes be changed? 32) Should children of parents who do not allow them to be vaccinated be allowed to attend public school? 33) Should unemployment regulations and benefits be changed? 34) Should rules requiring all members of a jury to agree for conviction be changed? 35) Should financial incentives be offered to high school students to perform well on standardized tests? 36) Should the government offer tax credits for the purchase of hybrid or alternative energy vehicles? 37) Should the U.S. Government prohibit companies from outsourcing jobs to people in foreign countries that do not have unions and / or fair labor laws? 38) Should the U.S. government provide financial assistance to people whose retirement funds were invested in the stock of companies that may have used unethical accounting practices (e.g., Enron, Arthur Andersen, ENG 215 – Appendices ©2012 Strayer University. All Rights Reserved. This document contains Strayer University Confidential and Proprietary information and may not be copied, further distributed, or otherwise disclosed in whole or in part, without the expressed written permission of Strayer University. ENG 215 Student Version 1122 (1118 2-7-2012) Final Page 41 of 41 etc.)? 39) Should citizens be permitted to carry a concealed weapon to their workplace (e.g., office, school, construction site)? 40) Should the U.S. Tax Social Security income ceilings for contributions be raised? 41) Should colleges and universities expel students who are caught cheating on exams and / or plagiarizing their homework assignments? 42) Should the U.S. prohibit trade with countries that have poor records on human rights? 43) Should vehicles (cars, trucks, vans, SUVs) be required to have backup cameras? 44) Should the states be allowed to determine the dates of their primary elections? 45) Should tax vouchers be provided to parents who send their children to private schools? 46) Should banks be allowed to charge fees for using Debit cards? 47) Should the U.S. require all S.S. recipients to have their checks delivered to a bank account rather than by mail? (To go into effect in 2013) 48) Should all U.S. students be required to take three years of foreign language in high school? 49) Should the state and / or federal government provide subsidies to organic farmers? 50) Should the U.S. eliminate farm subsidies? 51) Should all states require motorcyclists and passengers to wear helmets? 52) Should non-instructional services (e.g., food service, janitorial service) be provided by contract services rather than by school employees? 53) Should state and local governments provide health insurance only for retirees who have served 20 years in government service? 54) Should your state or local government enact different laws regarding certain animals (e.g., pit bulls)? 55) Should the federal government require mandatory service of all citizens between the ages of 18 and 35? Want an Answer? 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## mahmit2012 3 years ago ∫ sqrt [(a-x)(x-b)] dx reduce it to the form: ∫ sqrt [c/y-1] dy Delete Cancel Submit
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1. TuringTest
• 3 years ago
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ah from earlier... bookmark
2. mahmit2012
• 3 years ago
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|dw:1348115741471:dw|
3. mahmit2012
• 3 years ago
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4. mahmit2012
• 3 years ago
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6. mukushla
• 3 years ago
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u want us to change it with sub to the form$\int \sqrt{\frac{c}{y}-1} \ \text{d}y$right?
7. Callisto
• 3 years ago
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What's supposed to be the question :'(
8. mahmit2012
• 3 years ago
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reduce to another one.
9. mahmit2012
• 3 years ago
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and then get a solution for other one.
10. Callisto
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But how to reduce to that one (∫ sqrt [c/y-1] dy) ?
11. mahmit2012
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this is my question.
12. Callisto
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Sorry..
13. mahmit2012
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sorry for what ?
14. mahmit2012
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you just find a specific y=f(x)
15. mahmit2012
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999947547912598, "perplexity": 29780.579485658025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701153323.32/warc/CC-MAIN-20160205193913-00341-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://steamsplay.com/final-fantasy-vi-how-to-replace-the-default-font-guide/ | # FINAL FANTASY VI How to Replace the Default Font Guide
Replace the default font with the one from the Final Fantasy Advance and Final Fantasy DS games.
# INTRO:
Replaces the default font with the one from the Final Fantasy Advance and Final Fantasy DS games. Specifically the final version, from FFIV DS. A previous mod exists, but lacks support for non-English languages, and even for English, there were errors.
Supports all languages that use the Latin script, the Cyrillic script, and the Greek script, so long as they don’t require letters that use multiple diacritics at the same time. Height limitations prevented them. Japanese Hiragana and Katakana also supported, but not Kanji.
If you see any problems, let me know. Especially in regards to the Cyrillic script and Greek script since I’m not familiar with them. I’ll update the font and the bundle files if need be.
In the download, I included a TTF file of the font, so it can be used for other purposes too.
# INSTRUCTIONS:
Go to your Steam folder, then continue onward to:
steamapps\common\FINAL FANTASY VI PR\FINAL FANTASY VI_Data\StreamingAssets ,
and then copy-and-paste the BUNDLE files into the folder, replacing the pre-existing ones.
You can make a backup of the originals first, if you want, though I think just deleting the new ones should result in Steam re-downloading the originals.
These files also work on the first five games, in the same manner. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9589086174964905, "perplexity": 2985.181677748938}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662578939.73/warc/CC-MAIN-20220525023952-20220525053952-00226.warc.gz"} |
https://dsp.stackexchange.com/questions/4825/why-is-the-fft-mirrored | Why is the FFT “mirrored”?
If you do an FFT plot of a simple signal, like:
t = 0:0.01:1 ;
N = max(size(t));
x = 1 + sin( 2*pi*t ) ;
y = abs( fft( x ) ) ;
stem( N*t, y )
FFT of above
I understand that the number in the first bin is "how much DC" there is in the signal.
y(1) %DC
> 101.0000
The number in the second bin should be "how much 1-cycle over the whole signal" there is:
y(2) %1 cycle in the N samples
> 50.6665
But it's not 101! It's about 50.5.
There's another entry at the end of the fft signal, equal in magnitude:
y(101)
> 50.2971
So 50.5 again.
My question is, why is the FFT mirrored like this? Why isn't it just a 101 in y(2) (which would of course mean, all 101 bins of your signal have a 1 Hz sinusoid in it?)
Would it be accurate to do:
mid = round( N/2 ) ;
% Prepend y(1), then add y(2:middle) with the mirror FLIPPED vector
% from y(middle+1:end)
z = [ y(1), y( 2:mid ) + fliplr( y(mid+1:end) ) ];
stem( z )
Flip and add-in the second half of the FFT vector
I thought now, the mirrored part on the right hand side is added in correctly, giving me the desired "all 101 bins of the FFT contain a 1Hz sinusoid"
>> z(2)
ans =
100.5943
• A similar question has been answered here: dsp.stackexchange.com/questions/3466/… – pichenettes Oct 28 '12 at 17:35
• But this is specifically about the symmetry (I believe it's called Hermetian symmetry?) of the signal. – bobobobo Oct 28 '12 at 17:44
• For a pure real signals F(k)=conj(F(N-k)), this is why the Fourier transform of a pure real signal is symmetric. – WebMonster Oct 28 '12 at 18:02
• Ask yourself: what result would you expect if your signal was 1 + cos(2*pit)... And 1 + i cos(2*pit)... And 1 + i sin(2*pi*t)... – pichenettes Oct 28 '12 at 18:21
• Because a Fourier transform breaks up a signal into complex exponentials, and a sine wave is the sum of 2 complex exponentials. dsp.stackexchange.com/a/449/29 – endolith Oct 28 '12 at 19:55
Real signals are "mirrored" in the real and negative halves of the Fourier transform because of the nature of the Fourier transform. The Fourier transform is defined as the following-
$H(f) = \int h(t)e^{-j2\pi ft}dt$
Basically it correlates the signal with a bunch of complex sinusoids, each with its own frequency. So what do those complex sinusoids look like? The picture below illustrates one complex sinusoid.
The "corkscrew" is the rotating complex sinusoid in time, while the two sinusoids that follow it are the extracted real and imaginary components of the complex sinusoid. The astute reader will note that the real and imaginary components are the exact same, only they are out of phase with each other by 90 degrees ($\frac{\pi}{2}$). Because they are 90 degrees out of phase they are orthogonal and can "catch" any component of the signal at that frequency.
The relationship between the exponential and the cosine/sine is given by Euler's formula-
$e^{jx} = cos(x) + j*sin(x)$
This allows us to modify the Fourier transform as follows- $$H(f) = \int h(t)e^{-j2\pi ft}dt \\ = \int h(t)(cos(2\pi ft) - j*sin(2\pi ft))dt$$
At the negative frequencies the Fourier transform becomes the following- $$H(-f) = \int h(t)(cos(2\pi (-f)t) - j*sin(2\pi (-f)t))dt \\ = \int h(t)(cos(2\pi ft) + j*sin(2\pi ft))dt$$
Comparing the negative frequency version with the positive frequency version shows that the cosine is the same while the sine is inverted. They are still 90 degrees out of phase with each other, though, allowing them to catch any signal component at that (negative) frequency.
Because both the positive and negative frequency sinusoids are 90 degrees out of phase and have the same magnitude, they will both respond to real signals in the same way. Or rather, the magnitude of their response will be the same, but the correlation phase will be different.
EDIT: Specifically, the negative frequency correlation is the conjugate of the positive frequency correlation (due to the inverted imaginary sine component) for real signals. In mathematical terms, this is, as Dilip pointed out, the following-
$H(-f) = [H(f)]^*$
Another way to think about it:
Imaginary components are just that..Imaginary! They are a tool, which allows the employ of an extra plane to view things on and makes much of digital (and analog) signal processing possible, if not much easier than using differential equations!
But we can't break the logical laws of nature, we can't do anything 'real' with the imaginary content$^\dagger$ and so it must effectively cancel itself out before returning to reality. How does this look in the Fourier Transform of a time based signal(complex frequency domain)? If we add/sum the positive and negative frequency components of the signal the imaginary parts cancel, this is what we mean by saying the positive and negative elements are conjugate to each-other. Notice that when an FT is taken of a time-signal there exists these conjugate signals, with the 'real' part of each sharing the magnitude, half in the positive domain, half in the negative, so in effect adding the conjugates together removes the imaginary content and provides the real content only.
$^\dagger$ Meaning we can't create a voltage that is $5i$ volts. Obviously, we can use imaginary numbers to represent real-world signals that are two-vector-valued, such as circularly polarized EM waves.
• Good answer - one slight nitpick though, I am not on-board with "Because they are the same, anything that one correlates with, the other will too with the exact same magnitude and a 90 degree phase shift.". I know what you are trying to say, however (as you know), a sine correlates with a sine (score 1), but wont correlate at all with a cosine at all, (score 0). They are the same signal, but with different phases afterall. – Spacey Oct 29 '12 at 12:54
• You're right. There's another more serious problem too. I will fix it later. – Jim Clay Oct 29 '12 at 13:23
• It would be nice if you could edit your answer to be more responsive to the question which is about DFTs (though it says FFT in the title) rather than giving the general theory of Fourier transforms. – Dilip Sarwate Oct 29 '12 at 22:35
• @DilipSarwate My goal is to help the questioner understand, and I think my approach is best for that. I have upvoted your answer, though, for doing the discrete math. – Jim Clay Oct 29 '12 at 23:01
• @JimClay Your approach is greatly appreciated by the entire readership of dsp.SE, and I hope that you will find the time to make your answer a truly great answer by explicitly including in your answer what is currently left for the reader to deduce: viz. that the equations show that $H(-f) = [H(f)]^*$ (and hence $|H(-f)| = |H(f)|$) when $x(t)$ is a real-valued signal and that this is the "mirroring" that the OP was asking about. In other words, I request that you edit your answer to be more responsive to the question actually asked (as I requested in my previous comment). – Dilip Sarwate Oct 30 '12 at 12:42
The FFT (or Fast Fourier Transform) is actually an algorithm for the computation of the Discrete Fourier Transform or DFT. The typical implementation achieves speed-up over the conventional computation of the DFT by exploiting the fact that $N$, the number of data points, is a composite integer which is not the case here since $101$ is a prime number. (While FFTs exist for the case when $N$ is a prime, they use a different formulation that might or might not be implemented in MATLAB). Indeed, many people deliberately choose $N$ to be of the form $2^k$ or $4^k$ so as to speed up the DFT computation via the FFT.
Turning to the question as to why the mirroring occurs, hotpaw2 has essentially stated the reason, and so the following is just a filling in of the details. The DFT of a sequence $\mathbf x = \bigr(x[0], x[1], x[2], \ldots, x[N-1]\bigr)$ of $N$ data points is defined to be a sequence $\mathbf X =\bigr(X[0], X[1], X[2], \ldots, X[N-1]\bigr)$ where $$X[m] = \sum_{n=0}^{N-1} x[n]\left(\exp\left(-j2\pi \frac{m}{N}\right)\right)^n, m = 0, 1, \ldots, N-1$$ where $j = \sqrt{-1}$. It will be obvious that $\mathbf X$ is, in general a complex-valued sequence even when $\mathbf x$ is a real-valued sequence. But note that when $\mathbf x$ is a real-valued sequence, $\displaystyle X[0]=\sum_{n=0}^{N-1} x[n]$ is a real number. Furthermore, if $N$ is an even number, then, since $\exp(-j\pi) = -1$, we also have that $$X\left[\frac{N}{2}\right] = \sum_{n=0}^{N-1} x[n]\left(\exp\left(-j2\pi \frac{N/2}{N}\right)\right)^n = \sum_{n=0}^{N-1} x[n](-1)^n$$ is a real number. But, regardless of whether $N$ is odd or even, the DFT $\mathbf X$ of a real-valued sequence $\mathbf x$ has Hermitian symmetry property that you have mentioned in a comment. We have for any fixed $m$, $1 \leq m \leq N-1$, \begin{align*} X[m] &= \sum_{n=0}^{N-1} x[n]\left(\exp\left(-j2\pi \frac{m}{N}\right)\right)^n\\ X[N-m] &= \sum_{n=0}^{N-1} x[n]\left(\exp\left(-j2\pi \frac{N-m}{N}\right)\right)^n\\ &= \sum_{n=0}^{N-1} x[n]\left(\exp\left(-j2\pi + j2\pi\frac{m}{N}\right)\right)^n\\ &= \sum_{n=0}^{N-1} x[n]\left(\exp\left(j2\pi\frac{m}{N}\right)\right)^n\\ &= \left(X[m]\right)^* \end{align*} Thus, for $1 \leq m \leq N-1$, $X[N-m] = \left(X[m]\right)^*$. As a special case of this, note that if we choose $m = N/2$ when $N$ is even, we get that $X[N/2] = \left(X[N/2]\right)^*$, thus confirming our earlier conclusion that $X[N/2]$ is a real number. Note that an effect of the Hermitian symmetry property is that
the $m$-th bin in the DFT of a real-valued sequence has the same magnitude as the $(N-m)$-th bin.
MATLABi people will need to translate this to account for the fact that MATLAB arrays are numbered from $1$ upwards.
Turning to your actual data, your $\mathbf x$ is a DC value of $1$ plus slightly more than one period of a sinusoid of frequency $1$ Hz. Indeed, what you are getting is $$x[n] = 1 + \sin(2\pi (0.01n)), ~ 0 \leq n \leq 100$$ where $x[0] = x[100] = 1$. Thus, the first and the last of $101$ samples has the same value. The DFT that you are computing is thus given by $$X[m] = \sum_{n=0}^{100} \left(1+\sin\left(2\pi \left(\frac{n}{100}\right)\right)\right)\left(\exp\left(-j2\pi \frac{m}{101}\right)\right)^n$$ The mismatch between $100$ and $101$ causes clutter in the DFT: the values of $X[m]$ for $2 \leq m \leq 99$ are nonzero, albeit small. On the other hand, suppose you were to adjust the array t in your MATLAB program to have $100$ samples taken at $t=0, 0.01, 0.02, \ldots, 0.99$ so that what you have is $$x[n] = 1 + \sin(2\pi (0.01n)), ~ 0 \leq n \leq 99.$$ Then the DFT is $$X[m] = \sum_{n=0}^{99} \left(1+\sin\left(2\pi \left(\frac{n}{100}\right)\right)\right)\left(\exp\left(-j2\pi \frac{m}{100}\right)\right)^n,$$ you will see that your DFT will be exactly $\mathbf X = (100, -50j, 0, 0, \ldots, 0, 50j)$ (or at least within round-off error), and the inverse DFT will give that for $0 \leq n \leq 99$, \begin{align*} x[n] &= \frac{1}{100}\sum_{m=0}^{99}X[m]\left(\exp\left(j2\pi \frac{n}{100}\right)\right)^m\\ &= \frac{1}{100}\left[100 - 50j\exp\left(j2\pi \frac{n}{100}\right)^1 + 50j \left(\exp\left(j2\pi \frac{n}{100}\right)\right)^{99}\right]\\ &= 1 + \frac{1}{2j}\left[\exp\left(j2\pi \frac{n}{100}\right) - \exp\left(j2\pi \frac{-n}{100}\right)\right]\\ &= 1 + \sin(2\pi (0.01n)) \end{align*} which is precisely what you started from.
• So, is it possible to tell from the FFT if a signal is periodic or not? – displayname Sep 18 '16 at 14:01
• @displayname That is a separate question that should be asked in its own right (and perhaps has been asked and answered already). – Dilip Sarwate Sep 20 '16 at 15:58
• When I carefully pry out the conjugate symmetrical bins [By writing a 0 + 0i into them] and reconstruct the time domain signal using ifft, the magnitude of the reconstructed time domain signal has halved. Is this natural or is it a tooling problem? I do take care of FFT output normalization and its reverse after iFFT. – Raj Aug 15 '17 at 4:51
Note that an FFT result is mirrored (as in conjugate symmetric) only if the input data is real.
For strictly real input data, the two conjugate mirror images in the FFT result cancel out the imaginary parts of any complex sinusoids, and thus sum to a strictly real sinusoid (except for tiny numerical rounding noise), thus leaving you with a representation of strictly real sine waves.
If the FFT result wasn't conjugate mirrored, it would represent a waveform that had complex values (non-zero imaginary components), not something strictly real valued. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8852511644363403, "perplexity": 540.2994671171074}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986693979.65/warc/CC-MAIN-20191019114429-20191019141929-00009.warc.gz"} |
https://qiuyiwu.github.io/2018/01/17/Tensorflow-for-Deep-Learning-1/ | I’m learning how to use Google’s TensorFlow framework to create artificial neural networks for deep learning with Python from Udemy. I’m using Jupiter notebook to practice and blog my learning progress here.
TensorFlow is an open source software library for numerical computation using data flow graphs. Nodes in the graph represent mathematical operations, while the graph edges represent the multidimensional data arrays (tensors) communicated between them. This architecture allows users to deploy computation to one or more CPUs or GPUs, in a desktop, server, or mobile device with a single API (Application programming interface).
# Install TensorFlow Environment
Download Anaconda Distribution for Python 3.6 Version. Tutorial comes in that page.
For MacOS: Open Terminal, use cd to the target directory
Create the environment file: run conda env create -f tfdl_env.yml
Activate the file: run source activate tfdeeplearning
Now you are in the virtual environment of tfdeeplearning
If you want to get out of this, run source deactivate
Note: How is Anaconda related to Python?
Anaconda is a python and R distribution. It aims to provide everything you need (python wise) for data science “out of the box”.
It includes:
• The core python language
• 100+ python “packages” (libraries)
• Spyder (IDE/editor - like pycharm) and Jupyter
• conda, Anaconda’s own package manager, used for updating Anaconda and packages
Also Anaconda is used majorly for the data science. which manipulates large datasets based on statistical methods. ie. Many statistical packages are already available in anaconda libraries(packages)
Vanilla python installed from python.org comew with standard library is okay, in which case using pip to install manually (which comes with most python dists and you should have it if you downloaded from python.org).
# TensorFlow Basic Syntax
Output: 1.3.0
Create a tensor ($\approx$ n-dimension array), the basic one (constant)
Output: tensorflow.python.framework.ops.Tensor
Run this operation inside of a session:
Output: b'HelloWorld'
Note:
Use with is to make sure we don’t close the session until we run a block of code then close the session.
The b character prefix signifies that HelloWorld is a byte string, use result.decode('utf-8') to convert byte str to str.
Output: 30
Numpy Operations:
Note:
Interactive Session is particularly useful for Jupyter Notebook, it allows you to constantly call it through multiple cells.
In the Interactive Session, instead of using sess.run(op), we can use op.eval(), it means “evaluate this operation”, and generates the same result.
Matrix multiplication (common in neural networks)
\begin{align*} \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \times \begin{bmatrix} 10 \\ 100 \end{bmatrix} = \begin{bmatrix} 210 \\ 430 \end{bmatrix} \end{align*}
Note: sess.run(result) can also use result.eval() instead.
# TensorFlow Graphs
Graphs are sets of connected nodes(vertices), and the connections are called edges. In TensorFlow each node is an operation with possible inputs that can supply some outputs. When TenserFlow is started, a default graph is created.
Output:
fixed default graph: <tensorflow.python.framework.ops.Graph object at 0x11f4c92b0>
Dynamic random graph: <tensorflow.python.framework.ops.Graph object at 0x11f707dd8>
Output: True
Output: False
# Variables and Placeholders
Variables and Placeholders are two main types of tensor objects in a Graph. During the optimization process, TensorFlow tunes the parameters of the model. Variables can hold the values of weights and biases throughout the session. Variables need to be initialized. Placeholders are initially empty and are used to feed in the actual training examples. However they do need a declared expected data type (tf.float32) with an optiional shape argument.
Output: array([[ 0.27756679, 0.82726526, 0.80544853, 0.43891859], [ 0.56279469, 0.57444489, 0.82595968, 0.63165414], [ 0.16034544, 0.86095798, 0.74416387, 0.17536163], [ 0.44427669, 0.69035304, 0.55842543, 0.00723565]], dtype=float32)
# TensorFlow Neural Network
Create a neuron that performs a simple linear fit to some 2-D data. Graph of $wx+b = z$
1. Build a Graph
2. Initiate the Session
3. Feed Data In and get Output
4. Add in the cost function in order to train the network to optimize the parameters
Output:
[[ 151.07165527 156.49855042 102.27921295 116.58396149 167.95948792]
[ 135.45622253 82.76316071 141.42784119 124.22093201 71.06043243]
[ 113.30171204 93.09214783 76.06819153 136.43911743 154.42727661]
[ 96.7172699 81.83804321 133.83674622 146.38117981 101.10578918]
[ 122.72680664 105.98292542 59.04463196 67.98310089 72.89292145]]
[[ 5134.64404297 5674.25 283.12432861 1705.47070312 6813.83154297]
[ 4341.8125 1598.26696777 4652.73388672 3756.8293457 988.9463501 ]
[ 3207.8112793 2038.10290527 1052.77416992 4546.98046875 5588.11572266]
[ 1707.37902832 614.02526855 4434.98876953 5356.77734375 2029.85546875]
[ 3714.09838867 2806.64379883 262.76763916 747.19854736 1013.29199219]]
Output: [[ 0.81314439 0.98195159 0.73793817]]
Now I want the neural network to solve $y = mx + b$ with 10 training steps:
# TensorFlow Regression
Regression example with huge dataset:
For real cases, usually the datasets are humongous and we do not use all of them at once. Instead, we use batch method to feed the data batch by batch into the network to save the time. The number of batches depends on the size of the data. Here we feed 1000 batches of data, with each batch has 8 corresponding data points (x data points with corresponding y labels). To make batches useful, we grab 8 random data points via rand_ind = np.random.randint(len(x_data), size = batch_size), then train the optimizer.
# TensorFlow Estimator API
This section is to solve the regression task with TensorFlow estimator API. Wait a minute, what is API? Technically, API stands for Application Programming Interface, but still, what is that? Basically, it is part of the server, that can be distinctively separated from its environment, that receives requests and sends responses. Here is an excellent article from Petr Gazarov explaining API.
There are many other higher levels of APIs (Keras, Layers…). The tf.estimator API has several model types to choose from:
• tf.estimator.LinearClassifier: Constructs a linear classification model
• tf.estimator.LinearRegressor: Constructs a linear regression model
• tf.estimator.DNNClassifier: Constructs a neural network classification model
• tf.estimator.DNNRegressor: Constructs a neural network regression model
• tf.estimator.DNNLinearCombinedRegressor: Constructs a neural network and linear combined regression model
Steps for using the Estimator API:
• Define a list of feature columns
• Create the Estimator Model
• Create a Data Input Function
• Call train, evaluate, and predict methods on the estimator object
Output:
Training data matrics {'loss': 8.7310658, 'average_loss': 1.0913832, 'global_step': 1000} Test data matrics {'loss': 8.6690454, 'average_loss': 1.0836307, 'global_step': 1000}
This is a good way to check if the model is overfitting (very low loss on training data but very high loss on test data). We want the loss of training data and test data are very close to each other.
Output:
[{'predictions': array([ 4.43396044], dtype=float32)}, {'predictions': array([ 5.06833887], dtype=float32)}, {'predictions': array([ 5.7027173], dtype=float32)}, {'predictions': array([ 6.33709526], dtype=float32)}, {'predictions': array([ 6.97147369], dtype=float32)}, {'predictions': array([ 7.60585213], dtype=float32)}, {'predictions': array([ 8.24023056], dtype=float32)}, {'predictions': array([ 8.87460899], dtype=float32)}, {'predictions': array([ 9.50898743], dtype=float32)}, {'predictions': array([ 10.14336586], dtype=float32)}]
# TensorFlow Classification
Use real dataset “Pima Indians Diabetes Dataset”, including both categorical and continuous features, to use tf.estimator switching models – from linear classifier to dense neural network classifier.
## Linear Classifier
Output: Index(['Number_pregnant', 'Glucose_concentration', 'Blood_pressure', 'Triceps', 'Insulin', 'BMI', 'Pedigree', 'Age', 'Class', 'Group'], dtype='object')
The distribution of Age from the histgram shows that most of the people are 20s. And instead of treating this variable as a continuous variable, we can bucket these values together, making boundary for each decade or so. Basically we use bucket system to transform continuous variable into categorial variable.
Create the model!
Output:
{'accuracy': 0.73160172, 'accuracy_baseline': 0.64935064, 'auc': 0.79658431, 'auc_precision_recall': 0.6441071, 'average_loss': 0.52852213, 'global_step': 1000, 'label/mean': 0.35064936, 'loss': 5.0870256, 'prediction/mean': 0.35784912}
The accuracy is 73.16%.
Prediction!
## Dense Neural Network Classifier
Output:
{'accuracy': 0.75757575, 'accuracy_baseline': 0.64935064, 'auc': 0.82814813, 'auc_precision_recall': 0.67539084, 'average_loss': 0.49014509, 'global_step': 1000, 'label/mean': 0.35064936, 'loss': 4.7176466, 'prediction/mean': 0.36287409}
0% | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32937541604042053, "perplexity": 9048.74815724205}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655886516.43/warc/CC-MAIN-20200704170556-20200704200556-00234.warc.gz"} |
https://www.logicmatters.net/2020/01/21/empty-domains-again/ | # Empty domains, again
Here’s a rewritten four-page chapter from IFL2 on empty domains. Difficult to know how to handle this topic. Many intro texts just skate over the issue. An earlier draft perhaps said a bit too much a bit too confusingly. Hope this strikes a better balance. Last-minute comments always welcome!
(By the way, “sets*” with a star is my usage in the book for when I really mean sets as objects in their own right — the ones that play a starring role in full-blown set* theory — as opposed to when I’m occasionally using lightweight talk of virtual classes which can be translated away.)
### 9 thoughts on “Empty domains, again”
1. This is a nice tour of the concerns that lead to free logic. As your text makes clear, the unrelativized quantifiers $\forall$ and $\exists$ behave quite differently from their relativized versions, $\forall x\in D$ and $\exists x\in D$. This difference in behaviour, by the way, underlies to the modern criticism made by logicians of the hidden assumptions of the “subalternation” relation in the Traditional Square of Oppositions. You might want to add a brief comment on that? It is worth noting —or so I claim— that mathematicians hardly ever write sentences that are naturally translated in terms of unrelativized quantifiers. If that is the case, though, wouldn’t it seem worthy for them to use the corresponding natural deduction system, with primitive introduction / elimination rules for $\forall x\in D$ and $\exists x\in D$? The rules for the unrelativized quantifiers may of course easily be derived from the rules for the latter (more natural?) relativized quantifiers.
2. In IFL, the discussion of empty domains is carried out using concepts from natural deduction while, if I remember rightly, the formal semantics for first-order logic comes much later in the book. That’s fine, but it might be a good idea to add, at that later stage, a short paragraph on the empty domain from the perspective of the semantics. I do not think that it would affect your general conclusion on the matter which, personally, I see as very reasonable, but would perhaps help appreciate it from a different angle. Namely, there are no functions taking the (non-empty) sets of individual constants and individual variables into the empty set, so the very notion of an interpretation in the empty set is ill-defined; nor is it clear how it might profitably be reconstructed without affecting the treatment of non-empty domains or creating endless complications.
1. Good point: I’ll double check what I’ve written in the formal semantics chapter to signal were the assumption that domains are non-empty is doing some work. Thanks!
3. Mostly small things (and I hope it’s clear from comments I’ve made before that I’m pretty happy with the approach it takes).
I found it a bit confusing at the start.
You bring in an argument from §32.3 that concludes ∀xGx, and then an argument said to justify it that concludes Fa instead. Well, ok, you say it starts like that. Still, I headed for §32.3 to see what was going on. The first argument in §32.3 concludes Gm. Reading on, I found the intended argument, B′. It’s just a bit harder to find than I’d like.
[BTW, looking earlier in §32, I can’t make sense of the examples of sentences at the bottom of p 300. Why is m in ∃y Mmy not a dummy name? Or n in ∀x(Lx → ∃y(Fy ∧ Rxyn))? Are there special rules for m and n somewhere?]
p 330, “Which is what happens in A. There are no such things as tachyons. So the stipulated domain of quantification is empty.” — Rather than say there are no such things, which seems questionable as a flat out assertion, perhaps say: This is what happens in A when there are no such things as tachyons, because then the stipulated domain of quantification is empty.
I don’t think it’s a good idea to call set theory “set* theory”. It seemed ok when I read your post saying ‘“sets*” with a star is my usage in the book for when I really mean sets as objects in their own right’, but not once I saw how it actually was used.
I think it’s fine to raise the issue of when there’s a commitment to sets existing and when it’s just a way of talking, but saying “set*” whenever you mention set theory seems too heavy-handed and ideological to me — especially since you’ve eliminated most of the unnecessary set-talk that was in the first edition. I don’t think an introductory logic text should be pushing that issue that hard.
1. I’ve clarified the backreference to §32.3 and also added dots to the first displayed proof in §34.1 to make it doubly clear that it is indeed a proof-fragment.
2. Middle alphabet lower case letters, proper names; early alphabet, dummy names. And ne’er the twain shall meet. Clear I think to a reader coming from working on earlier chapters. But I’m adding a sentence to §32.1(b) which re-emphasizes the point.
3. Fair point about the tachyons.
4. I’ve been wavering about the use of “sets*”! Another worry is introducing any non-standard terminology in an intro book. I agree that the passage you are commenting on is better without.
4. NORMAN M BIRKETT
Excellent chapter. I noticed no substantive problems. Just an extra ‘is’ in the final line of paragraph (c) on page 330.
I’m quite enthusiastic about the fact that you go into this in an introductory text. The fact that you do has persuaded me to buy a copy of IFL2 when it comes out.
5. On a first reading, I see no glaring errors (as usual, from my perspective as an intelligent layman; the professionals may disagree!).
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# In a school there are two sections section A and section B of class X . There are 32 students in section A and 36 students in section B . Determine the minimum number of books required for their class library so that they can be distributed equally among students of section A or section B .
Updated On: 27-06-2022 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9341356754302979, "perplexity": 855.686989768533}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710503.24/warc/CC-MAIN-20221128102824-20221128132824-00315.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/176787-solving-equations-factor-ring-z-x-x.html | # Thread: Solving Equations in a factor Ring Z[x] / <x³>
1. ## Solving Equations in a factor Ring Z[x] / <x³>
How do I solve y² -2y + 1 = 0 in the factor ring Z[x] / <x³> ?
I know how to solve this in Z or Z_n (where n is small), but I'm not too familiar with factor rings.
How do I solve y² -2y + 1 = 0 in the factor ring Z[x] / <x³> ?
I know how to solve this in Z or Z_n (where n is small), but I'm not too familiar with factor rings.
In any unitary ring, $y^2-2y+1=(y-1)^2$ , so...
Tonio
3. I know that y = 1 is one solution, but are there others? Like in Z_n, there can be other solutions than just y = 1.
You know that $(y-1)^2=0$. You now need to decide whether there are any nonzero elements in this ring whose square is 0. If not, then you can conclude that $y-1=0.$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8365876078605652, "perplexity": 470.35531375113965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823360.1/warc/CC-MAIN-20171019175016-20171019195016-00841.warc.gz"} |
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https://www.groundai.com/project/importance-resampling-for-off-policy-prediction/ | Importance Resampling for Off-policy Prediction
# Importance Resampling for Off-policy Prediction
Matthew Schlegel
University of Alberta
[email protected]
&Wesley Chung
University of Alberta
[email protected]
&Daniel Graves
Huawei
[email protected]
&Jian Qian
University of Alberta
[email protected]
&Martha White
University of Alberta
[email protected]
###### Abstract
Importance sampling (IS) is a common reweighting strategy for off-policy prediction in reinforcement learning. While it is consistent and unbiased, it can result in high variance updates to the weights for the value function. In this work, we explore a resampling strategy as an alternative to reweighting. We propose Importance Resampling (IR) for off-policy prediction, which resamples experience from a replay buffer and applies standard on-policy updates. The approach avoids using importance sampling ratios in the update, instead correcting the distribution before the update. We characterize the bias and consistency of IR, particularly compared to Weighted IS (WIS). We demonstrate in several microworlds that IR has improved sample efficiency and lower variance updates, as compared to IS and several variance-reduced IS strategies, including variants of WIS and V-trace which clips IS ratios. We also provide a demonstration showing IR improves over IS for learning a value function from images in a racing car simulator.
Importance Resampling for Off-policy Prediction
Matthew Schlegel University of Alberta [email protected] Wesley Chung University of Alberta [email protected] Daniel Graves Huawei [email protected] Jian Qian University of Alberta [email protected] Martha White University of Alberta [email protected]
\@float
noticebox[b]Preprint. Under review.\end@float
## 1 Introduction
An emerging direction for reinforcement learning systems is to learn many predictions, formalized as value function predictions contingent on many different policies. The idea is that such predictions can provide a powerful abstract model of the world. Some examples of systems that learn many value functions are the Horde architecture composed of General Value Functions (GVFs) (Sutton et al., 2011; Modayil et al., 2014), systems that use options (Sutton et al., 1999; Schaul et al., 2015a), predictive representation approaches (Sutton et al., 2005; Schaul and Ring, 2013; Silver et al., 2017) and systems with auxiliary tasks (Jaderberg et al., 2017). Off-policy learning is critical for learning many value functions with different policies, because it enables data to be generated from one behavior policy to update the values for each target policy in parallel.
The typical strategy for off-policy learning is to reweight updates using importance sampling (IS). For a given state , with action selected according to behavior , the IS ratio is the ratio between the probability of the action under the target policy and the behavior: . The update is multiplied by this ratio, adjusting the action probabilities so that the expectation of the update is as if the actions were sampled according to the target policy . Though the IS estimator is unbiased and consistent (Kahn and Marshall, 1953; Rubinstein and Kroese, 2016), it can suffer from high or even infinite variance due to large magnitude IS ratios, in theory (Andradottir et al., 1995) and in practice (Precup et al., 2001; Mahmood et al., 2014, 2017).
There have been some attempts to modify off-policy prediction algorithms to mitigate this variance.111There is substantial literature on variance reduction for another area called off-policy policy evaluation, but which estimates only a single number or value for a policy (e.g., see (Thomas and Brunskill, 2016)). The resulting algorithms differ substantially, and are not appropriate for learning the value function. Weighted IS (WIS) algorithms have been introduced (Precup et al., 2001; Mahmood et al., 2014; Mahmood and Sutton, 2015), which normalize each update by the sample average of the ratios. These algorithms improve learning over standard IS strategies, but are not straightforward to extend to nonlinear function approximation. In the offline setting, a reweighting scheme, called importance sampling with unequal support (Thomas and Brunskill, 2017), was introduced to account for samples where the ratio is zero, in some cases significantly reducing variance. Another strategy is to rescale or truncate the IS ratios, as used by V-trace (Espeholt et al., 2018) for learning value functions and Tree-Backup (Precup et al., 2000), Retrace (Munos et al., 2016) and ABQ (Mahmood et al., 2017) for learning action-values. Truncation of IS-ratios in V-trace can incur significant bias, and this additional truncation parameter needs to be tuned.
An alternative to reweighting updates is to instead correct the distribution before updating the estimator using weighted bootstrap sampling: resampling a new set of data from the previously generated samples (Smith et al., 1992; Arulampalam et al., 2002). Consider a setting where a buffer of data is stored, generated by a behavior policy. Samples for policy can be obtained by resampling from this buffer, proportionally to for state-action pairs in the buffer. In the sampling literature, this strategy has been proposed under the name Sampling Importance Resampling (SIR) (Rubin, 1988; Smith et al., 1992; Gordon et al., 1993), and has been particularly successful for Sequential Monte Carlo sampling (Gordon et al., 1993; Skare et al., 2003). Such resampling strategies have also been popular in classification, with over-sampling or under-sampling typically being preferred to weighted (cost-sensitive) updates (Lopez et al., 2013).
A resampling strategy has several potential benefits for off-policy prediction.222We explicitly use the term prediction rather than policy evaluation to make it clear that we are not learning value functions for control. Rather, our goal is to learn value functions solely for the sake of prediction. Resampling could even have larger benefits for learning approaches, as compared to averaging or numerical integration problems, because updates accumulate in the weight vector and change the optimization trajectory of the weights. For example, very large importance sampling ratios could destabilize the weights. This problem does not occur for resampling, as instead the same transition will be resampled multiple times, spreading out a large magnitude update across multiple updates. On the other extreme, with small ratios, IS will waste updates on transitions with very small IS ratios. By correcting the distribution before updating, standard on-policy updates can be applied. The magnitude of the updates vary less—because updates are not multiplied by very small or very large importance sampling ratios—potentially reducing variance of stochastic updates and simplifying learning rate selection. We hypothesize that resampling (a) learns in a fewer number of updates to the weights, because it focuses computation on samples that are likely under the target policy and (b) is less sensitive to learning parameters and target and behavior policy specification.
In this work, we investigate the use of resampling for online off-policy prediction for known, unchanging target and behavior policies. We first introduce Importance Resampling (IR), which samples transitions from a buffer of (recent) transitions according to IS ratios. These sampled transitions are then used for on-policy updates. We show that IR has the same bias as WIS, and that it can be made unbiased and consistent with the inclusion of a batch correction term—even under a sliding window buffer of experience. We provide additional theoretical results characterizing when we might expect the variance to be lower for IR than IS. We then empirically investigate IR on three microworlds and a racing car simulator, learning from images, highlighting that (a) IR is less sensitive to learning rate than IS and V-trace (IS with clipping) and (b) IR converges more quickly in terms of the number of updates.
## 2 Background
We consider the problem of learning General Value Functions (GVFs) (Sutton et al., 2011). The agent interacts in an environment defined by a set of states , a set of actions and Markov transition dynamics, with probability of transitions to state when taking action in state . A GVF is defined for policy , cumulant and continuation function , with and for a (random) transition . The value for a state is
V(s)\makebox[0.0pt]def=Eπ[Gt|St=s] where Gt\makebox[0.0pt]def=Ct+1+γt+1Ct+2+γt+1γt+2Ct+3+….
The operator indicates an expectation with actions selected according to policy . GVFs encompass standard value functions, where the cumulant is a reward. Otherwise, GVFs enable predictions about discounted sums of others signals into the future, when following a target policy . These values are typically estimated using parametric function approximation, with weights defining approximate values .
In off-policy learning, transitions are sampled according to behavior policy, rather than the target policy. To get an unbiased sample of an update to the weights, the action probabilities need to be adjusted. Consider on-policy temporal difference (TD) learning, with update for a given , for learning rate and TD-error . If actions are instead sampled according to a behavior policy , then we can use importance sampling (IS) to modify the update, giving the off-policy TD update for IS ratio . Given state , if when , then the expected value of these two updates are equal. To see why, notice that
Eμ[αtρtδt∇θVθ(s)|St=s]=αt∇θVθ(s)Eμ[ρtδt|St=s]
which equals because
Eμ[ρtδt|St=s] =∑a∈Aμ(a|s)π(a|s)μ(a|s)E[δt|St=s,At=a]= Eπ[δt|St=s].
Though unbiased, IS can be high-variance. A lower variance alternative is Weighted IS (WIS). For a batch consisting of transitions , batch WIS uses a normalized estimate for the update. For example, an offline batch WIS TD algorithm, denoted WIS-Optimal below, would use update . Obtaining an efficient WIS update is not straightforward, however, when learning online and has resulted in algorithms specialized to the tabular setting (Precup et al., 2001) or linear functions (Mahmood et al., 2014; Mahmood and Sutton, 2015). We nonetheless use WIS as a baseline in the experiments and theory.
## 3 Importance Resampling
In this section, we introduce Importance Resampling (IR) for off-policy prediction and characterize its bias and variance. A resampling strategy requires a buffer of samples, from which we can resample. Replaying experience from a buffer was introduced as a biologically plausible way to reuse old experience (Lin, 1992, 1993), and has become common for improving sample efficiency, particularly for control (Mnih et al., 2015; Schaul et al., 2015b). In the simplest case—which we assume here—the buffer is a sliding window of the most recent samples, , at time step . We assume samples are generated by taking actions according to behavior . The transitions are generated with probability , where is the stationary distribution for policy . The goal is to obtain samples according to , as if we had taken actions according to policy from states333The assumption that states are sampled from underlies most off-policy learning algorithms. Only a few attempt to adjust probabilities to , either by multiplying IS ratios before a transition (Precup et al., 2001) or by directly estimating state distributions (Hallak and Mannor, 2017; Liu et al., 2018). In this work, we focus on using resampling to correct the action distribution—the standard setting. We expect, however, that some insights will extend to how to use resampling to correct the state distribution, particularly because wherever IS ratios are used it should be straightforward to use our resampling approach. .
The IR algorithm is simple: resample a mini-batch of size on each step from the buffer of size , proportionally to in the buffer. Standard on-policy updates, such as on-policy TD or on-policy gradient TD, can then used on this resample. The key difference to IS and WIS is that the distribution itself is corrected, before the update, whereas IS and WIS correct the update itself. This small difference, however, can have larger ramifications practically, as we show in this paper.
We consider two variants of IR: with and without bias correction. For point sampled from the buffer, let be the on-policy update for that transition. For example, for TD, . The first step for either variant is to sample a mini-batch of size from the buffer, proportionally to . Bias-Corrected IR (BC-IR) additionally pre-multiplies with the average ratio in the buffer , giving the following estimators for the update direction
XIR \makebox[0.0pt]def=1kk∑j=1ΔijXBC\makebox[0.0pt]def=¯ρkk∑j=1Δij
BC-IR negates bias introduced by the average ratio in the buffer deviating significantly from the true mean. For reasonably large buffers, will be close to 1 making IR and BC-IR have near-identical updates. Nonetheless, they do have different theoretical properties, particularly for small buffer sizes , so we characterize both.
Across all results, we make the following assumption.
###### Assumption 1.
Transition tuples are sampled i.i.d. according to the distribution , for .
To denote expectations under and , we overload the notation from above, using operators and respectively. To reduce clutter, we write to mean , because most expectations are under the sampling distribution. All proofs can be found in Appendix B.
### 3.1 Bias of IR
We first show that IR is biased, and that its bias is actually equal to WIS-Optimal, in Theorem 3.1.
###### Theorem 3.1.
[Bias for a fixed buffer of size ] Assume a buffer of transitions is sampled i.i.d., according to . Let be the WIS-Optimal estimator of the update. Then,
E[XIR]=E[XWIS∗]
and so the bias of is proportional to
Bias(XIR)=E[XIR]−Eπ[Δ]∝1n(Eπ[Δ]σ2ρ−σρ,ΔσρσΔ) (1)
where is the expected update across all transitions, with actions from taken by the target policy ; ; ; and covariance .
This bias of IR will be small for reasonably large , both because it is proportional to and because larger will result in lower variance of the average ratios and average update for the buffer in Equation (1). In particular, as grows, these variances decay proportionally to . Nonetheless, for smaller buffers, such bias could have an impact. We can, however, easily mitigate this bias with a bias-correction term, as shown in the next corollary and proven in Appendix B.2.
###### Corollary 3.1.1.
BC-IR is unbiased: .
### 3.2 Consistency of IR
Consistency of IR in terms of an increasing buffer, with , is a relatively straightforward extension of prior results for SIR, with or without the bias correction, and from the derived bias of both estimators (see Theorem B.1 in Appendix B.3). More interesting, and reflective of practice, is consistency with a fixed length buffer and increasing interactions with the environment, . IR, without bias correction, is asymptotically biased in this case; in fact, its asymptotic bias is the one characterized above for a fixed length buffer in Theorem 3.1. BC-IR, on the other hand, is consistent, even with a sliding window, as we show in the following theorem.
###### Theorem 3.2.
Let be the buffer of the most recent transitions sampled by time , i.i.d. as specified in Assumption 1. Let be the bias-corrected IR estimator, with samples from buffer . Define the sliding-window estimator . Assume there exists a such that . Then, as , converges in probability to .
It might seem that resampling avoids high-variance in updates, because it does not reweight with large magnitude IS ratios. The notion of effective sample size from statistics, however, provides some intuition about why large magnitude IS ratios can also negatively affect IR, not just IS. Effective sample size is between 1 and , with one estimator (Kong et al., 1994; Martino et al., 2017). When the effective sample size is low, this indicates that most of the probability is concentrated on a few samples. For high magnitude ratios, IR will repeatedly sample the same transitions, and potentially never sample some of the transitions with small IS ratios.
Fortunately, we find that, despite this dependence on effective sample size, IR can significantly reduce variance over IS. In this section, we characterize the variance of the BC-IR estimator. We choose this variant of IR, because it is unbiased and so characterizing its variance is a more fair comparison to IS. We define the mini-batch IS estimator , where indices are sampled uniformly from . This contrasts the indices for that are sampled proportionally to .
We begin by characterizing the variance, under a fixed dataset . For convenience, let . We characterize the sum of the variances of each component in the update estimator, which equivalently corresponds to normed deviation of the update from its mean,
V(Δ | B)\makebox[0.0pt]% def=trCov(Δ | B)=∑dm=1Var(Δm | B)=E[∥Δ−μB∥22 | B]
for an unbiased stochastic update . We show two theorems that BC-IR has lower variance than IS, with two different conditions on the norm of the update. We first start with more general conditions, and then provide a theorem for conditions that are likely only true in early learning.
###### Theorem 3.3.
Assume that, for a given buffer , for samples where , and that for samples where , for some . Then the BC-IR estimator has lower variance than the IS estimator: .
The conditions in Theorem 3.3 preclude having update norms for samples with small be quite large—larger than a number —and a small norm for samples with large . These conditions can be relaxed to a statement on average, where the cumulative weighted magnitude of the update norm for samples with below the median needs to be smaller than for samples with above the meanx (see the proof in Appendix B.5).
We next consider a setting where the magnitude of the update is independent of the given state and action. We expect this condition to hold in early learning, where the weights are randomly initialized and so potentially randomly incorrect across the state-action space. As learning progresses, and value estimates become more accurate in some states, it is unlikely for this condition to hold.
###### Theorem 3.4.
Assume and the magnitude of the update are independent
E[ρj∥Δj∥22 | B]=E[ρj | B] E[∥Δj∥22 | B]
Then the BC-IR estimator will have equal or lower variance than the IS estimator.
These results have focused on variance of each estimator, for a fixed buffer, which provided insight into variance of updates when executing the algorithms. We would, however, also like to characterize variability across buffers, especially for smaller buffers. Fortunately, such a characterization is a simple extension on the above results, because variability for a given buffer already demonstrates variability due to different samples. It is easy to check that . The variances can be written using the law of total variance
V(XBC) V(XIS) =E[V(XIS | B)]+V(μB) ⟹V(XBC) −V(XIS)=E[V(XBC | B)−V(XIS | B)]
with expectation across buffers. Therefore, the analysis of directly applies.
## 4 Empirical Results
We investigate the two hypothesized benefits of resampling as compared to reweighting: improved sample efficiency and reduced variance. These benefits are tested in two microworld domains—a Markov chain and the Four Rooms domain—where exhaustive experiments can be conducted. We also provide a demonstration that IR reduces sensitivity over IS and VTrace in a car simulator, TORCs, when learning from images.
We compare IR and BC-IR against several reweighting strategies, including importance sampling (IS); two online approaches to weighted important sampling, WIS-Minibatch with weighting and WIS-Buffer with weighting ; and V-trace444Retrace, ABQ and TreeBackup also use clipping to reduce variance. But, they are designed for learning action-values and for mitigating variance in eligibility traces. When trace parameter —as we assume here—there are no IS ratios and these methods become equivalent to using Sarsa(0) for learning action-values. , which corresponds to clipping importance weights (Espeholt et al., 2018). Where appropriate, we also include baselines using On-policy sampling; WIS-Optimal which uses the whole buffer to get an update; and Sarsa(0) which learns action-values—which does not require IS ratios—and then produces estimate . WIS-Optimal is included as an optimal baseline, rather than as a competitor, as it estimates the update using the whole buffer on every step.
In all the experiments, the data is generated off-policy. We compute the absolute value error (AVE) on every training step. The error bars represent the standard error over runs, which are featured on every plot — although not visible in some instances. For the microworlds, the true value function is found using dynamic programming with threshold , and we compute AVE over all the states. For TORCs and continuous Four Rooms, the true value function is approximated using rollouts from a random subset of states generated when running the behavior policy . A tabular representation is used in the microworld experiments, tilecoded features with 64 tilings and 8 tiles is used in continuous Four Rooms, and a convolutional neural network is used for TORCs, with the same architecture as previously defined for self-driving cars (Bojarski et al., 2016).
### 4.1 Investigating Convergence Rate
We first investigate the convergence rate of IR. We report learning curves in Four Rooms, as well as sensitivity to the learning rate. The Four Rooms domain (Stolle and Precup, 2002) has four rooms in an 11x11 grid world. The four rooms are positioned in a grid pattern with each room having two adjacent rooms. Each adjacent room is separated by a wall with a single connecting hallway. The target policy takes the down action deterministically. The cumulant for the value function is 1 when the agent hits a wall and 0 otherwise. The continuation function is , with termination when the agent hits a wall. The resulting value function can be thought of as distance to the bottom wall. The behavior policy is uniform random everywhere except for 25 randomly selected states which take the action down with probability 0.05 with remaining probability split equally amongst the other actions. The choice of behavior and target policy induce high magnitude IS ratios.
As shown in Figure 1, IR has noticeable improvements over the reweighting strategies tested. The fact that IR resamples more important transitions from the replay buffer seems to significantly increase the learning speed. Further, IR has a wider range of usable learning rates. The same effect is seen even as we reduce the total number of updates, where the uniform sampling methods perform significantly worse as the interactions between updates increases—suggesting improved sample efficiency. WIS-Buffer performs almost equivalently to IS, because for reasonably size buffers, its normalization factor because . WIS-Minibatch and V-trace both reduce the variance significantly, with their bias having only a limited impact on the final performance compared to IS. Even the most aggressive clipping parameter for V-trace—a clipping of 1.0— outperforms IS. The bias may have limited impact because the target policy is deterministic, and so only updates for exactly one action in a state. Sarsa—which is the same as Retrace(0)—performs similarly to the reweighting strategies.
The above results highlight the convergence rate improvements from IR, in terms of number of updates, without generalization across values. Conclusions might actually be different with function approximation, when updates for one state can be informative for others. For example, even if in one state the target policy differs significantly from the behavior policy, if they are similar in a related state, generalization could overcome effective sample size issues. We therefore further investigate if the above phenomena arise under function approximation with RMSProp learning rate selection.
We conduct a similar experiment above, in a continuous state Four Rooms variant. The agent is a circle with radius 0.1, and the state consists of a continuous tuple containing the x and y coordinates of the agent’s center point. The agent takes an action in one of the 4 cardinal directions moving in that directions with random drift in the orthogonal direction sampled from . The target policy, as before, deterministically takes the down action. The representation is a tile coded feature vector with 64 tilings and 8 tiles.
We find that generalization can mitigate some of the differences between IR and IS above in some settings, but in others the difference remains just as stark. If we use the behavior policy from the tabular domain, which skews the behavior in a sparse set of states, the nearby states mitigate this skew. However, if we use a behavior policy that selects all actions uniformly, then again IR obtains noticeable gains over IS and V-trace, for reducing the required number of updates, as shown in in Figure 2. Expanded results can be found in Appendix C.2.
### 4.2 Investigating Variance
To better investigate the update variance we use a Markov chain, where we can more easily control dissimilarity between and , and so control the magnitude of the IS ratios. The Markov chain is composed of 8 non-terminating states and 2 terminating states on the ends of the chain, with a cumulant of 1 on the transition to the right-most terminal state and 0 everywhere else. We consider policies with probabilities [left, right] equal in all states: ; further policy settings can be found in Appendix C.1.
We first measure the variance of the updates for fixed buffers. We compute the variance of the update—from a given weight vector—by simulating the many possible updates that could have occurred. We are interested in the variance of updates both for early learning—when the weight vector is quite incorrect and updates are larger—and later learning. To obtain a sequence of such weight vectors, we use the sequence of weights generated by WIS-Optimal. As shown in Figure 5, the variance of IR is lower than IS, particularly in early learning, where the difference is stark. Once the weight vector has largely converged, the variance of IR and IS is comparable and near zero.
We can also evaluate the variance by proxy using learning rate sensitivity curves. As seen in Figure 5 (a) and (b), IR has the lowest sensitivity to learning rates, on-par with On-Policy sampling. IS has the highest sensitivity, along with WIS-Buffer and WIS-Minibatch. Various clipping parameters with V-trace are also tested. V-trace does provide some level of variance reduction but incurs more bias as the clipping becomes more aggressive.
### 4.3 Demonstration on a Car Simulator
We use the TORCs racing car simulator to perform scaling experiments with neural networks to compare IR, IS, and V-trace. The simulator produces 64x128 cropped grayscale images. We use an underlying deterministic steering controller that produces steering actions and take an action with probability defined by a Gaussian . The target policy is a Gaussian , which corresponds to steering left. Pseudo-termination (i.e., ) occurs when the car nears the center of the road, and the cumulant becomes 1. Otherwise, the cumulant is zero and . The policy is specified using continuous action distributions and results in IS ratios as high as and highly variant updates for IS.
Again, we can see that IR provides benefits over IS and V-trace, in Figure 4. There is even more generalization from the neural network in this domain, than in Four Rooms where we found generalization did reduce some of the differences between IR and IS. Yet, IR still obtains the best performance, and avoids some of the variance seen in IS for two of the learning rates. Additionally, BC-IR actually performs differently here, having worse performance for the largest learning rate. This suggest IR has an effect in reducing variance.
## 5 Conclusion
In this paper we introduced a new approach to off-policy learning: Importance Resampling. We showed that IR is consistent, and that the bias is the same as for Weighted Importance Sampling. We also provided an unbiased variant of IR, called Bias-Corrected IR. We empirically showed that IR (a) has lower learning rate sensitivity than IS and V-trace, which is IS with varying clipping thresholds; (b) the variance of updates for IR are much lower in early learning than IS and (c) IR converges faster than IS and other competitors, in terms of the number of updates. These results confirm the theory presented for IR, which states that variance of updates for IR are lower than IS in two settings, one being an early learning setting. Such lower variance also explains why IR can converge faster in terms of number of updates, for a given buffer of data.
The algorithm and results in this paper suggest new directions for off-policy prediction, particularly for faster convergence. Resampling is promising for scaling to learning many value functions in parallel, because many fewer updates can be made for each value function. A natural next step is a demonstration of IR, in such a parallel prediction system. Resampling from a buffer also opens up questions about how to further focus updates. One such option is using an intermediate sampling policy. Another option is including prioritization based on error, such as was done for control with prioritized sweeping (Peng and Williams, 1993) and prioritized replay (Schaul et al., 2015b).
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## Appendix A Weighted Importance Sampling
We consider three weighted importance sampling updates as competitors to IR. is the size of the experience replay buffer, is the size of a single batch. WIS-Minibatch and WIS-Buffer both follow a similar protocol as IS, in that they uniformly sample a mini-batch from the experience replay buffer and use this to update the value functions. The difference comes in the scaling of the update. The first, WIS-Minibatch, uses the sum of the importance weights in the sampled mini-batch, while WIS-Buffer uses the sum of importance weights in the experience replay buffer. WIS-Buffer is also scaled by the size of the buffer and brought to the same effective scale as the other updates with . WIS-Optimal follows a different approach and performs the best possible version of WIS where the gradient descent update is calculated from the whole experience replay buffer. We do not provide analysis on the bias or consistency of WIS-Minibatch or WIS-Buffer, but are natural versions of WIS one might try.
Δθ =∑kiρiδi∇θV(si;θ)∑kjρj WIS-Minibatch Δθ =nk∑kiρiδi∇θV(si;θ)∑njρj WIS-Buffer Δθ =∑niρiδi∇θV(si;θ)∑njρj WIS-Optimal
## Appendix B Additional Theoretical Results and Proofs
### b.1 Bias of IR
Theorem 3.1(Bias for a fixed buffer of size ) Assume a buffer of transitions is sampled i.i.d., according to . Let be the WIS-Optimal estimator of the update. Then,
E[XIR]=E[XWIS∗]
and so the bias of is proportional to
Bias(XIR)=E[XIR]−Eπ[Δ]∝1n(Eπ[Δ]σ2ρ−σρ,ΔσρσΔ)
where is the expected update across all transitions, with actions from taken by the target policy ; ; ; and covariance .
###### Proof.
Notice first that when we weight with , this is equivalent to weighting with , and so is the correct IS ratio for the transition.
E[ XIR]=E[E[XIR|B]]=E[E[1kk∑j=1Δij|B]] =E[1kk∑j=1E[Δij|B]] ▹E[Δij|B]=n∑i=1ρi∑nj=1ρjΔi =E[n∑i=1ρi∑nj=1ρjΔi] =E[XWIS∗].
This bias of is the same as , which is characterized in Owen [2013], completing the proof. ∎
### b.2 Proof of Unbiasedness of BC-IR
Corollary 3.1.1 BC-IR is unbiased: .
###### Proof.
E[XBC] =E[¯ρkk∑j=1E[Δij|B]]=E[¯ρn∑i=1ρi∑nj=1ρjΔi] =E[1nn∑i=1ρiΔi]=1nn∑i=1E[π(Ai|Si)μ(Ai|Si)Δi] =1nn∑i=1E[dμ(Si)π(Ai|Si)P(Si+1|Si,Ai)dμ(Si)μ(Ai|Si)P(Si+1|Si,Ai)Δi]
### b.3 Consistency of the resampling distribution with a growing buffer
We show that the distribution when following a resampling strategy is consistent: as , the resampling distribution converges to the true distribution. Our approach closely follows that of [Smith et al., 1992], but we recreate it here for convenience.
###### Theorem B.1.
Let be a buffer of data sampled i.i.d. according to proposal density . Let be some distribution of interest with associated random variable and assume the proposal distribution samples everywhere where is non-zero, i.e . Also, let be a discrete random variable taking values with probability . Then, converges in distribution to as .
###### Proof.
Let . From the probability mass function of , we have that:
P[Y≤a] =n∑i=1P[Y=xi]\mathbbm1{xi≤a} =n−1∑ni=1ρi\mathbbm1{xi≤a}n−1∑ni=1ρi n→∞−−−→Eq[ρ(x)\mathbbm1{x≤a}]Eq[ρ(x)] =1⋅∫a−∞q(x)p(x)p(x)dx+0⋅∫∞aq(x)p(x)p(x)dx∫∞−∞q(x)p(x)p(x)dx =∫a−∞q(x)dx=P[Q≤a] Y d→Q
This means a resampling strategy effectively changes the distribution of random variable to that of , meaning we can use samples from to build statistics about the target distribution . This result motivates using resampling to correct the action distribution in off-policy learning. This result can also be used to show that the IR estimators are consistent, with .
### b.4 Consistency under a sliding window
Theorem 3.2 Let be the buffer of the most recent transitions sampled by time , i.i.d. as specified in Assumption 1. Let be the bias-corrected IR estimator, with samples from buffer . Define the sliding-window estimator . Assume there exists a such that . Then, as , converges in probability to .
###### Proof.
Notice first that is random because is random and because transitions are sampled from . Therefore, given , is independent of other random variables and for .
Now, using Corollary 3.1.1, we can show that BC-IR is unbiased for a sliding window
E[Xt] =E[1tt∑i=1X(i)BC]=1tt∑i=1E[E[X(i)BC|Bi]]=Eπ[Δ].
Next, we show that . For , and are independent, because they are disjoint sets of i.i.d. random variables. Correspondingly, is independent of . Explicitly, using the law of total covariance, we get that The first term is zero because is independent of given , and the second term is zero because and are independent. Therefore, .
Using the assumption on the variance, we can apply Lemma B.2 to to get the desired result. ∎
###### Lemma B.2.
Let be random variables with mean . Suppose there exists a such that and that . Then, as , converges in probability to .
###### Proof.
Let .
V(SN)=N∑i=1V(Zi)+2N∑i=1N∑j=i+1Cov(Zi,Zj)
The first term is bounded by from our assumption on the variance. Now, to bound the second term.
Fix and choose such that , (such an must exist since ). Assuming that , we can decompose the second term into
N∑i=1N∑j=i+1Cov(Zi,Zj) =N∑i=1i+M∑j=i+1Cov(Zi,Zj)+ N∑i=1N∑j=i+M+1Cov(Zi,Zj) ∣∣ ∣∣N∑i=1N∑j=i+1Cov(Zi,Zj)∣∣ ∣∣ ≤N∑i=1i+M∑j=i+1|Cov(Zi,Zj)|+ N∑i=1N∑j=i+M+1|Cov(Zi,Zj)|
By the Cauchy-Schwarz inequality and our variance assumption, . So, we get
∣∣ ∣∣N∑i=1N∑j=i+1Cov(Zi,Zj)∣∣ ∣∣ ≤N∑i=1i+M∑j=i+1c+N∑i=1N∑j=i+M+1δ ≤NMc+N2δ
Altogether, our upper bound is
V(SNN)≤cN+McN+δ
Finally, we apply Chebyshev’s inequality. For a fixed ,
P(∣∣∣SNN−μ∣∣∣>ϵ) ≤1ϵ2V(SNN) ≤1ϵ2(cN+McN+δ)
Since we can choose to be arbitrarily small (say ), the right-hand side goes to as , concluding the proof. ∎
### b.5 Variance of BC-IR and IS
This lemma characterizes the variance of the BC-IR and IS estimators for a fixed buffer.
###### Lemma B.3.
V(XIS | B) V(XBC | B)
###### Proof.
Because we have independent samples,
V(XBC | B)=1k2k∑j=1V(¯ρΔij | B)=1kV(¯ρΔi1 | B)
and similarly We can further simplify these expressions. For the IS estimator
V(ρz1Δz1|B) =E[ρ2z1Δ⊤z1Δz1|B]−E[ρz1Δz1|B]⊤E[ρz1Δz1|B] =1nn∑j=1ρ2j∥Δj∥22−μ⊤BμB
and for the BC-IR estimator, where recall ,
V(¯ρΔi1|B)=E[¯ρ2Δ⊤i1Δi1|B]−E[¯ρΔi1|B]⊤E[¯ρΔi1|B] =n∑j=1¯ρ2ρj∑ni=1ρi∥Δj∥22−μ⊤BμB =¯ρnn∑j=1ρj∥Δj∥22−μ⊤BμB
The following two theorems present certain conditions when the BC-IR estimator would have lower variance than the IS estimator.
Theorem 3.3 Assume that for samples where , and that for samples where , for some . Then the BC-IR estimator has lower variance than the IS estimator.
###### Proof.
We show :
V(XIS|B)−V(XBC|B)=1nkn∑j=1∥∥Δj∥∥22(ρ2j−¯ρρj) =1nk∑s:ρs<¯ρ∥Δs∥22≤c/ρsρs(ρs−¯ρ)≤0+1nk∑l:ρl≥¯ρ∥Δl∥22>c/ρsρl(ρl−¯ρ)≥0 >1nk∑s:ρs<¯ρcρsρs(ρs−¯ρ)+1nk∑l:ρl≥¯ρcρlρl(ρl−¯ρ) =cnkn∑j=1(ρj−¯ρ)=0
Theorem 3.4 Assume and the magnitude of the update | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.89418625831604, "perplexity": 2239.8727286645794}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251799918.97/warc/CC-MAIN-20200129133601-20200129163601-00013.warc.gz"} |
http://link.springer.com/article/10.1134/S1063772911100039 | , Volume 55, Issue 10, pp 867-877
Date: 29 Sep 2011
# Estimating the rate and luminosity function of all classes of GRBs
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## Abstract
The aim of the present work is to estimate the rate and luminosity functions of short, intermediate and long gamma-ray bursts (GRBs) by fitting their intensity distributions with parameterized explosion rates and luminosity functions. The results show that the parameters of the rate and luminosity function for long GRBs can be calculated with an accuracy of 10–30%. However, some parameters of intermediate and short GRBs have large uncertainties. An important conclusion is that there was initially a large outburst in the frequency of long GRBs, and consequently a large outburst in the star-formation rate, if they come from collapsars. Finally, a simulated intensity distribution has been constructed to test the ability of the method to recover the simulated parameters. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8786410689353943, "perplexity": 1293.5743680808134}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988650.6/warc/CC-MAIN-20150728002308-00269-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://www.intechopen.com/chapters/61684 | Open access peer-reviewed chapter
# Separability and Nonseparability of Elastic States in Arrays of One-Dimensional Elastic Waveguides
Written By
Pierre Alix Deymier, Jerome Olivier Vasseur, Keith Runge and Pierre Lucas
Submitted: February 20th, 2018 Reviewed: April 13th, 2018 Published: November 5th, 2018
DOI: 10.5772/intechopen.77237
From the Edited Volume
## Phonons in Low Dimensional Structures
Edited by Vasilios N. Stavrou
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## Abstract
We show that the directional projection of longitudinal waves propagating in a parallel array of N elastically coupled waveguides can be described by a nonlinear Dirac-like equation in a 2N dimensional exponential space. This space spans the tensor product Hilbert space of the two-dimensional subspaces of N uncoupled waveguides grounded elastically to a rigid substrate (called φ -bits). The superposition of directional states of a φ -bit is analogous to that of a quantum spin. We can construct tensor product states of the elastically coupled system that are nonseparable on the basis of tensor product states of N φ -bits. We propose a system of coupled waveguides in a ring configuration that supports these nonseparable states.
### Keywords
• one-dimensional elastic waveguides
• nonseparability
• elastic waves
• elastic pseudospin
• coupled waveguides
## 1. Introduction
Quantum bit-based computing platforms can capitalize on exponentially complex entangled states which allow a quantum computer to simultaneously process calculations well beyond what is achievable with serially interconnected transistor-based processors. Ironically, a pair of classical transistors can emulate some of the functions of a qubit. While current manufacturing can fabricate billions of transistors on a chip, it is inconceivable to connect them in the exponentially complex way that would be required to achieve nonseparable quantum superposition analogues. In contrast, quantum systems possess such complexity through the nature of the quantum world. Outside the quantum world, the notion of classical nonseparability [1, 2, 3] has been receiving a lot of attention from the theoretical and experimental point of views in the field of optics. Degrees of freedom of photon states that span different Hilbert spaces can be made to interact in a way that leads to local correlations. Correlation has been achieved between degrees of freedom that include spin angular momentum and orbital angular momentum (OAM) [4, 5, 6, 7, 8, 9], OAM, polarization and radial degrees of freedom of a beam of light [10] as well as propagation direction [11, 12]. Recently, we have extended this notion to correlation between directional and OAM degrees of freedom in elastic systems composed of arrays of elastic waveguides [13]. This classical nonseparability lies only in the tensor product Hilbert space of the subspaces associated with these degrees of freedom. This Hilbert space does not possess the exponential complexity of a multiqubit Hilbert space, for instance. It has been suggested theoretically and experimentally that classical systems coupled via nonlinear interactions may have computational capabilities approaching that of quantum computers [14, 15, 16].
We demonstrated in Ref. [17] that nonlinear elastic media can be used to produce phonons that can be correlated simultaneously in time and frequency. We have also shown an analogy between the propagation of elastic waves on elastically coupled one-dimensional (1D) wave guides and quantum phenomena [18, 19, 20, 21]. More specifically, the projection on the direction of propagation of elastic waves in an elastic system composed of a 1D waveguide grounded to a rigid substrate (denoted φ -bit) is isomorphic to the spin of a quantum particle. The pseudospin states of elastic waves in these systems can be described via a Dirac-like equation and possess 2 × 1 spinor amplitudes. Unlike the quantum systems, these amplitudes are, however, measurable through the measurement of transmission coefficients. The notion of measurement is an important one as it has been realized that separability is relative to the choice of the partitioning of a multipartite system. Indeed, it is known that given a multipartite physical system, whether quantum or classical, the way to subdivide it into subsystems is not unique [22, 23]. For instance, the states of a quantum system may not appear entangled relative to some decomposition but may appear entangled relative to another partitioning. The criterion for that choice may be the ability to perform observations and measurements of some degrees of freedom of the subsystems [23].
The objective of this paper is to investigate the notion of separability and nonseparability of multipartite classical mechanical systems supporting elastic waves. These systems are composed of 1D elastic waveguides that are elastically coupled along their length to each other and/or to some rigid substrate. The 1D waveguides support spinor-like amplitudes in the two-dimensional (2D) subspace of directional degrees of freedom. The amplitudes of N coupled waveguides span an N -dimensional subspace. Subsequently, the Hilbert space spanned by the elastic modes is a 2 N -dimensional space, comprised of the tensor product of the directional and waveguides subspaces. This representation is isomorphic to the degrees of freedom of photon states in a beam of light. While beams of light cannot be decomposed into subsystems, an elastic system composed of coupled 1D waveguides can. Indeed, the elastic system considered here forms a multipartite system composed of N 1D waveguide subsystems. We show that, since each waveguide possesses two directional degrees of freedom, one can represent the elastic states of the N -waveguide system in the 2 N dimensional tensor product Hilbert space of N 2D spinor subspaces associated with individual waveguides. The elastic modes in this representation obey a 2 N dimensional nonlinear Dirac-like equation. These modes span the same space as that of uncoupled waveguides grounded to a rigid substrate, i.e., N φ -bits. However, the modes’ solutions of the nonlinear Dirac equation cannot be expressed as tensor products of the states of N uncoupled grounded waveguides, i.e., φ -bit states.
In Section 2 of this chapter, we introduce the mathematical formalism that is needed to demonstrate the nonseparability of elastic states of coupled elastic waveguides in an exponentially complex space. Throughout this section, we use illustrations of the concepts in the case of systems composed of small numbers of waveguides. However, the approach is fully scalable and can be generalized to any large number of coupled waveguides. In Section 3, we draw conclusions concerning the applicability of this approach to solve complex problems.
## 2. Models and methods
We have previously considered systems constituted of N one-dimensional (1D) waveguides coupled elastically along their length [13]. In this section, we summarize the results of these previous investigations to develop a formalism to address our current considerations. The parallelly coupled waveguides can be arranged in any desired way. The propagation of elastic modes is limited to longitudinal modes along the waveguides in the long wavelength limit, i.e., the continuum limit. We consider the representations of the modes of the coupled waveguide systems in two spaces. The first space scales linearly with N. The second space scales as 2 N and leads to a description of the elastic system with exponential complexity. The linear representation enables us to operate easily on the states in the exponential space.
### 2.1. Representation of elastic states in a space scaling linearly with N
A compact form for the equations of motion of the N coupled waveguides is:
H . I N × N + α 2 M N × N u N × 1 = 0 E1
Here, the propagation of elastic waves in the direction x along the waveguides is modeled by the dynamical differential operator, H = 2 t 2 β 2 2 x 2 . The parameter β is proportional to the speed of sound in the medium constituting the waveguides and the parameter α 2 characterizes the strength of the elastic coupling between them (here, we consider that the strength is the same for all coupled waveguides). u N × 1 is a vector with components, u i , i = 1 N , representing the displacement of the ith waveguide. The coupling matrix operator M N × N describes the elastic coupling between waveguides which, in the case of N = 3 parallel waveguides in a closed ring arrangement with first neighbor coupling, takes the form:
M N = 3 × N = 3 = 2 1 1 1 2 1 1 1 2 E2
Eq. (1) takes the form of a generalized Klein-Gordon (KG) equation and its Dirac factorization introduces the notion of the square root of the operator H . I N × N + α 2 M N × N . In this factorization, the dynamics of the system are represented in terms of first derivatives with respect to time, t , and position along the waveguides, x . There are two possible Dirac equations:
U N × N σ x t + β U N × N i σ y x ± U 2 N × 2 N M N × N σ x Ψ 2 N × 1 = 0 E3
In Eq. (3), U N × N and U 2 N × 2 N are antidiagonal matrices with unit elements. σ x = 0 1 1 0 and σ y = 0 i i 0 are two of the Pauli matrices. Ψ 2 N × 1 is a 2 N dimensional vector which represents the modes of vibration of the N waveguides projected in the two possible directions of propagation (forward and backward) and M N × N is the square root of the coupling matrix. The square root of a matrix is not unique but we will show later that we can pick any form without loss of generality.
We choose components of the Ψ 2 N × 1 vector in the form of plane waves ψ I = a I e ikx e iωt with I = 1 , , 2 N and k and ω being the wave number and angular frequency, respectively, Eq. (3) becomes:
ωA 2 N × 2 N + βk B 2 N × 2 N ± α C 2 N × 2 N a 2 N × 1 = 0 E4
where
A 2 N × 2 N = I N × N I 2 × 2 E5a
B 2 N × 2 N = I N × N σ z E5b
C 2 N × 2 N = M N × N σ x E5c
In Eqs. (4) and (5), σ z = 1 0 0 1 is the third Pauli matrix, I N × N is the identity matrix of order N and a2Nx1 is a 2 N dimensional vector whose components are the amplitudes aI. In obtaining Eq. (4), we have multiplied all terms in Eq. (3) on the left by U 2 N × 2 N .
Writing Eq. (4) as a linear combination of tensor products of N × N and 2 × 2 matrix operators:
I N × N ωI 2 × 2 βk σ z ± α M N × N σ x a 2 N × 1 = 0 E6
we seek solutions in the form of tensor products:
a 2 N × 1 = E N × 1 s 2 × 1 .E7
While the degrees of freedom associated with E N × 1 span an N dimensional Hilbert subspace, the degrees of freedom associated with s 2 × 1 span a 2D space.
Replacing a 2 N × 1 from Eq. (7) in Eq. (6) yields:
I N × N E N × 1 ωI 2 × 2 βk σ z s 2 × 1 ± α M N × N E N × 1 σ x s 2 × 1 = 0 . E8
Choosing E N × 1 to be an eigenvector, e n , of the matrix M N × N with eigen value λ n Eq. (8) reduces to:
e n ωI 2 × 2 βk σ z ± α λ n σ x s 2 × 1 = 0 E9
For nontrivial eigenvectors e n , the problem in the space of the directions of propagation reduces to finding solutions of
ωI 2 × 2 βk σ z ± α λ n σ x s 2 × 1 = 0 E10
In obtaining Eq. (9), we have also used the fact that e n is an eigen vector of I N × N with eigen value 1 and we note that Eq. (9) is the 1D Dirac equation for an elastic system which solutions, s 2 × 1 , have the properties of Dirac spinors [18, 19, 20, 21]. The components of the spinor represent the amplitude of the elastic waves in the positive and negative directions along the waveguides, respectively.
Eq. (10), now written in the matrix form, can now be solved for a given λ n ;
ω n βk ± α λ n ± α λ n ω n + βk s 1 s 2 = 0 E11
This eigen equation gives the dispersion relation ω n 2 = βk 2 + α λ n 2 (vide infra) and the following eigen vectors projected into the space of directions of propagation:
s 2 × 1 = s 0 ω n + βk ± ω n βk E12
To determine the eigen vectors of M N × N , we note that they are identical to the eigen vectors of the coupling matrix M N × N and the eigen values of M N × N are also λ n 2 . These properties indicate that we do not have to determine the square root of the coupling matrix to find the solutions a 2 N × 1 . All that is required is to calculate the eigen vectors and the eigen values of the coupling matrix. Hence, the nonuniqueness of M N × N does not introduce difficulties in determining the elastic modes of the coupled system in the Dirac representation.
In the case of the coupling matrix, M 3 × 3 , presented in Eq. (2), the eigen values and real eigen vectors are obtained as λ 0 2 = 0 , λ 1 2 = λ 2 2 = 3 , and
e 0 = 1 3 1 1 1 , e 1 = 2 3 1 1 2 1 2 and e 2 = 2 3 1 2 1 1 2 E13
Eq. (3) being linear, its solutions can be written as linear combinations of elastic wave functions in the form:
Ψ 2 N × 1 n k = e n N s 2 × 1 k e ikx e i ω n k t E14
In Eq. (14), we have expressed the dependencies on the wave number k and the number of waveguides N. The eigen vectors e n N depend on the connectivity of the N waveguides. The space spanned by these solutions scales linearly with the number of waveguides, i.e., as 2N.
### 2.2. Representation of elastic states in a space scaling as 2 N
We first illustrate the notion of exponential space in the case of three waveguides. Each guide is connected to a rigid substrate and therefore constitutes a φ -bit. The waveguides are not coupled to each other. The dynamics of the system can be described by a single equation which is constructed as follows:
σ x σ x σ x t + σ y σ x σ x x 1 + σ x σ y σ x x 2 + σ x σ x σ y x 3 ± I 2 × 2 σ x σ x ± σ x I 2 × 2 σ x ± σ x σ x I 2 × 2 Ψ 8 × 1 = 0 E15
In Eq. (15), we are now defining a positional variable for each waveguide, namely, x 1 , x 2 , x 3 . The quantity α is a measure of the strength of the elastic coupling to the rigid substrate. The solutions are the 8 × 1 vectors Ψ 8 × 1 = Ψ 1 Ψ 2 Ψ 3 Ψ 4 Ψ 5 Ψ 6 Ψ 7 Ψ 8 . When seeking solutions in the form of tensor products of spinor solutions for the three waveguides (as indicated by the upper scripts)
Ψ 8 × 1 = ψ 1 ψ 2 ψ 3 = ψ 1 1 ψ 2 1 ψ 1 2 ψ 2 2 ψ 1 3 ψ 2 3 = ψ 1 1 ψ 1 2 ψ 1 3 ψ 1 1 ψ 1 2 ψ 2 3 ψ 1 1 ψ 2 2 ψ 1 3 ψ 1 1 ψ 2 2 ψ 2 3 ψ 2 1 ψ 1 2 ψ 1 3 ψ 2 1 ψ 1 2 ψ 2 3 ψ 2 1 ψ 2 2 ψ 1 3 ψ 2 1 ψ 2 2 ψ 2 3 E16
it is straightforward to show that one recovers from Eq. (15), the six Dirac equations of Eq. (3) with M N = 3 × N = 3 = I 3 × 3 . The solutions of Eq. (16) are obtained from the spinor solution for individual waveguides (j):
ψ j = s 0 ω + βk ± ω βk e ikx e iωt E17
The Hilbert space spanned by the solutions of Eq. (15) is the product space of the three 2D subspaces associated with each waveguide. The states of a system composed of N φ -bits span a space when dimension is 2 N .
The question that arises then concerns the possibility of writing an equation in the exponential Hilbert space for N waveguides coupled to each other. For instance, we wish to obtain the states of the system composed of three waveguides coupled in a ring arrangement from an equation of the form:
σ x σ x σ x t + σ y σ x σ x x 1 + σ x σ y σ x x 2 + σ x σ x σ y x 3 ± ε 8 × 8 Ψ 8 × 1 = 0 E18
The matrix αε 8 × 8 represents the coupling between the waveguides in the 2 N = 3 space. We are still seeking solutions in the form of tensor products (Eq. (16)). After a lengthy algebraic manipulation, we find that we can reproduce Eq. (3) with the coupling matrix of Eq. (2) if one chooses ε ij = 0 excepting
ε 14 = ε 41 = ε 23 = ε 31 = 2 ψ 1 1 ψ 1 2 ψ 1 3 ψ 1 1 ; ε 16 = ε 61 = ε 25 = ε 52 = 2 ψ 1 2 ψ 1 1 ψ 1 3 ψ 1 2 ; ε 17 = ε 71 = ε 35 = ε 53 = 2 ψ 1 3 ψ 1 1 ψ 1 2 ψ 1 3 ; ε 28 = ε 82 = ε 46 = ε 64 = 2 ψ 2 3 ψ 2 1 ψ 2 2 ψ 2 3 ; ε 38 = ε 83 = ε 47 = ε 74 = 2 ψ 2 2 ψ 2 1 ψ 2 3 ψ 2 2 ; ε 58 = ε 85 = ε 67 = ε 76 = 2 ψ 2 1 ψ 2 2 ψ 2 3 ψ 2 1 E19
The Dirac equation of the three coupled waveguides in the exponential space is therefore nonlinear. Generalization to N coupled chains will result in the following nonlinear equation:
σ x N t + σ y σ x N 1 x 1 + σ x σ y σ x N 2 x 2 + + σ x N 1 σ y x N ± i αε 2 N × 2 N Ψ 2 N × 1 = 0 E20
where nonzero components of ε 2 N × 2 N depend on the ψ i j , i = 1 , 2 ; j = 1 , N that appear in the solution Ψ 2 N × 1 = ψ 1 ψ 2 ψ N . The solutions of the nonlinear Dirac equation for the coupled waveguides span the same space as that of the system of φ -bits, i.e., uncoupled waveguides connected to rigid substrates. The next subsection addresses the question of separability of the coupled waveguide system into a system of uncoupled φ -bits.
### 2.3. Elastic states in the exponential space
For a system of waveguides that are not coupled, the elastic states, solutions of linear equations of the form of Eq. (15), are tensor products but also linear combinations of tensor products of spinor solution for individual waveguides (see Eq. (17)). It is therefore possible to construct nonseparable states in the exponential space for systems of uncoupled waveguides. For example, if we consider a system of two uncoupled waveguides, a possible state of the system in the 2 2 space can be constructed in the form of the following linear combination of tensor products:
Ψ 4 × 1 = s 0 2 ω + βk ± ω βk ω + βk ± ω βk e i 2 kx e i 2 ωt s 0 2 ω βk ± ω + βk ω βk ± ω + βk e i 2 kx e i 2 ωt E21
Choosing s 0 = s 0 and writing Eq. (21) at the location x = 0 , one gets:
Ψ 4 × 1 x = 0 = ω + βk ω + βk ± ω + βk ω βk ± ω βk ω + βk ω βk ω βk ω βk ω βk ± ω βk ω + βk ± ω + βk ω βk ω + βk ω + βk e i 2 ωt E22
The bracket takes the form:
ω + βk ω + βk ω βk ω βk 1 0 0 1 E23
The vector 1 0 0 1 is not separable into a tensor product of two 2 × 1 vectors. Considering on the basis 0 = 1 0 and 1 = 0 1 , one can write the state given in Eq. (22) in the form of the nonseparable Bell state:
Ψ 4 × 1 x = 0 = ω + βk ω + βk ω βk ω βk 0 0 1 1 e i 2 ωt E24
Since the waveguides are not coupled, it is, however, not possible to manipulate the state of one of the waveguides by manipulating the state of the other one. Simultaneous manipulation of the state of waveguides in the exponential space requires coupling. We now address elastic states in the coupled waveguides system.
For a system of N coupled waveguides, we construct a solution of Eq. (3) that takes the form of a linear combination of solutions given in Eq. (14):
Ψ 2 N × 1 n n k k = χ n e n N s 2 × 1 k e ikx e i ω n k t + χ n e n N s 2 × 1 k e ik x e i ω n k t E25
The n and n correspond to two different nonzero eigen values, λ n and λ n , i.e., they correspond to two different dispersion relations ω n k and ω n k . We also choose the wave number k such that ω n k = ω n k = ω 0 . These modes are illustrated in Figure 1 in the case of an N = 9 waveguide system. χ n and χ n are the coefficients of the linear combination.
With e n N = A 1 A 2 A N and e n N = A 1 A 2 A N where the specific values of the components A I and A I are determined by the connectivity and coupling of the waveguides, the state of Eq. (25) can be rewritten as:
Ψ 2 N × 1 n n k k = χ n A 1 ω 0 + βk e ikx + χ n A 1 ω 0 + βk e ik x χ n A 1 ω 0 βk e ikx + χ n A 1 ω 0 βk e ik x χ n A N ω 0 + βk e ikx + χ n A N ω 0 + βk e ik x χ n A N ω 0 βk e ikx + χ n A N ω 0 βk e ik x e i ω 0 t = φ 1 1 φ 2 1 φ 1 N φ 2 N E26
Here, we have chosen, for the sake of simplicity, the + of the ± in the s 2 × 1 terms.
The first two terms in Eq. (26) form a 2 × 1 spinor, φ 1 = φ 1 1 φ 2 1 , which corresponds to the first waveguide, the next two terms form a spinor φ 2 for the second waveguide, etc. We can then construct a solution of the nonlinear Dirac Eq. (20) in the exponential space as the tensor product:
Φ 2 N × 1 = φ 1 φ 2 φ N E27
Since Eq. (20) is nonlinear, linear combinations of tensor product solutions of the form above are not solutions. Solutions of the nonlinear Dirac equation always take the form of a tensor product when the spinor wave functions φ j are expressed on the basis of 2 × 1 vectors. 0 = 1 0 and 1 = 0 1 . If one desires to express Φ 2 N × 1 as a nonseparable state, one has to define a new basis in which this wave function cannot be expressed as a tensor product. This is done in Section 2.5. However, prior to demonstrating this, we illustrate in the next subsection how one can manipulate states of the form Φ 2 N × 1 in the exponential space.
### 2.4. Operating on exponentially-complex tensor product elastic states
In this subsection, we expand tensor product states of the form given in Eq. (27) in linear combinations of tensor products of pure states in the exponential space. We illustrate this expansion in the case of three parallel waveguides elastically coupled to each other. Each waveguide is also coupled elastically to a rigid substrate. We treat the case where the strength of all the couplings is the same. In that case, the coupling matrix is:
M N = 3 × N = 3 = 3 1 1 1 3 1 1 1 3
This matrix has three nonzero eigen values λ 0 2 = 1 , and λ 1 2 = λ 2 2 = 4 corresponding to two dispersion relations ω n 2 = βk 2 + α λ n 2 with cutoff frequencies. The second band is doubly degenerate. The eigen vectors are also given in Eq. (13). We now consider an elastic mode in the linear space that is a linear combination of these eigen modes (see Eq. (26)):
Ψ 6 × 1 n n k k = φ 1 1 φ 2 1 φ 1 2 φ 2 2 φ 1 3 φ 2 3 = χ n A 1 ω 0 + βk e ikx + χ n A 1 ω 0 + βk e ik x χ n A 1 ω 0 βk e ikx + χ n A 1 ω 0 βk e ik x χ n A 2 ω 0 + βk e ikx + χ n A 2 ω 0 + βk e ik x χ n A 2 ω 0 βk e ikx + χ n A 2 ω 0 βk e ik x χ n A 3 ω 0 + βk e ikx + χ n A 3 ω 0 + βk e ik x χ n A 3 ω 0 βk e ikx + χ n A 3 ω 0 βk e ik x e i ω 0 t E28
In Eq. (28), the A I ’s can be the components of the eigen vector e 0 and the A I ’s can be linear combinations of the components of the eigen vectors e 1 and e 2 . We can calculate the tensor product of the spinor components in the form of Eq. (27)
Φ 2 3 × 1 = φ 1 φ 2 φ 3 E29
Eq. (29) can be rewritten after some algebraic manipulations in the form of the linear combination:
Φ 2 3 × 1 = { ζ 1 ξ 1 ζ 2 ξ 2 ζ 3 ξ 3 + ζ 1 ξ 1 ζ 2 ξ 2 ζ 3 ξ 3 + ζ 1 ξ 1 ζ 2 ξ 2 ζ 3 ξ 3 + ζ 1 ξ 1 ζ 2 ξ 2 ζ 3 ξ 3 + ζ 1 ξ 1 ζ 2 ξ 2 ζ 3 ξ 3 + ζ 1 ξ 1 ζ 2 ξ 2 ζ 3 ξ 3 + ζ 1 ξ 1 ζ 2 ξ 2 ζ 3 ξ 3 + ζ 1 ξ 1 ζ 2 ξ 2 ζ 3 ξ 3 } e i 3 ω 0 t E30
In Eq. (30), we have defined
ζ I ξ I = χ n A I e ikx ω 0 + βk ω 0 βk = χ n A I e ikx s 2 × 1 E31a
ζ I ξ I = χ n A 1 e i k x ω 0 + βk ω 0 βk = χ n A 1 e i k x s 2 × 1 E31b
The tensor product of Eq. (30) then reduces to
Φ 2 3 × 1 = { χ n 3 A 1 A 2 A 3 e i 3 kx s 2 × 1 s 2 × 1 s 2 × 1 + χ n 2 χ n A 1 A 2 A 3 e i 2 kx e i k x s 2 × 1 s 2 × 1 s 2 × 1 + χ n 2 χ n A 1 A 2 A 3 e i 2 kx e i k x s 2 × 1 s 2 × 1 s 2 × 1 + χ n 2 χ n A 1 A 2 A 3 e i 2 kx e i k x s 2 × 1 s 2 × 1 s 2 × 1 + χ n 2 χ n A 1 A 2 A 3 e ikx e i 2 k x s 2 × 1 s 2 × 1 s 2 × 1 + χ n 2 χ n A 1 A 2 A 3 e ikx e i 2 k x s 2 × 1 s 2 × 1 s 2 × 1 + χ n 2 χ n A 1 A 2 A 3 e ikx e i 2 k x s 2 × 1 s 2 × 1 s 2 × 1 + χ n 3 A 1 A 2 A 3 e i 3 k x s 2 × 1 s 2 × 1 s 2 × 1 } e i 3 ω 0 t E32
The spinors s 2 × 1 and s 2 × 1 can be expressed on the basis 0 = 1 0 and 1 = 0 1 :
s 2 × 1 = s 1 0 + s 2 1 E33a
s 2 × 1 = s 1 0 + s 2 1 E33b
With s 1 = ω 0 + βk , s 2 = ω 0 βk , s 1 = ω 0 + βk and s 2 = ω 0 βk . Inserting Eqs. (33a) and (33b) into Eq. (32), we can express the tensor product Φ 2 3 × 1 on the basis 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 . In defining the basis vectors for the exponential space, we have omitted the symbols . It is also implicit that the left, middle, and right elements in the tensor product a b c correspond to the first, second, and third waveguides, respectively.
We find
Φ 2 3 × 1 = T 1 0 0 0 + T 2 0 0 1 + + T 8 1 1 1 e i 3 ω 0 t E34
with
T 1 = Q 1 s 1 s 1 s 1 + Q 2 s 1 s 1 s 1 + Q 3 s 1 s 1 s 1 + Q 4 s 1 s 1 s 1 + Q 5 s 1 s 1 s 1 + Q 6 s 1 s 1 s 1 + Q 7 s 1 s 1 s 1 + Q 8 s 1 s 1 s 1 E35a
T 2 = Q 1 s 1 s 1 s 2 + Q 2 s 1 s 1 s 2 + Q 3 s 1 s 1 s 2 + Q 4 s 1 s 1 s 2 + Q 5 s 1 s 1 s 2 + Q 6 s 1 s 1 s 2 + Q 7 s 1 s 1 s 2 + Q 8 s 1 s 1 s 2 E35b
T 3 = Q 1 s 1 s 2 s 1 + Q 2 s 1 s 2 s 1 + Q 3 s 1 s 2 s 1 + Q 4 s 1 s 2 s 1 + Q 5 s 1 s 2 s 1 + Q 6 s 1 s 2 s 1 + Q 7 s 1 s 2 s 1 + Q 8 s 1 s 2 s 1 E35c
T 4 = Q 1 s 2 s 1 s 1 + Q 2 s 2 s 1 s 1 + Q 3 s 2 s 1 s 1 + Q 4 s 2 s 1 s 1 + Q 5 s 2 s 1 s 1 + Q 6 s 2 s 1 s 1 + Q 7 s 2 s 1 s 1 + Q 8 s 2 s 1 s 1 E35d
T 5 = Q 1 s 1 s 2 s 2 + Q 2 s 1 s 2 s 2 + Q 3 s 1 s 2 s 2 + Q 4 s 1 s 2 s 2 + Q 5 s 1 s 2 s 2 + Q 6 s 1 s 2 s 2 + Q 7 s 1 s 2 s 2 + Q 8 s 1 s 2 s 2 E35e
T 6 = Q 1 s 2 s 1 s 2 + Q 2 s 2 s 1 s 2 + Q 3 s 2 s 1 s 2 + Q 4 s 2 s 1 s 2 + Q 5 s 2 s 1 s 2 + Q 6 s 2 s 1 s 2 + Q 7 s 2 s 1 s 2 + Q 8 s 2 s 1 s 2 E35f
T 7 = Q 1 s 2 s 2 s 1 + Q 2 s 2 s 2 s 1 + Q 3 s 2 s 2 s 1 + Q 4 s 2 s 2 s 1 + Q 5 s 2 s 2 s 1 + Q 6 s 2 s 2 s 1 + Q 7 s 2 s 2 s 1 + Q 8 s 2 s 2 s 1 E35g
T 8 = Q 1 s 2 s 2 s 2 + Q 2 s 2 s 2 s 2 + Q 3 s 2 s 2 s 2 + Q 4 s 2 s 2 s 2 + Q 5 s 2 s 2 s 2 + Q 6 s 2 s 2 s 2 + Q 7 s 2 s 2 s 2 + Q 8 s 2 s 2 s 2 E35h
with
Q 1 = χ n 3 A 1 A 2 A 3 e i 3 kx ; Q 2 = χ n 2 χ n e i 2 kx e i k x A 1 A 2 A 3 ; Q 3 = χ n 2 χ n e i 2 kx e i k x A 1 A 2 A 3 ; Q 4 = χ n 2 χ n e i 2 kx e i k x A 1 A 2 A 3 ; Q 5 = χ n 2 χ n e ikx e i 2 k x A 1 A 2 A 3 ; Q 6 = χ n 2 χ n e ikx e i 2 k x A 1 A 2 A 3 ; Q 7 = χ n 2 χ n e ikx e i 2 k x A 1 A 2 A 3 ; Q 8 = χ n 3 A 1 A 2 A 3 e i 3 k x .
In a true quantum system composed of three spins for instance, states can be created in the form of linear combinations like m 1 0 0 0 + m 2 0 0 1 + + m 8 1 1 1 . For the quantum system, the linear coefficients m 1 , m 2 ,…, m 8 are independent. The classical elastic analogue, introduced here, states which are given in Eq. (34) possesses linear coefficients T 1 ,…, T 8 are interdependent. While somewhat restrictive compared to true quantum systems, the coefficients T I depend on an extraordinary number of degrees of freedom which allows exploration of a large volume of the exponential tensor product space. In the case of the three waveguides, these degrees of freedom include (a) the components (or linear combinations) of the eigen vectors of the coupling matrix through the choice of the eigen modes or the application of a rotational operation that creates cyclic permutations of the eigen vector components, (b) the linear coefficients χ n and χ n used to form the multiband linear superposition of states in the linear space, (c) the frequency and therefore wave number which affect the spinor states and the phase factors e ikx and e i k x , and (d) a phase added to the terms e ikx and e i k x .
In the case of N > 3 , Eq. (21) can be extended to linear combinations of more than two modes with the same frequency, leading to additional freedom in the control of the T I . Furthermore, the elastic coefficients β of the waveguides and the coupling elastic coefficient α could also be modified by using constitutive materials with tunable elastic properties via, for instance, the piezoelectric, magneto-elastic or photoelastic effects [24, 25, 26]. Also note that in all the examples we considered, the coupling of the waveguides had the same strength. Tunability of the coupling elastic medium would lead to the ability to modify the connectivity of the waveguides and therefore the coupling matrix. Exploration of the elastic modes given in Eq. (34) can be realized by varying any number of these variables. We illustrate in Figure 2 an example of operation in a very simple case. Figure 2b shows that by varying a single parameter one may achieve a wide variety of states. For instance, one can obtain states with T 1 > 0 and T 2 > 0 or T 1 > 0 and T 2 = 0 or T 1 > 0 and T 2 < 0 or T 1 = 0 and T 2 = 0 . Another interesting example occurs at χ n ˜ 0.6 , there only T 5 and T 8 are different from zero. Then, Φ 2 3 × 1 = T 5 0.6 0 1 1 + T 8 0.6 1 1 1 e i 3 ω 0 t can be written as the tensor product state T 5 0.6 0 + T 8 0.6 1 1 1 e i 3 ω 0 t . A similar state is also obtained for χ n 0.25 . This is the state T 1 0.25 0 + T 4 0.25 1 0 0 e i 3 ω 0 t . Varying χ n can be visualized as a matrix operator. For example, in this latter case, one can define the operation:
q 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 q 44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 T 1 χ n T 2 χ n T 3 χ n T 4 χ n T 5 χ n T 6 χ n T 7 χ n T 8 χ n = T 1 0.25 T 2 0.25 T 3 0.25 T 4 0.25 T 5 0.25 T 6 0.25 T 7 0.25 T 8 0.25 = T 1 0.25 0 0 T 4 0.25 0 0 0 0 E36
with q 11 = T 1 0.25 T 1 χ n and q 44 = T 4 0.25 T 4 χ n . Another interesting state occurs at χ n = 0.5 . Here, we have T 1 = T 5 , T 2 = T 3 , T 4 = T 8 and T 6 = T 7 . We also have T 3 = T 5 and T 4 = T 6 This state can be written as the tensor product T 1 0.5 0 T 6 0.5 1 0 1 0 1 .
This simple example indicates the large variability in T I ’s (i.e., of states) that we can achieve with a single variable. The large number of available variables will lead to even more flexibility in defining states and operators in the exponential tensor product space.
### 2.5. Nonseparability of states in exponentially complex space
States given in Eq. (27) are tensor products on the basis 0 0 0 0 0 1 0 1 0 1 1 1 . They are therefore always separable in that basis. Consequently these states cannot be written as nonseparable Bell states. However, we might be able to identify a basis in which Eq. (27) is not separable.
Since the Dirac equation (Eq. (15)) for the uncoupled waveguides is linear, its solutions can be a tensor product of a linear combination of N different individual spinors. For instance, we can write:
Ψ 2 N × 1 = ρ 1 ω 1 + β k 1 e i k 1 x + μ 1 ω 1 β k 1 e i k 1 x ρ 1 ω 1 β k 1 e i k 1 x + μ 1 ω 1 + β k 1 e i k 1 x e i ω 1 t ρ N ω N + β k N e i k N x + μ N ω N β k N e i k N x ρ N ω N β k N e i k N x + μ N ω N + β k N e i k N x e i ω N t E37
ρ I and μ I , I = 1 , , N are linear coefficients.
The state of the coupled waveguide system will be separable in the exponential space into the state of φ -bits if
Φ 2 N × 1 = Ψ 2 N × 1 E38
A necessary condition for satisfying Eq. (38) is that N ω 0 = ω 1 + + ω N .
Furthermore, the first two terms in the column vector Φ 2 N × 1 of the coupled system are φ 1 1 φ 1 2 φ 1 N and φ 1 1 φ 1 2 φ 2 N . Their ratio is simply equal to r N c = φ 1 N φ 2 N . Similarly, the ratio of the first two terms in the vector Ψ 2 N × 1 of the φ -bit system is given by r N u = ρ N ω N + β k N e i k N x + μ N ω N β k N e i k N x ρ N ω N β k N e i k N x + μ N ω N + β k N e i k N x . Anecessary condition for Eq. (38) to be satisfied is that
r N C = r N u E39
χ n A N ω 0 + βk e ikx + χ n A N ω 0 + βk e ik x χ n A N ω 0 βk e ikx + χ n A N ω 0 βk e ik x = ρ N ω N + β k N e i k N x + μ N ω N β k N e i k N x ρ N ω N β k N e i k N x + μ N ω N + β k N e i k N x
which can be rewritten as:
u e ikx + u e ik x v e ikx + v e ik x = γ e i k N x + γ e i k N x δ e i k N x + δ e i k N x
This condition takes the more compact form:
P e i k + k N x + Q e i k k N x + R e i k + k N x + S e i k k N x = 0 E40
P , Q , R , S are real. Eq. (40) is true for all values of position x . At x = 0 , we obtain the relation P + Q + R + S = 0 . Inserting that relation into Eq. (27) and eliminating Q yields:
{(R+S)coskNx[cos(kk)x1]+(RS)sin(kk)sinkNx}+i{(R+S)sin(kk)x+sinkNx[(RS)cos(kk)x+(R+S)]}
For this condition to be satisfied, one needs the real part of the right-hand side of the equation to be equal to zero. This can be achieved for all x ’s by setting k = k . In this case, equating the imaginary parts leads to R = P . However, when k k , Eq. (39) and therefore Eq. (38) are not satisfied. When k k which corresponds to considering a linear combination of multiband states, Φ 2 N × 1 is not separable into the tensor product of individually uncoupled φ -bit waveguides. Therefore, we conclude that there are a large number of solutions of the nonlinear Dirac equation (Eq. (20)) representing states of arrangements of elastically coupled 1-D waveguides that are not separable in the 2 N dimensional tensor product Hilbert space of individual φ -bits.
We illustrate the notion of nonseparability of exponentially complex states of a coupled system composed of N = 2 waveguides on a basis in the exponential Hilbert space of two individual φ -bits. The waveguides are coupled to each other but also to a rigid substrate such that the coupling matrix, M N × N , takes the form:
M 2 × 2 = 2 1 1 2
The eigen values and real eigen vectors of this coupling matrix are λ 0 2 = 1 , and λ 1 2 = 3 and
e 0 = A 1 A 2 = 1 2 1 1 , e 1 = A 1 A 2 = 1 2 1 1 E41
Following the procedure of Section 2.4, we construct a tensor product state in the 2 2 exponential space:
Φ 2 2 × 1 = { χ n 2 A 1 A 2 e i 2 kx s 2 × 1 s 2 × 1 + χ n χ n A 1 A 2 e ikx e ik x s 2 × 1 s 2 × 1 + χ n χ n A 1 A 2 e i k x e ikx s 2 × 1 s 2 × 1 + χ n 2 A 1 A 2 e i 2 k x s 2 × 1 s 2 × 1 } e i 2 ω 0 t E42
Eq. (42) is equivalent to Eq. (32) but for two coupled waveguides.
On the basis, η 1 = e i 2 ω 0 t e i 2 kx s 2 × 1 s 2 × 1 , η 2 = e i 2 ω 0 t e ikx e ik x s 2 × 1 s 2 × 1 , η 3 = e i 2 ω 0 t e i k x e ikx s 2 × 1 s 2 × 1 , and η 4 = e i 2 ω 0 t e i 2 k x s 2 × 1 s 2 × 1 , Eq. (42) can be rewritten as:
Φ 2 2 × 1 = a 11 η 1 + a 12 η 2 + a 21 η 3 + a 22 η 4 E43
with a 11 = χ n 2 A 1 A 2 = 1 2 χ n 2 , a 12 = χ n χ n A 1 A 2 = 1 2 χ n χ n , a 21 = χ n χ n A 1 A 2 = 1 2 χ n χ n , and a 22 = χ n 2 A 1 A 2 = 1 2 χ n 2 . It is then easy to demonstrate that det a 11 a 12 a 21 a 22 = 1 2 χ n 2 1 2 χ n χ n 1 2 χ n χ n 1 2 χ n 2 = 0 , which indicates that the state Φ 2 2 × 1 is separable on the basis η 1 η 2 η 3 η 4 . At this stage, there is nothing surprising as the state Φ 2 2 × 1 was constructed as a tensor product. We now try to express the state given in Eq. (42) on a basis of two individually uncoupled φ -bits. Considering the Hilbert space of the first φ -bit, H 1 , we use the spinor solutions for uncoupled waveguides given in Eq. (17) to construct the orthonormal basis
ψ 1 1 = 1 2 ω 1 ω 1 + β 1 k 1 ω 1 β 1 k 1 e i k 1 x e i ω 1 t = s 1 1 k 1 e i k 1 x e i ω 1 t E44a
ψ 2 1 = 1 2 ω 1 ω 1 β 1 k 1 ω 1 + β 1 k 1 e i k 1 x e i ω 1 t = s 2 1 k 1 e i k 1 x e i ω 1 t E44b
Similarly, we define the orthonormal basis in the Hilbert space, H 2 , of the second φ -bit,
ψ 1 2 = 1 2 ω 2 ω 2 + β 2 k 2 ω 2 β 2 k 2 e i k 2 x e i ω 2 t = s 1 2 k 2 e i k 2 x e i ω 2 t E45a
ψ 2 2 = 1 2 ω 2 ω 2 β 2 k 2 ω 2 + β 2 k 2 e i k 2 x e i ω 2 t = s 2 2 k 2 e i k 2 x e i ω 2 t E45b
In these equations, we have used s 1 1 k 1 , s 2 1 k 1 , s 1 2 k 2 , and s 2 2 k 2 as short-hands for the spinor parts of the basis functions.
The basis in the tensor product space H 1 H 2 is given by the four functions:
τ 1 = ψ 1 1 ψ 1 2 , τ 2 = ψ 1 1 ψ 2 2 , τ 3 = ψ 2 1 ψ 1 2 , τ 4 = ψ 2 1 ψ 2 2 E46
We have
τ 1 = s 1 1 k 1 s 1 2 k 2 e i k 1 + k 2 x e i ω 1 + ω 2 t E47a
τ 2 = s 1 1 k 1 s 2 2 k 2 e i k 1 k 2 x e i ω 1 + ω 2 t E47b
τ 3 = s 2 1 k 1 s 1 2 k 2 e i k 1 + k 2 x e i ω 1 + ω 2 t E47c
τ 4 = s 2 1 k 1 s 2 2 k 2 e i k 1 k 2 x e i ω 1 + ω 2 t E47d
It is straightforward to show that τ 1 τ 2 τ 3 τ 4 form an orthogonal basis. That is, τ i τ j = 0 if i j , where τ i is the Hermitian conjugate of τ i .
We want now to express the state Φ 2 2 × 1 in the τ basis:
Φ 2 2 × 1 = b 11 τ 1 + b 12 τ 2 + b 21 τ 3 + b 22 τ 4 E48
For this, we now need to expand the basis vectors η 1 η 2 η 3 η 4 on the basis τ 1 τ 2 τ 3 τ 4
We define the expansions:
η 1 = c 11 τ 1 + c 12 τ 2 + c 13 τ 3 + c 14 τ 4 E49a
η 2 = c 21 τ 1 + c 22 τ 2 + c 23 τ 3 + c 24 τ 4 E49b
η 3 = c 31 τ 1 + c 32 τ 2 + c 33 τ 3 + c 34 τ 4 E49c
η 4 = c 41 τ 1 + c 42 τ 2 + c 43 τ 3 + c 44 τ 4 E49d
Note that the c ij ’s are functions of k 1 , k 2 , x, and t.
We can find the coefficients c ij by exploiting the orthogonality of the τ i s . For instance, we can multiply Eq. (49a) to the left by the Hermitian conjugate τ 1 , leading to
τ 1 η 1 = c 11 τ 1 τ 1 + c 12 τ 1 τ 2 + c 13 τ 1 τ 3 + c 14 τ 1 τ 4 = c 11 τ 1 τ 1 E50
or
c 11 k 1 k 2 x t = s 1 1 k 1 s 1 2 k 2 s 2 × 1 s 2 × 1 e i k 1 + k 2 x e i 2 kx e i ω 1 + ω 2 t e i 2 ω 0 t / s 1 1 k 1 s 1 2 k 2 s 1 1 k 1 s 1 2 k 2 E51
We can obtain all other c ij ’s in a similar fashion. Eqs. (49a)–(49d) can be rewritten in the form:
η 1 η 2 η 3 η 1 = η 4 × 1 = c 11 c 12 c 13 c 14 c 21 c 22 c 23 c 24 c 31 c 32 c 33 c 34 c 41 c 42 c 43 c 44 τ 1 τ 2 τ 3 τ 4 = C 4 × 4 τ 4 × 1 E52
The matrix C 4 × 4 can be diagonalized. Let d 1 , d 2 , d 3 , and d 4 be the four eigen values of C 4 × 4 with their associated eigen vectors v 11 v 12 v 13 v 14 , v 21 v 22 v 23 v 24 , v 31 v 32 v 33 v 34 and v 41 v 42 v 43 v 44 . We can construct the following matrix out of the four eigen vectors:
V 4 × 4 = v 11 v 21 v 31 v 41 v 12 v 22 v 32 v 42 v 13 v 23 v 33 v 43 v 14 v 24 v 34 v 44
On the new basis τ ˜ 1 τ ˜ 2 τ ˜ 3 τ ˜ 4 constructed by using the relation τ ˜ 4 × 1 = V 4 × 4 1 τ 4 × 1 V 4 × 4 , the matrix that couples the η basis and the τ basis takes the form: C ˜ 4 × 4 = d 1 0 0 0 0 d 2 0 0 0 0 d 3 0 0 0 0 d 4 so η 1 = d 1 τ ˜ 1 , η 2 = d 2 τ ˜ 2 , η 3 = d 3 τ ˜ 3 and η 4 = d 4 τ ˜ 4 . On the τ ˜ basis, Eq. (43) can be rewritten as
Φ 2 2 × 1 = a 11 d 1 τ ˜ 1 + a 12 d 2 τ ˜ 2 + a 21 d 3 τ ˜ 3 + a 22 d 4 τ ˜ 4 E53
Then on the basis τ ˜ , we can investigate the separability or nonseparability of Φ 2 2 × 1 by calculating the determinant of the linear coefficients in Eq. (53), that is
det a 11 d 1 a 12 d 2 a 21 d 3 a 22 d 4 = 1 2 χ n 2 d 1 1 2 χ n χ n d 2 1 2 χ n χ n d 3 1 2 χ n 2 d 4 = 1 4 χ n 2 χ n 2 d 1 d 4 d 2 d 3 E54
Only in the unlikely event of degenerate eigen values, d 1 , d 2 , d 3 , and d 4 , would this determinant be equal to zero. A nonzero determinant given in Eq. (54) indicates that the state Φ 2 2 × 1 is nonseparable on the basis τ ˜ 1 τ ˜ 2 τ ˜ 3 τ ˜ 4 .
The existence of nonseparable solutions to the nonlinear Dirac equation raises the possibility of exploiting these solutions for storing and manipulating data within the 2N dimensional tensor product Hilbert space. The exploration of algorithms for exploiting these solutions is beyond the scope of this chapter; however, we note that these solutions may well be observed in physical systems including elastic waveguides which are embedded in a coupling matrix. The manipulation of the system could be achieved either by externally altering the parameters of the system, i.e., the elastic properties of the waveguides, or by changing the frequency and wavenumber of input waves. These possibilities are illustrated for a five-waveguide system driven by transducers in Section 2.6.
### 2.6. Physical realization and actuation
Figure 3 illustrates a possible realization of a five waveguide system. The parallel elastic waveguides are embedded in an elastic medium which couples them elastically. The waveguides are arranged in a ring pattern.
Modes of the form given in Eq. (21) can be excited with N transducers attached to the input ends of the N waveguides and connected to N phase-locked signal generators to excite the appropriate eigen vectors e n and e n . These modes can be excited by applying a superposition of signals on the transducers with the appropriate phase, amplitude and frequency relations. The frequencies ω n k and ω n k are used to control the spinor parts of the wave functions s 2 × 1 k and s 2 × 1 k . The spinor components which represent a quasistanding wave can be quantified by measuring the transmission coefficient (normalized transmitted amplitude) along any one of the waveguides. It is then possible to operate on the eigen vectors e n and e n without affecting the spinor states or vice versa. For instance, one could apply a rotation that permutes cyclically the components of e n by changing the phase of the signal generators. Such an operation could be quantified by measuring the phase of the transmission amplitude at the output end of the waveguides.
## 3. Conclusions
We have shown that the directional projection of elastic waves supported by a parallel array of N elastically coupled waveguides can be described by a nonlinear Dirac-like equation in a 2 N dimensional exponential space. This space spans the tensor product Hilbert space of the two-dimensional subspaces of N uncoupled waveguides grounded elastically to a rigid substrate (which we called φ-bits). We demonstrate that we can construct tensor product states of the elastically coupled system that are nonseparable on the basis of tensor product states of N uncoupled φ-bits. A φ-bit exhibits superpositions of directional states that are analogous to those of a quantum spin, hence it acts as a pseudospin. Since parallel arrays of coupled waveguides span the same exponentially complex space as that of uncoupled pseudospins, the type of elastic systems described here may serve as a simulator of interacting spin networks. The possibility of tuning the elastic coefficients and the elastic coupling constants of the waveguides would allow us to explore the properties of spin networks with variable connectivity and coupling strength. The mapping between the 2 N dimensional and the 2 N dimensional representations of the elastic system leads to the capacity for exploring an exponentially scaling space by handling a linearly growing number of waveguides (i.e., preparation, manipulation, and measurement of these states). The scalability of the elastic system, the coherence of elastic waves at room temperature, and the ability to measure classical superpositions of states may offer an attractive way for addressing exponentially complex problem through the analogy with quantum systems.
## Acknowledgments
We acknowledge the financial support of the W.M. Keck Foundation. We thank Saikat Guha and Zheshen Zhang for useful discussions.
## Conflict of interest
The authors declare that they have no affiliations with or involvement in any organization or entity with any financial interest or nonfinancial interest in the subject matter or materials discussed in this manuscript.
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24. 24. Croënne C, Vasseur JO, Bou Matar O, Ponge M-F, Deymier PA, Hladky-Hennion A-C, Dubus B. Brillouin scattering-like effect and non-reciprocal propagation of elastic waves due to spatio-temporal modulation of electrical boundary conditions in piezoelectric media. Applied Physics Letters. 2017;110:061901
25. 25. Bou Matar O, Robillard JF, Vasseur JO, Hladky-Hennion A-C, Deymier PA, Pernod P, Preobrazhensky V. Band gap tunability of magneto-elastic phononic crystal. Journal of Applied Physics. 2012;111:054901
26. 26. Swinteck N, Matsuo S, Runge K, Vasseur JO, Lucas P, Deymier PA. Bulk elastic waves with unidirectional backscattering-immune topological states in a time-dependent superlattice. Journal of Applied Physics. 2015;118:063103
Written By
Pierre Alix Deymier, Jerome Olivier Vasseur, Keith Runge and Pierre Lucas
Submitted: February 20th, 2018 Reviewed: April 13th, 2018 Published: November 5th, 2018 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9409633278846741, "perplexity": 1173.6800078636593}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337731.82/warc/CC-MAIN-20221006061224-20221006091224-00030.warc.gz"} |
http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=DBSHCJ_2013_v28n4_799 | AN ELEMENTARY PROOF OF SFORZA-SANTALÓ RELATION FOR SPHERICAL AND HYPERBOLIC POLYHEDRA
Title & Authors
AN ELEMENTARY PROOF OF SFORZA-SANTALÓ RELATION FOR SPHERICAL AND HYPERBOLIC POLYHEDRA
Cho, Yunhi;
Abstract
We defined and studied a naturally extended hyperbolic space (see [1] and [2]). In this study, we describe Sforza`s formula [7] and Santal$\small{\acute{o}}$`s formula [6], which were rediscovered and later discussed by many mathematicians (Milnor [4], Su$\small{\acute{a}}$rez-Peir$\small{\acute{o}}$ [8], J. Murakami and Ushijima [5], and Mednykh [3]) in the spherical space in an elementary way. Thereafter, using the extended hyperbolic space, we apply the same method to prove their results in the hyperbolic space.
Keywords
hyperbolic space;spherical space;polyhedron;volume;
Language
English
Cited by
References
1.
Y. Cho, Trigonometry in extended hyperbolic space and extended de Sitter space, Bull. Korean Math. Soc. 46 (2009), no. 6, 1099-1133.
2.
Y. Cho and H. Kim, The analytic continuation of hyperbolic space, Geom. Dedicata 161 (2012), no. 1, 129-155.
3.
A. D. Mednykh, Hyperbolic and spherical volume for knots, links and polyhedra, Summer school and conference on Geometry and Topology of 3-manifolds, Trieste-Italy, 6-24 June 2005.
4.
J. Milnor, The Schlafli Differential Equality, Collected papers, Vol. 1, Publish or Perish, Houston, Texas, 1994.
5.
J. Murakami and A. Ushijima, A volume formula for hyperbolic tetrahedra in terms of edge lengths, J. Geom. 83 (2005), no. 1-2, 153-163.
6.
L. Santalo, Integral Geometry and Geometric Probability, Encyclopedia of Mathematics and its Applications, Vol. 1, Addison-Wesley, 1976.
7.
G. Sforza, Spazi metrico-proiettivi, Ricerche di Estensionimetria differenziale, Serie III, VIII (1906), 3-66.
8.
E. Suarez-Peiro, A Schlafli differential formula for simplices in semi-Riemannian hyperquadrics, Gauss-Bonnet formulas for simplices in the de Sitter sphere and the dual volume of a hyperbolic simplex, Pacific J. Math. 194 (2000), no. 1, 229-255. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 3, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9803687334060669, "perplexity": 2117.223547705715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512161.28/warc/CC-MAIN-20181018235424-20181019020924-00160.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/53472-d-print.html | # d
• October 13th 2008, 11:17 AM
I Congruent
Subspaces
OOPS I MESSED UP THE TITLE CAN ANY1 TELL ME HOW I CAN CHANGE IT?
Let $V = R^3$, and consider the following subsets of V.
$U_1 = \{ t \begin{pmatrix}
1\\
0\\
0\end{pmatrix} : t \in R \}$
$U_2 = \{ t \begin{pmatrix}
0\\
1\\
0\end{pmatrix} : t \in R \}$
$U_3 = \{t \begin{pmatrix}
1\\
1\\
1\end{pmatrix} : t \in R \}$
$U_4 = \{ \begin{pmatrix}
r\\
s\\
0\end{pmatrix} : r,s \in R \}$
$U_5 = \{ \begin{pmatrix}
r\\
s\\
1\end{pmatrix} : r,s \in R \}$
$U_6 = \{ \begin{pmatrix}
r\\
s\\
0\end{pmatrix} : r,s,t \in R \text{ and } r+s+t=1 \}$
$U_7 = U_1 \cap U_2$
$U_8 = U_1 \cup U_2$
a) For each of the 8 sets sat whether it is a subspace, and briefly explain your answer.
b) For each of the 8 sets, classify it as one of
i. A line passing through the origin.
ii. A line not passing through the origin.
iii. A plane passing through the origin.
iv. A plane not passing through the origin.
v. none of the above
c) What do you conclude about the subspaces of $R^3$?
• October 13th 2008, 11:20 AM
I Congruent
I am not too confident with my answers and im completely stuck on part b) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7181892395019531, "perplexity": 798.6980318866202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438044271733.81/warc/CC-MAIN-20150728004431-00200-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3828479/definition-of-scalar-coextension?noredirect=1 | # Definition of "Scalar coextension"
Let $$\phi: A \rightarrow B$$ be a ring homomorphism. Here $$A$$ and $$B$$ are commutative rings. Suppose we have an $$A$$-module $$M$$, and we hope to construct a $$B$$-module. A traditional way is via base change, namely construct the module $$M_B:= B \otimes_A M$$. Then this is a $$B$$-module.
Yet in the posts
and
MSE 2780723: Induced representation: which adjoint is it?
People also constructed a $$B$$-module $$M^B := \text{Hom}_A(B, M)$$ and call this a scalar coextension (as in the math.SE post quoted above answered by @Qiaochu Yuan). My question is: What is the $$B$$-module structure on $$M^B$$? It is indeed an $$A$$-module, but I looked up many posts and books but have not found any definition of it. So could someone provide me with some references or give me the definition of it?
My guess: Let $$f \in M^B := \text{Hom}_A(B, M)$$ and $$b \in B$$, then the $$A$$-module homomorphism $$b \cdot f$$ is defined by sending any element $$r \in B$$ to $$f(br)$$. Is this definition correct? It seems that there should be a correct definition, since people usually regard (or define) this as the right adjoint to the functor of the restriction of scalars, i.e. view a $$B$$-module $$N$$ as an $$A$$-module via $$\phi$$, by defining $$a \cdot x := \phi(a) \cdot x$$ for any $$a \in A$$ and $$x \in N$$.
• Your guess is correct. Sep 16, 2020 at 13:00
• Coextension of scalars makes sense with no commutativity assumptions and then your guess is not correct; you should multiply on the right if you want a left module. Sep 16, 2020 at 16:30
• @QiaochuYuan Thank you so much! Sep 18, 2020 at 2:40
• @Hanno Thank you for your comments! Sep 18, 2020 at 2:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 26, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9654693603515625, "perplexity": 250.73957323121653}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573630.12/warc/CC-MAIN-20220819070211-20220819100211-00533.warc.gz"} |
https://mathematica.stackexchange.com/questions/187290/what-is-the-the-proper-way-to-define-a-function-from-an-expression/187295 | What is the the proper way to define a function from an expression? [duplicate]
Say after some long computation we get an expression
expr=x^2
We do not know what the value of expr beforehand. Now we want to turn this in a function. We can use either
f[x_]=expr
or
f[x_]:=Evaluate[expr]
as suggested in this question.
However, when we do
f[x_]=Expand[expr]
or
f[x_]:=Evaluate[Expand[expr]]
The Expand will not have any effect.
Is there any way to make this work? Of course, we can define another function
g[x_]:=Expand[f[x]]
But is there any way to do it a bit more concisely?
Update:
If you do what suggested by Kuba in the comment, you get
In[89]:= With[{expr = expr}, f11[x_] := Expand[expr]]
In[90]:= f11[a + b]
Out[90]= x^2
In[91]:= ?? f11
Notebook34$907690f11 f11[x$_]:=Expand[x^2]
• I think f[x_] = Expand[expr] actually works fine. It expands expr and then turns x into a function slot. Just try it with expr = (1 + x)^10 and then evaluate f[y] after defining f. Or were you expecting something different? – Sjoerd Smit Dec 4 '18 at 15:47
• I was expecting to have f[a+b]==Expand[(a+b)^2]=a^2+2 a b+b^2 – ablmf Dec 4 '18 at 16:36
• In that case I would say that the g[x] := Expand[f[x]] method is really the way to go here, because it makes the evaluation process easiest to follow. Any other method is just going to be confusing one way or another. – Sjoerd Smit Dec 4 '18 at 17:02
• Closely related: (69590) – Mr.Wizard Nov 11 '19 at 14:27
Sorry, I was too hasty in comments:
With[{expr = expr}, SetDelayed @@ Hold[f[x_], Expand[expr]]]
SetDelayed @@ Hold is needed because of: Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs
• why not With[{expr = Expand[expr]}, SetDelayed @@ Hold[f[x_], expr]] – Ali Hashmi Dec 4 '18 at 12:36
• @AliHashmi Because the point is not to evaluate Expand. Compare ?f in my and your case. – Kuba Dec 4 '18 at 12:37
• sorry i misinterpreted the question. I thought the purpose was for Evaluate to do its job before the definitions are saved. – Ali Hashmi Dec 4 '18 at 14:49
(f[x_] := Expand@#) &@expr
• FYI, I'd accept that. This is what I usually do anyway :p – Kuba Dec 5 '18 at 9:24
Here are a couple more possibilities. Using Block:
Clear[f]
Block[{Expand}, f[x_] = Expand[expr]];
Definition[f]
f[x_]=Expand[(1+x)^2]
Using With:
Clear[f]
With[{expr = expr, lhs = f[x_]},
lhs := Expand[expr]
];
Definition[f]
f[x_]:=Expand[(1+x)^2]
This works, and the general idea is useful for other things too,
ToExpression["f[x_]:= Expand[" <> ToString[InputForm[expr]] <> "]"]
To test it, let's try something not already expanded,
expr = (1 + x)^2
Using the above way to make f, one finds that Definition[f] // InputForm returns
f[x_] := Expand[(1 + x)^2]
as required. But we don't want to have to remember how to do all that, so let's just do it once for any f and any expr,
MakeFunction[f_, expr_]:=
ToExpression[ToString[f] <> "[x_]:=
Expand[" <> ToString[InputForm[expr]] <> "]"]
Next thing to do would be define Options for MakeFunction so that instead of just Expand, you could instead use Simplify, etc.
Dear @ablmf you can use the following syntax in Mathematica.
f[x_]:=x^2;
When you input any desired value for x, Mathematica gives you its value in f[x]. Say, you want f[2], Mathematica gives you 4
f[2]
4
You can also use it to obtain a list. Consider the following code
ClearAll["Global*"];
f[x_] := x^2;
Table[
f[x]
, {x, 0, 10}]
it gives you
{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
• I'm sorry, but this isn't what OP asks for, is it? – xzczd Dec 4 '18 at 12:09
• Sorry, this is not what I asked. – ablmf Dec 4 '18 at 13:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.700834333896637, "perplexity": 2416.2500268413564}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400274441.60/warc/CC-MAIN-20200927085848-20200927115848-00751.warc.gz"} |
https://support.bioconductor.org/p/102530/#9148013 | 2
0
Entering edit mode
@ogiannakopoulou-13991
Last seen 3.0 years ago
Hello,
I'm using the champ.load to read and filter my data and it works well. However when I want to proceed with the champ.QC I receive an error because the column "Sample_Group" in the csv file provided is empty.
So I tried to add the information of that column ("first" or "second") and use the modified csv file to load the idat files. However at that point I'm getting the following error:
"Error in champ.import(directory, arraytype = arraytype) : Error Match between pd file and Green Channel IDAT file."
I went through the pipeline to check how ChAMP imports the data but I did not manage to pick which is the mistake. I know It would be great if you could help so that I can include this information and proceed with champ.QC.
Thank you,
Olga Giannakopoulou
champ • 3.6k views
1
Entering edit mode
Yuan Tian ▴ 250
@yuan-tian-13904
Last seen 17 months ago
United Kingdom
Hello Olga:
Firstly, champ.QC() failed because of lacing of Sample_Group column, which could because your csv file does not contain Sample_Group. That's OK because different research have different column name on most interested covariates. In champ.QC() there should be a parameter called "pheno", you just need to change it as myLoad$pd$your_phenotype, then it should be good.
Based on my experience, the most possible error is because you used Excel to open original CSV file, then added information on that, then same it as CSV again. By doing this, original Sentrix_ID (a very long number) could be changed. I guess it's some format problem with Excel.
Than after you modify the file, ChAMP will load your csv file, then get Sentrix_ID and Sentrix_Position, and map them to IDAT data, since Sentrix_ID has changed, no IDAT file would be matched.
I think this is the most possible reason. Please check you modified CSV file and original one, focus on the Sentrix_ID column.
If not this reason, I would check closer into code.
Best
Yuan Tian
0
Entering edit mode
Indeed the problem was with editing the excel file. As you guessed, when I was saving the csv file, after adding Sample_Group information, the Sentrix_ID was changing. I managed to make it work after making sure that Sentrix_ID was in "Numeric" format each time.
Thank you again for the help
Best wishes,
Olga
0
Entering edit mode
Firstly i'm a beginner. i have the same problem when I use champ.load("Error Match between pd file and Green Channel IDAT file"). my sample_ sheet is edited using excel by myself. but i don't know how to make sure that Sentrix_ID was in "Numeric" format.
thank you, may
0
Entering edit mode
Before editing the excel sheet (adding sample group data) press ctrl+1, then under "category" see that "NUMBER" is pressed. then press F2 and "ENTER". now enter your'e sample group data, save and "champ.load()". this way you can make sure that "sentrix_ID" stays "NUMERIC". Roi Horwitz
0
Entering edit mode
Roi • 0
@c837bf67
Last seen 9 weeks ago
Israel
Before editing the excel sheet (adding sample group data) press ctrl+1, then under "category" see that "NUMBER" is pressed. then press F2 and "ENTER". now enter your'e sample group data, save and "champ.load()". this way you can make sure that "sentrix_ID" stays "NUMERIC". Roi Horwitz | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3498629331588745, "perplexity": 4848.308732150662}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500619.96/warc/CC-MAIN-20230207134453-20230207164453-00185.warc.gz"} |
http://mmore500.com/2020/06/26/regulation-dishtiny.html | ## 🔗 Introduction
The DISHTINY artificial life system [Moreno and Ofria, 2019] is designed to study fraternal transitions in individuality, evolutionary events where independently replicating entities unify into a higher-level individual. Multicellular organisms and eusocial insect colonies, which survive and propagate through the cooperation of lower-level kin, are typical exemplars of fraternal transitions [Smith and Szathmary, 1997].
## 🔗 Methods
DISHTINY tracks autonomous self-replicating digital cells with heritable behavioral strategies situated on a two-dimensional toroidal grid. Cells can form spatial kin groups to cooperatively collect resources. The morphology of these groups is determined by where offspring are placed and whether they remain part of the parent’s group or are expelled to bud a new group. These conditions yield evolved strategies where individual cells perform actions contrary to their immediate interests (\textit{e.g.}, suppressing reproduction, giving away resources, or even self-destructing) to benefit their kin group [Moreno and Ofria, in prep].
In current work with DISHTINY, SignalGP programs manage cellular behavior. Within each cell, four interconnected hardware instances independently execute a single genetic program; each instance controls cell behavior with respect to a cardinal direction. Sensor instructions and event-driven cues allow cells to react to local information. Likewise, special instructions enable local actions (such as reproduction, resource sharing, and messaging). SignalGP function regulation operates as in the repeated- and changing-signal tasks, except function regulation decays to a neutral baseline unless explicitly renewed.
Evolved DISHTINY populations analyzed here were drawn from ongoing work investigating cell-cell interconnects. We analyze 64 replicate populations each evolved independently for 200 compute-hours under identical evolutionary conditions (mean 62912, S.D. 32840 cellular generations elapsed).
(See [Moreno and Ofria, 2020b] for details.)
## 🔗 Implementation
We implemented our experimental system using the Empirical library for scientific software development in C++, available at https://github.com/devosoft/Empirical [Ofria et al., 2019]. We used OpenMP to parallelize our main evolutionary replicates, distributing work over two threads. The code used to perform and analyze our experiments, our figures, data from our experiments, and a live in-browser demo of our system is available via the Open Science Framework at https://osf.io/kqvmn/ [Foster and Deardorff, 2017].
## 🔗 Results
We used knockout experiments to measure the fraction of replicates that adaptively employ genetic regulation. We harvested a representative genotype from each of the 64 evolved DISHTINY populations. For each independently-evolved population, we performed 16 competition experiments between the representative genotype and a corresponding strain where gene regulation was knocked out. We seeded these runs half-and-half with wild-type and derived knockout genotypes. After one hour of compute time, we assessed the relative abundance of cells descended from wild-type and knockout ancestors. Within the one-hour window, a mean of 91 (S.D. 38) cellular generations elapsed and 17\% of competition runs had coalesced to only the wild type or the knockout strain.
For 10 out of 64 populations, all 16 competition runs exhibited greater abundance of cells descended from the wild-type strain than the knockout strain. Gene regulation contributed significantly to fitness in these runs (Fisher’s exact test with Bonferroni correction, each $p < 0.001$). Among these 10 independently-evolved genotypes, gene regulation plays an adaptive role. However, it is possible that in these cases, gene regulation represents non-plastic contingency rather than contributing to meaningful functionality.
To address this question, we compared the fitnesses of strains that relied on regulation to strains that did not. We measured strain fitness by competing it against a randomly sampled panel of 20 evolved genotypes. We did not find evidence that strains that used gene regulation outperformed strains that did not.
Figure PVOGR: PCA visualization of gene regulation in case-study evolved genotype.
Shifting our approach, we selected a strain from among the 10 to evaluate further as a case study to test for a functional role of gene regulation (Figure PVOGR; live in-browser viewer at mmore500.com/hopto/5). We confirmed that in this strain gene regulation plays a bona fide functional role facilitating coordination among same-cell SignalGP instances. Figure FCOGR(a) summarizes the functional context of gene regulation in this strain. We inferred relationships between components in this diagram by monitoring hardware execution in a monoculture population with mutation disabled. Component-by-component knockout experiments confirmed the adaptive significance of each element of the interaction diagram. We hypothesize that gene regulation mediates intracell mutual exclusion (see Figure FCOGR(b)).
(a) Regulation governs cell division based on environmental state and intracellular state. In baseline conditions, stimulus 1 would activate module A, expressing cell division instructions. However, when module B represses module A, this stimulus instead activates module C — leaving module A unexpressed. This mechanism conditions expression of module A on stimulus 1, but neither of stimulus 2 or 3. Module A also contains instructions to broadcast an intracellular message that activates module B in a cell’s other independently-executing SignalGP instances.
(b) Intracellular broadcast delivers a message to each of a cell’s other SignalGP instances, activating their module 14 and subsequently repressing their module 2.
Figure FCOGR: Functional context of gene regulation in a case-study evolved genotype.
Figure SPOGR shows the spatial expression and regulation patterns of modules A, B, and C. Indeed, in some instances, we can observe expression of module A in a single hardware instance within cells next to two different-group neighbors. However, we can also observe the opposite in other instances, presumably due to interfering cellular mechanisms and virtual hardware limitations (e.g., inbox capacity, thread capacity, concurrency effects, latency effects, conditional message blocking, and thread requisition).
(a) Module 0 expression snapshot.
(b) Module 2 expression snapshot.
(c) Module 14 expression snapshot.
(d) Module 2 regulation snapshot.
Figure SPOGR: Spatial patterns of gene regulation and module expression. Square tiles represent individual cells. Black borders divide cells belonging to different organisms. Cells are divided into four triangle slices, each corresponding to a independently-executing SignalGP instance. In module expression snapshots, white denotes no expression, green denotes a module running on a single hardware core, blue on two, purple on three, red on four, and silver on five. In module regulation shapshots, white denotes baseline state and blue denotes repression.
## 🔗 Let’s Chat
I would love to hear your thoughts on artificial life models of gene regulation and studying major transitions in evolution!!
Pop on there and drop me a line or make a comment
## 🔗 Cite This Post
APA
Lalejini, A., Moreno, M. A., & Ofria, C. (2020, June 27). Case Study of Adaptive Gene Regulation in DISHTINY. https://doi.org/10.17605/OSF.IO/KQVMN
MLA
Lalejini, Alexander, Matthew A Moreno, and Charles Ofria. “Case Study of Adaptive Gene Regulation in DISHTINY.” OSF, 27 June 2020. Web.
Chicago
Lalejini, Alexander, Matthew A Moreno, and Charles Ofria. 2020. “Case Study of Adaptive Gene Regulation in DISHTINY.” OSF. June 27. doi:10.17605/OSF.IO/KQVMN.
BibTeX
@misc{Lalejini_Moreno_Ofria_2020,
title={Case Study of Adaptive Gene Regulation in DISHTINY},
url={osf.io/kqvmn},
DOI={10.17605/OSF.IO/KQVMN},
publisher={OSF},
author={Lalejini, Alexander and Moreno, Matthew A and Ofria, Charles},
year={2020},
month={Jun}
}
## 🔗 References
Foster, E. D. and Deardorff, A. (2017). Open science framework (osf). Journal of the Medical Library Association: JMLA, 105(2):203.
Lalejini, A. and Ofria, C. (2018). Evolving event-driven programs with signalgp. In Proceedings of the Genetic and Evolutionary Computation Conference, pages 1135–1142.
Moreno, M. A. and Ofria, C. (2019). Toward open-ended fraternal transitions in individuality. Artificial life, 25(2):117–133.
Moreno, M. A. and Ofria, C. (2020a). Case Study of Adaptive Gene Regulation in DISHTINY. DOI: 10.17605/OSF.IO/KQVMN; URL: https://osf.io/kqvmn.
Moreno, M. A. and Ofria, C. (in prep.). Spatial constraints and kin recognition can produce open-ended major evolutionary transitions in a digital evolution system. https://doi.org/10.17605/OSF.IO/G58XK.
Ofria, C., Dolson, E., Lalejini, A., Fenton, J., Moreno, M. A., Jorgensen, S., Miller, R., Stredwick, J., Zaman, L., Schossau, J., Gillespie, L., G, N. C., and Vostinar, A. (2019). Empirical.
Smith, J. M. and Szathmary, E. (1997). The major transitions in evolution. Oxford University Press.
## 🔗 Acknowledgements
This research was supported in part by NSF grants DEB-1655715 and DBI-0939454, and by Michigan State University through the computational resources provided by the Institute for Cyber-Enabled Research. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1424871. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.327727735042572, "perplexity": 8422.090849693419}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655882934.6/warc/CC-MAIN-20200703184459-20200703214459-00241.warc.gz"} |
https://www.physicsforums.com/threads/complex-representation-of-fourier-series.180556/ | # Complex representation of fourier series
1. Aug 15, 2007
### tronxo
1. The problem statement, all variables and given/known data
Using the complex representation of fourier series, find the Fourier coefficients of the periodic function shown below. Hence, sketch the magnitude and phase spectra for the first five terms of the series, indicating clearly the spectral lines and their magnitudes
2. Relevant equations
Firstable, I dont know how indicate the spectral lines.
The other problem that i have is when i try to calculate the Cn coefficient and, therefore, the final serie. I dont know if it is right or not, and in case of it is right, im not able to rewrite "my final function" into the correct answer, which i have it in one of my books.
3. The attempt at a solution
what i have done is:
Cn= 1/T∫(from 0 to T) f(t)*e^(-j*n*omega*t) dt
Cn=1/T ( ∫(from 0 to d) Vm*e^(-j*n*omega*t) dt + ∫(from d to T) 0 *e^(-j*n*omega*t) dt )
The second part of the integral is equal to 0, therefore:
Cn=1/T ∫(from 0 to d) Vm*e^(-j*n*omega*t) dt where omega= (2*pi/T)
Cn=1/T ∫(from 0 to d) Vm*e^(-j*n*(2*pi/T)*t) dt
Cn= Vm/T ∫(from 0 to d) e^(-j*n*(2*pi/T)*t) dt
Cn= Vm/(-j*n*(2*pi/T)*T) (limits of the resulting integral from 0 to d)[e^(-j*n*(2*pi/T)*t)]
Cn= Vm/ (-j*n*2*pi) [e^(-j*n*(2*pi/T)*d) - 1]
what is next?
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2. Apr 1, 2009
### haydez98
bump...
i am having a similar problem...
i am given a signal which can be written as:
s(t) = -1 {-1 < t < 0}, 1 {0 < t < 1}, 0 {1 < t < 2} [it's a pulse train]
the period, T, is 3.
i have calculated the trig. fourier series representation, which in matlab turns out to be correct, yet when i calculate the exponentical fsr, i get a version of the trig. fsr which has its amplitude halved.
for the trig fsr:
s(t) = 2/(pi * n) * (1 - cos((2 * pi * n)/3)) * sin((2 * pi * n * t)/3);
for the exp fsr:
s(t) = -1/(i * pi * n) * (cos((2 * pi * n)/3) - 1) * exp((i * 2 * pi * n * t)/3)
i also tried
c_n = 0.5 (a_n - i * b_n) = -0.5 * i * ( 2/(pi * n) * (1 - cos((2 * pi * n)/3))
either case, my complex fsr was a scaled amplitude version of my trig fsr
any guidance would be much appreciated
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http://math.stackexchange.com/questions/720310/can-i-use-strong-induction-to-prove-graph-theory-hamilton-path-tournament-gra | # Can I use Strong Induction to prove graph theory? - Hamilton Path/Tournament Graphs
I am working on the below proof. I am still new to proves so I am wondering if you guys can answer the following questions:
1) Did I use the inductive hypothesis correctly here? (By the inductive hypothesis, we know that both From and To are smaller versions of the larger tournament so there is a Hamiltonian path in both From and To.)
1b) is there a better way to show that these subsets have a Hamiltonian path?
2) Does my proof flow logically and is it clear?
3) Is this proof correct?
Graph to represent the outcome of a round-robin tournament, in which every player plays every other player. An edge goes from the victor of each match to the loser.
Definition 1. A tournament graph is a directed graph G = (V, E) without loops, in which for every two vertices u and v, exactly one of (u, v) or (v, u) are in E.
Definition 3. A Hamiltonian path through a graph is a path that visits each vertex exactly once. Note that a Hamiltonian path is not a cycle.
Prove using strong induction that every tournament graph has a Hamiltonian path.
For a graph with the number of vertices n = 1 then there is a Hamiltonian path of that single vertex. When n > 1, we can consider a graph with n + 1 vertices where the vertices 1…..n contain a Hamiltonian path. An arbitrary vertex v can be chosen from this graph in which, by the definition of a tournament graph, every other vertex has an edge from v or to v. These vertices are be split up into two sets, From and To, where From contains all the vertices with an edge from v and To contains all the vertices with an edge to v. By the inductive hypothesis, we know that both From and To are smaller versions of the larger tournament so there is a Hamiltonian path in both From and To. These two Hamiltonian paths can be join by the edge To v and the edge From v to form a Hamiltonian path throughout the entire graph. Thus there is a Hamiltonian path in the tournament graph n + 1 so, by strong induction, there is a Hamiltonian path in every tournament graph.
-
Definition 1 looks weird, what is $e$? – fgp Mar 20 at 20:29
I'm guessing that was edges but I am not sure myself. – DrJonesYu Mar 20 at 20:31
According to en.wikipedia.org/wiki/Tournament_%28graph_theory%29, it should read "...exactly one of $(u,v)$ or $(v,u)$ are in E.", not "... or $(v,e)$". Thus, a turnament graph is a directed graph that becomes the complete graph if you ignore the directions... – fgp Mar 20 at 20:33
Thanks for the catch. – DrJonesYu Mar 20 at 20:35
And you state the induction hypothesis incorrectly. It's true that vertices $1,\ldots,n$ contain a hamiltonian path, but that not sufficient for the rest of your proof - you need that all subgraphs contain one. You actually do state that later, so just drop the confusing statement about the first $n$ vertices. Just say "Pick a vertex, partition the graph into sets TO and FROM (disjoint!), both contain a hamiltonian path per the induction hypothesis, and thus $P_{FROM} \to v \to P_{TO}$ is a hamiltonian path." – fgp Mar 20 at 20:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9077067375183105, "perplexity": 329.1492032132353}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802766295.3/warc/CC-MAIN-20141217075246-00048-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://www.eevblog.com/forum/testgear/siglent-sds1204x-e-released-for-domestic-markets-in-china/375/ | ### Author Topic: Siglent SDS1104X-E and SDS1204X-E Mixed Signal Oscilloscopes (Read 181388 times)
n3mmr, zabox909, HendriXML, sbh, Willem2018 and 5 Guests are viewing this topic.
#### JPortici
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #375 on: November 29, 2017, 07:16:51 pm »
Same principle for the AWG, so why buy the single channel USB AWG that BTW has a limited output range (p-p) if you already have a standalone Siglent AWG The literature indicates it can control all existing Siglent AWG's, SDG1032X works fine with it, Bode plots and all.
Yes 2 parts for this option makes perfect sense too.
huh, i didn't know that. makes sense i guess
#### simone.pignatti
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #376 on: November 29, 2017, 07:19:06 pm »
I think the FG SW option is not a requirement for Bode Plot
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#### tautech
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #377 on: November 29, 2017, 07:36:06 pm »
I think the FG SW option is not a requirement for Bode Plot
Hard to know for sure as new units will have trial licences for all the SW options.
My beta unit has permanent licensing so I can't test this.
Thinking about it, the AWG SW maybe controls the standalone AWG too for Bode plots.
Use a unit without AWG permanent option with standalone AWG , do Bode plot and look for reduction in trial usage #'s.
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#### TK
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #378 on: November 29, 2017, 08:17:49 pm »
Same principle for the AWG, so why buy the single channel USB AWG that BTW has a limited output range (p-p) if you already have a standalone Siglent AWG The literature indicates it can control all existing Siglent AWG's, SDG1032X works fine with it, Bode plots and all.
Yes 2 parts for this option makes perfect sense too.
If it can drive a Siglent AWG that the customer already owns, there should be no extra license to use it. Siglent should charge only for the AWG Hardware. It is a really bad marketing decision if they are charging for the software on the scope if it is driving a Siglent AWG. If it is to drive a non-Siglent AWG, maybe they can charge for it.
#### tautech
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #379 on: November 29, 2017, 09:11:24 pm »
Same principle for the AWG, so why buy the single channel USB AWG that BTW has a limited output range (p-p) if you already have a standalone Siglent AWG The literature indicates it can control all existing Siglent AWG's, SDG1032X works fine with it, Bode plots and all.
Yes 2 parts for this option makes perfect sense too.
If it can drive a Siglent AWG that the customer already owns, there should be no extra license to use it. Siglent should charge only for the AWG Hardware. It is a really bad marketing decision if they are charging for the software on the scope if it is driving a Siglent AWG.
Good point.
Let's see how this develops, maybe that will be revised.
Quote
If it is to drive a non-Siglent AWG, maybe they can charge for it.
Maybe ?
It's very unlikely command protocols will work with other brands.
When doing Bode plots the AWG is swept through many frequencies/second so commands must be correct.
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#### IAmBack
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #380 on: November 29, 2017, 10:37:12 pm »
a very nice thing keysight 3000x can do compared to scopes in simillar and lower class is that it can decode CAN and apply a dbc file to the decoded data (so ID 0xABCD will read as "Engine ECU #1" for example)
can this siglent or any siglent do that? makes it a lot easier to interpret data before going to a canbus analyzer... (if none can, please appropriate people, take note..)
by the way i was looking at simone's video
liking what i'm seeing so far..
It'd be nice to look at some high speed SPI and see how good/bad is it when reducing the timebase. I'd be happy to test it myself or bring a board to test but i have no reason to come to bologna before the new year, i'm busy all weekends... (well i'll probably be there at new year's but no work, all play )
Please feel free to come to visit us!
Could You please show us, how 100M and 200M units display the same signal (eg. 25/50/75M square wave)?
I'm thinking about one of these, but I'm not sure how much 200M in reality differs from 100M...
#### hexpope
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #381 on: November 30, 2017, 12:08:47 am »
I just ordered one from the EU, I am wondering and can't figure it out. Can you have a gen function on one of the outputs with a software license only or do you have to buy the license and the hardware module to have wave gen?
#### tautech
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #382 on: November 30, 2017, 12:35:33 am »
I just ordered one from the EU, I am wondering and can't figure it out. Can you have a gen function on one of the outputs with a software license only or do you have to buy the license and the hardware module to have wave gen?
There is NO inbuilt AWG. The optional 25 MHz external AWG is USB powered and controlled by the scope. For this you need buy the HW and SW.
You can see it on this link near the bottom of the page on the right.
http://www.siglenteu.com/pdxx.aspx?id=2771&T=2&tid=1
So if you already have a Siglent SDG**** AWG then you would only need to buy the AWG SW option.
Edit.
Above last sentence is true for Bode plot usage only, not general Siglent AWG control usage.
« Last Edit: November 30, 2017, 04:05:26 am by tautech »
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#### tautech
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #383 on: November 30, 2017, 01:41:43 am »
a very nice thing keysight 3000x can do compared to scopes in simillar and lower class is that it can decode CAN and apply a dbc file to the decoded data (so ID 0xABCD will read as "Engine ECU #1" for example)
can this siglent or any siglent do that? makes it a lot easier to interpret data before going to a canbus analyzer... (if none can, please appropriate people, take note..)
by the way i was looking at simone's video
liking what i'm seeing so far..
It'd be nice to look at some high speed SPI and see how good/bad is it when reducing the timebase. I'd be happy to test it myself or bring a board to test but i have no reason to come to bologna before the new year, i'm busy all weekends... (well i'll probably be there at new year's but no work, all play )
Please feel free to come to visit us!
Could You please show us, how 100M and 200M units display the same signal (eg. 25/50/75M square wave)?
I'm thinking about one of these, but I'm not sure how much 200M in reality differs from 100M...
Above is very poor connection techniques to even attempt to show signal fidelity.
Some lessons can be learnt from this thread on the pitfalls of displaying square waves.
https://www.eevblog.com/forum/testgear/show-us-your-square-wave/
For reference a screenshot from the above video.
Compare with:
SDG1032X, 20 MHz, cheap Siglent BNC cable and terminated into also cheapish Pintek 50 2GHz feedthrough.
Scope SDS1104X-E 100 MHz
I have always used Tek 1x 50 BNC feedthrough but a new Pintek one bought recently offers less square wave attenuation so is now my first choice.
http://www.pintek.com.tw/product_detail/landersound/index.php?Product_SN=19282&PHPSESSID=344qv7ar5g7s19evvgtktt76l4&Company_SN=6002&Product_Site_Classify_SN=17075
« Last Edit: November 30, 2017, 07:27:08 pm by tautech »
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #384 on: November 30, 2017, 02:34:21 am »
So if you already have a Siglent SDG**** AWG then you would only need to buy the AWG SW option.
Edit.
Above last sentence is true for Bode plot usage only, not general Siglent AWG control usage.
That's really disappointing to have to purchase the software license even if you already have a Siglent AWG, those are not cheap. I see the license price is $109, seems like a heavy punishment for existing customers. Edit: This may be incorrect. « Last Edit: November 30, 2017, 03:50:59 am by alreadystarted » #### tautech • Super Contributor • Posts: 15963 • Country: • Taupaki Technologies Ltd. NZ Siglent Distributor ##### Re: Siglent SDS1204X-E released for domestic markets in China « Reply #385 on: November 30, 2017, 03:13:31 am » So if you already have a Siglent SDG**** AWG then you would only need to buy the AWG SW option. Edit. Above last sentence is true for Bode plot usage only, not general Siglent AWG control usage. That's really disappointing to have to purchase the software license even if you already have a Siglent AWG, those are not cheap. I see the license price is$109, seems like a heavy punishment for existing customers.
I mentioned I can't test this to be sure until new stock arrives.
Siglent sent me this:
1. Siglent SDG**** AWG don't need to buy the SW option.
2. SDS1004X-E also can't control the SDG*** AWG.
Only the SAG1021 hardware module can be controlled by SDS1004X-E.
1. I take this to mean any Siglent SDG**** can be used for Bode plot.
2. DSO can only control SDG**** for Bode plot usage.
So it may seem that the AWG SW option is only needed for general AWG usage control of the SAG1021 HW.
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #386 on: November 30, 2017, 03:56:53 am »
I mentioned I can't test this to be sure until new stock arrives.
Siglent sent me this:
1. Siglent SDG**** AWG don't need to buy the SW option.
2. SDS1004X-E also can't control the SDG*** AWG.
Only the SAG1021 hardware module can be controlled by SDS1004X-E.
1. I take this to mean any Siglent SDG**** can be used for Bode plot.
2. DSO can only control SDG**** for Bode plot usage.
So it may seem that the AWG SW option is only needed for general AWG usage control of the SAG1021 HW.
That would be completely reasonable. There’s not really a need to control a separate box, as long as the Bode plot function is supported. Please confirm when you can for us.
#### rf-loop
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #387 on: November 30, 2017, 07:02:10 am »
Time ago somewhere here was discussed about vertical offset setting when change V/div setting when channel mode is DC.
It was really frustrating to turn Vertical position (offset) if example look some ripple etc over DC and need change V/div for look more "close" this ripple or what ever riding on DC and need also watch DC level or very low frequencies what need mostly that channel is DC coupled.
Now in SDS1kX-E 4-chan have solution for this.
Lets hope they implement this feature also to 2 channel models FW.
Is it right place that this selection is under Utility menu is other question. So or so, but this feature is good to have.
There is available now fixed offset voltage setting. User can select fixed Voltage offset or this Fixed "position" offset what have been there previously as fixed default).
Fixed voltage offset means that it keep offset voltage constant when you change V/div.
Example (in image) there is small signal (or ripple or what ever) riding over 1.5V DC.
I have set 1.5V fixed vertical offset.
First image just example with 100mV/div (ans also slow timebase, nite it can still measure rise time with 1ns resolution)
Then next image I want change V/div for look better this "ripple". I turn it to 10mV/div
I do not need now turn nearly endless this vertical position adjustment when I change V/div. I can change to what ever V/div and offset is fixed 1.5V. (in this image I have also changed time base but this is not relevant for this offset feature.)
Previously it was some times really frustrating to use time for turning this vert, position all time when change V/div.
There is also available fixed delay time setting but this is other story.
« Last Edit: November 30, 2017, 07:05:02 am by rf-loop »
If practice and theory is not equal it tells that used application of theory is wrong or the theory itself is wrong.
It is much easier to think an apple fall to the ground than to think that the earth and the apple will begin to move toward each other and collide.
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#### Performa01
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #388 on: November 30, 2017, 08:25:19 am »
Is it right place that this selection is under Utility menu is other question. So or so, but this feature is good to have.
This is only a first shot, not the final solution, which will go even further. Stay tuned
#### rf-loop
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #389 on: November 30, 2017, 10:54:27 am »
Is it right place that this selection is under Utility menu is other question. So or so, but this feature is good to have.
This is only a first shot, not the final solution, which will go even further. Stay tuned
Yes.
One thing what I hope is that Siglent develop zoomed display more nice for eyes.
Least when I use horizontal zoomed window my priority is looking this zoomed window.
It feels bit annoying that display is vertically divided 1:1. I feel better if zoomed window height is more than unzoomed upper part. Unzoomed upper part is only for select what part of whole waveform I want zoom. But for signal details I look zoomed bottom part. It is much better if this part get more height on display. Example 1/4 for unzoomed and 3/4 for zoomed. Why user use zoom. Because he want see details. So, who do not show details as good as can.
If practice and theory is not equal it tells that used application of theory is wrong or the theory itself is wrong.
It is much easier to think an apple fall to the ground than to think that the earth and the apple will begin to move toward each other and collide.
#### kahe40
• Contributor
• Posts: 16
• Country:
##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #390 on: November 30, 2017, 11:06:23 am »
Could You please show us, how 100M and 200M units display the same signal (eg. 25/50/75M square wave)?
I'm thinking about one of these, but I'm not sure how much 200M in reality differs from 100M...
the first difference I see, are 357€ ... (WTF, Rigol1054 sells for 379€, the entire scope)
prices from Batronix are: 1202X-E = 427€ 1204X-E = 784€ (VAT and shipping included)
so 357€ more to spend for 2CH more and another ADC, not bad Siglent!
The 1104X-E is 510€, so 274€ more only for the 200M Bw?
I hope it can be hacked, otherwise I have to wait for the new Rigols.
They should bring the 1054 to the next level, 2GSa one CH and each CH with 500MSa?
Would be a DS2072A with 4CH for roundabout 1000€ - maybe only a dream?
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#### Performa01
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• Posts: 815
• Country:
##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #391 on: November 30, 2017, 11:51:22 am »
One thing what I hope is that Siglent develop zoomed display more nice for eyes.
Least when I use horizontal zoomed window my priority is looking this zoomed window.
It feels bit annoying that display is vertically divided 1:1. I feel better if zoomed window height is more than unzoomed upper part. Unzoomed upper part is only for select what part of whole waveform I want zoom. But for signal details I look zoomed bottom part. It is much better if this part get more height on display. Example 1/4 for unzoomed and 3/4 for zoomed. Why user use zoom. Because he want see details. So, who do not show details as good as can.
I agree, yet it might not be that simple a decision.
Full display means 1 ADC LSB = 2 screen pixels.
Split display (50 + 50% as it is now) means 1 ADC LSB = 1 screen pixel.
Split display (25 + 75%) means ...
Optical appearance of the trace rendition as well as performance might suffer.
#### pascal_sweden
• Super Contributor
• Posts: 1404
• Country:
##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #392 on: November 30, 2017, 06:12:10 pm »
Cool to hear that it works with an existing AWG! I have access to an SDG1025
Still not entirely clear whether I would need a software license option or not, and for which functionality.
And why does Siglent write "SDS1004X-E can't control the SDG**** AWG"? If the scope can't control the AWG, how can it generate a Bode plot?
The scope should be able to control the AWG in order to generate a Bode plot.
Or do they mean that it can't control *ALL* parameters of the AWG, and just a minimal set of parameters to generate a Bode plot?
What would that minimal set be? Frequency/Amplitude/Phase parameters applied on a standard Sine wave?
« Last Edit: November 30, 2017, 06:38:16 pm by pascal_sweden »
#### simone.pignatti
• Frequent Contributor
• Posts: 325
• Country:
##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #393 on: November 30, 2017, 06:47:06 pm »
So if you already have a Siglent SDG**** AWG then you would only need to buy the AWG SW option.
Edit.
Above last sentence is true for Bode plot usage only, not general Siglent AWG control usage.
That's really disappointing to have to purchase the software license even if you already have a Siglent AWG, those are not cheap. I see the license price is $109, seems like a heavy punishment for existing customers. Edit: This may be incorrect. No need of FG software option for Bode Plot Technical Support #### Siglent America • Regular Contributor • Posts: 221 • Country: ##### Re: Siglent SDS1204X-E released for domestic markets in China « Reply #394 on: November 30, 2017, 09:38:20 pm » So if you already have a Siglent SDG**** AWG then you would only need to buy the AWG SW option. Edit. Above last sentence is true for Bode plot usage only, not general Siglent AWG control usage. That's really disappointing to have to purchase the software license even if you already have a Siglent AWG, those are not cheap. I see the license price is$109, seems like a heavy punishment for existing customers.
Edit: This may be incorrect.
No need of FG software option for Bode Plot
You are correct.
You can use an external Siglent SDG to make your Bode Plots without having to use the software (FW) option. The SDG is connected to the SDS1XX4X-E scope via USB and SCPI commands are sent to it from the scope.
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#### gray
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #395 on: December 01, 2017, 12:54:00 am »
I have been watching development around new Siglent scopes for some time. Considering SDS1104X-E.
Have a question. The WiFi adapter for 4-channel scopes on Siglent US site http://www.siglentamerica.com/prodcut-detailxx.aspx?id=5109&tid=1&T=2 is listed as TL_WN725N. Google resolves it as TP-Link N150 Wireless Nano USB Adapter (TL-WN725N) listed on Amazon for $7.99. Can someone with the scope check if this TP-Link in fact works? Does WiFi option require license fees? « Last Edit: December 01, 2017, 12:56:51 am by gray » #### tautech • Super Contributor • Posts: 15963 • Country: • Taupaki Technologies Ltd. NZ Siglent Distributor ##### Re: Siglent SDS1204X-E released for domestic markets in China « Reply #396 on: December 01, 2017, 02:01:48 am » I have been watching development around new Siglent scopes for some time. Considering SDS1104X-E. Have a question. The WiFi adapter for 4-channel scopes on Siglent US site http://www.siglentamerica.com/prodcut-detailxx.aspx?id=5109&tid=1&T=2 is listed as TL_WN725N. Google resolves it as TP-Link N150 Wireless Nano USB Adapter (TL-WN725N) listed on Amazon for$7.99. Can someone with the scope check if this TP-Link in fact works? Does WiFi option require license fees?
Welcome to the forum.
Yes and yes, but mine does have a permanent WiFi option. It should work with the option Trial usages until there are none left. You can purchase any option later from your dealer if/when required.
I've only tried the gold version as was recommended by my contacts at Siglent and it was plug and play, no problems at all.
My experience was outlined in reply #352
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#### gray
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #397 on: December 01, 2017, 02:32:14 am »
So, let me get it straight. $49 paid for WiFi adapter buys an adapter and a license key? On top of that, one needs to buy a software for$69 (prices taken from Saelig site)? Somewhat steep.
#### tautech
• Super Contributor
• Posts: 15963
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• Taupaki Technologies Ltd. NZ Siglent Distributor
##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #398 on: December 01, 2017, 02:50:12 am »
So, let me get it straight. $49 paid for WiFi adapter buys an adapter and a license key? No, just the WiFi adapter/dongle at Siglent retail price. Quote On top of that, one needs to buy a software for$69 (prices taken from Saelig site)? Somewhat steep.
You just need buy the SW (license key) IF you can source the dongle cheaper elsewhere.
But not all will need WiFi connectivity as the LAN port accomplishes the same functionality.
As time passes other WiFi dongles will be tried and a list of 'working' ones made.
The silver (not gold) version of TL-WN725N may work fine too, we just don't know yet.
For quick and easy small size (Kb's) screenshots, a USB stick is still the most convenient.
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#### gray
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##### Re: Siglent SDS1204X-E released for domestic markets in China
« Reply #399 on: December 01, 2017, 03:08:45 am »
So, let me get it straight. $49 paid for WiFi adapter buys an adapter and a license key? No, just the WiFi adapter/dongle at Siglent retail price. OK, this makes life a little easier.$8 is better than \$49
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http://math.stackexchange.com/questions/145120/why-are-the-gegenbauer-polynomials-called-ultraspherical | # Why are the Gegenbauer polynomials called “ultraspherical”?
There has to be a good reason why the Gegenbauer polynomials were also named "ultraspherical" polynomials. I am aware that when $\alpha=\frac{1}{2}$, the Gegenbauer polynomials reduce to the Legendre polynomials, and the Legendre polynomials are used in defining Spherical harmonics. But that is as far as I know how to take that reasoning.
Is there a visualization of these polynomials that fits on a sphere? What is an ultrasphere anyway?
-
I am aware that when $\alpha=\frac12$, the Gegenbauer polynomials reduce to the Legendre polynomials, and the Legendre polynomials are used in defining spherical harmonics.
You pretty much nailed it. From here:
In the theory of hyperspherical harmonics, Gegenbauer polynomials play a role which is analogous to the role played by Legendre polynomials in the theory of the familiar three-dimensional spherical harmonics.
As a compressed version of the discussion in the book (look there for more details), the ultraspherical/hyperspherical harmonics involve Gegenbauer polynomials of the form $C_n^{\frac{d}{2}-1}(x)$, where $d$ is the dimension of the hyperspherical harmonics being considered. For the usual case of $d=3$, we have $C_n^{\frac{3}{2}-1}(x)=P_n(x)$.
-
Legendre polynomials arise when solving 3D Laplace's equation in spherical coordinates by separation of variables, i.e. $f(x,y,z) = f_1(r) Y(\theta, \phi)$.
Legendre polynomials appear in spherical harmonics, specifically for $\ell \in \mathbb{Z}_{\geqslant 0}$ and $m\in \mathbb{Z}$, such that $-\ell \leqslant m \leqslant \ell$: $$Y_{\ell,m}(\theta, \phi) = \sqrt{\frac{2 \ell+1}{4 \pi}} \sqrt{\frac{(\ell-m)!}{(\ell+m)!}} P_\ell^m(\cos \theta) \mathrm{e}^{i m \phi}$$
Solving Laplace's equation in $\mathbb{R}^d$ in hyper-spherical coordinates (in older literature a.k.a ultra-spherical coordinates) by separation of variables, gives rise to ultraspherical polynomials.
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9575398564338684, "perplexity": 323.57344977108846}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500829754.11/warc/CC-MAIN-20140820021349-00309-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/107753/geodesics-and-paths-for-non-unit-quaternions | # Geodesics and paths for non-unit quaternions
Given two unit quaternions $\mathbf{q}_1$ and $\mathbf{q}_2$ $\in \mathbb{H}_{1}$, it is well known that the unique geodesic parametrized by the length, $t \mapsto \gamma(t)$, joining the two quaternions is
$\gamma(t) = \mathbf{q}_{1}\left(\mathbf{q}_{1}^{-1}\mathbf{q}_{2}\right)^{t}$
It corresponds to the geodesic in $\mathbb{S}^3$. The corresponding geodesic distance can be written using the logarithm of quaternions
$d(\mathbf{q}_1 , \mathbf{q}_2 )=||\log\left( \mathbf{q}_{1}^{-1} \mathbf{q}_{2} \right) ||$
Let now us consider that we are dealing with general quaternions in $\mathbb{H}$, of type $\mathbf{q}_i = |\mathbf{q}_i |U\mathbf{q}_i$, where $\mathbf{q}_i$ is the norm and $U\mathbf{q}_i$ the corresponding versor. Ìf we consider now the same expression than above for a parametrized path between $|\mathbf{q}_1 |U\mathbf{q}_1$ and $|\mathbf{q}_2 |U\mathbf{q}_2$, i.e.,
$\gamma(t) = |\mathbf{q}_1 |^{1-t} |\mathbf{q}_2 |^t U\mathbf{q}_{1}\left(U\mathbf{q}_{1}^{*}U\mathbf{q}_{2}\right)^{t}$
Thus, a path defined by the product of a geodesic in $\mathbb{R}^+$ (weighted geometric mean of the norms) and a geodesic in $\mathbb{S}^3$. The length of the path involves also a decoupling between both manifolds, i.e.,
${\cal l}(\mathbf{q}_1,\mathbf{q}_1 )^2 =$ $|\log(|\mathbf{q}_2|) - \log(|\mathbf{q}_1|)|^2 + ||\log\left( U\mathbf{q}_{1}^{*} U\mathbf{q}_{2} \right) ||^2$
Curved paths $\gamma(t)$ are of course longer than the straight lines in $\mathbb{R}^4$ and therefore this is not the minimal geodesic of $\mathbb{H}$
Questions:
• Is the path $\gamma(t)$ a geodesic of the embedding of $\mathbb{H}$ in $\mathbb{R}^+ \times \mathbb{S}^3$?
• What happens in particular if $|\mathbf{q}_i| \leq 1$ (i.e., quaternions lying inside the sphere $\mathbb{S}^3$)
• Is the corresponding line element given by $ds^2 = (d\log(|\mathbf{q}_{i}|))^2 + (dU\mathbf{q}_{i})^2$ ?
• More generally, what are the strucutre of the manifold $\mathbb{R}^+ \times \mathbb{S}^3$ with this kind of metric?... compact, completeness, bounds of curvature, etc.
-
The metric you have written down is the standard bi-invariant metric on the Lie group of nonzero quaternions. I.e., it is the metric such that the left-invariant 1-form $\omega = \mathbf{q}^{-1}\ d\mathbf{q}$ with values in $T_{\mathbf{1}}\mathbb{H}\simeq\mathbb{H}$ is an isometry at every point. I.e., for every $\mathbf{p}$ a nonzero quaternion, $\omega_{\mathbf{p}}:T_{\mathbf{p}}\mathbb{H}\to \mathbb{H}$ induces an isometry between $T_{\mathbf{p}}\mathbb{H}$ under this metric with $\mathbb{H}$ given the standard quaternion norm.
This metric (which is complete and homogeneous) is a product metric and the Riemannian manifold is isometric to $\mathbb{R}\times\mathbb{S}^3$. Thus, it is not compact, it is complete, the sectional curvature everywhere is bounded by $1$, etc. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9898565411567688, "perplexity": 237.8640857118988}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042991951.97/warc/CC-MAIN-20150728002311-00145-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://infoscience.epfl.ch/record/257798?ln=en | ## Synthesis, structural characterisation and nuclear magnetic resonance study of [Ru6C(CO)15(µ3-η1:η2:η2-C16H16-µ-O)]: an intermediate in the formation of [Ru6C(CO)14(µ3-η2:η2:η2-C16H16)]
Published in:
Journal of the Chemical Society, Dalton Transactions, 24, 4113-4119
Year:
1995
Other identifiers:
Laboratories: | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9715893268585205, "perplexity": 22504.158057512013}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195523840.34/warc/CC-MAIN-20190715175205-20190715201205-00256.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-2x-2-7x-9-0-algebraically#513610 | Algebra
Topics
# How do you solve 2x^2+7x+9=0 algebraically?
Nov 30, 2017
In fraction form:
$\setminus \rightarrow x = \setminus \frac{i \setminus \sqrt{23}}{4} - \setminus \frac{7}{4}$
Simplified form:
$\setminus \rightarrow x \setminus \approx - 1.75 \setminus \pm 1.19895788 i$
#### Explanation:
We’ll solve this two ways: by completing the square and using the quadratic formula. Here’s the first way:
$2 {x}^{2} + 7 x + 9 = 0$
First divide everything by $2$, since $a$ cannot have a coefficient:
$\setminus \rightarrow {x}^{2} + \setminus \frac{7}{2} x + \setminus \frac{9}{2} = 0$
Now, move $c$ to the RHS:
$\setminus \rightarrow {x}^{2} + \setminus \frac{7}{2} x = - \setminus \frac{9}{2}$
Now add ${\left(\setminus \frac{b}{2}\right)}^{2}$ to both sides. Here, $b = 7$.
$\setminus \rightarrow {x}^{2} + \setminus \frac{7}{2} x + \setminus \frac{49}{16} = \setminus \frac{49}{16} - \setminus \frac{9}{2}$
Simplify the RHS:
$\setminus \rightarrow {x}^{2} + \setminus \frac{7}{2} x + \setminus \frac{49}{16} = - \setminus \frac{23}{16}$
Factor the LHS into ${\left(x + \setminus \frac{b}{2}\right)}^{2}$:
$\setminus \rightarrow {\left(x + \setminus \frac{\setminus \frac{7}{2}}{2}\right)}^{2} = - \setminus \frac{23}{16}$
$\setminus \rightarrow {\left(x + \setminus \frac{7}{4}\right)}^{2} = - \setminus \frac{23}{16}$
Take the square root of both sides:
$\setminus \rightarrow x + \setminus \frac{7}{4} = \setminus \sqrt{- \setminus \frac{23}{16}}$
Isolate $x$:
$\setminus \rightarrow x = \setminus \sqrt{- \setminus \frac{23}{16}} - \setminus \frac{7}{4}$
$\setminus \rightarrow x = i \setminus \sqrt{\setminus \frac{23}{16}} - \setminus \frac{7}{4}$
$\setminus \rightarrow x = i \setminus \frac{\setminus \sqrt{23}}{4} - \setminus \frac{7}{4}$
$\setminus \rightarrow x \setminus \approx - 1.75 \setminus \pm 1.19895788 i$
Here’s the second way, using the quadratic formula:
$2 {x}^{2} + 7 x + 9 = 0$
First, we need to identify $a$, $b$, and $c$:
$a = 2$
$b = 7$
$c = 9$
Now, plug them into the formula:
$x = \setminus \frac{- b \setminus \pm \setminus \sqrt{{b}^{2} - 4 a c}}{2 a}$
$\setminus \rightarrow x = \setminus \frac{- 7 \setminus \pm \setminus \sqrt{{7}^{2} - 4 \left(2\right) \left(9\right)}}{2 \left(2\right)}$
$\setminus \rightarrow x = \setminus \frac{- 7 \setminus \pm \setminus \sqrt{49 - 72}}{4}$
$\setminus \rightarrow x = \setminus \frac{- 7 \setminus \pm \setminus \sqrt{- 23}}{4}$
$\setminus \rightarrow x = \setminus \frac{- 7 \setminus \pm i \setminus \sqrt{23}}{4}$
Rearranging yields:
$\setminus \rightarrow x = \setminus \frac{i \setminus \sqrt{23}}{4} - \setminus \frac{7}{4}$
$\setminus \rightarrow x \setminus \approx - 1.75 \setminus \pm 1.19895788 i$
It’s the same answer we got by completing the square, so we know the answer is correct.
##### Impact of this question
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http://www.ats.ucla.edu/stat/r/faq/missing.htm | ### R FAQ How does R handle missing values?
Version info: Code for this page was tested in R Under development (unstable) (2012-02-22 r58461) On: 2012-03-28 With: knitr 0.4
Like other statistical software packages, R is capable of handling missing values. However, to those accustomed to working with missing values in other packages, the way in which R handles missing values may require a shift in thinking. On this page, we will present first the basics of how missing values are represented in R. Next, for those coming from SAS, SPSS, and/or Stata, we will outline some of the differences between missing values in R and missing values elsewhere. Finally, we will introduce some of the tools for working with missing values in R, both in data management and analysis.
#### Very basics
Missing data in R appears as NA. NA is not a string or a numeric value, but an indicator of missingness. We can create vectors with missing values.
x1 <- c(1, 4, 3, NA, 7)
x2 <- c("a", "B", NA, "NA")
NA is the one of the few non-numbers that we could include in x1 without generating an error (and the other exceptions are letters representing numbers or numeric ideas like infinity). In x2, the third value is missing while the fourth value is the character string "NA". To see which values in each of these vectors R recognizes as missing, we can use the is.na function. It will return a TRUE/FALSE vector with as any elements as the vector we provide.
is.na(x1)
## [1] FALSE FALSE FALSE TRUE FALSE
is.na(x2)
## [1] FALSE FALSE TRUE FALSE
We can see that R distinguishes between the NA and "NA" in x2--NA is seen as a missing value, "NA" is not.
#### Differences from other packages
• NA cannot be used in comparisons: In other packages, a "missing" value is assigned an extreme numeric value--either very high or very low. As a result, values coded as missing can 1) be compared to other values and 2) other values can be compared to missing. In the example SAS code below, we compare the values in y to 0 and to the missing symbol and see that both comparisons are valid (and that the missing symbol is valued at less than zero).
• data test;
input x y;
datalines;
2 .
3 4
5 1
6 0
;
data test; set test;
lowy = (y < 0);
missy = (y = .);
run;
proc print data = test; run;
Obs x y lowy missy
1 2 . 1 1
2 3 4 0 0
3 5 1 0 0
4 6 0 0 0
We can try the equivalent in R.
x1 < 0
## [1] FALSE FALSE FALSE NA FALSE
x1 == NA
## [1] NA NA NA NA NA
Our missing value cannot be compared to 0 and none of our values can be compared to NA because NA is not assigned a value--it simply is or it isn't.
• NA is used for all kinds of missing data: In other packages, missing strings and missing numbers might be represented differently--empty quotations for strings, periods for numbers. In R, NA represents all types of missing data. We saw a small example of this in x1 and x2. x1 is a "numeric" object and x2 is a "character" object.
• Non-NA values cannot be interpreted as missing: Other packages allow you to designate values as "system missing" so that these values will be interpreted in the analysis as missing. In R, you would need to explicitly change these values to NA. The is.na function can also be used to make such a change:
• is.na(x1) <- which(x1 == 7)
x1
## [1] 1 4 3 NA NA
#### NA options in R
We have introduced is.na as a tool for both finding and creating missing values. It is one of several functions built around NA. Most of the other functions for NA are options for na.action.
Just as there are default settings for functions, there are similar underlying defaults for R as a software. You can view these current settings with options(). One of these is the "na.action" that describes how missing values should be treated. The possible na.action settings within R include:
• na.omit and na.exclude: returns the object with observations removed if they contain any missing values; differences between omitting and excluding NAs can be seen in some prediction and residual functions
• na.pass: returns the object unchanged
• na.fail: returns the object only if it contains no missing values
To see the na.action currently in in options, use getOption("na.action"). We can create a data frame with missing values and see how it is treated with each of the above.
(g <- as.data.frame(matrix(c(1:5, NA), ncol = 2)))
## V1 V2
## 1 1 4
## 2 2 5
## 3 3 NA
na.omit(g)
## V1 V2
## 1 1 4
## 2 2 5
na.exclude(g)
## V1 V2
## 1 1 4
## 2 2 5
na.fail(g)
## Error: missing values in object
na.pass(g)
## V1 V2
## 1 1 4
## 2 2 5
## 3 3 NA
#### Missing values in analysis
In some R functions, one of the arguments the user can provide is the na.action. For example, if you look at the help for the lm command, you can see that na.action is one of the listed arguments. By default, it will use the na.action specified in the R options. If you wish to use a different na.action for the regression, you can indicate the action in the lm command.
Two common options with lm are the default, na.omit and na.exclude which does not use the missing values, but maintains their position for the residuals and fitted values.
## use the famous anscombe data and set a few to NA
anscombe <- within(anscombe, {
y1[1:3] <- NA
})
anscombe # view
## x1 x2 x3 x4 y1 y2 y3 y4
## 1 10 10 10 8 NA 9.14 7.46 6.58
## 2 8 8 8 8 NA 8.14 6.77 5.76
## 3 13 13 13 8 NA 8.74 12.74 7.71
## 4 9 9 9 8 8.81 8.77 7.11 8.84
## 5 11 11 11 8 8.33 9.26 7.81 8.47
## 6 14 14 14 8 9.96 8.10 8.84 7.04
## 7 6 6 6 8 7.24 6.13 6.08 5.25
## 8 4 4 4 19 4.26 3.10 5.39 12.50
## 9 12 12 12 8 10.84 9.13 8.15 5.56
## 10 7 7 7 8 4.82 7.26 6.42 7.91
## 11 5 5 5 8 5.68 4.74 5.73 6.89
model.omit <- lm(y2 ~ y1, data = anscombe, na.action = na.omit)
model.exclude <- lm(y2 ~ y1, data = anscombe,
na.action = na.exclude)
## compare effects on residuals
resid(model.omit)
## 4 5 6 7 8 9 10 11
## 0.727 1.575 -0.799 -0.743 -1.553 -0.425 2.190 -0.971
resid(model.exclude)
## 1 2 3 4 5 6 7 8 9 10
## NA NA NA 0.727 1.575 -0.799 -0.743 -1.553 -0.425 2.190
## 11
## -0.971
## compare effects on fitted (predicted) values
fitted(model.omit)
## 4 5 6 7 8 9 10 11
## 8.04 7.69 8.90 6.87 4.65 9.55 5.07 5.71
fitted(model.exclude)
## 1 2 3 4 5 6 7 8 9 10 11
## NA NA NA 8.04 7.69 8.90 6.87 4.65 9.55 5.07 5.71
Using na.exclude pads the residuals and fitted values with NAs where there were missing values. Other functions do not use the na.action, but instead have a different argument (with some default) for how they will handle missing values. For example, the mean command will, by default, return NA if there are any NAs in the passed object.
mean(x1)
## [1] NA
If you wish to calculate the mean of the non-missing values in the passed object, you can indicate this in the na.rm argument (which is, by default, set to FALSE).
mean(x1, na.rm = TRUE)
## [1] 2.67
Two common commands used in data management and exploration are summary and table. The summary command (when used with numeric vectors) returns the number of NAs in a vector, but the table command ignores NAs by default.
summary(x1)
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 1.00 2.00 3.00 2.67 3.50 4.00 2
table(x1)
## x1
## 1 3 4
## 1 1 1
To see NA among the table output, you can indicate "ifany" or "always" in the useNA argument. The first will show NA in the output only if there is some missing data in the object. The second will include NA in the output regardless.
table(x1, useNA = "ifany")
## x1
## 1 3 4
## 1 1 1 2
table(1:3, useNA = "always")
##
## 1 2 3
## 1 1 1 0
Sorting data containing missing values in R is again different from other packages because NA cannot be compared to other values. By default, sort removes any NA values and can therefore change the length of a vector.
(x1s <- sort(x1))
## [1] 1 3 4
length(x1s)
## [1] 3
The user can specify if NA should be last or first in a sorted order by indicating TRUE or FALSE for the na.last argument.
sort(x1, na.last = TRUE)
## [1] 1 3 4 NA NA
No matter the goal of your R code, it is wise to both investigate missing values in your data and use the help files for all functions you use. You should be either aware of and comfortable with the default treatments of missing values or specifying the treatment of missing values you want for your analysis.
The content of this web site should not be construed as an endorsement of any particular web site, book, or software product by the University of California. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4205830693244934, "perplexity": 1738.5635895565106}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119646351.12/warc/CC-MAIN-20141024030046-00045-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://quickmath.com/webMathematica3/quickmath/numbers/percentages/basic.jsp | Algebra
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#### Numbers : Percentages
Enter the value(s) for the required question and click the adjacent Go button.
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Tutors | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8923810124397278, "perplexity": 2481.697758940738}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510267876.49/warc/CC-MAIN-20140728011747-00201-ip-10-146-231-18.ec2.internal.warc.gz"} |
http://clay6.com/qa/45063/three-charges-q-q-and-q-are-placed-as-shown-at-equal-distances-on-a-straigh | # Three charges – q. Q and – q are placed as shown at equal distances on a straight line. If the total potential energy of the system of three charges is zero. What is the ratio Q : q?
$(B) \frac{1}{4}$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8876146674156189, "perplexity": 266.7724491701536}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886104631.25/warc/CC-MAIN-20170818082911-20170818102911-00465.warc.gz"} |
https://www.deepdyve.com/lp/ou_press/high-dimensional-finite-elements-for-multiscale-maxwell-type-equations-labSJOLTE4 | # High-dimensional finite elements for multiscale Maxwell-type equations
High-dimensional finite elements for multiscale Maxwell-type equations Abstract We consider multiscale Maxwell-type equations in a domain $$D\subset\mathbb{R}^d$$ ($$d=2,3$$), which depend on $$n$$ microscopic scales. Using multiscale convergence, we derive the multiscale homogenized problem, which is posed in $$\mathbb{R}^{(n+1)d}$$. Solving it, we get all the necessary macroscopic and microscopic information. Sparse tensor product finite elements (FEs) are employed, using edge FEs. The method achieves a required level of accuracy with essentially an optimal number of degrees of freedom, which, apart from a multiplying logarithmic term, is equal to that for solving a problem in $$\mathbb{R}^d$$. Numerical correctors are constructed from the FE solutions. In the two-scale case, an explicit homogenization error is deduced. To get this error, the standard procedure in the homogenization literature requires the solution $$u_0$$ of the homogenized problem to belong to $$H^1({\rm curl\,},D)$$. However, in polygonal domains, $$u_0$$ belongs only to a weaker regularity space $$H^s({\rm curl\,},D)$$ for $$0<s<1$$. We derive a homogenization error estimate for this case. Though we prove the result for two-scale Maxwell-type equations, the approach works verbatim for elliptic and elasticity problems when the solution to the homogenized equation belongs to $$H^{1+s}(D)$$ (standard procedure requires $$H^2(D)$$ regularity). This homogenization error estimate is new in the literature. Thus, for two-scale problems, an explicit error for the numerical corrector is obtained; it is of the order of the sum of the homogenization error and the FE error. For the case of more than two scales, we construct a numerical corrector, albeit without a rate of convergence, as such a homogenization error is not available. Numerical experiments confirm the theoretical results. 1. Introduction We consider Maxwell-type equations that depend on $$n$$ separable microscopic scales in a domain $$D\in \mathbb{R}^d,$$ where $$d=2,3$$. The coefficients are assumed to be locally periodic with respect to each microscopic scale. We use the multiscale convergence of a bounded sequence in $$H({\rm curl\,},D)$$ to derive the multiscale homogenized equation, which contains all the necessary information. Solving it, we get the solution of the homogenized equation that describes the multiscale solution macroscopically and the scale interacting terms (the corrector terms) that encode the multiscale information. However, this equation is posed in high-dimensional product domains. It depends on $$n+1$$ variables in $$\mathbb{R}^d$$, one for each scale that the original multiscale problem depends on. The full tensor product finite element (FE) method requires a large number of degrees of freedom, and thus is prohibitively expensive. We develop the sparse tensor FE product approach, using edge FEs, for this multiscale homogenized Maxwell-type equation. The approach achieves accuracy essentially equal to that obtained by the full tensor product FEs but requires an essentially optimal level of complexity that is essentially equal to that for solving a problem in $$\mathbb{R}^d$$ only. Analytic homogenization for two-scale Maxwell-type equations is well developed. We mention the standard references Bensoussan et al. (1978), Sanchez-Palencia (1980) and Jikov et al. (1994). However, there has been little effort on numerical analysis of multiscale Maxwell-type equations. As for other multiscale problems, a direct numerical treatment needs a fine mesh which is at most of the order of the smallest scale, leading to a prohibitive level of complexity. The multiscale FE method (Hou & Wu, 1997; Efendiev & Hou, 2009) and the heterogeneous multiscale method (E & Engquist, 2003; Abdulle et al., 2012) are designed to overcome this difficulty but their applications to multiscale Maxwell-type equations have not been adequately studied. Solving cell problems to establish the homogenized equation and using the cell problems’ solutions to compute the correctors for two-scale Maxwell-type equations are performed in Zhang et al. (2010). However, as for other multiscale problems, this approach is rather expensive, especially when the coefficients are only locally periodic, as for each macroscopic point, several cell problems need to be solved. We contribute in this article a feasible general numerical method for locally periodic multiscale Maxwell-type problems. We employ the sparse tensor product FE approach developed by Hoang & Schwab (2004/05) for multiscale elliptic equations (see also Hoang, 2008; Harbrecht & Schwab, 2011; Xia & Hoang, 2014, 2015a,b). It achieves the required level of accuracy with an essentially optimal number of degrees of freedom. We note that sparse tensor edge FEs are considered in Hiptmair et al. (2013) in the context of computing the moments of the solutions to stochastic Maxwell-type problems. However, our setting is quite different, and does not require constructing the detail spaces for edge FEs. We only need the detail spaces for the nodal FEs that approximate functions in the Lebesgue spaces $$L^2$$. We then construct a numerical corrector for the solution of the original multiscale problem, using the FE solutions of the multiscale homogenized problem. In the case of two scales, we derive an explicit error estimate in terms of the homogenization error and the FE error. It is well known that for two-scale elliptic problems in a domain $$D$$, if the solution of the homogenized problem belongs to $$H^2(D)$$, and the solutions to the cell problems are sufficiently smooth, the homogenization error in the $$H^1(D)$$ norm is $${\mathcal O}(\varepsilon^{1/2}),$$ where $$\varepsilon$$ is the microscopic scale (Bensoussan et al., 1978; Jikov et al., 1994). For two-scale Maxwell-type equations, the $${\mathcal O}(\varepsilon^{1/2})$$ homogenization error in the $$H({\rm curl},D)$$ norm is obtained when the solution $$u_0$$ of the homogenized problem (4.7) belongs to $$H^1({\rm curl},D)$$. However, for polygonal domains that are of interest in FE discretization, $$u_0$$ generally belongs only to a weaker regularity space $$H^s({\rm curl\,},D)$$ for $$0<s<1$$ (see e.g., Hiptmair, 2002). For this case, we develop an approach to deriving a new homogenization error estimate. Though we present the result for Maxwell-type equations, the approach works verbatim for two-scale elliptic and elasticity problems when the solution to the homogenized problem is in $$H^{1+s}(D)$$. As far as we are aware, this is a new result in the homogenization theory and forms another main contribution of the article. For the case of more than two scales, an analytic homogenization error is not available. However, we can still derive a corrector from the FE solution of the multiscale homogenized problem, albeit without an explicit rate of convergence. This article is organized as follows. In the next section, we formulate the multiscale Maxwell-type equation. Homogenization of the multiscale Maxwell-type equation (2.4) is studied in Bensoussan et al. (1978) in the two-scale case, using two-scale asymptotic expansion. Here, we use the multiscale convergence method to study (2.4) in the general multiscale setting. We thus develop multiscale convergence for a bounded sequence in $$H({\rm curl\,},D)$$. Two-scale convergence for a bounded sequence in $$H({\rm curl\,},D)$$ is developed in Wellander & Kristensson (2003). Since we consider the general $$(n+1)$$-scale convergence and the limiting result that we use is in a slightly different form from that of Wellander & Kristensson (2003) in the two-scale case, so we present the proofs in full. FE approximations of the multiscale homogenized Maxwell-type problem are studied in Section 3. We prove the FE error estimates in cases of both full and sparse tensor product FE approximations. The errors are essentially equal (apart from a logarithmic multiplying factor), but the dimension of the sparse tensor product FE space is much lower than that of the full tensor product FE space and is essentially equal to that for solving a problem in $$\mathbb{R}^d$$ only. In Section 4, we construct numerical correctors for the solution to the original multiscale problem. For two-scale problems, we prove the general homogenization error estimate for the case where $$u_0$$ belongs to the weaker regularity space $$H^s({\rm curl\,},D),$$ where $$0<s<1$$. From that we deduce the error estimate for the numerical corrector, which is of the order of the sum of the homogenization error estimate and the FE error. For the case of more than two scales, we derive a numerical corrector but without a rate of convergence. In Section 5, we prove that the regularity required to get the FE error estimate for the sparse tensor product FEs and to get the homogenization error in the two-scale case is achievable. Section 6 contains numerical experiments that confirm our analysis. Finally, the two Appendices A and B contain the long proofs of some previous results: the proof of the homogenization error when $$u_0$$ belongs to a weaker regularity space is presented in Appendix A. Throughout the article, by $$\#$$ we denote the spaces of functions that are periodic with the period being the unit cube $$Y\subset \mathbb{R}^d$$. Repeated indices indicate summation. The notations $$\nabla$$ and $${\rm curl\,}$$ without indicating the variable explicitly denote the gradient and the $${\rm curl\,}$$ operator with respect to $$x$$ of a function of $$x$$ only, where $$\nabla_x$$ and $${\rm curl\,}_{\!x}$$ denote the partial gradient and partial $${\rm curl\,}$$ of a function depending on $$x$$ and also on other variables. We generally present the theoretical results for the three-dimensional case and mention the two-dimensional case only when it is necessary, as the two cases are largely similar. 2. Problem setting 2.1 Multiscale Maxwell-type problems Let $$D$$ be a domain in $$\mathbb{R}^d$$ ($$d=2,3$$). Let $$Y$$ be the unit cube in $$\mathbb{R}^d$$. By $$Y_1,\ldots,Y_n$$ we denote $$n$$ copies1 of $$Y$$. We denote by $${\bf Y}$$ the product set $$Y_1\times Y_2\times\cdots\times Y_n$$ and by $$\boldsymbol{y}\in{\bf Y}$$ the vector $$\boldsymbol{y}=(y_1,y_2,\ldots,y_n)$$. For each $$i=1,\ldots,n$$, we denote by $${\bf Y}_i$$ the set of vectors $$\boldsymbol{y}_i=(y_1,\ldots,y_i),$$ where $$y_j\in Y_j$$ for $$j=1,\ldots,i$$. For $$d=3$$, let $$a$$ and $$b$$ be functions with symmetric matrix values from $$D\times {\bf Y}$$ to $$\mathbb{R}^{d\times d}_{\rm sym}$$; $$a$$ and $$b$$ are continuous in $$D\times {\bf Y}$$ and are periodic with respect to each variable $$y_i$$ with the period being $$Y_i$$. We assume that for all $$x\in D$$ and $$\boldsymbol{y}\in{\bf Y}$$, and all $$\xi,\zeta\in \mathbb{R}^d$$, c∗|ξ|2≤aij(x,y)ξiξj, aij(x,y)ξiζj≤c∗|ξ||ζ|,c∗|ξ|2≤bij(x,y)ξiξj, bij(x,y)ξiζj≤c∗|ξ||ζ|, (2.1) where $$c_*$$ and $$c^*$$ are positive numbers; $$|\cdot|$$ denotes the Euclidean norm in $$\mathbb{R}^3$$. Let $$\varepsilon$$ be a small positive value, and $$\varepsilon_1,\ldots,\varepsilon_n$$ be $$n$$ functions of $$\varepsilon$$ that denote the $$n$$ microscopic scales that the problem depends on. We assume the following scale separation properties: for all $$i=1,\ldots,n-1$$, limε→0εi+1(ε)εi(ε)=0. (2.2) Without loss of generality, we assume that $$\varepsilon_1=\varepsilon$$. We define $$a^\varepsilon, b^\varepsilon: D\to\mathbb{R}^{d\times d}_{\rm sym}$$ as aε(x)=a(x,xε1,…,xεn), bε(x)=b(x,xε1,…,xεn). (2.3) Let W=H0(curl,D)={u∈L2(D)3, curlu∈L2(D)3, u×ν=0}, where $$\nu$$ denotes the outward normal vector on the boundary $$\partial D$$. Let $$f\in W'$$. We consider the problem curl(aε(x)curluε(x))+bε(x)uε(x)=f(x), (2.4) with the boundary condition $$u^{\varepsilon}\times \nu=0$$ on $$\partial D$$. We formulate this problem in the variational form as follows: find $$u^{\varepsilon}\in W$$ so that ∫D[aε(x)curluε(x)⋅curlϕ(x)+bε(x)uε(x)⋅ϕ(x)]dx=∫Df(x)⋅ϕ(x)dx (2.5) for all $$\phi\in W$$ (by $$\int_D\,f\cdot\phi\, {\rm d}x$$ we denote the duality pairing between $$W'$$ and $$W$$). The Lax–Milgram lemma guarantees the existence of a unique solution $$u^{\varepsilon}$$ that satisfies ‖uε‖W≤c‖f‖W′, (2.6) where the constant $$c$$ depends only on $$c_*$$ and $$c^*$$ in (2.1). For $$d=2$$, the matrix function $$b^\varepsilon:D\times{\bf Y}\to \mathbb{R}^{2\times 2}$$ is defined as above. As $${\rm curl\,}u^{\varepsilon}$$ is now a scalar function, $$a(x,\boldsymbol{y})$$ is a continuous function from $$D\times{\bf Y}$$ to $$\mathbb{R},$$ which is periodic with respect to each variable $$y_i$$ with the period being $$Y_i$$. In the place of (2.1), we have c∗≤a(x,y)≤c∗ ∀x∈D and y∈Y. The variational formulation in two dimensions becomes ∫D[aε(x)curluε(x)curlϕ(x)+bε(x)uε(x)⋅ϕ(x)]dx=∫Df(x)⋅ϕ(x)dx ∀ϕ∈W. (2.7) In the rest of the article, we present the results for the three-dimensional case and only mention the two-dimensional case when necessary; the results for two dimensions are similar. 2.2 Multiscale convergence We use multiscale convergence to derive the homogenized equation. We first recall the definition of multiscale convergence (see Nguetseng, 1989; Allaire, 1992; Allaire & Briane, 1996). Definition 2.1 A sequence of functions $$\{w^\varepsilon\}_\varepsilon\subset L^2(D)$$$$(n+1)$$-scale converges to a function $$w^0\in L^2(D\times {\bf Y})$$ if for all smooth functions $$\phi\in C^\infty(D\times{\bf Y}),$$ which are periodic with respect to $$y_i$$ with the period being $$Y_i$$ for $$i=1,\ldots,n$$, limε→0∫Dwε(x)ϕ(x,xε1,…,xεn)dx=∫D∫Yw0(x,y)ϕ(x,y)dydx. We have the following result. Proposition 2.2 From a bounded sequence in $$L^2(D),$$ we can extract an $$(n+1)$$-scale convergent subsequence. For a bounded sequence in $$H({\rm curl\,},D)$$, we have the following results on $$(n+1)$$-scale convergence. These results were first established in Wellander & Kristensson (2003) for the two-scale case. We present below the multiscale convergence of a bounded sequence in $$H({\rm curl\,},D),$$ which will be used to study the multiscale equations (2.5) and (2.7). By $$\tilde H_\#({\rm curl\,},Y_i)$$ we denote the equivalent classes of functions in $$H_\#({\rm curl\,},Y_i)$$ such that if $${\rm curl\,} v={\rm curl\,} w$$ we regard $$v=w$$ in $$\tilde H_\#({\rm curl\,},Y_i)$$. Proposition 2.3 Let $$\{w^\varepsilon\}_\varepsilon$$ be a bounded sequence in $$H({\rm curl\,},D)$$. There is a subsequence (not renumbered), a function $$w_0\in H({\rm curl\,},D)$$, $$n$$ functions $${\frak w_i}\in L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#(Y_i)/\mathbb{R})$$ such that wε⟶(n+1)−scalew0+∑i=1n∇yiwi. Further, there are $$n$$ functions $$w_i\in L^2(D\times Y_1\times\cdots\times Y_{i-1},\tilde H_\#({\rm curl\,},Y_i))$$ such that curlwε⟶(n+1)−scalecurlw0+∑i=1ncurlyiwi. Proof. Let $$\xi\in L^2(D\times{\bf Y})^3$$ be the $$(n+1)$$-scale limit of $$\{w^\varepsilon\}_\varepsilon$$. Consider the function $$\phi=\varepsilon_n{\it{\Phi}}(x,y_1,\ldots,y_n),$$ where $${\it{\Phi}}$$ is a function in $$C^\infty_0(D,C^\infty_\#(Y_1,\ldots,C^\infty_\#(Y_n),\ldots))^3$$ and is periodic with respect to $$y_1, \ldots,y_n$$ with the period being $$Y_1,\ldots,Y_n,$$ respectively. We then have limε→0∫Dcurlwε⋅εnΦ(x,xε1,…,xεn)dx=0. On the other hand, limε→0∫Dcurlwε⋅εnΦ(x,xε1,…,xεn)dx = limε→0∫Dwε⋅εncurlΦ(x,xε1,…,xεn)dx = limε→0∫Dwε⋅curlynΦ(x,xε1,…,xεn)dx = ∫D∫Yξ(x,y)⋅curlynΦ(x,y)dydx. Thus, there is a function $$\xi_{n-1}(x,\boldsymbol{y}_{n-1})\in L^2(D\times{\bf Y}_{n-1})$$ and a function $${\frak w_n}(x,\boldsymbol{y}_n)\in L^2(D\times{\bf Y}_{n-1},H^1_\#(Y_n)/\mathbb{R})$$ such that ξ(x,y)=ξn−1(x,yn−1)+∇ynwn(x,y). Next we choose $$\phi=\varepsilon_{n-1}{\it{\Phi}}(x,y_1,\ldots,y_{n-1})$$ for a function $${\it{\Phi}}\in C^\infty_0(D,C^\infty_\#(Y_1,\ldots,C^\infty_\#(Y_{n-1}),\ldots),$$ which is periodic with respect to $$y_1,\ldots,y_{n-1}$$. We then have 0 = limε→0∫Dcurlwε⋅εn−1Φ(x,xε1,…,xεn−1)=limε→0∫Dwε⋅curlyn−1Φ(x,xε1,…,xεn−1)dx = ∫D∫Y(ξn−1(x,yn−1)+∇ynwn(x,y))⋅curlyn−1Φ(x,y1,…,yn−1)dyn−1dx = ∫D∫Yn−1ξn−1(x,yn−1)⋅curlyn−1Φ(x,y1,…,yn−1)dyn−1dx. From this, there is a function $$\xi_{n-2}(x,\boldsymbol{y}_{n-2})\in L^2(D\times {\bf Y}_{n-2})$$ and a function $${\frak w_{n-1}}(x,\boldsymbol{y}_{n-1})\in L^2(D\times {\bf Y}_{n-2},H^1_\#(Y_{n-1})/\mathbb{R})$$ so that ξn−1(x,yn−1)=ξn−2(x,yn−2)+∇yn−1wn−1(x,yn−1), so ξ(x,y)=ξn−2(x,yn−2)+∇yn−1wn−1(x,yn−1)+∇ynwn(x,y). Continuing this process, we have ξ(x,y)=w0(x)+∑i=1n∇yiwi(x,yi), where $$w_0\in L^2(D)^3$$ and $${\frak w_i}(x,\boldsymbol{y}_i)\in L^2(D\times {\bf Y}_{i-1},H^1_\#(Y_i))$$. As $$\int_Y\xi(x,\boldsymbol{y})\,{\rm d}\boldsymbol{y}=w_0(x)$$, $$w_0$$ is the weak limit of $$w^\varepsilon$$ in $$L^2(D)^3$$. Let $$\eta(x,\boldsymbol{y})$$ be the $$(n+1)$$-scale convergence limit of $${\rm curl\,} w^\varepsilon$$ in $$L^2(D\times{\bf Y})$$. Let $${\it{\Phi}}(x,y_1,\ldots,y_n)\in C^\infty_0(D,C^\infty_\#(Y_1,\ldots,C^\infty_\#(Y_n),\ldots))$$. We have ∫Dcurlwε⋅∇Φ(x,xε1,…,xεn)dx =∫Dwε⋅curl∇Φ(x,xε1,…,xεn)dx−∫∂D(wε×ν)⋅∇Φ(x,xε1,…,xεn)ds=0. Thus, 0 = limε→ 0∫Dcurlwε⋅εn∇Φ(x,xε1,…,xεn)dx=limε→0∫Dcurlwε⋅∇ynΦ(x,xε1,…,xεn)dx = ∫D∫Yη(x,y)⋅∇ynΦ(x,y1,…,yn)dydx. Therefore, there is a function $$w_n(x,\boldsymbol{y}_n)\in L^2(D\times{\bf Y}_{n-1},\tilde H_\#({\rm curl\,},Y_n))$$ and a function $$\eta_{n-1}(x,\boldsymbol{y}_{n-1})\in L^2(D\times{\bf Y}_{n-1})$$ such that η(x,y)=ηn−1(x,yn−1)+curlynwn(x,y). Let $${\it{\Phi}}(x,y_1,\ldots,y_{n-1})\in C^\infty_0(D,C^\infty_\#(Y_1,\ldots,C^\infty_\#(Y_{n-1}),\ldots))$$. We have 0 = limε→ 0∫Dcurlwε⋅εn−1∇Φ(x,xε1,…,xεn−1)dx=limε→0∫Dcurlwε⋅∇yn−1Φ(x,xε1,…,xεn−1)dx = ∫D∫Y(ηn−1(x,yn−1)+curlynwn(x,y))⋅∇yn−1Φ(x,y1,…,yn−1)dydx = ∫D∫Yn−1ηn−1(x,yn−1)⋅∇yn−1ϕ(x,y1,…,yn−1)dyn−1dx. Therefore, there is a function $$w_{n-1}(x,\boldsymbol{y}_{n-1})\in L^2(D\times{\bf Y}_{n-2},\tilde H_\#({\rm curl\,},Y_{n-1}))$$ and a function $$\eta_{n-2}(x,\boldsymbol{y}_{n-2})\in L^2(D\times {\bf Y}_{n-2})^3$$ so that ηn−1(x,yn−1)=ηn−2(x,yn−2)+curlyn−1wn−1(x,yn−1) so η(x,y)=ηn−2(x,yn−2)+curlyn−1wn−1(x,yn−1)+curlynwn(x,y). Continuing, we find that there is a function $$\eta_0(x)\in L^2(D)^3$$ and functions $$w_i(x,\boldsymbol{y}_{i})\in L^2(D\times{\bf Y}_{i-1},\tilde H_\#({\rm curl\,},Y_i))$$ so that η(x,y)=η0(x)+∑i=1ncurlyiwi(x,yi). As for all $$\phi(x)\in C^\infty_0(D)^3$$ limε→0∫Dcurlwε(x)⋅ϕ(x)dx=∫Dη0(x)⋅ϕ(x)dx,$$\eta_0$$ is the weak limit of $${\rm curl\,} w^\varepsilon$$ in $$L^2(D)^3$$. Thus, $$\eta_0={\rm curl\,} w_0$$. We then get the conclusion. □ 2.3 Multiscale homogenized Maxwell-type problem From (2.6) and Proposition 2.3, we can extract a subsequence (not renumbered), a function $$u_0\in H_0({\rm curl\,}, D)$$, $$n$$ functions $${\frak u_i}\in L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#(Y_i)/\mathbb{R})$$ and $$n$$ functions $$u_i\in L^2(D\times Y_1\times\cdots\times Y_{i-1},\tilde H_\#({\rm curl\,},Y_i))$$ such that uε⟶(n+1)−scaleu0+∑i=1n∇yiui (2.8) and curluε⟶(n+1)−scalecurlu0+∑i=1ncurlyiui. (2.9) For $$i=1,\ldots,n$$, let $$W_i=L^2(D\times Y_1\times\cdots\times Y_{i-1},\tilde H_\#({\rm curl\,},Y_i))$$ and $$V_i=L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#(Y_i)/\mathbb{R})$$. We define the space $${\bf V}$$ as V=W×W1×⋯×Wn×V1×⋯×Vn. For $$\boldsymbol{v}=(v_0,\{v_i\},\{\frak v_i\})\in {\bf V}$$, we define the norm |||v|||=‖v0‖H(curl,D)+∑i=1n‖vi‖L2(D×Yi−1,H~#(curl,Yi))+∑i=1n‖vi‖L2(D×Yi−1,H#1(Yi)/R). We then have the following result. Proposition 2.4 We define $$\boldsymbol{u}=(u_0,\{u_i\}, \{\frak u_i\})\in{\bf V}$$. Then $$\boldsymbol{u}$$ satisfies B(u,v):=∫D∫Y[a(x,y)(curlu0+∑i=1ncurlyiui)⋅(curlv0+∑i=1ncurlyivi) +b(x,y) (u0+∑i=1n∇yiui)⋅(v0+∑i=1n∇yivi)]dydx=∫Df(x)⋅v0(x)dx (2.10) for all $$\boldsymbol{v}=(v_0,\{v_i\},\{\frak v_i\})\in {\bf V}$$. Proof. Let $$v_0\in C^\infty_0(D)^3$$, $$v_i\in C^\infty_0(D, C^\infty_\#(Y_1,\ldots,C^\infty_\#(Y_i),\ldots))^3$$ and $${\frak v_i}\in C^\infty_0(D,C^\infty_\#(Y_1,\ldots,C^\infty_\# (Y_i),\ldots))$$ for $$i=1,\ldots,n$$. Let the test function $$v$$ in (2.5) be v(x)=v0(x)+∑i=1nεi(vi(x,xε1,…,xεi)+∇vi(x,xε1,…,xεi)). We have ∫D[aε(x)curluε(x)⋅(curlv0(x)+∑i=1nεicurlxvi(x,xε1,…,xεi)+∑i=1n∑j=1iεiεjcurlyjvi(x,xε1,…,xεi) + ∑i=1nεicurl∇vi(x,xε1,…,xεi)) +bε(x)uε(x)⋅(v0(x)+∑i=1nεivi(x,xε1,…,xεi) +∑i=1nεi∇xvi(x,xε1,…,xεi)+∑i=1n∑j=1iεiεj∇yjvi(x,xε1,…,xεi))]dx =∫Df(x)⋅(v0(x)+∑i=1nεivi(x,xε1,…,xεi) +∑i=1nεi∇xvi(x,xε1,…,xεn)+∑i=1n∑j=1iεiεj∇yjvi(x,xε1,…,xεi)). Using multiscale convergence and the scale separation (2.2), letting $$\varepsilon$$ go to 0, we have ∫D∫Y[a(x,y)(curlu0+∑i=1ncurlyiui)⋅(curlv0+∑i=1ncurlyivi) +b(x,y)(u0+∑i=1n∇yiui)⋅(v0+∑i=1n∇yivi)]dydx =∫Df(x)⋅v0(x)dx+∫D∫Yf(x)⋅∑i=1n∇yivi(x,y1,…,yi)dydx =∫Df(x)⋅v0(x)dx. Using a density argument, we have (2.10). □ Proposition 2.5 The bilinear form $$B:{\bf V}\times{\bf V}\to \mathbb{R}$$ is coercive and bounded, i.e., there are positive constants $$C^*$$ and $$C_*$$ so that B(u,v)≤C∗|||u||||||v|||andC∗|||u||||||u|||≤B(u,u) (2.11) for all $$\boldsymbol{u},\boldsymbol{v}\in {\bf V}$$. Problem (2.10) thus has a unique solution. The convergence relations (2.8) and (2.9) hold for the whole sequence $$\{u^{\varepsilon}\}_\varepsilon$$. Proof. It is easy to see that there is a positive constant $$C^*$$ such that B(u,v)≤C∗|||u||||||v|||. Now we show that $$B$$ is coercive. We have from (2.1), B(u,u) ≥c∗∫D∫Y(|curlu0+∑i=1ncurlyiui|2+|u0+∑i=1n∇yiui|2)dydx ≥c∫D∫Y(|curlu0|2+∑i=1n|curlyiui|2+|u0|2+|∇yiui|2)dydx≥c|||u|||2. We then get the conclusion from Lax–Milgram lemma. □ 3. FE discretization Let $$D$$ be a polygonal domain in $$\mathbb{R}^3$$. We consider a hierarchy of simplices $$\mathcal{T}^l$$ ($$l=0,1,\ldots$$), where $$\mathcal{T}^{l+1}$$ is obtained from $$\mathcal{T}^l$$ by dividing each simplex in $$\mathcal{T}^l$$ into eight tedrahedra. The mesh size of $$\mathcal{T}^l$$ is $$h_l={\mathcal O}(2^{-l})$$. For each tedrahedron $$T$$, we consider the edge FE space R(T)={v: v=α+β×x, α,β∈R3}. When $$d=2$$, $$\mathcal{T}^{l+1}$$ is obtained from $$\mathcal{T}^l$$ by dividing each simplex in $$\mathcal{T}^l$$ into four congruent triangles. For each triangle $$T$$, we consider the edge FE space R(T)={v: v=(α1α2)+β(x2−x1)}, where $$\alpha_1,\alpha_2$$ and $$\beta$$ are constants. Alternatively, if the domain can be partitioned into a set of cubes, we can use edge FE on a cubic mesh instead (see Monk, 2003). We denote by $$\mathcal{P}_1(T)$$ the set of linear polynomials in each simplex $$T$$. In the following, we present the analysis for the three-dimensional case only; the two-dimensional case is similar. For the cube $$Y$$, we partition it into a hierarchy of simplices $$\mathcal{T}^l_\#,$$ which are distributed periodically. We consider the FE spaces Wl ={v∈H0(curl,D), v|T∈R(T) ∀T∈Tl},Vl ={v∈H1(D), v|T∈P1(T) ∀T∈Tl},W#l ={v∈H#(curl,Y), v|T∈R(T) ∀T∈T#l} and V#l={v∈H#1(Y), v|T∈P1(T) ∀T∈T#l}. For $$d=2,3$$, we have the following estimates (see Ciarlet, 1978; Monk, 2003): infvl∈Wl‖v−vl‖H(curl,D)≤chls(‖v‖Hs(D)d+‖curlv‖Hs(D)d) for all $$v\in H_0({\rm curl\,}, D)\bigcap H^s({\rm curl\,},D)$$; infvl∈W#l‖v−vl‖H#(curl,Y)≤chls(‖v‖Hs(Y)d+‖curlv‖Hs(Y)d) for all $$v\in H_\#({\rm curl\,}, Y)\bigcap H^s({\rm curl\,}, Y)$$; infvl∈Vl‖v−vl‖L2(D)≤chls‖v‖Hs(D) for all $$v\in H^s(D)$$; infvl∈V#l‖v−vl‖L2(Y)≤chls‖v‖Hs(Y) for all $$v\in H^s_\#(Y)$$ and infvl∈V#l‖v−vl‖H#1(Y)≤chls‖v‖H1+s(Y) for all $$v\in H^1_\#(Y)\bigcap H^{1+s}(Y)$$. 3.1 Full tensor product FEs As $$L^2(D\times{\bf Y}_{i-1},\tilde H_\#({\rm curl\,},Y_i))\cong L^2(D)\otimes L^2(Y_1)\otimes\cdots\otimes L^2(Y_{i-1})\otimes \tilde H_\#({\rm curl\,},Y_i),$$ we use the tensor product FE space Wil=Vl⊗V#l⊗⋯⊗V#l⏟i−1 times ⊗W#l to approximate $$u_i$$. Similarly, as $${\frak u_i}\in L^2(D\times{\bf Y}_{i-1},H^1_\#(Y))$$, we use the FE space Vil=Vl⊗V#l⊗⋯⊗V#l⏟i times to approximate $${\frak u_i}$$. We define the space Vl=Wl×W1l×⋯×Wnl×V1l×⋯×Vnl. The full tensor product FE approximating problem is, find $$\boldsymbol{u}^L\in{\bf V}^L$$ so that B(uL,vL)=∫Df(x)⋅v0L(x)dx ∀vL=(v0L,{viL},viL)∈VL. (3.1) To get an error estimate for this FE approximating problem, we define the following regularity spaces for $${\frak u_i}$$ and $$u_i$$. For the functions $$u_i$$, we define the regularity space $$\mathcal{H}_i$$ of functions $$w$$ in $$L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#({\rm curl\,},Y_i))$$ such that for all $$k=1,2,3$$, ∂w∂xk∈L2(D×Y1×⋯×Yi−1,H~#(curl,Yi)) and for all $$j=1,\ldots,i-1$$ and $$k=1,2,3$$, ∂w∂(yj)k∈L2(D×Y1×⋯×Yi−1,H~#(curl,Yi)). In other words, for all $$w\in \mathcal{H}_i$$, $$w$$ belongs to $$L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#({\rm curl\,},Y_i))$$, $$L^2(Y_1\times\cdots\times Y_{i-1},H^1(D,\tilde H_\#({\rm curl\,},Y_i)))$$ and $$L^2(D\times\prod_{k<i,k\ne j}Y_k,H^1_\#(Y_j,\tilde H_\#({\rm curl\,},Y_i)))$$ for $$j=1,\ldots,i-1$$. For $$0<s<1$$, we define the space $$\mathcal{H}^s_i$$ by interpolation. It consists of functions $$w$$ such that $$w$$ belongs to $$L^2(D\times Y_1\times\cdots\times Y_{i-1},H^s_\#({\rm curl\,},Y_i))$$, $$L^2(Y_1\times\cdots\times Y_{i-1},H^s(D,\tilde H_\#({\rm curl\,},Y_i)))$$ and $$L^2(D\times\prod_{k<i,k\ne j}Y_k,H^s_\#(Y_j,\tilde H_\#({\rm curl\,},Y_i)))$$. We equip $$\mathcal{H}_i^s$$ with the norm ‖w‖His =‖w‖L2(D×Y1×⋯×Yi−1,H#s(curl,Yi))+‖w‖L2(Y1×⋯×Yi−1,Hs(D,H~#(curl,Yi))) +∑j=1i−1‖w‖L2(D×∏k<i,k≠j,H#s(Yj,H~#(curl,Yi))). We then have the following lemma. Lemma 3.1 For $$w\in \mathcal{H}_i^s$$, infwl∈Wil‖w−wl‖L2(D×Y1×⋯×Yi−1,H~#(curl,Yi))≤chls‖w‖His. The proof of this lemma is similar to that for full tensor product FEs in Hoang & Schwab (2004/05) and Bungartz & Griebel (2004), using orthogonal projection. We refer to Hoang & Schwab (2004/05) and Bungartz & Griebel (2004) for details. We define $${\frak H_i}^s$$ as the space of functions $$w\in L^2(D\times Y_1\times\cdots\times Y_{i-1},H^{1+s}_\#(Y_i))$$ such that $$w\in L^2(Y_1\times\cdots\times Y_{i-1},H^s(D,H^1_\#(Y_i)))$$ and for all $$j=1,\ldots,i-1$$, $$w\in L^2(D\times\prod_{k<i,k\ne j}Y_k,H^s_\#(Y_{j},H^1_\#(Y_i)))$$. We then define the norm ‖w‖His =‖w‖L2(D×Y1×⋯×Yi−1,H#1+s(Yi))+‖w‖L2(Y1×⋯×Yi−1,Hs(D,H1(Yi))) +∑j=1i−1‖w‖L2(D×∏k<i,k≠jYk,Hs(Yj,H1(Yi))). We have the following result. Lemma 3.2 For $$w\in {\frak H_i}^s$$, infwl∈Vil‖w−wl‖L2(D×Y1×⋯×Yi−1,H#1(Yi))≤chls‖w‖His. We then define the regularity space Hs=Hs(curl,D)×H1s×⋯×Hns×H1s×⋯×Hns with the norm ‖w‖Hs=‖w0‖Hs(curl,D)+∑i=1n‖wi‖His+∑i=1n‖wi‖His for $$\boldsymbol{w}=(w_0,\{w_i\},\{\frak w_i\})\in \boldsymbol{\mathcal{H}}^s$$. We have the following approximation result. Lemma 3.3 For $$\boldsymbol{w}\in \boldsymbol{\mathcal{H}}^s$$ infwl∈Vl‖w−wl‖V≤chls‖w‖Hs. From the boundedness and coerciveness conditions (2.11), using Cea’s lemma, we deduce the following result. Proposition 3.4 If $$\boldsymbol{u}\in \boldsymbol{\mathcal{H}}^s$$, for the full tensor product FE approximating problem (3.1) we have the error estimate ‖u−uL‖V≤chLs‖u‖Hs. (3.2) 3.2 Sparse tensor product FEs We define the following orthogonal projection: Pl0:L2(D)→Vl,P#l0:L2(Y)→V#l with the convention $$P^{-10}=0$$, $$P^{-10}_\#=0$$. We define the following detail spaces: Vl=(Pl0−P(l−1)0)Vl, V#l=(P#l0−P#(l−1)0)Vl. Since Vl=⨁0≤i≤lViandV#l=⨁0≤i≤lV#i, the full tensor product spaces $$W_i^L$$ and $$V_i^L$$ are defined as WiL=(⨁0≤l0,…,li−1≤LVl0⊗V#l1⊗⋯⊗V#li−1)⊗W#L and ViL=(⨁0≤l0,…,li−1≤LVl0⊗V#l1⊗⋯⊗V#li−1)⊗V#L. We then define the sparse tensor product FE spaces as W^iL=⨁l0+⋯+li−1≤LVl0⊗V#l1⊗⋯⊗V#li−1⊗W#L−(l0+⋯+li−1) and V^iL=⨁l0+⋯+li−1≤LVl0⊗V#l1⊗⋯⊗V#li−1⊗V#L−(l0+⋯+li−1). The function $$\boldsymbol{u}$$ is approximated by the space V^L=WL⊗W^1L⊗⋯⊗W^nL⊗V^1L⊗⋯⊗V^nL. The sparse tensor product FE approximating problem is, find $$\widehat {\bf{u}}^L\in \hat{\bf V}^L$$ such that B(u^L,v^L)=∫Df(x)⋅v^0L(x)dx ∀v^L=(v^0L,{v^iL},{v^iL})∈V^L. (3.3) From the coerciveness and boundedness conditions in (2.11), using Cea’s lemma we deduce the error estimate for the sparse tensor product approximating problem ‖u−u^L‖V≤cinfv^L∈VL‖u−v^L‖V. To quantify the error estimate, we use the following regularity spaces. We define $$\hat{\mathcal{H}}_i$$ as the space of functions $$w\in L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#({\rm curl\,},Y_i)),$$ which are periodic with respect to $$y_j$$ with the period being $$Y_j$$ ($$j=1,\ldots,i-1$$) such that for any $$\alpha_0,\alpha_1,\ldots,\alpha_{i-1}\in \mathbb{N}_0^d$$ with $$|\alpha_k|\le 1$$ for $$k=0,\ldots,i-1$$, ∂|α0|+|α1|+⋯+|αi−1|∂xα0∂y1α1⋯∂yi−1αi−1w∈L2(D×Y1×⋯×Yi−1,H#1(curl,Yi)). We equip $$\hat{\mathcal{H}}_i$$ with the norm ‖w‖H^i=∑αj∈Rd,|αj|≤10≤j≤i−1‖∂|α0|+|α1|+⋯+|αi−1|∂xα0∂y1α1⋯∂yi−1αi−1w‖L2(D×Y1×⋯×Yi−1,H#1(curl,Yi)). We can write $$\hat{\mathcal{H}}_i$$ as $$H^1(D,H^1_\#(Y_1,\ldots,H^1_\#(Y_{i-1},H^1_\#({\rm curl\,},Y_i)),\ldots))$$. By interpolation, we define $$\hat{\mathcal{H}}_i^s=H^s(D,H^s_\#(Y_1,\ldots,H^s_\#(Y_{i-1},H^s_\#({\rm curl\,},Y_i)),\ldots))$$ for $$0<s<1$$. We define $$\hat{\frak H}_i$$ as the space of functions $$w\in L^2(D\times Y_1\times\cdots\times Y_{i-1},H^2_\#(Y_i))$$ that are periodic with respect to $$y_j$$ with the period being $$Y_j$$ for $$j=1,\ldots,i-1$$ such that $$\alpha_0,\alpha_1,\ldots,\alpha_{i-1}\in \mathbb{N}_0^d$$ with $$|\alpha_k|\le 1$$ for $$k=0,\ldots,i-1$$, ∂|α0|+|α1|+⋯+|αi−1|∂xα0∂y1α1⋯∂yi−1αi−1w∈L2(D×Y1×⋯×Yi−1,H#2(Yi)). The space $$\hat{\frak H}_i$$ is equipped with the norm ‖w‖H^i=∑αj∈Rd,|αj|≤10≤j≤i−1‖∂|α0|+|α1|+⋯+|αi−1|∂xα0∂y1α1⋯∂yi−1αi−1w‖L2(D×Y1×⋯×Yi−1,H#2(Yi)). We can write $$\hat{\frak H}_i$$ as $$H^1(D,H^1_\#(Y_1,\ldots,H^1_\#(Y_{i-1},H^2_\#(Y_i))))$$. By interpolation, we define the space $$\hat{\frak H}_i^s:=H^s(D,H^s(Y_1,\ldots,H^s(Y_{i-1},H^{1+s}_\#(Y_i))))$$. The regularity space $$\hat{\boldsymbol{\mathcal{H}}}^s$$ is defined as H^s=Hs(curl,D)×H^1s×⋯H^ns×H^1s×⋯×H^ns. Lemmas 3.5 and 3.6 present the approximating properties of functions in $$\hat{\mathcal{H}}_i^s$$ and $${\hat{\frak H}_i^s}$$. The proofs follow from those for sparse tensor products in Hoang & Schwab (2004/05) and Bungartz & Griebel (2004). Lemma 3.5 For $$w\in \hat{\mathcal{H}}_i^s$$, infwL∈W^iL‖w−wL‖L2(D×Y1×⋯×Yi−1,H#(curl,Yi))≤cLi/2hLs‖w‖H^is. Similarly we have the following lemma. Lemma 3.6 For $$w\in \hat{\frak H}_i^s$$, infwL∈V^iL‖w−wL‖L2(D×Y1×⋯×Yi−1,H#1(Yi))≤cLi/2hLs‖w‖H^is. From these lemmas we deduce the following result. Lemma 3.7 For $$\boldsymbol{w}\in \hat{\boldsymbol{\mathcal{H}}}^s$$, infwL∈V^L‖w−wL‖V≤cLn/2hLs‖w‖H^s. From this we deduce the following error estimate for the sparse tensor product FE problem (3.3). Proposition 3.8 If the solution $$\boldsymbol{u}$$ of problem (2.10) belongs to $$\hat{\boldsymbol{\mathcal{H}}}^s$$ then ‖u−u^‖V≤cLn/2hLs‖u‖H^s. Remark 3.9 The dimension of the full tensor product FE space $${\bf V}^L$$ is $${\mathcal O}(2^{dnL}),$$ which is very large when $$L$$ is large. The dimension of the sparse tensor product FE space $$\hat{\bf V}^L$$ is $${\mathcal O}(L^n2^{dL}),$$ which is essentially equal to the number of degrees of freedom for solving a problem in $$\mathbb{R}^d$$ obtaining the same level of accuracy. 4. Convergence in physical variables We employ the FE solutions for the multiscale homogenized Maxwell-type equation (2.10) in the previous section to derive numerical correctors for the solution $$u^{\varepsilon}$$ of the multiscale problem (2.4). In the two-scale case, we derive the homogenization error explicitly in terms of $$\varepsilon$$ so that an error in terms of the microscopic scale $$\varepsilon$$ and the mesh size is obtained for the numerical corrector. We consider the general case, where the solution $$u^0$$ of the homogenized problem belongs to the space $$H^s({\rm curl\,},D)$$ for $$0<s\le 1$$, thus generalizing the standard homogenization rate of convergence $$\varepsilon^{1/2}$$ for elliptic problems (see e.g, Bensoussan et al., 1978; Jikov et al., 1994). This is a new result in homogenization theory. We present it for two-scale Maxwell-type equations, but the procedure works verbatim for two-scale elliptic and elasticity problems, where the solutions of the homogenized problems belong to $$H^{1+s}(D)$$. We present this section for the case $$d=3$$; the case $$d=2$$ is similar. 4.1 Two-scale problems For the two-scale case, we denote the function $$a(x,\boldsymbol{y})$$ by $$a(x,y)$$. The two-scale homogenized equation becomes ∫D∫Y[a(x,y)(curlu0+curlyu1)⋅(curlv0+curlyv1)+b(x,y)(u0+∇yu1)⋅(v0+∇yv1)]dydx =∫Df(x)⋅v0(x)dx. We first let $$v_0=0$$, $$v_1=0$$ and deduce that ∫D∫Yb(x,y)(u0+∇yu1)⋅∇yv1dydx=0. For each $$r=1,2,3$$, let $$w^r(x,\cdot)\in L^2(D, H^1_\#(Y)/\mathbb{R})$$ be the solution of the problem ∫D∫Yb(x,y)(er+∇ywr)⋅∇yψdydx=0 ∀ψ∈L2(D,H#1(Y)/R), (4.1) where $$e_r$$ is the vector in $$\mathbb{R}^3$$ with all the components being 0, except the $$r$$th component, which equals 1. This is the standard cell problem in elliptic homogenization. From this we have u1(x,y)=wr(x,y)u0r(x). (4.2) Therefore, ∫D∫Yb(x,y)(u0+∇yu1)⋅v0dxdy=∫Db0(x)u0(x)⋅v0(x)dx, where the positive-definite matrix $$b^0(x)$$ is defined as bij0(x)=∫Yb(x,y)(ej+∇wj(x,y))⋅(ei+∇ywi(x,y))dy, (4.3) which is the usual homogenized coefficient for elliptic problems with the two-scale coefficient matrix $$b^\varepsilon$$. Let $$v_0=0$$ and $${\frak v_1}=0$$. We have ∫D∫Ya(x,y)(curlu0+curlyu1)⋅curlyv1dydx=0 for all $$v_1\in L^2(D, \tilde H_\#({\rm curl\,},Y))$$. For each $$r=1,2,3$$, let $$N^r\in L^2(D,\tilde H_\#({\rm curl\,},Y))$$ be the solution of ∫D∫Ya(x,y)(er+curlyNr)⋅curlyvdydx=0 (4.4) for all $$v\in L^2(D, \tilde H_\#({\rm curl\,},Y))$$. We have u1=(curlu0(x))rNr(x,y). (4.5) The homogenized coefficient $$a^0$$ is determined by aij0(x)=∫Ya(x,y)ip(ejp+(curlyNj)p)dy=∫Ya(x,y)(ej+curlyNj)⋅(ei+curlyNi)dy. (4.6) We have ∫D∫Ya(x,y)(curlu0+curlyu1)⋅curlv0dxdy=∫Da0(x)curlu0(x)⋅curlv0(x)dx. The homogenized problem is ∫D[a0(x)curlu0(x)⋅curlv0(x)+b0(x)u0(x)⋅v0(x)]dx=∫Df(x)⋅v0(x)dx ∀v0∈H0(curl,D). (4.7) Following the procedure for deriving the homogenization error (Bensoussan et al., 1978; Jikov et al., 1994), we have the following homogenization error estimate. Theorem 4.1 Assume that $$a\in C(\bar D, C(\bar Y))^{3\times 3}$$, $$u_0\in H^1({\rm curl\,};D)$$, $$N^r\in C^1(\bar D,C(\bar Y))^3$$, $${\rm curl}_yN^r\in C^1(\bar D,C(\bar Y))^3$$, $$w^r\in C^1(\bar D,C^1(\bar Y))$$ for all $$r=1,2,3$$, then2 ‖uε−[u0+∇yu1(⋅,⋅ε)]‖L2(D)3≤cε1/2 and ‖curluε−[curlu0+curlyu1(⋅,⋅ε)]‖L2(D)3≤cε1/2. The proof of this theorem uses the functions $$G_r$$ and $$g_r$$ defined in (A.2) and (A.3) below. For $$u_0\in H^s({\rm curl\,},D)$$ when $$0<s<1$$, we have the following homogenization error estimate. Theorem 4.2 Assume that $$a\in C(\bar D,C(\bar Y))^{3\times 3}$$, $$u_0\in H^s({\rm curl\,},D)$$, $$N^r\in C^1(\bar D, C(\bar Y))^3$$, $${\rm curl}_yN^r\in C^1(\bar D,C(\bar Y))^3$$ and $$w^r\in C^1(\bar D,C^1(\bar Y))$$ for all $$r=1,2,3$$, then ‖uε−[u0+∇yu1(⋅,⋅ε)‖L2(D)3≤cεs/(1+s) and ‖curluε−[curlu0+curlyu1(⋅,⋅ε)]‖L2(D)3≤cεs/(1+s). We present the proof of this theorem in Appendix A. To employ the FE solutions to construct numerical correctors for $$u^{\varepsilon}$$, we define the following operator: Uε(Φ)(x)=∫YΦ(ε[xε]+εz,{xε})dz. (4.8) Let $$D^\varepsilon$$ be a $$2\varepsilon$$ neighbourhood of $$D$$. Regarding $${\it{\Phi}}$$ as zero when $$x$$ is outside $$D$$, we have ∫DεUε(Φ)(x)dx=∫D∫YΦ(x,y)dxdy. (4.9) The proof of (4.9) may be found in Cioranescu et al. (2008). We have the following result. Lemma 4.3 Assume that for $$r=1,2,3$$, $${\rm curl}_yN^r(x,y)\in C^1(\bar D, C(\bar Y))^3$$ and $$u_0\in H^s({\rm curl\,},D)$$, then ‖curlyu1(⋅,⋅ε)−Uε(curlyu1)‖L2(D)3≤cεs. We prove this lemma in Appendix B. We then have the following result. Theorem 4.4 Assume that $$a\in C(\bar D,C(\bar Y))^{3\times 3}$$, $$u_0\in H^s({\rm curl\,},D)$$, $$N^r\in C^1(\bar D,C(\bar Y))^3$$, $${\rm curl}_yN^r\in C^1(\bar D,C(\bar Y))^3$$ and $$w^r\in C^1(\bar D,C^1(\bar Y))$$ for all $$r=1,2,3$$. Then for the full tensor product FE solution $$(u_0^L,u_1^L,{\frak u_1}^L)$$ we have ‖uε−u0L−Uε(∇uu1L)‖L2(D)3≤c(εs/(1+s)+hLs) and ‖curluε−curlu0L−Uε(curlyu1L)‖L2(D)3≤c(εs/(1+s)+hLs). Proof. From Lemma 4.3, we have ‖curluε−curlu0L−Uε(curlyu1L)‖L2(D)3 ≤‖curluε−curlu0−curlyu1(⋅,⋅ε)‖L2(D)3 +‖curlu0−curlu0L‖L2(D)3+‖curlyu1(⋅,⋅ε)−Uε(curlyu1)‖L2(D)3 +‖Uε(curlyu1)−Uε(curlyu1L)‖L2(D)3. Using the fact that $$(\mathcal{U}^\varepsilon({\it{\Phi}}))^2\le \mathcal{U}({\it{\Phi}}^2)$$ and (4.9), we have ‖Uε(curlyu1)−Uε(curlyu1L)‖L2(D)3≤‖curlyu1−curlyu1L‖L2(D×Y)3≤chLs. This together with (3.2), Theorem 4.2 and Lemma 4.3 gives ‖curluε−curlu0L−Uε(curlyu1L)‖L2(D)3≤c(εs/(1+s)+hLs). Similarly, we have ‖uε−u0L−Uε(∇uu1L)‖L2(D)3≤c(εs/(1+s)+hLs). □ For the sparse tensor product FE approximation, we have the following result. Theorem 4.5 Assume that $$a\in C(\bar D,C(\bar Y))^{3\times 3}$$, $$u_0\in H^s({\rm curl\,},D)$$, $$N^r\in C^1(\bar D,C(\bar Y))^3$$, $${\rm curl}_yN^r\in C^1(\bar D,C(\bar Y))^3$$ and $$w^r\in C^1(\bar D,C^1(\bar Y))$$ for all $$r=1,2,3$$. Then for the sparse tensor product FE solution $$(\hat u_0^L,\hat u_1^L,\hat{\frak u}_1^L)$$ we have ‖uε−u^0L−Uε(∇yu^1L)‖L2(D)3≤c(εs/(1+s)+Ln/2hLs) and ‖curluε−curlu^0L−Uε(curlyu^1L)‖L2(D)3≤c(εs/(1+s)+Ln/2hLs). 4.2 Multiscale problems For multiscale problems, we do not have an explicit homogenization rate of convergence. However, for the case where $$\varepsilon_i/\varepsilon_{i+1}$$ is an integer for all $$i=1,\ldots,n-1$$ we can derive a corrector for the solution $$u^{\varepsilon}$$ of the multiscale problem from the FE solutions of the multiscale homogenized problem. For each function $$\phi\in L^1(D),$$ which is understood as 0 outside $$D$$, we define a function in $$L^1(D\times{\bf Y})$$: Tnε(ϕ)(x,y)=ϕ(ε1[xε1]+ε2[y1ε2/ε1]+⋯+εn[yn−1εn/εn−1]+εnyn). Letting $$D^{\varepsilon_1}$$ be the $$2\varepsilon_1$$ neighbourhood of $$D$$, we have ∫Dϕdx=∫Dε1∫Y1⋯∫YnTnε(ϕ)dyn⋯dy1dx (4.10) for all $$\phi \in L^1(D)$$. If a sequence $$\{\phi^\varepsilon\}_\varepsilon$$$$(n+1)$$-scale converges to $$\phi(x,y_1,\ldots,y_n)$$ then Tnε(ϕ)⇀ϕ(x,y1,…,yn) in $$L^2(D\times Y_1\times\ldots\times Y_n)$$. Thus, when $$\varepsilon\to 0$$, Tnε(curluε)⇀curlu0+curly1u1+⋯+curlynun (4.11) and Tnε(uε)⇀u0+∇y1u1+⋯+∇ynun (4.12) in $$L^2(D\times{\bf Y})^3$$. To deduce an approximation of $$u^{\varepsilon}$$ in $$H({\rm curl\,},D)$$ in terms of the FE solution, we use the operator $$\mathcal{U}_n^\varepsilon$$ , which is defined as Unε(Φ)(x) =∫Y1⋯∫YnΦ(ε1[xε1]+ε1t1,ε2ε1[ε1ε2{xε1}] +ε2ε1t2,⋯, εnεn−1[εn−1εn{xεn−1}]+εnεn−1tn,{xεn})dtn⋯dt1 for all functions $${\it{\Phi}}\in L^1(D\times{\bf Y})$$. For each function $${\it{\Phi}}\in L^1(D\times{\bf Y})$$ we have ∫Dε1Unε(Φ)dx=∫D∫YΦ(x,y)dydx. (4.13) The proofs for these facts may be found in Cioranescu et al. (2008). We then have the following corrector result. Proposition 4.6 The solution $$u^{\varepsilon}$$ of problem (2.5) and the solution $$(u_0,\{u_i\}\,\{{\frak u_i}\})$$ of problem (2.10) satisfies limε→0‖uε−[u0+Unε(∇y1u1)+⋯+Unε(∇ynun)‖L2(D)3=0 (4.14) and limε→0‖curluε−[curlu0+Unε(curly1u1)+⋯+Unε(curlynun)]‖L2(D)3=0. (4.15) Proof. We consider the expression ∫D∫Y[Tnε(aε)(Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun)) ⋅(Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun)) +Tnε(bε)(Tnε(uε)−(u0+∇y1u1+⋯+∇ynun))⋅(Tnε(uε)−(u0+∇y1u1+⋯+∇ynun))dydx. Using (2.5), (2.10), (4.10), (4.11) and (4.12), we deduce that this expression converges to 0. From (2.1) we have limε→0‖Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun)‖L2(D×Y1×…×Yn)3=0 and limε→0‖Tnε(uε)−(u0+∇y1u1+⋯+∇ynun)‖L2(D×Y1×⋯×Yn)3=0. From (4.13) and the fact that $$\mathcal{U}^\varepsilon_n({\it{\Phi}})^2\le \mathcal{U}^\varepsilon_n({\it{\Phi}}^2)$$, we have ∫D|Unε(Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun)(x)|2dx ≤∫DUnε(|Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun|2)(x)|dx ≤∫D∫Y|Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun|2)dydx, which converges to 0 when $$\varepsilon\to 0$$. Using $$\mathcal{U}^\varepsilon_n(\mathcal{T}^\varepsilon_n({\it{\Phi}}))={\it{\Phi}}$$, we get (4.15). We derive (4.14) similarly. □ We then deduce the numerical corrector result. Theorem 4.7 For the full tensor product FE approximation solution $$\boldsymbol{u}^L=(u_0^L,\{u_i^L\},\{{\frak u_i}^L\})$$ in (3.1), we have limε→0L→∞‖uε−[u0L+Unε(∇y1u1L)+⋯+Unε(∇ynunL)]‖L2(D)3=0 (4.16) and limε→0L→∞‖curluε−[curlu0L+Unε(curly1u1L)+⋯+Unε(curlynunL)]‖L2(D)3=0. (4.17) Proof. We note that ‖Unε(curly1u1+⋯+curlynun)−Unε(curly1u1L+⋯+curlynunL)‖L2(D)3 ≤∫DUnε(|(curly1u1+⋯+curlynun)−(curly1u1L+⋯+curlynunL)|2)(x)dx ≤∫D∫Y|(curly1u1+⋯+curlynun)−(curly1u1L+⋯+curlynunL)|2dydx, which converges to 0 when $$L\to \infty$$. From this and (4.15), we get (4.17). We obtain (4.16) in the same way. □ Remark 4.8 As $${\bf V}^{\lceil L/n\rceil}\subset\hat{\bf V}^L$$, the result in Theorem 4.7 also holds for the sparse tensor product FE solution $$\widehat {\bf{u}}^L$$. Since we do not have an explicit homogenization error for problems with more than two scales, we do not distinguish the two cases of full and sparse tensor FE approximations. 5. Regularity of $$\boldsymbol{N^r}$$, $$\boldsymbol{w^r}$$ and $$\boldsymbol{u_0}$$ We show in this section that the regularity requirements for obtaining the sparse tensor product FE error estimate and the homogenization error estimate in the previous sections are achievable. We present the results for the two-scale case in detail. The multiscale case is similar; we summarize it in Remark 5.7. We first prove the following lemma. Lemma 5.1 Let $$\psi\in H_\#({\rm curl\,},Y)\bigcap H_\#({\rm div},Y)$$. Assume further that $$\int_Y\psi(y)\,{\rm d}y=0$$. Then $$\psi\in H^1_\#(Y)^3$$ and ‖ψ‖H1(Y)3≤c(‖curlyψ‖L2(Y)3+‖divyψ‖L2(Y)). Proof. Let $$\omega\subset\mathbb{R}^3$$ be a smooth domain such that $$\omega\supset Y$$. Let $$\eta\in \mathcal{D}(\omega)$$ be such that $$\eta(y)=1$$ when $$y\in Y$$. We have curly(ηψ)=ηcurlyψ+∇yη×ψ∈L2(ω)3 and divy(ηψ)=∇yη⋅ψ+ηdivyψ∈L2(ω)3. Together with the zero boundary condition, we conclude that $$\eta\psi\in H^1(\omega)^3$$ so $$\psi\in H^1(Y)^3$$. We note that ∫Y(divyψ(y)2+|curlyψ(y)|2)dy=∑i,j=13∫Y(∂ψi∂yj)2+∑i≠j∫Y∂ψi∂yi∂ψj∂yjdy−∑i≠j∫Y∂ψj∂yi∂ψi∂yjdy. Assume that $$\psi$$ is a smooth periodic function. We have ∫Y∂ψi∂yi∂ψj∂yjdy=∫Y[∂∂yi(ψi∂ψj∂yj)−ψi∂2ψj∂yi∂yj]dy=−∫Yψi∂2ψj∂yi∂yjdy as $$\psi$$ is periodic. Similarly, we have ∫Y∂ψi∂yj∂ψj∂yidy=∫Y[∂∂yj(ψi∂ψj∂yi)−ψi∂2ψj∂yj∂yi]dy=−∫Yψi∂2ψj∂yj∂yidy. Thus, ∫Y∂ψi∂yi∂ψj∂yjdy=∫Y∂ψi∂yj∂ψj∂yidy. Therefore, ‖∇yψ‖L2(Y)32=‖divyψ‖L2(Y)2+‖curlyψ‖L2(Y)32. Using a density argument, this holds for all $$\psi\in H^1_\#(Y)^3$$. As $$\int_Y\psi(y)\,{\rm d}y=0$$, from the Poincaré inequality we deduce ‖ψ‖H1(Y)3≤c(‖divyψ‖L2(Y)+‖curlyψ‖L2(Y)3). □ Lemma 5.2 Let $$\alpha\in C^1_\#(\bar Y)^{3\times 3}$$ be uniformly bounded, positive definite and symmetric for all $$y\in \bar Y$$. Let $$F\in L^2(Y)$$, extending periodically to $$\mathbb{R}^3$$. Let $$\psi\in H^1_\#(Y)^3$$ satisfy the equation curly(α(y)curlyψ(y))=F(y). Then $${\rm curl}_y\psi\in H^1_\#(Y)^3$$ and ‖curlyψ‖H1(Y)3≤c(‖F‖L2(Y)3+‖ψ‖H1(Y)3). Proof. Let $$\omega\supset Y$$ be a smooth domain. Let $$\eta\in \mathcal{D}(\omega)$$ be such that $$\eta(y)=1$$ for $$y\in Y$$. We have curly(αcurly(ηψ)) =curly(αηcurlyψ)+curly(α∇yη×ψ) =ηcurly(αcurlyψ)+∇yη×(αcurlyψ)+curly(α∇yη×ψ). Let $$U=\alpha{\rm curl}_y(\eta\psi)$$. We have ‖curlyU‖L2(ω)3≤c(‖F‖L2(ω)+‖ψ‖H1(ω)3)≤c(‖F‖L2(Y)3+‖ψ‖H1(Y)3). Further, ‖U‖L2(ω)3=‖α(∇yη×ψ+ηcurlyψ)‖|L2(ω)3≤c‖ψ‖H1(ω)3≤c‖ψ‖H1(Y)3. As $$\eta\in\mathcal{D}(\omega)$$, $$U$$ has compact support in $$\omega$$ so $$U$$ belongs to $$H_0({\rm curl\,},\omega)$$. Thus, we can write U=z+∇Φ, where $$z\in H^1_0(\omega)^3$$ and $${\it{\Phi}}\in H^1_0(\omega)$$ satisfy ‖z‖H1(ω)3≤c‖U‖H(curl,ω) and ‖Φ‖H1(ω)≤c‖U‖H(curl,ω). From $${\rm div}_y(\alpha^{-1}U)=0$$ we deduce that divy(α−1∇Φ)=−divy(α−1z)∈L2(ω). Since $$\alpha\in C^1(\bar\omega)^{3\times 3}$$ and is uniformly bounded and positive definite, $$\alpha^{-1}\in C^1(\bar\omega)^{3\times 3}$$ and is uniformly positive definite. Therefore, $${\it{\Phi}}\in H^2(\omega)$$ and satisfies ‖Φ‖H2(ω)≤c‖z‖H1(ω)3≤c‖U‖H(curl,ω). Thus, $$U\in H^1(\omega)^3$$ and $$\|U\|_{H^1(\omega)^3}\le c\|U\|_{H({\rm curl\,},\omega)}\le c(\|F\|_{L^2(Y)^3}+\|\psi\|_{H^1(Y)^3})$$. From $${\rm curl}_y(\eta\psi)=\alpha^{-1}U$$, we deduce that $${\rm curl}_y(\eta\psi)\in H^1(\omega)^3$$ so $${\rm curl}_y\psi\in H^1(Y)^3$$ and ‖curlyψ‖H1(Y)3≤c(‖F‖L2(Y)3+‖ψ‖H1(Y)3). □ We then prove the following result on the regularity of $$N^r$$. Proposition 5.3 Assume that $$a(x,y)\in C^1(\bar D,C^2(\bar Y))^{3\times 3}$$; then $${\rm curl}_yN^r(x,y)\in C^1(\bar D,C(\bar Y))^3$$ and we can choose a version of $$N^r$$ in $$L^2(D,\tilde H_\#({\rm curl\,},Y))$$ so that $$N^r(x,y)\in C^1(\bar D, C(\bar Y))^3$$. Proof. We can choose a version of $$N^r$$ so that $${\rm div}_yN^r=0$$. Indeed, let $${\it{\Phi}}(x,\cdot)\in L^2(D, H^1_\#(Y))$$ be such that $$\Delta_y{\it{\Phi}}=-{\rm div}_yN^r$$; then $${\rm curl}_y(N^r+\nabla_y{\it{\Phi}})={\rm curl}_y N^r$$ and $${\rm div}_y(N^r+\nabla_y{\it{\Phi}})=0$$. Further we can choose $$N^r$$ so that $$\int_YN^r(x,y)\,{\rm d}y=0$$. From Lemma 5.1, we have ‖Nr(x,⋅)‖H1(Y)3≤c‖curlyNr(x,⋅)‖L2(Y)3, which is uniformly bounded with respect to $$x$$. From (4.4) and Lemma 5.2, we deduce that ‖curlyNr(x,⋅)‖H1(Y)3≤c‖curly(a(x,⋅)er‖L2(Y)3+‖Nr(x,⋅)‖H1(Y)3, which is uniformly bounded with respect to $$x$$. For each index $$q=1,2,3$$, we have that $${\rm curl}_y{\partial\over\partial y_q}N^r(x,\cdot)$$ is uniformly bounded in $$L^2(Y)$$ and $${\rm div}_y{\partial\over\partial y_q}N^r(x,\cdot)=0$$. Therefore, from Lemma 5.1, $${\partial\over\partial y_q}N^r(x,\cdot)$$ is uniformly bounded in $$H^1(Y)$$. We note that ∂∂yq(curly(a(x,⋅)curlyNr))=−∂∂yqcurly(a(x,⋅)er)∈L2(Y). Thus, curly(acurly∂Nr∂yq)=∂∂yq(curly(a(x,y)curlyNr))−curly(∂a∂yqcurlyNr)∈L2(Y). From Lemma 5.2 we deduce that $${\rm curl}_y{\partial N^r\over\partial y_q}(x,\cdot)$$ is uniformly bounded in $$H^1(Y)$$ so that $${\rm curl}_y N^r(x,\cdot)$$ is uniformly bounded in $$H^2(Y)\subset C(\bar Y)$$. We now show that $${\rm curl}_yN^r\in C^1(\bar D,H^2(Y))^3\subset C^1(\bar D,C(\bar Y))^3$$. Fix $$h\in\mathbb{R}^3$$. From (4.4) we have curly(a(x,y)curly(Nr(x+h,y)−Nr(x,y))) =−curly((a(x+h,y)−a(x,y))er) −curly((a(x+h,y)−a(x,y))curlyNr(x+h,y)). The smoothness of $$a$$ and the uniform boundedness of $${\rm curl}_yN^r(x,\cdot)$$ in $$L^2(Y)^3$$ gives limh→0‖curly(Nr(x+h,⋅)−Nr(x,⋅))‖L2(Y)3=0. (5.1) From Lemma 5.1 we have that $$N^r(x+h,\cdot)-N^r(x,\cdot)\in H^1(Y)^3$$ and ‖Nr(x+h,⋅)−Nr(x,⋅)‖H1(Y)3≤c‖curly(Nr(x+h,⋅)−Nr(x,⋅))‖L2(Y)3, which converges to 0 when $$|h|\to 0$$. From Lemma 5.2, we have ‖curly(Nr(x+h,⋅)−Nr(x,⋅))‖H1(Y)3 ≤‖−curly((a(x+h,⋅)−a(x,⋅))er)−curly((a(x+h,⋅)−a(x,⋅))curlyNr(x+h,⋅))‖L2(Y)3 +‖Nr(x+h,⋅)−Nr(x,⋅)‖H1(Y)3→0 when |h|→0. (5.2) We have further that curly(a(x,y)curly∂∂yq(Nr(x+h,y)−Nr(x,y)))=−curly(∂a∂yq(x,y)curly(Nr(x+h,y)−Nr(x,y))) −∂∂yqcurly((a(x+h,y)−a(x,y))er)−∂∂yqcurly((a(x+h,y)−a(x,y))curlyNr(x+h,y)). (5.3) From this we have ‖curly∂∂yq(Nr(x+h,y)−Nr(x,y))‖L2(Y)3 ≤c‖curly(Nr(x+h,⋅)−Nr(x,⋅))‖L2(Y)3 +c‖a(x+h,⋅)−a(x,⋅)‖W1,∞(Y)3→0 when |h|→0, so from Lemma 5.1 we have ‖∂∂yq(Nr(x+h,y)−Nr(x,y))‖H1(Y)3→0 when |h|→0. As the right-hand side of (5.3) converges to 0 in the $$L^2(Y)^3$$ norm when $$|h|\to 0$$, we deduce from Lemma 5.2 that ‖curly∂∂yq(Nr(x+h,y)−Nr(x,y))‖H1(Y)3→0 when |h|→0. (5.4) We have curly[a(x,y)curly(Nr(x+h,y)−Nr(x,y)h)] =−curly((a(x+h,y)−a(x,y)h)er) −curly(a(x+h,y)−a(x,y)hcurlyNr(x+h,y)). Let $$\chi^r(x,\cdot)\in \tilde H_\#({\rm curl\,},Y)$$ with $${\rm div}_y\chi^r(x,)=0$$ be the solution of the problem curly(a(x,y)curlyχr(x,⋅))=−curly(∂a∂xqer)−curly(∂a∂xqcurlyNr(x,y)). We deduce that curly(a(x,y)curly(Nr(x+h,y)−Nr(x,y)h−χr(x,y))) =−curly((a(x+h,y)−a(x,y)h−∂a∂xq(x,y))er) −curly((a(x+h,y)−a(x,y)h−∂a∂xq(x,y))curlyNr(x+h,y)) −curly(∂a∂xq(x,y)curly(Nr(x+h,y)−Nr(x,y))):=I1. (5.5) Let $$h\in \mathbb{R}^3$$ be a vector with all components 0 except for the $$q$$th component. We have ‖curly(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖L2(Y)3 ≤c‖a(x+h,⋅)−a(x,⋅)h−∂a∂xq(x,⋅)‖L∞(Y) +c‖curly(Nr(x+h,⋅)−Nr(x,⋅)‖L2(Y)3, (5.6) which converges to 0 when $$|h|\to 0$$ due to (5.1). Thus, we deduce from Lemma 5.1 that lim|h|→0‖Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅)‖H1(Y)3=0. (5.7) From Lemma 5.2, we have lim|h|→0‖curly(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖H1(Y)3 ≤lim|h|→0‖I1(x,⋅)‖L2(Y)3+‖Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅)‖H1(Y)3=0 (5.8) due to (5.2) and (5.7). Let $$p=1,2,3$$. We then have curly(a(x,y)curly∂∂yp(Nr(x+h,y)−Nr(x,y)h−χr(x,y))) =−curly(∂a∂yp(x,y)curly(Nr(x+h,y)−Nr(x,y)h−χr(x,y))) −∂∂ypcurly((a(x+h,y)−a(x,y)h−∂a(x,y)∂xq)er) −∂∂ypcurly((a(x+h,y)−a(x,y)h−∂a∂xq(x,y))curlyNr(x+h,y)) −∂∂ypcurly(∂a∂xq(x,y)curly(Nr(x+h,y)−Nr(x,y))), which converges to 0 in $$L^2(Y)$$ for each $$x$$ due to (5.4), (5.8) and the uniform boundedness of $$\|{\rm curl\,} N^r(x,\cdot)\|_{H^2(Y)^3}$$. We have ‖curly∂∂yp(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖L2(Y)3 ≤c‖curly(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖L2(Y)3 +c‖a(x+h,⋅)−a(x,⋅)h−∂a(x,⋅)∂xq‖W1,∞(Y)3+c‖curly(Nr(x+h,⋅)−Nr(x,⋅)‖H1(Y)3, which converges to 0 when $$|h|\to 0$$, so from Lemma 5.1, lim|h|→0‖∂∂yp(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖H1(Y)3=0. (5.9) Therefore, $$N^r\in C^1(\bar D,H^2(Y))^3\subset C^1(\bar D,C(\bar Y))^3$$. We then get from Lemma 5.2 that lim|h|→0‖curly∂∂yp(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖H1(Y)3=0. Thus, $${\rm curl}_yN^r\in C^1(\bar D,H^2(Y))^3\subset C^1(\bar D,C(\bar Y))^3$$. □ Proposition 5.4 Assume that $$b(x,y)\in C^1(\bar D,C^2(\bar Y))^{3\times 3}$$. The solution $$w^r$$ of cell problem (4.1) belongs to $$C^1(\bar D, C^1(\bar Y))$$. Proof. The cell problem (4.1) can be written as −∇y⋅(b(x,y)∇ywr(x,y))=∇y(b(x,y)er). Fixing $$x\in \bar D$$, the right-hand side is bounded uniformly in $$H^1(Y)$$ so $$w^r(x,\cdot)$$ is uniformly bounded in $$H^3(Y)$$ from elliptic regularity (see McLean, 2000, Theorem 4.16). For $$h\in \mathbb{R}^3$$, we note that −∇y⋅[b(x,y)∇y(wr(x+h,y)−wr(x,y))] =∇y⋅[(b(x+h,y)−b(x,y))er] +∇y⋅[(b(x+h,y)−b(x,y))∇ywr(x+h,y)]:=i1. As $$\int_Yw^r(x,y)\,{\rm d}y=0$$, we have ‖wr(x+h,⋅)−wr(x,⋅)‖H1(Y) ≤c‖∇y(wr(x+h,⋅)−wr(x,⋅))‖L2(Y) ≤c‖(b(x+h,⋅)−b(x,⋅))er‖L2(Y) +c‖(b(x+h,⋅)−b(x,⋅))∇ywr(x+h,⋅)‖L2(Y), which converges to 0 when $$|h|\to 0$$. Fixing $$x\in\bar D$$, we then have from McLean (2000, Theorem 4.16) that ‖wr(x+h,⋅)−wr(x,⋅)‖H3(Y)≤‖wr(x+h,⋅)−wr(x,⋅)‖H1(Y)+‖i1(x,⋅)‖H1(Y), (5.10) which converges to 0 when $$|h|\to 0$$. Fixing an index $$q=1,2,3$$, let $$h\in \mathbb{R}^3$$ be a vector whose components are all zero except the $$q$$th component. Let $$\eta(x,\cdot)\in H^1_\#(Y)/\mathbb{R}$$ be the solution of the problem −∇y⋅[b(x,y)∇yη(x,y)]=∇y⋅[∂b∂xqer]+∇y⋅[∂b∂xq∇ywr(x,y)]. We have −∇y⋅[b(x,y)∇y(wr(x+h,y)−wr(x,y)h−η(x,y))] =∇y⋅[(b(x+h,y)−b(x,y)h−∂b∂xq(x,y))er] +∇y⋅[(b(x+h,y)−b(x,y)h−∂b∂xq(x,y))∇ywr(x+h,y)] +∇y⋅[∂b(x,y)∂xq(∇ywr(x+h,y)−∇ywr(x,y))]:=i2. From (5.10) and the regularity of $$b$$, $$\lim_{|h|\to 0}\|i_2(x,\cdot)\|_{H^1(Y)}=0$$. As $$\int_Yw^r(x,y)\,{\rm d}y=0$$ and $$\int_Y\eta(x,y)\,{\rm d}y=0$$, we have lim|h|→0‖wr(x+h,⋅)−wr(x,⋅)h−η(x,⋅)‖H1(Y)=0. Therefore from McLean (2000, Theorem 4.16), we have ‖wr(x+h,⋅)−wr(x,⋅)h−η(x,⋅)‖H3(Y)≤‖wr(x+h,⋅)−wr(x,⋅)h−η(x,⋅)‖H1(Y)+‖i2(x,⋅)‖H1(Y), which converges to 0 when $$|h|\to 0$$. Thus, $$w^r\in C^1(\bar D,H^3(Y))\subset C^1(\bar D,C^1(\bar Y))$$. □ For the regularity of the solution $$u_0$$ of the homogenized problem (4.7) we have the following result. Proposition 5.5 Assume that $$D$$ is a Lipschitz polygonal domain, and the coefficient $$a(\cdot,y)$$, as a function of $$x$$, is Lipschitz, uniformly with respect to $$y$$; then there is a constant $$0<s<1$$ so that $${\rm curl\,} u_0\in H^s(D)$$. Proof. When $$a(x,y)$$ is Lipschitz with respect to $$x$$, from (4.4), $$\|{\rm curl}_y N^r(x,\cdot)\|_{L^2(Y)}$$ is a Lipschitz function of $$x$$, so from (4.6) we have that $$a^0$$ is Lipschitz with respect to $$x$$. As $$a^0$$ is positive definite, $$(a^0)^{-1}$$ is Lipschitz. Let $$U=a^0{\rm curl\,} u_0$$. We have from (4.7) that $$U\in H({\rm curl\,},D)$$, $${\rm div}((a^0)^{-1}U)=0$$ and $$(a^0)^{-1}U\cdot \nu=0$$ on $$\partial D,$$ where $$\nu$$ is the outward normal vector on $$\partial D$$. The conclusion follows from Hiptmair (2002, Lemma 4.2). □ Remark 5.6 If $$a^0$$ is isotropic, we have from (4.7) that curlcurlu0=−(a0)−1∇a0×curlu0−(a0)−1b0u0+(a0)−1f∈L2(D)3 so $$u_0\in H^1({\rm curl},D)$$. However, even if $$a$$ is isotropic, $$a^0$$ may not be isotropic. Remark 5.7 The homogenized equation for the multiscale case is determined as follows. We denote by $$a^n(x,\boldsymbol{y})=a(x,\boldsymbol{y})$$. Recursively, for $$i=1,\ldots,n-1$$, the $$i$$-th level homogenized coefficient is determined as follows. For $$r=1,2,3$$, let $$N_{i+1}^r\in L^2(D\times{\bf Y}_i,\tilde H({\rm curl}_{y_{i+1}},Y_{i+1}))$$ be the solution of the cell problem ∫D∫Y1…∫Yi+1ai+1(x,yi,yi+1)(er+curlyi+1Ni+1r)⋅curlyi+1ψdyi+1dyidx=0 for all $$\psi\in L^2(D\times{\bf Y}_i,\tilde H({\rm curl}_{y_{i+1}},Y_{i+1}))$$. The $$i$$-th level homogenized coefficient $$a^{i}$$ is determined by arsi(x,yi)=∫Yi+1ai+1(x,yi,yi+1)(es+curlyi+1Ni+1s)⋅(er+curlyi+1Ni+1r)dyi+1. Let $$b^n(x,\boldsymbol{y})=b(x,\boldsymbol{y})$$. Similarly, let $$w_{i+1}^{r}\in L^2(D\times{\bf Y}_i,H^1_\#(Y_{i+1})/\mathbb{R})$$ be the solution of the problem ∫D∫Y1…∫Yi+1bi+1(x,yi,yi+1)(er+∇yi+1wi+1r)⋅∇yi+1ψdyi+1dyidx=0 for all $$\psi\in L^2(D\times{\bf Y}_i,H^1_\#(Y_{i+1})/\mathbb{R})$$. The $$i$$-th level homogenized coefficient $$b^i$$ is determined by brsi(x,yi)=∫Yi+1bi+1(x,yi,yi+1)(es+∇yi+1wi+1s)⋅(er+∇yi+1wi+1r)dyi+1. We then have the equation ∫D∫Yi[ai(x,yi)(curlu0+curly1u1+⋯+curlyiui)⋅(curlv0+curly1v1+⋯+curlyivi)dyidx +bi(x,yi)(u0+∇y1u1+⋯+∇yiui)⋅(v0+∇y1v1+⋯+∇yivi)]dyidx=∫Df(x)⋅v0(x)dx. The coefficients $$a^0(x)$$ and $$b^0(x)$$ are the homogenized coefficients. We have ui(x,yi) = [curlu0(x)r+curly1u1(x,y1)r+⋯+curlyi−1ui−1(x,yi−1)r]Nir(x,yi) =curlu0(x)r0(δr0r1+curly1N1r0(x,y1)r1)(δr1r2+curly2N2r1(x,y2)r2)⋯ (δri−2ri−1+curlyi−1Ni−1ri−2(x,yi−1)ri−1)Niri−1(x,yi). If $$a(x,\boldsymbol{y})\in C^1(\bar D,C^2(\bar Y_1,\ldots,C^2(\bar Y_n),\ldots))^{3\times 3}$$, by following the same procedure as above, we can show inductively that $${\rm curl}_{y_i}N_i^r(x,\boldsymbol{y}_i)\in C^1(\bar D,C^2(\bar Y_1,\ldots,C^2(\bar Y_{i-1},H^2(Y_i)),\ldots))$$ and $$a^i(x,\boldsymbol{y}_i)\in C^1(\bar D,C^2(\bar Y_1,\ldots,C^2(\bar Y_i),\ldots))$$. Thus, if $$u_0\in H^s({\rm curl\,},D)$$ for $$0<s\le 1$$, $$u_i\in \hat{\mathcal{H}}_i^s$$. Similarly, we can show that if $$b\in C^1(\bar D, C^2(\bar Y_1,\ldots,C^2(\bar Y_n)\ldots))$$ then $$w^{ir}\in C^1(\bar D,C^2(\bar Y_1,\ldots,C^2(\bar Y_{i-1},H^3(Y_i))\ldots))$$. As ui=u0r0(x)(δr0r1+∂w1r0∂y1r1(x,y1))…(δri−2ri−1+∂wi−1ri−2∂y(i−1)ri−1(x,yi−1))wiri−1(x,yi), if $$u_0\in H^s(D)$$, $${\frak u_i}\in \hat{\frak H}_i^s$$. 6. Numerical results The detail spaces $$\mathcal{V}^l$$ and $$\mathcal{V}^l_\#$$, which are difficult to construct in numerical implementations, are defined via orthogonal projection in Section 3.2. We employ Riesz basis functions and define equivalent norms, which facilitate the construction of these spaces. We make the following assumption. Assumption 6.1 (i) For each multidimensional vector $$j \in \mathbb{N}_0^d$$, there exists a set of indices $$I^j \subset \mathbb{N}^d_0$$ and a set of basis functions $$\phi^{jk}\in L^2(D)$$ for $$k\in I^j$$, such that $$V^l = \text{span}\left\{\phi^{jk} : |\,j|_{\infty}\le l\right\}$$. There are constants $$c_2>c_1>0$$ such that if $$\phi = \sum_{|\,j|_{\infty}\leq l,k\in I^j}\phi^{jk}c_{jk}\in V^l$$, then the following norm equivalences hold: c1∑|j|∞≤lk∈Ij|cjk|2≤‖ϕ‖L2(D)2≤c2∑|j|∞≤lk∈Ij|cjk|2, where $$c_1$$ and $$c_2$$ are independent of $$\phi$$ and $$l$$. (ii) For the space $$L^2(Y)$$, for each $$j \in \mathbb{N}_0^d$$, there exists a set of indices $$I^j_0 \subset \mathbb{N}_0^d$$ and a set of basis functions $$\phi^{jk}_0\in L^2(Y)$$, $$k\in I^j_0$$, such that $$V^l_\# = \text{span}\{\phi^{jk}_0 : |\,j|_{\infty}\le l\}$$. There are constants $$c_4>c_3>0$$ such that if $$\phi = \sum_{|\,j|_{\infty}\leq l,k\in I^{\,j}_{\,0}}\phi^{jk}_0c_{jk}\in V^l$$ then c3∑|j|∞≤lk∈I0j|cjk|2≤‖ϕ‖L2(Y)2≤c4∑|j|∞≤lk∈I0j|cjk|2, where $$c_3$$ and $$c_4$$ are independent of $$\phi$$ and $$l$$. Because of the norm equivalence, we can use $$\mathcal{V}^l=\text{span}\{\phi^{jk} : |\,j|_{\infty}= l\}$$ and $$\mathcal{V}^l_\#=\text{span}\{\phi^{jk}_0 : |\,j|_{\infty}= l\}$$ to construct the sparse tensor product FE spaces. Example 6.2 (i) We can construct a hierarchical basis for $$L^2(0,1)$$ as follows. We first take three piecewise linear functions as the basis for level $$j=0$$: $$\psi^{01}$$ obtains values $$(1,0)$$ at $$(0,1/2)$$ and is 0 in $$(1/2,1)$$, $$\psi^{02}$$ is piecewise linear and obtains values $$(0, 1, 0)$$ at $$(0, 1/2, 1)$$ and $$\psi^{03}$$ obtains values $$(0,1)$$ at $$(1/2, 1)$$ and is 0 in $$(0,1/2)$$. The basis functions for other levels are constructed from the wavelet function $$\psi$$ that takes values $$(0,-1,2,-1,0)$$ at $$(0,1/2,1,3/2,2)$$, the left boundary function $$\psi^{\rm left}$$ taking values $$(-2,2,-1,0)$$ at $$(0,1/2,1,3/2)$$ and the right boundary function $$\psi^{\rm right}$$ taking values $$(0, -1,2,-2)$$ at $$(1/2,1,3/2,2)$$. For levels $$j\geq 1$$, $$I^j=\{1,2,\ldots,2^j\}$$. The wavelet basis functions are defined as $$\psi^{j1}(x) = 2^{j/2}\psi^{\rm left}(2^j x)$$, $$\psi^{jk}(x)=2^{j/2}\psi(2^j x - k + 3/2)$$ for $$k = 2, \ldots, 2^j-1$$ and $$\psi^{j2^j} = 2^{j/2}\psi^{\rm right}(2^j x - 2^j+2)$$. This base satisfies Assumption 6.1 (i). (ii) For $$Y = (0,1)$$, we can construct a hierarchy of periodic basis functions for $$L^2(Y)$$ that satisfies Assumption 6.1 (ii) from those in (i). For level 0, we exclude $$\psi^{01}$$, $$\psi^{03}$$ and include the periodic piecewise linear function that takes values $$(1,0,1)$$ at $$(0,1/2,1),$$ respectively. At other levels, the functions $$\psi^{\rm left}$$ and $$\psi^{\rm right}$$ are replaced by the piecewise linear functions that take values $$(0,2, -1, 0)$$ at $$(0,1/2,1,3/2)$$ and values $$(0, -1,2,0)$$ at $$(1/2,1, 3/2 ,2),$$ respectively. When $$D=(0,1)^d$$, the basis functions can be constructed by taking the tensor products of the basis functions in $$(0,1)$$. They satisfy Assumption 6.1 after appropriate scaling (see Griebel & Oswald, 1995). Remark 6.3 When the norm equivalence for the basis functions in $$L^2(D)$$ and in $$L^2(Y)$$ does not hold, in many cases, we can still prove a rate of convergence similar to those in Lemmas 3.5 and 3.6 for the sparse tensor product FE approximations. For example, with the division of the domain $$D$$ into sets of triangles $$\mathcal{T}^l$$, the set of continuous piecewise linear functions with value 1 at one vertex and 0 at all the others forms a basis of $$V^l$$. Let $$S^l$$ be the set of vertices of the set of simplices $$\mathcal{T}^l$$. We can define $$\mathcal{V}^l$$ as the linear span of functions that are 1 at a vertex in $$S^l\setminus S^{l-1}$$ and 0 at all the other vertices. We can then construct the sparse tensor product FE approximations with these spaces but the norm equivalence does not hold. A rate of convergence for sparse tensor product FEs similar to those in Lemmas 3.5 and 3.6 can be deduced (see e.g, Hoang, 2008). In the first example, we consider a two-scale Maxwell-type equation in the two-dimensional domain $$D=(0,1)^2$$. The coefficients a(x,y)=(1+x1)(1+x2)(1+cos22πy1)(1+cos22πy2) and b(x,y)=1(1+x1)(1+x2)(1+cos22πy1)(1+cos22πy2). We can compute the homogenized coefficients exactly. In this case, a0=4(1+x1)(1+x2)9 and b0=23(1+x1)(1+x2). We choose f=(49(1+x1)(1+2x2−x1)+23(1+x1)(1+x2)x1x2(1−x2)49(1+x2)(1+2x1−x2)+23(1+x1)(1+x2)x1x2(1−x1)) so that the solution to the homogenized equation is u0=(x1x2(1−x2)x1x2(1−x1)). In Fig. 1, we plot the energy error versus the mesh size for the sparse tensor product FE approximations of the two-scale homogenized Maxwell-type problem. The figure agrees with the error estimate in Proposition 3.8. Fig. 1. View largeDownload slide The sparse tensor energy error $$B(\boldsymbol{u}-\widehat {\bf{u}}^L,\boldsymbol{u}-\widehat {\bf{u}}^L).$$ Fig. 1. View largeDownload slide The sparse tensor energy error $$B(\boldsymbol{u}-\widehat {\bf{u}}^L,\boldsymbol{u}-\widehat {\bf{u}}^L).$$ In the second example, we consider the case where $$b$$ is the identity matrix, i.e., it does not depend on $$y$$. In this case, from (2.10) we note that the function $${\frak u_1}=0$$. We choose a(x,y)=(1+x1)(1+x2)(1+cos22πy1)(1+cos22πy2) and f=(4(2π(1+x1)(1+x2)sin2πx2+(1+x1)(cos2πx1−cos2πx2))9+12πsin2πx24(2π(1+x1)(1+x2)sin2πx1−(1+x2)(cos2πx1−cos2πx2))9+12πsin2πx1) so that the solution to the homogenized problem is u0=(12πsin2πx212πsin2πx1). Figure 2 plots the energy error versus the mesh size for the sparse tensor product FE approximations for the two-scale homogenized Maxwell-type problem. The plot confirms the analysis. Fig. 2. View largeDownload slide The sparse tensor energy error $$B(\boldsymbol{u}-\widehat {\bf{u}}^L,\boldsymbol{u}-\widehat {\bf{u}}^L).$$ Fig. 2. View largeDownload slide The sparse tensor energy error $$B(\boldsymbol{u}-\widehat {\bf{u}}^L,\boldsymbol{u}-\widehat {\bf{u}}^L).$$ Acknowledgements The authors gratefully acknowledge a postgraduate scholarship of Nanyang Technological University, the AcRF Tier 1 grant RG69/10, the Singapore A*Star SERC grant 122-PSF-0007 and the AcRF Tier 2 grant MOE 2013-T2-1-095 ARC 44/13. Footnotes 1 The notations $$Y_1,\ldots,Y_n$$, which denote the same unit cube $$Y$$, are introduced for convenience only, especially in the case where the Cartesian product of several of them is used, to avoid the necessity of indicating how many times the unit cube appears in the product. The functions $$a$$ and $$b$$ depend on the macroscopic scale only and are periodic with respect to $$y_i$$ with the period being the unit cube $$Y$$. 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( 2010) Multiscale computations for 3D time-dependent Maxwell’s equations in composite materials. SIAM J. Sci. Comput. , 32, 2560– 2583. Google Scholar CrossRef Search ADS Appendix A. We present the proof of Theorem 4.2 in this appendix. We consider a set of $$M$$ open cubes $$Q_i$$ ($$i=1,\ldots,M$$) of size $$\varepsilon^t$$ for $$t>0$$ to be chosen later such that $$D\subset\bigcup_{i=1}^MQ_i$$ and $$Q_i\bigcap D\ne\emptyset$$. Each cube $$Q_i$$ intersects with only a finite number, which does not depend on $$\varepsilon$$, of other cubes. We consider a partition of unity that consists of $$M$$ functions $$\rho_i$$ such that $$\rho_i$$ has support in $$Q_i$$, $$\sum_{i=1}^M\rho_i(x)=1$$ for all $$x\in D$$ and $$|\nabla\rho_i(x)|\le c\varepsilon^{-t}$$ for all $$x$$ (indeed such a set of cubes $$Q_i$$ and a partition of unity can be constructed from a fixed set of cubes of size $${\mathcal O}(1)$$ by rescaling). For $$r=1,2,3$$ and $$i=1,\ldots,M$$, we define Uir=1|Qi|∫Qicurlu0(x)rdx and Vir=1|Qi|∫Qiu0(x)rdx (as $$u_0\in H^s(D)^3$$ and $${\rm curl\,} u_0\in H^s(D)^3$$, for the Lipschitz domain $$D$$, we can extend each of them, separately, continuously outside $$D$$ and understand $$u_0$$ and $${\rm curl\,} u_0$$ as these extensions; see Wloka, 1987, Theorem 5.6). Let $$U_i$$ and $$V_i$$ denote the vectors $$(U_i^1, U_i^2,U_i^3)$$ and $$(V_i^1,V_i^2,V_i^3),$$ respectively. Let $$B$$ be the unit cube in $$\mathbb{R}^3$$. From the Poincaré inequality, we have ∫B|ϕ−∫Bϕ(x)dx|2dx≤c∫B|∇ϕ(x)|2dx ∀ϕ∈H1(B). By translation and scaling, we deduce that ∫Qi|ϕ−1|Qi|∫Qiϕ(x)dx|2dx≤cε2t∫Qi|∇ϕ(x)|2dx ∀ϕ∈H1(Qi), i.e., ‖ϕ−1|Qi|∫Qiϕ(x)dx‖L2(Qi)≤cεt‖ϕ‖H1(Qi). Together with ‖ϕ−1|Qi|∫Qiϕ(x)dx‖L2(Qi)≤c‖ϕ‖L2(Qi), we deduce from interpolation that ‖ϕ−1|Qi|∫Qiϕ(x)dx‖L2(Qi)≤cεts‖ϕ‖Hs(Qi) ∀ϕ∈Hs(Qi). Thus, ∫Qi|curlu0(x)r−Uir|2dx≤cε2ts‖(curlu0)r‖Hs(Qi)2. (A.1) Let u1ε(x)=u0(x)+εNr(x,xε)Ujrρj(x)+ε∇[wr(x,xε)Vjrρj(x)]. We have curl(aε(x)curlu1ε(x))+bε(x)u1ε(x) =curla(x,xε)[curlu0(x)+εcurlxNr(x,xε)Ujrρj(x)+curlyNr(x,xε)Ujrρj+ε(Ujr∇ρj)×Nr(x,xε)] +b(x,xε)[u0(x)+εNr(x,xε)Ujrρj(x)+ε∇xwr(x,xε)Vjrρj(x)+∇ywr(x,xε)Vjrρj(x) + εwr(x,xε)Vjr∇ρj(x)] =curl(a0(x)curlu0(x))+b0(x)u0(x)+curl[Gr(x,xε)Ujrρj(x)]+gr(x,xε)Vjrρj(x)+εcurlI(x) +εJ(x)+curl[(aε(x)−a0(x))(curlu0(x)−Ujρj(x))]+(bε(x)−b0(x))(u0(x)−Vjρj(x)), where the vector functions $$G_r(x,y)$$ and $$g_r(x,y)$$ are defined by (Gr)i(x,y) =air(x,y)+aij(x,y)curlyNr(x,y)j−air0(x), (A.2) (gr)i(x,y) =bir(x,y)+bij(x,y)∂wr∂yj(x,y)−bir0(x) (A.3) and I(x) =a(x,xε)[curlxNr(x,xε)Ujrρj(x)+(Ujr∇ρj(x))×Nr(x,xε)],J(x) =b(x,xε)[Nr(x,xε)Ujrρj(x)+∇xwr(x,xε)Vjrρj(x)+wr(x,xε)Vjr∇ρj(x)]. Therefore, for $$\phi\in W$$, ⟨curl(aεcurlu1ε)+bεu1ε−curl(a0curlu0)−b0u0,ϕ⟩ =∫DUjrρj(x)Gr(x,xε)⋅curlϕdx+∫DVjrρj(x)gr(x,xε)⋅ϕ(x)dx +ε∫DI(x)⋅curlϕ(x)dx+ε∫DJ(x)⋅ϕ(x)dx+∫D(aε−a0)(curlu0(x)−Ujρj)⋅curlϕ(x)dx +∫D(bε−b0)(u0−Vjρj)⋅ϕdx (here $$\langle\cdot\rangle$$ denotes the duality pairing between $$W'$$ and $$W$$). From (4.4), we have that $${\rm curl}_yG_r(x,y)=0$$. Further, from (4.6) $$\int_YG_r(x,y)\,{\rm d}y=0$$. Therefore, there is a function $$\tilde G_r(x,y)$$ such that $$G_r(x,y)=\nabla_y \tilde G_r(x,y)$$. From (4.1), we have $${\rm div}_yg_r(x,y)=0$$ and from (4.6) $$\int_Yg_r(x,y)\,{\rm d}y=0$$. Hence, there is a function $$\tilde g_r$$ such that $$g_r(x,y)={\rm curl}_y\tilde g_r(x,y)$$. As $$\nabla_y\tilde G_r(x,\cdot)=G_r(x,\cdot)\in H^1(Y)^3$$ so $$\Delta_y\tilde G_r(x,\cdot)\in L^2(Y)$$. Thus, $$\tilde G_r(x,\cdot)\in H^2(Y),$$ which implies $$\tilde G_r(x,\cdot)\in C(\bar Y)$$. As $$G_r(x,\cdot)\in C^1(\bar D,H^1_\#(Y)^3)$$, we deduce that $$\tilde G_r(x,y)\in C^1(\bar D, H^2(Y))\subset C^1(\bar D,C(\bar Y))$$. The construction of $$\tilde g_r$$ in Jikov et al. (1994) implies that $$\tilde g_r\in C^1(\bar D, C(\bar Y))$$ (see Hoang & Schwab, 2013). We have ∫DUjrρjGr(x,xε)⋅curlϕdx=∫DUjrρj(x)[ε∇G~r(x,xε)−ε∇xG~r(x,xε)]⋅curlϕdx =−ε∫DG~r(x,xε)div[(Ujrρj)curlϕ]dx−ε∫DUjrρj∇xG~r(x,xε)⋅curlϕdx. We note that |∫DUjrρj∇xG~r(x,xε)⋅curlϕdx|≤c‖(Ujrρj)‖L2(D)‖curlϕ‖L2(D)3. From ‖Ujrρj‖L2(D)2=∫D(Ujr)2ρj(x)2dx+∑i≠j∫DUirUjrρi(x)ρj(x)dx, and the fact that the support of each function $$\rho_i$$ intersects only with the support of a finite number (which does not depend on $$\varepsilon$$) of other functions $$\rho_j$$ in the partition of unity, we deduce ‖Ujrρj‖L2(D)2 ≤c∑j=1M(Ujr)2|Qj| =c∑j=1M1|Qj|(∫Qjcurlu0(x)rdx)2≤c∑j=1M∫Qjcurlu0(x)r2dx≤c∫Dcurlu0(x)r2dx. Thus, |ε∫DUjrρj∇xG~r(x,xε)⋅curlϕdx|≤cε‖curlϕ‖L2(D)3. We have further that ε∫DG~r(x,xε)div[(Ujrρj)curlϕ]dx =ε∫DG~r(x,xε)[(Ujr∇ρj(x))]⋅curlϕdx ≤cε‖Ujr∇ρj‖L2(D)3‖curlϕ‖L2(D)3. As the support of each function $$\rho_i$$ intersects with the support of a finite number of other functions $$\rho_j$$ and $$\|\nabla\rho_j\|_{L^\infty(D)}\le c\varepsilon^{-t}$$, we have ‖Ujr∇ρj‖L2(D)32≤c∑j=1M(Ujr)2|Qj|‖∇ρj‖L∞(D)2≤cε−2t∑j=1M(Ujr)2|Qj|≤cε−2t, so ε∫DG~r(x,xε)div[(Ujrρj)curlϕ]dx≤cε‖Ujr∇ρj‖L2(D)3‖curlϕ‖L2(D)3≤cε1−t‖curlϕ‖L2(D)3. We therefore deduce that |∫DUjrρjGr(x,xε)⋅curlϕdx|≤cε1−t‖curlϕ‖L2(D)3. We have ∫DVjrρjgr(x,xε)⋅ϕ(x)dx=∫DVjrρj[εcurlg~r(x,xε)−εcurlxg~r(x,xε)]⋅ϕdx. Arguing similarly to above, we have |ε∫DVjrρjcurlxg~r(x,xε)⋅ϕdx|≤cε‖Vjrρj‖L2(D)3‖ϕ‖L2(D)3≤cε‖ϕ‖L2(D)3 and |ε∫DVjrρjcurlg~r(x,xε)⋅ϕdx| = |ε∫Dg~r(x,xε)⋅curl[(Vjrρj)ϕ]dx| ≤ |ε∫Dg~r(x,xε)⋅[(Vjrρj)curlϕ+ϕ×(Vjr∇ρj)]dx ≤c(ε‖curlϕ‖L2(D)3+cε1−t‖ϕ‖L2(D)3)(∑j=1M(Vjr)2|Qj|)1/2 ≤c(ε‖curlϕ‖L2(D)3+cε1−t‖ϕ‖L2(D)3). We note that ‖I‖L2(D)3≤csupr[‖Ujrρj‖L2(D)+‖Ujr∇ρj‖L2(D)]≤cε−t and ‖J‖L2(D)3≤csupr[‖Ujrρj‖L2(D)+c‖Vjrρj‖L2(D)+c‖Vjr∇ρj‖L2(D)]≤cε−t. We have further that ⟨curl((aε−a0)(curlu0−Ujρj)),ϕ⟩≤c‖curlu0−(Ujρj))‖L2(D)3‖curlϕ‖L2(D)3. From ∫D|(curlu0)r−(Ujrρj)|2dx=∫D|∑j=1M((curlu0)r−Ujr)ρj|2dx, using the support property of $$\rho_j$$, we have from (A.1), ∫D|(curlu0)r−(Ujrρj)|2dx ≤c∑j=1M∫Qj|(curlu0)r−Ujr|2dx≤cε2st∑j=1M‖(curlu0)r‖Hs(Qj)2 =cε2st∑j=1M[∫Qj(curlu0)r2dx+∫Qj×Qj(curlu0(x)r−curlu0(x′)r)2|x−x′|3+2sdxdx′] ≤cε2st[‖(curlu0)r‖L2(D)2+∫D×D(curlu0(x)r−curlu0(x′)r)2|x−x′|3+2sdxdx′] =cε2st‖(curlu0)r‖Hs(D)2. (A.4) Thus, ⟨curl((aε−a0)(curlu0−Ujρj)),ϕ⟩≤cεst‖curlϕ‖L2(D)3. Similarly, we have |∫D(bε−b0)(u0−∑j=1MVjρj)⋅ϕdx|≤c‖∑j=1M(u0−Vj)ρj‖L2(D)3‖ϕ‖L2(D)3≤cεst‖ϕ‖L2(D)3. Therefore, |⟨curl(aεcurlu1ε)+bεu1ε−curl(a0curlu0)−b0u0,ϕ⟩|≤c(ε1−t+εst)‖ϕ‖V i.e., ‖curl(aεcurlu1ε)+bεu1ε−curl(a0curlu0)−b0u0‖W′≤c(ε1−t+εst). Thus, ‖curl(aεcurlu1ε)+bεu1ε−curl(aεcurluε)−bεuε‖W′≤c(ε1−t+εst). (A.5) Let $$\tau^\varepsilon(x)$$ be a function in $$\mathcal{D}(D)$$ such that $$\tau^\varepsilon(x)=1$$ outside an $$\varepsilon$$ neighbourhood of $$\partial D$$ and $${\rm sup}_{x\in D}\varepsilon|\nabla\tau^\varepsilon(x)|<c,$$ where $$c$$ is independent of $$\varepsilon$$. We consider the function w1ε(x)=u0(x)+ετε(x)Ujrρj(x)Nr(x,xε)+ε∇[Vjrρjτε(x)wr(x,xε)]. We then have u1ε−w1ε=ε(1−τε(x))Ujrρj(x)Nr(x,xε)+ε∇[(1−τε(x))Vjrρjwr(x,xε)] and curl(u1ε−w1ε) =εcurlxNr(x,xε)Ujrρj(x)(1−τε(x))+curlyNr(x,xε)Ujrρj(x)(1−τε(x)) −εUjrρj(x)∇τε(x)×Nr(x,xε)+ε(1−τε(x))Ujr∇ρj(x)×Nr(x,xε). As shown above, $$\|U_j^r\rho_j\|_{L^2(D)}$$ is uniformly bounded, so ‖εcurlxNr(x,xε)(Ujrρj)(1−τε(x))‖L2(D)3≤cε. Let $$\tilde D^\varepsilon$$ be the $$3\varepsilon^{t}$$ neighbourhood of $$\partial D$$. We note that $${\rm curl\,} u_0$$ is extended continuously into a function in $$H^s(\mathbb{R}^3)$$ outside $$D$$. As shown in Hoang & Schwab (2013), for $$\phi\in H^1(\tilde D^\varepsilon)$$, ‖ϕ‖L2(D~ε)≤cεt/2‖ϕ‖H1(D~ε). From this and ‖ϕ‖L2(D~ε)≤‖ϕ‖L2(D~ε), using interpolation, we get ‖ϕ‖L2(D~ε)≤cεst/2‖ϕ‖Hs(D~ε)≤cεst/2‖ϕ‖Hs(D) for all $$\phi\in H^s(D)$$ extended continuously outside $$D$$. We then have ‖Ujrρj‖L2(Dε)2 ≤c∑j=1M∫Qj⋂Dε(Ujr)2ρj2dx ≤c∑j=1M|Qj⋂Dε|1|Qj|2(∫Qj(curlu0)rdx)2 ≤c∑Qj⋂Dε≠∅|Qj⋂Dε||Qj|∫Qj(curlu0)r2dx. As $$D^\varepsilon$$ is the $$\varepsilon$$ neighbourhood of $$\partial D$$, $$\partial D$$ is Lipschitz and $$Q_j$$ has size $$\varepsilon^t$$, $$|Q_j\bigcap D^\varepsilon|\le c\varepsilon^{1+(d-1)t}$$ so $$|Q_j\bigcap D^\varepsilon|/|Q_j|\le c\varepsilon^{1-t}$$. When $$Q_j\bigcap D^\varepsilon\ne\emptyset$$, $$Q_j\subset\tilde D^\varepsilon$$. Thus, ‖Ujrρj‖L2(Dε)2≤cε1−t‖(curlu0)r‖L2(D~ε)2≤cε1−t+st‖curlu0‖Hs(D)32. Therefore, ‖curlyNr(x,xε)(Ujrρj)(1−τε(x))‖L2(D)3≤cε(1−t+st)/2 and ‖ε(Ujrρj)∇τε(x)×Nr(x,xε)‖L2(D)3≤cε(1−t+st)/2. Similarly, we have ‖Ujr∇ρj‖L2(Dε)32 ≤cε−2t∑Qj⋂Dε≠∅|Qj⋂Dε||Qj|∫Qj(curlu0)r2dx ≤cε−2t+1−t‖curlu0‖L2(D~ε)32≤cε1−3t+st‖curlu0‖Hs(D)32. Thus, ‖ε(1−τε(x))(Ujr∇ρj)×Nr(x,xε)‖L2(D)≤cε(1−t)+(1−t+st)/2. Therefore, ‖curl(u1ε−w1ε)‖L2(D)3≤c(ε(1−t+st)/2+ε(1−t)+(1−t+st)/2). We further have ε∇[(1−τε(x))wr(x,xε)(Vjrρj)] = −ε∇τε(x)wr(x,xε)(Vjrρj)+ε(1−τε(x))∇xwr(x,xε)(Vjrρj) +(1−τε(x))∇ywr(x,xε)(Vjrρj)+ε(1−τε(x))wr(x,xε)(Vjr∇ρj). Arguing as above, we deduce that ‖Vjrρj‖L2(Dε)≤cε(1−t+st)/2, ‖Vjr∇ρj‖L2(Dε)≤cε(1−t+st)/2−t. Therefore, ‖ε∇[(1−τε(x))wr(x,xε)(Vjrρj)]‖L2(D)3≤c(ε(1−t+st)/2+ε1−t+(1−t+st)/2). Thus, ‖u1ε−w1ε‖L2(D)3≤c(ε(1−t+st)/2+ε(1−t)+(1−t+st)/2). Choosing $$t=1/(s+1)$$ we have ‖curl(aεcurl(u1ε−w1ε))+bε(u1ε−w1ε)‖W′≤cεs/(s+1). This together with (A.5) gives ‖curl(aεcurl(uε−w1ε))+bε(uε−w1ε)‖W′≤cεs/(s+1). Thus, ‖uε−w1ε‖W≤cεs/(s+1), which implies ‖uε−u1ε‖W≤cεs/(s+1). (A.6) We note that curlu1ε=curlu0(x)+curlyNr(x,xε)(Ujrρj)+εcurlxNr(x,xε)(Ujrρj)+ε(Ujr∇ρj)×Nr(x,xε). From ‖εcurlxNr(x,xε)(Ujrρj)‖L2(D)3≤cε and ‖ε(Ujr∇ρj)×Nr(x,xε)‖L2(D)3≤cεε−t=cεs/(1+s), we deduce that ‖curlu1ε−curlu0−curlyNr(x,xε)(Ujrρj)‖L2(D)3≤cεs/(s+1). From (A.4), ‖curlu0−(Ujrρj)‖L2(D)3≤cεts=cεs/(s+1), we get ‖curlu1ε−[curlu0+curlyNr(x,xε)(curlu0)r‖L2(D)3≤cεs/(s+1). This together with (A.6) implies ‖curluε−[curlu0+curlyNr(x,xε)(curlu0)r‖L2(D)3≤cεs/(s+1). □ Appendix B. We prove Lemma 4.3 in this appendix. We adapt the proof of Hoang & Schwab (2013, Lemma 5.5). As u1(x,y)=∑r=13curlu0(x)rNr(x,y), it is sufficient to show that for each $$r=1,2,3$$, ∫D|curlu0(x)rcurlyNr(x,xε)−∫Ycurlu0(ε[xε]+εt)rcurlyNr(ε[xε]+εt,xε)dt|2dx≤cε2s. The expression on the left-hand side is bounded by ∫D∫Y|curlu0(x)rcurlyNr(x,xε)−curlu0(ε[xε]+εt)rcurlyNr(ε[xε]+εt,xε)|2dtdx ≤2∫D∫Y|(curlu0(x)r−curlu0(ε[xε]+εt)r)curlyNr(ε[xε]+εt,xε)|2dtdx +2∫D∫Y|curlu0(x)r|2|curlyNr(x,xε)−curlyNr(ε[xε]+εt,xε)|2dtdx. As $${\rm curl}_yN^r\in C^1(\bar D,C(\bar Y))^3$$, there exists a constant $$c$$ such that supx∈Dsupt∈Y|curlyNr(x,xε)−curlyNr(ε[xε]+εt,xε)|≤cε. From this we have ∫D|curlu0(x)rcurlyNr(x,xε)−Uε(curlu0(⋅)rcurlyNr(⋅,⋅))(x)|2dx≤c∫D∫Y|curlu0(x)r−curlu0(ε[xε]+εt)r|2dtdx+cε2. We now show that for $${\rm curl\,} u_0\in H^s(D)$$, ∫D∫Y|curlu0(x)r−curlu0(ε[xε]+εt)r|2dtdx≤cε2s. (B.1) Letting $$\phi(x)$$ be a smooth function, we have ∫D∫Y|ϕ(x)−ϕ(ε[xε]+εt)|2dtdx ≤∑i=1d∫D∫Y|ϕ(ε[x1ε]+εt1,…,ε[xi−1ε]+εti−1,xi,…,xd) −ϕ(ε[x1ε]+εt1,…,ε[xiε]+εti,xi+1,…,xd)|2dtdx ≤∑i=1d∫D∫Y|ε∫ti{xi/ε}∂ϕ∂xi(ε[x1ε]+εt1,…,ε[xiε]+εζi,xi+1,…,xd)dζi|2dtdx ≤ε2∑i=1d∫D∫Y∫01|∂ϕ∂xi(ε[x1ε]+εt1,…,ε[xiε]+εζi,xi+1,…,xd)|2dζidtdx ≤ε2∑i=1d∫D|∂ϕ∂xi|2dx, which follows from (4.13); here we freeze the variables $$x_{i+1},\ldots,x_d$$. Let $$\psi\in H^1(D)$$. We consider a sequence $$\{\phi_n\}_n\subset C^\infty(\bar D),$$ which converges to $$\psi$$ in $$H^1(D)$$. As $$n\rightarrow \infty$$, ∫D∫Y(ϕn(ε[xε]+εt)−ψ(ε[xε]+εt))2dtdx = ∫DUε((ϕn−ψ)2)(x)dx ≤ ∫D(ϕn(x)−ψ(x))2dx→0. Therefore, ∫D∫Y(ψ(x)−ψ(ε[xε]+εt))2dtdx ≤3∫D(ψ−ϕn)2dx+3∫D∫Y(ϕn−ϕn(ε[xε]+εt))2dtdx +3∫D∫Y(ϕn(ε[xε]+εt)−ψ(ε[xε]+εt))2dtdx ≤6∫D(ψ−ϕn)2dx+3ε2∑i=1d∫D|∂ϕn∂xi|2dx. Letting $$n\to\infty$$, we have ∫D∫Y(ψ(x)−ψ(ε[xε]+εt))2dtdx≤3ε2∑i=1d∫D|∂ψ∂xi|2dx. Let $$T$$ be the linear map from $$L^2(D)$$ to $$L^2(D\times Y)$$ so that T(ϕ)(x,y)=ϕ(x)−ϕ(ε[xε]+εt). We thus have ‖T‖H1(D)→L2(D×Y)≤cε. On the other hand, ‖T‖L2(D)→L2(D×Y)≤c. From interpolation theory, we deduce that ‖T‖Hs(D)→L2(D×Y)≤cεs. We then get (B.1). The conclusion follows. □ Notes added after the proof stage: After the article is accepted, we learnt about the related recent article: P. Henning, M. Ohlberger and B. Verfürth (2016), A new heterogeneous multiscale method for time-harmonic Maxwell’s equations, SIAM J. Numer. Anal., 54, 3493–3522. This article considers a locally periodic two-scale time harmonic Maxwell equation, but the variational form is still assumed to be strictly coercive, uniformly with respect to the microscopic scale, similar to the equation considered in our present article. These authors formulate the two-scale homogenized equation in a slightly different manner. The Heterogeneous Multiscale Method (HMM) is used to solve the two-scale problem, and is shown to be equivalent to solving the two-scale homogenized equation by using the full tensor finite element spaces. © The authors 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png IMA Journal of Numerical Analysis Oxford University Press
# High-dimensional finite elements for multiscale Maxwell-type equations
, Volume 38 (1) – Jan 1, 2018
44 pages
/lp/ou_press/high-dimensional-finite-elements-for-multiscale-maxwell-type-equations-labSJOLTE4
Publisher
Oxford University Press
ISSN
0272-4979
eISSN
1464-3642
D.O.I.
10.1093/imanum/drx001
Publisher site
See Article on Publisher Site
### Abstract
Abstract We consider multiscale Maxwell-type equations in a domain $$D\subset\mathbb{R}^d$$ ($$d=2,3$$), which depend on $$n$$ microscopic scales. Using multiscale convergence, we derive the multiscale homogenized problem, which is posed in $$\mathbb{R}^{(n+1)d}$$. Solving it, we get all the necessary macroscopic and microscopic information. Sparse tensor product finite elements (FEs) are employed, using edge FEs. The method achieves a required level of accuracy with essentially an optimal number of degrees of freedom, which, apart from a multiplying logarithmic term, is equal to that for solving a problem in $$\mathbb{R}^d$$. Numerical correctors are constructed from the FE solutions. In the two-scale case, an explicit homogenization error is deduced. To get this error, the standard procedure in the homogenization literature requires the solution $$u_0$$ of the homogenized problem to belong to $$H^1({\rm curl\,},D)$$. However, in polygonal domains, $$u_0$$ belongs only to a weaker regularity space $$H^s({\rm curl\,},D)$$ for $$0<s<1$$. We derive a homogenization error estimate for this case. Though we prove the result for two-scale Maxwell-type equations, the approach works verbatim for elliptic and elasticity problems when the solution to the homogenized equation belongs to $$H^{1+s}(D)$$ (standard procedure requires $$H^2(D)$$ regularity). This homogenization error estimate is new in the literature. Thus, for two-scale problems, an explicit error for the numerical corrector is obtained; it is of the order of the sum of the homogenization error and the FE error. For the case of more than two scales, we construct a numerical corrector, albeit without a rate of convergence, as such a homogenization error is not available. Numerical experiments confirm the theoretical results. 1. Introduction We consider Maxwell-type equations that depend on $$n$$ separable microscopic scales in a domain $$D\in \mathbb{R}^d,$$ where $$d=2,3$$. The coefficients are assumed to be locally periodic with respect to each microscopic scale. We use the multiscale convergence of a bounded sequence in $$H({\rm curl\,},D)$$ to derive the multiscale homogenized equation, which contains all the necessary information. Solving it, we get the solution of the homogenized equation that describes the multiscale solution macroscopically and the scale interacting terms (the corrector terms) that encode the multiscale information. However, this equation is posed in high-dimensional product domains. It depends on $$n+1$$ variables in $$\mathbb{R}^d$$, one for each scale that the original multiscale problem depends on. The full tensor product finite element (FE) method requires a large number of degrees of freedom, and thus is prohibitively expensive. We develop the sparse tensor FE product approach, using edge FEs, for this multiscale homogenized Maxwell-type equation. The approach achieves accuracy essentially equal to that obtained by the full tensor product FEs but requires an essentially optimal level of complexity that is essentially equal to that for solving a problem in $$\mathbb{R}^d$$ only. Analytic homogenization for two-scale Maxwell-type equations is well developed. We mention the standard references Bensoussan et al. (1978), Sanchez-Palencia (1980) and Jikov et al. (1994). However, there has been little effort on numerical analysis of multiscale Maxwell-type equations. As for other multiscale problems, a direct numerical treatment needs a fine mesh which is at most of the order of the smallest scale, leading to a prohibitive level of complexity. The multiscale FE method (Hou & Wu, 1997; Efendiev & Hou, 2009) and the heterogeneous multiscale method (E & Engquist, 2003; Abdulle et al., 2012) are designed to overcome this difficulty but their applications to multiscale Maxwell-type equations have not been adequately studied. Solving cell problems to establish the homogenized equation and using the cell problems’ solutions to compute the correctors for two-scale Maxwell-type equations are performed in Zhang et al. (2010). However, as for other multiscale problems, this approach is rather expensive, especially when the coefficients are only locally periodic, as for each macroscopic point, several cell problems need to be solved. We contribute in this article a feasible general numerical method for locally periodic multiscale Maxwell-type problems. We employ the sparse tensor product FE approach developed by Hoang & Schwab (2004/05) for multiscale elliptic equations (see also Hoang, 2008; Harbrecht & Schwab, 2011; Xia & Hoang, 2014, 2015a,b). It achieves the required level of accuracy with an essentially optimal number of degrees of freedom. We note that sparse tensor edge FEs are considered in Hiptmair et al. (2013) in the context of computing the moments of the solutions to stochastic Maxwell-type problems. However, our setting is quite different, and does not require constructing the detail spaces for edge FEs. We only need the detail spaces for the nodal FEs that approximate functions in the Lebesgue spaces $$L^2$$. We then construct a numerical corrector for the solution of the original multiscale problem, using the FE solutions of the multiscale homogenized problem. In the case of two scales, we derive an explicit error estimate in terms of the homogenization error and the FE error. It is well known that for two-scale elliptic problems in a domain $$D$$, if the solution of the homogenized problem belongs to $$H^2(D)$$, and the solutions to the cell problems are sufficiently smooth, the homogenization error in the $$H^1(D)$$ norm is $${\mathcal O}(\varepsilon^{1/2}),$$ where $$\varepsilon$$ is the microscopic scale (Bensoussan et al., 1978; Jikov et al., 1994). For two-scale Maxwell-type equations, the $${\mathcal O}(\varepsilon^{1/2})$$ homogenization error in the $$H({\rm curl},D)$$ norm is obtained when the solution $$u_0$$ of the homogenized problem (4.7) belongs to $$H^1({\rm curl},D)$$. However, for polygonal domains that are of interest in FE discretization, $$u_0$$ generally belongs only to a weaker regularity space $$H^s({\rm curl\,},D)$$ for $$0<s<1$$ (see e.g., Hiptmair, 2002). For this case, we develop an approach to deriving a new homogenization error estimate. Though we present the result for Maxwell-type equations, the approach works verbatim for two-scale elliptic and elasticity problems when the solution to the homogenized problem is in $$H^{1+s}(D)$$. As far as we are aware, this is a new result in the homogenization theory and forms another main contribution of the article. For the case of more than two scales, an analytic homogenization error is not available. However, we can still derive a corrector from the FE solution of the multiscale homogenized problem, albeit without an explicit rate of convergence. This article is organized as follows. In the next section, we formulate the multiscale Maxwell-type equation. Homogenization of the multiscale Maxwell-type equation (2.4) is studied in Bensoussan et al. (1978) in the two-scale case, using two-scale asymptotic expansion. Here, we use the multiscale convergence method to study (2.4) in the general multiscale setting. We thus develop multiscale convergence for a bounded sequence in $$H({\rm curl\,},D)$$. Two-scale convergence for a bounded sequence in $$H({\rm curl\,},D)$$ is developed in Wellander & Kristensson (2003). Since we consider the general $$(n+1)$$-scale convergence and the limiting result that we use is in a slightly different form from that of Wellander & Kristensson (2003) in the two-scale case, so we present the proofs in full. FE approximations of the multiscale homogenized Maxwell-type problem are studied in Section 3. We prove the FE error estimates in cases of both full and sparse tensor product FE approximations. The errors are essentially equal (apart from a logarithmic multiplying factor), but the dimension of the sparse tensor product FE space is much lower than that of the full tensor product FE space and is essentially equal to that for solving a problem in $$\mathbb{R}^d$$ only. In Section 4, we construct numerical correctors for the solution to the original multiscale problem. For two-scale problems, we prove the general homogenization error estimate for the case where $$u_0$$ belongs to the weaker regularity space $$H^s({\rm curl\,},D),$$ where $$0<s<1$$. From that we deduce the error estimate for the numerical corrector, which is of the order of the sum of the homogenization error estimate and the FE error. For the case of more than two scales, we derive a numerical corrector but without a rate of convergence. In Section 5, we prove that the regularity required to get the FE error estimate for the sparse tensor product FEs and to get the homogenization error in the two-scale case is achievable. Section 6 contains numerical experiments that confirm our analysis. Finally, the two Appendices A and B contain the long proofs of some previous results: the proof of the homogenization error when $$u_0$$ belongs to a weaker regularity space is presented in Appendix A. Throughout the article, by $$\#$$ we denote the spaces of functions that are periodic with the period being the unit cube $$Y\subset \mathbb{R}^d$$. Repeated indices indicate summation. The notations $$\nabla$$ and $${\rm curl\,}$$ without indicating the variable explicitly denote the gradient and the $${\rm curl\,}$$ operator with respect to $$x$$ of a function of $$x$$ only, where $$\nabla_x$$ and $${\rm curl\,}_{\!x}$$ denote the partial gradient and partial $${\rm curl\,}$$ of a function depending on $$x$$ and also on other variables. We generally present the theoretical results for the three-dimensional case and mention the two-dimensional case only when it is necessary, as the two cases are largely similar. 2. Problem setting 2.1 Multiscale Maxwell-type problems Let $$D$$ be a domain in $$\mathbb{R}^d$$ ($$d=2,3$$). Let $$Y$$ be the unit cube in $$\mathbb{R}^d$$. By $$Y_1,\ldots,Y_n$$ we denote $$n$$ copies1 of $$Y$$. We denote by $${\bf Y}$$ the product set $$Y_1\times Y_2\times\cdots\times Y_n$$ and by $$\boldsymbol{y}\in{\bf Y}$$ the vector $$\boldsymbol{y}=(y_1,y_2,\ldots,y_n)$$. For each $$i=1,\ldots,n$$, we denote by $${\bf Y}_i$$ the set of vectors $$\boldsymbol{y}_i=(y_1,\ldots,y_i),$$ where $$y_j\in Y_j$$ for $$j=1,\ldots,i$$. For $$d=3$$, let $$a$$ and $$b$$ be functions with symmetric matrix values from $$D\times {\bf Y}$$ to $$\mathbb{R}^{d\times d}_{\rm sym}$$; $$a$$ and $$b$$ are continuous in $$D\times {\bf Y}$$ and are periodic with respect to each variable $$y_i$$ with the period being $$Y_i$$. We assume that for all $$x\in D$$ and $$\boldsymbol{y}\in{\bf Y}$$, and all $$\xi,\zeta\in \mathbb{R}^d$$, c∗|ξ|2≤aij(x,y)ξiξj, aij(x,y)ξiζj≤c∗|ξ||ζ|,c∗|ξ|2≤bij(x,y)ξiξj, bij(x,y)ξiζj≤c∗|ξ||ζ|, (2.1) where $$c_*$$ and $$c^*$$ are positive numbers; $$|\cdot|$$ denotes the Euclidean norm in $$\mathbb{R}^3$$. Let $$\varepsilon$$ be a small positive value, and $$\varepsilon_1,\ldots,\varepsilon_n$$ be $$n$$ functions of $$\varepsilon$$ that denote the $$n$$ microscopic scales that the problem depends on. We assume the following scale separation properties: for all $$i=1,\ldots,n-1$$, limε→0εi+1(ε)εi(ε)=0. (2.2) Without loss of generality, we assume that $$\varepsilon_1=\varepsilon$$. We define $$a^\varepsilon, b^\varepsilon: D\to\mathbb{R}^{d\times d}_{\rm sym}$$ as aε(x)=a(x,xε1,…,xεn), bε(x)=b(x,xε1,…,xεn). (2.3) Let W=H0(curl,D)={u∈L2(D)3, curlu∈L2(D)3, u×ν=0}, where $$\nu$$ denotes the outward normal vector on the boundary $$\partial D$$. Let $$f\in W'$$. We consider the problem curl(aε(x)curluε(x))+bε(x)uε(x)=f(x), (2.4) with the boundary condition $$u^{\varepsilon}\times \nu=0$$ on $$\partial D$$. We formulate this problem in the variational form as follows: find $$u^{\varepsilon}\in W$$ so that ∫D[aε(x)curluε(x)⋅curlϕ(x)+bε(x)uε(x)⋅ϕ(x)]dx=∫Df(x)⋅ϕ(x)dx (2.5) for all $$\phi\in W$$ (by $$\int_D\,f\cdot\phi\, {\rm d}x$$ we denote the duality pairing between $$W'$$ and $$W$$). The Lax–Milgram lemma guarantees the existence of a unique solution $$u^{\varepsilon}$$ that satisfies ‖uε‖W≤c‖f‖W′, (2.6) where the constant $$c$$ depends only on $$c_*$$ and $$c^*$$ in (2.1). For $$d=2$$, the matrix function $$b^\varepsilon:D\times{\bf Y}\to \mathbb{R}^{2\times 2}$$ is defined as above. As $${\rm curl\,}u^{\varepsilon}$$ is now a scalar function, $$a(x,\boldsymbol{y})$$ is a continuous function from $$D\times{\bf Y}$$ to $$\mathbb{R},$$ which is periodic with respect to each variable $$y_i$$ with the period being $$Y_i$$. In the place of (2.1), we have c∗≤a(x,y)≤c∗ ∀x∈D and y∈Y. The variational formulation in two dimensions becomes ∫D[aε(x)curluε(x)curlϕ(x)+bε(x)uε(x)⋅ϕ(x)]dx=∫Df(x)⋅ϕ(x)dx ∀ϕ∈W. (2.7) In the rest of the article, we present the results for the three-dimensional case and only mention the two-dimensional case when necessary; the results for two dimensions are similar. 2.2 Multiscale convergence We use multiscale convergence to derive the homogenized equation. We first recall the definition of multiscale convergence (see Nguetseng, 1989; Allaire, 1992; Allaire & Briane, 1996). Definition 2.1 A sequence of functions $$\{w^\varepsilon\}_\varepsilon\subset L^2(D)$$$$(n+1)$$-scale converges to a function $$w^0\in L^2(D\times {\bf Y})$$ if for all smooth functions $$\phi\in C^\infty(D\times{\bf Y}),$$ which are periodic with respect to $$y_i$$ with the period being $$Y_i$$ for $$i=1,\ldots,n$$, limε→0∫Dwε(x)ϕ(x,xε1,…,xεn)dx=∫D∫Yw0(x,y)ϕ(x,y)dydx. We have the following result. Proposition 2.2 From a bounded sequence in $$L^2(D),$$ we can extract an $$(n+1)$$-scale convergent subsequence. For a bounded sequence in $$H({\rm curl\,},D)$$, we have the following results on $$(n+1)$$-scale convergence. These results were first established in Wellander & Kristensson (2003) for the two-scale case. We present below the multiscale convergence of a bounded sequence in $$H({\rm curl\,},D),$$ which will be used to study the multiscale equations (2.5) and (2.7). By $$\tilde H_\#({\rm curl\,},Y_i)$$ we denote the equivalent classes of functions in $$H_\#({\rm curl\,},Y_i)$$ such that if $${\rm curl\,} v={\rm curl\,} w$$ we regard $$v=w$$ in $$\tilde H_\#({\rm curl\,},Y_i)$$. Proposition 2.3 Let $$\{w^\varepsilon\}_\varepsilon$$ be a bounded sequence in $$H({\rm curl\,},D)$$. There is a subsequence (not renumbered), a function $$w_0\in H({\rm curl\,},D)$$, $$n$$ functions $${\frak w_i}\in L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#(Y_i)/\mathbb{R})$$ such that wε⟶(n+1)−scalew0+∑i=1n∇yiwi. Further, there are $$n$$ functions $$w_i\in L^2(D\times Y_1\times\cdots\times Y_{i-1},\tilde H_\#({\rm curl\,},Y_i))$$ such that curlwε⟶(n+1)−scalecurlw0+∑i=1ncurlyiwi. Proof. Let $$\xi\in L^2(D\times{\bf Y})^3$$ be the $$(n+1)$$-scale limit of $$\{w^\varepsilon\}_\varepsilon$$. Consider the function $$\phi=\varepsilon_n{\it{\Phi}}(x,y_1,\ldots,y_n),$$ where $${\it{\Phi}}$$ is a function in $$C^\infty_0(D,C^\infty_\#(Y_1,\ldots,C^\infty_\#(Y_n),\ldots))^3$$ and is periodic with respect to $$y_1, \ldots,y_n$$ with the period being $$Y_1,\ldots,Y_n,$$ respectively. We then have limε→0∫Dcurlwε⋅εnΦ(x,xε1,…,xεn)dx=0. On the other hand, limε→0∫Dcurlwε⋅εnΦ(x,xε1,…,xεn)dx = limε→0∫Dwε⋅εncurlΦ(x,xε1,…,xεn)dx = limε→0∫Dwε⋅curlynΦ(x,xε1,…,xεn)dx = ∫D∫Yξ(x,y)⋅curlynΦ(x,y)dydx. Thus, there is a function $$\xi_{n-1}(x,\boldsymbol{y}_{n-1})\in L^2(D\times{\bf Y}_{n-1})$$ and a function $${\frak w_n}(x,\boldsymbol{y}_n)\in L^2(D\times{\bf Y}_{n-1},H^1_\#(Y_n)/\mathbb{R})$$ such that ξ(x,y)=ξn−1(x,yn−1)+∇ynwn(x,y). Next we choose $$\phi=\varepsilon_{n-1}{\it{\Phi}}(x,y_1,\ldots,y_{n-1})$$ for a function $${\it{\Phi}}\in C^\infty_0(D,C^\infty_\#(Y_1,\ldots,C^\infty_\#(Y_{n-1}),\ldots),$$ which is periodic with respect to $$y_1,\ldots,y_{n-1}$$. We then have 0 = limε→0∫Dcurlwε⋅εn−1Φ(x,xε1,…,xεn−1)=limε→0∫Dwε⋅curlyn−1Φ(x,xε1,…,xεn−1)dx = ∫D∫Y(ξn−1(x,yn−1)+∇ynwn(x,y))⋅curlyn−1Φ(x,y1,…,yn−1)dyn−1dx = ∫D∫Yn−1ξn−1(x,yn−1)⋅curlyn−1Φ(x,y1,…,yn−1)dyn−1dx. From this, there is a function $$\xi_{n-2}(x,\boldsymbol{y}_{n-2})\in L^2(D\times {\bf Y}_{n-2})$$ and a function $${\frak w_{n-1}}(x,\boldsymbol{y}_{n-1})\in L^2(D\times {\bf Y}_{n-2},H^1_\#(Y_{n-1})/\mathbb{R})$$ so that ξn−1(x,yn−1)=ξn−2(x,yn−2)+∇yn−1wn−1(x,yn−1), so ξ(x,y)=ξn−2(x,yn−2)+∇yn−1wn−1(x,yn−1)+∇ynwn(x,y). Continuing this process, we have ξ(x,y)=w0(x)+∑i=1n∇yiwi(x,yi), where $$w_0\in L^2(D)^3$$ and $${\frak w_i}(x,\boldsymbol{y}_i)\in L^2(D\times {\bf Y}_{i-1},H^1_\#(Y_i))$$. As $$\int_Y\xi(x,\boldsymbol{y})\,{\rm d}\boldsymbol{y}=w_0(x)$$, $$w_0$$ is the weak limit of $$w^\varepsilon$$ in $$L^2(D)^3$$. Let $$\eta(x,\boldsymbol{y})$$ be the $$(n+1)$$-scale convergence limit of $${\rm curl\,} w^\varepsilon$$ in $$L^2(D\times{\bf Y})$$. Let $${\it{\Phi}}(x,y_1,\ldots,y_n)\in C^\infty_0(D,C^\infty_\#(Y_1,\ldots,C^\infty_\#(Y_n),\ldots))$$. We have ∫Dcurlwε⋅∇Φ(x,xε1,…,xεn)dx =∫Dwε⋅curl∇Φ(x,xε1,…,xεn)dx−∫∂D(wε×ν)⋅∇Φ(x,xε1,…,xεn)ds=0. Thus, 0 = limε→ 0∫Dcurlwε⋅εn∇Φ(x,xε1,…,xεn)dx=limε→0∫Dcurlwε⋅∇ynΦ(x,xε1,…,xεn)dx = ∫D∫Yη(x,y)⋅∇ynΦ(x,y1,…,yn)dydx. Therefore, there is a function $$w_n(x,\boldsymbol{y}_n)\in L^2(D\times{\bf Y}_{n-1},\tilde H_\#({\rm curl\,},Y_n))$$ and a function $$\eta_{n-1}(x,\boldsymbol{y}_{n-1})\in L^2(D\times{\bf Y}_{n-1})$$ such that η(x,y)=ηn−1(x,yn−1)+curlynwn(x,y). Let $${\it{\Phi}}(x,y_1,\ldots,y_{n-1})\in C^\infty_0(D,C^\infty_\#(Y_1,\ldots,C^\infty_\#(Y_{n-1}),\ldots))$$. We have 0 = limε→ 0∫Dcurlwε⋅εn−1∇Φ(x,xε1,…,xεn−1)dx=limε→0∫Dcurlwε⋅∇yn−1Φ(x,xε1,…,xεn−1)dx = ∫D∫Y(ηn−1(x,yn−1)+curlynwn(x,y))⋅∇yn−1Φ(x,y1,…,yn−1)dydx = ∫D∫Yn−1ηn−1(x,yn−1)⋅∇yn−1ϕ(x,y1,…,yn−1)dyn−1dx. Therefore, there is a function $$w_{n-1}(x,\boldsymbol{y}_{n-1})\in L^2(D\times{\bf Y}_{n-2},\tilde H_\#({\rm curl\,},Y_{n-1}))$$ and a function $$\eta_{n-2}(x,\boldsymbol{y}_{n-2})\in L^2(D\times {\bf Y}_{n-2})^3$$ so that ηn−1(x,yn−1)=ηn−2(x,yn−2)+curlyn−1wn−1(x,yn−1) so η(x,y)=ηn−2(x,yn−2)+curlyn−1wn−1(x,yn−1)+curlynwn(x,y). Continuing, we find that there is a function $$\eta_0(x)\in L^2(D)^3$$ and functions $$w_i(x,\boldsymbol{y}_{i})\in L^2(D\times{\bf Y}_{i-1},\tilde H_\#({\rm curl\,},Y_i))$$ so that η(x,y)=η0(x)+∑i=1ncurlyiwi(x,yi). As for all $$\phi(x)\in C^\infty_0(D)^3$$ limε→0∫Dcurlwε(x)⋅ϕ(x)dx=∫Dη0(x)⋅ϕ(x)dx,$$\eta_0$$ is the weak limit of $${\rm curl\,} w^\varepsilon$$ in $$L^2(D)^3$$. Thus, $$\eta_0={\rm curl\,} w_0$$. We then get the conclusion. □ 2.3 Multiscale homogenized Maxwell-type problem From (2.6) and Proposition 2.3, we can extract a subsequence (not renumbered), a function $$u_0\in H_0({\rm curl\,}, D)$$, $$n$$ functions $${\frak u_i}\in L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#(Y_i)/\mathbb{R})$$ and $$n$$ functions $$u_i\in L^2(D\times Y_1\times\cdots\times Y_{i-1},\tilde H_\#({\rm curl\,},Y_i))$$ such that uε⟶(n+1)−scaleu0+∑i=1n∇yiui (2.8) and curluε⟶(n+1)−scalecurlu0+∑i=1ncurlyiui. (2.9) For $$i=1,\ldots,n$$, let $$W_i=L^2(D\times Y_1\times\cdots\times Y_{i-1},\tilde H_\#({\rm curl\,},Y_i))$$ and $$V_i=L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#(Y_i)/\mathbb{R})$$. We define the space $${\bf V}$$ as V=W×W1×⋯×Wn×V1×⋯×Vn. For $$\boldsymbol{v}=(v_0,\{v_i\},\{\frak v_i\})\in {\bf V}$$, we define the norm |||v|||=‖v0‖H(curl,D)+∑i=1n‖vi‖L2(D×Yi−1,H~#(curl,Yi))+∑i=1n‖vi‖L2(D×Yi−1,H#1(Yi)/R). We then have the following result. Proposition 2.4 We define $$\boldsymbol{u}=(u_0,\{u_i\}, \{\frak u_i\})\in{\bf V}$$. Then $$\boldsymbol{u}$$ satisfies B(u,v):=∫D∫Y[a(x,y)(curlu0+∑i=1ncurlyiui)⋅(curlv0+∑i=1ncurlyivi) +b(x,y) (u0+∑i=1n∇yiui)⋅(v0+∑i=1n∇yivi)]dydx=∫Df(x)⋅v0(x)dx (2.10) for all $$\boldsymbol{v}=(v_0,\{v_i\},\{\frak v_i\})\in {\bf V}$$. Proof. Let $$v_0\in C^\infty_0(D)^3$$, $$v_i\in C^\infty_0(D, C^\infty_\#(Y_1,\ldots,C^\infty_\#(Y_i),\ldots))^3$$ and $${\frak v_i}\in C^\infty_0(D,C^\infty_\#(Y_1,\ldots,C^\infty_\# (Y_i),\ldots))$$ for $$i=1,\ldots,n$$. Let the test function $$v$$ in (2.5) be v(x)=v0(x)+∑i=1nεi(vi(x,xε1,…,xεi)+∇vi(x,xε1,…,xεi)). We have ∫D[aε(x)curluε(x)⋅(curlv0(x)+∑i=1nεicurlxvi(x,xε1,…,xεi)+∑i=1n∑j=1iεiεjcurlyjvi(x,xε1,…,xεi) + ∑i=1nεicurl∇vi(x,xε1,…,xεi)) +bε(x)uε(x)⋅(v0(x)+∑i=1nεivi(x,xε1,…,xεi) +∑i=1nεi∇xvi(x,xε1,…,xεi)+∑i=1n∑j=1iεiεj∇yjvi(x,xε1,…,xεi))]dx =∫Df(x)⋅(v0(x)+∑i=1nεivi(x,xε1,…,xεi) +∑i=1nεi∇xvi(x,xε1,…,xεn)+∑i=1n∑j=1iεiεj∇yjvi(x,xε1,…,xεi)). Using multiscale convergence and the scale separation (2.2), letting $$\varepsilon$$ go to 0, we have ∫D∫Y[a(x,y)(curlu0+∑i=1ncurlyiui)⋅(curlv0+∑i=1ncurlyivi) +b(x,y)(u0+∑i=1n∇yiui)⋅(v0+∑i=1n∇yivi)]dydx =∫Df(x)⋅v0(x)dx+∫D∫Yf(x)⋅∑i=1n∇yivi(x,y1,…,yi)dydx =∫Df(x)⋅v0(x)dx. Using a density argument, we have (2.10). □ Proposition 2.5 The bilinear form $$B:{\bf V}\times{\bf V}\to \mathbb{R}$$ is coercive and bounded, i.e., there are positive constants $$C^*$$ and $$C_*$$ so that B(u,v)≤C∗|||u||||||v|||andC∗|||u||||||u|||≤B(u,u) (2.11) for all $$\boldsymbol{u},\boldsymbol{v}\in {\bf V}$$. Problem (2.10) thus has a unique solution. The convergence relations (2.8) and (2.9) hold for the whole sequence $$\{u^{\varepsilon}\}_\varepsilon$$. Proof. It is easy to see that there is a positive constant $$C^*$$ such that B(u,v)≤C∗|||u||||||v|||. Now we show that $$B$$ is coercive. We have from (2.1), B(u,u) ≥c∗∫D∫Y(|curlu0+∑i=1ncurlyiui|2+|u0+∑i=1n∇yiui|2)dydx ≥c∫D∫Y(|curlu0|2+∑i=1n|curlyiui|2+|u0|2+|∇yiui|2)dydx≥c|||u|||2. We then get the conclusion from Lax–Milgram lemma. □ 3. FE discretization Let $$D$$ be a polygonal domain in $$\mathbb{R}^3$$. We consider a hierarchy of simplices $$\mathcal{T}^l$$ ($$l=0,1,\ldots$$), where $$\mathcal{T}^{l+1}$$ is obtained from $$\mathcal{T}^l$$ by dividing each simplex in $$\mathcal{T}^l$$ into eight tedrahedra. The mesh size of $$\mathcal{T}^l$$ is $$h_l={\mathcal O}(2^{-l})$$. For each tedrahedron $$T$$, we consider the edge FE space R(T)={v: v=α+β×x, α,β∈R3}. When $$d=2$$, $$\mathcal{T}^{l+1}$$ is obtained from $$\mathcal{T}^l$$ by dividing each simplex in $$\mathcal{T}^l$$ into four congruent triangles. For each triangle $$T$$, we consider the edge FE space R(T)={v: v=(α1α2)+β(x2−x1)}, where $$\alpha_1,\alpha_2$$ and $$\beta$$ are constants. Alternatively, if the domain can be partitioned into a set of cubes, we can use edge FE on a cubic mesh instead (see Monk, 2003). We denote by $$\mathcal{P}_1(T)$$ the set of linear polynomials in each simplex $$T$$. In the following, we present the analysis for the three-dimensional case only; the two-dimensional case is similar. For the cube $$Y$$, we partition it into a hierarchy of simplices $$\mathcal{T}^l_\#,$$ which are distributed periodically. We consider the FE spaces Wl ={v∈H0(curl,D), v|T∈R(T) ∀T∈Tl},Vl ={v∈H1(D), v|T∈P1(T) ∀T∈Tl},W#l ={v∈H#(curl,Y), v|T∈R(T) ∀T∈T#l} and V#l={v∈H#1(Y), v|T∈P1(T) ∀T∈T#l}. For $$d=2,3$$, we have the following estimates (see Ciarlet, 1978; Monk, 2003): infvl∈Wl‖v−vl‖H(curl,D)≤chls(‖v‖Hs(D)d+‖curlv‖Hs(D)d) for all $$v\in H_0({\rm curl\,}, D)\bigcap H^s({\rm curl\,},D)$$; infvl∈W#l‖v−vl‖H#(curl,Y)≤chls(‖v‖Hs(Y)d+‖curlv‖Hs(Y)d) for all $$v\in H_\#({\rm curl\,}, Y)\bigcap H^s({\rm curl\,}, Y)$$; infvl∈Vl‖v−vl‖L2(D)≤chls‖v‖Hs(D) for all $$v\in H^s(D)$$; infvl∈V#l‖v−vl‖L2(Y)≤chls‖v‖Hs(Y) for all $$v\in H^s_\#(Y)$$ and infvl∈V#l‖v−vl‖H#1(Y)≤chls‖v‖H1+s(Y) for all $$v\in H^1_\#(Y)\bigcap H^{1+s}(Y)$$. 3.1 Full tensor product FEs As $$L^2(D\times{\bf Y}_{i-1},\tilde H_\#({\rm curl\,},Y_i))\cong L^2(D)\otimes L^2(Y_1)\otimes\cdots\otimes L^2(Y_{i-1})\otimes \tilde H_\#({\rm curl\,},Y_i),$$ we use the tensor product FE space Wil=Vl⊗V#l⊗⋯⊗V#l⏟i−1 times ⊗W#l to approximate $$u_i$$. Similarly, as $${\frak u_i}\in L^2(D\times{\bf Y}_{i-1},H^1_\#(Y))$$, we use the FE space Vil=Vl⊗V#l⊗⋯⊗V#l⏟i times to approximate $${\frak u_i}$$. We define the space Vl=Wl×W1l×⋯×Wnl×V1l×⋯×Vnl. The full tensor product FE approximating problem is, find $$\boldsymbol{u}^L\in{\bf V}^L$$ so that B(uL,vL)=∫Df(x)⋅v0L(x)dx ∀vL=(v0L,{viL},viL)∈VL. (3.1) To get an error estimate for this FE approximating problem, we define the following regularity spaces for $${\frak u_i}$$ and $$u_i$$. For the functions $$u_i$$, we define the regularity space $$\mathcal{H}_i$$ of functions $$w$$ in $$L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#({\rm curl\,},Y_i))$$ such that for all $$k=1,2,3$$, ∂w∂xk∈L2(D×Y1×⋯×Yi−1,H~#(curl,Yi)) and for all $$j=1,\ldots,i-1$$ and $$k=1,2,3$$, ∂w∂(yj)k∈L2(D×Y1×⋯×Yi−1,H~#(curl,Yi)). In other words, for all $$w\in \mathcal{H}_i$$, $$w$$ belongs to $$L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#({\rm curl\,},Y_i))$$, $$L^2(Y_1\times\cdots\times Y_{i-1},H^1(D,\tilde H_\#({\rm curl\,},Y_i)))$$ and $$L^2(D\times\prod_{k<i,k\ne j}Y_k,H^1_\#(Y_j,\tilde H_\#({\rm curl\,},Y_i)))$$ for $$j=1,\ldots,i-1$$. For $$0<s<1$$, we define the space $$\mathcal{H}^s_i$$ by interpolation. It consists of functions $$w$$ such that $$w$$ belongs to $$L^2(D\times Y_1\times\cdots\times Y_{i-1},H^s_\#({\rm curl\,},Y_i))$$, $$L^2(Y_1\times\cdots\times Y_{i-1},H^s(D,\tilde H_\#({\rm curl\,},Y_i)))$$ and $$L^2(D\times\prod_{k<i,k\ne j}Y_k,H^s_\#(Y_j,\tilde H_\#({\rm curl\,},Y_i)))$$. We equip $$\mathcal{H}_i^s$$ with the norm ‖w‖His =‖w‖L2(D×Y1×⋯×Yi−1,H#s(curl,Yi))+‖w‖L2(Y1×⋯×Yi−1,Hs(D,H~#(curl,Yi))) +∑j=1i−1‖w‖L2(D×∏k<i,k≠j,H#s(Yj,H~#(curl,Yi))). We then have the following lemma. Lemma 3.1 For $$w\in \mathcal{H}_i^s$$, infwl∈Wil‖w−wl‖L2(D×Y1×⋯×Yi−1,H~#(curl,Yi))≤chls‖w‖His. The proof of this lemma is similar to that for full tensor product FEs in Hoang & Schwab (2004/05) and Bungartz & Griebel (2004), using orthogonal projection. We refer to Hoang & Schwab (2004/05) and Bungartz & Griebel (2004) for details. We define $${\frak H_i}^s$$ as the space of functions $$w\in L^2(D\times Y_1\times\cdots\times Y_{i-1},H^{1+s}_\#(Y_i))$$ such that $$w\in L^2(Y_1\times\cdots\times Y_{i-1},H^s(D,H^1_\#(Y_i)))$$ and for all $$j=1,\ldots,i-1$$, $$w\in L^2(D\times\prod_{k<i,k\ne j}Y_k,H^s_\#(Y_{j},H^1_\#(Y_i)))$$. We then define the norm ‖w‖His =‖w‖L2(D×Y1×⋯×Yi−1,H#1+s(Yi))+‖w‖L2(Y1×⋯×Yi−1,Hs(D,H1(Yi))) +∑j=1i−1‖w‖L2(D×∏k<i,k≠jYk,Hs(Yj,H1(Yi))). We have the following result. Lemma 3.2 For $$w\in {\frak H_i}^s$$, infwl∈Vil‖w−wl‖L2(D×Y1×⋯×Yi−1,H#1(Yi))≤chls‖w‖His. We then define the regularity space Hs=Hs(curl,D)×H1s×⋯×Hns×H1s×⋯×Hns with the norm ‖w‖Hs=‖w0‖Hs(curl,D)+∑i=1n‖wi‖His+∑i=1n‖wi‖His for $$\boldsymbol{w}=(w_0,\{w_i\},\{\frak w_i\})\in \boldsymbol{\mathcal{H}}^s$$. We have the following approximation result. Lemma 3.3 For $$\boldsymbol{w}\in \boldsymbol{\mathcal{H}}^s$$ infwl∈Vl‖w−wl‖V≤chls‖w‖Hs. From the boundedness and coerciveness conditions (2.11), using Cea’s lemma, we deduce the following result. Proposition 3.4 If $$\boldsymbol{u}\in \boldsymbol{\mathcal{H}}^s$$, for the full tensor product FE approximating problem (3.1) we have the error estimate ‖u−uL‖V≤chLs‖u‖Hs. (3.2) 3.2 Sparse tensor product FEs We define the following orthogonal projection: Pl0:L2(D)→Vl,P#l0:L2(Y)→V#l with the convention $$P^{-10}=0$$, $$P^{-10}_\#=0$$. We define the following detail spaces: Vl=(Pl0−P(l−1)0)Vl, V#l=(P#l0−P#(l−1)0)Vl. Since Vl=⨁0≤i≤lViandV#l=⨁0≤i≤lV#i, the full tensor product spaces $$W_i^L$$ and $$V_i^L$$ are defined as WiL=(⨁0≤l0,…,li−1≤LVl0⊗V#l1⊗⋯⊗V#li−1)⊗W#L and ViL=(⨁0≤l0,…,li−1≤LVl0⊗V#l1⊗⋯⊗V#li−1)⊗V#L. We then define the sparse tensor product FE spaces as W^iL=⨁l0+⋯+li−1≤LVl0⊗V#l1⊗⋯⊗V#li−1⊗W#L−(l0+⋯+li−1) and V^iL=⨁l0+⋯+li−1≤LVl0⊗V#l1⊗⋯⊗V#li−1⊗V#L−(l0+⋯+li−1). The function $$\boldsymbol{u}$$ is approximated by the space V^L=WL⊗W^1L⊗⋯⊗W^nL⊗V^1L⊗⋯⊗V^nL. The sparse tensor product FE approximating problem is, find $$\widehat {\bf{u}}^L\in \hat{\bf V}^L$$ such that B(u^L,v^L)=∫Df(x)⋅v^0L(x)dx ∀v^L=(v^0L,{v^iL},{v^iL})∈V^L. (3.3) From the coerciveness and boundedness conditions in (2.11), using Cea’s lemma we deduce the error estimate for the sparse tensor product approximating problem ‖u−u^L‖V≤cinfv^L∈VL‖u−v^L‖V. To quantify the error estimate, we use the following regularity spaces. We define $$\hat{\mathcal{H}}_i$$ as the space of functions $$w\in L^2(D\times Y_1\times\cdots\times Y_{i-1},H^1_\#({\rm curl\,},Y_i)),$$ which are periodic with respect to $$y_j$$ with the period being $$Y_j$$ ($$j=1,\ldots,i-1$$) such that for any $$\alpha_0,\alpha_1,\ldots,\alpha_{i-1}\in \mathbb{N}_0^d$$ with $$|\alpha_k|\le 1$$ for $$k=0,\ldots,i-1$$, ∂|α0|+|α1|+⋯+|αi−1|∂xα0∂y1α1⋯∂yi−1αi−1w∈L2(D×Y1×⋯×Yi−1,H#1(curl,Yi)). We equip $$\hat{\mathcal{H}}_i$$ with the norm ‖w‖H^i=∑αj∈Rd,|αj|≤10≤j≤i−1‖∂|α0|+|α1|+⋯+|αi−1|∂xα0∂y1α1⋯∂yi−1αi−1w‖L2(D×Y1×⋯×Yi−1,H#1(curl,Yi)). We can write $$\hat{\mathcal{H}}_i$$ as $$H^1(D,H^1_\#(Y_1,\ldots,H^1_\#(Y_{i-1},H^1_\#({\rm curl\,},Y_i)),\ldots))$$. By interpolation, we define $$\hat{\mathcal{H}}_i^s=H^s(D,H^s_\#(Y_1,\ldots,H^s_\#(Y_{i-1},H^s_\#({\rm curl\,},Y_i)),\ldots))$$ for $$0<s<1$$. We define $$\hat{\frak H}_i$$ as the space of functions $$w\in L^2(D\times Y_1\times\cdots\times Y_{i-1},H^2_\#(Y_i))$$ that are periodic with respect to $$y_j$$ with the period being $$Y_j$$ for $$j=1,\ldots,i-1$$ such that $$\alpha_0,\alpha_1,\ldots,\alpha_{i-1}\in \mathbb{N}_0^d$$ with $$|\alpha_k|\le 1$$ for $$k=0,\ldots,i-1$$, ∂|α0|+|α1|+⋯+|αi−1|∂xα0∂y1α1⋯∂yi−1αi−1w∈L2(D×Y1×⋯×Yi−1,H#2(Yi)). The space $$\hat{\frak H}_i$$ is equipped with the norm ‖w‖H^i=∑αj∈Rd,|αj|≤10≤j≤i−1‖∂|α0|+|α1|+⋯+|αi−1|∂xα0∂y1α1⋯∂yi−1αi−1w‖L2(D×Y1×⋯×Yi−1,H#2(Yi)). We can write $$\hat{\frak H}_i$$ as $$H^1(D,H^1_\#(Y_1,\ldots,H^1_\#(Y_{i-1},H^2_\#(Y_i))))$$. By interpolation, we define the space $$\hat{\frak H}_i^s:=H^s(D,H^s(Y_1,\ldots,H^s(Y_{i-1},H^{1+s}_\#(Y_i))))$$. The regularity space $$\hat{\boldsymbol{\mathcal{H}}}^s$$ is defined as H^s=Hs(curl,D)×H^1s×⋯H^ns×H^1s×⋯×H^ns. Lemmas 3.5 and 3.6 present the approximating properties of functions in $$\hat{\mathcal{H}}_i^s$$ and $${\hat{\frak H}_i^s}$$. The proofs follow from those for sparse tensor products in Hoang & Schwab (2004/05) and Bungartz & Griebel (2004). Lemma 3.5 For $$w\in \hat{\mathcal{H}}_i^s$$, infwL∈W^iL‖w−wL‖L2(D×Y1×⋯×Yi−1,H#(curl,Yi))≤cLi/2hLs‖w‖H^is. Similarly we have the following lemma. Lemma 3.6 For $$w\in \hat{\frak H}_i^s$$, infwL∈V^iL‖w−wL‖L2(D×Y1×⋯×Yi−1,H#1(Yi))≤cLi/2hLs‖w‖H^is. From these lemmas we deduce the following result. Lemma 3.7 For $$\boldsymbol{w}\in \hat{\boldsymbol{\mathcal{H}}}^s$$, infwL∈V^L‖w−wL‖V≤cLn/2hLs‖w‖H^s. From this we deduce the following error estimate for the sparse tensor product FE problem (3.3). Proposition 3.8 If the solution $$\boldsymbol{u}$$ of problem (2.10) belongs to $$\hat{\boldsymbol{\mathcal{H}}}^s$$ then ‖u−u^‖V≤cLn/2hLs‖u‖H^s. Remark 3.9 The dimension of the full tensor product FE space $${\bf V}^L$$ is $${\mathcal O}(2^{dnL}),$$ which is very large when $$L$$ is large. The dimension of the sparse tensor product FE space $$\hat{\bf V}^L$$ is $${\mathcal O}(L^n2^{dL}),$$ which is essentially equal to the number of degrees of freedom for solving a problem in $$\mathbb{R}^d$$ obtaining the same level of accuracy. 4. Convergence in physical variables We employ the FE solutions for the multiscale homogenized Maxwell-type equation (2.10) in the previous section to derive numerical correctors for the solution $$u^{\varepsilon}$$ of the multiscale problem (2.4). In the two-scale case, we derive the homogenization error explicitly in terms of $$\varepsilon$$ so that an error in terms of the microscopic scale $$\varepsilon$$ and the mesh size is obtained for the numerical corrector. We consider the general case, where the solution $$u^0$$ of the homogenized problem belongs to the space $$H^s({\rm curl\,},D)$$ for $$0<s\le 1$$, thus generalizing the standard homogenization rate of convergence $$\varepsilon^{1/2}$$ for elliptic problems (see e.g, Bensoussan et al., 1978; Jikov et al., 1994). This is a new result in homogenization theory. We present it for two-scale Maxwell-type equations, but the procedure works verbatim for two-scale elliptic and elasticity problems, where the solutions of the homogenized problems belong to $$H^{1+s}(D)$$. We present this section for the case $$d=3$$; the case $$d=2$$ is similar. 4.1 Two-scale problems For the two-scale case, we denote the function $$a(x,\boldsymbol{y})$$ by $$a(x,y)$$. The two-scale homogenized equation becomes ∫D∫Y[a(x,y)(curlu0+curlyu1)⋅(curlv0+curlyv1)+b(x,y)(u0+∇yu1)⋅(v0+∇yv1)]dydx =∫Df(x)⋅v0(x)dx. We first let $$v_0=0$$, $$v_1=0$$ and deduce that ∫D∫Yb(x,y)(u0+∇yu1)⋅∇yv1dydx=0. For each $$r=1,2,3$$, let $$w^r(x,\cdot)\in L^2(D, H^1_\#(Y)/\mathbb{R})$$ be the solution of the problem ∫D∫Yb(x,y)(er+∇ywr)⋅∇yψdydx=0 ∀ψ∈L2(D,H#1(Y)/R), (4.1) where $$e_r$$ is the vector in $$\mathbb{R}^3$$ with all the components being 0, except the $$r$$th component, which equals 1. This is the standard cell problem in elliptic homogenization. From this we have u1(x,y)=wr(x,y)u0r(x). (4.2) Therefore, ∫D∫Yb(x,y)(u0+∇yu1)⋅v0dxdy=∫Db0(x)u0(x)⋅v0(x)dx, where the positive-definite matrix $$b^0(x)$$ is defined as bij0(x)=∫Yb(x,y)(ej+∇wj(x,y))⋅(ei+∇ywi(x,y))dy, (4.3) which is the usual homogenized coefficient for elliptic problems with the two-scale coefficient matrix $$b^\varepsilon$$. Let $$v_0=0$$ and $${\frak v_1}=0$$. We have ∫D∫Ya(x,y)(curlu0+curlyu1)⋅curlyv1dydx=0 for all $$v_1\in L^2(D, \tilde H_\#({\rm curl\,},Y))$$. For each $$r=1,2,3$$, let $$N^r\in L^2(D,\tilde H_\#({\rm curl\,},Y))$$ be the solution of ∫D∫Ya(x,y)(er+curlyNr)⋅curlyvdydx=0 (4.4) for all $$v\in L^2(D, \tilde H_\#({\rm curl\,},Y))$$. We have u1=(curlu0(x))rNr(x,y). (4.5) The homogenized coefficient $$a^0$$ is determined by aij0(x)=∫Ya(x,y)ip(ejp+(curlyNj)p)dy=∫Ya(x,y)(ej+curlyNj)⋅(ei+curlyNi)dy. (4.6) We have ∫D∫Ya(x,y)(curlu0+curlyu1)⋅curlv0dxdy=∫Da0(x)curlu0(x)⋅curlv0(x)dx. The homogenized problem is ∫D[a0(x)curlu0(x)⋅curlv0(x)+b0(x)u0(x)⋅v0(x)]dx=∫Df(x)⋅v0(x)dx ∀v0∈H0(curl,D). (4.7) Following the procedure for deriving the homogenization error (Bensoussan et al., 1978; Jikov et al., 1994), we have the following homogenization error estimate. Theorem 4.1 Assume that $$a\in C(\bar D, C(\bar Y))^{3\times 3}$$, $$u_0\in H^1({\rm curl\,};D)$$, $$N^r\in C^1(\bar D,C(\bar Y))^3$$, $${\rm curl}_yN^r\in C^1(\bar D,C(\bar Y))^3$$, $$w^r\in C^1(\bar D,C^1(\bar Y))$$ for all $$r=1,2,3$$, then2 ‖uε−[u0+∇yu1(⋅,⋅ε)]‖L2(D)3≤cε1/2 and ‖curluε−[curlu0+curlyu1(⋅,⋅ε)]‖L2(D)3≤cε1/2. The proof of this theorem uses the functions $$G_r$$ and $$g_r$$ defined in (A.2) and (A.3) below. For $$u_0\in H^s({\rm curl\,},D)$$ when $$0<s<1$$, we have the following homogenization error estimate. Theorem 4.2 Assume that $$a\in C(\bar D,C(\bar Y))^{3\times 3}$$, $$u_0\in H^s({\rm curl\,},D)$$, $$N^r\in C^1(\bar D, C(\bar Y))^3$$, $${\rm curl}_yN^r\in C^1(\bar D,C(\bar Y))^3$$ and $$w^r\in C^1(\bar D,C^1(\bar Y))$$ for all $$r=1,2,3$$, then ‖uε−[u0+∇yu1(⋅,⋅ε)‖L2(D)3≤cεs/(1+s) and ‖curluε−[curlu0+curlyu1(⋅,⋅ε)]‖L2(D)3≤cεs/(1+s). We present the proof of this theorem in Appendix A. To employ the FE solutions to construct numerical correctors for $$u^{\varepsilon}$$, we define the following operator: Uε(Φ)(x)=∫YΦ(ε[xε]+εz,{xε})dz. (4.8) Let $$D^\varepsilon$$ be a $$2\varepsilon$$ neighbourhood of $$D$$. Regarding $${\it{\Phi}}$$ as zero when $$x$$ is outside $$D$$, we have ∫DεUε(Φ)(x)dx=∫D∫YΦ(x,y)dxdy. (4.9) The proof of (4.9) may be found in Cioranescu et al. (2008). We have the following result. Lemma 4.3 Assume that for $$r=1,2,3$$, $${\rm curl}_yN^r(x,y)\in C^1(\bar D, C(\bar Y))^3$$ and $$u_0\in H^s({\rm curl\,},D)$$, then ‖curlyu1(⋅,⋅ε)−Uε(curlyu1)‖L2(D)3≤cεs. We prove this lemma in Appendix B. We then have the following result. Theorem 4.4 Assume that $$a\in C(\bar D,C(\bar Y))^{3\times 3}$$, $$u_0\in H^s({\rm curl\,},D)$$, $$N^r\in C^1(\bar D,C(\bar Y))^3$$, $${\rm curl}_yN^r\in C^1(\bar D,C(\bar Y))^3$$ and $$w^r\in C^1(\bar D,C^1(\bar Y))$$ for all $$r=1,2,3$$. Then for the full tensor product FE solution $$(u_0^L,u_1^L,{\frak u_1}^L)$$ we have ‖uε−u0L−Uε(∇uu1L)‖L2(D)3≤c(εs/(1+s)+hLs) and ‖curluε−curlu0L−Uε(curlyu1L)‖L2(D)3≤c(εs/(1+s)+hLs). Proof. From Lemma 4.3, we have ‖curluε−curlu0L−Uε(curlyu1L)‖L2(D)3 ≤‖curluε−curlu0−curlyu1(⋅,⋅ε)‖L2(D)3 +‖curlu0−curlu0L‖L2(D)3+‖curlyu1(⋅,⋅ε)−Uε(curlyu1)‖L2(D)3 +‖Uε(curlyu1)−Uε(curlyu1L)‖L2(D)3. Using the fact that $$(\mathcal{U}^\varepsilon({\it{\Phi}}))^2\le \mathcal{U}({\it{\Phi}}^2)$$ and (4.9), we have ‖Uε(curlyu1)−Uε(curlyu1L)‖L2(D)3≤‖curlyu1−curlyu1L‖L2(D×Y)3≤chLs. This together with (3.2), Theorem 4.2 and Lemma 4.3 gives ‖curluε−curlu0L−Uε(curlyu1L)‖L2(D)3≤c(εs/(1+s)+hLs). Similarly, we have ‖uε−u0L−Uε(∇uu1L)‖L2(D)3≤c(εs/(1+s)+hLs). □ For the sparse tensor product FE approximation, we have the following result. Theorem 4.5 Assume that $$a\in C(\bar D,C(\bar Y))^{3\times 3}$$, $$u_0\in H^s({\rm curl\,},D)$$, $$N^r\in C^1(\bar D,C(\bar Y))^3$$, $${\rm curl}_yN^r\in C^1(\bar D,C(\bar Y))^3$$ and $$w^r\in C^1(\bar D,C^1(\bar Y))$$ for all $$r=1,2,3$$. Then for the sparse tensor product FE solution $$(\hat u_0^L,\hat u_1^L,\hat{\frak u}_1^L)$$ we have ‖uε−u^0L−Uε(∇yu^1L)‖L2(D)3≤c(εs/(1+s)+Ln/2hLs) and ‖curluε−curlu^0L−Uε(curlyu^1L)‖L2(D)3≤c(εs/(1+s)+Ln/2hLs). 4.2 Multiscale problems For multiscale problems, we do not have an explicit homogenization rate of convergence. However, for the case where $$\varepsilon_i/\varepsilon_{i+1}$$ is an integer for all $$i=1,\ldots,n-1$$ we can derive a corrector for the solution $$u^{\varepsilon}$$ of the multiscale problem from the FE solutions of the multiscale homogenized problem. For each function $$\phi\in L^1(D),$$ which is understood as 0 outside $$D$$, we define a function in $$L^1(D\times{\bf Y})$$: Tnε(ϕ)(x,y)=ϕ(ε1[xε1]+ε2[y1ε2/ε1]+⋯+εn[yn−1εn/εn−1]+εnyn). Letting $$D^{\varepsilon_1}$$ be the $$2\varepsilon_1$$ neighbourhood of $$D$$, we have ∫Dϕdx=∫Dε1∫Y1⋯∫YnTnε(ϕ)dyn⋯dy1dx (4.10) for all $$\phi \in L^1(D)$$. If a sequence $$\{\phi^\varepsilon\}_\varepsilon$$$$(n+1)$$-scale converges to $$\phi(x,y_1,\ldots,y_n)$$ then Tnε(ϕ)⇀ϕ(x,y1,…,yn) in $$L^2(D\times Y_1\times\ldots\times Y_n)$$. Thus, when $$\varepsilon\to 0$$, Tnε(curluε)⇀curlu0+curly1u1+⋯+curlynun (4.11) and Tnε(uε)⇀u0+∇y1u1+⋯+∇ynun (4.12) in $$L^2(D\times{\bf Y})^3$$. To deduce an approximation of $$u^{\varepsilon}$$ in $$H({\rm curl\,},D)$$ in terms of the FE solution, we use the operator $$\mathcal{U}_n^\varepsilon$$ , which is defined as Unε(Φ)(x) =∫Y1⋯∫YnΦ(ε1[xε1]+ε1t1,ε2ε1[ε1ε2{xε1}] +ε2ε1t2,⋯, εnεn−1[εn−1εn{xεn−1}]+εnεn−1tn,{xεn})dtn⋯dt1 for all functions $${\it{\Phi}}\in L^1(D\times{\bf Y})$$. For each function $${\it{\Phi}}\in L^1(D\times{\bf Y})$$ we have ∫Dε1Unε(Φ)dx=∫D∫YΦ(x,y)dydx. (4.13) The proofs for these facts may be found in Cioranescu et al. (2008). We then have the following corrector result. Proposition 4.6 The solution $$u^{\varepsilon}$$ of problem (2.5) and the solution $$(u_0,\{u_i\}\,\{{\frak u_i}\})$$ of problem (2.10) satisfies limε→0‖uε−[u0+Unε(∇y1u1)+⋯+Unε(∇ynun)‖L2(D)3=0 (4.14) and limε→0‖curluε−[curlu0+Unε(curly1u1)+⋯+Unε(curlynun)]‖L2(D)3=0. (4.15) Proof. We consider the expression ∫D∫Y[Tnε(aε)(Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun)) ⋅(Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun)) +Tnε(bε)(Tnε(uε)−(u0+∇y1u1+⋯+∇ynun))⋅(Tnε(uε)−(u0+∇y1u1+⋯+∇ynun))dydx. Using (2.5), (2.10), (4.10), (4.11) and (4.12), we deduce that this expression converges to 0. From (2.1) we have limε→0‖Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun)‖L2(D×Y1×…×Yn)3=0 and limε→0‖Tnε(uε)−(u0+∇y1u1+⋯+∇ynun)‖L2(D×Y1×⋯×Yn)3=0. From (4.13) and the fact that $$\mathcal{U}^\varepsilon_n({\it{\Phi}})^2\le \mathcal{U}^\varepsilon_n({\it{\Phi}}^2)$$, we have ∫D|Unε(Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun)(x)|2dx ≤∫DUnε(|Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun|2)(x)|dx ≤∫D∫Y|Tnε(curluε)−(curlu0+curly1u1+⋯+curlynun|2)dydx, which converges to 0 when $$\varepsilon\to 0$$. Using $$\mathcal{U}^\varepsilon_n(\mathcal{T}^\varepsilon_n({\it{\Phi}}))={\it{\Phi}}$$, we get (4.15). We derive (4.14) similarly. □ We then deduce the numerical corrector result. Theorem 4.7 For the full tensor product FE approximation solution $$\boldsymbol{u}^L=(u_0^L,\{u_i^L\},\{{\frak u_i}^L\})$$ in (3.1), we have limε→0L→∞‖uε−[u0L+Unε(∇y1u1L)+⋯+Unε(∇ynunL)]‖L2(D)3=0 (4.16) and limε→0L→∞‖curluε−[curlu0L+Unε(curly1u1L)+⋯+Unε(curlynunL)]‖L2(D)3=0. (4.17) Proof. We note that ‖Unε(curly1u1+⋯+curlynun)−Unε(curly1u1L+⋯+curlynunL)‖L2(D)3 ≤∫DUnε(|(curly1u1+⋯+curlynun)−(curly1u1L+⋯+curlynunL)|2)(x)dx ≤∫D∫Y|(curly1u1+⋯+curlynun)−(curly1u1L+⋯+curlynunL)|2dydx, which converges to 0 when $$L\to \infty$$. From this and (4.15), we get (4.17). We obtain (4.16) in the same way. □ Remark 4.8 As $${\bf V}^{\lceil L/n\rceil}\subset\hat{\bf V}^L$$, the result in Theorem 4.7 also holds for the sparse tensor product FE solution $$\widehat {\bf{u}}^L$$. Since we do not have an explicit homogenization error for problems with more than two scales, we do not distinguish the two cases of full and sparse tensor FE approximations. 5. Regularity of $$\boldsymbol{N^r}$$, $$\boldsymbol{w^r}$$ and $$\boldsymbol{u_0}$$ We show in this section that the regularity requirements for obtaining the sparse tensor product FE error estimate and the homogenization error estimate in the previous sections are achievable. We present the results for the two-scale case in detail. The multiscale case is similar; we summarize it in Remark 5.7. We first prove the following lemma. Lemma 5.1 Let $$\psi\in H_\#({\rm curl\,},Y)\bigcap H_\#({\rm div},Y)$$. Assume further that $$\int_Y\psi(y)\,{\rm d}y=0$$. Then $$\psi\in H^1_\#(Y)^3$$ and ‖ψ‖H1(Y)3≤c(‖curlyψ‖L2(Y)3+‖divyψ‖L2(Y)). Proof. Let $$\omega\subset\mathbb{R}^3$$ be a smooth domain such that $$\omega\supset Y$$. Let $$\eta\in \mathcal{D}(\omega)$$ be such that $$\eta(y)=1$$ when $$y\in Y$$. We have curly(ηψ)=ηcurlyψ+∇yη×ψ∈L2(ω)3 and divy(ηψ)=∇yη⋅ψ+ηdivyψ∈L2(ω)3. Together with the zero boundary condition, we conclude that $$\eta\psi\in H^1(\omega)^3$$ so $$\psi\in H^1(Y)^3$$. We note that ∫Y(divyψ(y)2+|curlyψ(y)|2)dy=∑i,j=13∫Y(∂ψi∂yj)2+∑i≠j∫Y∂ψi∂yi∂ψj∂yjdy−∑i≠j∫Y∂ψj∂yi∂ψi∂yjdy. Assume that $$\psi$$ is a smooth periodic function. We have ∫Y∂ψi∂yi∂ψj∂yjdy=∫Y[∂∂yi(ψi∂ψj∂yj)−ψi∂2ψj∂yi∂yj]dy=−∫Yψi∂2ψj∂yi∂yjdy as $$\psi$$ is periodic. Similarly, we have ∫Y∂ψi∂yj∂ψj∂yidy=∫Y[∂∂yj(ψi∂ψj∂yi)−ψi∂2ψj∂yj∂yi]dy=−∫Yψi∂2ψj∂yj∂yidy. Thus, ∫Y∂ψi∂yi∂ψj∂yjdy=∫Y∂ψi∂yj∂ψj∂yidy. Therefore, ‖∇yψ‖L2(Y)32=‖divyψ‖L2(Y)2+‖curlyψ‖L2(Y)32. Using a density argument, this holds for all $$\psi\in H^1_\#(Y)^3$$. As $$\int_Y\psi(y)\,{\rm d}y=0$$, from the Poincaré inequality we deduce ‖ψ‖H1(Y)3≤c(‖divyψ‖L2(Y)+‖curlyψ‖L2(Y)3). □ Lemma 5.2 Let $$\alpha\in C^1_\#(\bar Y)^{3\times 3}$$ be uniformly bounded, positive definite and symmetric for all $$y\in \bar Y$$. Let $$F\in L^2(Y)$$, extending periodically to $$\mathbb{R}^3$$. Let $$\psi\in H^1_\#(Y)^3$$ satisfy the equation curly(α(y)curlyψ(y))=F(y). Then $${\rm curl}_y\psi\in H^1_\#(Y)^3$$ and ‖curlyψ‖H1(Y)3≤c(‖F‖L2(Y)3+‖ψ‖H1(Y)3). Proof. Let $$\omega\supset Y$$ be a smooth domain. Let $$\eta\in \mathcal{D}(\omega)$$ be such that $$\eta(y)=1$$ for $$y\in Y$$. We have curly(αcurly(ηψ)) =curly(αηcurlyψ)+curly(α∇yη×ψ) =ηcurly(αcurlyψ)+∇yη×(αcurlyψ)+curly(α∇yη×ψ). Let $$U=\alpha{\rm curl}_y(\eta\psi)$$. We have ‖curlyU‖L2(ω)3≤c(‖F‖L2(ω)+‖ψ‖H1(ω)3)≤c(‖F‖L2(Y)3+‖ψ‖H1(Y)3). Further, ‖U‖L2(ω)3=‖α(∇yη×ψ+ηcurlyψ)‖|L2(ω)3≤c‖ψ‖H1(ω)3≤c‖ψ‖H1(Y)3. As $$\eta\in\mathcal{D}(\omega)$$, $$U$$ has compact support in $$\omega$$ so $$U$$ belongs to $$H_0({\rm curl\,},\omega)$$. Thus, we can write U=z+∇Φ, where $$z\in H^1_0(\omega)^3$$ and $${\it{\Phi}}\in H^1_0(\omega)$$ satisfy ‖z‖H1(ω)3≤c‖U‖H(curl,ω) and ‖Φ‖H1(ω)≤c‖U‖H(curl,ω). From $${\rm div}_y(\alpha^{-1}U)=0$$ we deduce that divy(α−1∇Φ)=−divy(α−1z)∈L2(ω). Since $$\alpha\in C^1(\bar\omega)^{3\times 3}$$ and is uniformly bounded and positive definite, $$\alpha^{-1}\in C^1(\bar\omega)^{3\times 3}$$ and is uniformly positive definite. Therefore, $${\it{\Phi}}\in H^2(\omega)$$ and satisfies ‖Φ‖H2(ω)≤c‖z‖H1(ω)3≤c‖U‖H(curl,ω). Thus, $$U\in H^1(\omega)^3$$ and $$\|U\|_{H^1(\omega)^3}\le c\|U\|_{H({\rm curl\,},\omega)}\le c(\|F\|_{L^2(Y)^3}+\|\psi\|_{H^1(Y)^3})$$. From $${\rm curl}_y(\eta\psi)=\alpha^{-1}U$$, we deduce that $${\rm curl}_y(\eta\psi)\in H^1(\omega)^3$$ so $${\rm curl}_y\psi\in H^1(Y)^3$$ and ‖curlyψ‖H1(Y)3≤c(‖F‖L2(Y)3+‖ψ‖H1(Y)3). □ We then prove the following result on the regularity of $$N^r$$. Proposition 5.3 Assume that $$a(x,y)\in C^1(\bar D,C^2(\bar Y))^{3\times 3}$$; then $${\rm curl}_yN^r(x,y)\in C^1(\bar D,C(\bar Y))^3$$ and we can choose a version of $$N^r$$ in $$L^2(D,\tilde H_\#({\rm curl\,},Y))$$ so that $$N^r(x,y)\in C^1(\bar D, C(\bar Y))^3$$. Proof. We can choose a version of $$N^r$$ so that $${\rm div}_yN^r=0$$. Indeed, let $${\it{\Phi}}(x,\cdot)\in L^2(D, H^1_\#(Y))$$ be such that $$\Delta_y{\it{\Phi}}=-{\rm div}_yN^r$$; then $${\rm curl}_y(N^r+\nabla_y{\it{\Phi}})={\rm curl}_y N^r$$ and $${\rm div}_y(N^r+\nabla_y{\it{\Phi}})=0$$. Further we can choose $$N^r$$ so that $$\int_YN^r(x,y)\,{\rm d}y=0$$. From Lemma 5.1, we have ‖Nr(x,⋅)‖H1(Y)3≤c‖curlyNr(x,⋅)‖L2(Y)3, which is uniformly bounded with respect to $$x$$. From (4.4) and Lemma 5.2, we deduce that ‖curlyNr(x,⋅)‖H1(Y)3≤c‖curly(a(x,⋅)er‖L2(Y)3+‖Nr(x,⋅)‖H1(Y)3, which is uniformly bounded with respect to $$x$$. For each index $$q=1,2,3$$, we have that $${\rm curl}_y{\partial\over\partial y_q}N^r(x,\cdot)$$ is uniformly bounded in $$L^2(Y)$$ and $${\rm div}_y{\partial\over\partial y_q}N^r(x,\cdot)=0$$. Therefore, from Lemma 5.1, $${\partial\over\partial y_q}N^r(x,\cdot)$$ is uniformly bounded in $$H^1(Y)$$. We note that ∂∂yq(curly(a(x,⋅)curlyNr))=−∂∂yqcurly(a(x,⋅)er)∈L2(Y). Thus, curly(acurly∂Nr∂yq)=∂∂yq(curly(a(x,y)curlyNr))−curly(∂a∂yqcurlyNr)∈L2(Y). From Lemma 5.2 we deduce that $${\rm curl}_y{\partial N^r\over\partial y_q}(x,\cdot)$$ is uniformly bounded in $$H^1(Y)$$ so that $${\rm curl}_y N^r(x,\cdot)$$ is uniformly bounded in $$H^2(Y)\subset C(\bar Y)$$. We now show that $${\rm curl}_yN^r\in C^1(\bar D,H^2(Y))^3\subset C^1(\bar D,C(\bar Y))^3$$. Fix $$h\in\mathbb{R}^3$$. From (4.4) we have curly(a(x,y)curly(Nr(x+h,y)−Nr(x,y))) =−curly((a(x+h,y)−a(x,y))er) −curly((a(x+h,y)−a(x,y))curlyNr(x+h,y)). The smoothness of $$a$$ and the uniform boundedness of $${\rm curl}_yN^r(x,\cdot)$$ in $$L^2(Y)^3$$ gives limh→0‖curly(Nr(x+h,⋅)−Nr(x,⋅))‖L2(Y)3=0. (5.1) From Lemma 5.1 we have that $$N^r(x+h,\cdot)-N^r(x,\cdot)\in H^1(Y)^3$$ and ‖Nr(x+h,⋅)−Nr(x,⋅)‖H1(Y)3≤c‖curly(Nr(x+h,⋅)−Nr(x,⋅))‖L2(Y)3, which converges to 0 when $$|h|\to 0$$. From Lemma 5.2, we have ‖curly(Nr(x+h,⋅)−Nr(x,⋅))‖H1(Y)3 ≤‖−curly((a(x+h,⋅)−a(x,⋅))er)−curly((a(x+h,⋅)−a(x,⋅))curlyNr(x+h,⋅))‖L2(Y)3 +‖Nr(x+h,⋅)−Nr(x,⋅)‖H1(Y)3→0 when |h|→0. (5.2) We have further that curly(a(x,y)curly∂∂yq(Nr(x+h,y)−Nr(x,y)))=−curly(∂a∂yq(x,y)curly(Nr(x+h,y)−Nr(x,y))) −∂∂yqcurly((a(x+h,y)−a(x,y))er)−∂∂yqcurly((a(x+h,y)−a(x,y))curlyNr(x+h,y)). (5.3) From this we have ‖curly∂∂yq(Nr(x+h,y)−Nr(x,y))‖L2(Y)3 ≤c‖curly(Nr(x+h,⋅)−Nr(x,⋅))‖L2(Y)3 +c‖a(x+h,⋅)−a(x,⋅)‖W1,∞(Y)3→0 when |h|→0, so from Lemma 5.1 we have ‖∂∂yq(Nr(x+h,y)−Nr(x,y))‖H1(Y)3→0 when |h|→0. As the right-hand side of (5.3) converges to 0 in the $$L^2(Y)^3$$ norm when $$|h|\to 0$$, we deduce from Lemma 5.2 that ‖curly∂∂yq(Nr(x+h,y)−Nr(x,y))‖H1(Y)3→0 when |h|→0. (5.4) We have curly[a(x,y)curly(Nr(x+h,y)−Nr(x,y)h)] =−curly((a(x+h,y)−a(x,y)h)er) −curly(a(x+h,y)−a(x,y)hcurlyNr(x+h,y)). Let $$\chi^r(x,\cdot)\in \tilde H_\#({\rm curl\,},Y)$$ with $${\rm div}_y\chi^r(x,)=0$$ be the solution of the problem curly(a(x,y)curlyχr(x,⋅))=−curly(∂a∂xqer)−curly(∂a∂xqcurlyNr(x,y)). We deduce that curly(a(x,y)curly(Nr(x+h,y)−Nr(x,y)h−χr(x,y))) =−curly((a(x+h,y)−a(x,y)h−∂a∂xq(x,y))er) −curly((a(x+h,y)−a(x,y)h−∂a∂xq(x,y))curlyNr(x+h,y)) −curly(∂a∂xq(x,y)curly(Nr(x+h,y)−Nr(x,y))):=I1. (5.5) Let $$h\in \mathbb{R}^3$$ be a vector with all components 0 except for the $$q$$th component. We have ‖curly(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖L2(Y)3 ≤c‖a(x+h,⋅)−a(x,⋅)h−∂a∂xq(x,⋅)‖L∞(Y) +c‖curly(Nr(x+h,⋅)−Nr(x,⋅)‖L2(Y)3, (5.6) which converges to 0 when $$|h|\to 0$$ due to (5.1). Thus, we deduce from Lemma 5.1 that lim|h|→0‖Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅)‖H1(Y)3=0. (5.7) From Lemma 5.2, we have lim|h|→0‖curly(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖H1(Y)3 ≤lim|h|→0‖I1(x,⋅)‖L2(Y)3+‖Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅)‖H1(Y)3=0 (5.8) due to (5.2) and (5.7). Let $$p=1,2,3$$. We then have curly(a(x,y)curly∂∂yp(Nr(x+h,y)−Nr(x,y)h−χr(x,y))) =−curly(∂a∂yp(x,y)curly(Nr(x+h,y)−Nr(x,y)h−χr(x,y))) −∂∂ypcurly((a(x+h,y)−a(x,y)h−∂a(x,y)∂xq)er) −∂∂ypcurly((a(x+h,y)−a(x,y)h−∂a∂xq(x,y))curlyNr(x+h,y)) −∂∂ypcurly(∂a∂xq(x,y)curly(Nr(x+h,y)−Nr(x,y))), which converges to 0 in $$L^2(Y)$$ for each $$x$$ due to (5.4), (5.8) and the uniform boundedness of $$\|{\rm curl\,} N^r(x,\cdot)\|_{H^2(Y)^3}$$. We have ‖curly∂∂yp(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖L2(Y)3 ≤c‖curly(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖L2(Y)3 +c‖a(x+h,⋅)−a(x,⋅)h−∂a(x,⋅)∂xq‖W1,∞(Y)3+c‖curly(Nr(x+h,⋅)−Nr(x,⋅)‖H1(Y)3, which converges to 0 when $$|h|\to 0$$, so from Lemma 5.1, lim|h|→0‖∂∂yp(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖H1(Y)3=0. (5.9) Therefore, $$N^r\in C^1(\bar D,H^2(Y))^3\subset C^1(\bar D,C(\bar Y))^3$$. We then get from Lemma 5.2 that lim|h|→0‖curly∂∂yp(Nr(x+h,⋅)−Nr(x,⋅)h−χr(x,⋅))‖H1(Y)3=0. Thus, $${\rm curl}_yN^r\in C^1(\bar D,H^2(Y))^3\subset C^1(\bar D,C(\bar Y))^3$$. □ Proposition 5.4 Assume that $$b(x,y)\in C^1(\bar D,C^2(\bar Y))^{3\times 3}$$. The solution $$w^r$$ of cell problem (4.1) belongs to $$C^1(\bar D, C^1(\bar Y))$$. Proof. The cell problem (4.1) can be written as −∇y⋅(b(x,y)∇ywr(x,y))=∇y(b(x,y)er). Fixing $$x\in \bar D$$, the right-hand side is bounded uniformly in $$H^1(Y)$$ so $$w^r(x,\cdot)$$ is uniformly bounded in $$H^3(Y)$$ from elliptic regularity (see McLean, 2000, Theorem 4.16). For $$h\in \mathbb{R}^3$$, we note that −∇y⋅[b(x,y)∇y(wr(x+h,y)−wr(x,y))] =∇y⋅[(b(x+h,y)−b(x,y))er] +∇y⋅[(b(x+h,y)−b(x,y))∇ywr(x+h,y)]:=i1. As $$\int_Yw^r(x,y)\,{\rm d}y=0$$, we have ‖wr(x+h,⋅)−wr(x,⋅)‖H1(Y) ≤c‖∇y(wr(x+h,⋅)−wr(x,⋅))‖L2(Y) ≤c‖(b(x+h,⋅)−b(x,⋅))er‖L2(Y) +c‖(b(x+h,⋅)−b(x,⋅))∇ywr(x+h,⋅)‖L2(Y), which converges to 0 when $$|h|\to 0$$. Fixing $$x\in\bar D$$, we then have from McLean (2000, Theorem 4.16) that ‖wr(x+h,⋅)−wr(x,⋅)‖H3(Y)≤‖wr(x+h,⋅)−wr(x,⋅)‖H1(Y)+‖i1(x,⋅)‖H1(Y), (5.10) which converges to 0 when $$|h|\to 0$$. Fixing an index $$q=1,2,3$$, let $$h\in \mathbb{R}^3$$ be a vector whose components are all zero except the $$q$$th component. Let $$\eta(x,\cdot)\in H^1_\#(Y)/\mathbb{R}$$ be the solution of the problem −∇y⋅[b(x,y)∇yη(x,y)]=∇y⋅[∂b∂xqer]+∇y⋅[∂b∂xq∇ywr(x,y)]. We have −∇y⋅[b(x,y)∇y(wr(x+h,y)−wr(x,y)h−η(x,y))] =∇y⋅[(b(x+h,y)−b(x,y)h−∂b∂xq(x,y))er] +∇y⋅[(b(x+h,y)−b(x,y)h−∂b∂xq(x,y))∇ywr(x+h,y)] +∇y⋅[∂b(x,y)∂xq(∇ywr(x+h,y)−∇ywr(x,y))]:=i2. From (5.10) and the regularity of $$b$$, $$\lim_{|h|\to 0}\|i_2(x,\cdot)\|_{H^1(Y)}=0$$. As $$\int_Yw^r(x,y)\,{\rm d}y=0$$ and $$\int_Y\eta(x,y)\,{\rm d}y=0$$, we have lim|h|→0‖wr(x+h,⋅)−wr(x,⋅)h−η(x,⋅)‖H1(Y)=0. Therefore from McLean (2000, Theorem 4.16), we have ‖wr(x+h,⋅)−wr(x,⋅)h−η(x,⋅)‖H3(Y)≤‖wr(x+h,⋅)−wr(x,⋅)h−η(x,⋅)‖H1(Y)+‖i2(x,⋅)‖H1(Y), which converges to 0 when $$|h|\to 0$$. Thus, $$w^r\in C^1(\bar D,H^3(Y))\subset C^1(\bar D,C^1(\bar Y))$$. □ For the regularity of the solution $$u_0$$ of the homogenized problem (4.7) we have the following result. Proposition 5.5 Assume that $$D$$ is a Lipschitz polygonal domain, and the coefficient $$a(\cdot,y)$$, as a function of $$x$$, is Lipschitz, uniformly with respect to $$y$$; then there is a constant $$0<s<1$$ so that $${\rm curl\,} u_0\in H^s(D)$$. Proof. When $$a(x,y)$$ is Lipschitz with respect to $$x$$, from (4.4), $$\|{\rm curl}_y N^r(x,\cdot)\|_{L^2(Y)}$$ is a Lipschitz function of $$x$$, so from (4.6) we have that $$a^0$$ is Lipschitz with respect to $$x$$. As $$a^0$$ is positive definite, $$(a^0)^{-1}$$ is Lipschitz. Let $$U=a^0{\rm curl\,} u_0$$. We have from (4.7) that $$U\in H({\rm curl\,},D)$$, $${\rm div}((a^0)^{-1}U)=0$$ and $$(a^0)^{-1}U\cdot \nu=0$$ on $$\partial D,$$ where $$\nu$$ is the outward normal vector on $$\partial D$$. The conclusion follows from Hiptmair (2002, Lemma 4.2). □ Remark 5.6 If $$a^0$$ is isotropic, we have from (4.7) that curlcurlu0=−(a0)−1∇a0×curlu0−(a0)−1b0u0+(a0)−1f∈L2(D)3 so $$u_0\in H^1({\rm curl},D)$$. However, even if $$a$$ is isotropic, $$a^0$$ may not be isotropic. Remark 5.7 The homogenized equation for the multiscale case is determined as follows. We denote by $$a^n(x,\boldsymbol{y})=a(x,\boldsymbol{y})$$. Recursively, for $$i=1,\ldots,n-1$$, the $$i$$-th level homogenized coefficient is determined as follows. For $$r=1,2,3$$, let $$N_{i+1}^r\in L^2(D\times{\bf Y}_i,\tilde H({\rm curl}_{y_{i+1}},Y_{i+1}))$$ be the solution of the cell problem ∫D∫Y1…∫Yi+1ai+1(x,yi,yi+1)(er+curlyi+1Ni+1r)⋅curlyi+1ψdyi+1dyidx=0 for all $$\psi\in L^2(D\times{\bf Y}_i,\tilde H({\rm curl}_{y_{i+1}},Y_{i+1}))$$. The $$i$$-th level homogenized coefficient $$a^{i}$$ is determined by arsi(x,yi)=∫Yi+1ai+1(x,yi,yi+1)(es+curlyi+1Ni+1s)⋅(er+curlyi+1Ni+1r)dyi+1. Let $$b^n(x,\boldsymbol{y})=b(x,\boldsymbol{y})$$. Similarly, let $$w_{i+1}^{r}\in L^2(D\times{\bf Y}_i,H^1_\#(Y_{i+1})/\mathbb{R})$$ be the solution of the problem ∫D∫Y1…∫Yi+1bi+1(x,yi,yi+1)(er+∇yi+1wi+1r)⋅∇yi+1ψdyi+1dyidx=0 for all $$\psi\in L^2(D\times{\bf Y}_i,H^1_\#(Y_{i+1})/\mathbb{R})$$. The $$i$$-th level homogenized coefficient $$b^i$$ is determined by brsi(x,yi)=∫Yi+1bi+1(x,yi,yi+1)(es+∇yi+1wi+1s)⋅(er+∇yi+1wi+1r)dyi+1. We then have the equation ∫D∫Yi[ai(x,yi)(curlu0+curly1u1+⋯+curlyiui)⋅(curlv0+curly1v1+⋯+curlyivi)dyidx +bi(x,yi)(u0+∇y1u1+⋯+∇yiui)⋅(v0+∇y1v1+⋯+∇yivi)]dyidx=∫Df(x)⋅v0(x)dx. The coefficients $$a^0(x)$$ and $$b^0(x)$$ are the homogenized coefficients. We have ui(x,yi) = [curlu0(x)r+curly1u1(x,y1)r+⋯+curlyi−1ui−1(x,yi−1)r]Nir(x,yi) =curlu0(x)r0(δr0r1+curly1N1r0(x,y1)r1)(δr1r2+curly2N2r1(x,y2)r2)⋯ (δri−2ri−1+curlyi−1Ni−1ri−2(x,yi−1)ri−1)Niri−1(x,yi). If $$a(x,\boldsymbol{y})\in C^1(\bar D,C^2(\bar Y_1,\ldots,C^2(\bar Y_n),\ldots))^{3\times 3}$$, by following the same procedure as above, we can show inductively that $${\rm curl}_{y_i}N_i^r(x,\boldsymbol{y}_i)\in C^1(\bar D,C^2(\bar Y_1,\ldots,C^2(\bar Y_{i-1},H^2(Y_i)),\ldots))$$ and $$a^i(x,\boldsymbol{y}_i)\in C^1(\bar D,C^2(\bar Y_1,\ldots,C^2(\bar Y_i),\ldots))$$. Thus, if $$u_0\in H^s({\rm curl\,},D)$$ for $$0<s\le 1$$, $$u_i\in \hat{\mathcal{H}}_i^s$$. Similarly, we can show that if $$b\in C^1(\bar D, C^2(\bar Y_1,\ldots,C^2(\bar Y_n)\ldots))$$ then $$w^{ir}\in C^1(\bar D,C^2(\bar Y_1,\ldots,C^2(\bar Y_{i-1},H^3(Y_i))\ldots))$$. As ui=u0r0(x)(δr0r1+∂w1r0∂y1r1(x,y1))…(δri−2ri−1+∂wi−1ri−2∂y(i−1)ri−1(x,yi−1))wiri−1(x,yi), if $$u_0\in H^s(D)$$, $${\frak u_i}\in \hat{\frak H}_i^s$$. 6. Numerical results The detail spaces $$\mathcal{V}^l$$ and $$\mathcal{V}^l_\#$$, which are difficult to construct in numerical implementations, are defined via orthogonal projection in Section 3.2. We employ Riesz basis functions and define equivalent norms, which facilitate the construction of these spaces. We make the following assumption. Assumption 6.1 (i) For each multidimensional vector $$j \in \mathbb{N}_0^d$$, there exists a set of indices $$I^j \subset \mathbb{N}^d_0$$ and a set of basis functions $$\phi^{jk}\in L^2(D)$$ for $$k\in I^j$$, such that $$V^l = \text{span}\left\{\phi^{jk} : |\,j|_{\infty}\le l\right\}$$. There are constants $$c_2>c_1>0$$ such that if $$\phi = \sum_{|\,j|_{\infty}\leq l,k\in I^j}\phi^{jk}c_{jk}\in V^l$$, then the following norm equivalences hold: c1∑|j|∞≤lk∈Ij|cjk|2≤‖ϕ‖L2(D)2≤c2∑|j|∞≤lk∈Ij|cjk|2, where $$c_1$$ and $$c_2$$ are independent of $$\phi$$ and $$l$$. (ii) For the space $$L^2(Y)$$, for each $$j \in \mathbb{N}_0^d$$, there exists a set of indices $$I^j_0 \subset \mathbb{N}_0^d$$ and a set of basis functions $$\phi^{jk}_0\in L^2(Y)$$, $$k\in I^j_0$$, such that $$V^l_\# = \text{span}\{\phi^{jk}_0 : |\,j|_{\infty}\le l\}$$. There are constants $$c_4>c_3>0$$ such that if $$\phi = \sum_{|\,j|_{\infty}\leq l,k\in I^{\,j}_{\,0}}\phi^{jk}_0c_{jk}\in V^l$$ then c3∑|j|∞≤lk∈I0j|cjk|2≤‖ϕ‖L2(Y)2≤c4∑|j|∞≤lk∈I0j|cjk|2, where $$c_3$$ and $$c_4$$ are independent of $$\phi$$ and $$l$$. Because of the norm equivalence, we can use $$\mathcal{V}^l=\text{span}\{\phi^{jk} : |\,j|_{\infty}= l\}$$ and $$\mathcal{V}^l_\#=\text{span}\{\phi^{jk}_0 : |\,j|_{\infty}= l\}$$ to construct the sparse tensor product FE spaces. Example 6.2 (i) We can construct a hierarchical basis for $$L^2(0,1)$$ as follows. We first take three piecewise linear functions as the basis for level $$j=0$$: $$\psi^{01}$$ obtains values $$(1,0)$$ at $$(0,1/2)$$ and is 0 in $$(1/2,1)$$, $$\psi^{02}$$ is piecewise linear and obtains values $$(0, 1, 0)$$ at $$(0, 1/2, 1)$$ and $$\psi^{03}$$ obtains values $$(0,1)$$ at $$(1/2, 1)$$ and is 0 in $$(0,1/2)$$. The basis functions for other levels are constructed from the wavelet function $$\psi$$ that takes values $$(0,-1,2,-1,0)$$ at $$(0,1/2,1,3/2,2)$$, the left boundary function $$\psi^{\rm left}$$ taking values $$(-2,2,-1,0)$$ at $$(0,1/2,1,3/2)$$ and the right boundary function $$\psi^{\rm right}$$ taking values $$(0, -1,2,-2)$$ at $$(1/2,1,3/2,2)$$. For levels $$j\geq 1$$, $$I^j=\{1,2,\ldots,2^j\}$$. The wavelet basis functions are defined as $$\psi^{j1}(x) = 2^{j/2}\psi^{\rm left}(2^j x)$$, $$\psi^{jk}(x)=2^{j/2}\psi(2^j x - k + 3/2)$$ for $$k = 2, \ldots, 2^j-1$$ and $$\psi^{j2^j} = 2^{j/2}\psi^{\rm right}(2^j x - 2^j+2)$$. This base satisfies Assumption 6.1 (i). (ii) For $$Y = (0,1)$$, we can construct a hierarchy of periodic basis functions for $$L^2(Y)$$ that satisfies Assumption 6.1 (ii) from those in (i). For level 0, we exclude $$\psi^{01}$$, $$\psi^{03}$$ and include the periodic piecewise linear function that takes values $$(1,0,1)$$ at $$(0,1/2,1),$$ respectively. At other levels, the functions $$\psi^{\rm left}$$ and $$\psi^{\rm right}$$ are replaced by the piecewise linear functions that take values $$(0,2, -1, 0)$$ at $$(0,1/2,1,3/2)$$ and values $$(0, -1,2,0)$$ at $$(1/2,1, 3/2 ,2),$$ respectively. When $$D=(0,1)^d$$, the basis functions can be constructed by taking the tensor products of the basis functions in $$(0,1)$$. They satisfy Assumption 6.1 after appropriate scaling (see Griebel & Oswald, 1995). Remark 6.3 When the norm equivalence for the basis functions in $$L^2(D)$$ and in $$L^2(Y)$$ does not hold, in many cases, we can still prove a rate of convergence similar to those in Lemmas 3.5 and 3.6 for the sparse tensor product FE approximations. For example, with the division of the domain $$D$$ into sets of triangles $$\mathcal{T}^l$$, the set of continuous piecewise linear functions with value 1 at one vertex and 0 at all the others forms a basis of $$V^l$$. Let $$S^l$$ be the set of vertices of the set of simplices $$\mathcal{T}^l$$. We can define $$\mathcal{V}^l$$ as the linear span of functions that are 1 at a vertex in $$S^l\setminus S^{l-1}$$ and 0 at all the other vertices. We can then construct the sparse tensor product FE approximations with these spaces but the norm equivalence does not hold. A rate of convergence for sparse tensor product FEs similar to those in Lemmas 3.5 and 3.6 can be deduced (see e.g, Hoang, 2008). In the first example, we consider a two-scale Maxwell-type equation in the two-dimensional domain $$D=(0,1)^2$$. The coefficients a(x,y)=(1+x1)(1+x2)(1+cos22πy1)(1+cos22πy2) and b(x,y)=1(1+x1)(1+x2)(1+cos22πy1)(1+cos22πy2). We can compute the homogenized coefficients exactly. In this case, a0=4(1+x1)(1+x2)9 and b0=23(1+x1)(1+x2). We choose f=(49(1+x1)(1+2x2−x1)+23(1+x1)(1+x2)x1x2(1−x2)49(1+x2)(1+2x1−x2)+23(1+x1)(1+x2)x1x2(1−x1)) so that the solution to the homogenized equation is u0=(x1x2(1−x2)x1x2(1−x1)). In Fig. 1, we plot the energy error versus the mesh size for the sparse tensor product FE approximations of the two-scale homogenized Maxwell-type problem. The figure agrees with the error estimate in Proposition 3.8. Fig. 1. View largeDownload slide The sparse tensor energy error $$B(\boldsymbol{u}-\widehat {\bf{u}}^L,\boldsymbol{u}-\widehat {\bf{u}}^L).$$ Fig. 1. View largeDownload slide The sparse tensor energy error $$B(\boldsymbol{u}-\widehat {\bf{u}}^L,\boldsymbol{u}-\widehat {\bf{u}}^L).$$ In the second example, we consider the case where $$b$$ is the identity matrix, i.e., it does not depend on $$y$$. In this case, from (2.10) we note that the function $${\frak u_1}=0$$. We choose a(x,y)=(1+x1)(1+x2)(1+cos22πy1)(1+cos22πy2) and f=(4(2π(1+x1)(1+x2)sin2πx2+(1+x1)(cos2πx1−cos2πx2))9+12πsin2πx24(2π(1+x1)(1+x2)sin2πx1−(1+x2)(cos2πx1−cos2πx2))9+12πsin2πx1) so that the solution to the homogenized problem is u0=(12πsin2πx212πsin2πx1). Figure 2 plots the energy error versus the mesh size for the sparse tensor product FE approximations for the two-scale homogenized Maxwell-type problem. The plot confirms the analysis. Fig. 2. View largeDownload slide The sparse tensor energy error $$B(\boldsymbol{u}-\widehat {\bf{u}}^L,\boldsymbol{u}-\widehat {\bf{u}}^L).$$ Fig. 2. View largeDownload slide The sparse tensor energy error $$B(\boldsymbol{u}-\widehat {\bf{u}}^L,\boldsymbol{u}-\widehat {\bf{u}}^L).$$ Acknowledgements The authors gratefully acknowledge a postgraduate scholarship of Nanyang Technological University, the AcRF Tier 1 grant RG69/10, the Singapore A*Star SERC grant 122-PSF-0007 and the AcRF Tier 2 grant MOE 2013-T2-1-095 ARC 44/13. Footnotes 1 The notations $$Y_1,\ldots,Y_n$$, which denote the same unit cube $$Y$$, are introduced for convenience only, especially in the case where the Cartesian product of several of them is used, to avoid the necessity of indicating how many times the unit cube appears in the product. The functions $$a$$ and $$b$$ depend on the macroscopic scale only and are periodic with respect to $$y_i$$ with the period being the unit cube $$Y$$. 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( 2010) Multiscale computations for 3D time-dependent Maxwell’s equations in composite materials. SIAM J. Sci. Comput. , 32, 2560– 2583. Google Scholar CrossRef Search ADS Appendix A. We present the proof of Theorem 4.2 in this appendix. We consider a set of $$M$$ open cubes $$Q_i$$ ($$i=1,\ldots,M$$) of size $$\varepsilon^t$$ for $$t>0$$ to be chosen later such that $$D\subset\bigcup_{i=1}^MQ_i$$ and $$Q_i\bigcap D\ne\emptyset$$. Each cube $$Q_i$$ intersects with only a finite number, which does not depend on $$\varepsilon$$, of other cubes. We consider a partition of unity that consists of $$M$$ functions $$\rho_i$$ such that $$\rho_i$$ has support in $$Q_i$$, $$\sum_{i=1}^M\rho_i(x)=1$$ for all $$x\in D$$ and $$|\nabla\rho_i(x)|\le c\varepsilon^{-t}$$ for all $$x$$ (indeed such a set of cubes $$Q_i$$ and a partition of unity can be constructed from a fixed set of cubes of size $${\mathcal O}(1)$$ by rescaling). For $$r=1,2,3$$ and $$i=1,\ldots,M$$, we define Uir=1|Qi|∫Qicurlu0(x)rdx and Vir=1|Qi|∫Qiu0(x)rdx (as $$u_0\in H^s(D)^3$$ and $${\rm curl\,} u_0\in H^s(D)^3$$, for the Lipschitz domain $$D$$, we can extend each of them, separately, continuously outside $$D$$ and understand $$u_0$$ and $${\rm curl\,} u_0$$ as these extensions; see Wloka, 1987, Theorem 5.6). Let $$U_i$$ and $$V_i$$ denote the vectors $$(U_i^1, U_i^2,U_i^3)$$ and $$(V_i^1,V_i^2,V_i^3),$$ respectively. Let $$B$$ be the unit cube in $$\mathbb{R}^3$$. From the Poincaré inequality, we have ∫B|ϕ−∫Bϕ(x)dx|2dx≤c∫B|∇ϕ(x)|2dx ∀ϕ∈H1(B). By translation and scaling, we deduce that ∫Qi|ϕ−1|Qi|∫Qiϕ(x)dx|2dx≤cε2t∫Qi|∇ϕ(x)|2dx ∀ϕ∈H1(Qi), i.e., ‖ϕ−1|Qi|∫Qiϕ(x)dx‖L2(Qi)≤cεt‖ϕ‖H1(Qi). Together with ‖ϕ−1|Qi|∫Qiϕ(x)dx‖L2(Qi)≤c‖ϕ‖L2(Qi), we deduce from interpolation that ‖ϕ−1|Qi|∫Qiϕ(x)dx‖L2(Qi)≤cεts‖ϕ‖Hs(Qi) ∀ϕ∈Hs(Qi). Thus, ∫Qi|curlu0(x)r−Uir|2dx≤cε2ts‖(curlu0)r‖Hs(Qi)2. (A.1) Let u1ε(x)=u0(x)+εNr(x,xε)Ujrρj(x)+ε∇[wr(x,xε)Vjrρj(x)]. We have curl(aε(x)curlu1ε(x))+bε(x)u1ε(x) =curla(x,xε)[curlu0(x)+εcurlxNr(x,xε)Ujrρj(x)+curlyNr(x,xε)Ujrρj+ε(Ujr∇ρj)×Nr(x,xε)] +b(x,xε)[u0(x)+εNr(x,xε)Ujrρj(x)+ε∇xwr(x,xε)Vjrρj(x)+∇ywr(x,xε)Vjrρj(x) + εwr(x,xε)Vjr∇ρj(x)] =curl(a0(x)curlu0(x))+b0(x)u0(x)+curl[Gr(x,xε)Ujrρj(x)]+gr(x,xε)Vjrρj(x)+εcurlI(x) +εJ(x)+curl[(aε(x)−a0(x))(curlu0(x)−Ujρj(x))]+(bε(x)−b0(x))(u0(x)−Vjρj(x)), where the vector functions $$G_r(x,y)$$ and $$g_r(x,y)$$ are defined by (Gr)i(x,y) =air(x,y)+aij(x,y)curlyNr(x,y)j−air0(x), (A.2) (gr)i(x,y) =bir(x,y)+bij(x,y)∂wr∂yj(x,y)−bir0(x) (A.3) and I(x) =a(x,xε)[curlxNr(x,xε)Ujrρj(x)+(Ujr∇ρj(x))×Nr(x,xε)],J(x) =b(x,xε)[Nr(x,xε)Ujrρj(x)+∇xwr(x,xε)Vjrρj(x)+wr(x,xε)Vjr∇ρj(x)]. Therefore, for $$\phi\in W$$, ⟨curl(aεcurlu1ε)+bεu1ε−curl(a0curlu0)−b0u0,ϕ⟩ =∫DUjrρj(x)Gr(x,xε)⋅curlϕdx+∫DVjrρj(x)gr(x,xε)⋅ϕ(x)dx +ε∫DI(x)⋅curlϕ(x)dx+ε∫DJ(x)⋅ϕ(x)dx+∫D(aε−a0)(curlu0(x)−Ujρj)⋅curlϕ(x)dx +∫D(bε−b0)(u0−Vjρj)⋅ϕdx (here $$\langle\cdot\rangle$$ denotes the duality pairing between $$W'$$ and $$W$$). From (4.4), we have that $${\rm curl}_yG_r(x,y)=0$$. Further, from (4.6) $$\int_YG_r(x,y)\,{\rm d}y=0$$. Therefore, there is a function $$\tilde G_r(x,y)$$ such that $$G_r(x,y)=\nabla_y \tilde G_r(x,y)$$. From (4.1), we have $${\rm div}_yg_r(x,y)=0$$ and from (4.6) $$\int_Yg_r(x,y)\,{\rm d}y=0$$. Hence, there is a function $$\tilde g_r$$ such that $$g_r(x,y)={\rm curl}_y\tilde g_r(x,y)$$. As $$\nabla_y\tilde G_r(x,\cdot)=G_r(x,\cdot)\in H^1(Y)^3$$ so $$\Delta_y\tilde G_r(x,\cdot)\in L^2(Y)$$. Thus, $$\tilde G_r(x,\cdot)\in H^2(Y),$$ which implies $$\tilde G_r(x,\cdot)\in C(\bar Y)$$. As $$G_r(x,\cdot)\in C^1(\bar D,H^1_\#(Y)^3)$$, we deduce that $$\tilde G_r(x,y)\in C^1(\bar D, H^2(Y))\subset C^1(\bar D,C(\bar Y))$$. The construction of $$\tilde g_r$$ in Jikov et al. (1994) implies that $$\tilde g_r\in C^1(\bar D, C(\bar Y))$$ (see Hoang & Schwab, 2013). We have ∫DUjrρjGr(x,xε)⋅curlϕdx=∫DUjrρj(x)[ε∇G~r(x,xε)−ε∇xG~r(x,xε)]⋅curlϕdx =−ε∫DG~r(x,xε)div[(Ujrρj)curlϕ]dx−ε∫DUjrρj∇xG~r(x,xε)⋅curlϕdx. We note that |∫DUjrρj∇xG~r(x,xε)⋅curlϕdx|≤c‖(Ujrρj)‖L2(D)‖curlϕ‖L2(D)3. From ‖Ujrρj‖L2(D)2=∫D(Ujr)2ρj(x)2dx+∑i≠j∫DUirUjrρi(x)ρj(x)dx, and the fact that the support of each function $$\rho_i$$ intersects only with the support of a finite number (which does not depend on $$\varepsilon$$) of other functions $$\rho_j$$ in the partition of unity, we deduce ‖Ujrρj‖L2(D)2 ≤c∑j=1M(Ujr)2|Qj| =c∑j=1M1|Qj|(∫Qjcurlu0(x)rdx)2≤c∑j=1M∫Qjcurlu0(x)r2dx≤c∫Dcurlu0(x)r2dx. Thus, |ε∫DUjrρj∇xG~r(x,xε)⋅curlϕdx|≤cε‖curlϕ‖L2(D)3. We have further that ε∫DG~r(x,xε)div[(Ujrρj)curlϕ]dx =ε∫DG~r(x,xε)[(Ujr∇ρj(x))]⋅curlϕdx ≤cε‖Ujr∇ρj‖L2(D)3‖curlϕ‖L2(D)3. As the support of each function $$\rho_i$$ intersects with the support of a finite number of other functions $$\rho_j$$ and $$\|\nabla\rho_j\|_{L^\infty(D)}\le c\varepsilon^{-t}$$, we have ‖Ujr∇ρj‖L2(D)32≤c∑j=1M(Ujr)2|Qj|‖∇ρj‖L∞(D)2≤cε−2t∑j=1M(Ujr)2|Qj|≤cε−2t, so ε∫DG~r(x,xε)div[(Ujrρj)curlϕ]dx≤cε‖Ujr∇ρj‖L2(D)3‖curlϕ‖L2(D)3≤cε1−t‖curlϕ‖L2(D)3. We therefore deduce that |∫DUjrρjGr(x,xε)⋅curlϕdx|≤cε1−t‖curlϕ‖L2(D)3. We have ∫DVjrρjgr(x,xε)⋅ϕ(x)dx=∫DVjrρj[εcurlg~r(x,xε)−εcurlxg~r(x,xε)]⋅ϕdx. Arguing similarly to above, we have |ε∫DVjrρjcurlxg~r(x,xε)⋅ϕdx|≤cε‖Vjrρj‖L2(D)3‖ϕ‖L2(D)3≤cε‖ϕ‖L2(D)3 and |ε∫DVjrρjcurlg~r(x,xε)⋅ϕdx| = |ε∫Dg~r(x,xε)⋅curl[(Vjrρj)ϕ]dx| ≤ |ε∫Dg~r(x,xε)⋅[(Vjrρj)curlϕ+ϕ×(Vjr∇ρj)]dx ≤c(ε‖curlϕ‖L2(D)3+cε1−t‖ϕ‖L2(D)3)(∑j=1M(Vjr)2|Qj|)1/2 ≤c(ε‖curlϕ‖L2(D)3+cε1−t‖ϕ‖L2(D)3). We note that ‖I‖L2(D)3≤csupr[‖Ujrρj‖L2(D)+‖Ujr∇ρj‖L2(D)]≤cε−t and ‖J‖L2(D)3≤csupr[‖Ujrρj‖L2(D)+c‖Vjrρj‖L2(D)+c‖Vjr∇ρj‖L2(D)]≤cε−t. We have further that ⟨curl((aε−a0)(curlu0−Ujρj)),ϕ⟩≤c‖curlu0−(Ujρj))‖L2(D)3‖curlϕ‖L2(D)3. From ∫D|(curlu0)r−(Ujrρj)|2dx=∫D|∑j=1M((curlu0)r−Ujr)ρj|2dx, using the support property of $$\rho_j$$, we have from (A.1), ∫D|(curlu0)r−(Ujrρj)|2dx ≤c∑j=1M∫Qj|(curlu0)r−Ujr|2dx≤cε2st∑j=1M‖(curlu0)r‖Hs(Qj)2 =cε2st∑j=1M[∫Qj(curlu0)r2dx+∫Qj×Qj(curlu0(x)r−curlu0(x′)r)2|x−x′|3+2sdxdx′] ≤cε2st[‖(curlu0)r‖L2(D)2+∫D×D(curlu0(x)r−curlu0(x′)r)2|x−x′|3+2sdxdx′] =cε2st‖(curlu0)r‖Hs(D)2. (A.4) Thus, ⟨curl((aε−a0)(curlu0−Ujρj)),ϕ⟩≤cεst‖curlϕ‖L2(D)3. Similarly, we have |∫D(bε−b0)(u0−∑j=1MVjρj)⋅ϕdx|≤c‖∑j=1M(u0−Vj)ρj‖L2(D)3‖ϕ‖L2(D)3≤cεst‖ϕ‖L2(D)3. Therefore, |⟨curl(aεcurlu1ε)+bεu1ε−curl(a0curlu0)−b0u0,ϕ⟩|≤c(ε1−t+εst)‖ϕ‖V i.e., ‖curl(aεcurlu1ε)+bεu1ε−curl(a0curlu0)−b0u0‖W′≤c(ε1−t+εst). Thus, ‖curl(aεcurlu1ε)+bεu1ε−curl(aεcurluε)−bεuε‖W′≤c(ε1−t+εst). (A.5) Let $$\tau^\varepsilon(x)$$ be a function in $$\mathcal{D}(D)$$ such that $$\tau^\varepsilon(x)=1$$ outside an $$\varepsilon$$ neighbourhood of $$\partial D$$ and $${\rm sup}_{x\in D}\varepsilon|\nabla\tau^\varepsilon(x)|<c,$$ where $$c$$ is independent of $$\varepsilon$$. We consider the function w1ε(x)=u0(x)+ετε(x)Ujrρj(x)Nr(x,xε)+ε∇[Vjrρjτε(x)wr(x,xε)]. We then have u1ε−w1ε=ε(1−τε(x))Ujrρj(x)Nr(x,xε)+ε∇[(1−τε(x))Vjrρjwr(x,xε)] and curl(u1ε−w1ε) =εcurlxNr(x,xε)Ujrρj(x)(1−τε(x))+curlyNr(x,xε)Ujrρj(x)(1−τε(x)) −εUjrρj(x)∇τε(x)×Nr(x,xε)+ε(1−τε(x))Ujr∇ρj(x)×Nr(x,xε). As shown above, $$\|U_j^r\rho_j\|_{L^2(D)}$$ is uniformly bounded, so ‖εcurlxNr(x,xε)(Ujrρj)(1−τε(x))‖L2(D)3≤cε. Let $$\tilde D^\varepsilon$$ be the $$3\varepsilon^{t}$$ neighbourhood of $$\partial D$$. We note that $${\rm curl\,} u_0$$ is extended continuously into a function in $$H^s(\mathbb{R}^3)$$ outside $$D$$. As shown in Hoang & Schwab (2013), for $$\phi\in H^1(\tilde D^\varepsilon)$$, ‖ϕ‖L2(D~ε)≤cεt/2‖ϕ‖H1(D~ε). From this and ‖ϕ‖L2(D~ε)≤‖ϕ‖L2(D~ε), using interpolation, we get ‖ϕ‖L2(D~ε)≤cεst/2‖ϕ‖Hs(D~ε)≤cεst/2‖ϕ‖Hs(D) for all $$\phi\in H^s(D)$$ extended continuously outside $$D$$. We then have ‖Ujrρj‖L2(Dε)2 ≤c∑j=1M∫Qj⋂Dε(Ujr)2ρj2dx ≤c∑j=1M|Qj⋂Dε|1|Qj|2(∫Qj(curlu0)rdx)2 ≤c∑Qj⋂Dε≠∅|Qj⋂Dε||Qj|∫Qj(curlu0)r2dx. As $$D^\varepsilon$$ is the $$\varepsilon$$ neighbourhood of $$\partial D$$, $$\partial D$$ is Lipschitz and $$Q_j$$ has size $$\varepsilon^t$$, $$|Q_j\bigcap D^\varepsilon|\le c\varepsilon^{1+(d-1)t}$$ so $$|Q_j\bigcap D^\varepsilon|/|Q_j|\le c\varepsilon^{1-t}$$. When $$Q_j\bigcap D^\varepsilon\ne\emptyset$$, $$Q_j\subset\tilde D^\varepsilon$$. Thus, ‖Ujrρj‖L2(Dε)2≤cε1−t‖(curlu0)r‖L2(D~ε)2≤cε1−t+st‖curlu0‖Hs(D)32. Therefore, ‖curlyNr(x,xε)(Ujrρj)(1−τε(x))‖L2(D)3≤cε(1−t+st)/2 and ‖ε(Ujrρj)∇τε(x)×Nr(x,xε)‖L2(D)3≤cε(1−t+st)/2. Similarly, we have ‖Ujr∇ρj‖L2(Dε)32 ≤cε−2t∑Qj⋂Dε≠∅|Qj⋂Dε||Qj|∫Qj(curlu0)r2dx ≤cε−2t+1−t‖curlu0‖L2(D~ε)32≤cε1−3t+st‖curlu0‖Hs(D)32. Thus, ‖ε(1−τε(x))(Ujr∇ρj)×Nr(x,xε)‖L2(D)≤cε(1−t)+(1−t+st)/2. Therefore, ‖curl(u1ε−w1ε)‖L2(D)3≤c(ε(1−t+st)/2+ε(1−t)+(1−t+st)/2). We further have ε∇[(1−τε(x))wr(x,xε)(Vjrρj)] = −ε∇τε(x)wr(x,xε)(Vjrρj)+ε(1−τε(x))∇xwr(x,xε)(Vjrρj) +(1−τε(x))∇ywr(x,xε)(Vjrρj)+ε(1−τε(x))wr(x,xε)(Vjr∇ρj). Arguing as above, we deduce that ‖Vjrρj‖L2(Dε)≤cε(1−t+st)/2, ‖Vjr∇ρj‖L2(Dε)≤cε(1−t+st)/2−t. Therefore, ‖ε∇[(1−τε(x))wr(x,xε)(Vjrρj)]‖L2(D)3≤c(ε(1−t+st)/2+ε1−t+(1−t+st)/2). Thus, ‖u1ε−w1ε‖L2(D)3≤c(ε(1−t+st)/2+ε(1−t)+(1−t+st)/2). Choosing $$t=1/(s+1)$$ we have ‖curl(aεcurl(u1ε−w1ε))+bε(u1ε−w1ε)‖W′≤cεs/(s+1). This together with (A.5) gives ‖curl(aεcurl(uε−w1ε))+bε(uε−w1ε)‖W′≤cεs/(s+1). Thus, ‖uε−w1ε‖W≤cεs/(s+1), which implies ‖uε−u1ε‖W≤cεs/(s+1). (A.6) We note that curlu1ε=curlu0(x)+curlyNr(x,xε)(Ujrρj)+εcurlxNr(x,xε)(Ujrρj)+ε(Ujr∇ρj)×Nr(x,xε). From ‖εcurlxNr(x,xε)(Ujrρj)‖L2(D)3≤cε and ‖ε(Ujr∇ρj)×Nr(x,xε)‖L2(D)3≤cεε−t=cεs/(1+s), we deduce that ‖curlu1ε−curlu0−curlyNr(x,xε)(Ujrρj)‖L2(D)3≤cεs/(s+1). From (A.4), ‖curlu0−(Ujrρj)‖L2(D)3≤cεts=cεs/(s+1), we get ‖curlu1ε−[curlu0+curlyNr(x,xε)(curlu0)r‖L2(D)3≤cεs/(s+1). This together with (A.6) implies ‖curluε−[curlu0+curlyNr(x,xε)(curlu0)r‖L2(D)3≤cεs/(s+1). □ Appendix B. We prove Lemma 4.3 in this appendix. We adapt the proof of Hoang & Schwab (2013, Lemma 5.5). As u1(x,y)=∑r=13curlu0(x)rNr(x,y), it is sufficient to show that for each $$r=1,2,3$$, ∫D|curlu0(x)rcurlyNr(x,xε)−∫Ycurlu0(ε[xε]+εt)rcurlyNr(ε[xε]+εt,xε)dt|2dx≤cε2s. The expression on the left-hand side is bounded by ∫D∫Y|curlu0(x)rcurlyNr(x,xε)−curlu0(ε[xε]+εt)rcurlyNr(ε[xε]+εt,xε)|2dtdx ≤2∫D∫Y|(curlu0(x)r−curlu0(ε[xε]+εt)r)curlyNr(ε[xε]+εt,xε)|2dtdx +2∫D∫Y|curlu0(x)r|2|curlyNr(x,xε)−curlyNr(ε[xε]+εt,xε)|2dtdx. As $${\rm curl}_yN^r\in C^1(\bar D,C(\bar Y))^3$$, there exists a constant $$c$$ such that supx∈Dsupt∈Y|curlyNr(x,xε)−curlyNr(ε[xε]+εt,xε)|≤cε. From this we have ∫D|curlu0(x)rcurlyNr(x,xε)−Uε(curlu0(⋅)rcurlyNr(⋅,⋅))(x)|2dx≤c∫D∫Y|curlu0(x)r−curlu0(ε[xε]+εt)r|2dtdx+cε2. We now show that for $${\rm curl\,} u_0\in H^s(D)$$, ∫D∫Y|curlu0(x)r−curlu0(ε[xε]+εt)r|2dtdx≤cε2s. (B.1) Letting $$\phi(x)$$ be a smooth function, we have ∫D∫Y|ϕ(x)−ϕ(ε[xε]+εt)|2dtdx ≤∑i=1d∫D∫Y|ϕ(ε[x1ε]+εt1,…,ε[xi−1ε]+εti−1,xi,…,xd) −ϕ(ε[x1ε]+εt1,…,ε[xiε]+εti,xi+1,…,xd)|2dtdx ≤∑i=1d∫D∫Y|ε∫ti{xi/ε}∂ϕ∂xi(ε[x1ε]+εt1,…,ε[xiε]+εζi,xi+1,…,xd)dζi|2dtdx ≤ε2∑i=1d∫D∫Y∫01|∂ϕ∂xi(ε[x1ε]+εt1,…,ε[xiε]+εζi,xi+1,…,xd)|2dζidtdx ≤ε2∑i=1d∫D|∂ϕ∂xi|2dx, which follows from (4.13); here we freeze the variables $$x_{i+1},\ldots,x_d$$. Let $$\psi\in H^1(D)$$. We consider a sequence $$\{\phi_n\}_n\subset C^\infty(\bar D),$$ which converges to $$\psi$$ in $$H^1(D)$$. As $$n\rightarrow \infty$$, ∫D∫Y(ϕn(ε[xε]+εt)−ψ(ε[xε]+εt))2dtdx = ∫DUε((ϕn−ψ)2)(x)dx ≤ ∫D(ϕn(x)−ψ(x))2dx→0. Therefore, ∫D∫Y(ψ(x)−ψ(ε[xε]+εt))2dtdx ≤3∫D(ψ−ϕn)2dx+3∫D∫Y(ϕn−ϕn(ε[xε]+εt))2dtdx +3∫D∫Y(ϕn(ε[xε]+εt)−ψ(ε[xε]+εt))2dtdx ≤6∫D(ψ−ϕn)2dx+3ε2∑i=1d∫D|∂ϕn∂xi|2dx. Letting $$n\to\infty$$, we have ∫D∫Y(ψ(x)−ψ(ε[xε]+εt))2dtdx≤3ε2∑i=1d∫D|∂ψ∂xi|2dx. Let $$T$$ be the linear map from $$L^2(D)$$ to $$L^2(D\times Y)$$ so that T(ϕ)(x,y)=ϕ(x)−ϕ(ε[xε]+εt). We thus have ‖T‖H1(D)→L2(D×Y)≤cε. On the other hand, ‖T‖L2(D)→L2(D×Y)≤c. From interpolation theory, we deduce that ‖T‖Hs(D)→L2(D×Y)≤cεs. We then get (B.1). The conclusion follows. □ Notes added after the proof stage: After the article is accepted, we learnt about the related recent article: P. Henning, M. Ohlberger and B. Verfürth (2016), A new heterogeneous multiscale method for time-harmonic Maxwell’s equations, SIAM J. Numer. Anal., 54, 3493–3522. This article considers a locally periodic two-scale time harmonic Maxwell equation, but the variational form is still assumed to be strictly coercive, uniformly with respect to the microscopic scale, similar to the equation considered in our present article. These authors formulate the two-scale homogenized equation in a slightly different manner. The Heterogeneous Multiscale Method (HMM) is used to solve the two-scale problem, and is shown to be equivalent to solving the two-scale homogenized equation by using the full tensor finite element spaces. © The authors 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
### Journal
IMA Journal of Numerical AnalysisOxford University Press
Published: Jan 1, 2018
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Export lists, citations | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9901425838470459, "perplexity": 434.4491168926726}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158011.18/warc/CC-MAIN-20180922024918-20180922045318-00040.warc.gz"} |
https://www.hydrol-earth-syst-sci.net/20/1151/2016/ | Journal topic
Hydrol. Earth Syst. Sci., 20, 1151–1176, 2016
https://doi.org/10.5194/hess-20-1151-2016
Hydrol. Earth Syst. Sci., 20, 1151–1176, 2016
https://doi.org/10.5194/hess-20-1151-2016
Research article 17 Mar 2016
Research article | 17 Mar 2016
# The importance of topography-controlled sub-grid process heterogeneity and semi-quantitative prior constraints in distributed hydrological models
Remko C. Nijzink1, Luis Samaniego2, Juliane Mai2, Rohini Kumar2, Stephan Thober2, Matthias Zink2, David Schäfer2, Hubert H. G. Savenije1, and Markus Hrachowitz1 Remko C. Nijzink et al.
• 1Delft University of Technology, Stevinweg 1, 2628 CN Delft, the Netherlands
• 2UFZ – Helmholtz Centre for Environmental Research, Permoserstraße 15, 04318 Leipzig, Germany
Abstract. Heterogeneity of landscape features like terrain, soil, and vegetation properties affects the partitioning of water and energy. However, it remains unclear to what extent an explicit representation of this heterogeneity at the sub-grid scale of distributed hydrological models can improve the hydrological consistency and the robustness of such models. In this study, hydrological process complexity arising from sub-grid topography heterogeneity was incorporated into the distributed mesoscale Hydrologic Model (mHM). Seven study catchments across Europe were used to test whether (1) the incorporation of additional sub-grid variability on the basis of landscape-derived response units improves model internal dynamics, (2) the application of semi-quantitative, expert-knowledge-based model constraints reduces model uncertainty, and whether (3) the combined use of sub-grid response units and model constraints improves the spatial transferability of the model.
Unconstrained and constrained versions of both the original mHM and mHMtopo, which allows for topography-based sub-grid heterogeneity, were calibrated for each catchment individually following a multi-objective calibration strategy. In addition, four of the study catchments were simultaneously calibrated and their feasible parameter sets were transferred to the remaining three receiver catchments. In a post-calibration evaluation procedure the probabilities of model and transferability improvement, when accounting for sub-grid variability and/or applying expert-knowledge-based model constraints, were assessed on the basis of a set of hydrological signatures. In terms of the Euclidian distance to the optimal model, used as an overall measure of model performance with respect to the individual signatures, the model improvement achieved by introducing sub-grid heterogeneity to mHM in mHMtopo was on average 13 %. The addition of semi-quantitative constraints to mHM and mHMtopo resulted in improvements of 13 and 19 %, respectively, compared to the base case of the unconstrained mHM. Most significant improvements in signature representations were, in particular, achieved for low flow statistics. The application of prior semi-quantitative constraints further improved the partitioning between runoff and evaporative fluxes. In addition, it was shown that suitable semi-quantitative prior constraints in combination with the transfer-function-based regularization approach of mHM can be beneficial for spatial model transferability as the Euclidian distances for the signatures improved on average by 2 %. The effect of semi-quantitative prior constraints combined with topography-guided sub-grid heterogeneity on transferability showed a more variable picture of improvements and deteriorations, but most improvements were observed for low flow statistics. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8639799356460571, "perplexity": 6515.354746204475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251684146.65/warc/CC-MAIN-20200126013015-20200126043015-00506.warc.gz"} |
https://www.physicsforums.com/threads/maybe-im-onto-something-or-i-dont-have-a-clue-what-im-on-ablout.156139/ | # Maybe im onto something or i dont have a clue what im on ablout
1. Feb 13, 2007
### superstonerman
Iv been reading up about einsteins relativity business. I currentley understand that the faster an object moves the slower time will pass for that object relative to a staionairy observor. I understand the twin parodox where if one object is traveling closer to the speed of light it will age slower than an object that is staionairy relative to earth. If this is the case then the following has me a bit mistifed, appreciate someone clearing this up:
The sun moves at 600,000 metres per second relative to the milky way this is double the speed of light (i thought matter could not travel faster than the speed of light??). This must mean that earth is in a time dilation field relative to the rest of the universe or at least other galaxies. Also when we use telescopes to look into the sky and observe distant stars and galaxies they too are also moving near the speed of light relative to us. So might we be looking at these stars in the past relative to our present?????
Maybe im talking jibburish can soemone set me straight. Thanks for your help
2. Feb 13, 2007
### imaplanck
Light speed is a smidgen less than 3x10^8, not 3x10^5.
3. Feb 13, 2007
### imaplanck
If I recall, the gamma of a velocity 300,000m/s is negligible to say the least.
4. Feb 13, 2007
### Magister
The galaxies are not moving near the speed of light!!!
5. Feb 13, 2007
### rbj
quasars might be.
6. Feb 13, 2007
### superstonerman
the galaxies arnt moving at the speed of light?
are you sure the galaxies arnt moving at the speed of light even relevent to us?
7. Feb 13, 2007
### ZapperZ
Staff Emeritus
2. Rather than arguing back and forth about "galaxies moving at the speed of light", you should find a proper source first to back this claim.
3. You migth want to brush up on the postulates of Special Relativity first before coming up with this. Many people on here who tried to violate this physics didn't make it out alive.
Zz.
8. Feb 13, 2007
### superstonerman
yes i relise now that i was wrong about my speed of light when using the suns intertial frame but please verify this statement for me:
Other galaxies experience time diliation due to their speed of movment relative to our galaxy
9. Feb 13, 2007
### ZapperZ
Staff Emeritus
But this is irrelevant to the rest of what you are proposing. First of all, we really don't care about the "time dilation" going on in other system. It has no bearing on our observations. The light coming from those source does not change in speed just because that galaxy happens to be "time dilated". Secondly, WE are not in a "time dilation field", since our proper time doesn't charge.
Zz.
10. Feb 13, 2007
### DaveC426913
We have a super-powerful telescope and we point it at a few galaxies.
- a galaxy that's moving along with us through space at a similar speed: no see no time dilation on their planets
- a galaxy that's moving fast relative to us: we see them slow down significantly
- we fly to that 2nd galaxy (the one moving fast relative to us) and we point our scope back at the Milky Way: we see the Milky Way slowed down relative to our new location
There is no preferred viewpooint in the universe, it's all based on the frame of reference we are in, and what we are looking at
11. Feb 13, 2007
### MeJennifer
The term "seeing" needs some qualification and also the direction of movement should be supplied to avoid ambiguity.
For instance the validity of the statement:
"a galaxy that's moving fast toward us relative to us: we see them slow down significantly"
would completely depend on what you mean by "see".
12. Feb 13, 2007
### nakurusil
He said "moving along with us", did you miss that?
13. Feb 13, 2007
### anantchowdhary
14. Feb 13, 2007
### DaveC426913
If it's moving along with us, then it's not moving at all (since the Milky Way is also not moving), thus it experiences no relativistic effects.
But MeJennifer was referring to my examples where I talk about galaxies that ARE moving relative to us. I deliberately left out the direction so as not to complicate the issue for the OP.
Last edited: Feb 13, 2007
15. Feb 14, 2007
### superstonerman
Ok say you had two galaxies moving away from each other at exactely half the speed of light. If each galaxie had a clock assigned to it after 1 year would both the clocks stay synched? As both the galaxies are moving at the same speed but away from each other. But im confused because if this is the case how do you know one galaxy isnt moving at the speed of light and the other galaxie is staionairy in this case time would come to a stop for the moving galaxy. Soemone help me out hre cuz im confused????????????????????
16. Feb 14, 2007
### ZapperZ
Staff Emeritus
Look up http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html" [Broken] in special relativity. If all SR does is adds velocity the SAME way, it wouldn't have been THAT revolutionary.
Zz.
Last edited by a moderator: May 2, 2017
17. Feb 14, 2007
### HallsofIvy
"how do you know one galaxy isnt moving at the speed of light and the other galaxie is staionairy " Relative to what? The whole point is that velocity is always relative to something.
You first postulated "two galaxies moving away from each other at exactely half the speed of light." I had assumed you meant the usual convention "half the speed of light relative to each other. That would mean that galaxy A sees galaxy B moving away from it at c/2, galaxy B sees galaxy A moving away from it at c/2. It would make no sense to add their speeds.
If, instead, you mean "two galaxies are moving, in exactly opposite directions, each at half the speed of light relative to some third frame of reference, kit would make sense to add their speeds but not in the way you think. If two objects are moving directly away from one another with speeds relative to some third frame of reverence v1 and v2 then the speed of each one relative to the other is given by
$$\frac{v_1+ v_2}{1+ \frac{v_1v_2}{c^2}}$$
In particular, if two galaxies are moving directly away from each other at, relative to some third frame of reference, c/2, then the speed of each, relative to the othe is
$$\frac{c/2+ c/2}{1+ \frac{c^2}{4c^2}}= \frac{c}{5/4}= \frac{4}{5}c$$
still less than the speed of light.
18. Feb 18, 2007
### Quantumgravity
First of all superstonerman, 600,000 meters per second is not double the speed of light. The speed of light is about 186,000 MILES per second or 299, 792,458 meters per second. So the sun is not going anywhere near the speed of light relative to the Milky Way.
But I commend you for thinking about the time dilation for galaxies speeding away from each other. I've never thought about that. It does seem that they should be experiencing different rates of time. That's a really cool thought. Thanks.
19. Feb 19, 2007
### DaveC426913
That should have been 600,000 KILOmeters per second.
BTW, in a thread elsewhere I'd posted that our speed around the Milky Way according to Wiki is about 200km/s, so that's ~1/3000th of c.
20. Feb 19, 2007
### HallsofIvy
The crucial point to make is that motion is relative! It makes no sense to say "how do you know one galaxy isnt moving at the speed of light and the other galaxie is staionairy" . All motion must be measured relative to some frame of reference. I assume that when you say "two galaxies moving away from each other at exactely half the speed of light", that is relative to some third frame of reference. Of course, in a frame of reference attached to either of the two galaxies, that galaxy is stationary. The other galaxy would not be moving at the speed of light in that galaxy's frame of reference but at
$$\frac{\frac{1}{2}c+ \frac{1}{2}c}{1+ \frac{\left(\frac{1}{2}c\right)\left(\frac{1}{2}c\right)}{c^2}}= \frac{c}{1+ \frac{1}{4}}= \frac{4}{5}c$$
still well under the speed of light. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6985448598861694, "perplexity": 696.9460203188655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583681597.51/warc/CC-MAIN-20190119201117-20190119223117-00010.warc.gz"} |
https://math.stackexchange.com/questions/3046000/example-of-a-parallelizable-smooth-manifold-which-is-not-a-lie-group | # Example of a parallelizable smooth manifold which is not a Lie Group
All the examples I know of manifolds which are parallelizable are Lie Groups. Can anyone point out an easy example of a parallelizable smooth manifold which is not a Lie Group? Are there conditions on a parallelizable smooth manifold which forces it to be a lie group?
• In the opposite direction, there's a result due to Wolf that $S^7$ is the only exception in the simply-connected case: specifically, for a $X$ compact and simply-connected manifold, $X$ is parallelizable only if it's the product of Lie groups and copies of $S^7$. – anomaly Dec 31 '18 at 16:13
• @anomaly Thanks a lot. I was looking for some result like that. I am not experienced to find this results. Can you please mention where can I find this or may be share a link if possible. – Larsson Dec 31 '18 at 16:16
• I don't have a reference to the original paper, but it's mentioned after Proposition 5.15 in Lee's "Introduction to Smooth Manifolds." – anomaly Dec 31 '18 at 17:22
• Noted with thanks. I will definitely look into it. – Larsson Dec 31 '18 at 17:23
Any closed, orientable $$3$$-manifold $$X$$ is parallelizable. On the other hand, Lie groups have $$\pi_2$$ trivial, and there are a lot of such $$X$$ that don't. (It's not trivial to find them, though. Note that any such $$X$$ must have $$\pi_1 X\not = 0$$ by Poincare duality, and aspherical (e.g., hyperbolic) $$X$$ have $$\pi_2 X = 0$$ as well. $$3$$-manifolds are weird.)
(The easiest way to prove the first assertion is to note that the only obstructions to the triviality of $$TX$$ are the Stiefel-Whitney classes; and $$w_1 = 0$$ by orientability and $$w_2 = 0$$ by the Wu formula, since we're conveniently in low dimension. The second is practically a folklore theorem, but it's not that hard to prove directly either via Morse theory or minimal models.)
• You beat me to this answer! Also, we can readily construct examples of oriented, compact $3$-manifolds that do not admit a Lie group structure: Any Lie group $G$ has abelian fundamental group $\pi_1(G)$, but the product of $S^1$ and an orientable, compact surface $\Sigma$ with genus $> 1$ has nonabelian fundamental group $\pi_1(S^1 \times \Sigma) \cong \pi_1(S^1) \times \pi_1(\Sigma) \cong \Bbb Z \times \pi_1(\Sigma)$. (And +1, by the way.) – Travis Dec 19 '18 at 5:09
• Good point! I ignored the hyperbolic case because of $\pi_2$, but $\pi_1$ also presents an obstruction to Lie-groupness. – anomaly Dec 19 '18 at 5:25
The classical example is $$S^7$$. This comes from the octonions, which are non-associative, so the unit octonions don't form a Lie group.
• Thanks, I was wondering that $S^7$ still has a group structure which is non-associative, are there examples which can not be given a group structure at all. – Larsson Dec 19 '18 at 4:50
• Group operations are by definition associative. The restriction of octonionic multiplication to the unit sphere in the octonions still, however, forms a loop (an operation $S \times S \to S$ with identity and inverses), and the multiplication and inversion maps are smooth with respect to the usual smooth structure. – Travis Dec 19 '18 at 4:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7497643232345581, "perplexity": 284.37331376434884}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578528702.42/warc/CC-MAIN-20190420060931-20190420082903-00066.warc.gz"} |
https://www.authorea.com/doi/full/10.1002/essoar.10506217.1 | Comparing the permeability of shale to deionized water, liquid CO2 and NaCl solution
• Shugang Yang,
• Qingchun Yu
Shugang Yang
China University of Geosciences (Beijing)
Author Profile
Qingchun Yu
China University of Geosciences (Beijing)
Corresponding Author:[email protected]
Author Profile
## Abstract
The permeability of shale is a controlling factor in fluid migration, solute transport, and overpressure development in a sedimentary basin. However, shale permeabilities measured with different fluids can be very different. To investigate the effects of fluid type on shale liquid permeability, a series of flow experiments on three samples were conducted using deionized water, liquid CO2 and 1 mol/L NaCl solution as permeating fluids. The results indicate that the liquid CO2 flow obeys Darcy’s law, showing a constant permeability. The liquid CO2 permeabilities of samples C01, C02 and C03 are 6.90×10-19 m2, 3.80×10-20 m2 and 1.59×10-18 m2, respectively. The transport of the deionized water and NaCl solution in these samples deviates from Darcy’s law, and threshold pressure gradient is observed. The permeabilities measured with these two fluids exhibit nearly identical ranges (10-20~10-21 m2). The sample permeated with NaCl solution generally shows a lower permeability (under the same pressure gradient) but a higher threshold pressure gradient. The relationship between water permeability and pressure gradient follows a power function, with exponents ranging from 0.96~3.41 for deionized water and 0.34~3.30 for NaCl solution. The permeability reduction magnitude (ω) was defined to describe the difference between the three liquid permeabilities and the helium absolute permeability. The range of ω is 0.25~0.96 for liquid CO2, 1.44~2.32 for deionized water and 1.89~3.09 for NaCl solution. The dependence of permeability on fluid type results from the differences in the fluid properties (viscosity and polarity) and fluid-mineral interactions. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8994152545928955, "perplexity": 6678.087068906231}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00466.warc.gz"} |
https://docs.openmc.org/en/stable/pythonapi/generated/openmc.deplete.IndependentOperator.html | # openmc.deplete.IndependentOperator¶
class openmc.deplete.IndependentOperator(materials, micro_xs, chain_file=None, keff=None, normalization_mode='fission-q', fission_q=None, dilute_initial=1000.0, prev_results=None, reduce_chain=False, reduce_chain_level=None, fission_yield_opts=None)[source]
Transport-independent transport operator that uses one-group cross sections to calculate reaction rates.
Instances of this class can be used to perform depletion using one-group cross sections and constant flux or constant power. Normally, a user needn’t call methods of this class directly. Instead, an instance of this class is passed to an integrator class, such as openmc.deplete.CECMIntegrator.
New in version 0.13.1.
Parameters
• materials (openmc.Materials) – Materials to deplete.
• micro_xs (MicroXS) – One-group microscopic cross sections in [b] .
• chain_file (str) – Path to the depletion chain XML file. Defaults to openmc.config['chain_file'].
• keff (2-tuple of float, optional) – keff eigenvalue and uncertainty from transport calculation. Default is None.
• prev_results (Results, optional) – Results from a previous depletion calculation.
• normalization_mode ({"fission-q", "source-rate"}) – Indicate how reaction rates should be calculated. "fission-q" uses the fission Q values from the depletion chain to compute the flux based on the power. "source-rate" uses a the source rate (assumed to be neutron flux) to calculate the reaction rates.
• fission_q (dict, optional) – Dictionary of nuclides and their fission Q values [eV]. If not given, values will be pulled from the chain_file. Only applicable if "normalization_mode" == "fission-q".
• dilute_initial (float, optional) – Initial atom density [atoms/cm^3] to add for nuclides that are zero in initial condition to ensure they exist in the decay chain. Only done for nuclides with reaction rates.
• reduce_chain (bool, optional) – If True, use openmc.deplete.Chain.reduce() to reduce the depletion chain up to reduce_chain_level.
• reduce_chain_level (int, optional) – Depth of the search when reducing the depletion chain. Only used if reduce_chain evaluates to true. The default value of None implies no limit on the depth.
• fission_yield_opts (dict of str to option, optional) – Optional arguments to pass to the openmc.deplete.helpers.FissionYieldHelper object. Will be passed directly on to the helper. Passing a value of None will use the defaults for the associated helper.
Variables
• materials (openmc.Materials) – All materials present in the model
• cross_sections (MicroXS) – Object containing one-group cross-sections in [cm^2].
• dilute_initial (float) – Initial atom density [atoms/cm^3] to add for nuclides that are zero in initial condition to ensure they exist in the decay chain. Only done for nuclides with reaction rates.
• output_dir (pathlib.Path) – Path to output directory to save results.
• round_number (bool) – Whether or not to round output to OpenMC to 8 digits. Useful in testing, as OpenMC is incredibly sensitive to exact values.
• number (openmc.deplete.AtomNumber) – Total number of atoms in simulation.
• nuclides_with_data (set of str) – A set listing all unique nuclides available from cross_sections.xml.
• chain (openmc.deplete.Chain) – The depletion chain information necessary to form matrices and tallies.
• reaction_rates (openmc.deplete.ReactionRates) – Reaction rates from the last operator step.
• burnable_mats (list of str) – All burnable material IDs
• heavy_metal (float) – Initial heavy metal inventory [g]
• local_mats (list of str) – All burnable material IDs being managed by a single process
• prev_res (Results or None) – Results from a previous depletion calculation. None if no results are to be used.
__call__(vec, source_rate)[source]
Obtain the reaction rates
Parameters
• vec (list of numpy.ndarray) – Total atoms to be used in function.
• source_rate (float) – Power in [W] or flux in [neutron/cm^2-s]
Returns
Eigenvalue and reaction rates resulting from transport operator
Return type
openmc.deplete.OperatorResult
classmethod from_nuclides(volume, nuclides, micro_xs, chain_file, nuc_units='atom/b-cm', keff=None, normalization_mode='fission-q', fission_q=None, dilute_initial=1000.0, prev_results=None, reduce_chain=False, reduce_chain_level=None, fission_yield_opts=None)[source]
Alternate constructor from a dictionary of nuclide concentrations
volumefloat
Volume of the material being depleted in [cm^3]
nuclidesdict of str to float
Dictionary with nuclide names as keys and nuclide concentrations as values.
micro_xsMicroXS
One-group microscopic cross sections.
chain_filestr
Path to the depletion chain XML file.
nuc_units{‘atom/cm3’, ‘atom/b-cm’}
Units for nuclide concentration.
keff2-tuple of float, optional
keff eigenvalue and uncertainty from transport calculation. Default is None.
normalization_mode{“fission-q”, “source-rate”}
Indicate how reaction rates should be calculated. "fission-q" uses the fission Q values from the depletion chain to compute the flux based on the power. "source-rate" uses the source rate (assumed to be neutron flux) to calculate the reaction rates.
fission_qdict, optional
Dictionary of nuclides and their fission Q values [eV]. If not given, values will be pulled from the chain_file. Only applicable if "normalization_mode" == "fission-q".
dilute_initialfloat
Initial atom density [atoms/cm^3] to add for nuclides that are zero in initial condition to ensure they exist in the decay chain. Only done for nuclides with reaction rates.
prev_resultsResults, optional
Results from a previous depletion calculation.
reduce_chainbool, optional
If True, use openmc.deplete.Chain.reduce() to reduce the depletion chain up to reduce_chain_level. Default is False.
reduce_chain_levelint, optional
Depth of the search when reducing the depletion chain. Only used if reduce_chain evaluates to true. The default value of None implies no limit on the depth.
fission_yield_optsdict of str to option, optional
Optional arguments to pass to the openmc.deplete.helpers.FissionYieldHelper class. Will be passed directly on to the helper. Passing a value of None will use the defaults for the associated helper.
initial_condition()[source]
Performs final setup and returns initial condition.
Returns
Total density for initial conditions.
Return type
list of numpy.ndarray | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44278663396835327, "perplexity": 11023.2099559831}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500392.45/warc/CC-MAIN-20230207071302-20230207101302-00201.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-equation-x-intercept-and-the-y-intercept-for-the-line-that-p | Algebra
Topics
# How do you find the equation, x-intercept, and the y-intercept for the line that passes through (-3,1) with a slope of zero?
Jul 24, 2017
See a solution process below:
#### Explanation:
A line with slope $0$ by definition is a horizontal line.
Horizontal lines have the same value for $y$ for each and every value of $x$.
Because the $y$ value of the point given in the problem is $1$ then the equation is:
$y = 1$
y-intercept
Because the value of the equation is the same for each and every value of $x$, when we set $x$ equal to $0$ to find the $y$ intercept, $y = 1$
Therefore, the $y$-intercept is: $1$ or $\left(0 , 1\right)$
x-intercept
Because this is a horizontal line it is by definition parallel to the $x$ axis. Because it is parallel to the $x$ axis it never crosses the $x$ axis.
Therefore the is no $x$-intercept.
##### Impact of this question
829 views around the world | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 18, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9160181879997253, "perplexity": 289.23082950785874}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487582767.0/warc/CC-MAIN-20210612103920-20210612133920-00513.warc.gz"} |
https://webwork.libretexts.org/webwork2/html2xml?answersSubmitted=0&sourceFilePath=Library/AlfredUniv/anton8e/chapter3/3.5/prob6.pg&problemSeed=1234567&courseID=anonymous&userID=anonymous&course_password=anonymous&showSummary=1&displayMode=MathJax&problemIdentifierPrefix=102&language=en&outputformat=libretexts | Find $\>f'(x)\>$ if $\>f(x) = \frac{\sin\!\left(x\right)\sec\!\left(x\right)}{3+x\tan\!\left(x\right)}$. | {"extraction_info": {"found_math": true, "script_math_tex": 2, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7211917042732239, "perplexity": 222.7946111699514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662584398.89/warc/CC-MAIN-20220525085552-20220525115552-00293.warc.gz"} |
http://math.stackexchange.com/questions/48508/how-are-the-integral-parts-of-9-4-sqrt5n-and-9-4-sqrt5n-relate?answertab=active | # How are the integral parts of $(9 + 4\sqrt{5})^n$ and $(9 − 4\sqrt{5})^n$ related to the parity of $n$?
I am stuck on this question,
The integral parts of $(9 + 4\sqrt{5})^n$ and $(9 − 4\sqrt{5})^n$ are:
1. even and zero if $n$ is even;
2. odd and zero if $n$ is even;
3. even and one if $n$ is even;
4. odd and one if $n$ is even.
I think either the problem or the options are wrong. To me it seems that answer should be odd irrespective of $n$. Consider the following:
\begin{align*} (9 \pm 4 \sqrt{5})^4 &= 51841 \pm 23184\sqrt{5} \\ (9 \pm 4 \sqrt{5})^5 &= 930249 \pm 416020\sqrt{5} \end{align*}
Am I missing something?
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I think you are confusing "integral part". You are interpreting it as the value of $a$ if you write $(9\pm 4\sqrt{5})^n = a+b\sqrt{n}$ with $a,b\in\mathbb{Z}$. But what they mean is the floor of $(9+4\sqrt{5})^n$, i.e., $\lfloor (9\pm 4\sqrt{5})^n\rfloor$. With that in mind, see Beni Bogosel's answer. – Arturo Magidin Jun 29 '11 at 20:26
@Arturo Magidin:Yes,I confused on "integral part".Thanks! – Quixotic Jun 30 '11 at 11:17
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## 3 Answers
The idea is to see that $(9+4\sqrt{5})^n+(9-4\sqrt{5})^n=2d_n$ is an even number for every $n$. This can be seen using the binomial expansion formula, and seeing that odd terms appear once with $+$ once with $-$, and even terms are always with $+$ and integers.
Moreover, $0<(9-4\sqrt{5})=9-\sqrt{80}=\frac{1}{\sqrt{81}+\sqrt{80}}<1$. This means that the integer part of the second term is zero. And for the other one, think as this
$$2d_n-1<(9+4\sqrt{5})^n<2d_n$$ so the integer part of the first term is always odd. The correct answer would be the second one (although this happens for every $n$).
As Arturo Magidin wrote in his comment, the integer part of a real number $x$, often denoted $\lfloor x \rfloor$ is the unique integer $\lfloor x \rfloor=k$ such that $k \leq x < k+1$, and it does not equal $a$ from the expansion $(9\pm 4\sqrt{5})^n=a\pm b\sqrt{5},\ a,b \in \Bbb{Z}$.
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Alternative to binomial expansion, one can deduce that $\rm\:w = (9+4\sqrt{5})^n + (9-4\sqrt{5})^n\:$ is even by noting that the notion of parity uniquely extends from $\;\mathbb Z\:$ to $\:\mathbb Z[\sqrt{5}]\:$ by defining $\rm\:\sqrt{5}\:$ to be odd. Hence, since $\rm\:w'= w\:,\:$ we infer that $\rm\:w\in \mathbb Z\:$ with parity $\rm\ odd^n +\: odd^n\: =\ odd+odd\ =\ even\:.\$ Then the desired result follows easily as Beni explained. Notice, in particular, how this viewpoint is a very natural higher-degree extension of ubiquitous parity-based proofs in $\mathbb Z\:.$
Alternatively, it follows immediately from the fact that, mod $2$, the sequence $\rm\:w_n\:$ satisfies a monic integer-coefficient recurrence, and the first $2$ (= degree) terms are $\equiv 0\:.\:$ Hence by induction so are all subsequent terms, viz. $\rm\ f_{n+2} \equiv\ a\ f_{n+1} + b\ f_{n} \equiv\ 0\$ since by induction $\rm\ f_{n+1},\ f_{n}\ \equiv\ 0\:.\:$ Said equivalently $\rm\:f_n \equiv 0\$ by the uniqueness theorem for solutions of difference equations (recurrences). As I frequently emphasize uniqueness theorems provide very powerful tools for proving equalities.
Here the uniqueness theorem is rather trivial, amounting to the trivial induction that if two solutions of a degree $\rm\:d\:$ monic integer coefficient recurrence agree for $\rm\:d\:$ initial values then they agree at all subsequent values; equivalently, taking differences, if a solution is $\:0\:$ for $\rm\:d\:$ initial values then it is identically $\:0\:$.
More generally the same holds true for integer-linear combinations of roots of any monic integer coefficient equation (i.e. algebraic integer roots) since they too will satisfy a monic integer coefficient recurrence, viz. the characteristic equation associated to the polynomial having said roots (the quadratic case is the widely studied Lucas sequence). Thus every term of the sequence will be divisible by $\rm\:m\:$ iff it is true for the first $\rm\:d\:$ (= degree) terms. More generally one easily checks that the gcd of all terms is simply the gcd of the initial values.
Note that, as above, one requires only the knowledge of the existence of such a recurrence. There is no need to explicitly calculate the coefficients of the recurrence; rather, only its degree is employed.
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Nice point of view :) – Beni Bogosel Jun 30 '11 at 11:44
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To prove that $$a_n:=\left(9+4\sqrt5\right)^n+\left(9-4\sqrt5\right)^n$$ is an even integer, it suffices to observe that $a_0=2,a_1=18$ and $$a_{n+2}=18\ a_{n+1}-a_n$$ for $n\ge0$.
Variation.
Note that $a_n$ is an integer. Indeed $a_n$ is of the form $b_n+c_n\sqrt5$ with $b_n,c_n$ integers, and $a_n$ doesn't depend on the choice of the square root of $5$, so $c_n=0$.
Once we know that $a_n$ is an integer, we can compute it in the field $\mathbb F_2$ with two elements (in which $\sqrt5$ exists).
EDIT. The above arguments show this: If $a,b,d,n$ are integers, and if $n\ge0$, then $$\left(a+b\sqrt d\right)^n+\left(a-b\sqrt d\right)^n$$ is an even integer.
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The recursion comes from the quadratic equation that defines $9 \pm 4 \sqrt{5}$. – lhf Dec 23 '11 at 11:32
Dear @lhf: Yes, the minimal polynomial is $X^2-\tau\ X+\nu$, where $\tau$ is the trace and $\nu$ the norm. – Pierre-Yves Gaillard Dec 23 '11 at 11:38
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http://neon.nervanasys.com/index.html/design.html | # Design Decisions¶
## Computation backend¶
• All objects inherit from NervanaObject which has a static be variable which is the computation backend being used (gpu, mkl, or cpu).
• be stores other important attributes like batch size and data type.
• A backend must first be generated before running a model using gen_backend.
• If swapping backends, then buffers must be reinitialized by reinstantiating the model layers and calling fprop with the new generated backend.
## Data Layout¶
Neon’s layers internally store data as two-dimensional tensors. For convolution and pooling layers, the data is formatted in $$(C, H, W, N)$$ layout ($$C$$ = channels, $$H$$ = height, $$W$$ = width, $$N$$ = batch size), and represented as a tensor of shape $$(F, N)$$, where $$F = C * H *W$$.
For recurrent layers, the time dimension $$T$$ is added to the $$N$$ dimension, so the data format is $$(F, T*N)$$. The second dimension is ordered by incrementing the batch index first: $$t_1n_1, t_1n_2, ... t_1n_N, t_2n_1, t_2n_2, ...$$
## Layers¶
• Most layers are in layer.py, recurrent layers are in recurrent.py, and merge layers for concatenating or summing input are in merge.py.
### Composite layers¶
• Some layers (for convenience) are composite layers made as lists of other layers.
• Conv is a list of Convolution, Bias, and Activation layers
• Affine is a list of Linear, Bias, and Activation layers
• This allows flexibility in adding optional bias and activation layers without having to specify these as separate layers.
### Layer buffer allocations¶
• Data buffers
• A layer infers input shape from previous layers and initializes buffers accordingly.
• Pre-allocating activation buffers allows buffer reuse and reduces memory usage.
• Buffers will be reinitialized during the next fprop if the layer is reinstantiated.
• Parameter layers (Linear, Bias, Convolution, and BatchNorm) maintain their own parameters W, gradients dW, and states states (for the optimizer).
• In general, layer buffer allocation is kicked off by the containing model, being called prior to the first fit or eval call.
### Initialization¶
• Weight initialization routines are in initializers.py and all have a fill method that describe how they will fill a given param buffer.
• The weight initialization object is passed to the layer constructor and the layer will fill the parameters during init_params.
## Models¶
### Model container¶
• The model provides a container of all the network layers and provides function calls to run and train the network. It is also responsible for initializing and allocating layer parameter buffers.
• We can create a list of layers and give that to the model.
• When forward or backward propagation functions are called, the model will iterate through all the layers to forward pass the inputs and backward pass the errors.
### Learning¶
• When training the model, the following necessary components will be provided:
• a training set object that can iterate over training data
• an optimizer that applies to all the layer updates or a multi-optimizer that maps different optimizers to different layers by layer name
• a cost function to compute the error
• callback object that configures whether to use a validation set and how frequent in the training to validate, whether to get progress bar display, etc. For more information, see neon fundamentals – callbacks.
• During update, the model sends a list containing all layers with learnable parameters to the optimizer.
• The optimizer will then grab a tuple of (W, dW, state) from each layer and apply the updates.
## Choice of sizes¶
• We will get better utilization if we pick more friendly sizes for batch size, sequence length, or feature size.
• Our GPU kernels are optimized for sizes being multiples of 4.
• In many of our examples, we use parameters from reference implementations. However, it is recommended to use multiples of 4. In many cases, zero-padding is needed to implement the same model. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21374277770519257, "perplexity": 3150.174609258644}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267868237.89/warc/CC-MAIN-20180625170045-20180625190045-00436.warc.gz"} |
https://www.ias.ac.in/listing/bibliography/pram/S_V_Moharil | • S V Moharil
Articles written in Pramana – Journal of Physics
• Reflectance spectra and thermoluminescence of NaF coloured in an electrodeless discharge
A comparative study ofγ-ray colouration and electrodeless discharge excitation is reported for NaF. New absorption bands and glow peaks were found. These are shown to be characteristic of electrodeless discharge method of colouration. These are attributed to the multiple types of defects. Further, it is shown that the process by which such defects are formed is strongly temperature dependant. A tentative explanation for the peculiar characteristic of the electrodeless discharge excitation is put forth. The possibility of exploiting these peculiarities for the study of certain properties of colour centres is pointed out.
• Colour centres in powdered KI
Fine powder of KI was coloured in an electrodeless discharge. Due to quick bleaching of the F centres produced in this method, it was possible to prepare the samples that were almost free from the F centres. High concentration of the electron deficient centres could be produced, which were studied by measuring the diffused reflectance. A band at 354 nm is shown to be composed of two overlapping bands. Further, growth of a band appearing at 265 nm is studied. Bleaching characteristics of the samples are studied and it is shown that, similar to F centre bleaching, bleaching of these samples also proceeds in at least two steps. The difference between two components of the bleaching curves is quite marked. Further it is showed that the components are related to the presence of different absorption bands and appear at different stages of colouration.
• Reflectance spectra and thermoluminescence of NaBr coloured in an electrodeless discharge
A comparative study of the optical and thermoluminescent properties ofγ irradiated NaBr and NaBr coloured in an electrodeless discharge is reported. In discharge coloured NaBrF centre absorption maxima shifted with the colouration time. This is tentatively attributed to the formation ofE centres. Correspondingly, an additional peak was observed in thermoluminescence glow curve. It is suggested that the results are not characteristic of the method of colouration but rather of the imperfections inherent to the powders, and in a perfect (undeformed) single crystal such a phenomenon should not be observed.
• Reflectance spectra and thermoluminescence of alkali halides coloured in an electrodeless discharge
Microcrystalline powders of NaCl, KCl and KBr are coloured in electrodeless discharge. Reflectance and TL studies of these coloured powders are reported. It is concluded that colouration of powders can be understood by considering them as an admixture of perfect and imperfect lattices, and differs from that of single crystals. It is suggested that some of the descrepancies reported on TL data may be due to such a difference. Further, it is shown that a better correlation can be had if TL data are presented along with the corresponding optical measurements. Adoption of such a procedure may help to remove the descrepancy in TL data.
• Mechanoluminescence excitation in alkali halide crystals and colouration decay in microcrystalline powders
The mechanoluminescence (ML) of NaCl, NaBr, NaF, LiCl and LiF crystals ceases at 105, 58, 170, 151 and 175°C respectively. Both the temperatureTc at whichML disappears and the temperatureTs required to induce a particular percentage of colouration decay in a given time, decreases with increasing nearest neighbour distance in alkali halide crystals. This perhaps suggests that similar processes cause the disappearance ofml in alkali halide crystals and the colouration decay in their microcrystalline powders. It is shown that mobile dislocations may cause the leakage of surface charge and the decay of colouration in microcrystalline powders.
• Pramana – Journal of Physics
Volume 96, 2022
All articles
Continuous Article Publishing mode
• Editorial Note on Continuous Article Publication
Posted on July 25, 2019 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8185836672782898, "perplexity": 2842.9088070916587}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571472.69/warc/CC-MAIN-20220811133823-20220811163823-00622.warc.gz"} |
http://mathhelpforum.com/pre-calculus/93158-how-find-changed-base.html | # Thread: How to find the Changed Base
1. ## How to find the Changed Base
The formula A = P(1.09)^t is an example of exponential growth with base 1.09. Determine an equivalent continuous growth formula using base e.
Also, what if it asks me to use a different base? (eg. 2)
2. Originally Posted by AlphaRock
The formula A = P(1.09)^t is an example of exponential growth with base 1.09. Determine an equivalent continuous growth formula using base e.
Also, what if it asks me to use a different base? (eg. 2)
3. Hello, AlphaRock!
The formula $A = P(1.09)^t$ is an example of exponential growth with base 1.09.
Determine an equivalent continuous growth formula using base $e$.
Also, what if it asks me to use a different base?
Suppose we wish to change to base $b.$
Instead of $(1.09)^t$, we want $b^{kt}$, where $k$ is a constant to be determined.
We have: . $b^{kt} \:=\:(1.09)^t$
Take logs (base $b$): . $\log_b\left(b^{kt}\right) \:=\:\log_b(1.09)^t$
. . $\text{We have: }\;kt\underbrace{\log_b(b)}_{\text{This is 1}} \:=\:t\log_b(1.09) \quad\Rightarrow\quad kt \:=\:t\log_b(1.09)$
. . Hence: . $k \:=\:\log_b(1.09)$
Therefore: . $A \;=\;P\,b^{\log_b(1.09)\cdot t}$
4. Originally Posted by Soroban
Hello, AlphaRock!
Suppose we wish to change to base $b.$
Instead of $(1.09)^t$, we want $b^{kt}$, where $k$ is a constant to be determined.
We have: . $b^{kt} \:=\1.09)^t" alt="b^{kt} \:=\1.09)^t" />
Take logs (base $b$): . $\log_b\left(b^{kt}\right) \:=\:\log_b(1.09)^t$
. . $\text{We have: }\;kt\underbrace{\log_b(b)}_{\text{This is 1}} \:=\:t\log_b(1.09) \quad\Rightarrow\quad kt \:=\:t\log_b(1.09)$
. . Hence: . $k \:=\:\log_b(1.09)$
Therefore: . $A \;=\;P\,b^{\log_b(1.09)\cdot t}$
Un, Soroban, since $b^{\log_b(a)}= a$, that reduces to $A= 1.09^t$, the formula we started with.
If we want to write $1.09^t$ as an exponential with base b, we have, as Soroban said, $1.09^t= b^{kt}$. Now take the natural logarithm of both sides: $ln(1.09^t)= t ln(1.09)$ and $ln(b^{kt}= kt ln(b)$ so the equation becomes $t ln(1.09)= kt ln(b)$ and $k= \frac{ln(1.09)}{ln(b)}$.
The advantage is that your calculator has a "ln" key but not a " $log_b$" key!
In particular, if b= e, then ln(b)= 1 so $k= ln(1.09)= 0.0862$ and $1.09^t= e^{t ln(1.09)}= e^{0.0862 t}$.
If b= 2, then ln(b)= ln(2)= 0.6931 so $k= \frac{ln(1.09)}{ln(2)}= \frac{0.0862}{0.6931}= 0.1243$ and $1.09^t= 2^{0.1243 t}$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 35, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9758851528167725, "perplexity": 4160.826623760525}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608058.57/warc/CC-MAIN-20170525102240-20170525122240-00057.warc.gz"} |
http://www.maa.org/publications/periodicals/convergence/benjamin-bannekers-inscribed-equilateral-triangle-transcription-of-bannekers-problem | # Benjamin Banneker's Inscribed Equilateral Triangle - Transcription of Banneker's Problem
Author(s):
John F. Mahoney (Benjamin Banneker Academic High School)
Required the Lengths of the Sides of an Equilateral Triangle inscribed in a Circle whose Diameter is 200 perches, with a general Theorem for all such Questions
Solution of the above problem
10.00 ….. 3.142 …… 200
200
1000)628400
Lenght of the periphery 628.400
1/3 of the length of the periphery 209.466
1/3 of 1/3 of the periphery 69.822
2
2/3 of 1/3 of the periphery 139.644
Length of the Sides required 349.110
Note: In Banneker's journal there is a big X crossing out the last five numbers in his calculations and adjacent to each of the 175's in his figure is 349.110
This example deals with the problem of finding the lengths of the sides of an inscribed equilateral triangle in a circle of diameter 200 perches. A perch, a synonym of a rod, is a unit of measurement equal to 16½ feet. There are 320 perches in a mile. A surveyor could find the number of acres in a rectangular piece of land by multiplying the length in perches by the width in perches and dividing the product by 160.
What did Banneker do to solve this problem? First of all he calculated the circumference, which he calls periphery, by multiplying an approximation of $$\pi$$ (3.142) by 200. He did this by multiplying 3.142 by 200 to get 628.400 and then dividing that by 1000 to get 628.400 (How often have do we, as teachers, pull our hair out when we see our students multiplying or dividing by powers of 10?) He then finds 1/3 the length (misspelled in his journal) of the circumference and later 2/9 of the circumference. He adds those numbers together to get 349.110, but clearly he knew that the side of the equilateral triangle had to be less than the diameter. He crossed out his work and then labeled the sides of triangle 175 which is approximately half of 349.110.
Using the properties of a 30º-60º-90º triangle and a circle of radius 100, one can see that the length of the side of the equilateral triangle is 173.205 which shows that Banneker's solution is within 1% of the actual one. The side of the equilateral triangle is the square root of 3 times the radius of the circumscribed circle.
How did Banneker figure this out without using the properties of a 30º-60º-90º triangle or trigonometry? Banneker calculated 5/9 of the circumference to get 349.110 and by taking half of that he essentially computed 5/18 of the circumference. Since (5/18)(2$$\pi$$)100 is approximately equal to 174.533, Banneker's method is quite good. It would have been even better if he had taken exactly half of 349.110 to get 174.555. Banneker's method essentially uses (5/9)$$\pi$$ to approximate the square root of 3. Perhaps this approximation was a rule of thumb that surveyors used in the 18th century.
John F. Mahoney (Benjamin Banneker Academic High School), "Benjamin Banneker's Inscribed Equilateral Triangle - Transcription of Banneker's Problem," Loci (July 2010) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8654367327690125, "perplexity": 824.2854854953267}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042981921.1/warc/CC-MAIN-20150728002301-00005-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://www.effortlessmath.com/math-topics/10-most-common-asvab-math-questions/ | # 10 Most Common ASVAB Math Questions
Preparing for the ASVAB Math test? Want a preview of the most common mathematics questions on the ASVAB Math test? If so, then you are in the right place.
The mathematics section of ASVAB can be a challenging area for many test-takers, but with enough patience, it can be easy and even enjoyable!
Preparing for the ASVAB Math test can be a nerve-wracking experience. Learning more about what you’re going to see when you take the ASVAB can help to reduce those pre-test jitters. Here’s your chance to review the 10 most common ASVAB Math questions to help you know what to expect and what to practice most. Try these 10 most common ASVAB Math questions to hone your mathematical skills and to see if your math skills are up to date on what’s being asked on the exam or if you still need more practice.
Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.
$14.99 Satisfied 226 Students ## 10 Sample ASVAB Math Practice Questions 1- A family owns 15 dozen of magazines. After donating 57 magazines to the public library, how many magazines are still with the family? A. 180 B. 152 C. 123 D. 98 2- In the deck of cards, there are 4 spades, 3 hearts, 7 clubs, and 10 diamonds. What is the probability that William will pick out a spade? A. $$\frac{1}{6}$$ B. $$\frac{1}{8}$$ C. $$\frac{1}{9}$$ D. $$\frac{1}{5}$$ 3- What is the prime factorization of 560? A. $$2 × 2 × 5 × 7$$ B. $$2 × 2 × 2 × 2 × 5 × 7$$ C. $$2 × 7$$ D. $$2 × 2 × 2 × 5 × 7$$ 4- William is driving a truck that can hold 5 tons maximum. He has a shipment of food weighing 32,000 pounds. How many trips will he need to make to deliver all of the food? A. 1 Trip B. 3 Trip C. 4 Trip D. 6 Trip 5- A man goes to a casino with$180. He loses $40 on blackjack, then loses another$50 on roulette. How much money does he have left?
A. $75 B.$90
C. $105 D.$120
6- A woman owns a dog walking business. If 3 workers can walk 9 dogs, how many dogs can 5 workers walk?
A. 13
B. 14
C. 15
D. 19
7- If $$a = 3$$, what is the value of $$b$$ in this equation?
A. 10
B. 8
C. 6
D. 4
8- The eighth root of 256 is:
A. 6
B. 4
C. 8
D. 2
9-A circle has a radius of 5 inches. What is its approximate area? ($$π = 3.14$$)
A. 90.7 square inches
B. 78.5 square inches
C. 31.4 square inches
D. 25 square inches
10- If $$- 8a = 64$$, then $$a =$$ ?
A. $$-8$$
B. 8
C. 16
D. 0
$15.99 Satisfied 196 Students ## Answers: 1- C 15 dozen of magazines are 180 magazines: $$15 × 12 = 180$$ $$180 – 57 = 123$$ 2- A $$probability=\frac{desired \space outcomes}{possible \space outcomes}=\frac{4}{4+3+7+10}=\frac{4}{24}=\frac{1}{6}$$ 3- B Find the value of each choice: $$A. \space 2 × 2 × 5 × 7 = 140$$ $$B. \space 2 × 2 × 2 × 2 × 5 × 7 = 560$$ $$C. \space 2 × 7 = 14$$ $$D. \space 2 × 2 × 2 × 5 × 7 = 280$$ 4- C 1 ton $$= 2,000$$ pounds 5 ton $$= 10,000$$ pounds $$\frac{32,000}{10,000}=3.2$$ William needs to make at least 4 trips to deliver all of the food. 5- B $$180 – 40 – 50 = 90$$ 6- C Each worker can walk 3 dogs: $$9 ÷ 3 = 3$$ 5 workers can walk 15 dogs. $$5 × 3 = 15$$ 7- C If $$a = 3$$ then: $$b = \frac{a^2}{3}+ 3 ⇒ b =\frac{3^2}{3}+ 3 = 3 + 3 = 6$$ 8- D $$\sqrt[8]{256}$$ $$(2^8=2×2×2×2×2×2×2×2=256)$$ 9- B (r = radius) Area of a circle = $$πr^2 = π × (5)^2 = 3.14 × 25 = 78.5$$ 10- A $$- 8a = 64 ⇒ a = \frac{64}{-8}= – 8$$ Looking for the best resource to help you succeed on the ASVAB Math test? ## The most comprehensive workbook forthe ASVAB Math test$16.99
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SAVE $40 It was$76.99 now it is \$36.99 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5642554759979248, "perplexity": 1647.8954613527487}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499954.21/warc/CC-MAIN-20230202003408-20230202033408-00823.warc.gz"} |
https://www.mathssciencecorner.com/2021/04/maths-std-8-ch-14-ex-142-part-2-video.html | Maths Std 8 Ch 14 Ex 14.2 Part 2 Video - Maths Science Corner
# Maths Science Corner
Math and Science for all competitive exams
# Exercise 14.2 (Swadhyay 14.2) Part 2 Video
On maths science corner you can now download new NCERT 2020 Gujarati Medium Textbook Standard 8 Maths Chapter 14 Avayavikaran (Factorization) in Video format for your easy reference.
On Maths Science Corner you will get all the printable study material of Maths and Science Including answers of prayatn karo, Swadhyay, Chapter Notes, Unit tests, Online Quiz etc..
This material is very helpful for preparing Competitive exam like Tet 1, Tet 2, Htat, tat for secondary and Higher secondary, GPSC etc..
Highlight of the chapter
14.1 Introduction
14.1.1 Factors of natural numbers
14.1.2 Factors of algebraic expressions
14.2 What is factorization?
14.2.1 Method of common factors
14.2.2 Factorization by regrouping terms
14.2.3 Factorization using identities
14.2.4 Factorization of the terms (x + a) (x + b)
14.3 Division of algebraic expressions
14.3.1 Division of a monomial by another monomial
14.3.2 Division of a polynomial by a monomial
14.4 Division of algebraic expressions (Polynomial /Polynomial)
14.5 Can you find the error?
14.6 Summary
You will be able to learn above topics in Chapter 14 of NCERT Maths Standard 8 (Class 8) Textbook chapter.
Earlier Maths Science Corner had given Completely solved NCERT Maths Standard 8 (Class 8) Textbook Chapter 14 Avayavikaran (Factorization) in the PDF form which you can get from following :
Mathematics Standard 8 (Class 8) Textbook Chapter 14 in PDF Format
Today Maths Science Corner is giving you the Video Lecture of Chapter 14 in the form of Video Lectures of NCERT Maths Standard 8 (Class 8) in Video format for your easy reference.
Mathematics Standard 8 Chapter 14 Avayavikaran (Factorization) Exercise 14.2 (Swadhyay 14.2) Part 2 Video
In this Chapter you will be able to learn various factorization methods.
You can get Std 6 Material from here.
You can get Std 7 Material from here.
You can get Std 8 Material from here.
You can get Std 10 Material from here. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9323229789733887, "perplexity": 9571.728212061777}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500056.55/warc/CC-MAIN-20230203122526-20230203152526-00766.warc.gz"} |
http://math.stackexchange.com/questions/530747/logical-proof-of-the-statement-xy-0-implies-x-0-text-or-y-0/530749 | # Logical proof of the statement $xy = 0 \implies x=0\text{ or } y=0$
Claim:
If $xy=0$, then $x=0$ or $y=0$.
My proof is as follows:
• case 1: $x=0$, so $0y=0$
• case 2: $y=0$, so $x0=0$
Either way, $xy=0$.
I'm very confused by this myself. So if I let $xy=0$ be $P$, and $x=0$ or $y=0$ be $Q$, then the claim "if $xy=0$, then either $x=0$ or $y=0$" is asking me to prove that $P \implies Q$. But I feel as if the proof I gave is $Q \implies P$, which is very different from $P \implies Q$. Can anyone enlighten me on the subject of proving if-then statements?
-
You have to specify the domain you are working in. An example: In ${\mathbb Z}_6$ we have $2\ne0$, $3\ne0$, but $2\cdot 3=0$. – Christian Blatter Oct 18 '13 at 9:17
Your feeling is right: What you have done is the opposite direction. Your argument proves $$(x = 0 \text{ or } y = 0) \implies xy = 0.$$
How can you prove a statement of the form $$A \implies B$$ in general? The direct method is to assume that $A$ is true, and then to conclude that also $B$ is true under this assumption.
Let's apply this to prove the statement $$xy = 0 \implies (x = 0 \text{ or } y = 0).$$ In this case \begin{align*} A & = \text{''}xy = 0\text{''} \\ B & = \text{''}x = 0\text{ or }y = 0\text{''} \end{align*}
So we assume that $xy = 0$ is true. Now we have to show that $(x = 0 \text{ or } y = 0)$ is true. The nature of an "or"-statement often involves a case by case study:
1. If $x = 0$, then of course $(x = 0 \text{ or } y = 0)$ is true.
2. Otherwise, we have $x \neq 0$. Now we may divide our assumption (the equation $xy = 0$) by $x$ to get $y = 0$, so $(x = 0 \text{ or } y = 0)$ is true also in this case.
We have just proven $$xy = 0 \implies (x = 0 \text{ or } y = 0),$$ and the argument in your question proves $$xy = 0 \Longleftarrow (x = 0 \text{ or } y = 0).$$ So in fact, we have an equivalence, which we can write down as $$xy = 0 \iff (x = 0 \text{ or } y = 0).$$
-
well, it only happens in an integral domain, or fields as we generally works in which are integral domains automatically. if you are in, say, Z6 , its not true, as take 3*2=6mod6=0 where none of 3 and 2 are zero. but i guess u have already assumed it over reals which is a field, in that case, T.P xy=0⟹x=0 or y=0, you can assume y≠0, and then multiply on both sides by y^-1 which will give you x.1=0*y^-1=0 implies x=0. for integral domains, its basically the definition if an integral domain.
-
You should consider using MathJax. – Student Jul 8 '14 at 18:47
Not quite right, as you have it written you merely show that if either $x$ or $y$ are zero then their product is zero. Not that if the product is zero then either $x$ or $y$ must necessarily be zero.
You can show this by contradiction; assume $xy=0$ but $x\neq0$ and $y\neq 0$ then $xy\neq 0$ which contradicts our original assumption that $xy=0$ so we cannot have that both $x$ and $y$ are non zero. In other words at if $xy=0$ at least one of $x$ and $y$ must be zero.
-
‘Not quite right’ is an understatement: it’s simply wrong, I’m afraid. – Brian M. Scott Oct 18 '13 at 8:16
If $x\ne0$, what happens if you multiply both sides by $\frac1x$?
-
Just another way. It might not be a formal method.
The solution satisfying the following equation $$A \times B =0$$ is $A=0$ (for any $B$) or $B=0$ (for any $A$).
You cannot apply the same pattern for the case in which the right hand side is not zero. Why? For example, $$A\times B = 2$$ If you choose $A=2$ then $B$ must be $1$ (rather than for any $B$). If you choose $B=2$ then $A$ must be $1$ (rather than for any $A$).
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https://www.gmlscripts.com/forums/viewtopic.php?id=1940 | # GMLscripts.com
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## #1 2013-04-21 15:18:08
Marchal_Mig12
Member
Registered: 2009-05-21
Posts: 74
### Isometric lighting engine
Hi everyone,
I've been developping a testing a lot of ways to render fast, efficient, and customizable isometric engines. All that came up after my friend and I released Zombie Movie
Gameplay video here :
Now in this game, I was using pure isometric collisions which means I had to calculate every diagonals collisions. Now, this method is kind of reckless because it limits the collisions. Then, I though, what if I made everything coded using top-down algorithms and then render as isometric. I found this solution to be clever. All I have to do is create blocks, and render them as isometric tile. This even gave the possibility to rotate the view in the isometric world.
(the top-view version of the isometric render making collision much fast and easier to handle)
So here's what I did. Each block's information (x,y,depth,height,blend) were stored into a grid's list. For optimisation sake, I did not want an object for each and every isometric tile so I destroyed the top-view block's and I used tiles as isometric block. With a few simple calculations it was possible to determine each tile's x, y and depth.
Expandvar i,n,xx,yy,nx,ny,tile;
for(i=0;i<room_width/32;i+=1)
for(n=0;n<room_height/32;n+=1)
{
tile = global.tile_id[i,n]
if tile then
{
xx = global.tile_x[i,n];
yy = global.tile_y[i,n];
switch(global.iso_dir)
{
case 45: nx = ( xx+yy)*1/2-16; ny = (-xx+yy)*1/4-global.tile_height[i,n]-24;break;
case 135: nx = (-xx+yy)*1/2-16; ny = (-xx-yy)*1/4-global.tile_height[i,n]-24;break;
case 225: nx = (-xx-yy)*1/2-16; ny = ( xx-yy)*1/4-global.tile_height[i,n]-24;break;
case 315: nx = ( xx-yy)*1/2-16; ny = ( xx+yy)*1/4-global.tile_height[i,n]-24;break;
}
global.tile_depth[i,n] = -ny-global.tile_height[i,n]*2-24;
tile_set_position(tile,nx,ny);
tile_set_depth(tile,global.tile_depth[i,n]);
}
}
Given the huge customization possibilities this method gave me, I even thought of a simple lighting engine that could add up to this. It was as simple as casting a light and change the tiles blend depending on the distance between the tile and the light.
I have also made sure the engine runs as fast as possible. So far it keep hovering at about 900 fps on the debug mode of Game Maker Studio. I will be uploading a little demo and maybe the source a bit later
Here's how it looks like so far (if you look carefully you will see the view has rotated on the second image) :
I can't think of any other faster and efficient method. By the way, I am making a full game out of it. I hope I will be able to show it to you guys soon.
What do you guys think of this method? Any thoughts?
Last edited by Marchal_Mig12 (2013-04-21 15:28:17)
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## #2 2013-04-22 18:23:01
xot
Registered: 2007-08-18
Posts: 1,202
### Re: Isometric lighting engine
Looks good!
I think running the game in a 2D top-down manner and rendering as isometric is they way most people go. It certainly simplifies things and is what I usually recommend (not that I've successfully built an isometric game). Using tiles instead of objects is very sensible as well. Using color blending for the lighting is the way to go too.
Calculating distances for every cell might be a bit expensive, especially as the number of lights goes up. If I was doing this, my instinct would be to use ds_grids instead of arrays for the light accumulation. With grids I could use a second small grid with the lighting pre-computed (basically a circular gradient, light in the middle, dark at the edges and corners), and use it like a stamp by adding it to the light accumulation grid with ds_grid_add_grid_region(). Each light gets added as needed to the accumulation lighting grid, offset according to its position. Then when you want to light your tiles, you can read the value from the lighting accumulation grid and use it as an index to a look-up table (list or array) of blend colors.
If you wanted to get fancy, instead of a look-up table, you could use separate accumulators for red, green, and blue for full-colored lighting.
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## #3 2013-04-22 18:43:38
Marchal_Mig12
Member
Registered: 2009-05-21
Posts: 74
### Re: Isometric lighting engine
Pre-calculated light accumulation into a ds_grid is a clever idea. What is the most expensive so far is resetting the tiles from colored to black after the player walked on it. The best way would probably be to calculate the tile offset that the player has moved from and then only reset tiles for that region.
Now I am thinking about lights appearing on walls. I do not have a clear idea of how I will do this but I do have a few ideas on my mind. One would be to color up the floor part of an isometric block. Then, whenever a block with height's higher than player's height is in light range, swap between the two tiles and then blend the new tile (with floor colored in black) which should only affect the wall part of the block.
2d isometric lighting system can be hard to manage sometimes.
Thanks for your suggestion. I will try it out and post a small demo afterwards.
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## #4 2013-07-13 19:34:38
Marchal_Mig12
Member
Registered: 2009-05-21
Posts: 74
### Re: Isometric lighting engine
Here's a little video showing the progress using the method you suggested me.
it is coming along pretty well although I gave up on the shadows since I had trouble with it.
I have also been thinking about something similar to 3d where a grid of points with height values stored in it would define the field. Then accessing to that grid, I could change any object's height based on those values. How would that work? Do you think it would be too heavy to process for game maker?
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## #5 2013-07-13 20:24:34
xot
Registered: 2007-08-18
Posts: 1,202
### Re: Isometric lighting engine
Looking good!
A height-map would be good thing to try. If you store the heights of each of cell corners in a ds_grid, you can get the height at any point within a grid cell using some bilinear interpolation.
NOTE: This would require that the heights be continuous, ie. the corner of one cell is the same height as the corners of the other three cells that share that point.
I made a script for exactly this kind of thing:
http://www.gmlscripts.com/forums/viewtopic.php?id=1718
Last edited by xot (2013-07-13 20:31:02)
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## #6 2013-07-13 20:53:18
Marchal_Mig12
Member
Registered: 2009-05-21
Posts: 74
### Re: Isometric lighting engine
If I understand the script correctly, that would return the adjusted height between 4 grid coordinates?
Last edited by Marchal_Mig12 (2013-07-13 20:53:56)
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## #7 2013-07-13 23:15:04
xot
Registered: 2007-08-18
Posts: 1,202
### Re: Isometric lighting engine
That's right.
Abusing forum power since 1986.
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## #8 2013-07-15 14:16:14
Marchal_Mig12
Member
Registered: 2009-05-21
Posts: 74
### Re: Isometric lighting engine
Hey Xot,
I did a little experiment using the script you gave me.
Heightmap is working well too. Next step is to find an efficient way to be able to cut the edges straight. Sometimes you don't want to create a slope between two points and create a wall instead. Although I could work around this with invisible walls and a different visual.
Hope you like it. Feel free to suggest any improvement that could be done.
EDIT : Just noticed, it is just not optimized at all, I did that really quick to have a running demonstration.
Last edited by Marchal_Mig12 (2013-07-15 14:17:29)
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## #9 2013-07-16 20:43:25
xot
Registered: 2007-08-18
Posts: 1,202
### Re: Isometric lighting engine
Getting something like this working with discontinuous terrain like cliffs and pits and such complicates it some.
I think the simplest solution, using the current system, is to use a quadrant of grid cells to store the four corner heights of a single terrain cell. Adjacent terrain cells use an adjacent quad of cells in the grid. When you look-up the bilinear height, you double the integer portions of the coordinates first.
In the figure below, each terrain cell is marked with a number, each letter is a cell in the height grid. Each terrain cell has four corner heights (A,B,C,D).
ExpandA-----B-----A-----B-----A-----B
| 1 |\\\\\| 2 |\\\\\| 3 |
C-----D-----C-----D-----C-----D
|\\\\\|\\\\\|\\\\\|\\\\\|\\\\\|
A-----B-----A-----B-----A-----B
| 4 |\\\\\| 5 |\\\\\| 6 |
C-----D-----C-----D-----C-----D
Hope that makes sense, it's kind of hard to explain. The idea just occurred to me and I haven't tested it yet.
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## #10 2013-07-17 18:53:39
Marchal_Mig12
Member
Registered: 2009-05-21
Posts: 74
### Re: Isometric lighting engine
Indeed, I am not sure to fully understand
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## #11 2013-07-18 01:54:23
xot
Registered: 2007-08-18
Posts: 1,202
### Re: Isometric lighting engine
Maybe this illustration will help make things more clear.
Last edited by xot (2013-07-28 08:21:24)
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## #12 2013-07-18 06:35:31
icuurd12b42
Member
Registered: 2008-12-11
Posts: 303
### Re: Isometric lighting engine
That means the method can be used to define slopes and pillars/plateaus... discontinuous. guess continuous would mean corners would be shared but you would loose the ability to make pillars
Last edited by icuurd12b42 (2013-07-18 06:36:03)
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## #13 2013-07-18 09:08:08
xot
Registered: 2007-08-18
Posts: 1,202
### Re: Isometric lighting engine
Right.
Abusing forum power since 1986.
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## #14 2013-07-18 13:31:40
Marchal_Mig12
Member
Registered: 2009-05-21
Posts: 74
### Re: Isometric lighting engine
Got it. Thanks. Not as useful for the kind of game I am making atm but certainly will in the future.
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## #15 2020-04-12 17:55:07
Marchal_Mig12
Member
Registered: 2009-05-21
Posts: 74
### Re: Isometric lighting engine
Wow. it's been like 7 years since the last post. I haven't touched GM for the same amount of time. Just got back into it now that I have time for myself (COVID-19).
It's nice to see this website still active. How have you been doing Xot ? Funny enough, I am still working on Isometric Engines. Here's a picture. Got around with the depth sorting. Can now use blocks of different dimensions.
I was thinking about making a lighting/shadow casting engine for it too. It is however a bit complex for me as I don't know how to make a shader work. I am also not sure about the best way to fake 3D shadows in an isometric world.
Any ideas ?
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## #16 2020-04-15 13:34:29
xot
Registered: 2007-08-18
Posts: 1,202
### Re: Isometric lighting engine
That sounds like a tricky problem. Faking it would probably be much harder than doing it with 3D geometry and a stencil buffer. There are probably other ways to approach it with shaders but I'm not imagining anything that would be as efficient.
Abusing forum power since 1986.
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## #17 2020-04-21 00:03:11
Marchal_Mig12
Member
Registered: 2009-05-21
Posts: 74
### Re: Isometric lighting engine
Here's the link to the new engine by the way.
Isometric Engine
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[31] Henrik Bresinsky and Lê Tuân Hoa. On the reduction number of some graded algebras. Proc. Amer. Math. Soc. 127 (1999) 1257-1263. MR 1473657. Abstract, references, and article information View Article: PDF This article is available free of charge [32] Alberto Corso, William Heinzer and Craig Huneke. A generalized Dedekind-Mertens lemma and its converse . Trans. Amer. Math. Soc. 350 (1998) 5095-5109. MR 1473435. Abstract, references, and article information View Article: PDF This article is available free of charge [33] William Heinzer and Craig Huneke. The Dedekind-Mertens Lemma and the contents of polynomials. Proc. Amer. Math. Soc. 126 (1998) 1305-1309. MR 1425124. Abstract, references, and article information View Article: PDF This article is available free of charge [34] D. D. Anderson and Moshe Roitman. A characterization of cancellation ideals. Proc. Amer. Math. Soc. 125 (1997) 2853-2854. MR 1415571. 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Soc. 347 (1995) 639-650. MR 1242087. Abstract, references, and article information View Article: PDF This article is available free of charge [39] D. D. Anderson. A note on minimal prime ideals . Proc. Amer. Math. Soc. 122 (1994) 13-14. MR 1191864. Abstract, references, and article information View Article: PDF This article is available free of charge [40] Songqing Ding. Auslander's $\delta$-invariants of Gorenstein local rings . Proc. Amer. Math. Soc. 122 (1994) 649-656. MR 1203983. Abstract, references, and article information View Article: PDF This article is available free of charge [41] Henri Dichi and Daouda Sangare. Filtrations, asymptotic and Pr\"uferian closures, cancellation laws . Proc. Amer. Math. Soc. 113 (1991) 617-624. MR 1064901. Abstract, references, and article information View Article: PDF This article is available free of charge [42] Raymond C. Heitmann and Stephen McAdam. Comaximizable primes . Proc. Amer. Math. Soc. 112 (1991) 661-669. MR 1049136. Abstract, references, and article information View Article: PDF This article is available free of charge [43] Mutsumi Amasaki. Application of the generalized Weierstrass preparation theorem to the study of homogeneous ideals . Trans. Amer. Math. Soc. 317 (1990) 1-43. MR 992603. Abstract, references, and article information View Article: PDF This article is available free of charge [44] Melvin Hochster and Craig Huneke. Tight closure, invariant theory, and the Brian\c con-Skoda theorem . J. Amer. Math. Soc. 3 (1990) 31-116. MR 1017784. Abstract, references, and article information View Article: PDF This article is available free of charge [45] William J. Heinzer and Ira J. Papick. Remarks on a remark of Kaplansky . Proc. Amer. Math. Soc. 105 (1989) 1-9. MR 973834. Abstract, references, and article information View Article: PDF This article is available free of charge [46] Louis J. Ratliff. $\Delta$-closures of ideals and rings . Trans. Amer. Math. Soc. 313 (1989) 221-247. MR 961595. 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Abstract, references, and article information View Article: PDF This article is available free of charge [51] L. J. Ratliff. Note on simple integral extension domains and maximal chains of prime ideals . Proc. Amer. Math. Soc. 77 (1979) 179-185. MR 542081. Abstract, references, and article information View Article: PDF This article is available free of charge [52] Raymond C. Heitmann. Examples of noncatenary rings . Trans. Amer. Math. Soc. 247 (1979) 125-136. MR 517688. Abstract, references, and article information View Article: PDF This article is available free of charge [53] H. G. Dales and J. Esterle. Discontinuous homomorphisms from $C\left( X \right)$. Bull. Amer. Math. Soc. 83 (1977) 257-259. MR 0430786. Abstract, references, and article information View Article: PDF [54] Augusto Nobile. A note on flat algebras . Proc. Amer. Math. Soc. 64 (1977) 206-208. MR 0498548. Abstract, references, and article information View Article: PDF This article is available free of charge [55] Thomas C. Craven. Stability in Witt rings . Trans. Amer. Math. Soc. 225 (1977) 227-242. MR 0424800. Abstract, references, and article information View Article: PDF This article is available free of charge [56] Phillip Lestmann. Simple going down in PI rings . Proc. Amer. Math. Soc. 63 (1977) 41-45. MR 0432619. Abstract, references, and article information View Article: PDF This article is available free of charge [57] L. J. Ratliff and S. McAdam. Maximal chains of prime ideals in integral extension domains. I . Trans. Amer. Math. Soc. 224 (1976) 103-116. MR 0437513. Abstract, references, and article information View Article: PDF This article is available free of charge [58] L. J. Ratliff. Maximal chains of prime ideals in integral extension domains. II . Trans. Amer. Math. Soc. 224 (1976) 117-141. MR 0437514. Abstract, references, and article information View Article: PDF This article is available free of charge [59] Ira J. Papick. Topologically defined classes of going-down domains. Bull. Amer. Math. Soc. 81 (1975) 718-721. MR 0379481. Abstract, references, and article information View Article: PDF [60] Judith D. Sally. On the number of generators of powers of an ideal . Proc. Amer. Math. Soc. 53 (1975) 24-26. MR 0392969. Abstract, references, and article information View Article: PDF This article is available free of charge
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https://tex.stackexchange.com/questions/141176/is-there-a-way-to-get-the-skype-logo-in-the-cvtheme-document-class | # Is there a way to get the Skype logo in the cvtheme document class?
I'm using the cvtheme document class and \moderncv{classic} to create a CV. The field I am applying for jobs in often conduct their interviews over Skype. The are command to get small phone (phone), cellphone (\mobile) and email (\email) logos. Would it be possible to add a small Skype logo in the same manner? This would be a lot more aestheically pleasing than having to have "Skype: skypename" in the final output.
• Have you checked the copyrights for this logo first? – Ludovic C. Oct 28 '13 at 20:54
• @LudovicC. No. Good point. – Danger Fourpence Oct 28 '13 at 21:01
• The current font awesome has the skype icon. It seems that the current LaTeX package hasn't been updated with the new icons. You should be able to do that yourself by installing (or copying) the new font file (otf) and using them with LuaLaTeX. – Juri Robl Oct 28 '13 at 22:47
It's included in the latest version of font awesome. There is a LaTeX package for Font Awesome, but it doesn't include a command for the Skype logo, so you have to add it manually.
\documentclass{article}
\usepackage{fontawesome}
\begin{document}
\noindent
\faPhone{} Phone \\
\end{document}
Another solution I can think of is manually accessing it. Here's how:
\documentclass{article}
\usepackage{fontspec}
\newfontfamily\fontawesome
[ Path = /Path/to/font-awesome-4.0.1/fonts/ ,
Extension = .otf ]
{FontAwesome}
\newcommand\fasymbol[1]{{\fontawesome\symbol{"F#1}}}
\newcommand\faPhone{\fasymbol{095}}
\begin{document}
\noindent
\faPhone{} Phone \\
\end{document}
For the symbol codes you can check the cheatsheet on their site. You'll find the icon name (eg: fa-skype) along with the hexadecimal unicode code for the symbol (eg: ). From the unicode code you can use the last three numbers/letters in capitals (17E) in the custom \fasymbol command. For this example I've created three macro's.
• Concerning your first solution I cannot have skype icon while having added it manually. Also how could we have an icon for mobile? – Y_gr Jun 10 '14 at 8:50
• @giannis: have you tried installing Font Awesome as a system font? – Silke Jun 11 '14 at 15:17
• yes i have tried it, but still I have no result. – Y_gr Jun 14 '14 at 12:15
• @giannis: In that case either try the second method or wait for an update. – Silke Jun 18 '14 at 10:14
I used this solution found on the net and adapted to my needs, working on classic theme of moderncv:
\usepackage{tikz}
\pgfdeclareimage[height=.7\baselineskip]{SK}{skype_gray.png}
\makeatletter
\newcommand*{\skypesocialsymbol}{
\begin{tikzpicture}[overlay,remember picture] {\pgfuseimage{SK}};
\end{tikzpicture}
}
You have to place into your project directory a image of skype logo, here called skype_gray.png. Now you can write:
\skype{yourskypename} | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5505154728889465, "perplexity": 3164.6296712383187}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178375096.65/warc/CC-MAIN-20210306131539-20210306161539-00136.warc.gz"} |
https://www.rieti.go.jp/jp/publications/summary/13110014.html | # Does Competition Improve Industrial Productivity? An analysis of Japanese industries on the basis of the industry-level panel data
執筆者 安橋 正人 (コンサルティングフェロー) 2013年11月 13-E-098
## 概要（英語）
This study mainly investigates the causal relation between the degree of competition, which is measured by the Lerner index, and the total factor productivity (TFP) growth rate on the basis of the Japanese industry-level panel data (Japan Industrial Productivity (JIP) Database) from 1980 to 2008. The central finding indicates that, although a positive effect of competition on the TFP growth rate is clearly observable in the manufacturing industries throughout the sample period, such effect in the non-manufacturing industries may be slightly negative in the latter half of the sample period (1995-2008). This finding of a negative competition effect may lend support to the claim that the Schumpeterian hypothesis can be applied in the case of the non-manufacturing industries. Furthermore, a weak inverted-U shape relation between the competition measure and TFP growth proposed by Aghion et al. (2005) can be seen limitedly almost exclusively in all industries.
Published: Ambashi, Masahito, 2017. "Competition effects and industrial productivity: Lessons from Japanese industry," Asian Economic Paper Vol. 16(3), pp. 214-249
http://www.mitpressjournals.org/doi/abs/10.1162/asep_a_00568 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9197221398353577, "perplexity": 4503.3668479593125}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662562410.53/warc/CC-MAIN-20220524014636-20220524044636-00119.warc.gz"} |
https://support.bioconductor.org/p/116891/ | read.FCS memory limit? - $PnRNAis larger than R's numeric limit 0 0 Entering edit mode lloyd.izard ▴ 80 @lloydizard-15069 Last seen 2.8 years ago Good morning, I am trying to read from a FCS file but I get the following error: Error in readFCSdata(con, offsets, txt, transformation, which.lines, scale, :$PnRNAis larger than R's numeric limit:1.79769313486232e+308
In readFCSdata(con, offsets, txt, transformation, which.lines, scale, :
NAs introduced by coercion
The thing is, when I try to read the same file in .csv format, I can read it!
# library
library('flowCore')
library('Biobase')
library('data.table')
# data
data <- read.table('file.csv', dec = ".", sep = ",")
data <- read.FCS('file.fcs', alter.names = F, transformation = "linearize")
My question is: is there a memory limit for read.FCS()? And if so, how do I extend it?
All the best, Lloyd Izard
flowCore read.FCS memory_limit • 643 views
1
Entering edit mode
Hi,
I don't suspect a memory limit there. The read.FCS has been extended recently to cope with file bigger than 2GB. The error sounds like a problem in reading and interpreting the TEXT segment of the FCS file. Of course reading a CSV file avoids this problem because there is no such meta data. I think you should report the error onto https://github.com/RGLab/flowCore. You should report the sessionInfo() result and share some information about the FCS: instrument...
Meanwhile, you could verify that the FCS complies with FCS standard using flowIO http://bioinformin.cesnet.cz/flowIO/ (CLIP, Prague) or https://primitybio.github.io/fcs-validator/ (Zach Bjornson).
Best.
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Use of this site constitutes acceptance of our User Agreement and Privacy Policy. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1814958155155182, "perplexity": 7500.463937470217}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323583087.95/warc/CC-MAIN-20211015222918-20211016012918-00683.warc.gz"} |
http://blog.plover.com/2012/08/24/ | # The Universe of Discourse
Fri, 24 Aug 2012
More about ZF's asymmetry between union and intersection
In an article earlier this week, I explored some oddities of defining a toplogy in terms of closed sets rather than open sets, mostly as a result of analogous asymmetry in the ZF set theory axioms.
Let's review those briefly. The relevant axioms concern the operations by which sets can be constructed. There are two that are important. First is the axiom of union, which says that if !!{\mathcal F}!! is a family of sets, then we can form !!\bigcup {\mathcal F}!!, which is the union of all the sets in the family.
The other is actually a family of axioms, the specification axiom schema. It says that for any one-place predicate !!\phi(x)!! and any set !!X!! we can construct the subset of !!X!! for which !!\phi!! holds:
$$\{ x\in X \;|\; \phi(x) \}$$
Both of these are required. The axiom of union is for making bigger sets out of smaller ones, and the specification schema is for extracting smaller sets from bigger ones. (Also important is the axiom of pairing, which says that if !!x!! and !!y!! are sets, then so is the two-element set !!\{x, y\}!!; with pairing and union we can construct all the finite sets. But we won't need it in this article.)
Conspicuously absent is an axiom of intersection. If you have a family !!{\mathcal F}!! of sets, and you want a set of every element that is in some member of !!{\mathcal F}!!, that is easy; it is what the axiom of union gets you. But if you want a set of every element that is in every member of !!{\mathcal F}!!, you have to use specification.
Let's begin by defining this compact notation: $$\bigcap_{(X)} {\mathcal F}$$
for this longer formula: $$\{ x\in X \;|\; \forall f\in {\mathcal F} . x\in f \}$$
This is our intersection of the members of !!{\mathcal F}!!, taken "relative to !!X!!", as we say in the biz. It gives us all the elements of !!X!! that are in every member of !!{\mathcal F}!!. The !!X!! is mandatory in !!\bigcap_{(X)}!!, because ZF makes it mandatory when you construct a set by specification. If you leave it out, you get the Russell paradox.
Most of the time, though, the !!X!! is not very important. When !!{\mathcal F}!! is nonempty, we can choose some element !!f\in {\mathcal F}!!, and consider !!\bigcap_{(f)} {\mathcal F}!!, which is the "normal" intersection of !!{\mathcal F}!!. We can easily show that $$\bigcap_{(X)} {\mathcal F}\subseteq \bigcap_{(f)} {\mathcal F}$$ for any !!X!! whatever, and this immediately implies that $$\bigcap_{(f)} {\mathcal F} = \bigcap_{(f')}{\mathcal F}$$ for any two elements of !!{\mathcal F}!!, so when !!{\mathcal F}!! contains an element !!f!!, we can omit the subscript and just write $$\bigcap {\mathcal F}$$ for the usual intersection of members of !!{\mathcal F}!!.
Even the usually troublesome case of an empty family !!{\mathcal F}!! is no problem. In this case we have no !!f!! to use for !!\bigcap_{(f)} {\mathcal F}!!, but we can still take some other set !!X!! and talk about !!\bigcap_{(X)} \emptyset!!, which is just !!X!!.
Now, let's return to topology. I suggested that we should consider the following definition of a topology, in terms of closed sets, but without an a priori notion of the underlying space:
A co-topology is a family !!{\mathcal F}!! of sets, called "closed" sets, such that:
1. The union of any two elements of !!{\mathcal F}!! is again in !!{\mathcal F}!!, and
2. The intersection of any subfamily of !!{\mathcal F}!! is again in !!{\mathcal F}!!.
Item 2 begs the question of which intersection we are talking about here. But now that we have nailed down the concept of intersections, we can say briefly and clearly what we want: It is the intersection relative to !!\bigcup {\mathcal F}!!. This set !!\bigcup {\mathcal F}!! contains anything that is in any of the closed sets, and so !!\bigcup {\mathcal F}!!, which I will henceforth call !!U!!, is effectively a universe of discourse. It is certainly big enough that intersections relative to it will contain everything we want them to; remember that intersections of subfamilies of !!{\mathcal F}!! have a maximum size, so there is no way to make !!U!! too big.
It now immediately follows that !!U!! itself is a closed set, since it is the intersection !!\bigcap_{(U)} \emptyset!! of the empty subfamily of !!{\mathcal F}!!.
If !!{\mathcal F}!! itself is empty, then so is !!U!!, and !!\bigcap_{(U)} {\mathcal F} = \emptyset!!, so that is all right. From here on we will assume that !!{\mathcal F}!! is nonempty, and therefore that !!\bigcap {\mathcal F}!!, with no relativization, is well-defined.
We still cannot prove that the empty set is closed; indeed, it might not be, because even !!M = \bigcap {\mathcal F}!! might not be empty. But as David Turner pointed out to me in email, the elements of !!M!! play a role dual to the extratoplogical points of a topological space that has been defined in terms of open sets. There might be points that are not in any open set anywhere, but we may as well ignore them, because they are topologically featureless, and just consider the space to be the union of the open sets. Analogously and dually, we can ignore the points of !!M!!, which are topologically featureless in the same way. Rather than considering !!{\mathcal F}!!, we should consider !!{\mathcal F}HAT!!, whose members are the members of !!{\mathcal F}!!, but with !!M!! subtracted from each one:
$${\mathcal F}HAT = \{\hat{f}\in 2^U \;|\; \exists f\in {\mathcal F} . \hat{f} = f\setminus M \}$$
So we may as well assume that this has been done behind the scenes and so that !!\bigcap {\mathcal F}!! is empty. If we have done this, then the empty set is closed.
Now we move on to open sets. An open set is defined to be the complement of a closed set, but we have to be a bit careful, because ZF does not have a global notion of the complement !!S^C!! of a set. Instead, it has only relative complements, or differences. !!X\setminus Y!! is defined as: $$X\setminus Y = \{ x\in X \;|\; x\notin Y\}$$
Here we say that the complement of !!Y!! is taken relative to !!X!!.
For the definition of open sets, we will say that the complement is taken relative to the universe of discourse !!U!!, and a set !!G!! is open if it has the form !!U\setminus f!! for some closed set !!f!!.
Anatoly Karp pointed out on Twitter that we know that the empty set is open, because it is the relative complement of !!U!!, which we already know is closed. And if we ensure that !!\bigcap {\mathcal F}!! is empty, as in the previous paragraph, then since the empty set is closed, !!U!! is open, and we have recovered all the original properties of a topology.
Order General Topology with kickback no kickback
But gosh, what a pain it was; in contrast recovering the missing axioms from the corresponding open-set definition of a topology was painless. (John Armstrong said it was bizarre, and probably several other people were thinking that too. But I did not invent this bizarre idea; I got it from the opening paragraph of John L. Kelley's famous book General Topology, which has been in print since 1955.
Here Kelley deals with the empty set and the universe in two sentences, and never worries about them again. In contrast, doing the same thing for closed sets was fraught with technical difficulties, mostly arising from ZF. (The exception was the need to repair the nonemptiness of the minimal closed set !!M!!, which was not ZF's fault.)
Order On Numbers and Games with kickback no kickback
I don't think I have much of a conclusion here, except that whatever the advantages of ZF as a millieu for doing set theory, it is overrated as an underlying formalism for actually doing mathematics. (Another view on this is laid out by J.H. Conway in the Appendix to Part Zero of On Numbers and Games (Academic Press, 1976).) None of the problems we encountered were technically illuminating, and nothing was clarified by examining them in detail.
On the other hand, perhaps this conclusion is knocking down a straw man. I think working mathematicians probably don't concern themselves much with whether their stuff works in ZF, much less with what silly contortions are required to make it work in ZF. I think day-to-day mathematical work, to the extent that it needs to deal with set theory at all, handles it in a fairly naïve way, depending on a sort of folk theory in which there is some reasonably but not absurdly big universe of discourse in which one can take complements and intersections, and without worrying about this sort of technical detail.
[ MathJax doesn't work in Atom or RSS syndication feeds, and can't be made to work, so if you are reading a syndicated version of this article, such as you would in Google Reader, or on Planet Haskell or PhillyLinux, you are seeing inlined images provided by the Google Charts API. The MathJax looks much better, and if you would like to compare, please visit my blog's home site. ] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8271920084953308, "perplexity": 851.4039261507569}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170569.99/warc/CC-MAIN-20170219104610-00097-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://link.springer.com/chapter/10.1007%2F978-3-030-12988-0_1 | # Formal Stability Analysis of Control Systems
• Osman Hasan
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1008)
## Abstract
Stability of a control system ensures that its output is under control and thus is the most important characteristic of control systems. Stability is characterized by the roots of the characteristic equation of the given control system in the complex-domain. Traditionally, paper-and-pencil proof methods and computer-based tools are used to analyze the stability of control systems. However, paper-and-pencil proof methods are error prone due to the human involvement. Whereas, computer based tools cannot model the continuous behavior in its true form due to the involvement of computer arithmetic and the associated truncation errors. Therefore, these techniques do not provide an accurate and complete analysis, which is unfortunate given the safety-critical nature of control system applications. In this paper, we propose to overcome these limitations by using higher-order-logic theorem proving for the stability analysis of control systems. For this purpose, we present a higher-order-logic based formalization of stability and the roots of the quadratic, cubic and quartic complex polynomials. The proposed formalization is based on the complex number theory of the HOL-Light theorem prover. A distinguishing feature of this work is the automatic nature of the formal stability analysis, which makes it quite useful for the control engineers working in the industry who have very little expertise about formal methods. For illustration purposes, we present the stability analysis of power converter controllers used in smart grids.
## Keywords
Stability Control systems Polynomials HOL-light
## Notes
### Acknowledgments
This work is supported by ICT Fund UAE, fund number 21N206 at UAE University, Al Ain, United Arab Emirates.
## References
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Ahmad, M., Hasan, O.: Formal verification of steady-state errors in unity-feedback control systems. In: Lang, F., Flammini, F. (eds.) FMICS 2014. LNCS, vol. 8718, pp. 1–15. Springer, Cham (2014).
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Ahmed, A.: System Analysis and Verification (SAVe) Lab. http://save.seecs.nust.edu.pk/projects/fsacs/. Accessed 12 Sept 2018
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Amin, S.M., Wollenberg, B.F.: Toward a smart grid: power delivery for the 21st century. IEEE Power Energ. Mag. 3(5), 34–41 (2005)
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Dyke, P.: An Introduction to Laplace Transforms and Fourier Series. SUMS. Springer, London (2014).
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Ekanayake, J., Jenkins, N.: Comparison of the response of doubly fed and fixed-speed induction generator wind turbines to changes in network frequency. IEEE Trans. Energy Convers. 19(4), 800–802 (2004)
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Giordano, V., et al.: Smart grid projects in Europe. JRC Ref Rep Sy 8. Publications Office of the European Union, Luxembourg (2011).
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Harrison, J.: HOL light: an overview. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 60–66. Springer, Heidelberg (2009).
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Harrison, J.: Theorem Proving with the Real Numbers. Springer, London (2012)
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Hasan, O., Ahmad, M.: Formal analysis of steady state errors in feedback control systems using HOL-Light. In: Proceedings of the Conference on Design, Automation and Test in Europe, pp. 1423–1426. EDA Consortium, San Jose (2013)Google Scholar
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Hornik, T., Zhong, Q.C.: A current-control strategy for voltage-source inverters in microgrids based on H$$^\infty$$ and repetitive control. IEEE Trans. Power Electron. 26(3), 943–952 (2011)
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MathWorks: Control System Toolbox. https://ch.mathworks.com/products/control.html. Accessed 12 Sept 2018
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Momoh, J.A.: Smart Grid: Fundamentals of Design and Analysis, vol. 63. Wiley, Hoboken (2012)
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Nise, N.S.: Control Systems Engineering. Wiley, Hoboken (2007)
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Rashid, A., Hasan, O.: Formal analysis of linear control systems using theorem proving. In: Duan, Z., Ong, L. (eds.) ICFEM 2017. LNCS, vol. 10610, pp. 345–361. Springer, Cham (2017).
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Rashid, A., Siddique, U., Hasan, O.: Formal verification of platoon control strategies. In: Johnsen, E.B., Schaefer, I. (eds.) SEFM 2018. LNCS, vol. 10886, pp. 223–238. Springer, Cham (2018).
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Sanwal, M.U., Hasan, O.: Formally analyzing continuous aspects of cyber-physical systems modeled by homogeneous linear differential equations. In: Berger, C., Mousavi, M.R. (eds.) CyPhy 2015. LNCS, vol. 9361, pp. 132–146. Springer, Cham (2015).
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Siddique, U., Aravantinos, V., Tahar, S.: Formal stability analysis of optical resonators. In: Brat, G., Rungta, N., Venet, A. (eds.) NFM 2013. LNCS, vol. 7871, pp. 368–382. Springer, Heidelberg (2013).
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Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control: Analysis and Design, vol. 2. Wiley, New York (2007)
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Zhong, Q.C., Hornik, T.: Control of Power Inverters in Renewable Energy and Smart Grid Integration, vol. 97. Wiley, Hoboken (2012) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8911542296409607, "perplexity": 11870.083997726926}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247489933.47/warc/CC-MAIN-20190219101953-20190219123953-00540.warc.gz"} |
http://clay6.com/qa/3240/find-the-equation-of-the-curve-through-the-point-1-0-if-the-slope-of-the-ta | # Find the equation of the curve through the point (1,0) if the slope of the tangent to the curve at any point (x,y) is $\Large \frac{y-1}{x^2+x}.$
Toolbox:
• The slope of the tangent to the curve is $\large\frac{dy}{dx}$
• If a proper rational expression is $\large\frac{1}{(x+a)(x+b)},$ then it can be resolved into its partial fraction as $\large\frac{A}{x+a}+\frac{B}{x+b}$
• A linear differential equation of the form $\large\frac{dy}{dx}$$=f(x) can be solved by seperating the variables and then integrating it . Given :The slope of the tangent to the curve at any point is \large\frac{y-1}{x^2+x} The slope of the tangent to the curve is \large\frac{dy}{dx} Therefore \large\frac{dy}{dx}=\frac{y-1}{x^2+x} Seperating the variables we get \large\frac{dy}{y-1}=\frac{dx}{x(x+1)} Now \large\frac{1}{x(x+1)} can be resolved into paritial fractions as \large\frac{A}{x}+\frac{B}{x+1} Hence 1=A(x+1)+B(x) Now let us equate the coefficient of like terms First let us equate the 'x' term 0=A+B-----(1) Equating the constant term 1=+A\qquad B=-1 Hence \large\frac{1}{x(x+1)}=\frac{1}{x}-\frac{1}{x+1} Therefore \large \frac{dy}{y-1}$$=+\large\frac{dx}{x}-\frac{dx}{x+1}$
Integrating on both sides we get,
$\int \large \frac{dy}{y-1}$$=+\int \large\frac{dx}{x}-\int \frac{dx}{x+1}$
=>$\log (y-1)=+\log x-\log (x+1)+\log c$
=>$\log (y-1)=\log \large\frac{c(x)}{(x+1)}$
=>$(y-1)=\Large\frac{cx}{x+1}$
=>$(y-1)(x+1)=cx$
To evaluate the value of c,let us now substitute the value of x and y with the given point (1,0)
$(0-1)(1+1)=c(1)$
=>$c=-2$
$(y-1)(x+1)=-2x$
$(y-1)(x+1)+2x=0$ is the required solution. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9846416711807251, "perplexity": 730.2353580159837}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948545526.42/warc/CC-MAIN-20171214163759-20171214183759-00349.warc.gz"} |
https://wiki.kidzsearch.com/wiki/Svalbard | kidzsearch.com > wiki Explore:images videos games
# Svalbard
Svalbard
Capital
and largest city
Longyearbyen
Official languages Norwegian
Ethnic groups
Government Region of Norway
- Governor Odd Olsen Ingerø (2009–)
Area
- Total 61,022 km2
23,561 sq mi
Population
- 2012[1] estimate 2,642
Currency Norwegian krone (NOK)
Time zone CET (UTC+1)
- Summer (DST) CEST (UTC+2)
Calling code +47
Internet TLD .no a
a. .sj allocated but not used.[2]
Svalbard is a group of islands in the Arctic Ocean. It is the most northern part of Norway. It is about halfway between mainland Norway and the North Pole. Spitsbergen is the largest island, followed by Nordaustlandet and Edgeøya. The islands are governed by the Governor of Svalbard. The government is located at Longyearbyen. Other settlements include research outposts, the Russian mining community of Barentsburg, the research community of Ny-Ålesund and the mining outpost of Sveagruva.
The islands were first used as a whaling base in the 17th and 18th centuries. After this, they were abandoned. Coal mining started at the beginning of the 20th century, and several permanent villages were built. The Spitsbergen Treaty of 1920 states that Norway is in control of Svalbard. The 1925 Svalbard Act made Svalbard part of Norway. These treaties also set out rules that economic activities could be done freely and that no military activities can take place. There are only two mining companies, one Norwegian and one Russian. Research and tourism are important industries. There are no roads to connect the settlements. Instead, snowmobiles, aircraft and boats serve as transport. Svalbard Airport in Longyearbyen is the main airport.
The islands have an Arctic climate. It has higher temperatures than other areas that far north. In summer, the plants grow quickly during the midnight sun. Svalbard is a breeding ground for many seabirds. There are also polar bears, reindeer, and mammals that live in the sea. Seven national parks and 23 nature reserves cover two-thirds of Svalbard. This protects the fragile natural environment. Sixty percent of land is covered by glaciers, and the islands have many mountains and fjords.
## References
1. "Population in the settlements. Svalbard". Statistics Norway. 22 October 2009. Archived from the original on 28 July 2011. Retrieved 24 March 2010.
2. "The .bv and .sj top level domains". Norid. Retrieved 24 March 2010. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26813584566116333, "perplexity": 8995.126320438143}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987779528.82/warc/CC-MAIN-20191021143945-20191021171445-00172.warc.gz"} |
http://clay6.com/qa/5176/differentiate-with-respect-to-x- | Browse Questions
# Differentiate with respect to x $\sec(\tan(\sqrt x))$
Toolbox:
• $\; \large \frac{d(\sec x)}{dx} $$= \sec x.\tan x • \; \large \frac{d(\tan x)}{dx}$$= \sec^2x$
Given :
$y=\sec(\tan \sqrt x)$
Differentiating with respect to $x$ we get,
$\large\frac{1}{2\sqrt x}=\frac{du}{dx}$
Let $\tan u=v$
Diff w.r.t $u$ we get,
$\sec^2u=\large\frac{dv}{du}$
Step 2:
Let $y=\sec v$
Diff w.r.t $v$ we get,
$\large\frac{dy}{dv}$$=\sec v\tan v \large\frac{dy}{dx}=\frac{dy}{dv}\times \frac{du}{dx} Step 3: Now substituting the values we get, \large\frac{dy}{dx}$$=\sec v.\tan v\times \sec^2 u\times \large\frac{1}{2\sqrt x}$
Substituting back for $u$ and $v$ we get,
$(\sec(\tan \sqrt x)\tan (\tan \sqrt x)\times \sec^2(\sqrt x)\times \large\frac{1}{2\sqrt x}$
Hence $\large\frac{dy}{dx}=\frac{\sec(\tan \sqrt x)\tan(\tan \sqrt x).\sec^2 \sqrt x}{2\sqrt x}$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9488385319709778, "perplexity": 12639.544888102506}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218186774.43/warc/CC-MAIN-20170322212946-00317-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/elementary-doubts-i-i-got-confronted-with-while-reading-qft.769395/ | # Elementary doubts i i got confronted with while reading qft
1. Sep 6, 2014
### kau
why should Proca eqn be like ∂γ Fγμ + m2 Aμ = 0 but not ∂γ Fμγ + m2 Aμ = 0 ???? another doubt is (λ-1 ω λ)μγ = λ-1 ρμ ωρσ λσγ ??? why in λ-1 transformation got upper index in the second place but not in the first place????
if someone clear my doubts...I would be thanful...
regards..
Kau
2. Sep 6, 2014
### Freddieknets
Your first problem is easily solved:
First note that the gauge field tensor is antisymmetric, i.e. $F_{\gamma\mu}=-F_{\mu\gamma}$.
If $\partial^\gamma F_{\gamma\mu} + m^2 A_\mu =0$, then $\partial^\gamma F_{\gamma\mu} = -m^2 A_\mu$.
Filling this in the second equation, we have $\partial^\gamma F_{\mu\gamma} +m^2 A_\mu=-\partial^\gamma F_{\gamma\mu} +m^2 A_\mu =m^2 A_\mu+m^2 A_\mu\neq 0$.
The second equation needs a minus sign, i.e.
$$\partial^\gamma F_{\gamma\mu} + m^2 A_\mu =0$$
$$\partial^\gamma F_{\mu\gamma} - m^2 A_\mu =0$$
are both correct.
For your second question, i.e. $(\lambda^{-1}\omega\lambda)_{\mu\gamma}$ I don't understand what the problem is.
Last edited: Sep 6, 2014
3. Sep 6, 2014
Just use $$at the beginning and [ /tex] (without the space) at the end. Or $for inline equations. The is not rendered by MathJax. 4. Sep 6, 2014 ### Freddieknets Jup, actually I knew that, switched too fast from thesis writing to physicsforums.. :-) 5. Sep 6, 2014 ### kau I said in the second one suppose λ is lorentz transformation , λ-1 is inverse lorentz transformation and δωμγ is some parameter boost or rotation. now if you write its components explicitly. then it would be λ-1 μρ δωμγ λγ σ ... ok.. look the difference in λ-1 μρ μ is written upstair in 2nd position and ρ is written downstair ad 1st position which says that λ-1 μ ρ = λμ ρ ... but in λγ σ here y is in upstair 1st postion and σ is in downstair second position .. but this I understand it represents direct transformation. so if you write γ in the second position and σ in the 1st position that would imply and inverse lorentz transformation. my ques when we wrote that inverse transformation part why we wrote λ-1 μρ but not λ-1μ ρ ? I am sorry if you still didn't get it.. I am using this first time.. so don't know proper way to write eqns. so my eqns may look misleading... but if you get my point please answer me. thanks. Last edited: Sep 6, 2014 6. Sep 6, 2014 ### ChrisVer Another way to see the Proca equation, is by taking the Lagrangian of a spin-1 massive vector field without sources: [itex] L= -aF_{\mu \nu} F^{\mu \nu} + \frac{1}{2} m^{2} A_{\mu} A^{\mu}$ The first term contains the gauge invariant kinetic terms and the second is the mass term. $F_{\mu \nu} \equiv \partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$ Now if you try to find the EOM: $\partial_{\rho}\frac{\partial L}{\partial (\partial_{\rho} A_{\sigma})}- \frac{ \partial L}{\partial A_{\sigma}}=0$ You have for the 2nd term: $\frac{ \partial L}{\partial A_{\sigma}}= m^{2} A^{\sigma}$ and for the 1st term: $-a \partial_{\rho}\frac{\partial (F_{\mu \nu} F^{\mu \nu})}{\partial (\partial_{\rho} A_{\sigma})}=-2a \partial_{\rho} F^{\mu \nu} \frac{\partial (\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu})}{\partial (\partial_{\rho} A_{\sigma})} = -2a \partial_{\rho} F^{\mu \nu} (\delta^{\rho}_{\mu} \delta^{\sigma}_{\nu}-\delta^{\rho}_{\nu} \delta^{\sigma}_{\mu})=-2a \partial_{\rho} (F^{\rho \sigma} - F^{\sigma \rho})= -4 a \partial_{\rho} F^{\rho \sigma}$ So that's a reason why someone can choose $a= \frac{1}{4}$ and have: $-\partial_{\rho} F^{\rho \sigma} - m^{2} A^{\sigma} =0$ And you get what you ask for. Now what would your "2nd" choice mean? it would have to mean that $a= - \frac{1}{4} <0$ and so the 1st term in the Lagrangian would have a positive sign. That's bad I guess because then the vacuum would have to have negative energy ... Also in general you can reach this lagrangian (without the mass) from the "classical" electromagnetic lagrangian with the correct signs which leads to the term: $-\frac{1}{4}F^{2}$ As for your second question... The positioning of the indices can be very tough to follow, and sometimes people in notes or books can mix them up without a problem, because afterall what they want to say becomes clear... The only time someone has to be careful with the indices is when they denote the representation and not the rows-columns. It's difficult for you to try explaining in words what you are asking, so it's better to show us what you mean. To me, as you write them, there is no 1st or 2nd position. In general what you wrote as $(\Lambda ^{-1} \omega \Lambda)_{\mu \nu}$ means the mu nu component of the matrix $(\Lambda ^{-1} \omega \Lambda)$...So take the $\Lambda$ its inverse and mix them with the $\omega_{\rho \sigma}$ as: $[\Lambda^{-1}] [\omega] [\Lambda]$ where by brackets I mean matrices. Last edited: Sep 6, 2014 7. Sep 7, 2014 ### samalkhaiat The second equation leads to wrong sign for the mass term. Remember, you always need to satisfy the dispersion relation $E^{2} = p^{2} + m^{2}$. The “first place” is already occupied by the index $\mu$. [tex]\left( \lambda^{ - 1 } \omega \lambda \right)_{ \mu \nu } = ( \lambda^{ - 1 } )_{ \mu }{}^{ \rho } \omega_{ \rho \sigma } \lambda^{ \sigma }{}_{ \nu } .$$
For Lorentz transformation, we have
$$( \lambda^{ - 1 } )_{ \mu }{}^{ \rho } = \lambda^{ \rho }{}_{ \mu } .$$
So, the $\mu \nu$ matrix element is
$$\left( \lambda^{ - 1 } \omega \lambda \right)_{ \mu \nu } = \omega_{ \rho \sigma } \lambda^{ \rho }{}_{ \mu } \lambda^{ \sigma }{}_{ \nu } .$$
In the Euclidean space, i.e. when we don’t distinguish between upstairs from down stairs indices, the $\mu \nu$ matrix element of $(ABC)$ is found by usual multiplication of matrices
$$( A B C )_{ \mu \nu } = A_{ \mu \rho } B_{ \rho \sigma } C_{ \sigma \nu } .$$
In Minkowski space, this matrix element has the following equivalent forms
$$A_{ \mu }{}^{ \rho } B_{ \rho \sigma } C^{ \sigma }{}_{ \nu } = A_{ \mu \rho } B^{ \rho \sigma } C_{ \sigma \nu } = A_{ \mu \rho } B^{ \rho }{}_{ \sigma } C^{ \sigma }{}_{ \nu } = A_{ \mu }{}^{ \rho } B_{ \rho }{}^{ \sigma } C_{ \sigma \nu } .$$
Sam
8. Sep 7, 2014
### kau
tensor notation contraction and ordering of elements
Last edited: Sep 7, 2014
9. Sep 7, 2014
### ChrisVer
You can write it as such, you only have to be careful about what you actually did... In your case you renamed mu into nu and vice versa, and also exchanged the indices of the omega [which would have to give you a minus which I don't see].
As for the other question: $\lambda^{a}_{b} C_{ac} = C_{bc}$. Do you want more explanation on that?
As for the position of the elements of the tensor, yes in most cases you can do that. Except for if your elements are not commuting. No such case comes in my mind now.
Last edited: Sep 7, 2014
10. Sep 7, 2014
### kau
here you have assume the metric to be of form (-,+,+,+).
if you work with (+,-,-,-) probably you could have written it like
$-\partial_{\rho} F^{\sigma \rho} - m^{2} A^{\sigma} =0$ ~ to get the energy relation correct. so in any case checking energy relation would give the right choice. isn't it??
11. Sep 7, 2014
### ChrisVer
I don't see where you used the metric in what you did [flipping the indices of the F without changing the sign is not a part of metric choice, but the fact that F is an antisymmetric tensor]. In fact the metric choice doesn't really play any difference - the ones you said are opposite to each other, and in the Lagrangian the metrics appear twice in the kinetic term: $F_{\mu \nu} F^{\mu \nu} = \eta^{\mu \rho} \eta^{\nu \sigma} F_{\mu \nu} F_{\rho \sigma}$
Also energy results don't depend on the choice of the metric.
Last edited: Sep 7, 2014
12. Sep 7, 2014
### kau
yeah if you change ${ \mu}$ and ${ \nu}$ in w and x and ∂ in all places then you will get $-L^{ \nu \mu}$ which is equivalent to $L^{ \mu \nu}$ .. but my question is in the first place why I can't write $δω_{ \mu \nu} x^{ \nu} ∂^{ \mu}$??? why writing in this way leads to an expression which is not quite right??? [/QUOTE]
if you want to explain it,please do. I understand this result. but really i do not have clue why that quantity should not be$C_{cb}$??
Last edited: Sep 7, 2014
13. Sep 7, 2014
### kau
so, I have following eqn of motion
$-∂_{\rho}F^{\rho \sigma }-m^{2}A^{\sigma}=0$
therefore, $-∂^{2} A^{/sigma}-m^{2}A^{\sigma}=0$ using Lorentz gauge.
now if $∂^{2}=-E^{2}+p^{2}$ then I will have correct form $E^{2}-p^{2}=m^{2}$ for other choice of metric I will get an extra negative sign.
14. Sep 7, 2014
### ChrisVer
Because $\lambda$ tensor will act on the 1st components of the $C$... Or in other words you will have the tensor product which will give you [in components] $S^{a}_{dac} = S_{dc}$. At least that's how I understand it.
As for your last, then my metric choice is (+ - - - ), because the final result was $(\partial F)^{\sigma} + m^{2} A^{\sigma} =0$
Now if you suddenly change the sign of the metric, there should appear an extra change in the sign of the mass term... because in the EOM you had to take the derivative of $A^{2} = \eta_{\mu \nu} A^{\mu} A^{\nu}$ wrt $A^{\sigma}$. The result always remains the wanted one, that's why I said the energy result doesn't depend on the metric choice... Otherwise you wouldn't be able to compare energetically results of different metric choices.
Ah and I forgot the other question... Because then you are not getting a well defined matrix multiplication... you have to take the transpose of omega ... or else you are writting that the rows will multiply rows or collumns will multiply collumns...
In matrices when you have $A^a C_{ba} B^{b}= A^{T} C^{T} B \ne A^{T}CB$
Last edited: Sep 7, 2014
15. Sep 7, 2014
### kau
ok .. I got you. but for the last question I still find any reason which stops me from writing
$∂ω_{\mu \nu} x^{\nu} ∂^{\mu}$ .... say$∂ω = C_{ba}$ and $x =A^a$ and $∂{\mu}=B^{b}$ then it's all fine. I can understand that what you are saying is true but I am not getting what is wrong in my choice?? would you little elaborate this part??
16. Sep 7, 2014
### ChrisVer
Nevertheless, in Schrednicki's you have 34.1, where you insert 34.5:
$(I - \frac{i}{2} \delta \omega_{\mu \nu} M^{\mu \nu}) \psi_{a}(x) (I + \frac{i}{2} \delta \omega_{\mu \nu} M^{\mu \nu}) = (\delta^{~b}_{a} + \frac{i}{2} \delta \omega_{\mu \nu} (S^{\mu \nu})^{~b}_{a}) \psi_{b}$
$\psi_{a}\frac{i}{2} \delta \omega_{\mu \nu} M^{\mu \nu}-\frac{i}{2} \delta \omega_{\mu \nu} M^{\mu \nu} \psi_{a} = -\delta \omega_{\nu \mu} x^{\nu} \partial^{\mu} \psi(x)_{a}+ \frac{i}{2} \delta \omega_{\mu \nu} (S^{\mu \nu})^{~b}_{a}\psi_{b}$
So you are asking why you get it like that?
In general what he does is a Taylor expansion of $\psi ( (I+\delta \omega^{T}) x)$ from that you get the indices...
Last edited: Sep 7, 2014
17. Sep 7, 2014
### samalkhaiat
No, you can’t. $\omega_{ \mu \nu } x^{ \nu } \partial^{ \mu } = - \omega_{ \mu \nu } x^{ \mu } \partial^{ \nu }$
Use the fact that contracted (dummy) indices can be relabelled freely. So, you can write
$$\omega_{ \mu \nu } x^{ \mu } \ \partial^{ \nu } \phi = \omega_{ \rho \sigma } \ x^{ \rho } \ \partial^{ \sigma } \phi . \ \ \ (1)$$
Using the identity, $A = ( A + A ) / 2$, we can rewrite (1) as
$$\omega_{ \mu \nu } \ x^{ \mu } \ \partial^{ \nu } \phi = \frac{ 1 }{ 2 } \left( \omega_{ \mu \nu } \ x^{ \mu } \ \partial^{ \nu } \phi + \omega_{ \rho \sigma } \ x^{ \rho } \ \partial^{ \sigma } \phi \right) .$$
Now, letting $\rho = \nu$ and $\sigma = \mu$, we get
$$\omega_{ \mu \nu } \ x^{ \mu } \ \partial^{ \nu } \phi = \frac{ 1 }{ 2 } \left( \omega_{ \mu \nu } \ x^{ \mu } \ \partial^{ \nu } \phi + \omega_{ \nu \mu } \ x^{ \nu } \ \partial^{ \mu } \phi \right) .$$
But $\omega_{ \nu \mu } = - \omega_{ \mu \nu }$. Thus
$$\omega_{ \mu \nu } \ x^{ \mu } \ \partial^{ \nu } \phi = \frac{ 1 }{ 2 } \omega_{ \mu \nu } \left( x^{ \mu } \partial^{ \nu } - x^{ \nu } \partial^{ \mu } \right) \phi . \ \ \ \ \ \ (2)$$
You don’t need to mention any textbook for me. Instead, I think it is better to show you a step by step derivation of this equation. Under the Lorentz group, finite-component fields on space-time transform by finite-dimensional (matrix) representations
$$\bar{ \phi }_{ a } ( \bar{ x } ) = D_{ a }{}^{ b } \phi_{ b } ( x ) , \ \ \ \ \ \ \ (3)$$
where $D$ is a representation matrix
$$D_{ a }{}^{ c }( \Lambda_{ 1 } ) \ D_{ c }{}^{ b }( \Lambda_{ 2 } ) = D_{ a }{}^{ b }( \Lambda_{ 1 } \Lambda_{ 2 } ) .$$
Infinitesimally, we may write
$$D_{ a }{}^{ b } = \delta_{ a }^{ b } - \frac{ i }{ 2 } \omega_{ \mu \nu } ( S^{ \mu \nu } )_{ a }{}^{ b } , \ \ \ \ \ \ \ (4)$$
where $S^{ \mu \nu }$ are the appropriate spin matrices for the field $\phi$. They satisfy the Lorentz algebra.
However, since $\phi_{ a }( x )$ (for all a’s) is an operator-valued field, it also transforms by (infinite-dimensional) unitary representation,$U( \Lambda )$, of the Lorentz group.
$$\bar{ \phi }_{ a } ( \bar{ x } ) = U^{ - 1 } \ \phi_{ a } ( \bar{ x } ) \ U . \ \ \ \ \ (5)$$
In terms of the abstract Lorentz generators, $M^{ \mu \nu }$, and the infinitesimal parameters $\omega_{ \mu \nu }$, we may write the unitary operator as
$$U( \Lambda ) = 1 - \frac{ i }{ 2 } \omega_{ \mu \nu } \ M^{ \mu \nu } . \ \ \ \ \ (6)$$
From (3) and (5), we find the finite transformation rule for the field operator
$$\bar{ \phi }_{ a } ( \bar{ x } ) = U^{ - 1 } \ \phi_{ a } ( \bar{ x } ) \ U = D_{ a }{}^{ b } \ \phi_{ b } ( x ) . \ \ \ (7)$$
Using
$$x = \Lambda^{ - 1 } \ \bar{ x } ,$$
we rewrite (7) as
$$\bar{ \phi }_{ a } ( \bar{ x } ) = U^{ - 1 } \ \phi_{ a } ( \bar{ x } ) \ U = D_{ a }{}^{ b } \phi_{ b } ( \Lambda^{ - 1 } \ \bar{ x } ) .$$
Dropping the bars from the coordinates, we get
$$\bar{ \phi }_{ a } ( x ) = U^{ - 1 } \ \phi_{ a } ( x ) \ U = D_{ a }{}^{ b } \ \phi_{ b } ( \Lambda^{ - 1 } x ) . \ \ \ \ (8)$$
Now, we will try to find the infinitesimal version of (8). Using
$$( \Lambda^{ - 1 } )^{ \mu \nu } x_{ \nu } = x^{ \mu } - \omega^{ \mu \nu } \ x_{ \nu } ,$$
we expand $\phi ( \Lambda^{ - 1 } x )$ to first order as
$$\phi_{ b } ( \Lambda^{ - 1 } x ) = \phi_{ b } ( x ) - \omega^{ \mu \nu } \ x_{ \nu } \ \partial_{ \mu } \phi_{ b } ( x ) . \ \ \ \ \ (9)$$
Substituting the equations (4), (6) and (9) in equation (8) and keeping only first order terms, we find
$$\bar{ \phi }_{ a } ( x ) - \phi_{ a } ( x ) = \frac{ i }{ 2 } \omega_{ \mu \nu } \ [ M^{ \mu \nu } , \phi_{ a } ( x ) ] = - \omega^{ \mu \nu } \ x_{ \nu } \ \partial_{ \mu } \phi_{ a } - \frac{ i }{ 2 } \omega_{ \mu \nu } ( S^{ \mu \nu } )_{ a }{}^{ b } \phi_{ b } ( x ) . \ (10)$$
Using $\omega^{ \mu \nu } = - \omega^{ \nu \mu }$ and
$$\omega^{ \nu \mu } \ x_{ \nu } \ \partial_{ \mu } = \omega_{ \nu \mu } \ x^{ \nu } \ \partial^{ \mu } = \omega_{ \mu \nu } \ x^{ \mu } \ \partial^{ \nu } ,$$
equation (10) becomes
$$\delta \phi_{ a } ( x ) = \frac{ i }{ 2 } \omega_{ \mu \nu } \ [ M^{ \mu \nu } , \phi_{ a } ( x ) ] = \omega_{ \mu \nu } \ x^{ \mu } \ \partial^{ \nu } \phi_{ a } - \frac{ i }{ 2 } \omega_{ \mu \nu } ( S^{ \mu \nu } )_{ a }{}^{ b } \phi_{ b } ( x ) .$$
Now, if we use (2) in the first term on the right-hand-side, we find
$$\delta \phi_{ a } ( x ) = \frac{ i }{ 2 } \omega_{ \mu \nu } \ [ M^{ \mu \nu } , \phi_{ a } ( x ) ] = \frac{ 1 }{ 2 } \omega_{ \mu \nu } \ ( x^{ \mu } \partial^{ \nu } - x^{ \nu } \partial^{ \mu } ) \phi_{ a } ( x ) - \frac{ i }{ 2 } \omega_{ \mu \nu } \ ( S^{ \mu \nu } )_{ a }{}^{ b } \phi_{ b } ( x ) .$$
So, the equation you are after follows from
$$[ i M^{ \mu \nu } , \phi_{ a } ( x ) ] = ( x^{ \mu } \partial^{ \nu } - x^{ \nu } \partial^{ \mu } ) \phi_{ a } ( x ) - i ( S^{ \mu \nu } )_{ a }{}^{ b } \phi_{ b } ( x ) .$$
Neither! The question does not make sense. $\lambda^{ n }{}_{ a } C_{ n u } = C_{ a u }$ if and only if $\lambda^{ n }{}_{ a }$ is equal to the Kronecker delta $\delta^{ n }_{ a }$.
Yes, for numerical tensors and matrix elements the order does not matter.
Sam
18. Sep 7, 2014
### ChrisVer
Samal I think the problem is that you derived:
$[\phi_{a}, M^{\mu \nu}] = L^{\nu \mu} \phi_{a} + i (S^{\mu \nu})^{~~b}_{a} \phi_{b}$
while in Schrednicki [the one kau mentions to have problem with] is:
$[\phi_{a}, M^{\mu \nu}] = L^{\mu \nu} \phi_{a} + i (S^{\mu \nu})^{~~b}_{a} \phi_{b}$
However I also reached your result.
19. Sep 7, 2014
### samalkhaiat
With the D matrix and the U operator are given by
$$D = 1 - \frac{ i }{ 2 } \omega_{ \mu \nu } \ S^{ \mu \nu } \ , \ \ U = 1 - \frac{ i }{ 2 } \omega_{ \mu \nu } \ M^{ \mu \nu } ,$$
and in any metric convention, the correct transformation is given by
$$[i M^{ \mu \nu } , \phi_{ a } ] = ( x^{ \mu } \ \partial^{ \nu } - x^{ \nu } \ \partial^{ \mu } ) \phi_{ a } - i ( S^{ \mu \nu } )_{ a }{}^{ b } \phi_{ b } .$$
Notice that I did not write $L^{ \mu \nu }$ because its definition depends on the metric one uses.
Any way, who is Steven ?
Sam
20. Sep 12, 2014
### kau
let me tell you what I actually mean in this part.
$\lambda^{\mu \nu} X^{\alpha}{}_{mu}= Y^{\nu \alpha} or y^{\alpha \nu}$
now I guess my question makes sense..
and you have written that numerical and matrix component tensor cases order does not matter. ok fine.. but for just to get one clarification i am asking you this.. so the point is we should only worry about tensor or matrix component ordering when they are non commutating.???
thanks.
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https://www.physicsforums.com/threads/entropy-is-a-measure-of-energy-availiable-for-work.659598/ | # Entropy is a measure of energy availiable for work ?
1. ### Rap
789
Entropy is a measure of energy availiable for work ????
"Entropy is a measure of energy availiable for work". Can someone explain this to me? Give some examples that show in what sense it is true. It has to come with a lot of caveats, proviso's etc. because its simply not true on its face.
I mean, if I have a container of gas at some temperature above 0 K, then I can extract all of its internal energy as work, just let it quasistatically expand to infinity.
2. ### Studiot
Re: Entropy is a measure of energy availiable for work ????
Such a container has internal pressure P.
Expanding from P into a vacuum does no work.
Expanding from P against an external pressure P' < P does work, but as this happens P diminishes until P = P' when the system is in equilibrium.
How would you proceed from this equilibrium to infinity, where P = 0 ?
3. ### Rap
789
Re: Entropy is a measure of energy availiable for work ????
Yes, you would need initial pressure (P) greater than zero, and ambient pressure (P') equal to zero, i.e. in outer space. But the point remains, the statement that "entropy is a measure of energy unavailable for work" is contradicted by this example.
4. ### Studiot
Re: Entropy is a measure of energy availiable for work ????
This is fundamental, pushing against something that offers no resistance does no work.
### Staff: Mentor
Re: Entropy is a measure of energy availiable for work ????
Where did you get that quote? It is wrong: it is missing the word "not"!
http://en.wikipedia.org/wiki/Entropy
6. ### Studiot
Re: Entropy is a measure of energy availiable for work ????
Agreed - I think that was a typo -, but we also need to dispel the misconception in the proposed counterexample that follows.
Once that is done it is easy to explain the correct reasoning.
7. ### Rap
789
Re: Entropy is a measure of energy availiable for work ????
Yes, sorry, I misquoted it. It should be something like "Entropy is a measure of the energy NOT available for useful work". I also see the point that the example I gave is not good. In order for the expansion to be slow, there has to be an opposing force almost equal to the pressure force, and that force has to diminish as the volume increases (and pressure decreases). This opposing force would be the mechanism by which work was done on the environment. Something like a mass in a gravitational field, in which the mass is slowly being reduced by removal.
I found a web site http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node48.html which seems to give an explanation, I will have to look at it closely.
Also the Wikipedia quote says it is "energy per unit temperature" not available for work, which I cannot immediately decipher.
8. ### Rap
789
Re: Entropy is a measure of energy availiable for work ????
Looking at the above site, it seems to me what it is saying is that the amount of energy unavailable for useful work in a Carnot cycle is equal to the entropy extracted from the hot reservoir (which is equal to the entropy deposited in the cold reservoir) times the temperature of the cold reservoir. How you get from this to the idea that "Entropy is a measure of the energy unavailable for work" still eludes me.
Entropy of what? I tried assuming that the hot reservoir was actually a hot system with a finite amount of energy and entropy. Again, you can prove that if you extract entropy ∆S from the hot body, the amount of unavailable energy is Tc ∆S where Tc is the temperature of the cold reservoir. But you can only extract so much entropy from the hot body using a working body at the cold reservoir temperature. If their temperatures are very close, you can extract very little entropy and energy. The great majority of the internal energy of the hot body is unavailable for work in this case.
If you set the cold reservoir to zero degrees, then the amount of energy unavailable for work is zero. You could extract all of the internal energy of the hot body as work. (right?).
I still don't get it.
9. ### Andrew Mason
6,846
Re: Entropy is a measure of energy availiable for work ????
We have hashed this over before. The problem with "entropy is a measure of the energy unavailable for work" is that standing alone it is not clear and open to a number of interpretations. It requires a special definition of "energy unavailable for work" as the explanation shows. Without that explanation it can easily lead to misinterpretation.
For example, between two temperatures, Th and Tc, the heat flow Q is capable of producing an amount of work, W = Q(1-Tc/Th) ie. with a Carnot engine. So there is energy E = QTc/Th energy that is, in that sense, "unavailable" for doing work. Yet, as we know, ΔS = 0 for a Carnot engine. So one could well ask, how is 0 a measure of QTc/Th? The answer is: "well, that is not what we mean by 'energy unavailable to do work'. We really mean 'lost work' which is the potential work that could be extracted minus the work that was actually extracted, or the amount of additional work required to restore the system and surroundings to their original state if you saved the output work and used it to drive the process in reverse." Hence the confusion.
So, as I have said before, this particular statement should not be used to introduce the concept of entropy. By itself it explains nothing and leads to great confusion.
AM
Last edited: Dec 19, 2012
10. ### Rap
789
Re: Entropy is a measure of energy availiable for work ????
Well, I kind of thought that was case, but there was also the possibility I was missing something. Thanks for the clarification.
11. ### Studiot
Re: Entropy is a measure of energy availiable for work ????
The time for hand waving is over, here is some mathematics.
Consider a universe consisting of a system contained in a heat bath or reservoir at uniform constant temperature T.
Consider changes in the function Z = entropy of bath plus entropy of the system = entropy of this universe.
dZ = dSb + dSs.................1
Where b refers to the bath and s refers to the system.
If the system absorbs heat dq the same amount of heat is lost by the bath so the entropy change
dSb =-dq/T...................2
substituting this into equation 1
dZ = dSs - dq/T..............3
Now consider a change of state of the system from state A to state B
By the first law
dUs = dq - dw ..................4
Combining equations 3 and 4 and rearranging
dSs = (dUs+dw)/T + dZ
re-arranging
dw = TdSs - dUs -TdZ
Since TdZ is always a positive quantity or zero
dw ≤ TdSs - dUs
Where dw is the work done by the system
This is the principle of maximum work and calculates the maximum work that can be obtained from the system. As you can see it has two components vis from the entropy created and from the change in internal energy and these act in opposite directions so in this sense the TdSs term reduces the amount of work obtainable from the internal energy of the system and accounts for unavailable energy since TdSs has the dimensions of energy.
Note the usual caveat
The inequality refers to irreversible processes, the equality to reversible ones.
Last edited: Dec 19, 2012
12. ### Darwin123
741
Re: Entropy is a measure of energy availiable for work ????
What you said is only possible if the gas expands both adiabatically and reversibly. In an adiabatic and reversible expansion, the change in entropy of the gas is zero. Under that condition, one could turn all the internal energy into work.
Any deviation from the conditions of adiabatic and reversible would result in some internal energy not being turned to work.
First, I prove that one can extract all the internal energy from a monotonic ideal gas using an expansion that is BOTH adiabatic and reversible.
Suppose one were to take an ideal gas in a closed chamber and expand it both adiabatically and slowly, so that it is in a state near thermal equilibrium at all times. No entropy goes in or out of the chamber.
At the end of the expansion, even in the limit of infinite volume, you would end up with a gas of finite temperature.
The ideal gas law is:
1) PV=nRT
where P is the pressure of the gas, V is the volume of the chamber, n is the molarity of the gas, R is the gas constant and T is the temperature.
The internal energy of the ideal gas is:
2) U=(3/2)nRT
where U is the internal energy of the gas and everything else is the same.
Substituting equation 2 into equation 1:
3)U=(3/2)PV
Before the gas starts expanding, let P=P0, V=V0, T=T0, and U=U0. The chamber is closed, so "n" is constant the entire time. There are three degrees of freedom for each atom in a mono atomic gas. Therefore, for a mono atomic gas:
3) U0=1.5 P0 V0
The adiabatic expansion of an mono-atomic gas is:
4) P0 V0 ^(5/3)= P V^(1.5)
Therefore,
5) P = P0 (V0/V)^(5/3)
The work, W, done by the gas is
6) W = ∫[V0→∞] P dV
Substituting equation 5 into equation 6:
7) W = (P0 V0^(5/3)))∫[V0→∞] V^(-5/3) dV
Evaluating the integral in equation 6:
8) W = (3/2)(P0 V0^5/3)V0^(-2/3)
9) W=(1.5) P0 V0
The expression for W in equation 9 is the same as the expression for U0 in equation 3. Therefore, the internal energy has been taken out completely.
I’ll solve the problem later (a week or so) for an expansion with sliding friction. There, the increase in entropy characterizes the amount of internal energy not turned into work. However, I will set up the problem. I will show the two equations that makes the case with sliding friction different from the reversible condition.
One remove the reversibility condition by adding sliding friction,
10) Wf = ∫[V0→Vf] (P-Pf) dV
where Pf is the pressure due to sliding friction and Vf is the volume when the P=Pf. The chamber stops expanding when P=Pf.
However, another expression is necessary to describe how much entropy is created.
11) dQ = Pf dV
Equation merely says that the energy used up by the sliding friction causes entropy to be created. The heat energy, dQ, is the energy used up by friction.
I don’t have time now, so I leave it as an exercise. Honest, moderator, I promise to get back to it. However, he wants an example where the creation of entropy limits the work that can be extracted. This is a good one.
Spoiler
Wf<W. Not all the internal energy is turned into work with sliding friction included. Let Q be the work done by the sliding force alone. The increase in entropy is enough to explain why the internal energy is not being turned into work.
13. ### Studiot
Re: Entropy is a measure of energy availiable for work ????
Do you not agree that the maximum possible work is extracted in a reversible isothermal expansion?
Are you sure you mean this: you have different values of gamma on each side?
14. ### Darwin123
741
Re: Entropy is a measure of energy availiable for work ????
In an isothermal expansion, energy is entering the gas from a hot reservoir. Therefore, one can't say that one is extracting the energy from the ideal gas. Most of the energy is being extracted from the hot reservoir, not from the ideal gas.
In the corresponding isothermal expansion, the ideal gas is acting like a conduit for energy and entropy. The ideal gas is not acting as a storage matrix for the energy.
The OP was saying that the work was being extracted from the internal energy that was initially embedded in the ideal gas. All work energy comes from the container of gas, not outside reservoirs. So the walls of the container have to be thermal insulators.
If you allow heat energy to conduct through the walls of the container, then the work may exceed the initial value of the internal energy. The hot reservoir can keep supplying energy long after the internal energy is used up.
So I stick to my guns with regards to the specificity of the OPs hypothesis. He was unconsciously assuming that the expansion is both adiabatic and reversible.
I diagree with those people who said that the gas would remain the same temperature during the expansion, and that not all the energy could be extracted from the internal energy. I showed that the internal energy could be entirely extracted for an ideal monotonic gas under adiabatic and reversible conditions.
The big problem that I have with the OP's question is with the word "quasistatic". I conjecture that the OP thought that "quasistatic" meant "both adiabatic and reversible".
A quasistatic process can be both nonadiabatic and irreversible. However, "quasistatic" is a useful hypothesis. The word "quasistatic" implies spatial uniformity. In this case, the word quasistatic implies that the temperature and the pressure of the ideal gas is uniform in the chamber.
Quasistatic implies that enough time has passed between steps that both temperature and pressure are effectively constant in space. Thus, temperature is not a function of position. Pressure is not a function of position.
I think this is correct. I didn't spend much time checking my work. If you see an arithmetic blunder, feel free to correct me.
Also, I specified a specific case to simplify the problem. So even if I did it correctly, the gamma value that I used was atypical. Next time, I will let gamma be a parameter of arbitrary value.
I specified a monotonic gas. The gas is comprise of individual atoms. There are no internal degrees of freedom in these atoms. Any correlation between coefficients may be due to my choice.
There are many ways an expansion can be irreversible. I think the one most people think of is where the expansion is not quasistatic. Suppose the gas is allowed to expand freely, so that temperature and pressure are not uniform. This is irreversible. However, the mathematics is way beyond my level of expertise.
The problem is tractable if the process is quasistatic. So, I think the best thing would be to show how it works with an quasistatic but irreversible. For instance, what happens if one turns on the sliding friction and the static friction in this expansion. That would result in a process where entropy is created. In other words, friction would result in an irreversible expansion even under quasistatic conditions.
I don't have time now. I will post a solution to that later. For now, just remember that not all quasistatic processes are reversible.
15. ### Studiot
Re: Entropy is a measure of energy availiable for work ????
I wanted to be more subtle and polite but
$${P_1}{V_1}^\gamma = {P_2}{V_2}^\gamma$$
Whereas you have
$${P_0}{V_0}^{\frac{5}{3}} = {P_1}{V_1}^{\frac{3}{2}}$$
Is this a rejection of Joule's experiment and the definition of an ideal gas?
If so you should make it clear that your view is not mainstream physics.
It should be noted that Joules experiment was both adiabatic and isothermal and has been repeated successfully many times.
You are correct in observing that during an isothermal expansion neither q nor w are zero.
However what makes you think the internal energy is the same at the beginning and end, in the light of your above statement?
One definition (or property derivable from an equivalent definition) of an ideal gas is that its internal energy is a function of temperature alone so if the temperature changes the internal energy changes. To remove all the internal energy you would have to remove all the kinetic energy of all its molecules.
16. ### Andrew Mason
6,846
Re: Entropy is a measure of energy availiable for work ????
I think it was a typo. Darwin did write: P = P0 (V0/V)^(5/3) a little farther down.
I am not sure that you are both talking about the same process. Darwin was referring to a quasi-static adiabatic expansion of an ideal gas. Temperature is given by the adiabatic condition:
$$TV^{(\gamma - 1)} = \text{constant}$$
So, if volume changes this cannot be isothermal. Temperature has to change.
I think you (Studiot) may be talking about free expansion, not quasi-static expansion, in which case T is constant for an ideal gas.
AM
17. ### Rap
789
Re: Entropy is a measure of energy availiable for work ????
Studiot - I agree with your derivation but with regard to the OP, the correct statement would then be: "an infinitesimal change in entropy is a measure of the minimum infinitesimal amount of energy unavailable for work given a particular ambient temperature."
Darwin123 - Thank you for clarifying the muddled OP. Depending on conditions, all, some, or none of a system's internal energy can be converted to work, and so the statement "Entropy is a measure of the energy unavailable for work" is ambiguous at best, wrong at worst. You are right, I was assuming adiabatic and reversible. Adiabatic or else you are potentially using energy from somewhere else to do the work. Reversible, because it will give the miniumum amount of work unavailable. I should have said that instead of quasistatic. I take quasistatic to mean, by definition, a process can be described as a continuum of equilibrium states.
18. ### Darwin123
741
Re: Entropy is a measure of energy availiable for work ????
Oops. My typo. I meant,
No, it was a typo. Certainly not mainstream physics. However, I did not insert that mistake into my later equations.
Good for Joule! More power to him!
The internal energy of an ideal gas varies only with its temperature. The internal energy is not explicitly determined by either its pressure or its temperature. If you know how many atoms are in a molecule of the ideal, the number of molecules and the temperature, then you can uniquely determine the internal energy.
The quantity of the ideal gas in the closed container is constant. The number of atoms per molecule is constant. For an isothermal expansion, the temperature of the ideal gas is constant.
Therefore, the internal energy of the ideal gas is constant for an isothermal expansion. The internal energy never changes during the entire expansion, even in the limit of infinite volume. However, work is being done for the entire time. Therefore, the work can't come from the internal energy.
An isothermal expansion is actually the most inefficient way to use the internal energy of the ideal gas. None of the internal energy of the ideal gas becomes work in an isothermal expansion. All heat energy absorbed by the ideal gas instantly turns into work on the surroundings.
In an isothermal expansion, not a single picojoule of work comes from the internal energy of the gas. It all comes from the heat reservoir connected to the ideal gas.
One should note that the total amount of work done by the gas in the isothermal expansion is infinite. The work done by the gas increases with the logarithm of volume. So an infinite volume means that an infinite amount of work is performed. Do the calculations for yourself.
Obviously, the infinite energy that is going to become work is not in the internal energy of the gas. In fact, the internal energy of the gas remains the same even in the extreme limit of infinite work.
The energy for work is being supplied by the heat reservoir, not the ideal gas. In order to maintain a constant temperature, the container has to be in thermal contact with
Therefore, the kinetic energy of the molecules in the gas can not change during an isothermal expansion.
If you want to extract all the internal energy of the ideal gas to work on the surroundings, then you have to decrease the temperature to absolute zero. This can be done in an adiabatic expansion. It can't be done in an isothermal expansion.
Entropy can change only two ways. It can move or it can be created. In an adiabatic process, entropy can't move. The temperature changes instead. In an isothermal process, the entropy moves in such a way as to keep the temperature constant.
19. ### Rap
789
Re: Entropy is a measure of energy availiable for work ????
Note, that is only for a simple system (homogeneous).
For complex systems contained inside a thermally insulating boundary, entropy may move around inside the system, driven by temperature differences inside the system, equalizing them when possible, but can never be transferred across the boundary. During these internal sub-processes, entropy may also be created. In an isothermal process, the boundary is thermally open, and entropy may move across the boundary, again driven by temperature differences between the system and the environment, in such a way as to equalize internal temperatures at the constant temperature of the environment, when possible.
Entropy transfer goes hand in hand with energy transfer via dU=T dS. If a process is converting energy to work, and you want to know how much of that energy is converted to work, in order to keep the bookwork straight, you cannot bring in energy or entropy from somewhere else to accomplish that work. To ensure this, the process has to be adiabatic, i.e. inside a thermally insulating boundary which prevents entropy and energy coming in from somewhere else.
For finite temperature differences, transfer of entropy across a thermally open boundary causes creation of entropy at the boundary which is transferred to the lower temperature system. The transfer of entropy is of order ∆T, the creation of entropy at the boundary is of order ∆T^2, so, in the limit of small ∆T, entropy may be transferred without creation at the boundary. If ∆T is identically zero, there will be no transfer of entropy, since only temperature differences will drive entropy transfer.
Last edited: Dec 20, 2012
20. ### Andrew Mason
6,846
Re: Entropy is a measure of energy availiable for work ????
I think you have to qualify this statement. You have to speaking about a reversible process. Entropy can and certainly does change in an adiabatic irreversible expansion.
And I wouldn't say it moves because entropy is not a conserved quantity such as energy or momentum. We can speak of energy or momentum transfer because the loss of energy/momentum must result in the gain of energy/momentum of some other body so it behaves as if it moves. Entropy does not behave like. So I would suggest that the concept of entropy moving is not a particularly helpful one.
In a reversible isothermal process total entropy change is 0. In a real isothermal process, the entropy of the system + surroundings inevitably increases. It is not entropy that moves. It is energy. And the faster the energy moves, the greater the increase in entropy. So I might suggest that entropy increase is related more to the speed of energy transfer (heat flow) than to the fact that a body remains at the same temperature.
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## Abstract
Purity and Danger, published in 1966, remains Dame Mary Douglas's most famous book and “The Abominations of Leviticus” its most widely read chapter. In 2005, only two years before her death and in preparation for the Hebrew translation of Purity and Danger, which appeared in 2010, Douglas wrote a preface for that publication. With the likely interests of the Hebrew reader in mind, the preface expresses Douglas's final reflections on the history of her engagement with “The Abominations of Leviticus.” It includes a restatement of her conclusions in light of Valerio Valeri's work, in which she found the preferred approach to the questions she had asked over the years. This article presents Douglas's preface after setting it in the context of her contributions.
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## Reflections on COVID-19
COVID-19, Religious Markets, and the Black Church, Marla Frederick
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## Abstract
Drawing on observations of the performances of street preachers in the United States—as well as the texts that inform them—this article explores the concept of rhythm within and beyond the anthropology of religion. More specifically, it develops an expansive concept of rhythm as multiple and interactive, focusing not on a singular rhythm, but on the rhythmic translations that shape the practice of street preaching. First, I argue that the material rhythms of urban infrastructure constrain the narrative rhythms of the street preacher's sermon, producing a distinct homiletics. I then suggest that the ideological rhythms of war animate the narrative rhythms of the street preacher's sermon, linking military strategies with tactics of evangelism. Examining the material, narrative, and ideological rhythms of streets, sermons, and military doctrine, this article advances an analytic framework whereby the intersecting rhythmic tensions that shape performance can be registered.
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## Abstract
Allegations of religious intolerance push courts to deliberate on questions that are constitutive of the problem space of secularism. In addition to legal opinions on the character and scope of religious freedom vis-à-vis conflicting rights, these arbitrations result in authoritative statements on what constitutes religion, how it may inhabit public space, and, ultimately, what interests and values underpin the national collective. This article analyzes three high-profile court cases alleging religious intolerance against Afro-Brazilian religions that were tried in Brazil during the first two decades of the 2000s. It demonstrates how at this time of rapid religious transformation the adjudication of such cases acted as a key site for the Brazilian legal establishment to redefine the place of religion in the broader context of rights and laws that regulate religion in public spaces.
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## Book Reviews
BIELO, James, Materializing the Bible. Digital project. http://www.materializingthebible.com.
CASSELBERRY, Judith, The Labor of Faith: Gender and Power in Black Apostolic Pentecostalism, 240 pp., notes, index. Durham, NC: Duke University Press, 2017. Paperback, $25.95. ISBN 9780822369035. CLARK, Emily Suzanne, A Luminous Brotherhood: Afro-Creole Spiritualism in Nineteenth-Century New Orleans, 280 pp., notes, index. Chapel Hill: University of North Carolina Press, 2016. Hardback,$34.95. ISBN 9781469628783.
COWAN, Douglas E., America´s Dark Theologian: The Religious Imagination of Stephen King, 272 pp., notes, index. New York: NYU Press, 2018. Hardback, $30.00. ISBN 9781479894734. DARIEVA, Tsypylma, Florian MüHLFRIED, and Kevin TUITE, eds., Sacred Places, Emerging Spaces: Religious Pluralism in the Post-Soviet Caucasus, 246 pp., illustrations, bibliography, index. New York: Berghahn Books, 2018. Hardback,$90.00. ISBN 9781785337826.
DASWANI, Girish, Looking Back, Moving Forward: Transformation and Ethical Practice in the Ghanaian Church of Pentecost, 280 pages, figures, notes, index. Toronto: University of Toronto Press, 2015. Paperback, $30.95. ISBN 9781442626584. GIRALDO HERRERA, César E., Microbes and Other Shamanic Beings, 274 pp., index. New York: Palgrave Macmillan, 2018. Paperback,$99.99. ISBN 9783030100414.
KAELL, Hillary, ed., Everyday Sacred: Religion in Contemporary Quebec, 356 pp., figures, notes, index. Montreal: McGill-Queen's University Press, 2017. Hardback, $110.00. ISBN 9780773550940. KRIPAL, Jeffrey J., Secret Body: Erotic and Esoteric Currents in the History of Religions, 448 pp., appendix, notes, index. Chicago: University of Chicago Press, 2017. Paperback,$35.00. ISBN 9780226679082.
CABOT, Zayin, Ecologies of Participation: Agents, Shamans, Mystics and Diviners, 352 pp., preface, index. London: Rowman & Littlefield, 2018. Hardback, $110.00. ISBN 9781498568159. LAUTERBACH, Karen, Christianity, Wealth, and Spiritual Power in Ghana, 221 pp., appendix, index. New York: Palgrave Macmillan, 2017. Paperback,$119.99. ISBN 9783319815299.
LIBERATORE, Giulia, Somali, Muslim, British: Striving in Securitized Britain, 304 pp., figures, index. London: Bloomsbury, 2017. Paperback, $32.50. ISBN 9781350094628. MANSUR, Marcia, and Marina THOMé, dirs., The Sound of Bells (O Som dos Sinos), documentary film, Portuguese, 70 min. Estúdio Crua, 2016.$320.00. https://store.der.org/the-sound-of-bells-p1012.aspx.
OOSTERBAAN, Martijn, Transmitting the Spirit: Religious Conversion, Media, and Urban Violence, 264 pp., notes, bibliography, index. University Park: Pennsylvania State University Press, 2017. Paperback, $39.95. ISBN 9780271078441. SRINIVAS, Tulasi, The Cow in the Elevator: An Anthropology of Wonder, 296 pp., notes, references, index. Durham, NC: Duke University Press, 2018. Paperback,$26.95. ISBN 9780822370796.
TANEJA, Anand Vivek, Jinnealogy: Time, Islam and Ecological Thought in the Medieval Ruins of Delhi, 336 pp., illustrations, notes, references, index. Stanford, CA: Stanford University Press, 2018. Paperback, $30.00. ISBN 9781503603936. WILCOX, Melissa M., Queer Nuns: Religion, Activism, and Serious Parody, 336 pp., notes, bibliography, index. New York: NYU Press, 2018. Paperback,$30.00. ISBN 9781479820368.
Restricted access
## Commentary on “Siting Pluralism”
There are some things we seem to need to learn over and over and over. Among them are the ways in which modern legal efforts to expel the sacred—or, perhaps more pointedly, as Neena Mahadev shows in her article, interventions to end it—condemn us to its constant reproduction. State secularism results not in the evacuation of the sacred but in an almost neurotic picking at the scab of the wound—and the continuous management of what Hussein Agrama (2012: 186) has called the “problem-space of secularism.”
The four articles collected here are exemplary in their fine-grained analysis of this reality, both of the often pathetic inadequacy of regulatory efforts and, even more interestingly, of the glimpses we have of religious life lived in the in-between spaces of formal policing efforts, whether of church or state. The spatial gesture uniting this collection—siting pluralism—proves particularly potent. Sometimes imagined as uncompromisingly singular (i.e., spatial ‘locative’ religion as opposed to utopian portable religion) and at other times as spatial in a plural, less exclusive sense, the spaces/places of these articles are teeming with contradiction and multiplicity.
Open access
## Abstract
This article explores the tension between Pope Francis as a ‘trickster’ and as a much-needed reformer of the Catholic Church at large. He is an exemplar of the longue durée of an embodied ‘Atlantic Return’ from the Americas to the ‘heart’ of Catholicism (Rome and the Vatican), with its ambivalent, racialized history. Through the mobilization of material religion, sensuous mediations, and the case of the Lampedusa crosses in particular, I engage with an anthropological analysis of Francis as a Criollo and the first-ever Jesuit pope. Examining Francis's papacy overlapping racial and ethico-political dimensions, I identify coordinates around which the rhetorical, affective, and charismatic force of Francis as a Criollo has been actualized—between, most crucially, proximity and distance, as well as pastoral versus theological impulses. This article advances an understanding of Francis that emerges from a study of the conjuncture of affective fields, political theology, racialized aesthetics, and mediatic interface.
Free access
## Introduction
### A Decade of Religion and Society
This volume of Religion and Society is a special one. First, with this edition we celebrate our 10th anniversary. While our personnel have changed to some degree, our remit has remained largely the same. We present theoretically and methodologically challenging studies of religion through a variety of formats that place religion at the center of analysis and enable those who study religious phenomena to engage in debate and dialogue with each other. In recent years, our approach has also cemented ties with the Society for the Anthropology of Religion, a subsection of the American Anthropological Association. Over the entirety of the last decade, we have continued to publish exceptional interdisciplinary scholarship in social and cultural analyses of religion.
Free access
## Abstract
The introduction to this special section foregrounds the key distinction between ‘religious plurality’ and ‘interreligious pluralism’. Building from the example of a recent controversy over an exhibition on shared religious sites in Thessaloniki, Greece, we analyze the ways in which advocates and adversaries of pluralism alternately place minority religions at the center or attempt to relegate them to the margins of visual, spatial, and political fields. To establish the conceptual scaffolding that supports this special section, we engage the complex relations that govern the operations of state and civil society, sacrality and secularity, as well as spectacular acts of disavowal that simultaneously coincide with everyday multiplicities in the shared use of space. We conclude with brief summaries of the four articles that site religious plurality and interreligious pluralism in the diverse contexts of Brazil, Russia, Sri Lanka, and the Balkans.
Restricted access
## Abstract
Amid growing interest in mindfulness studies focusing on Buddhist and Buddhism-derived practices, this article argues for a comparative and ethnographic approach to analogous practices in different religious traditions and to their vernacular significance in the everyday lives of practitioners. The Jewish contemplative tradition identified with Chabad Hasidism is worth consideration in this context because of its long-standing indigenous tradition of contemplative practice, the recent adoption of ‘mindfulness’ practices or terminology by some Hasidim, and its many intersections with so-called Buddhist modernism. These intersections include the personal trajectories of individuals who have engaged in both Buddhist and Hasidism-derived mindfulness practices, the shared invocation and adaptation of contemporary psychology, and the promotion of secularized forms of contemplative practice. We argue that ‘Hasidic modernism’ is a better frame than ‘neo-Hasidism’ for comparative purposes, and that Hasidic modernism complicates the taxonomies of secularity in comparable but distinctive ways to those that arise in Buddhist-modernism contexts. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20808880031108856, "perplexity": 12505.781091310559}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337855.83/warc/CC-MAIN-20221006191305-20221006221305-00330.warc.gz"} |
http://tex.stackexchange.com/questions/129575/how-to-split-a-figure-over-multiple-pages-using-subfigure-package | # How to split a figure over multiple pages using subfigure package
I am using subfigure package and would like to split a figure (that has a number of subfigures in it) into two pages, rather than one single page. I have seen few posts about how to do this with subfig package and the use of \subfloat. But that requires me to change to subfig package and change every \subfigure to \subfloat and so on.
I would be thankful in you guys could help. Here is my code:
\begin{figure}[ht]
\centering
\subfigure{\includegraphics[width=0.19\textwidth]{figures/truck1}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/truckLSD1}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/truckEDL2}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/truckDu3}}
\subfigure{\includegraphics[width=0.19\textwidth]{figures/truckPWA}}\
\\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/zebra}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/zebra}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/zebra}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/zebra}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/zebra}}\
\\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/office}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/office}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/office}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/office}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/office}}\
\\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/micro}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/micro}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/micro}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/micro}}\
\subfigure{\includegraphics[width=0.19\textwidth]{figures/micro}}\
\caption[XXXXXXXXXXXXXX.}
\label{fig:natural}
\end{figure}
-
To allow continued floats with subfigure, use the captcont package from the same author. But: What's so difficult about replacing all \subfigure with \subfloat, every text editor should handle this. – Axel Sommerfeldt Aug 22 '13 at 14:39
You should consider using subcaption but @AxelSommerfeldt. – dustin Aug 22 '13 at 14:47
Thanks, \captcont did work. – user2335132 Aug 22 '13 at 16:43
Welcome to TeX.SX! You can have a look at our starter guide to familiarize yourself further with our format. – Heiko Oberdiek Aug 25 '13 at 7:32
To allow continued floats with subfigure, use the captcont package from the same author.
Please note that both packages has been marked as obsolete by its author, and the successor of both is the subfig package which only got a different name because it's not fully compatible with the subfigure package. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.626466691493988, "perplexity": 2571.045641161002}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783395346.6/warc/CC-MAIN-20160624154955-00173-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://puzzling.stackexchange.com/questions/84536/express-the-squares-of-first-20-numbers-with-only-numbers-found-in-their-sum-of/84538 | # Express the Squares of first 20 Numbers with only numbers found in their Sum of Digits
Allowed Operations ...Addition, Subtraction, Multiplication, Division, Exponentiation, Simple Factorial. Left and Right Brackets allowed.
Expression should involve minimum number of total characters:
Example:
Number 7. Square. 49. Sum of Digits. 13
Using only digits 1 and 3, express 49
One possibility is. 49 = (3! + 1) * (3! + 1)
• Sure..only restriction is among all the possibilities with allowed signs, come up with minimum footprint – Uvc May 30 '19 at 15:30
• is square root allowed? – Omega Krypton May 30 '19 at 15:30
• No..only given signs(operations allowed) – Uvc May 30 '19 at 15:31
• Are concatenations allowed? E.g. given 13 in your example, could we use the number 13, or only 1 and 3? – Rand al'Thor May 30 '19 at 15:33
• No concatenation..only mentioned operations..in the example, 1 and 3 can be used with any mentioned allowable operations – Uvc May 30 '19 at 15:35
1: sod=1
$$1$$
4: sod=4
$$4$$
9: sod=9
$$9$$
16: sod=7
$$(7+\frac77)(\frac{7+7}{7})$$
25: sod=7
$$(7-\frac{7+7}{7})^{\frac{7+7}{7}}$$
36: sod=9
$$9+9+9+9$$
49: sod=13
$$(3!+1)^{1+1}$$
64: sod=10
$$(1+1)^{(1+1+1)!}$$
81: sod=9
$$9\times9$$
100: sod=1
$$((1+1+1)^{1+1}+1))^{1+1}$$
121: sod=4
$$(4+\frac44)!+\frac44$$
144: sod=9
$$(9-\frac99)(9+9)$$
169: sod=16
$$(6+6+1)^{1+1}$$
196: sod=16
$$(6+6+1+1)^{1+1}$$
225: sod=9
$$9\times(9+9+9)-9-9$$
256: sod=13
$$(1+1)^{(1+1)^3}$$
289: sod=19
$$(9+9-1)^{1+1}$$
324: sod=9
$$(9+9)(9+9)$$
361: sod=10
$$\frac{(1+1+1)!!}{1+1}+1$$
400: sod=4
$$4\times(4\cdot4!+4)$$
• no- the 10 is not allowed... sorry – Omega Krypton May 30 '19 at 15:39
• No concatenation of 1 and 0 allowed – Uvc May 30 '19 at 15:41
• why does the 400 case work? 4.4! is like 48 point something – Omega Krypton May 30 '19 at 15:47
• using dot notation for multiply @OmegaKrypton – JMP May 30 '19 at 15:48
• good game! +1 JMP! – Omega Krypton May 30 '19 at 15:49
Partial
notation: sod = sum of digits, sq = square
1) sq=1, sod=1
$$1=1$$
2) sq=4, sod=4
$$4=4$$
3) sq=9, sod=9
$$9=9$$
4) sq=16, sod=7
$$16=7+7+7/7+7/7$$
5) sq=25, sod=7
6) sq=36, sod=9
$$36=9+9+9+9$$
7) sq=49, sod=13
$$49=(3!+1)*(3!+1)$$ (from OP)
8) sq=64, sod=10
$$64=\big((1+1)^{(1+1+1)}\big)^{(1+1)}$$
17) sq=289, sod=19
289=(9+9-1)^(1+1)
18) sq=324, sod=9
324=(9+9)^(9/9+9/9)
• @omega..answers for 19 and 20 missing – Uvc May 30 '19 at 22:38
• @Uvc sorry, didnt bother to finish this while Rand and JMP have finished... ;) – Omega Krypton May 31 '19 at 0:07
• Still..whatever you have done is pretty good. – Uvc May 31 '19 at 0:08
1. Square 1. Sum of digits 1.
$$1=1$$.
2. Square 4. Sum of digits 4.
$$4=4$$.
3. Square 9. Sum of digits 9.
$$9=9$$.
4. Square 16. Sum of digits 7.
$$16=7+7+\frac{7}{7}+\frac{7}{7}$$.
5. Square 25. Sum of digits 7.
$$25=\frac{(7\times7)+\frac{7}{7}}{\frac{7}{7}+\frac{7}{7}}$$.
6. Square 36. Sum of digits 9.
$$36=9+9+9+9$$.
7. Square 49. Sum of digits 13.
$$49=(3!+1)\times(3!+1)$$.
8. Square 64. Sum of digits 10.
$$64=(1+1+1+1)^{1+1+1}$$.
9. Square 81. Sum of digits 9.
$$81=9\times9$$.
10. Square 100. Sum of digits 1.
$$100=((1+1+1+1+1)\times(1+1))^{1+1}$$.
11. Square 121. Sum of digits 4.
$$121=(4+4+4-\frac{4}{4})^{\frac{4}{4}+\frac{4}{4}}$$.
12. Square 144. Sum of digits 9.
$$144=9\times(9+9)-9-9$$.
13. Square 169. Sum of digits 16. (Most interesting one!)
$$169=(6-1)!+(6+1)^{1+1}$$.
14. Square 196. Sum of digits 16.
$$196=(6+6+1+1)^{1+1}$$.
15. Square 225. Sum of digits 9.
$$225=9\times(9+9+9)-9-9$$.
16. Square 256. Sum of digits 13.
$$256=(3+1)^{3+1}$$.
17. Square 289. Sum of digits 19.
$$289=(9+9-1)^{1+1}$$.
18. Square 324. Sum of digits 9.
$$324=(9+9)\times(9+9)$$.
19. Square 361. Sum of digits 10.
$$361=\frac{(1+1+1+1+1+1)!}{1+1}+1$$.
20. Square 400. Sum of digits 4.
$$400=4\times(4\times4!+4)$$.
• good game! +1 Rand! – Omega Krypton May 30 '19 at 15:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 47, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5172303318977356, "perplexity": 14243.260346348445}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146004.9/warc/CC-MAIN-20200225014941-20200225044941-00275.warc.gz"} |
http://math.lanl.gov/Research/Publications/asipauskas-2003-a-texture.shtml | T-5 HomeResearchPublications › asipauskas-2003-a-texture
Cite Details
Marius Asipauskas, Miguel Aubouy, James A. Glazier, Francois Graner and Yi Jiang, "A texture tensor to quantify deformations: the example of two-dimensional flowing foams ", Granular Matter, vol. 5, pp. 71-76, 2003
Abstract
In a continuum description of materials, the stress tensor field $\overline{\overline{\sigma }}$ quantifies the internal forces the neighbouring regions exert on a region of the material. The classical theory of elastic solids assumes that $\overline{\overline{\sigma }}$ determines the strain, while hydrodynamics assumes that $\overline{\overline{\sigma }}$ determines the strain rate. To extend both successful theories to more general materials, which display both elastic and fluid properties, we recently introduced a descriptor generalizing the classical strain to include plastic deformations: the statistical strain'', based on averages on microscopic details (A texture tensor to quantify deformations'' M.Au., Y.J., J.A.G., F.G, companion paper, Granular Matter , same issue). Here, we apply such a statistical analysis to a two-dimensional foam steadily flowing through a constriction, a problem beyond reach of both theories, and prove that the foam has the elastic properties of a (linear and isotropic) continuous medium.
BibTeX Entry
@article{asipauskas-2003-a-texture,
author = {Marius Asipauskas and Miguel Aubouy and James A. Glazier and Francois Graner and Yi Jiang},
title = {A texture tensor to quantify deformations: the example of two-dimensional flowing foams },
year = {2003},
urlpdf = {http://math.lanl.gov/~yi/Papers/GranularMatterExp.pdf},
journal = {Granular Matter},
volume = {5},
pages = {71-76}
} | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7987608313560486, "perplexity": 6630.287481620225}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887729.45/warc/CC-MAIN-20180119030106-20180119050106-00622.warc.gz"} |
https://socratic.org/questions/how-do-you-find-three-consecutive-even-integers-whose-sum-is-16-more-than-two-ti | Algebra
Topics
# How do you find three consecutive even integers whose sum is 16 more than two times the middle integer?
Oct 24, 2016
The three consecutive even integers are $14$, $16$ and $18$.
#### Explanation:
We shall consider the three consecutive even integers as $x$, $x + 2$ and $x + 4$.
From the details we know that the sum of all three is $16$ more than the twice the middle integer.: Expressing this in an equation:
$x + \left(x + 2\right) + \left(x + 4\right) = 2 \left(x + 2\right) + 16$
Opening the brackets and simplifying:
$x + x + 2 + x + 4 = 2 x + 4 + 16$
$3 x + 6 = 2 x + 20$
Shifting terms and simplifying:
$3 x - 2 x = 20 - 6$
$x = 14$
$\therefore x = 14 , x + 2 = 16 , x + 4 = 18$
##### Impact of this question
1684 views around the world | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 13, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41453275084495544, "perplexity": 590.3266998529647}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662534669.47/warc/CC-MAIN-20220520191810-20220520221810-00249.warc.gz"} |
http://www.reference.com/browse/electric%20currents | Definitions
# Electric current
Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere. Electric current is measured using an ammeter.
The electric charge may be either electrons or ions. The nature of the electric current is basically the same for either type.
## Current in a metal wire
A solid conductive metal contains a large population of mobile, or free, electrons. These electrons are bound to the metal lattice but not to any individual atom. Even with no external electric field applied, these electrons move about randomly due to thermal energy but, on average, there is zero net current within the metal. Given a plane through which the wire passes, the number of electrons moving from one side to the other in any period of time is on average equal to the number passing in the opposite direction.
When a metal wire is connected across the two terminals of a DC voltage source such as a battery, the source places an electric field across the conductor. The moment contact is made, the free electrons of the conductor are forced to drift toward the positive terminal under the influence of this field. The free electrons are therefore the current carrier in a typical solid conductor. For an electric current of 1 ampere, 1 coulomb of electric charge (which consists of about 6.242 × 1018 electrons) drifts every second through any plane through which the conductor passes.
The current I in amperes can be calculated with the following equation:
$I = \left\{Q over t\right\}$
where
$Q !$ is the electric charge in coulombs (ampere seconds)
$t !$ is the time in seconds
It follows that:
$Q=It !$ and $t = \left\{Q over I\right\}$
More generally, electric current can be represented as the time rate of change of charge, or
$I = frac\left\{dQ\right\}\left\{dt\right\}$.
## Current density
Current density is a measure of the density of electric current. It is defined as a vector whose magnitude is the electric current per cross-sectional area. In SI units, the current density is measured in amperes per square meter.
## The drift speed of electric charges
The mobile charged particles within a conductor move constantly in random directions, like the particles of a gas. In order for there to be a net flow of charge, the particles must also move together with an average drift rate. Electrons are the charge carriers in metals and they follow an erratic path, bouncing from atom to atom, but generally drifting in the direction of the electric field. The speed at which they drift can be calculated from the equation:
$I=nAvQ !$
where
$I !$ is the electric current
$n !$ is number of charged particles per unit volume
$A !$ is the cross-sectional area of the conductor
$v !$ is the drift velocity, and
$Q !$ is the charge on each particle.
Electric currents in solids typically flow very slowly. For example, in a copper wire of cross-section 0.5 mm², carrying a current of 5 A, the drift velocity of the electrons is of the order of a millimetre per second. To take a different example, in the near-vacuum inside a cathode ray tube, the electrons travel in near-straight lines ("ballistically") at about a tenth of the speed of light.
Any accelerating electric charge, and therefore any changing electric current, gives rise to an electromagnetic wave that propagates at very high speed outside the surface of the conductor. This speed is usually a significant fraction of the speed of light, as can be deduced from Maxwell's Equations, and is therefore many times faster than the drift velocity of the electrons. For example, in AC power lines, the waves of electromagnetic energy propagate through the space between the wires, moving from a source to a distant load, even though the electrons in the wires only move back and forth over a tiny distance.
The ratio of the speed of the electromagnetic wave to the speed of light in free space is called the velocity factor, and depends on the electromagnetic properties of the conductor and the insulating materials surrounding it, and on their shape and size.
The nature of these three velocities can be illustrated by an analogy with the three similar velocities associated with gases. The low drift velocity of charge carriers is analogous to air motion; in other words, winds. The high speed of electromagnetic waves is roughly analogous to the speed of sound in a gas; while the random motion of charges is analogous to heat - the thermal velocity of randomly vibrating gas particles.
## Ohm's law
Ohm's law predicts the current in an (ideal) resistor (or other ohmic device) to be the applied voltage divided by resistance:
I = frac {V}{R}
where
I is the current, measured in amperes
V is the potential difference measured in volts
R is the resistance measured in ohms
## Conventional current
A flow of positive charge gives the same electric current as an opposite flow of negative charge. Thus, opposite flows of opposite charges contribute to a single electric current. For this reason, the polarity of the flowing charges can usually be ignored during measurements. All the flowing charges are assumed to have positive polarity, and this flow is called Conventional current.
In solid metals such as wires, the positive charge carriers are immobile, and only the negatively charged electrons flow. Because the electron carries negative charge, the electron motion in a metal is in the direction opposite to that of conventional (or electric) current.
In many other conductive materials, the electric current is due to the flow of both positively and negatively charged particles at the same time. In still others, the current is entirely due to positive charge flow. For example, the electric currents in electrolytes are flows of electrically charged atoms (ions), which exist in both positive and negative varieties. In a common lead-acid electrochemical cell, electric currents are composed of positive hydrogen ions (protons) flowing in one direction, and negative sulfate ions flowing in the other. Electric currents in sparks or plasma are flows of electrons as well as positive and negative ions. In ice and in certain solid electrolytes, the electric current is entirely composed of flowing protons. For conceptual simplicity, Conventional current is used to conceal these issues by summing the various currents together into a single value.
There are also materials where the electric current is due to the flow of electrons, and yet it is conceptually easier to think of the current as due to the flow of positive "holes" (the spots that should have an electron to make the conductor neutral). This is the case in a p-type semiconductor.
## Examples
Natural examples include lightning and the solar wind, the source of the polar auroras (the aurora borealis and aurora australis). The artificial form of electric current is the flow of conduction electrons in metal wires, such as the overhead power lines that deliver electrical energy across long distances and the smaller wires within electrical and electronic equipment. In electronics, other forms of electric current include the flow of electrons through resistors or through the vacuum in a vacuum tube, the flow of ions inside a battery or a neuron, and the flow of holes within a semiconductor.
## Electromagnetism
Electric current produces a magnetic field. The magnetic field can be visualized as a pattern of circular field lines surrounding the wire.
Electric current can be directly measured with a galvanometer, but this method involves breaking the circuit, which is sometimes inconvenient. Current can also be measured without breaking the circuit by detecting the magnetic field associated with the current. Devices used for this include Hall effect sensors, current clamps, current transformers, and Rogowski coils.
## Reference direction
When solving electrical circuits, the actual direction of current through a specific circuit element is usually unknown. Consequently, each circuit element is assigned a current variable with an arbitrarily chosen reference direction. When the circuit is solved, the circuit element currents may have positive or negative values. A negative value means that the actual direction of current through that circuit element is opposite that of the chosen reference direction.
## Electrical safety
The most obvious hazard is electrical shock, where a current passes through part of the body. It is the amount of current passing through the body that determines the effect, and this depends on the nature of the contact, the condition of the body part, the current path through the body and the voltage of the source. While a very small amount can cause a slight tingle, too much can cause severe burns if it passes through the skin or even cardiac arrest if enough passes through the heart. The effect also varies considerably from individual to individual. (For approximate figures see Shock Effects under electric shock.)
Due to this and the fact that passing current cannot be easily predicted in most practical circumstances, any supply of over 50 volts should be considered a possible source of dangerous electric shock. In particular, note that 110 volts (a minimum voltage at which AC mains power is distributed in much of the Americas, and 4 other countries, mostly in Asia) can certainly cause a lethal amount of current to pass through the body.
Electric arcs, which can occur with supplies of any voltage (for example, a typical arc welding machine has a voltage between the electrodes of just a few tens of volts), are very hot and emit ultra-violet (UV) and infra-red radiation (IR). Proximity to an electric arc can therefore cause severe thermal burns, and UV is damaging to unprotected eyes and skin.
Accidental electric heating can also be dangerous. An overloaded power cable is a frequent cause of fire. A battery as small as an AA cell placed in a pocket with metal coins can lead to a short circuit heating the battery and the coins which may inflict burns. NiCad, NiMh cells, and lithium batteries are particularly risky because they can deliver a very high current due to their low internal resistance. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 13, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9034416079521179, "perplexity": 429.70059725326547}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929956.54/warc/CC-MAIN-20150521113209-00110-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://link.springer.com/article/10.1007/s00020-018-2442-x | # Local Index Formula for Quantum Double Suspension
• Partha Sarathi Chakraborty
• Bipul Saurabh
Article
## Abstract
Our understanding of the local index formula in noncommutative geometry has stalled for a while because we do not have more than one explicit computation, namely that of Connes for quantum SU(2), and we do not understand the meaning of the various multilinear functionals involved in the formula. In such a situation further progress in understanding necessitates more explicit computations, and here we execute the second explicit computation for the quantum double suspension, a construction inspired by the Toeplitz extension. More specifically, we compute the local index formula for the quantum double suspensions of $$C(\mathcal {S}^2)$$ and the noncommutative 2-torus.
## Keywords
Spectral triples Noncommutative geometry Local index formula Quantum double suspension Noncommutative torus
## Mathematics Subject Classification
Primary: 46L87 58B34 Secondary: 19K56
## Notes
### Acknowledgements
We would like to thank the anonymous referee for his insightful comments and suggestions.
## References
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Carey, A.L., Phillips, J., Rennie, A., Sukochev, F.A.: The local index formula in semifinite von Neumann algebras. I. Spectral flow. Adv. Math. 202(2), 451–516 (2006)
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Carey, A.L., Phillips, J., Rennie, A., Sukochev, F.A.: The local index formula in semifinite von Neumann algebras. II. The even case. Adv. Math. 202(2), 517–554 (2006)
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Carey, A.L., Phillips, J., Rennie, A., Sukochev, F.A.: The local index formula in noncommutative geometry revisited. In: Noncommutative Geometry and Physics 3, volume 1 of Keio COE Lecture Series in Mathematics and Computer Science. World Science Publisher, Hackensack, pp. 3–36 (2013)Google Scholar
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Chakraborty, P.S., Sundar, S.: Quantum double suspension and spectral triples. J. Funct. Anal. 260(9), 2716–2741 (2011)
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Connes, A.: Cyclic cohomology, quantum group symmetries and the local index formula for $${\rm SU}_q(2)$$. J. Inst. Math. Jussieu 3(1), 17–68 (2004)
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Connes, A.: Interview of A. Connes for EMS. In: Skandalis, G., Goldstein, C. http://www.ems-ph.org/journals/newsletter/pdf/2007-03-63.pdf
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Connes, A., Moscovici, H.: Modular curvature for noncommutative two-tori. J. Am. Math. Soc. 27(3), 639–684 (2014)
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Fathizadeh, F., Khalkhali, M.: Scalar curvature for noncommutative four-tori. J. Noncommutative Geom. 9(2), 473–503 (2015)
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Gilkey, P.B.: Invariance Theory, the Heat Equation, and the Atiyah–Singer Index Theorem. Studies in Advanced Mathematics, p. x+516. CRC Press, Boca Raton (1995)
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Higson, N.: The local index formula in noncommutative geometry. Contemp. Dev. Algeb. K Theory 15, 444 (2003)
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Hong, J.H., Szymański, W.: Quantum spheres and projective spaces as graph algebras. Commun. Math. Phys. 232(1), 157–188 (2002)
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Pal, A., Sundar, S.: Regularity and dimension spectrum of the equivariant spectral triple for the odd-dimensional quantum spheres. J. Noncommutative Geom. 4(3), 389–439 (2010)
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Rosenberg, S.: The Laplacian on a Riemannian Manifold. An Introduction to Analysis on Manifolds. London Mathematical Society Student Texts, vol. 31. Cambridge University Press, Cambridge (1997)
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van Suijlekom, W., Dabrowski, L., Landi, G., Sitarz, A., Várilly, J.C.: The local index formula for $$SU_q(2)$$. K Theory 35 (2005)(3–4), 375–394 (2006)
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Wodzicki, M.: Local invariants of spectral asymmetry. Invent. Math. 75(1), 143–177 (1984) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7953035831451416, "perplexity": 5376.337326665131}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583516480.46/warc/CC-MAIN-20181023153446-20181023174946-00514.warc.gz"} |
https://wordassociations.net/en/words-associated-with/Periodic | # Associations to the word «Periodic»
## Wiktionary
PERIODIC, adjective. Relative to a period or periods.
PERIODIC, adjective. Occurring at regular intervals.
PERIODIC, adjective. (astronomy) Pertaining to the revolution of a celestial object in its orbit.
PERIODIC, adjective. (mathematics) (stochastic processes) (of a state) For which any return to it must occur in multiples of $$k$$ time steps, for some $$k>1$$.
PERIODIC, adjective. (rhetoric) Having a structure characterized by periodic sentences.
PERIODIC, adjective. (chemistry) Relating to, derived from, or designating, the highest oxygen acid (HIO) of iodine.
PERIODIC, adjective. Of or derived from a periodic acid.
PERIODIC ACID, noun. (inorganic compound) HIO4, the oxyacid of iodine in which iodine has the highest oxidation number; it is a white crystalline substance, and a strong oxidizing agent
PERIODIC COMET, noun. (astronomy) A comet which orbits the Sun and which returns to the innermost point of its orbit at known, regular intervals.
PERIODIC COMETS, noun. Plural of periodic comet
PERIODIC FUNCTION, noun. (mathematics) Any function whose value repeats after the regular addition of a period to its independent variable; i.e. f(x+t) = f(x) for some t over all x
PERIODIC FUNCTIONS, noun. Plural of periodic function
PERIODIC LAW, noun. (chemistry) The principle that chemical properties of the elements are periodic functions of their atomic numbers
PERIODIC SENTENCE, noun. (rhetoric) A sentence whose main clause appears at its end.
PERIODIC STRUCTURE, noun. A sentence whose main clause appears at the end, after other, especially dependent, clauses.
PERIODIC STRUCTURES, noun. Plural of periodic structure
PERIODIC TABLE, noun. (chemistry) A tabular chart of the chemical elements according to their atomic numbers so that elements with similar properties are in the same column.
PERIODIC TABLES, noun. Plural of periodic table
## Dictionary definition
PERIODIC, adjective. Happening or recurring at regular intervals; "the periodic appearance of the seventeen-year locust".
PERIODIC, adjective. Recurring or reappearing from time to time; "periodic feelings of anxiety".
## Wise words
Where words fail, music speaks.
Hans Christian Anderson | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20399783551692963, "perplexity": 11153.221037385592}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824912.16/warc/CC-MAIN-20181213145807-20181213171307-00307.warc.gz"} |
https://together.jolla.com/question/197163/current-status-of-file-transfer-sailfish-to-mac/ | # current status of file transfer (sailfish to mac)
This post is a wiki. Anyone with karma >75 is welcome to improve it.
What is the current status of file transfer between sailfish and macos? There are a number of options mentioned here, but unfortunately they either don't work on my system (SyncMate won't discover the phone, DropBox clients are all broken), are impractical (Bluetooth is too slow), or are really complicated (SD-card file transfer is a bit of mess).
I always used to use android file manager, but this has ceased to work for sony xperia plus sailfish 3.
Being able to move files out of a phone is a pretty basic feature. I suspect there are workarounds that others use which are not mentioned anywhere yet.
edit retag close delete
Are you afraid of the command line / terminal? I am using SCP (https://en.wikipedia.org/wiki/Secure_copy) on Mac OS X (not sure whether it is installed by default) with enabled developer mode on the Sailfish phone... It is fast and works with Wifi. Use following command to download files from the phone (IP: u.v.w.x) to the Mac's current directory: scp -r [email protected]:/home/nemo/Pictures/Camera/* .
( 2019-01-10 14:24:18 +0300 )edit
If you prefer a GUI you could use Cyberduck for Mac, which is FOSS. Mac and Phone have to be in the same network. Enable "developer mode" and "remote connection" on the phone and set a password. On Cyberduck make a new connection using SFTP (SSH) to the IP of the phone, username nemo. Then you can easily browse the phones file system. There is write access to everything, so take care..
( 2019-01-10 22:14:46 +0300 )edit
1
You can use AirSail Transfer to transfer files to/from your phone using your computer's web browser.
( 2019-01-11 01:29:32 +0300 )edit
Help article updated - thank you for the hints!
( 2019-01-11 16:17:14 +0300 )edit
excellent, thanks for your suggestions. I'll let you know how it worked here.
( 2019-01-12 18:01:24 +0300 )edit | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17939992249011993, "perplexity": 6711.718090203764}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575627.91/warc/CC-MAIN-20190922180536-20190922202536-00409.warc.gz"} |
https://www.mathswithmum.com/subtracting-unlike-fractions/ | # How to Subtract Fractions with Unlike Denominators
How to Subtract Fractions with Unlike Denominators
• To subtract fractions, they must first have the same denominator on the bottom.
• Find the first number that is in the times tables of each denominator. We call this the least common denominator.
• The first number in both the 2 and 5 times table is 10. 10 is the least common denominator.
• Write each fraction out of this least common denominator using equivalent fractions.
• 1/2 can be written as 5/10 by multiplying the numbers by 5.
• 1/5 can be written as 2/10 by multiplying the numbers by 2.
• Once the denominators are the same, the fractions can be subtracted.
• Keep the denominator on the bottom the same and subtract the numerators on top.
• 5/10 - 2/10 = 3/10 and therefore 1/2 - 1/5 = 3/10 .
Convert the fractions to like fractions with the same denominator before subtracting them.
• To subtract fractions with different denominators, first write them as equivalent fractions with the same denominator.
• The denominators of 6 and 8 have a least common denominator of 24. This means that 24 is the first number in both the 6 and 8 times table.
• 4/6 can be written as 16/24 by multiplying the values by 4.
• 3/8 can be written as 9/24 by multiplying the values by 3.
• 16/24 - 9/24 = 7/24 .
• Therefore 4/6 - 3/8 = 7/24 .
Supporting Lessons
# Subtracting Fractions with Unlike Denominators
## How to Subtract Fractions with Unlike Denominators
To subtract fractions with unlike denominators, follow these steps:
1. Find the least common multiple of the denominators of the fractions.
2. Write equivalent fractions that have the least common multiple as the denominator.
3. Keep this least common multiple as the denominator of the answer.
4. Subtract the numerators in the question to get the numerator of the answer.
The most important rule when subtracting fractions is to first make a common denominator. The denominators of the fractions must be the same before subtracting them.
For example, here is 4/6 - 3/8 .
Denominators are the numbers on the bottom of the fraction. The denominators are 6 and 8, which are different. To subtract fractions, we need the denominators to be the same.
A common denominator is a number that is a multiple of all of the other denominators. It is usually chosen as the first number that appears in all of the times tables of the denominators. For example, with 4/6 - 3/8 , the common denominator is 24 because 24 is the first number in the 6 and 8 times tables.
To find the least common denominator, list the multiples of each denominator and write down the first number to appear in every list. Alternatively, a common denominator can be found by multiplying the denominators together.
The multiples of 6 are 6, 12, 18, 24 and the multiples of 8 are 8, 16, 24. 24 is the first number to appear in each list and so, it is the least common denominator of 6 and 8. The least common denominator is also commonly known as the lowest common denominator. It is the smallest common denominator that can be found.
The next step is to find equivalent fractions that have the least common denominator.
The first fraction denominator has been multiplied by 4. Therefore we need to multiply the numerator by 4 as well.
The denominator calculation is 6 × 4 = 24. The numerator calculation is 4 × 4 = 16. Both the numerator and denominator are multiplied by 4.
The second fraction denominator has been multiplied by 3. Therefore we need to multiply the numerator by 3 as well.
The denominator calculation is 8 × 3 = 24. The numerator calculation is 3 × 3 = 9. Both the numerator and denominator are multiplied by 3.
Now that the fractions have common denominators, the subtraction can be done. The denominator of the answer is the same as the common denominator.
The lowest common denominator is 24 and so, the denominator of the answer is also 24.
To find the numerator of the answer, simply subtract the numerators in the question.
16 - 9 = 7 and so, the numerator of the answer is 7.
4/6 - 3/8 = 7/24 .
Here is another example of subtracting unlike fractions step by step.
We have 1/2 - 1/5 .
The denominators are different and so, we need to find equivalent fractions with a common denominator.
The multiples of 2 are 2, 4, 6, 8, 10 and the multiples of 5 are 5 and 10.
We can see that 10 is the first number in both lists and so, 10 is the least common denominator of 2 and 5.
We write 1/2 as 5/10 .
We write 1/5 as 2/10 .
Now that we have a common denominator, we can subtract the fractions 5/10 - 2/10 = 3/10 .
If both denominators are prime, the least common denominator is found by multiplying the denominators together. For example in 1/2 - 1/5 , the least common denominator is 10 because 2 × 5 = 10.
## Subtracting Fractions with the Butterfly Method
The butterfly method is a short method that can be used for adding or subtracting 2 fractions. It involves multiplying the numerator of one fraction by the denominator of the other with the bubbles around each multiplication drawn to make an image of a butterfly.
To subtract fractions using the butterfly method, follow these steps:
1. Multiply the two denominators together to find the denominator of the answer.
2. Multiply the first numerator by the second denominator.
3. Multiply the second numerator by the first denominator.
4. Write both of these two answers on the numerator, separated by a subtraction sign.
5. Work out the subtraction to get one number as the numerator.
6. Simplify the fraction if possible.
For example, we have 4/5 - 2/3 .
The diagram below shows how the butterfly method works.
We first multiply the denominators of 5 and 3.
5 × 3 = 15 and so the denominator of the answer is 15.
Next we multiply the numerator of the first fraction by the denominator of the second fraction.
4 × 3 = 12, so we write 12 on the numerator of the fraction.
Next we multiply the numerator of the second fraction by the denominator of the first fraction.
2 × 5 = 10 and so we write a 10 alongside the 12 with a subtraction sign in between.
For each multiplication in the butterfly method, draw a bubble around the numbers. This makes the overall calculation look like a butterfly and can help make the method easier to remember and learn.
Finally, we work out the subtraction on the numerator.
12 - 10 = 2 and so, 2 is the numerator.
The result of the butterfly method calculation is 2/15
The butterfly method is an easy way to routinely solve the addition and subtraction of 2 fractions. The benefits of the butterfly method are that it reduces working out and the method is easier to remember due to the symmetrical butterfly pattern. It is a useful method to teach when the initial understanding of how to add and subtract fractions has been learnt.
The main problem with the butterfly method is that it only allows for the addition and subtraction of two fractions. It is not recommended to introduce adding and subtracting fractions with the butterfly method because it does not allow for a strong understanding of why the method works and it is limited to use on specific types of question.
## Subtracing Unlike Fractions Easy Examples
Here are some easier examples to practise with. When teaching subtracting fractions with unlike denominations, it is helpful to start with examples where only one fraction needs changing.
These examples only require one fraction to change in order to find a common denominator. If one fraction denominator is a multiple of the other, only one fraction needs to be changed.
The first easy example is 1/2 - 1/4 .
We can see that the denominator of 4 is a multiple of the denominator of 2.
This means that we can simply double the values in the fraction 1/2 to get a common denominator of 4. 1/2 = 2/4 .
We rewrite 1/2 - 1/4 as 2/4 - 1/4 .
2 - 1 = 1 and so, the numerator of the answer is 1. The denominator remains as 4.
Here is another easy example of subtracting fractions with different denominators.
We have 11/12 - 3/4 .
We can see that 12 is a multiple of 4 and so, only one fraction needs changing. The 4 needs to be multiplied by 3 to make 12.
We rewrite the fraction 3/4 as 9/12 .
11/12 - 9/12 = 2/12 .
It is possible to simplify this answer by halving both the numerator and denominator.
2/12 simplifies to 1/6 .
## How to Subtract Mixed Numbers with Unlike Denominators
To subtract mixed numbers with unlike denominators, follow these steps:
1. Write the mixed numbers as improper fractions.
2. Find the least common denominator.
3. Write the improper fractions as equivalent fractions that have the least common denominator.
4. The denominator of the answer is the same as this least common denominator.
5. Subtract the numerators to find the numerator of the answer.
For example, here is 5 1/4 - 2 2/3 .
The first step is to convert the mixed numbers into improper fractions.
To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. This result is the new numerator and the denominator is the same as the denominator of the mixed number.
5 × 4 = 20 and then 20 + 1 = 21.
The mixed number of 5 1/4 can be rewritten as an improper fraction as 21/4 .
2 × 3 = 6 and then 6 + 2 = 8.
The mixed number of 2 2/3 can be rewritten as an improper fraction as 8/3 .
Now that the mixed numbers have been written as improper fractions, the next step in the subtraction is to find the lowest common denominator.
The first number in both the 4 and 3 times table is 12. The least common denominator is 12.
We multiply the denominator and numerator of the first fraction by 3 and the second fraction by 4.
21/4 is rewritten as 63/12 .
8/3 is rewritten as 32/12 .
Now that the mixed numbers have been converted into improper fractions and the improper fractions now have common denominators, we can finally perform the subtraction.
The denominator remains the same and we subtract the numerators.
63/12 - 32/12 = 31/12 .
The final step is to write the improper fraction as a mixed number if necessary.
31 ÷ 12 = 2 remainder 7. We write the whole number down and the remainder as the numerator of the fraction.
The improper fraction of 31/12 is written as the mixed number of 2 7/12 . | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.977627694606781, "perplexity": 883.5216562474812}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334515.14/warc/CC-MAIN-20220925070216-20220925100216-00027.warc.gz"} |
https://www.juliafordatascience.com/first-steps-2-the-repl/ | # First Steps #2: The REPL
This is post #2 in our First Steps series. Want to learn Julia but don't know where to start? Start here!
## What is the REPL?
REPL stands for Read-Eval-Print-Loop. When you open Julia (double-click the icon or type julia in a terminal if you have it on your PATH), you'll enter Julia's REPL. You'll see something like this:
When you type something and press enter, Julia will take your input, evaluate it, and print the result, e.g. typing x = "Hello" and hitting enter will result in:
## REPL Modes
Julia's REPL has amazing modes that affect how Julia interprets your input. Here are the modes that are built-in:
### ? ➡ Help Mode 📖
Help Mode does a few things, best seen through example. Type ? to enter Help Mode. Then type println and press enter.
• The top line displays a fuzzy search of what you searched for. This will help you find items even if you mistype something.
• If your search term matches an existing identifier, the documentation for that identifier will print. In this example our search found the function println.
Press delete to go back to Julia mode and type x = 1. Now type ?x.
• Your search x matches with the x you just created. However, there is no documentation available, so a summary of x (its type information) is printed out instead. We'll talk about types in a future post.
This lets you run shell commands (as if you opened a terminal but didn't start Julia). A benefit of Julia's Shell Mode is that you can interpolate values into a command with $, e.g. ### ] ➡ Pkg Mode 📦 Pkg Mode lets you run commands with Julia's package manager (we'll cover this in-depth in a future post) . In the previous post we added packages with: using Pkg Pkg.add("StatsBase") Alternatively, we could have used Pkg Mode and entered add StatsBase instead 🎉! On a fresh install of Julia 1.6 you'll see something like: ### REPL Modes are extendable! 🔌 Julia packages can add their own REPL modes. Some examples are: • $RCall (interpret input as R)
• <Cxx (interpret intput as C++)
## Notable REPL Features
### Re-Run a Line
• Press the up key to display the previously-run command. Continue pressing up to go through your history.
• Press ctrl-r to activate a search of your history. Begin typing and the most recent line that contains your search will appear. You can continue pressing ctrl-r to move backwards through matching lines in your history and ctrl-s to move forward. If you've only run the commands seen in this and the previous post, typing x will then find the x = 1 line you entered earlier. Press enter to choose the matching line.
### The Value of the Previous Line
The Julia REPL stores the value of the previous line in a variable called ans.
### Tab-Completion
You can Auto-complete names, file paths, symbols, and emoji.
• Try typing prin and pressing tab. Your input will change to print. Now press tab again. Julia will show you that there are more identifiers available that also match with print.
• Julia can help you type out file/directory paths when you press tab inside of a string. For example, suppose you have a file at "/Users/<username>/file.csv". Typing "/Users/<username>/f" and then tab will autocomplete the f to file.csv (if it's the only file/directory that begins with f). If there are multiple matches, press tab again to display them.
• Try typing \pi and pressing tab. Your input will change to π ! 🎉
• Try typing \:smile: and pressing tab. Your input will change to 😄! Fun fact: This feature was introduced as an April Fool's Day joke but won traction in the Julia community. You can even use emoji as variables! There's no good reason to do this, but it's neat 🙃.
### Skip Printing
Sometime you may not want to display the return value of a line (e.g. the object prints a wall of text). You can always skip displaying an object by adding ; to the end of a line:
## That's It!
This is a high-level overview of the Julia REPL. It covers the things you'll need to know to get started with the REPL. If you want to go further into the weeds, check out the official docs here.
Next up is First Steps #3: Plots. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21693789958953857, "perplexity": 5541.9173595895845}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710777.20/warc/CC-MAIN-20221130225142-20221201015142-00333.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/7064-elementary-functions-solvable-group.html | # Math Help - Elementary Functions as a Solvable Group
1. ## Elementary Functions as a Solvable Group
I am not so happy with the defintion for a elementary function viewed as a finite number of combinations of addition, subtraction, multiplication, division and roots.
It sounds familar to the meaning of a "solutions by radicals" of a polynomial. Though it does has an alternate defintion, it is defined as a solvable group. Is there a way to define these functions also as some solvable group? The only thing I can think of is that the number of solutions to a polynomial is finite. Where the number of elementary functions is not. Thus, the compositions series does not exist. But if you can find one will it not make the proves based on showing there is no such elementary function simpler?
This is my 31th Post!!!
2. Originally Posted by ThePerfectHacker
I am not so happy with the defintion for a elementary function viewed as a finite number of combinations of addition, subtraction, multiplication, division and roots.
It sounds familar to the meaning of a "solutions by radicals" of a polynomial. Though it does has an alternate defintion, it is defined as a solvable group. Is there a way to define these functions also as some solvable group? The only thing I can think of is that the number of solutions to a polynomial is finite. Where the number of elementary functions is not. Thus, the compositions series does not exist. But if you can find one will it not make the proves based on showing there is no such elementary function simpler?
This is my 31th Post!!!
Just to get this straight, are you suggesting that we no longer consider the sine function elementary?
-Dan
3. Originally Posted by topsquark
Just to get this straight, are you suggesting that we no longer consider the sine function elementary?
-Dan
No, it is.
To be elementary we define a function as a finite sum difference multiplication division and composition of:
polynomials,trigonometric,inverse trigonometric, exponential, logarithmic.
4. I guess I was right there is such an area in mathematics.
Look Here. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8750512599945068, "perplexity": 269.83995285564635}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375096944.75/warc/CC-MAIN-20150627031816-00079-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://orange3-recommendation.readthedocs.io/en/latest/scripting/ranking.html | # Ranking (recommendation)¶
## CLiMF¶
CLiMF (Collaborative Less-is-More Filtering) is used in scenarios with binary relevance data. Hence, it’s focused on improving top-k recommendations through ranking by directly maximizing the Mean Reciprocal Rank (MRR).
Following a similar technique as other iterative approaches, the two low-rank matrices can be randomly initialize and then optimize through a training loss like this:
$F(U,V) = \sum _{ i=1 }^{ M }{ \sum _{ j=1 }^{ N }{ { Y }_{ ij }[\ln{\quad g({ U }_{ i }^{ T }V_{ i })} +\sum _{ k=1 }^{ N }{ \ln { (1-{ Y }_{ ik }g({ U }_{ i }^{ T }V_{ k }-{ U }_{ i }^{ T }V_{ j })) } } ] } } -\frac { \lambda }{ 2 } ({ \left\| U \right\| }^{ 2 }+{ \left\| V \right\| }^{ 2 })$
Note: Orange3 currently does not support ranking operations. Therefore, this model cannot be used neither in cross-validation nor in the prediction module available in Orange3
### Example¶
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 import Orange import numpy as np from orangecontrib.recommendation import CLiMFLearner # Load data data = Orange.data.Table('epinions_train.tab') # Train recommender learner = CLiMFLearner(num_factors=10, num_iter=10, learning_rate=0.0001, lmbda=0.001) recommender = learner(data) # Load test dataset testdata = Orange.data.Table('epinions_test.tab') # Sample users num_users = len(recommender.U) num_samples = min(num_users, 1000) # max. number to sample users_sampled = np.random.choice(np.arange(num_users), num_samples) # Compute Mean Reciprocal Rank (MRR) mrr, _ = recommender.compute_mrr(data=testdata, users=users_sampled) print('MRR: %.4f' % mrr) >>> MRR: 0.3975
class orangecontrib.recommendation.CLiMFLearner(num_factors=5, num_iter=25, learning_rate=0.0001, lmbda=0.001, preprocessors=None, optimizer=None, verbose=False, random_state=None, callback=None)[source]
CLiMF: Collaborative Less-is-More Filtering Matrix Factorization
This model uses stochastic gradient descent to find two low-rank matrices: user-feature matrix and item-feature matrix.
CLiMF is a matrix factorization for scenarios with binary relevance data when only a few (k) items are recommended to individual users. It improves top-k recommendations through ranking by directly maximizing the Mean Reciprocal Rank (MRR).
Attributes:
num_factors: int, optional
The number of latent factors.
num_iter: int, optional
The number of passes over the training data (aka epochs).
learning_rate: float, optional
The learning rate controlling the size of update steps (general).
lmbda: float, optional
Controls the importance of the regularization term (general). Avoids overfitting by penalizing the magnitudes of the parameters.
optimizer: Optimizer, optional
Set the optimizer for SGD. If None (default), classical SGD will be applied.
verbose: boolean or int, optional
Prints information about the process according to the verbosity level. Values: False (verbose=0), True (verbose=1) and INTEGER
random_state: int, optional
Set the seed for the numpy random generator, so it makes the random numbers predictable. This a debbuging feature.
callback: callable
fit_storage(data)[source]
Fit the model according to the given training data.
Args:
data: Orange.data.Table
Returns:
self: object
Returns self. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19773799180984497, "perplexity": 9455.50131310955}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178370752.61/warc/CC-MAIN-20210305091526-20210305121526-00177.warc.gz"} |
http://cmup.fc.up.pt/main/content/quadric-bundles-and-their-moduli-spaces | Quadric bundles and their moduli spaces
Title Quadric bundles and their moduli spaces Publication Type Preprint Year of Preprint 2016 Authors Oliveira A. Abstract We consider quadric bundles on a compact Riemann surface X. These generalise orthogonal bundles and arise naturally in the study of the moduli space of representations of \pi_1(X) in Sp(2n,R). We prove some basic results on the moduli spaces of quadric bundles over X of arbitrary rank and survey deeper results about these moduli spaces, for rank 2. [2016-10]
Geometry | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.995516300201416, "perplexity": 746.637097826414}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818686983.8/warc/CC-MAIN-20170920085844-20170920105844-00450.warc.gz"} |
http://iloctech.com/nabil-elouahabi-mupsg/6922e5-perceptron-convergence-theorem-ques10 | m[��]�sv��,�L�Ӥ!s�'�F�{�>����֨��1�>�� �0N1Š�� 1415–1442, (1990). Algorithms: Discrete and Continuous Perceptron Networks, Perceptron Convergence theorem, Limitations of the Perceptron Model, Applications. 0000009440 00000 n , zp ... Q NA RMA recurrent perceptron, convergence towards a point in the FPI sense does not depend on the number of external input signals (i.e. Fig. Convergence Theorem: if the training data is linearly separable, the algorithm is guaranteed to converge to a solution. /10 be such that-1 "/, Then Perceptron makes at most 243658795:3; 3 mistakes on this example sequence. << /BBox [ 0 0 612 792 ] /Filter /FlateDecode /FormType 1 /Matrix [ 1 0 0 1 0 0 ] /Resources << /Font << /F34 311 0 R /F35 283 0 R >> /ProcSet [ /PDF /Text ] >> /Subtype /Form /Type /XObject /Length 866 >> 0000063075 00000 n Unit- IV: Multilayer Feed forward Neural Networks Credit Assignment Problem, Generalized Delta Rule, Derivation of Backpropagation (BP) Training, Summary of Backpropagation Algorithm, Kolmogorov Theorem, Learning Difficulties and … Assume D is linearly separable, and let be w be a separator with \margin 1". Logical functions are a great starting point since they will bring us to a natural development of the theory behind the perceptron and, as a consequence, neural networks. 0000004302 00000 n When the set of training patterns is linearly non-separable, then for any set of weights, W. there will exist some training example. << /Ascent 668 /CapHeight 668 /CharSet (/A/L/M/P/one/quoteright/seven) /Descent -193 /Flags 4 /FontBBox [ -169 -270 1010 924 ] /FontFile 286 0 R /FontName /TVDNNQ+NimbusRomNo9L-ReguItal /ItalicAngle -15 /StemV 78 /Type /FontDescriptor /XHeight 441 >> %PDF-1.4 << /Annots [ 289 0 R 290 0 R 291 0 R 292 0 R 293 0 R 294 0 R 295 0 R 296 0 R 297 0 R 298 0 R 299 0 R 300 0 R 301 0 R 302 0 R 303 0 R 304 0 R ] /Contents [ 287 0 R 307 0 R 288 0 R ] /MediaBox [ 0 0 612 792 ] /Parent 257 0 R /Resources << /ExtGState 306 0 R /Font 305 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] /XObject << /Xi0 282 0 R >> >> /Type /Page >> Symposium on the Mathematical Theory of Automata, 12, 615–622. Perceptron Convergence Due to Rosenblatt (1958). The corresponding test must be introduced in the above pseudocode to make it stop and to transform it into a fully-fledged algorithm. Proof. 0000062734 00000 n I will not develop such proof, because involves some advance mathematics beyond what I want to touch in an introductory text. 0000038487 00000 n << /BaseFont /TVDNNQ+NimbusRomNo9L-ReguItal /Encoding 312 0 R /FirstChar 39 /FontDescriptor 285 0 R /LastChar 80 /Subtype /Type1 /Type /Font /Widths 284 0 R >> 0000011051 00000 n xref NOT logical function. 0000017806 00000 n 282 0 obj Introduction: The Perceptron Haim Sompolinsky, MIT October 4, 2013 1 Perceptron Architecture The simplest type of perceptron has a single layer of weights connecting the inputs and output. 6.c Delta Learning Rule (5 marks) 00. Step size = 1 can be used. 0000037666 00000 n 6.d McCulloh Pitts neuron model (5 marks) 00. question paper mumbai university (mu) • 2.3k views. 0000008943 00000 n Pages 43–50. << /Filter /FlateDecode /Length1 1647 /Length2 2602 /Length3 0 /Length 3406 >> 0000010275 00000 n Polytechnic Institute of Brooklyn. The routine can be stopped when all vectors are classified correctly. ���7�[s�8M�p� ���� �~��{�6m7 ��� E�J��̸H�u����s��0�?he7��:@l:3>�DŽ��r�y�>�¯�Â�Z�(x�< 0000009939 00000 n stream Collins, M. 2002. visualization in open space. 0000047049 00000 n 0000010605 00000 n Theorem: Suppose data are scaled so that kx ik 2 1. Let’s start with a very simple problem: Can a perceptron implement the NOT logical function? Perceptron convergence. 0000073290 00000 n 0000047745 00000 n 0000021688 00000 n Perceptron Convergence Theorem [ 41. Másképpen fogalmazva: 2.1.2 Tétel: perceptron konvergencia tétel: Legyen The perceptron convergence theorem guarantees that if the two sets P and N are linearly separable the vector w is updated only a finite number of times. If PCT holds, then: jj1 T P T t=1 v tjj˘O(1=T). And explains the convergence theorem of perceptron and its proof. endobj endobj Download our mobile app and study on-the-go. Convergence Proof for the Perceptron Algorithm Michael Collins Figure 1 shows the perceptron learning algorithm, as described in lecture. Widrow, B., Lehr, M.A., "30 years of Adaptive Neural Networks: Perceptron, Madaline, and Backpropagation," Proc. 0000010440 00000 n ADD COMMENT Continue reading. 0000018412 00000 n 0000010772 00000 n Let-. << /Metadata 276 0 R /Outlines 258 0 R /PageLabels << /Nums [ 0 << /P () >> ] >> /Pages 257 0 R /Type /Catalog >> Theory and Examples 4-2 Learning Rules 4-2 Perceptron Architecture 4-3 Single-Neuron Perceptron 4-5 Multiple-Neuron Perceptron 4-8 Perceptron Learning Rule 4-8 Test Problem 4-9 Constructing Learning Rules 4-10 Unified Learning Rule 4-12 Training Multiple-Neuron Perceptrons 4-13 Proof of Convergence 4-15 Notation 4-15 Proof 4-16 Limitations 4-18 Summary of Results 4-20 Solved … IEEE, vol 78, no 9, pp. 0000004570 00000 n 0000065821 00000 n That is, there exist a finite such that : = 0: Statistical Machine Learning (S2 2017) Deck 6: Perceptron convergence theorem • Assumptions ∗Linear separability: There exists ∗ so that : : ∗′ p-the AR part of the NARMA (p,q) process (411, nor on their values, QS long QS they are finite. You'll get subjects, question papers, their solution, syllabus - All in one app. ��z��p�B[����� �M���]�-p�ϐ�Su��./ْ��-KL�b�0��|g}�[(n���E��Z��_���X�f�����,zt:�^[ 4�ۊZ�Hxh)mNI ��q"k��?�?���2���Q�D�����RW�;e;}��1ʟge��BE0�� ��B]����lr�W������u�dAkB�oLJ��7��\���E��'�ͨ�0V���M#� �ֲ9�ߢ�Zpl,(R2�P �����˘w������endstream 0000020876 00000 n 0000010107 00000 n x�mUK��6��W�P���HJ��� �Alߒh���X���n��;�P^o�0�y�y���)��_;�e@���Q���l �u"j�r�t�.�y]�DF+�4��*�Y6���Nx�0AIU�d�'_�m㜙�,/�:��A}�M5J�9�.(L�Y��n��v�zD�.?�����.�lb�S8k��P:^C�u�xs��PZ. It's the best way to discover useful content. Sengupta, Department of Electronics and Electrical Communication Engineering, IIT Kharagpur. Frank Rosenblatt invented the perceptron algorithm in 1957 as part of an early attempt to build brain models'', artificial neural networks. 0000000015 00000 n Verified perceptron convergence theorem. ABSTRACT. Previous Chapter Next Chapter. The PCT immediately leads to the following result: Convergence Theorem. 0000010937 00000 n stream endobj . Definition of perceptron. Find answer to specific questions by searching them here. 0000008171 00000 n 279 0 obj Mumbai University > Computer Engineering > Sem 7 > Soft Computing. << /Linearized 1 /L 287407 /H [ 1812 637 ] /O 281 /E 73886 /N 8 /T 281727 >> 0000040138 00000 n Obviously, the author was looking at the materials from multiple different sources but did not generalize it very well to match his proceeding writings in the book. 0000009108 00000 n NOT(x) is a 1-variable function, that means that we will have one input at a time: N=1. The Winnow algorithm [4] has a very similar structure. On the other hand, it is possible to construct an additive algorithm that never makes more than N + 0( klog N) mistakes. 0000020703 00000 n (large margin = very The famous Perceptron Convergence Theorem [6] bounds the number of mistakes which the Perceptron algorithm can make: Theorem 1 Let be a sequence of labeled examples with! It's the best way to discover useful content. 278 0 obj The Perceptron learning algorithm has been proved for pattern sets that are known to be linearly separable. Perceptron algorithm is used for supervised learning of binary classification. PERCEPTRON CONVERGENCE THEOREM: Says that there if there is a weight vector w*such that f(w*p(q)) = t(q) for all q, then for any starting vector w, the perceptron learning rule will converge to a weight vector (not necessarily unique and not necessarily w*) that gives the correct response for all training patterns, and it will do so in a finite number of steps. D lineárisan szeparálható X 0 és X 1 halmazokra, hogyha: ahol ’’ a skaláris szorzás felett. Lecture Notes: http://www.cs.cornell.edu/courses/cs4780/2018fa/lectures/lecturenote03.html input x = $( I_1, I_2, I_3) = ( 5, 3.2, 0.1 ).$, Summed input $$= \sum_i w_iI_i = 5 w_1 + 3.2 w_2 + 0.1 w_3$$. endobj 0000009274 00000 n "# % & and (') +* for all,. ��@4���* ���"����2"�JA�!��:�"��IŢ�[�)D?�CDӶZ���� ��Aԭ\� ��($���Hdh�"����@�Qd�P�{�v~� �K�( Gߎ&n{�UD��8?E.U8'� Xk, such that Wk misclassifies Xk. Like all structured prediction learning frameworks, the structured perceptron can be costly to train as training complexity is proportional to inference, which is frequently non-linear in example sequence length. 8t 0: If wT tv 0, then there exists a constant M>0 such that kw t w 0k�m�8,���ǚ��@�a&��4)��&&E��#�[�AY�'=��ٮ�����cs��� 2 Perceptron konvergencia tétel 2.1 A tétel kimondása 2.1.1 Definíció: lineáris szeparálhatóság (5) Legyen . << /Filter /FlateDecode /S 383 /O 610 /Length 549 >> 0000073517 00000 n 6.b Binary Hopfield Network (5 marks) 00. , y(k - q + l), l,q,. [ 333 333 333 500 675 250 333 250 278 500 500 500 500 500 500 500 500 500 500 333 333 675 675 675 500 920 611 611 667 722 611 611 722 722 333 444 667 556 833 667 722 611 ] When the set of training patterns is linearly non-separable, then for any set of weights, W. there will exist some training example. 0000066348 00000 n Convergence. endobj endobj 0000041214 00000 n 0000008279 00000 n ��*r�� Yֈ_|��f����a?� S�&C+���X�l�\� ��w�LNf0_�h��8Er�A� ���s�a�q�� ����d2��a^����|H� 021�X� 2�8T 3�� 0000008609 00000 n 0000009773 00000 n 285 0 obj Legyen D két diszjunkt részhalmaza X 0 és X 1 (azaz ). By formalizing and proving perceptron convergence, we demon-strate a proof-of-concept architecture, using classic programming languages techniques like proof by refinement, by which further machine-learning algorithms with sufficiently developed metatheory can be implemented and verified. %���� 0000018127 00000 n 0000065914 00000 n It is immediate from the code that should the algorithm terminate and return a weight vector, then the weight vector must separate the points from the points. No such guarantees exist for the linearly non-separable case because in weight space, no solution cone exists. Chapters 1–10 present the authors' perceptron theory through proofs, Chapter 11 involves learning, Chapter 12 treats linear separation problems, and Chapter 13 discusses some of the authors' thoughts on simple and multilayer perceptrons and pattern recognition. 0000063410 00000 n ��D��*��P�Ӹ�Ï��m�*B��*����ʖ� γ • The perceptron algorithm is trying to find a weight vector w that points roughly in the same direction as w*. Perceptron algorithm in a fresh light: the language of dependent type theory as implemented in Coq (The Coq Development Team 2016). 0000039694 00000 n the data is linearly separable), the perceptron algorithm will converge. 0000008089 00000 n Subject: Electrical Courses: Neural Network and Applications. The proof that the perceptron will find a set of weights to solve any linearly separable classification problem is known as the perceptron convergence theorem. 0000040698 00000 n x�c�gacP�d�0����dٙɨQ��aKM��I����a'����t*Ȧ�I�?p��\����d���&jg�Yo�U٧����_X�5�k��������n9��]z�B^��g���|b�ʨ���oH:9�m�\�J����_.�[u�M�ּg���_�����"��F�\��\2�� Formally, the perceptron is defined by y = sign(PN i=1 wixi ) or y = sign(wT x ) (1) where w is the weight vector and is the threshold. %%EOF Consequently, the Perceptron learning algorithm will continue to make weight changes indefinitely. The theorem still holds when V is a finite set in a Hilbert space. 278 64 0000009606 00000 n trailer << /Info 277 0 R /Root 279 0 R /Size 342 /Prev 281717 /ID [<58ec75fda24c432cc812dba252618c1f><1aefbf0404691781113e5401cf827802>] >> 8���:�{��5�>k 6ں��V�O��;�K�����r�w�{���r K2�������i���qs�a o��h�)�]@��������*8c֝ ��"��G"�� The Perceptron learning algorithm has been proved for pattern sets that are known to be linearly separable. We also show that the Perceptron algorithm in its basic form can make 2k( N - k + 1) + 1 mistakes, so the bound is essentially tight. 0000003936 00000 n I found the authors made some errors in the mathematical derivation by introducing some unstated assumptions. 6.a Explain perceptron convergence theorem (5 marks) 00. 0000011087 00000 n ���\J[�bI�#*����O,$o_������E�0D�@?.%;"N ��w*+�}"� �-�-��o���ѿ. 0000002449 00000 n I was reading the perceptron convergence theorem, which is a proof for the convergence of perceptron learning algorithm, in the book “Machine Learning - An Algorithmic Perspective” 2nd Ed. Rosenblatt’s Perceptron Convergence Theorem γ−2 γ > 0 x ∈ D The idea of the proof: • If the data is linearly separable with margin , then there exists some weight vector w* that achieves this margin. By formalizing and proving perceptron convergence, we demon-strate a proof-of-concept architecture, using classic programming languages techniques like proof by refinement, by which further machine-learning algorithms with sufficiently developed metatheory can be implemented and verified. 0000047161 00000 n Lecture Series on Neural Networks and Applications by Prof.S. ۘ��Ħ�����ɜ��ԫU��d�������T2���-�~a��h����l�uq��r���=�����)������ 0000002830 00000 n This post is the summary of “Mathematical principles in Machine Learning” The perceptron convergence theorem was proved for single-layer neural nets. . endstream Perceptron convergence theorem COMP 652 - Lecture 12 9 / 37 The perceptron convergence theorem states that if the perceptron learning rule is applied to a linearly separable data set, a solution will be found after some finite number of updates. 0000039169 00000 n 0000001812 00000 n 0000021215 00000 n endobj 0000073192 00000 n startxref Perceptron Cycling Theorem (PCT). . Find more. 0 Explain the perceptron learning with example. 0000056654 00000 n xڭTgXTY�DAT���Cɱ�Cjr�i�/��N_�%��� J�"%6(iz�I�QA��^pg��������~꭪��)�_��0D_I$PT�u ;�K�8�vD���#�O���p �ipIK��A"LQTPp1�)�TU�% �It2䏥�.�nr���~X�\ _��I�� ��# �Ix�@�)��@'�X��p b��aigȚ۹ �$�M8�|q��� ��~D2��~ �D�j��sQ @!�h�� i:�@2�P�o � �d� 0000008444 00000 n 3�#0���o�9L�5��whƢ���a�F=n�� According to the perceptron convergence theorem, the perceptron learning rule guarantees to find a solution within a finite number of steps if the provided data set is linearly separable. I then tried to look up the right derivation on the i… 283 0 obj 0000008776 00000 n 0000040791 00000 n The Perceptron Convergence Theorem is, from what I understand, a lot of math that proves that a perceptron, given enough time, will always be able to find a … Winnow maintains … Then the perceptron algorithm will converge in at most kw k2 epochs. 0000001681 00000 n You must be logged in to read the answer. . �C��� lJ� 3 Theorem 3 (Perceptron convergence). No such guarantees exist for the linearly non-separable case because in weight space, no solution cone exists. endobj 284 0 obj [We’re not going to prove this, because perceptrons are obsolete.] 0000056131 00000 n 281 0 obj The Perceptron Learning Algorithm makes at most R2 2 updates (after which it returns a separating hyperplane). 0000040630 00000 n In this post, it will cover the basic concept of hyperplane and the principle of perceptron based on the hyperplane. 0000063827 00000 n 286 0 obj Convergence Convergence theorem –If there exist a set of weights that are consistent with the data (i.e. Perceptron Convergence Theorem: If data is linearly separable, perceptron algorithm will find a linear classifier that classifies all data correctly in at most O(R2/2) iterations, where R = max|X i| is “radius of data” and is the “maximum margin.” [I’ll define “maximum margin” shortly.] 0000056022 00000 n stream 0000004113 00000 n For the Perceptron learning algorithm, as described in lecture it stop and to transform it into a algorithm! 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D két diszjunkt részhalmaza X 0 és X 1 halmazokra, hogyha perceptron convergence theorem ques10 ’., l, q, be w be a separator with \margin 1 '' because... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.850111722946167, "perplexity": 4103.766674336016}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038061820.19/warc/CC-MAIN-20210411085610-20210411115610-00040.warc.gz"} |
https://worldwidescience.org/topicpages/s/surrounding+agricultural+fields.html | #### Sample records for surrounding agricultural fields
1. Radiofrequency fields in our surroundings
International Nuclear Information System (INIS)
2011-01-01
In 2010, the National Radiation Protection Authority (NRPA) with the Post and Telecommunications Authority carried out a project where it is measured radiofrequency fields from various telecom systems in homes, kindergartens, schools, offices, and urban environments. Close to 99 percent of the measurement points were found values of less than one thousandth of the maximum. No values were near the limits. (AG)
2. INTERSTELLAR MAGNETIC FIELD SURROUNDING THE HELIOPAUSE
International Nuclear Information System (INIS)
Whang, Y. C.
2010-01-01
This paper presents a three-dimensional analytical solution, in the limit of very low plasma β-ratio, for the distortion of the interstellar magnetic field surrounding the heliopause. The solution is obtained using a line dipole method that is the integration of point dipole along a semi-infinite line; it represents the magnetic field caused by the presence of the heliopause. The solution allows the variation of the undisturbed magnetic field at any inclination angle. The heliosphere is considered as having blunt-nosed geometry on the upwind side and it asymptotically approaches a cylindrical geometry having an open exit for the continuous outflow of the solar wind on the downwind side. The heliopause is treated as a magnetohydrodynamic tangential discontinuity; the interstellar magnetic field lines at the boundary are tangential to the heliopause. The interstellar magnetic field is substantially distorted due to the presence of the heliopause. The solution shows the draping of the field lines around the heliopause. The magnetic field strength varies substantially near the surface of the heliopause. The effect on the magnetic field due to the presence of the heliopause penetrates very deep into the interstellar space; the depth of penetration is of the same order of magnitude as the scale length of the heliosphere.
3. A Study of the Flow Field Surrounding Interacting Line Fires
Directory of Open Access Journals (Sweden)
Trevor Maynard
2016-01-01
Full Text Available The interaction of converging fires often leads to significant changes in fire behavior, including increased flame length, angle, and intensity. In this paper, the fluid mechanics of two adjacent line fires are studied both theoretically and experimentally. A simple potential flow model is used to explain the tilting of interacting flames towards each other, which results from a momentum imbalance triggered by fire geometry. The model was validated by measuring the velocity field surrounding stationary alcohol pool fires. The flow field was seeded with high-contrast colored smoke, and the motion of smoke structures was analyzed using a cross-correlation optical flow technique. The measured velocities and flame angles are found to compare reasonably with the predicted values, and an analogy between merging fires and wind-blown flames is proposed.
Energy Technology Data Exchange (ETDEWEB)
2011-07-01
In 2010, the National Radiation Protection Authority (NRPA) with the Post and Telecommunications Authority carried out a project where it is measured radiofrequency fields from various telecom systems in homes, kindergartens, schools, offices, and urban environments. Close to 99 percent of the measurement points were found values of less than one thousandth of the maximum. No values were near the limits. (AG)
5. Bienvenidos a Canadá? Globalization and the Migration Industry Surrounding Temporary Agricultural Migration in Canada
Directory of Open Access Journals (Sweden)
Jenna L. Hennebry
2008-12-01
participant observation in Ontario, and interviews with migrant workers and their families, farmers, government representatives and other intermediaries, this paper examines the extent to which a migration industry has formed around the Mexican-Canadian Seasonal Agricultural Worker Program.
6. Earthworm communities in arable fields and restored field margins, as related to management practices and surrounding landscape diversity
NARCIS (Netherlands)
Frazão, Joana; Goede, de Ron G.M.; Brussaard, Lijbert; Faber, Jack H.; Groot, Jeroen C.J.; Pulleman, Mirjam M.
2017-01-01
Agricultural intensification has negative impacts on biodiversity at spatial scales from field to landscape. Earthworms are important for soil functioning, so it is crucial to understand the responses of earthworm communities to agricultural management and land use. We aimed to: 1) investigate
7. Quality evaluation of commercially sold table water samples in Michael Okpara University of Agriculture, Umudike, Nigeria and surrounding environments
Directory of Open Access Journals (Sweden)
D.O. Okorie
2015-01-01
Full Text Available In Michael Okpara University of Agriculture, Umudike, Nigeria (MOUAU and surrounding environments, table water of different brands is commercially hawked by vendors. To the best of our knowledge, there is no scientific documentation on the quality of these water samples. Hence this study which evaluated the quality of different brands of water samples commercially sold in MOUAU and surrounding environments. The physicochemical properties (pH, total dissolved solids (TDS, biochemical oxygen demand (BOD, total hardness, dissolved oxygen, Cl, NO3, ammonium nitrogen (NH3N, turbidity, total suspended solids (TSS, Ca, Mg, Na and K of the water samples as indices of their quality were carried out using standard techniques. Results obtained from this study indicated that most of the chemical constituents of these table water samples commercially sold in Umudike environment conformed to the standards given by the Nigerian Industrial Standard (NIS, World Health Organization (WHO and American Public Health Association (APHA, respectively, while values obtained for ammonium nitrogen in these water samples calls for serious checks on methods of their production and delivery to the end users.
8. Fog in a marginal agricultural area surrounded by montane Andean cloud forest during El Niño climate
Science.gov (United States)
García-Santos, G.
2010-07-01
The aim of the present study was to evaluate temporal variations of water inputs, rainfall and fog (cloud water), and its contribution to the water balance in a marginal agricultural area of potato surrounded by tropical montane cloud forest in Colombia. Fog in the air boundary layer was estimated using a cylindrical fog collector. Liquid water content of fog events were evaluated before and during natural climate event of El Niño. Our study shows the temporal variation of these two water inputs in both daily and monthly cycles on Boyacá at 2900 m a.s.l. Rainfall was the most frequently observed atmospheric phenomenon, being present on average 62% of the days per year, whereas fog was 45% of the time. Reflected on the lower frequency, annual amount of fog was 11% of precipitation. However during the anomalous dry climate of El Niño, total amount of rainfall was negligible and the few fog events were the only water source for plant growth. Estimated water crop requirements were higher than the water inputs. The survival of the crops was explained by meteorological conditions during dew and fog events. High relative humidity might have eased the plant’s water stress by decreasing transpiration and temperature in leaves and soil, affecting the water balance and the heat exchange between the atmosphere-land interfaces in the marginal agricultural areas during exceptional dry climate.
9. Agricultural field reclamation utilizing native grass crop production
Science.gov (United States)
J. Cure
2013-01-01
Developing a method of agricultural field reclamation to native grasses in the Lower San Pedro Watershed could prove to be a valuable tool for educational and practical purposes. Agricultural field reclamation utilizing native grass crop production will address water table depletion, soil degradation and the economic viability of the communities within the watershed....
10. Creating optimized machine working patterns on agricultural fields
OpenAIRE
Mark Spekken
2015-01-01
In the current agricultural context, agricultural machine unproductivity on fields and their impacts on soil along pathways are unavoidable. These machines have direct and indirect costs associated to their work in field, with non-productive time spent in manoeuvres when these are reaching field borders; likewise, there is a double application of product when machines are covering headlands while adding farm inputs. Both issues aggravate under irregular field geometry. Moreover, unproductive ...
11. Investigations of Flare Gas Emissions in Taq Taq Oil Field on the Surrounding Land
Directory of Open Access Journals (Sweden)
Jafar A. Ali
2014-11-01
Full Text Available Environmental pollution caused by oil takes many different forms; one of the most damaging sources is simply the combustion of oil products, such as a well flare burn-off. This paper presents the results of a survey of the agriculture lands around the Taq Taq Oil Production Company. The aim of the survey was to determine the potential contamination caused by the gas emissions from the well flares. Taq Taq field is located in the Kurdistan Region of Iraq, 60 km north of the giant Kirkuk oil field, 85 km south-east of Erbil and 120 km north-west of Suleimani. Samples of soil were collected from several locations around the site and analyzed to determine the content of Polycyclic Aromatic Hydrocarbons PAH present. A gas chromatography linked to a mass spectrometry (GCMS machine was used for these measurements. The PAH contamination at each location of soil was determined and the 16-PAHs, as listed in the US Environmental Protection Agency (EPA documentation were investigated. The average content of total PAH in all samples of the agricultural soil was 0.654 mg·kg-1 with the concentrations ranging from 0.310 to 0.869 mg·kg-1. It was found that the PAH concentrations decreased with increasing distance from the TTOPCO oil field, indicating that pollution was evident, the area close to the field being more affected by the gas pollution.
12. A method of detecting a structure in a field, a method of steering an agricultural vehicle and an agricultural vehicle
DEFF Research Database (Denmark)
2011-01-01
An agricultural vehicle (2) comprises a steering system providing steering signals, said steering system comprising an imaging device (11) for imaging surroundings of the vehicle and an image processing device (13), said steering system operating to provide by means of the imaging device (11......) an image of the field (21), analyse the image to obtain texture information, assign to a plurality of areas of the image probability-values reflecting the likelihood that the respective area relates to a specific structure (12), assume at least one geometric property of said specific structure (12...
13. Attention operates uniformly throughout the classical receptive field and the surround
Science.gov (United States)
Verhoef, Bram-Ernst; Maunsell, John HR
2016-01-01
Shifting attention among visual stimuli at different locations modulates neuronal responses in heterogeneous ways, depending on where those stimuli lie within the receptive fields of neurons. Yet how attention interacts with the receptive-field structure of cortical neurons remains unclear. We measured neuronal responses in area V4 while monkeys shifted their attention among stimuli placed in different locations within and around neuronal receptive fields. We found that attention interacts uniformly with the spatially-varying excitation and suppression associated with the receptive field. This interaction explained the large variability in attention modulation across neurons, and a non-additive relationship among stimulus selectivity, stimulus-induced suppression and attention modulation that has not been previously described. A spatially-tuned normalization model precisely accounted for all observed attention modulations and for the spatial summation properties of neurons. These results provide a unified account of spatial summation and attention-related modulation across both the classical receptive field and the surround. DOI: http://dx.doi.org/10.7554/eLife.17256.001 PMID:27547989
14. Theory of the detection of the field surrounding half-dressed sources
International Nuclear Information System (INIS)
Compagno, G.; Passante, R.; Persico, F.
1988-01-01
Half-dressed sources are defined as sources deprived partially or totally of the cloud of virtual quanta which surrounds them in the ground state of the total system. Two models of a half-dressed point source S are considered, the first in the framework of the theory of massive scalar fields and the second in quantum electrodynamics (QED). In both cases the detector is modeled by a second fully dressed source T of the same field, which is also bound to an oscillation center by harmonic forces. It is shown that when S at time t = 0 is suddenly coupled to or decoupled from the field, the detector T, which is initially at rest, is set in motion after a time t = R 0 /c, where R 0 is the S-T distance. Neglecting the reaction back on the field due to the oscillatory motion of T, the amplitude of oscillation for t = ∞ is obtained as a function of R 0 . Thus the time-varying virtual field of S is shown to be capable of exerting a force which excites the model detector. For the QED case, this force is related to the properties of the energy density of the virtual field. This energy density displays a singularity at r = ct, and the mathematical nature of this singularity is studied in detail. In this way it is shown that the energy density of the time-dependent virtual field is rather different from that of a pulse of radiation emitted by a source during energy-conserving processes. The differences are discussed in detail, as well as the limitations of the model
15. Deformation-strain field in Sichuan and its surrounding areas based on GPS data
Directory of Open Access Journals (Sweden)
Fuchao Chen
2015-05-01
Full Text Available The strain rate in Sichuan and its surrounding areas, and the activity rate and strain rate in two block boundary fault zones were calculated according to the block movement parameters estimated using the station speed obtained from regional GPS station observation data in these areas for 2009–2011 and GPS continuous station data for 2011–2013. The movement field characteristics in these areas were analyzed with the Sichuan Basin as the reference. Results show that the principal strain rate and maximum shear strain rate of the Bayan Har block were the largest, followed by those of the Sichuan–Yunnan block and Sichuan Basin. The deep normal strain rate in the Longmenshan fault zone was compressive and large over the study period. The normal strain rate in the Xianshuihe fault zone was tensile.
16. Fungal biology and agriculture: revisiting the field
Science.gov (United States)
Yarden, O.; Ebbole, D.J.; Freeman, S.; Rodriguez, R.J.; Dickman, M. B.
2003-01-01
Plant pathology has made significant progress over the years, a process that involved overcoming a variety of conceptual and technological hurdles. Descriptive mycology and the advent of chemical plant-disease management have been followed by biochemical and physiological studies of fungi and their hosts. The later establishment of biochemical genetics along with the introduction of DNA-mediated transformation have set the stage for dissection of gene function and advances in our understanding of fungal cell biology and plant-fungus interactions. Currently, with the advent of high-throughput technologies, we have the capacity to acquire vast data sets that have direct relevance to the numerous subdisciplines within fungal biology and pathology. These data provide unique opportunities for basic research and for engineering solutions to important agricultural problems. However, we also are faced with the challenge of data organization and mining to analyze the relationships between fungal and plant genomes and to elucidate the physiological function of pertinent DNA sequences. We present our perspective of fungal biology and agriculture, including administrative and political challenges to plant protection research.
17. μ-PIV measurements of the ensemble flow fields surrounding a migrating semi-infinite bubble.
Science.gov (United States)
Yamaguchi, Eiichiro; Smith, Bradford J; Gaver, Donald P
2009-08-01
Microscale particle image velocimetry (μ-PIV) measurements of ensemble flow fields surrounding a steadily-migrating semi-infinite bubble through the novel adaptation of a computer controlled linear motor flow control system. The system was programmed to generate a square wave velocity input in order to produce accurate constant bubble propagation repeatedly and effectively through a fused glass capillary tube. We present a novel technique for re-positioning of the coordinate axis to the bubble tip frame of reference in each instantaneous field through the analysis of the sudden change of standard deviation of centerline velocity profiles across the bubble interface. Ensemble averages were then computed in this bubble tip frame of reference. Combined fluid systems of water/air, glycerol/air, and glycerol/Si-oil were used to investigate flows comparable to computational simulations described in Smith and Gaver (2008) and to past experimental observations of interfacial shape. Fluorescent particle images were also analyzed to measure the residual film thickness trailing behind the bubble. The flow fields and film thickness agree very well with the computational simulations as well as existing experimental and analytical results. Particle accumulation and migration associated with the flow patterns near the bubble tip after long experimental durations are discussed as potential sources of error in the experimental method.
18. μ-PIV measurements of the ensemble flow fields surrounding a migrating semi-infinite bubble
Science.gov (United States)
Yamaguchi, Eiichiro; Smith, Bradford J.; Gaver, Donald P.
2012-01-01
Microscale particle image velocimetry (μ-PIV) measurements of ensemble flow fields surrounding a steadily-migrating semi-infinite bubble through the novel adaptation of a computer controlled linear motor flow control system. The system was programmed to generate a square wave velocity input in order to produce accurate constant bubble propagation repeatedly and effectively through a fused glass capillary tube. We present a novel technique for re-positioning of the coordinate axis to the bubble tip frame of reference in each instantaneous field through the analysis of the sudden change of standard deviation of centerline velocity profiles across the bubble interface. Ensemble averages were then computed in this bubble tip frame of reference. Combined fluid systems of water/air, glycerol/air, and glycerol/Si-oil were used to investigate flows comparable to computational simulations described in Smith and Gaver (2008) and to past experimental observations of interfacial shape. Fluorescent particle images were also analyzed to measure the residual film thickness trailing behind the bubble. The flow fields and film thickness agree very well with the computational simulations as well as existing experimental and analytical results. Particle accumulation and migration associated with the flow patterns near the bubble tip after long experimental durations are discussed as potential sources of error in the experimental method. PMID:23049158
19. Collisional flow of vibrational energy into surrounding vibrational fields within S1 benzene
International Nuclear Information System (INIS)
Tang, K.Y.; Parmenter, C.S.
1983-01-01
Vapor phase fluorescence spectra are used to determine the absolute rate constants for the collisional transfer of vibrational energy from initial single vibronic levels of S 1 benzene into the surrounding S 1 vibronic field. 11 initial levels are probed with vibrational energies ranging to 2368 cm -1 where the level density is about 10 per cm -1 . CO, isopentane, and S 0 benzene are the collision partners. Benzene rate constants are three to four times gas kinetic for all levels, and electronic energy switching between the initial S 1 molecule and the S 0 collision partner probably makes important contributions. Isopentane efficiencies range from one to two times gas kinetic. Most of the transfer from low S 1 levels occurs with excitation of vibrational energy within isopentane. These V--V contributions decline to only about 10% for the high transfer. CO-induced transfer is by V-T,R processes for all levels. The CO efficiency rises from about 0.1 for low regions to about unity for levels above 1500 cm -1 . The CO efficiencies retain significant sensitivity to initial level identity even in the higher regions. Propensity rules derived from collisional mode-to-mode transfer among lower levels of S 1 benzene are used to calculate the relative CO efficiencies. The calculated efficiencies agree well enough with the data to suggest that it may be meaningful to model vibrational equilibration with the use of propensity rules. The rules suggest that only a small number of levels among the thousands surrounding a high initial level contribute significantly to the total relaxation cross section and that this number is rather independent of the level density
20. A contemporary decennial global sample of changing agricultural field sizes
Science.gov (United States)
White, E.; Roy, D. P.
2011-12-01
In the last several hundred years agriculture has caused significant human induced Land Cover Land Use Change (LCLUC) with dramatic cropland expansion and a marked increase in agricultural productivity. The size of agricultural fields is a fundamental description of rural landscapes and provides an insight into the drivers of rural LCLUC. Increasing field sizes cause a subsequent decrease in the number of fields and therefore decreased landscape spatial complexity with impacts on biodiversity, habitat, soil erosion, plant-pollinator interactions, diffusion of disease pathogens and pests, and loss or degradation in buffers to nutrient, herbicide and pesticide flows. In this study, globally distributed locations with significant contemporary field size change were selected guided by a global map of agricultural yield and literature review and were selected to be representative of different driving forces of field size change (associated with technological innovation, socio-economic conditions, government policy, historic patterns of land cover land use, and environmental setting). Seasonal Landsat data acquired on a decadal basis (for 1980, 1990, 2000 and 2010) were used to extract field boundaries and the temporal changes in field size quantified and their causes discussed.
1. Extending results from agricultural fields with intensively monitored data to surrounding areas for water quality management
Science.gov (United States)
A 45% reduction in riverine total nitrogen flux from the 1980-1996 time period is needed to meet water quality goals in the Mississippi Basin and Gulf of Mexico. This paper addresses the goal of reducing nitrogen in the Mississippi River through three objectives. First, the paper outlines an approac...
2. Electrolytic analogue study of the effect of openings and surrounds of various permeabilities on the performance of field drainage pipes
NARCIS (Netherlands)
Dierickx, W.
1980-01-01
The effect of various openings and surrounds of various permeabilities on the performance of field drainage pipes was studied by means of an electrolytic analogue. The results obtained were compared with these of analytical solutions. Rather simple and sufficiently accurate solutions exist to
3. Effects of fertilizers used in agricultural fields on algal blooms
DEFF Research Database (Denmark)
Chakraborty, Subhendu; Tiwari, P. K.; Sasmal, S. K.
2017-01-01
of factors and from observation it is difficult to identify the most important one. In the present paper, using a mathematical model we compare the effects of three human induced factors (fertilizer input in agricultural field, eutrophication due to other sources than fertilizers, and overfishing......) on the bloom dynamics and DO level. By applying a sophisticated sensitivity analysis technique, we found that the increasing use of fertilizers in agricultural field causes more rapid algal growth and decreases DO level much faster than eutrophication from other sources and overfishing. We also look...... at the mechanisms how fertilizer input rate affects the algal bloom dynamics and DO level. The model can be helpful for the policy makers in determining the influential factors responsible for the bloom formation....
4. Thrips densities in organic leek fields in relation to the surrounding landscapes. Landscape management for functional biodiversity
NARCIS (Netherlands)
Belder, den E.; Elderson, J.; Schelling, G.C.; Brink, van den W.J.
2003-01-01
The study assessed the effects of hedgerow networks (line elements containing shrubs less than 2 m), woodlots (height > 2 m), other natural areas, and agricultural and horticultural land (polygons) in the landscapes on the abundance of a generalist thrips species in organic leek fields. Landscape
5. Modeling of subthreshold characteristics of short channel junctionless cylindrical surrounding-gate nanowire metal–oxide–silicon field effect transistors
International Nuclear Information System (INIS)
Jin, Xiaoshi; Liu, Xi; Lee, Jung-Hee; Lee, Jong-Ho
2014-01-01
A subthreshold model of short-channel junctionless field effect transistors with cylindrical surrounding-gate nanowire structure has been proposed. It was based on an approximated solution of two-dimensional Poisson's equation. The derivation of this model was introduced and the accuracy of the proposed models have been verified by comparison with both previous models and the SILVACO Atlas TCAD simulation results, which show good agreement. (paper)
6. Modeling of cylindrical surrounding gate MOSFETs including the fringing field effects
International Nuclear Information System (INIS)
Gupta, Santosh K.; Baishya, Srimanta
2013-01-01
A physically based analytical model for surface potential and threshold voltage including the fringing gate capacitances in cylindrical surround gate (CSG) MOSFETs has been developed. Based on this a subthreshold drain current model has also been derived. This model first computes the charge induced in the drain/source region due to the fringing capacitances and considers an effective charge distribution in the cylindrically extended source/drain region for the development of a simple and compact model. The fringing gate capacitances taken into account are outer fringe capacitance, inner fringe capacitance, overlap capacitance, and sidewall capacitance. The model has been verified with the data extracted from 3D TCAD simulations of CSG MOSFETs and was found to be working satisfactorily. (semiconductor devices)
7. Wind field measurement in the nonprecipitous regions surrounding storms by an airborne pulsed Doppler lidar system, appendix A
Science.gov (United States)
Bilbro, J. W.; Vaughan, W. W.
1980-01-01
Coherent Doppler lidar appears to hold great promise in contributing to the basic store of knowledge concerning flow field characteristics in the nonprecipitous regions surrounding severe storms. The Doppler lidar, through its ability to measure clear air returns, augments the conventional Doppler radar system, which is most useful in the precipitous regions of the storm. A brief description of the Doppler lidar severe storm measurement system is provided along with the technique to be used in performing the flow field measurements. The application of the lidar is addressed, and the planned measurement program is outlined.
8. Influence of the surroundings conditions on the evolution of elastomers in the nuclear field
International Nuclear Information System (INIS)
Davenas, J.; Stevenson, I.; Celette, N.; David, L.; Vigier, G.; David, L.
2006-01-01
The evolution under radiations of EPDM elastomers used as cable insulators reveals the determining role of the surrounding atmosphere. The formation of unsaturated bonds and a recovery of the reticulation are revealed for irradiations in inert atmosphere, whereas a lot of oxidized species are formed in presence of oxygen. The dynamic mechanical relaxation spectroscopy shows a decrease of the molecular mobility in all the cases. This ones results of the reticulation under inert atmosphere, but its origin is less clear during the radio-oxidation where the chain cleavages constitute the main process. The evolution of the conservation modulus with the irradiation dose is in agreement with the waited evolution after the melting of the crystallites. The number of reticulation intersection increases until a dose corresponding to the complete consumption of diene, for decreasing then under the influence of the chain cleavages. The crystallites growth due to chain cleavages explains then the evolution at ambient temperature in presence of oxygen. The mechanical properties at the great deformations show the role of reinforcement of the crystallites at ambient temperature which disappears during the crystallites melting. The evolution of the EPDM properties results of a complex equilibrium between reticulations, chain cleavages and crystallites growth, which is controlled by the temperature and the atmosphere. (O.M.)
9. Parkinson's Disease Prevalence and Proximity to Agricultural Cultivated Fields
Science.gov (United States)
Yitshak Sade, Maayan; Zlotnik, Yair; Kloog, Itai; Novack, Victor; Peretz, Chava; Ifergane, Gal
2015-01-01
The risk for developing Parkinson's disease (PD) is a combination of multiple environmental and genetic factors. The Negev (Southern Israel) contains approximately 252.5 km2 of agricultural cultivated fields (ACF). We aimed to estimate the prevalence and incidence of PD and to examine possible geographical clustering and associations with agricultural exposures. We screened all “Clalit” Health Services members in the Negev (70% of the population) between the years 2000 and 2012. Individual demographic, clinical, and medication prescription data were available. We used a refined medication tracer algorithm to identify PD patients. We used mixed Poisson models to calculate the smoothed standardized incidence rates (SIRs) for each locality. We identified ACF and calculate the size and distance of the fields from each locality. We identified 3,792 cases of PD. SIRs were higher than expected in Jewish rural localities (median SIR [95% CI]: 1.41 [1.28; 1.53] in 2001–2004, 1.62 [1.48; 1.76] in 2005–2008, and 1.57 [1.44; 1.80] in 2009–2012). Highest SIR was observed in localities located in proximity to large ACF (SIR 1.54, 95% CI 1.32; 1.79). In conclusion, in this population based study we found that PD SIRs were higher than expected in rural localities. Furthermore, it appears that proximity to ACF and the field size contribute to PD risk. PMID:26357584
10. The new integrated aeromagnetic map of the Phlegrean Fields volcano and surrounding areas
Directory of Open Access Journals (Sweden)
A. Rapolla
2004-06-01
Full Text Available In this paper we present and analyze the new detailed aeromagnetic data set resulting from a recent survey carried out in the Phlegrean Fields volcanic area. The survey was aimed at gaining new insight into the volcanological characteristics of the region north of Phlegrean Fields (Parete-Villa Literno area where remarkable thickness of volcanic/sub- volcanic rocks were found in wells. Measurement of total magnetic field was performed on two different flight levels, 70 m and 400 m above the ground surface, along flight lines spaced 400 m apart. Both aeromagnetic maps show the noisy effect of linear anomalies evidently due to the presence of railway lines. To filter out these local anomalies a method based on discrete wavelet transform was used, allowing an accurate local filtering and leaving the rest of the field practically unchanged. The filtered data set was integrated with the existing Agip aeromagnetic map of the Phlegrean Fields, leading to a new aeromagnetic map of the whole Phlegrean volcanic area. The compilation of the pole reduced map and of the maps of the Analytic Signal and of the Horizontal Derivative of the integrated data set represents a first step for the interpretation of the maps in terms of geological structures of the whole Phlegrean volcanic district.
11. CHAOTIC MOTION OF CHARGED PARTICLES IN AN ELECTROMAGNETIC FIELD SURROUNDING A ROTATING BLACK HOLE
International Nuclear Information System (INIS)
Takahashi, Masaaki; Koyama, Hiroko
2009-01-01
The observational data from some black hole candidates suggest the importance of electromagnetic fields in the vicinity of a black hole. Highly magnetized disk accretion may play an importance rule, and large-scale magnetic field may be formed above the disk surface. Then, we expect that the nature of the black hole spacetime would be revealed by magnetic phenomena near the black hole. We will start investigating the motion of a charged test particle which depends on the initial parameter setting in the black hole dipole magnetic field, which is a test field on the Kerr spacetime. Particularly, we study the spin effects of a rotating black hole on the motion of the charged test particle trapped in magnetic field lines. We make detailed analysis for the particle's trajectories by using the Poincare map method, and show the chaotic properties that depend on the black hole spin. We find that the dragging effects of the spacetime by a rotating black hole weaken the chaotic properties and generate regular trajectories for some sets of initial parameters, while the chaotic properties dominate on the trajectories for slowly rotating black hole cases. The dragging effects can generate the fourth adiabatic invariant on the particle motion approximately.
12. General relativistic model for the gravitational field of active galactic nuclei surrounded by a disk
NARCIS (Netherlands)
Vogt, D.; Letelier, P.S.
2005-01-01
An exact but simple general relativistic model for the gravitational field of active galactic nuclei is constructed, based on the superposition in Weyl coordinates of a black hole, a Chazy-Curzon disk and two rods, which represent matter jets. The influence of the rods on the matter properties of
13. The long term behaviour of the near-field barrier surrounding a deep underground repository
International Nuclear Information System (INIS)
1992-02-01
This report describes research to identify the factors which govern or influence the long-term behaviour of the near-field of a nuclear waste repository. The near-field components include the engineered barriers and the natural rock mass although the behaviour of the rock mass is of greater significance over the long-term. The factors which govern the near-field behaviour consist of the processes which operate, and the properties or parameters of the rock mass which might be modified by them. The methods which are available for the prediction of the near-field behaviour have been identified, and the emphasis on computer based methods is noted. Summary details of generic computer techniques are provided for different process modelling requirements. An attempt is made to indicate how different processes will be important at various stages during the life of the repository and how the evaluation of performance assessment process modelling requires input from empirical models and the results of other process predictions. (Author)
14. Mechanical and hydrological characterization of the near-field surrounding excavations in a geologic salt formation
Energy Technology Data Exchange (ETDEWEB)
Howard, Clifford L. [Sandia National Laboratories, Albuquerque, NM (United States)
2014-09-01
The technical basis for salt disposal of nuclear waste resides in salt’s favorable physical, mechanical and hydrological characteristics. Undisturbed salt formations are impermeable. Upon mining, the salt formation experiences damage in the near-field rock proximal to the mined opening and salt permeability increases dramatically. The volume of rock that has been altered by such damage is called the disturbed rock zone (DRZ).
15. Effects of fertilizers used in agricultural fields on algal blooms
Science.gov (United States)
Chakraborty, Subhendu; Tiwari, P. K.; Sasmal, S. K.; Misra, A. K.; Chattopadhyay, Joydev
2017-06-01
The increasing occurrence of algal blooms and their negative ecological impacts have led to intensified monitoring activities. This needs the proper identification of the most responsible factor/factors for the bloom formation. However, in natural systems, algal blooms result from a combination of factors and from observation it is difficult to identify the most important one. In the present paper, using a mathematical model we compare the effects of three human induced factors (fertilizer input in agricultural field, eutrophication due to other sources than fertilizers, and overfishing) on the bloom dynamics and DO level. By applying a sophisticated sensitivity analysis technique, we found that the increasing use of fertilizers in agricultural field causes more rapid algal growth and decreases DO level much faster than eutrophication from other sources and overfishing. We also look at the mechanisms how fertilizer input rate affects the algal bloom dynamics and DO level. The model can be helpful for the policy makers in determining the influential factors responsible for the bloom formation.
16. High fidelity phase locked PIV measurements analysing the flow fields surrounding an oscillating piezoelectric fan
International Nuclear Information System (INIS)
Jeffers, Nicholas; Nolan, Kevin; Stafford, Jason; Donnelly, Brian
2014-01-01
Piezoelectric fans have been studied extensively and are seen as a promising technology for thermal management due to their ability to provide quiet, reliable cooling with low power consumption. The fluid mechanics of an unconfined piezoelectric fan are complex which is why the majority of the literature to date confines the fan in an attempt to simplify the flow field. This paper investigates the fluid mechanics of an unconfined fan operating in its first vibration frequency mode. The piezoelectric fan used in this study measures 12.7 mm × 70 mm and resonates at 92.5 Hz in air. A custom built experimental facility was developed to capture the fan's flow field using phase locked Particle Image Velocimetry (PIV). The phase locked PIV results are presented in terms of vorticity and show the formation of a horse shoe vortex. A three dimensional A2 criterion constructed from interpolated PIV measurements was used to identify the vortex core in the vicinity of the fan. This analysis was used to clearly identify the formation of a horse shoe vortex that turns into a hairpin vortex before it breaks up due to a combination of vortex shedding and flow along the fan blade. The results presented in this paper contribute to both the fluid dynamics and heat transfer literature concerning first mode fan oscillation.
17. About soil cover heterogeneity of agricultural research stations' experimental fields
Science.gov (United States)
Rannik, Kaire; Kõlli, Raimo; Kukk, Liia
2013-04-01
Depending on local pedo-ecological conditions (topography, (geo) diversity of soil parent material, meteorological conditions) the patterns of soil cover and plant cover determined by soils are very diverse. Formed in the course of soil-plant mutual relationship, the natural ecosystems are always influenced to certain extent by the other local soil forming conditions or they are site specific. The agricultural land use or the formation of agro-ecosystems depends foremost on the suitability of soils for the cultivation of feed and food crops. As a rule, the most fertile or the best soils of the area, which do not present any or present as little as possible constraints for agricultural land use, are selected for this purpose. Compared with conventional field soils, the requirements for the experimental fields' soil cover quality are much higher. Experimental area soils and soil cover composition should correspond to local pedo-ecological conditions and, in addition to that, represent the soil types dominating in the region, whereas the fields should be as homogeneous as possible. The soil cover heterogeneity of seven arable land blocks of three research stations (Jõgeva, Kuusiku and Olustvere) was studied 1) by examining the large scale (1:10 000) digital soil map (available via the internet), and 2) by field researches using the transect method. The stages of soils litho-genetic and moisture heterogeneities were estimated by using the Estonian normal soils matrix, however, the heterogeneity of top- and subsoil texture by using the soil texture matrix. The quality and variability of experimental fields' soils humus status, was studied more thoroughly from the aspect of humus concentration (g kg-1), humus cover thickness (cm) and humus stocks (Mg ha-1). The soil cover of Jõgeva experimental area, which presents an accumulative drumlin landscape (formed during the last glacial period), consist from loamy Luvisols and associated to this Cambisols. In Kuusiku area
18. Agriculture
International Nuclear Information System (INIS)
Goetz, B.; Riss, A.; Zethner, G.
2001-01-01
This chapter deals with fertilization techniques, bioenergy from agriculture, environmental aspects of a common agriculture policy in the European Union, bio-agriculture, fruit farming in Austria and with environmental indicators in agriculture. In particular renewable energy sources (bio-diesel, biogas) from agriculture are studied in comparison to fossil fuels and other energy sources. (a.n.)
19. Dynamic stabilization of the magnetic field surrounding the neutron electric dipole moment spectrometer at the Paul Scherrer Institute
Energy Technology Data Exchange (ETDEWEB)
Afach, S.; Fertl, M.; Franke, B., E-mail: [email protected], E-mail: [email protected]; Kirch, K. [Paul Scherrer Institute, Villigen (Switzerland); Institute for Particle Physics, Eidgenössische Technische Hochschule, Zürich (Switzerland); Bison, G.; Burri, F.; Chowdhuri, Z.; Daum, M.; Henneck, R.; Lauss, B., E-mail: [email protected], E-mail: [email protected]; Meier, M.; Schmidt-Wellenburg, P.; Zsigmond, G. [Paul Scherrer Institute, Villigen (Switzerland); Bodek, K.; Zejma, J. [Jagellonian University, Cracow (Poland); Grujic, Z.; Kasprzak, M.; Weis, A. [University of Fribourg (Switzerland); Hélaine, V. [Laboratoire de Physique Corpusculaire, Caen (France); Paul Scherrer Institute, Villigen (Switzerland); Koch, H.-C. [Institut für Physik, Johannes-Gutenberg-Universität, Mainz (Germany); University of Fribourg (Switzerland); and others
2014-08-28
The Surrounding Field Compensation (SFC) system described in this work is installed around the four-layer Mu-metal magnetic shield of the neutron electric dipole moment spectrometer located at the Paul Scherrer Institute. The SFC system reduces the DC component of the external magnetic field by a factor of about 20. Within a control volume of approximately 2.5 m × 2.5 m × 3 m, disturbances of the magnetic field are attenuated by factors of 5–50 at a bandwidth from 10{sup −3} Hz up to 0.5 Hz, which corresponds to integration times longer than several hundreds of seconds and represent the important timescale for the neutron electric dipole moment measurement. These shielding factors apply to random environmental noise from arbitrary sources. This is achieved via a proportional-integral feedback stabilization system that includes a regularized pseudoinverse matrix of proportionality factors which correlates magnetic field changes at all sensor positions to current changes in the SFC coils.
20. Optimization of agricultural field workability predictions for improved risk management
Science.gov (United States)
Risks introduced by weather variability are key considerations in agricultural production. The sensitivity of agriculture to weather variability is of special concern in the face of climate change. In particular, the availability of workable days is an important consideration in agricultural practic...
1. Development of the neutron reference calibration field using a {sup 252}Cf standard source surrounded with PMMA moderators
Energy Technology Data Exchange (ETDEWEB)
Yoshida, T.; Kanai, K.; Tsujimura, N. [Japan Nuclear Cycle Development Institute, Ibaraki-ken (Japan)
2002-07-01
The authors developed the neutron reference calibration fields using a {sup 252} Cf standard source surrounded with PMMA moderators at the Japan Nuclear Cycle Development (JNC), Tokai Works. The moderators are co-axial, hollow cylinders made of lead-contained PMMA with a thickness of 13.5, 35.0, 59.5 and 77.0mm, and the {sup 252} Cf source is guided to the geometric center of moderators by the pneumatic system. These fields can provide the moderated neutron spectra very similar to those encountered around the globe-boxes of the fabrication process of MOX (PuO{sub 2}-UO{sub 2} mixed oxide) fuel. The neutron energy spectrum at the reference calibration point was evaluated from the calculations by MCNP4B and the measurements by the INS-type Bonner multi-sphere spectrometer and the hydrogen-filled proportional counters. The calculated neutron spectra were in good agreements with the measured ones. These fields were characterized in terms of the neutron fluence rate, spectral composition and ambient dose equivalent rate, and have served for the response-characterization of various neutron survey instruments.
2. Development of the neutron reference calibration field using a 252Cf standard source surrounded with PMMA moderators
International Nuclear Information System (INIS)
Yoshida, T.; Kanai, K.; Tsujimura, N.
2002-01-01
The authors developed the neutron reference calibration fields using a 252 Cf standard source surrounded with PMMA moderators at the Japan Nuclear Cycle Development (JNC), Tokai Works. The moderators are co-axial, hollow cylinders made of lead-contained PMMA with a thickness of 13.5, 35.0, 59.5 and 77.0mm, and the 252 Cf source is guided to the geometric center of moderators by the pneumatic system. These fields can provide the moderated neutron spectra very similar to those encountered around the globe-boxes of the fabrication process of MOX (PuO 2 -UO 2 mixed oxide) fuel. The neutron energy spectrum at the reference calibration point was evaluated from the calculations by MCNP4B and the measurements by the INS-type Bonner multi-sphere spectrometer and the hydrogen-filled proportional counters. The calculated neutron spectra were in good agreements with the measured ones. These fields were characterized in terms of the neutron fluence rate, spectral composition and ambient dose equivalent rate, and have served for the response-characterization of various neutron survey instruments
3. Sociological studies on the surrounding field of perception of the population with regard to technological risks (here: nuclear power plants)
International Nuclear Information System (INIS)
Frantzen, D.; Schmid-Joerg, I.
1976-03-01
This study consisted of 950 enquiries and 32 group discussions on the topic 'largescale technological developments'. The fields to be studied were selected under the following aspects: 1) varying degrees of actual sensibilization to nuclear power plants in regions with similar social infrastructure; 2) cities with a different degree of acclimatization to permanent environmental pollution as compared to country regions. It was found that the surrounding field of perception for technological risks in the case of nuclear power plants is structured by the following important influencing factors: 1) the information available, modified by information barriers, information deficits, and selective reception and passing-on of information; 2) the fears based on reality in the field of technologies and environmental problems; these fears must be regarded as moderators of the information available; 3) extent and dimensions of environmental awareness, i.e. active participation or passive, apathic acceptance of environmental problems; 4) the factor 'group pressure', which is a decisive factor in the formation of location-specific patterns of recognition. (orig./HP) [de
4. Applied statistics for agriculture, veterinary, fishery, dairy and allied fields
CERN Document Server
2016-01-01
This book is aimed at a wide range of readers who lack confidence in the mathematical and statistical sciences, particularly in the fields of Agriculture, Veterinary, Fishery, Dairy and other related areas. Its goal is to present the subject of statistics and its useful tools in various disciplines in such a manner that, after reading the book, readers will be equipped to apply the statistical tools to extract otherwise hidden information from their data sets with confidence. Starting with the meaning of statistics, the book introduces measures of central tendency, dispersion, association, sampling methods, probability, inference, designs of experiments and many other subjects of interest in a step-by-step and lucid manner. The relevant theories are described in detail, followed by a broad range of real-world worked-out examples, solved either manually or with the help of statistical packages. In closing, the book also includes a chapter on which statistical packages to use, depending on the user’s respecti...
5. Forests to fields. Restoring tropical lands to agriculture.
Science.gov (United States)
Wood, D
1993-04-01
In discussing land use in tropical forest regions, there is an emphasis on the following topics: the need for the expansion of cropping areas, the precedent for use of the tropical forest for cropping based on past use patterns, the pressure from conservationists against cropping, debunking the mythology that forests are "natural" and refuting the claims that forest clearance is not reversible, the archeological evidence of past forest use for agricultural purposes, abandonment of tropical land to forest, and rotation of forest and field. The assumption is that the way to stop food importation is to increase crop production in the tropics. Crop production can be increased through 1) land intensification or clearing new land, 2) output per unit of land increases, or 3) reallocation to agriculture land previously cleared and overgrown with tropical forest. "Temporary" reuse of land, which reverted back to tropical forest, is recommended. This reuse would ease population pressure, and benefit bioconservation, while populations stabilize and further progress is made in international plant breeding. The land would eventually be returned to a forest state. Conservation of tropical forest areas should be accomplished, after an assessment has been made of its former uses. Primary forests need to identified and conversion to farming ceased. Research needs to be directed to understanding the process of past forest regeneration, and to devising cropping systems with longterm viability. The green revolution is unsuitable for traditional cropping systems, is contrary to demands of international funding agencies for sustainability, and is not affordable by most poor farmers. Only .48 million sq. km of closed forest loss was in tropical rainforests; 6.53 million sq. km was lost from temperate forests cleared for intensive small-scale peasant farming. The use of tropical forest land for farming has some benefits; crops in the wetter tropics are perennial, which would "reduce
6. Engineering and agronomy aspects of a long-term precision agriculture field experiment
Science.gov (United States)
Much research has been conducted on specific precision agriculture tools and implementation strategies, but little has been reported on long-term evaluation of integrated precision agriculture field experiments. In 2004 our research team developed and initiated a multi-faceted “precision agriculture...
7. Agriculture
Science.gov (United States)
The EPA Agriculture Resource Directory offers comprehensive, easy-to-understand information about environmental stewardship on farms and ranches; commonsense, flexible approaches that are both environmentally protective and agriculturally sound.
8. Smart Surroundings
NARCIS (Netherlands)
Havinga, Paul J.M.; Jansen, P.G.; Lijding, M.E.M.; Scholten, Johan
2004-01-01
Ambient systems are networked embedded systems integrated with everyday environments and supporting people in their activities. These systems will create a Smart Surrounding for people to facilitate and enrich daily life and increase productivity at work. Such systems will be quite different from
9. LiDAR, geophysical and field surveys at Ancient Epomanduodurum site and its surrounding country (Doubs, Eastern France)
Science.gov (United States)
Laplaige, Clement; Bossuet, Gilles; Thivet, Matthieu
2010-05-01
understand the connections, both in time and in space, between human occupation and the surrounding region, not only at the Roman period and the late Iron Age, but also during prehistoric, medieval and modern periods. In that way, we have defined a square window of 80 km², surrounding the Ancient site of Epomanduodurum This study is based on the LIDAR (Light Detection And Ranging) technology, particularly adapted for the detection and location of cultural resources (ancient fields, buried structures, graves) in forested environment and a multi-data crossing, including: - Geophysical prospecting (principally magnetic, electromagnetic and electric) - Studies of ancient maps, plans (18th and 19th) and archaeological inventories in order to spot the location of vestiges and the utilisation of former soils - Aerial and satellite picture analysis - Field walking and metal detector prospection in order to precise micro topographic anomalies obtained by LiDAR survey. We received first LiDAR results during August 2009 and the use of part of this data allows us to find new sites from different periods. We will present some results, mainly in an Ancient artisanal district built on a Latenian necropolis, on hilltop sites and also on mine plant.
10. Agriculture
International Nuclear Information System (INIS)
2002-01-01
The report entitled Climate Change Impacts and Adaptation : A Canadian Perspective, presents a summary of research regarding the impacts of climate change on key sectors over the past five years as it relates to Canada. This chapter on agriculture describes how climate change will affect primary agriculture production in Canada with particular focus on potential adaptation options, and vulnerability of agriculture at the farm level. Agriculture is a vital part of the Canadian economy, although only 7 per cent of Canada's land mass is used for agricultural purposes due to the limitations of climate and soils. Most parts of Canada are expected to experience warmer conditions, longer frost-free seasons and increased evapotranspiration. The impacts of these changes on agriculture will vary depending on precipitation changes, soil conditions, and land use. Northern regions may benefit from longer farming seasons, but poor soil conditions will limit the northward expansion of agricultural crops. Some of the negative impacts associated with climate change on agriculture include increased droughts, changes in pest and pathogen outbreaks, and moisture stress. In general, it is expected that the positive and negative impacts of climate change would offset each other. 74 refs., 2 tabs., 1 fig
11. 127 Field Practical Training Programme of Faculties of Agriculture in ...
African Journals Online (AJOL)
User
Keywords: Practical training, students of agriculture faculty ... fertility, agronomy and horticultural practices, crop protection activities, ... and Frick (2004) submitted that companies of today want graduates with ... The State accounts for 2.3% of Nigeria's total population. ..... Carrying out appropriate husbandry measures for.
12. Pesticide Leaching Models in a Brazilian Agricultural Field Scenario
NARCIS (Netherlands)
Scorza, R.P.; Oliveira Rigitano, de R.L.; Boesten, J.J.T.I.
2011-01-01
The use of Pesticide Leaching Models (PLM) for risk assessment may be an efficient and attractive way of assessing solutions to some agricultural and environmental problems. Many countries of the European Union and the USA have been using PLM for risk assessment already for a few decades. This
13. Increased spring flooding of agricultural fields will exhibit altered production of greenhouse gases
Science.gov (United States)
Paul, R. F.; Smith, C. M.; Smyth, E. M.; Kantola, I. B.; DeLucia, E. H.
2013-12-01
The U.S. Corn Belt currently is a net source of carbon dioxide and nitrous oxide to the atmosphere, but is also a sink of methane. Among the proposed effects of climate change in the North American Midwest region is an increase in the frequency and duration of spring flooding events. This would cause ponding in fields which may change the greenhouse gas balance of the region, especially by providing a suitable anoxic environment for the proliferation of methanogens, increasing methane emissions. To determine whether methanogenesis occurs in flooded agricultural soils of the Midwest and how other gas fluxes are affected, we installed collars into the ground of a research field located in central Illinois. The control group was maintained at the same conditions as the surrounding field. Two groups of collars were sustained with water flooding the headspaces via a drip irrigation system; one treatment was analyzed for gas fluxes of CH4, N2O, and CO2 evolving from the collars, and a separate treatment of flooded collars was used for soil sampling. Comparing flooded soils versus control we measured reduced N2O fluxes (-3.12 x 10-6 × 6.8 x 10-7 g N m-2 min-1), reduced CO2 fluxes (-6.13 x 10-3 × 9.3 x 10-4 g CO2 m-2 min-1), and increased methane fluxes (+2.72 x 10-6 × 5.8 x 10-7 g CH4 m-2 min-1). After only one week of treatment the flooded soils switched from being sinks to sources of methane, which continued across the duration of the experiment. These preliminary results indicate that methanogenesis occurs in flooded agricultural fields, and suggest including regional modeling into further study. Although the global warming potential of methane is 25 times greater than CO2, our measured rates of methane production were compensated by reductions in nitrous oxide and CO2 fluxes, reducing the total 100-year horizon global warming potential of the flooded soils we studied by 64.8%. This indicates that accounting for more frequent seasonal ponding would significantly
14. Assessing and modelling ecohydrologic processes at the agricultural field scale
Science.gov (United States)
Basso, Bruno
2015-04-01
One of the primary goals of agricultural management is to increase the amount of crop produced per unit of fertilizer and water used. World record corn yields demonstrated that water use efficiency can increase fourfold with improved agronomic management and cultivars able to tolerate high densities. Planting crops with higher plant density can lead to significant yield increases, and increase plant transpiration vs. soil water evaporation. Precision agriculture technologies have been adopted for the last twenty years but seldom have the data collected been converted to information that led farmers to different agronomic management. These methods are intuitively appealing, but yield maps and other spatial layers of data need to be properly analyzed and interpreted to truly become valuable. Current agro-mechanic and geospatial technologies allow us to implement a spatially variable plan for agronomic inputs including seeding rate, cultivars, pesticides, herbicides, fertilizers, and water. Crop models are valuable tools to evaluate the impact of management strategies (e.g., cover crops, tile drains, and genetically-improved cultivars) on yield, soil carbon sequestration, leaching and greenhouse gas emissions. They can help farmers identify adaptation strategies to current and future climate conditions. In this paper I illustrate the key role that precision agriculture technologies (yield mapping technologies, within season soil and crop sensing), crop modeling and weather can play in dealing with the impact of climate variability on soil ecohydrologic processes. Case studies are presented to illustrate this concept.
15. A contemporary decennial global Landsat sample of changing agricultural field sizes
Science.gov (United States)
White, Emma; Roy, David
2014-05-01
Agriculture has caused significant human induced Land Cover Land Use (LCLU) change, with dramatic cropland expansion in the last century and significant increases in productivity over the past few decades. Satellite data have been used for agricultural applications including cropland distribution mapping, crop condition monitoring, crop production assessment and yield prediction. Satellite based agricultural applications are less reliable when the sensor spatial resolution is small relative to the field size. However, to date, studies of agricultural field size distributions and their change have been limited, even though this information is needed to inform the design of agricultural satellite monitoring systems. Moreover, the size of agricultural fields is a fundamental description of rural landscapes and provides an insight into the drivers of rural LCLU change. In many parts of the world field sizes may have increased. Increasing field sizes cause a subsequent decrease in the number of fields and therefore decreased landscape spatial complexity with impacts on biodiversity, habitat, soil erosion, plant-pollinator interactions, and impacts on the diffusion of herbicides, pesticides, disease pathogens, and pests. The Landsat series of satellites provide the longest record of global land observations, with 30m observations available since 1982. Landsat data are used to examine contemporary field size changes in a period (1980 to 2010) when significant global agricultural changes have occurred. A multi-scale sampling approach is used to locate global hotspots of field size change by examination of a recent global agricultural yield map and literature review. Nine hotspots are selected where significant field size change is apparent and where change has been driven by technological advancements (Argentina and U.S.), abrupt societal changes (Albania and Zimbabwe), government land use and agricultural policy changes (China, Malaysia, Brazil), and/or constrained by
16. Alternative agricultures: Emphasis in contributions of the people of field of southwestern sector of Colombia
International Nuclear Information System (INIS)
Mejia Gutierrez, M.
1995-01-01
It offers a definition of alternative agricultures. Some antecedents are mentioned about the evolution of the Colombian movements from the chemical agriculture toward alternative forms. Some Colombian experiences are enumerated, making emphasis in people of field of the southwestern sector of the country contributions. Some conclusions settle down
17. The seasonal role of field characteristics on seed-eating bird abundances in agricultural landscapes
Science.gov (United States)
Codesido, Mariano; Abba, Agustín M.; Bilenca, David
2017-01-01
Abstract In temperate agroecosystems, avian responses in abundance and distribution to landscape attributes may be exacerbated by the coupling of natural seasons and farming practices. We assessed the seasonal roles of field type, field use in the surroundings, and distance from a field to the nearest woodlot on the abundance of seed-eating birds in a 225,000 km2 study area in the Pampas of central Argentina. During spring-summer and autumn of 2011–2013, we randomly selected 392 fields and used transect samples to collect data on abundance and presence of seed-eating bird species. We recorded a total of 11,579 individuals belonging to 15 seed-eating bird species. We used generalized lineal mixed models to relate bird abundance to field type, field use in the surroundings, and distance to the nearest woodlot. In spring-summer (breeding season) most bird responses were associated with their nesting requirements. Species that build their nests in trees, such as eared doves Zenaida auriculata, picazuro pigeons Patagioenas picazuro, and monk parakeets Myiopsitta monachus, were more abundant in fields closer to woodlots, whereas grassland yellow-finches Sicalis luteola, which nest at areas with tall grasses, were more abundant in fields with livestock use patches in the field surroundings. In autumn (non-breeding season), most bird responses were associated with foraging and refuge needs. The high abundance of eared doves in crop stubbles and the association of pigeons at field surroundings dominated by croplands or at crop stubbles surrounded by livestock use fields revealed the intimate association of these species to sites with high availability of food resources. In addition, both picazuro pigeons and spot-winged pigeons Patagioenas maculosa were associated with woodlots, which provide suitable roosting sites. Our results show that in temperate agroecosystems, the relationships between field characteristics and seed-eating bird abundances vary with season. PMID
18. Application of remote sensing to agricultural field trials
NARCIS (Netherlands)
Clevers, J.G.P.W.
1986-01-01
Remote sensing techniques enable quantitative information about a field trial to be obtained instantaneously and non-destructively. The aim of this study was to identify a method that can reduce inaccuracies in field trial analysis, and to identify how remote sensing can support and/or
19. Quantum field inspired model of decision making: Asymptotic stabilization of belief state via interaction with surrounding mental environment
OpenAIRE
Bagarello, Fabio; Basieva, Irina; Khrennikov, Andrei
2017-01-01
This paper is devoted to justification of quantum-like models of the process of decision making based on the theory of open quantum systems, i.e. decision making is considered as decoherence. This process is modeled as interaction of a decision maker, Alice, with a mental (information) environment ${\\cal R}$ surrounding her. Such an interaction generates "dissipation of uncertainty" from Alice's belief-state $\\rho(t)$ into ${\\cal R}$ and asymptotic stabilization of $\\rho(t)$ to a steady belie...
20. In pursuit of a science of agriculture: the role of statistics in field experiments.
Science.gov (United States)
Parolini, Giuditta
2015-09-01
Since the beginning of the twentieth century statistics has reshaped the experimental cultures of agricultural research taking part in the subtle dialectic between the epistemic and the material that is proper to experimental systems. This transformation has become especially relevant in field trials and the paper will examine the British agricultural institution, Rothamsted Experimental Station, where statistical methods nowadays popular in the planning and analysis of field experiments were developed in the 1920s. At Rothamsted statistics promoted randomisation over systematic arrangements, factorisation over one-question trials, and emphasised the importance of the experimental error in assessing field trials. These changes in methodology transformed also the material culture of agricultural science, and a new body, the Field Plots Committee, was created to manage the field research of the agricultural institution. Although successful, the vision of field experimentation proposed by the Rothamsted statisticians was not unproblematic. Experimental scientists closely linked to the farming community questioned it in favour of a field research that could be more easily understood by farmers. The clash between the two agendas reveals how the role attributed to statistics in field experimentation defined different pursuits of agricultural research, alternately conceived of as a scientists' science or as a farmers' science.
1. Field Monitoring of Deformations and Internal Forces of Surrounding Rocks and Lining Structures in the Construction of the Gangkou Double-Arched Tunnel—A Case Study
Directory of Open Access Journals (Sweden)
Qixiang Yan
2017-02-01
Full Text Available Double-arched tunnel is a special and complex underground structure which needs to be monitored carefully during construction. Taking the Gangkou tunnel as the engineering background, this paper presents a case study of field monitoring of a representative double-arched tunnel. Typical cross sections were chosen in each class of surrounding rock masses in the tunnel area and different types of sensors were embedded in designed locations, and the deformations and forces of both surrounding rocks and lining structures were monitored systematically. The dynamic evolution as well as the spatial distribution characteristics of the monitoring data including the internal displacements of surrounding rocks and the contact pressures between surrounding rocks and primary linings, the axial forces in rock bolts and the internal forces in both steel arches and secondary linings were analyzed. The monitoring and analysis results show that the deformations and forces of both surrounding rocks and lining structures are directly related to the construction procedures, geological conditions and locations in the double-arched tunnel. According to the results, some reasonable suggestions were provided for the improvement of the tunnel construction. This study will provide useful reference and guidance for the design, construction and monitoring of similar engineering projects in future.
2. GAOS: Spatial optimisation of crop and nature within agricultural fields
NARCIS (Netherlands)
Bruin, de S.; Janssen, H.; Klompe, A.; Lerink, P.; Vanmeulebrouk, B.
2010-01-01
This paper proposes and demonstrates a spatial optimiser that allocates areas of inefficient machine manoeuvring to field margins thus improving the use of available space and supporting map-based Controlled Traffic Farming. A prototype web service (GAOS) allows farmers to optimise tracks within
3. Effect of an external magnetic field on particle acceleration by a rotating black hole surrounded with quintessential energy
Science.gov (United States)
Shaymatov, Sanjar; Ahmedov, Bobomurat; Stuchlík, Zdeněk; Abdujabbarov, Ahmadjon
We investigate particle motion and collisions in the vicinity of rotating black holes immersed in combined cosmological quintessential scalar field and external magnetic field. The quintessential dark-energy field governing the spacetime structure is characterized by the quintessential state parameter ωq ∈ (‑1; ‑1/3) characterizing its equation of state, and the quintessential field-intensity parameter c determining the static radius where the black hole attraction is just balanced by the quintessential repulsion. The magnetic field is assumed to be test field that is uniform close to the static radius, where the spacetime is nearly flat, being characterized by strength B there. Deformations of the test magnetic field in vicinity of the black hole, caused by the Ricci non-flat spacetime structure are determined. General expression of the center-of-mass energy of the colliding charged or uncharged particles near the black hole is given and discussed in several special cases. In the case of nonrotating black holes, we discuss collisions of two particles freely falling from vicinity of the static radius, or one such a particle colliding with charged particle revolving at the innermost stable circular orbit. In the case of rotating black holes, we discuss briefly particles falling in the equatorial plane and colliding in close vicinity of the black hole horizon, concentrating attention to the interplay of the effects of the quintessential field and the external magnetic field. We demonstrate that the ultra-high center-of-mass energy can be obtained for black holes placed in an external magnetic field for an infinitesimally small quintessential field-intensity parameter c; the center-of-mass energy decreases if the quintessential field-intensity parameter c increases.
4. Improving the efficiency of spatially selective operations for agricultural robotics in cropping field
Directory of Open Access Journals (Sweden)
Y. L. Li
2013-01-01
Full Text Available Cropping fields often have well-defined poor-performing patches due to spatial and temporal variability. In an attempt to increase crop performance on poor patches, spatially selective field operations may be performed by agricultural robotics to apply additional inputs with targeted requirements. This paper addresses the route planning problem for an agricultural robot that has to treat some poor-patches in a field with row crops, with respect to the minimization of the total non-working distance travelled during headland turnings and in-field travel distance. The traversal of patches in the field is expressed as the traversal of a mixed weighted graph, and then the problem of finding an optimal patch sequence is formulated as an asymmetric traveling salesman problem and solved by the partheno-genetic algorithm. The proposed method is applied on a cropping field located in Northwestern China. Research results show that by using optimum patch sequences, the total non-working distance travelled during headland turnings and in-field travel distance can be reduced. But the savings on the non-working distance inside the field interior depend on the size and location of patches in the field, and the introduction of agricultural robotics is beneficial to increase field efficiency.
5. Improving the efficiency of spatially selective operations for agricultural robotics in cropping field
Energy Technology Data Exchange (ETDEWEB)
Li, Y. L.; Yi, S. P.
2013-05-01
Cropping fields often have well-defined poor-performing patches due to spatial and temporal variability. In an attempt to increase crop performance on poor patches, spatially selective field operations may be performed by agricultural robotics to apply additional inputs with targeted requirements. This paper addresses the route planning problem for an agricultural robot that has to treat some poor-patches in a field with row crops, with respect to the minimization of the total non-working distance travelled during headland turnings and in-field travel distance. The traversal of patches in the field is expressed as the traversal of a mixed weighted graph, and then the problem of finding an optimal patch sequence is formulated as an asymmetric traveling salesman problem and solved by the parthenogenetic algorithm. The proposed method is applied on a cropping field located in Northwestern China. Research results show that by using optimum patch sequences, the total non-working distance travelled during headland turnings and in-field travel distance can be reduced. But the savings on the non-working distance inside the field interior depend on the size and location of patches in the field, and the introduction of agricultural robotics is beneficial to increase field efficiency. (Author) 21 refs.
6. Assessment of metals pollution on agricultural soil surrounding a lead-zinc mining area in the Karst region of Guangxi, China.
Science.gov (United States)
Zhang, Chaolan; Li, Zhongyi; Yang, Weiwei; Pan, Liping; Gu, Minghua; Lee, DoKyoung
2013-06-01
Soil samples were collected on farmland in a lead-zinc mining area in the Karst region of Guangxi, China. The contamination of the soil by eight metals (Cd, Hg, As, Cu, Pb, Cr, Zn, Ni) was determined. Among all these metals, Cd is the most serious pollutant in this area. Zn, Hg as well asPb can also be measured at high levels, which may affect the crop production. All other metals contributed marginally to the overall soil contamination. Besides the evaluation of single metals, the Nemerow synthetic index indicated that the soil is not suitable for agricultural use.
7. Assessment of electromagnetic fields intensity emitted by cellular phone base stations in surrounding flats - a preliminary study
International Nuclear Information System (INIS)
Zmyslony, M.; Politanski, P.; Mamrot, P.; Bortkiewicz, A.
2006-01-01
A rapid development of mobile telecommunications (MT) has resulted in an increased concern about possible detrimental health effects of electromagnetic fields (EMFs) emitted by MT systems, and by MT base stations in particular. Research into EMFs effects on the health of inhabitants living in their vicinity requires first of all a solid assessment of the exposure level. Up to now, the reports in this field have been rather scant. This article presents the results of preliminary measurements of EMFs fields in selected flats around selected base stations in the city of Lodz. Measurements of electric field strength, E, to assess EMF exposure were based on the standard procedures currently in force in Poland. As the study is regarded as a preliminary one, the measurements were conducted in buildings with the expected largest radiation. The measurements show that in the flats located up to 500 m from the base station, EMFs are within the limits specified by relevant Polish regulations on the general public and environmental protection. It was also observed that in a few (less than 10%) flats the field with E exceeded 0.8 V/m. The results show that there are no correlations between electric field strength and distance between the flat and the base station. Therefore, the distance from the base station cannot be used to represent the exposure rate; to determine the latter, EMF measurements are necessary. (author)
8. Concentrations of 226Ra and 210Pb in agricultural products surrounding the first brazilian mine and mill in Pocos de Caldas, MG
International Nuclear Information System (INIS)
Vasconcellos, L.M.H.; Amaral, E.C.S.; Vianna, E.C.M.
1989-01-01
As a complement to the pre-operational environmental monitoring program of the Brazilian first uranium mine and mill, a survey of 226 Ra and 210 Pb in agriculture products, and in the corresponding soils, were carried out in the Pocos de Caldas Plateau. The survey intended to determine site specific transfer factors, in order to better estimate radiation doses on the population. Resulting from the plant operation. In local soils, 226 Ra and 210 Pb have similar concentrations. The average contents are comparable to the values found in areas of normal radioactivity, but the maximum values are higher by one order of magnitude. In the vegetables analyzed (beans, carrot, corn and potato), 226 Ra concentrations are slightly higher than those of 210 Pb, and the maximum values are also one order of magnitude greater than in normal regions. For both radionuclides, the average soil-to-plant transfer factors are of the order of 10 -3 and 10 -2 , when related to total and to exchangeable contents in soils, respectively. These results led to the conclusion that 226 Ra and 210 Pb have similar importance, concerning the population exposure via the foodstuff ingestion pathway. Therefore, it was recommended to carry on routine monitoring program for both radionuclides in the main agriculture crops. However, the naturally elevated radionuclide concentrations, in some local vegetables, will decrease the sensitivity for detecting small increments resulting from the plant operation. (author) [pt
9. The seasonal role of field characteristics on seed-eating bird abundances in agricultural landscapes
Institute of Scientific and Technical Information of China (English)
Emmanuel ZUFIAURRE; Mariano CODESIDO; Agustín M.ABBA; David BILENCA
2017-01-01
In temperate agroecosystems,avian responses in abundance and distribution to landscape attributes may be exacerbated by the coupling of natural seasons and farming practices.We assessed the seasonal roles of field WPe,field use in the surroundings,and distance from a field to the nearest woodlot on the abundance of seed-eating birds in a 225,000 km2 study area in the Pampas of central Argentina.During spring-summer and autumn of 2011-2013,we randomly selected 392 fields and used transect samples to collect data on abundance and presence of seed-eating bird species.We recorded a total of 11,579 individuals belonging to 15 seed-eating bird species.We used generalized lineal mixed models to relate bird abundance to field type,field use in the surroundings,and distance to the nearest woodlot.In spring-summer (breeding season) most bird responses were associated with their nesting requirements.Species that build their nests in trees,such as eared doves Zenaida auriculata,picazuro pigeons Patagioenas picazuro,and monk parakeets Myiopsitta monachus,were more abundant in fields closer to woodlots,whereas grassland yellow-finches Sicalis luteola,which nest at areas with tall grasses,were more abundant in fields with livestock use patches in the field surroundings.In autumn (non-breeding season),most bird responses were associated with foraging and refuge needs.The high abundance of eared doves in crop stubbles and the association of pigeons at field surroundings dominated by croplands or at crop stubbles surrounded by livestock use fields revealed the intimate association of these species to sites with high availability of food resources.In addition,both picazuro pigeons and spot-winged pigeons Patagioenas maculosa were associated with woodlots,which provide suitable roosting sites.Our results show that in temperate agroecosystems,the relationships between field characteristics and seed-eating bird abundances vary with season.
10. A Comparison between Standard and Functional Clustering Methodologies: Application to Agricultural Fields for Yield Pattern Assessment
Directory of Open Access Journals (Sweden)
Simone Pascucci
2018-04-01
Full Text Available The recognition of spatial patterns within agricultural fields, presenting similar yield potential areas, stable through time, is very important for optimizing agricultural practices. This study proposes the evaluation of different clustering methodologies applied to multispectral satellite time series for retrieving temporally stable (constant patterns in agricultural fields, related to within-field yield spatial distribution. The ability of different clustering procedures for the recognition and mapping of constant patterns in fields of cereal crops was assessed. Crop vigor patterns, considered to be related to soils characteristics, and possibly indicative of yield potential, were derived by applying the different clustering algorithms to time series of Landsat images acquired on 94 agricultural fields near Rome (Italy. Two different approaches were applied and validated using Landsat 7 and 8 archived imagery. The first approach automatically extracts and calculates for each field of interest (FOI the Normalized Difference Vegetation Index (NDVI, then exploits the standard K-means clustering algorithm to derive constant patterns at the field level. The second approach applies novel clustering procedures directly to spectral reflectance time series, in particular: (1 standard K-means; (2 functional K-means; (3 multivariate functional principal components clustering analysis; (4 hierarchical clustering. The different approaches were validated through cluster accuracy estimates on a reference set of FOIs for which yield maps were available for some years. Results show that multivariate functional principal components clustering, with an a priori determination of the optimal number of classes for each FOI, provides a better accuracy than those of standard clustering algorithms. The proposed novel functional clustering methodologies are effective and efficient for constant pattern retrieval and can be used for a sustainable management of
11. ANTHEM simulation of the early time magnetic field penetration of the plasma surrounding a high density Z-pinch
International Nuclear Information System (INIS)
Mason, R.J.
1989-01-01
The early time penetration of magnetic field into the low density coronal plasma of a Z-pinch fiber is studied with the implicit plasma simulation code ANTHEM. Calculations show the emission of electrons from the cathode, pinching of the electron flow, magnetic insulation of the electrons near the anode, and low density ion blow off. PIC-particle ion calculations show a late time clumping of the ion density not seen with a fluid ion treatment. 4 refs., 4 figs
12. Comparing erosion rates in burnt forests and agricultural fields for a mountain catchment in NW Iberia
Science.gov (United States)
Nunes, João Pedro; Marisa Santos, Juliana; Bernard-Jannin, Léonard; Keizer, Jan Jacob
2013-04-01
A large part of northwestern Iberia is nowadays covered by commercial forest plantations of eucalypts and maritime pines, which have partly replaced traditional agricultural land-uses. The humid Mediterranean climate, with mild wet winters and warm dry summers, creates favorable conditions for the occurrence of frequent and recurrent forest fires. Erosion rates in recently burnt areas have been the subject of numerous studies; however, there is still a lack of information on their relevance when compared with agricultural erosion rates, impairing a comprehensive assessment of the role of forests for soil protection. This study focuses on Macieira de Alcoba, head-water catchment in the Caramulo Mountain Range, north-central Portugal, with a mixture of agricultural fields (mostly a rotation between winter pastures and summer cereals) on the lower slopes and forest plantations (mostly eucalypts) on the upper slopes. Agricultural erosion in this catchment has been monitored since 2010; a forest fire in 2011 presented an opportunity to compare post-fire and agricultural erosion rates at nearby sites with comparable soil and climatic conditions. Erosion rates were monitored between 2010 and 2013 by repeated surveys of visible erosion features and, in particular, by mapping and measuring rills and gullies after important rainfall events. During the 2011/2012 hydrological year, erosion rates in the burnt forest were two orders of magnitude above those in agricultural fields, amounting to 17.6 and. 0.1 Mg ha-1, respectively. Rills were widespread in the burnt area, while in the agricultural area they were limited to a small number of fields with higher slope; these particular fields experienced an erosion rate of 2.3 Mg ha-1, still one order of magnitude lower than at the burnt forest site. The timing of the erosion features was also quite distinct for the burnt area and the agricultural fields. During the first nine months after the fire, rill formation was not observed in
13. Prediction of the glyphosate sorption coefficient across two loamy agricultural fields
DEFF Research Database (Denmark)
Paradelo Pérez, Marcos; Norgaard, Trine; Moldrup, Per
2015-01-01
, suggesting that different properties control glyphosate sorption in different locations and at different scales of analysis. Better predictions were obtained for the best-four set for the field in Estrup (R2 = 0.87) and for both fields (R2 = 0.70), while the field in Silstrup showed a lower predictability (R......2 = 0.36). Possibly, the low predictability for the field in Silstrup originated from opposing gradients in clay and oxalate-extractable Fe across the field. Also, whereas a lower clay content in Estrup may be the limiting variable for glyphosate sorption, the field in Silstrup has a higher clay...... sorption coefficient, Kd, from easily measurable soil properties in two loamy, agricultural fields in Denmark: Estrup and Silstrup. Forty-five soil samples in Estrup and 65 in Silstrup were collected fromthe surface in a rectangular grid of 15 × 15-mfromeach field, and selected soil properties...
14. Effects of microelements on soil nematode assemblages seven years after contaminating an agricultural field
NARCIS (Netherlands)
Nagy, P.; Bakonyi, G.; Bongers, A.M.T.; Kádár, I.; Fábián, M.; Kiss, I.
2004-01-01
Long-term effects of Cd, Cr, Cu, Se and Zn were studied 7 years after artificially contaminating plots of an agricultural field on a calcareous chernozem soil. Effects of three to four different contamination levels (originally 10, 30, 90 and 270 mg kg(-1)) were studied. Nematode density was
15. Ground penetrating radar (GPR) detects fine roots of agricultural crops in the field
Science.gov (United States)
Xiuwei Liu; Xuejun Dong; Qingwu Xue; Daniel I. Leskovar; John Jifon; John R. Butnor; Thomas Marek
2018-01-01
Aim Ground penetrating radar (GPR) as a non-invasive technique is widely used in coarse root detection. However, the applicability of the technique to detect fine roots of agricultural crops is unknown. The objective of this study was to assess the feasibility of utilizing GPR to detect fine roots in the field.
16. Spacial Variation in SAR Images of Different Resolution for Agricultural Fields
DEFF Research Database (Denmark)
Sandholt, Inge; Skriver, Henning
1999-01-01
The spatial variation in two types of Synthetic Aperture Radar (SAR) images covering agricultural fields is analysed. C-band polarimetric SAR data from the Danish airborne SAR, EMISAR, have been compared to space based ERS-1 C-band SAR with respect to scale and effect of polarization. The general...
17. Status of Job Motivation and Job Performance of Field Level Extension Agents in Ogun State: Implications for Agricultural Development
Science.gov (United States)
Fabusoro, E.; Awotunde, J. A.; Sodiya, C. I.; Alarima, C. I.
2008-01-01
The field level extension agents (FLEAs) are the lifeline of the agricultural extension system in Nigeria. Their motivation and job performance are therefore important to achieving faster agricultural development in Nigeria. The study identified the factors motivating the FLEAs working with Ogun State Agricultural development programme (OGADEP)…
18. Automated Agricultural Field Extraction from Multi-temporal Web Enabled Landsat Data
Science.gov (United States)
Yan, L.; Roy, D. P.
2012-12-01
Agriculture has caused significant anthropogenic surface change. In many regions agricultural field sizes may be increasing to maximize yields and reduce costs resulting in decreased landscape spatial complexity and increased homogenization of land uses with potential for significant biogeochemical and ecological effects. To date, studies of the incidence, drivers and impacts of changing field sizes have not been undertaken over large areas because of computational constraints and because consistently processed appropriate resolution data have not been available or affordable. The Landsat series of satellites provides near-global coverage, long term, and appropriate spatial resolution (30m) satellite data to document changing field sizes. The recent free availability of all the Landsat data in the U.S. Landsat archive now provides the opportunity to study field size changes in a global and consistent way. Commercial software can be used to extract fields from Landsat data but are inappropriate for large area application because they require considerable human interaction. This paper presents research to develop and validate an automated computational Geographic Object Based Image Analysis methodology to extract agricultural fields and derive field sizes from Web Enabled Landsat Data (WELD) (http://weld.cr.usgs.gov/). WELD weekly products (30m reflectance and brightness temperature) are classified into Satellite Image Automatic Mapper™ (SIAM™) spectral categories and an edge intensity map and a map of the probability of each pixel being agricultural are derived from five years of 52 weeks of WELD and corresponding SIAM™ data. These data are fused to derive candidate agriculture field segments using a variational region-based geometric active contour model. Geometry-based algorithms are used to decompose connected segments belonging to multiple fields into coherent isolated field objects with a divide and conquer strategy to detect and merge partial circle
19. The Effect of Slab Holes on the Surrounding Mantle Flow Field and the Surface from a Multi-Disciplinary Approach
Science.gov (United States)
Portner, D. E.; Kiraly, A.; Makushkina, A.; Parks, B. H.; Ghosh, T.; Haynie, K. L.; Metcalf, K.; Manga, M.; O'Farrell, K. A.; Moresi, L. N.; Jadamec, M. A.; Stern, R. J.
2017-12-01
Large-scale detachment of subducting slabs can have a significant geologic footprint by altering the slab-driven mantle flow field as hot subslab mantle can flow upward through the newly developed opening in the slab. The resulting increase in heat and vertical motion in the mantle wedge may contribute to volcanism and broad surface uplift. Recent geodynamic modeling results show that smaller tears and holes are similarly likely to form in many settings, such as where oceanic ridges or continental fragments subduct. High-resolution seismic tomography models are imaging an increasing number of these gaps and tears ranging in size from tens to hundreds of km in size, many of which occur proximal to alkali volcanism. Here we investigate the role of such gaps on the subduction-induced mantle flow field and related surface response. In particular, we address the relationships between slab hole size, depth, and distance from the slab edge and the magnitude of dynamic response of the mantle using analog experiments and numerical simulations. In the laboratory models, the subduction system is simplified to a two-layered Newtonian viscous sheet model. Our setup consists of a tank filled with glucose syrup and a plate made from silicon putty to model the upper mantle and subducting lithosphere, respectively. In each experiment, we pre-cut a rectangular hole with variable width into the silicon putty plate. Additionally, we perform a series of complementary numerical models using the Underworld geophysical modeling code to calculate the more detailed instantaneous mantle flow perturbation induced by the slab hole. Together, these results imply a strong effect of hole size on mantle flow. Similarly, the depth of the slab hole influences near-surface flow, with significant surface flow alteration when the hole is near the trench and diminishing surface deformation as the hole is dragged deeper into the mantle. The inferred consequence of the dependence of vertical mantle flux
20. P3-9: Roles of Subthreshold LFP Induced by Receptive Field Surround for Response Modulation in Monkey V1
Directory of Open Access Journals (Sweden)
Kayeon Kim
2012-10-01
Full Text Available A focal stimulus outside the receptive field robustly induces LFP change, while the same stimulus evokes no spike activity. We determined how this subthreshold LFP change interacted with spike response to the RF stimulus. Specifically, we sequentially presented two identical Gabor stimuli with a variable stimulus onset asynchrony (SOA; the first one (S1 was presented outside RF inducing a subthreshold LFP change, and the second one (S2 was subsequently presented within RF generating a spiking response. This enabled us to manipulate the temporal relation between subthreshold LFP and evoked spike activity and to determine whether subthreshold LFP contributed to modulation of spike activity in a SOA-dependent manner. We found that the subthreshold LFP propagated a considerably long distance, estimated to be more than 10 mm of cortical distance. The cross-correlation between the time course of subthreshold LFP and the pattern of SOA-dependency of spike activity was significant. These results indicate that signal integration is farther beyond the RF than previously estimated based on spike-triggered average, and suggest that subthreshold LFP modulate spike activity in a SOA-dependent manner.
1. Deriving a per-field land use and land cover map in an agricultural mosaic catchment
Science.gov (United States)
Seo, B.; Bogner, C.; Poppenborg, P.; Martin, E.; Hoffmeister, M.; Jun, M.; Koellner, T.; Reineking, B.; Shope, C. L.; Tenhunen, J.
2014-09-01
Detailed data on land use and land cover constitute important information for Earth system models, environmental monitoring and ecosystem services research. Global land cover products are evolving rapidly; however, there is still a lack of information particularly for heterogeneous agricultural landscapes. We censused land use and land cover field by field in the agricultural mosaic catchment Haean in South Korea. We recorded the land cover types with additional information on agricultural practice. In this paper we introduce the data, their collection and the post-processing protocol. Furthermore, because it is important to quantitatively evaluate available land use and land cover products, we compared our data with the MODIS Land Cover Type product (MCD12Q1). During the studied period, a large portion of dry fields was converted to perennial crops. Compared to our data, the forested area was underrepresented and the agricultural area overrepresented in MCD12Q1. In addition, linear landscape elements such as waterbodies were missing in the MODIS product due to its coarse spatial resolution. The data presented here can be useful for earth science and ecosystem services research. The data are available at the public repository Pangaea (doi:110.1594/PANGAEA.823677).
2. Towards an Open Software Platform for Field Robots in Precision Agriculture
Directory of Open Access Journals (Sweden)
Kjeld Jensen
2014-06-01
Full Text Available Robotics in precision agriculture has the potential to improve competitiveness and increase sustainability compared to current crop production methods and has become an increasingly active area of research. Tractor guidance systems for supervised navigation and implement control have reached the market, and prototypes of field robots performing precision agriculture tasks without human intervention also exist. But research in advanced cognitive perception and behaviour that is required to enable a more efficient, reliable and safe autonomy becomes increasingly demanding due to the growing software complexity. A lack of collaboration between research groups contributes to the problem. Scientific publications describe methods and results from the work, but little field robot software is released and documented for others to use. We hypothesize that a common open software platform tailored to field robots in precision agriculture will significantly decrease development time and resources required to perform experiments due to efficient reuse of existing work across projects and robot platforms. In this work we present the FroboMind software platform and evaluate the performance when applied to precision agriculture tasks.
3. Agricultural Conservation Planning Framework: 3. Land Use and Field Boundary Database Development and Structure.
Science.gov (United States)
Tomer, Mark D; James, David E; Sandoval-Green, Claudette M J
2017-05-01
Conservation planning information is important for identifying options for watershed water quality improvement and can be developed for use at field, farm, and watershed scales. Translation across scales is a key issue impeding progress at watershed scales because watershed improvement goals must be connected with implementation of farm- and field-level conservation practices to demonstrate success. This is particularly true when examining alternatives for "trap and treat" practices implemented at agricultural-field edges to control (or influence) water flows through fields, landscapes, and riparian corridors within agricultural watersheds. We propose that database structures used in developing conservation planning information can achieve translation across conservation-planning scales, and we developed the Agricultural Conservation Planning Framework (ACPF) to enable practical planning applications. The ACPF comprises a planning concept, a database to facilitate field-level and watershed-scale analyses, and an ArcGIS toolbox with Python scripts to identify specific options for placement of conservation practices. This paper appends two prior publications and describes the structure of the ACPF database, which contains land use, crop history, and soils information and is available for download for 6091 HUC12 watersheds located across Iowa, Illinois, Minnesota, and parts of Kansas, Missouri, Nebraska, and Wisconsin and comprises information on 2.74 × 10 agricultural fields (available through /). Sample results examining land use trends across Iowa and Illinois are presented here to demonstrate potential uses of the database. While designed for use with the ACPF toolbox, users are welcome to use the ACPF watershed data in a variety of planning and modeling approaches. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc.
4. Long-term monitoring of nitrate transport to drainage from three agricultural clayey till fields
Science.gov (United States)
Ernstsen, V.; Olsen, P.; Rosenbom, A. E.
2015-08-01
The application of nitrogen (N) fertilisers to crops grown on tile-drained fields is required to sustain most modern crop production, but it poses a risk to the aquatic environment since tile drains facilitate rapid transport pathways with no significant reduction in nitrate. To maintain the water quality of the aquatic environment and the provision of food from highly efficient agriculture in line with the EU's Water Framework Directive and Nitrates Directive, field-scale knowledge is essential for introducing water management actions on-field or off-field and producing an optimal differentiated N-regulation in future. This study strives to provide such knowledge by evaluating on 11 years of nitrate-N concentration measurements in drainage from three subsurface-drained clayey till fields (1.3-2.3 ha) representing approximately 71 % of the surface sediments in Denmark dominated by clay. The fields differ in their inherent hydrogeological field settings (e.g. soil-type, geology, climate, drainage and groundwater table) and the agricultural management of the fields (e.g. crop type, type of N fertilisers and agricultural practices). The evaluation revealed three types of clayey till fields characterised by: (i) low net precipitation, high concentration of nitrate-N, and short-term low intensity drainage at air temperatures often below 5 °C; (ii) medium net precipitation, medium concentration of nitrate-N, and short-term medium-intensity drainage at air temperatures often above 5 °C; and (iii) high net precipitation, low concentration of nitrate-N and long-term high intensity drainage at air temperatures above 5 °C. For each type, on-field water management actions, such as the selection of crop types and introduction of catch crops, appeared relevant, whereas off-field actions only seemed relevant for the latter two field types given the temperature-dependent reduction potential of nitrate off-field. This initial well-documented field-scale knowledge from fields
5. A mobile app for delivering in-field soil data for precision agriculture
Science.gov (United States)
Isaacs, John P.; Stojanovic, Vladeta; Falconer, Ruth E.
2015-04-01
In the last decade precision agriculture has grown from a concept to an emerging technology, largely due to the maturing of GPS and mobile mapping. We investigated methods for reliable delivery and display of appropriate and context aware in-field farm data on mobile devices by developing a prototype android mobile app. The 3D app was developed using OpenGL ES 2.0 and written in Java, using the Android Development Tools (ADT) SDK. The app is able to obtain GPS coordinates and automatically synchronise the view and load relevant data based on the user's location. The intended audience of the mobile app is farmers and agronomists. Apps are becoming an essential tool in an agricultural professional's arsenal however most existing apps are limited to 2D display of data even though the modern chips in mobile devices can support the display of 3D graphics at interactive rates using technologies such as webGL. This project investigated the use of games techniques in the delivery and 3D display of field data, recognising that this may be a departure from the way the field data is currently delivered and displayed to farmers and agronomists. Different interactive 3D visualisation methods presenting spatial and temporal variation in yield values were developed and tested. It is expected that this app can be used by farmers and agronomists to support decision making in the field of precision agriculture and this is a growing market in UK and Europe.
6. Profiling nematode communities in unmanaged flowerbed and agricultural field soils in Japan by DNA barcode sequencing.
Directory of Open Access Journals (Sweden)
Hisashi Morise
Full Text Available Soil nematodes play crucial roles in the soil food web and are a suitable indicator for assessing soil environments and ecosystems. Previous nematode community analyses based on nematode morphology classification have been shown to be useful for assessing various soil environments. Here we have conducted DNA barcode analysis for soil nematode community analyses in Japanese soils. We isolated nematodes from two different environmental soils of an unmanaged flowerbed and an agricultural field using the improved flotation-sieving method. Small subunit (SSU rDNA fragments were directly amplified from each of 68 (flowerbed samples and 48 (field samples isolated nematodes to determine the nucleotide sequence. Sixteen and thirteen operational taxonomic units (OTUs were obtained by multiple sequence alignment from the flowerbed and agricultural field nematodes, respectively. All 29 SSU rDNA-derived OTUs (rOTUs were further mapped onto a phylogenetic tree with 107 known nematode species. Interestingly, the two nematode communities examined were clearly distinct from each other in terms of trophic groups: Animal predators and plant feeders were markedly abundant in the flowerbed soils, in contrast, bacterial feeders were dominantly observed in the agricultural field soils. The data from the flowerbed nematodes suggests a possible food web among two different trophic nematode groups and plants (weeds in the closed soil environment. Finally, DNA sequences derived from the mitochondrial cytochrome oxidase c subunit 1 (COI gene were determined as a DNA barcode from 43 agricultural field soil nematodes. These nematodes were assigned to 13 rDNA-derived OTUs, but in the COI gene analysis were assigned to 23 COI gene-derived OTUs (cOTUs, indicating that COI gene-based barcoding may provide higher taxonomic resolution than conventional SSU rDNA-barcoding in soil nematode community analysis.
7. Profiling Nematode Communities in Unmanaged Flowerbed and Agricultural Field Soils in Japan by DNA Barcode Sequencing
Science.gov (United States)
Morise, Hisashi; Miyazaki, Erika; Yoshimitsu, Shoko; Eki, Toshihiko
2012-01-01
Soil nematodes play crucial roles in the soil food web and are a suitable indicator for assessing soil environments and ecosystems. Previous nematode community analyses based on nematode morphology classification have been shown to be useful for assessing various soil environments. Here we have conducted DNA barcode analysis for soil nematode community analyses in Japanese soils. We isolated nematodes from two different environmental soils of an unmanaged flowerbed and an agricultural field using the improved flotation-sieving method. Small subunit (SSU) rDNA fragments were directly amplified from each of 68 (flowerbed samples) and 48 (field samples) isolated nematodes to determine the nucleotide sequence. Sixteen and thirteen operational taxonomic units (OTUs) were obtained by multiple sequence alignment from the flowerbed and agricultural field nematodes, respectively. All 29 SSU rDNA-derived OTUs (rOTUs) were further mapped onto a phylogenetic tree with 107 known nematode species. Interestingly, the two nematode communities examined were clearly distinct from each other in terms of trophic groups: Animal predators and plant feeders were markedly abundant in the flowerbed soils, in contrast, bacterial feeders were dominantly observed in the agricultural field soils. The data from the flowerbed nematodes suggests a possible food web among two different trophic nematode groups and plants (weeds) in the closed soil environment. Finally, DNA sequences derived from the mitochondrial cytochrome oxidase c subunit 1 (COI) gene were determined as a DNA barcode from 43 agricultural field soil nematodes. These nematodes were assigned to 13 rDNA-derived OTUs, but in the COI gene analysis were assigned to 23 COI gene-derived OTUs (cOTUs), indicating that COI gene-based barcoding may provide higher taxonomic resolution than conventional SSU rDNA-barcoding in soil nematode community analysis. PMID:23284767
8. An optimized field coverage planning approach for navigation of agricultural robots in fields involving obstacle areas
DEFF Research Database (Denmark)
Hameed, Ibahim; Bochtis, D.; Sørensen, C.A.
2013-01-01
-field obstacle areas, the headland paths generation for the field and each obstacle area, the implementation of a genetic algorithm to optimize the sequence that the field robot vehicle will follow to visit the blocks, and an algorithmically generation of the task sequences derived from the farmer practices......Technological advances combined with the demand of cost efficiency and environmental considerations lead farmers to review their practices towards the adoption of new managerial approaches including enhanced automation. The application of field robots is one of the most promising advances among....... This approach has proven that it is possible to capture the practices of farmers and embed these practices in an algorithmic description providing a complete field area coverage plan in a form prepared for execution by the navigation system of a field robot....
9. Proximity to agricultural fields as proxy for environmental exposure to pesticides among children : The PIAMA birth cohort
NARCIS (Netherlands)
Bukalasa, Joseph S; Brunekreef, Bert; Brouwer, Maartje; Vermeulen, Roel; de Jongste, Johan C.; van Rossem, Lenie; Vonk, Judith M.; Wijga, Alet; Huss, Anke; Gehring, Ulrike
2017-01-01
Background: Agricultural pesticides are frequently used for crop protection. Residents living in close proximity to treated fields may be exposed to these pesticides. There is some indication that children living near agricultural fields have an increased risk of developing asthma and decreased lung
10. System and Field Devices (non Nuclear) in Agriculture Research in Malaysian Nuclear Agency
International Nuclear Information System (INIS)
Shyful Azizi Abdul Rahman; Abdul Rahim Harun
2015-01-01
Research to improve productivity on an ongoing basis in the agricultural sector is essential to ensure and guarantee the country's food security. Malaysian Nuclear Agency, agricultural research had begun in 1981 in which the focus of research is related to mutation breeding, irradiation and the use of isotopes in the study of plant nutrition. Although projects agricultural research carried out based on nuclear technology, other information relating to agricultural research such as agronomy, plant physiology, meteorology and ecology, soil characteristics and water is essential to obtain the understanding and research results that are relevant and significant. Data acquisition for other aspects also need a system and a modern and efficient equipment, in accordance with current technological developments. This paper describes the use, function and capabilities of the existing field equipment available in Agrotechnology and Biosciences Division, Malaysian Nuclear Agency in acquiring data related to weather, measurement and control of ground water, soil nutrients assessment and monitoring of plant physiology. The latest technological developments in sensor technology, computer technology and communication is very helpful in getting data more easily, quickly and accurately. Equipment and the data obtained is also likely to be used by researchers in other fields in Nuclear Malaysia. (author)
11. Agricultural terminology in Russian language on the Institute of field and vegetable crops example
Directory of Open Access Journals (Sweden)
Savin Dragana
2014-01-01
Full Text Available Contemporary science demands that scientists are following domestic and foreign scientific and technical achievements through conference attendances and scientific and professional literature. Agricultural science is based on practical data, field experiments, but nevertheless it is essential to be up to date with the work of foreign researchers, scientific centers and institutions through their publications. The aim of this paper was to present a part of the agricultural lexicon (with the accent on the plant species names, as well as the general scientific and organizational terms with the equivalents in Russian - Serbian and Serbian - Russian, which is of the great importance in activities of Institute of Field and Vegetable Crops, presented through perennial practices of translation. Those terms are recognized as important and frequent, without wishing to go into professional divisions in agriculture as science. This paper is dedicated to the scientists who posses basic linguistic knowledge of Russian language and are starting to use Russian scientific and professional literature in agriculture, as well as students of Russian language for the purpose of establishing and widening linguistic fund.
12. Time dependence of the field energy densities surrounding sources: Application to scalar mesons near point sources and to electromagnetic fields near molecules
International Nuclear Information System (INIS)
Persico, F.; Power, E.A.
1987-01-01
The time dependence of the dressing-undressing process, i.e., the acquiring or losing by a source of a boson field intensity and hence of a field energy density in its neighborhood, is considered by examining some simple soluble models. First, the loss of the virtual field is followed in time when a point source is suddenly decoupled from a neutral scalar meson field. Second, an initially bare point source acquires a virtual meson cloud as the coupling is switched on. The third example is that of an initially bare molecule interacting with the vacuum of the electromagnetic field to acquire a virtual photon cloud. In all three cases the dressing-undressing is shown to take place within an expanding sphere of radius r = ct centered at the source. At each point in space the energy density tends, for large times, to that of the ground state of the total system. Differences in the time dependence of the dressing between the massive scalar field and the massless electromagnetic field are discussed. The results are also briefly discussed in the light of Feinberg's ideas on the nature of half-dressed states in quantum field theory
13. Effects of agricultural practices of three crops on the soil communities under Mediterranean conditions: field evaluation.
Science.gov (United States)
Leitão, Sara; José Cerejeira, Maria; Abreu, Manuela; Sousa, José Paulo
2014-05-01
Sustainable agricultural production relies on soil communities as the main actors in key soil processes necessary to maintain sustainable soil functioning. Soil biodiversity influences soil physical and chemical characteristics and thus the sustainability of crop and agro-ecosystems functioning. Agricultural practices (e.g.: soil tillage, pesticides and fertilizer applications, irrigation) may affects negatively or positively soil biodiversity and abundances by modifying the relationships between organisms in the soil ecosystem. The present study aimed to study the influence of agricultural practices of three crops (potato, onion and maize) under Mediterranean climate conditions on soil macro- and mesofauna during their entire crop cycles. Effects on soil communities were assessed at a higher tier of environmental risk assessment comprising field testing of indigenous edaphic communities in a selected study-site located in a major agriculture region of Central Portugal, Ribatejo e Oeste, neighbouring protected wetlands. A reference site near the agricultural field site was selected as a Control site to compare the terrestrial communities' composition and variation along the crop cycle. The field soil and Control site soil are sandy loam soils. Crops irrigation was performed by center-pivot (automated sprinkler that rotates in a half a circle area) and by sprinklers. Soil macro- and mesofauna were collected at both sites (field and Control) using two methodologies through pitfall trapping and soil sampling. The community of soil macro- and mesofauna of the three crops field varied versus control site along the crops cycles. Main differences were due to arachnids, coleopterans, ants and adult Diptera presence and abundance. The feeding activity of soil fauna between control site and crop areas varied only for potato and onion crops vs. control site but not among crops. Concentration of pesticides residues in soil did not cause apparent negative effects on the soil
14. Towards an Open Software Platform for Field Robots in Precision Agriculture
DEFF Research Database (Denmark)
Jensen, Kjeld; Larsen, Morten; Nielsen, Søren H
2014-01-01
Robotics in precision agriculture has the potential to improve competitiveness and increase sustainability compared to current crop production methods and has become an increasingly active area of research. Tractor guidance systems for supervised navigation and implement control have reached...... the market, and prototypes of field robots performing precision agriculture tasks without human intervention also exist. But research in advanced cognitive perception and behaviour that is required to enable a more efficient, reliable and safe autonomy becomes increasingly demanding due to the growing...... software complexity. A lack of collaboration between research groups contributes to the problem. Scientific publications describe methods and results from the work, but little field robot software is released and documented for others to use. We hypothesize that a common open software platform tailored...
15. The dominant factors affecting agricultural land use (rice field change in Yogyakarta Special Province
Directory of Open Access Journals (Sweden)
2013-07-01
The research shows that the period of 1980 - 2000 in Yogyakarta Special Province has indicated very significantly the increase in population, the development of road and the extension of built up area. For the time being, agricultural land mainly in Sleman Regency, Bantul Regency and Yogyakarta Municipality has decreased. Sleman regency performed the largest decrease of rice field and followed after then by Bantul regency and Yogyakarta Municipality. The regency of Kulon Progo and Gunung Kidul have experienced reverse phenomenon i.e. the increase of rice field during this period. Individually or simultaneously, three variables used in this research (number of people, road's length and built up area have significantly influenced the agricultural land use.
16. Road verges and winter wheat fields as resources for wild bees in agricultural landscapes
DEFF Research Database (Denmark)
Henriksen, Casper Christian I; Langer, Vibeke
2013-01-01
The effects of farming system on plant density and flowering of dicotyledonous herbs of high value for bees were investigated in 14 organic and 14 conventional winter wheat fields and adjacent road verges. The organic and conventional winter wheat fields/road verges were paired based on the perce......The effects of farming system on plant density and flowering of dicotyledonous herbs of high value for bees were investigated in 14 organic and 14 conventional winter wheat fields and adjacent road verges. The organic and conventional winter wheat fields/road verges were paired based...... on the percentage of semi-natural habitats in the surrounding landscape at 1-km scale. Mean density of high value bee plants per Raunkiaer circle was significantly higher in organic winter wheat fields and their adjacent road verges than in their conventionally farmed counterparts. The effect of organic farming...... was even more pronounced on the flowering stage of high value bee plants, with 10-fold higher mean density of flowering plants in organic fields than in conventional fields and 1.9-fold higher in road verges bordering organic fields than in those bordering conventional fields. In summary, organic farming...
17. Innovating for skills enhancement in agricultural sciences in Africa: The centrality of field attachment programs
Directory of Open Access Journals (Sweden)
Anthony Egeru
2016-09-01
18. Keeping agricultural soil out of rivers: evidence of sediment and nutrient accumulation within field wetlands in the UK.
Science.gov (United States)
Ockenden, Mary C; Deasy, Clare; Quinton, John N; Surridge, Ben; Stoate, Chris
2014-03-15
Intensification of agriculture has resulted in increased soil degradation and erosion, with associated pollution of surface waters. Small field wetlands, constructed along runoff pathways, offer one option for slowing down and storing runoff in order to allow more time for sedimentation and for nutrients to be taken up by plants or micro-organisms. This paper describes research to provide quantitative evidence for the effectiveness of small field wetlands in the UK landscape. Ten wetlands were built on four farms in Cumbria and Leicestershire, UK. Annual surveys of sediment and nutrient accumulation in 2010, 2011 and 2012 indicated that most sediment was trapped at a sandy site (70 tonnes over 3 years), compared to a silty site (40 tonnes over 3 years) and a clay site (2 tonnes over 3 years). The timing of rainfall was more important than total annual rainfall for sediment accumulation, with most sediment transported in a few intense rainfall events, especially when these coincided with bare soil or poor crop cover. Nutrient concentration within sediments was inversely related to median particle size, but the total mass of nutrients trapped was dependent on the total mass of sediment trapped. Ratios of nutrient elements in the wetland sediments were consistent between sites, despite different catchment characteristics across the individual wetlands. The nutrient value of sediment collected from the wetlands was similar to that of soil in the surrounding fields; dredged sediment was considered to have value as soil replacement but not as fertiliser. Overall, small field wetlands can make a valuable contribution to keeping soil out of rivers. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.
19. Vegetation Water Content Mapping in a Diverse Agricultural Landscape: National Airborne Field Experiment 2006
Science.gov (United States)
Cosh, Michael H.; Jing Tao; Jackson, Thomas J.; McKee, Lynn; O'Neill, Peggy
2011-01-01
Mapping land cover and vegetation characteristics on a regional scale is critical to soil moisture retrieval using microwave remote sensing. In aircraft-based experiments such as the National Airborne Field Experiment 2006 (NAFE 06), it is challenging to provide accurate high resolution vegetation information, especially on a daily basis. A technique proposed in previous studies was adapted here to the heterogenous conditions encountered in NAFE 06, which included a hydrologically complex landscape consisting of both irrigated and dryland agriculture. Using field vegetation sampling and ground-based reflectance measurements, the knowledge base for relating the Normalized Difference Water Index (NDWI) and the vegetation water content was extended to a greater diversity of agricultural crops, which included dryland and irrigated wheat, alfalfa, and canola. Critical to the generation of vegetation water content maps, the land cover for this region was determined from satellite visible/infrared imagery and ground surveys with an accuracy of 95.5% and a kappa coefficient of 0.95. The vegetation water content was estimated with a root mean square error of 0.33 kg/sq m. The results of this investigation contribute to a more robust database of global vegetation water content observations and demonstrate that the approach can be applied with high accuracy. Keywords: Vegetation, field experimentation, thematic mapper, NDWI, agriculture.
20. Trade and agriculture policy conditions for the use of plant oils in the energy field
International Nuclear Information System (INIS)
Joerdens, R.
1994-01-01
Preservation of resources, ecology and agricultural policy supply the most important argument for an increased use of raw materials which grow again. Regenerative raw materials are at present grown on about 2.5% of the arable land area in Germany, where production for the chemical technical field is to the fore. Access to the energy field is, however, difficult due to the considerable economic deficit compared to fossil fuels. Possibilities of use exist mainly in heating plant and in Diesel engines. (BWI) [de
1. Soil nutrient content of old-field and agricultural ecosystems exposed to chronic gamma irradiation
International Nuclear Information System (INIS)
Armentano, T.V.; Holt, B.R.; Bottino, P.J.
1975-01-01
Soil nutrients (extractable P. and NO 3 -N, exchangeable Ca, Mg and K), exchangeable Al, pH and organic matter content were measured over the top six inches of the soils of the seven-year old-field portion and the cultivated portion of the Brookhaven gamma field. Although concentrations of all nutrient elements were higher in the agricultural soil, the distributions of Ca, P, Al, pH and organic matter were similar along the radiation gradient in both fields. There was also a regular reduction in the phosphorus with decreasing exposure, but distribution of other elements was not clearly related to radiation effects. The distribution of all elements except K was significantly correlated with pH in the agricultural soil. In the old-field only Ca, Mg and Al showed this relationship. The most conspicuous effects of nearly 25 yr of chronic irradiation of the site were a reduction in soil organic matter content and an increase in soil P in both fields. (author)
2. Rainfall-runoff of anthropogenic waste indicators from agricultural fields applied with municipal biosolids
Science.gov (United States)
Gray, James L.; Borch, Thomas; Furlong, Edward T.; Davis, Jessica; Yager, Tracy; Yang, Yun-Ya; Kolpin, Dana W.
2017-01-01
The presence of anthropogenic contaminants such as antimicrobials, flame-retardants, and plasticizers in runoff from agricultural fields applied with municipal biosolids may pose a potential threat to the environment. This study assesses the potential for rainfall-induced runoff of 69 anthropogenic waste indicators (AWIs), widely found in household and industrial products, from biosolids amended field plots. The agricultural field containing the test plots was treated with biosolids for the first time immediately prior to this study. AWIs present in soil and biosolids were isolated by continuous liquid-liquid extraction and analyzed by full-scan gas chromatography/mass spectrometry. Results for 18 AWIs were not evaluated due to their presence in field blank QC samples, and another 34 did not have sufficient detection frequency in samples to analyze trends in data. A total of 17 AWIs, including 4-nonylphenol, triclosan, and tris(2-butoxyethyl)phosphate, were present in runoff with acceptable data quality and frequency for subsequent interpretation. Runoff samples were collected 5 days prior to and 1, 9, and 35 days after biosolids application. Of the 17 AWIs considered, 14 were not detected in pre-application samples, or their concentrations were much smaller than in the sample collected one day after application. A range of trends was observed for individual AWI concentrations (typically from 0.1 to 10 μg/L) over the course of the study, depending on the combination of partitioning and degradation mechanisms affecting each compound most strongly. Overall, these results indicate that rainfall can mobilize anthropogenic contaminants from biosolids-amended agricultural fields, directly to surface waters and redistribute them to terrestrial sites away from the point of application via runoff. For 14 of 17 compounds examined, the potential for runoff remobilization during rainstorms persists even after three 100-year rainstorm-equivalent simulations and the
3. Rainfall-runoff of anthropogenic waste indicators from agricultural fields applied with municipal biosolids.
Science.gov (United States)
Gray, James L; Borch, Thomas; Furlong, Edward T; Davis, Jessica G; Yager, Tracy J; Yang, Yun-Ya; Kolpin, Dana W
2017-02-15
The presence of anthropogenic contaminants such as antimicrobials, flame-retardants, and plasticizers in runoff from agricultural fields applied with municipal biosolids may pose a potential threat to the environment. This study assesses the potential for rainfall-induced runoff of 69 anthropogenic waste indicators (AWIs), widely found in household and industrial products, from biosolids amended field plots. The agricultural field containing the test plots was treated with biosolids for the first time immediately prior to this study. AWIs present in soil and biosolids were isolated by continuous liquid-liquid extraction and analyzed by full-scan gas chromatography/mass spectrometry. Results for 18 AWIs were not evaluated due to their presence in field blank QC samples, and another 34 did not have sufficient detection frequency in samples to analyze trends in data. A total of 17 AWIs, including 4-nonylphenol, triclosan, and tris(2-butoxyethyl)phosphate, were present in runoff with acceptable data quality and frequency for subsequent interpretation. Runoff samples were collected 5days prior to and 1, 9, and 35days after biosolids application. Of the 17 AWIs considered, 14 were not detected in pre-application samples, or their concentrations were much smaller than in the sample collected one day after application. A range of trends was observed for individual AWI concentrations (typically from 0.1 to 10μg/L) over the course of the study, depending on the combination of partitioning and degradation mechanisms affecting each compound most strongly. Overall, these results indicate that rainfall can mobilize anthropogenic contaminants from biosolids-amended agricultural fields, directly to surface waters and redistribute them to terrestrial sites away from the point of application via runoff. For 14 of 17 compounds examined, the potential for runoff remobilization during rainstorms persists even after three 100-year rainstorm-equivalent simulations and the passage of a
4. Assessment of Agricultural Water Productivity for Tea Production in Tea Fields of Guilan Province
Directory of Open Access Journals (Sweden)
kourosh majdsalimi
2016-05-01
Full Text Available Water productivity index is one of the main factors in efficient use of water for agricultural products. In this study, the rate of water productivity (WP in six irrigated tea fields and three rainfed (no irrigation were assessed by farmer’s management for two years (2009-2010. Yield of each tea field in successive harvests, soil moisture monitoring by gravimetric soil and use of water balance equation was conducted during the growing seasons. Volume of water entered to irrigation system and amount of water reached to surface level were also measured. Tea mean yield in irrigated and rainfed field were 2843 and 1095 Kg. ha-1, respectively. Average of gross irrigation and effective rainfall (WP and irrigation water productivity (IWP in the irrigated fields were 4.39 and 4.55 kg (made tea ha-1 mm-1 and average of net WP (actual evaportanspiration and net IWP was 5.18 and 6.61 kg ha-1 mm-1, respectively. Average WP in rainfed tea fields was 3.4 kg ha-1 for each mm of effective rainfall. The most effective factors on WP reduction in tea fields were improper harvesting operations (un standard plucking and economic problems. Moreover, improper operation and maintenance and old irrigation systems and unprincipled irrigation scheduling in irrigated tea fields were also effective on WP reduction. Comparing the results of this study with other studies in past, showed that by implementing the proper methods in irrigation management and appropriate agricultural practices can improve water productivity in tea fields.
5. Pre-Columbian Agriculture: Construction history of raised fields in Bermeo, in the Bolivian Lowlands
Science.gov (United States)
Rodrigues, Leonor; Fehr, Seraina; Lombardo, Umberto; Veit, Heinz
2013-04-01
Since the beginning of the 1960s, research in the Amazon has revealed that in Pre-Columbian times, landscapes that were viewed as challenging living environments were nevertheless altered in several ways. Raised fields agriculture is one of the most impressive phenomena that can be found in South-eastern Amazonia. Pre-Columbian raised fields are earth platforms of differing shape and dimension that are elevated above the landscape's natural surface. The Llanos de Moxos, situated in the Bolivian Lowlands is one of the areas with the highest density of raised fields. In spite of the high interest in raised field agriculture, very few field-based investigations have been performed. As a result, there remains little explanation as to how they were constructed, managed or for what time frame they were in use. Recently, more detailed investigations have been performed on raised fields located in the indigenous community of Bermeo, in the vicinity of San Ignacio de Moxos. Combined data from fieldwork and laboratory analysis including particle size distribution, thin section micromorphology and radiocarbon analyses as well as optically stimulated luminescence analysis has given an insight into the history of their construction. Applied to the Bolivian Lowlands, the current study provides for the first time data showing aspects of the Pre-Columbian management of the raised fields, and a chronological sequence of utilization and abandonment of these fields. Radiocarbon dating has shown that the raised fields had been in use since as early as 900 AD. Two distinct paleosols identified in the field sequence point to the existence of two separate prolonged soil formation periods. The paleosols are characterized by initial stages of Bt-horizons. Each soil sequence indicates therefore a particular stable period of the field during which no new earth was heaped up. This suggests that contrary to the well supported theory that raised fields were managed through continuous
6. On dealing with the pollution costs in agriculture: A case study of paddy fields
Energy Technology Data Exchange (ETDEWEB)
Yaqubi, Morteza, E-mail: [email protected] [Faculty of Management and Economics, Department of Agricultural Economics, University of Sistan and Baluchestan Zahedan (Iran, Islamic Republic of); Shahraki, Javad, E-mail: [email protected] [Faculty of Management and Economics, Department of Agricultural Economics, University of Sistan and Baluchestan Zahedan (Iran, Islamic Republic of); Sabouhi Sabouni, Mahmood, E-mail: [email protected] [Department of Agricultural Economics, Ferdowsi University of Mashhad, Azadi Square, Mashhad (Iran, Islamic Republic of)
2016-06-15
The main purpose of this study is to evaluate marginal abatement cost of the main agricultural pollutants. In this sense, we construct three indices including Net Global Warming Potential (NGWP) and Nitrogen Surplus (NS), simulated by a biogeochemistry model, and also an Environmental Impact Quotient (EQI) for paddy fields. Then, using a Data Envelopment Analysis (DEA) model, we evaluate environmental inefficiencies and shadow values of these indices. The results show that there is still room for improvement at no extra cost just through a better input management. Besides, enormous potential for pollution reduction in the region is feasible. Moreover, in paddy cultivation, marginal abatement cost of pesticides and herbicides are much bigger than nitrogen surplus and greenhouse gasses. In addition, in the status quo, the mitigation costs are irrelevant to production decisions. Finally, to deal with the private pollution costs, market-based instruments are proved to be better than command-and-control regulation. - Highlights: • To evaluate agricultural pollution costs, a combination of two DNDC and DEA models was introduced. • The shadow values of three main agricultural pollutants in paddy fields were evaluated. • In the study area, a high potential for pollution reduction is feasible. • The pollution cost of pesticides are much bigger than nitrogen surplus and greenhouse gases. • From the farmers' viewpoint, a positive shadow value of undesirable outputs also is feasible. • To deal with the pollution costs, market-based instruments are preferred to command-and-control regulation.
7. On dealing with the pollution costs in agriculture: A case study of paddy fields
International Nuclear Information System (INIS)
Yaqubi, Morteza; Shahraki, Javad; Sabouhi Sabouni, Mahmood
2016-01-01
The main purpose of this study is to evaluate marginal abatement cost of the main agricultural pollutants. In this sense, we construct three indices including Net Global Warming Potential (NGWP) and Nitrogen Surplus (NS), simulated by a biogeochemistry model, and also an Environmental Impact Quotient (EQI) for paddy fields. Then, using a Data Envelopment Analysis (DEA) model, we evaluate environmental inefficiencies and shadow values of these indices. The results show that there is still room for improvement at no extra cost just through a better input management. Besides, enormous potential for pollution reduction in the region is feasible. Moreover, in paddy cultivation, marginal abatement cost of pesticides and herbicides are much bigger than nitrogen surplus and greenhouse gasses. In addition, in the status quo, the mitigation costs are irrelevant to production decisions. Finally, to deal with the private pollution costs, market-based instruments are proved to be better than command-and-control regulation. - Highlights: • To evaluate agricultural pollution costs, a combination of two DNDC and DEA models was introduced. • The shadow values of three main agricultural pollutants in paddy fields were evaluated. • In the study area, a high potential for pollution reduction is feasible. • The pollution cost of pesticides are much bigger than nitrogen surplus and greenhouse gases. • From the farmers' viewpoint, a positive shadow value of undesirable outputs also is feasible. • To deal with the pollution costs, market-based instruments are preferred to command-and-control regulation.
8. Rapid mineralisation of the herbicide isoproturon in soil from a previously treated Danish agricultural field.
Science.gov (United States)
Sørensen, Sebastian R; Aamand, Jens
2003-10-01
Mineralisation of the phenylurea herbicide isoproturon (3-(4-isopropylphenyl)-1,1-dimethylurea) and two of its known metabolites, 3-(4-isopropylphenyl)-1-methylurea (monodesmethyl-isoproturon) and 4-isopropylaniline, was studied in Danish agricultural soils with or without previous exposure to isoproturon. A potential for rapid mineralisation of isoproturon and the two metabolites was present in soils sampled from three plots within an agricultural field previously treated regularly with the herbicide, with 34-45%, 51-58% and 33-36% of the added [phenyl-U-14C]isoproturon, [phenyl-U-14C]monodesmethyl-isoproturon and [phenyl-U-14C]4-isopropylaniline metabolised to [14C]carbon dioxide within 30 days at 20 degrees C. In contrast, such extensive mineralisation of these three compounds was not observed within this period in soils sampled from two other agricultural fields without previous treatment with isoproturon. The mineralisation patterns indicated growth-linked metabolism of the three compounds in the previously exposed soils, and doubling times for [14C]carbon dioxide production ranged from 1.6 to 3.2, 1.0 to 2.1 and 1.3 to 1.7 days for isoproturon, monodesmethyl-isoproturon and 4-isopropylaniline, respectively. The ability to mineralise [phenyl-U-14C]isoproturon to [14C]carbon dioxide was successfully sub-cultured to a fresh mineral medium which provided isoproturon as sole source of carbon and nitrogen. One of the soils sampled from an agricultural field not previously treated with isoproturon showed accelerated mineralisation of [phenyl-U-14C]4-isopropylaniline toward the end of the experiment, with a doubling time for [14C]carbon dioxide production of 7.4days. This study indicates that the occurrence of rapid mineralisation of the phenyl ring of isoproturon to carbon dioxide is related to previous exposure to the herbicide, which suggests that microbial adaptation upon repeated isoproturon use may occur within agricultural fields.
9. More Gamma More Predictions: Gamma-Synchronization as a Key Mechanism for Efficient Integration of Classical Receptive Field Inputs with Surround Predictions
Science.gov (United States)
2016-01-01
During visual stimulation, neurons in visual cortex often exhibit rhythmic and synchronous firing in the gamma-frequency (30–90 Hz) band. Whether this phenomenon plays a functional role during visual processing is not fully clear and remains heavily debated. In this article, we explore the function of gamma-synchronization in the context of predictive and efficient coding theories. These theories hold that sensory neurons utilize the statistical regularities in the natural world in order to improve the efficiency of the neural code, and to optimize the inference of the stimulus causes of the sensory data. In visual cortex, this relies on the integration of classical receptive field (CRF) data with predictions from the surround. Here we outline two main hypotheses about gamma-synchronization in visual cortex. First, we hypothesize that the precision of gamma-synchronization reflects the extent to which CRF data can be accurately predicted by the surround. Second, we hypothesize that different cortical columns synchronize to the extent that they accurately predict each other’s CRF visual input. We argue that these two hypotheses can account for a large number of empirical observations made on the stimulus dependencies of gamma-synchronization. Furthermore, we show that they are consistent with the known laminar dependencies of gamma-synchronization and the spatial profile of intercolumnar gamma-synchronization, as well as the dependence of gamma-synchronization on experience and development. Based on our two main hypotheses, we outline two additional hypotheses. First, we hypothesize that the precision of gamma-synchronization shows, in general, a negative dependence on RF size. In support, we review evidence showing that gamma-synchronization decreases in strength along the visual hierarchy, and tends to be more prominent in species with small V1 RFs. Second, we hypothesize that gamma-synchronized network dynamics facilitate the emergence of spiking output that
10. Multiple routes of pesticide exposure for honey bees living near agricultural fields.
Directory of Open Access Journals (Sweden)
Christian H Krupke
Full Text Available Populations of honey bees and other pollinators have declined worldwide in recent years. A variety of stressors have been implicated as potential causes, including agricultural pesticides. Neonicotinoid insecticides, which are widely used and highly toxic to honey bees, have been found in previous analyses of honey bee pollen and comb material. However, the routes of exposure have remained largely undefined. We used LC/MS-MS to analyze samples of honey bees, pollen stored in the hive and several potential exposure routes associated with plantings of neonicotinoid treated maize. Our results demonstrate that bees are exposed to these compounds and several other agricultural pesticides in several ways throughout the foraging period. During spring, extremely high levels of clothianidin and thiamethoxam were found in planter exhaust material produced during the planting of treated maize seed. We also found neonicotinoids in the soil of each field we sampled, including unplanted fields. Plants visited by foraging bees (dandelions growing near these fields were found to contain neonicotinoids as well. This indicates deposition of neonicotinoids on the flowers, uptake by the root system, or both. Dead bees collected near hive entrances during the spring sampling period were found to contain clothianidin as well, although whether exposure was oral (consuming pollen or by contact (soil/planter dust is unclear. We also detected the insecticide clothianidin in pollen collected by bees and stored in the hive. When maize plants in our field reached anthesis, maize pollen from treated seed was found to contain clothianidin and other pesticides; and honey bees in our study readily collected maize pollen. These findings clarify some of the mechanisms by which honey bees may be exposed to agricultural pesticides throughout the growing season. These results have implications for a wide range of large-scale annual cropping systems that utilize neonicotinoid seed
11. An application to model traffic intensity of agricultural machinery at field scale
Science.gov (United States)
Augustin, Katja; Kuhwald, Michael; Duttmann, Rainer
2017-04-01
Several soil-pressure-models deal with the impact of agricultural machines on soils. In many cases, these models were used for single spots and consider a static machine configuration. Therefore, a statement about the spatial distribution of soil compaction risk for entire working processes is limited. The aim of the study is the development of an application for the spatial modelling of traffic lanes from agricultural vehicles including wheel load, ground pressure and wheel passages at the field scale. The application is based on Open Source software, application and data formats, using python programming language. Minimum input parameters are GPS-positions, vehicles and tires (producer and model) and the tire inflation pressure. Five working processes were distinguished: soil tillage, manuring, plant protection, sowing and harvest. Currently, two different models (Diserens 2009, Rücknagel et al. 2015) were implemented to calculate the soil pressure. The application was tested at a study site in Lower Saxony, Germany. Since 2015, field traffic were recorded by RTK-GPS and used machine set ups were noted. Using these input information the traffic lanes, wheel load and soil pressure were calculated for all working processes. For instance, the maize harvest in 2016 with a crop chopper and one transport vehicle crossed about 55 % of the total field area. At some places the machines rolled over up to 46 times. Approximately 35 % of the total area was affected by wheel loads over 7 tons and soil pressures between 163 and 193 kPa. With the information about the spatial distribution of wheel passages, wheel load and soil pressure it is possible to identify hot spots of intensive field traffic. Additionally, the use of the application enables the analysis of soil compaction risk induced by agricultural machines for long- and short-term periods.
12. Development and field testing of agricultural snowmelting agents made from recycled bio-waste materials
International Nuclear Information System (INIS)
Hirota, T.; Hasegawa, M.; Tanaka, H.; Suzuki, S.; Tadano, T.
2008-01-01
In snow-covering region of Japan, the promotion of snowmelting with application of agricultural snowmelting agents ('Yusetsuzai' in Japanese) has been widely carried out by farmers at the snowmelting season. When black colored materials with albedo-lowering effect are spread on snow surface, absorption of solar radiation by snow is increased, the snowmelting is promoted and snow thawing date becomes earlier. As a result, the growing season of crop plants is extended. Existing agricultural snowmelting agents have been mostly made from industrial waste materials or industrial processed products due to requirement for the low cost of the raw materials. These agents may contain harmful heavy metal elements and may lead to environmental pollution. To solve these problems, we developed the new agricultural snowmelting agents made from recycled bio-waste materials generated from the fields of agriculture and fishery. The developed snowmelting agents were made from shells of Patinopecten yessoensis, fowl droppings and processed wastes of fish and shellfish, etc. Especially, the shells of Patinopecten yessoensis has problems due to generation of a huge quantity in Hokkaido. Therefore, the recycling-use of these waste materials was strongly requested and expected. The developed snowmelting agents were possible to spread efficiently and safely on the snow-surface without wide scattering by controlling the particle size within the range larger than 100 microm and smaller than 1180 microm. Results obtained from the field experiment showed that the albedo was decreased from 0.70 for natural snow to 0.20 and the promotion of snowmelting for 11 days was recognized when 100 kg/10a of developed agent was spread. The promoting ability of the developed agent was equivalent to those of the existing commercial snowmelting agents. (author)
13. Leaf Area Index Estimation Using Chinese GF-1 Wide Field View Data in an Agriculture Region.
Science.gov (United States)
Wei, Xiangqin; Gu, Xingfa; Meng, Qingyan; Yu, Tao; Zhou, Xiang; Wei, Zheng; Jia, Kun; Wang, Chunmei
2017-07-08
Leaf area index (LAI) is an important vegetation parameter that characterizes leaf density and canopy structure, and plays an important role in global change study, land surface process simulation and agriculture monitoring. The wide field view (WFV) sensor on board the Chinese GF-1 satellite can acquire multi-spectral data with decametric spatial resolution, high temporal resolution and wide coverage, which are valuable data sources for dynamic monitoring of LAI. Therefore, an automatic LAI estimation algorithm for GF-1 WFV data was developed based on the radiative transfer model and LAI estimation accuracy of the developed algorithm was assessed in an agriculture region with maize as the dominated crop type. The radiative transfer model was firstly used to simulate the physical relationship between canopy reflectance and LAI under different soil and vegetation conditions, and then the training sample dataset was formed. Then, neural networks (NNs) were used to develop the LAI estimation algorithm using the training sample dataset. Green, red and near-infrared band reflectances of GF-1 WFV data were used as the input variables of the NNs, as well as the corresponding LAI was the output variable. The validation results using field LAI measurements in the agriculture region indicated that the LAI estimation algorithm could achieve satisfactory results (such as R² = 0.818, RMSE = 0.50). In addition, the developed LAI estimation algorithm had potential to operationally generate LAI datasets using GF-1 WFV land surface reflectance data, which could provide high spatial and temporal resolution LAI data for agriculture, ecosystem and environmental management researches.
14. The effectiveness of agrobusiness technical training and education model for the field agricultural extension officers
Directory of Open Access Journals (Sweden)
Kristiyo Sumarwono
2017-07-01
Full Text Available The study was to: (1 find the most effective agrobusiness technical training and education model for the Field Agricultural Extension Officers to be implemented; and (2 to identify the knowledge level, the highest agrobusiness skills and the strongest self-confidence that might be achieved by the participants through the implemented training and education patterns. The study was conducted by means of experiment method with the regular pattern of training and education program as the control and the mentoring pattern of training and education program as the treatment. The three patterns of training and education programs served as the independent variables while the knowledge, the skills and the self-confidence served as the dependent variables. The study was conducted in three locations namely: the Institution of Agricultural Human Resources Development in the Province of Yogyakarta Special Region (Balai Pengembangan Sumber Daya Manusia Pertanian Daerah Istimewa Yogyakarta – BPSMP DIY; the Institution of Agricultural Human Resources Empowerment (Balai Pemberdayaan Sumber Daya Manusia Pertanian – BPSDMTAN Soropadan Temanggung Provinsi Jawa Tengah in Soropadan, Temanggung, the Province of Central Java; and the Institution of Training and Education in Semarang, the Province of Central Java (Badan Pendidikan dan Pelatihan Semarang Provinsi Jawa Tengah. The study was conducted to all of the participants who attended the agrobusiness technical training and education program and, therefore, all of the participants became the subjects of the study. The study was conducted from October 2013 until March 2014. The results of the study showed that: (1 there had not been any significant difference on the knowledge and the skills of the participants who attended the regular pattern in training and education programs and those who attended the mentoring pattern in training and education programs; (2 the regular pattern in training and education programs
15. Factors influencing the survival and leaching of tetracycline-resistant bacteria and Escherichia coli through structured agricultural fields
DEFF Research Database (Denmark)
Bech, Tina B.; Rosenbom, Annette E.; Kjaer, Jeanne
2014-01-01
Intense use of antibiotics in agricultural production may lead to the contamination of surface and groundwater by antibiotic-resistant bacteria. In the present study, the survival and leaching of E. coli and tetracycline-resistant bacteria were monitored at two well-structured agricultural fields...
16. Parkinson’s Disease Prevalence and Proximity to Agricultural Cultivated Fields
Directory of Open Access Journals (Sweden)
2015-01-01
Full Text Available The risk for developing Parkinson’s disease (PD is a combination of multiple environmental and genetic factors. The Negev (Southern Israel contains approximately 252.5 km2 of agricultural cultivated fields (ACF. We aimed to estimate the prevalence and incidence of PD and to examine possible geographical clustering and associations with agricultural exposures. We screened all “Clalit” Health Services members in the Negev (70% of the population between the years 2000 and 2012. Individual demographic, clinical, and medication prescription data were available. We used a refined medication tracer algorithm to identify PD patients. We used mixed Poisson models to calculate the smoothed standardized incidence rates (SIRs for each locality. We identified ACF and calculate the size and distance of the fields from each locality. We identified 3,792 cases of PD. SIRs were higher than expected in Jewish rural localities (median SIR [95% CI]: 1.41 [1.28; 1.53] in 2001–2004, 1.62 [1.48; 1.76] in 2005–2008, and 1.57 [1.44; 1.80] in 2009–2012. Highest SIR was observed in localities located in proximity to large ACF (SIR 1.54, 95% CI 1.32; 1.79. In conclusion, in this population based study we found that PD SIRs were higher than expected in rural localities. Furthermore, it appears that proximity to ACF and the field size contribute to PD risk.
17. Fe and Mn levels regulated by agricultural activities in alluvial groundwaters underneath a flooded paddy field
Energy Technology Data Exchange (ETDEWEB)
Kim, Kangjoo [School of Civil and Environmental Engineering, Kunsan National University, Jeonbuk 573-701 (Korea, Republic of)], E-mail: [email protected]; Kim, Hyun-Jung; Choi, Byoung-Young; Kim, Seok-Hwi; Park, Ki-hoon [School of Civil and Environmental Engineering, Kunsan National University, Jeonbuk 573-701 (Korea, Republic of); Park, Eungyu [Department of Geology, Kyungpook National University, Daegu 702-701 (Korea, Republic of); Koh, Dong-Chan [Korea Institute of Geoscience and Mineral Resources, Daejeon 305-350 (Korea, Republic of); Yun, Seong-Taek [Department of Earth and Environmental Sciences, Korea University, Seoul 136-701 (Korea, Republic of)
2008-01-15
Iron and Mn concentrations in fresh groundwaters of alluvial aquifers are generally high in reducing conditions reflecting low SO{sub 4} concentrations. The mass balance and isotopic approaches of this study demonstrate that reduction of SO{sub 4}, supplied from agricultural activities such as fertilization and irrigation, is important in lowering Fe and Mn levels in alluvial groundwaters underneath a paddy field. This study was performed to investigate the processes regulating Fe and Mn levels in groundwaters of a point bar area, which has been intensively used for flood cultivation. Four multilevel-groundwater samplers were installed to examine the relationship between geology and the vertical changes in water chemistry. The results show that Fe and Mn levels are regulated by the presence of NO{sub 3} at shallow depths and by SO{sub 4} reduction at the greater depths. Isotopic and mass balance analyses revealed that NO{sub 3} and SO{sub 4} in groundwater are mostly supplied from the paddy field, suggesting that the Fe-and Mn-rich zone of the study area is confined by the agricultural activities. For this reason, the geologic conditions controlling the infiltration of agrochemicals are also important for the occurrence of Fe/Mn-rich groundwaters in the paddy field area.
18. Spatial Variability of Physical Soil Quality Index of an Agricultural Field
Directory of Open Access Journals (Sweden)
Sheikh M. Fazle Rabbi
2014-01-01
Full Text Available A field investigation was carried out to evaluate the spatial variability of physical indicators of soil quality of an agricultural field and to construct a physical soil quality index (SQIP map. Surface soil samples were collected using 10 m×10 m grid from an Inceptisol on Ganges Tidal Floodplain of Bangladesh. Five physical soil quality indicators, soil texture, bulk density, porosity, saturated hydraulic conductivity (KS, and aggregate stability (measured as mean weight diameter, MWD were determined. The spatial structures of sand, clay, and KS were moderate but the structure was strong for silt, bulk density, porosity, and MWD. Each of the physical soil quality indicators was transformed into 0 and 1 using threshold criteria which are required for crop production. The transformed indicators were the combined into SQIP. The kriged SQIP map showed that the agricultural field studied could be divided into two parts having “good physical quality” and “poor physical soil quality.”
19. Emissions of carbon dioxide and methane from fields fertilized with digestate from an agricultural biogas plant
Science.gov (United States)
Czubaszek, Robert; Wysocka-Czubaszek, Agnieszka
2018-01-01
Digestate from biogas plants can play important role in agriculture by providing nutrients, improving soil structure and reducing the use of mineral fertilizers. Still, less is known about greenhouse gas emissions from soil during and after digestate application. The aim of the study was to estimate the emissions of carbon dioxide (CO2) and methane (CH4) from a field which was fertilized with digestate. The gas fluxes were measured with the eddy covariance system. Each day, the eddy covariance system was installed in various places of the field, depending on the dominant wind direction, so that each time the results were obtained from an area where the digestate was distributed. The results showed the relatively low impact of the studied gases emissions on total greenhouse gas emissions from agriculture. Maximum values of the CO2 and CH4 fluxes, 79.62 and 3.049 µmol s-1 m-2, respectively, were observed during digestate spreading on the surface of the field. On the same day, the digestate was mixed with the topsoil layer using a disc harrow. This resulted in increased CO2 emissions the following day. Intense mineralization of digestate, observed after fertilization may not give the expected effects in terms of protection and enrichment of soil organic matter.
20. Fe and Mn levels regulated by agricultural activities in alluvial groundwaters underneath a flooded paddy field
International Nuclear Information System (INIS)
Kim, Kangjoo; Kim, Hyun-Jung; Choi, Byoung-Young; Kim, Seok-Hwi; Park, Ki-hoon; Park, Eungyu; Koh, Dong-Chan; Yun, Seong-Taek
2008-01-01
Iron and Mn concentrations in fresh groundwaters of alluvial aquifers are generally high in reducing conditions reflecting low SO 4 concentrations. The mass balance and isotopic approaches of this study demonstrate that reduction of SO 4 , supplied from agricultural activities such as fertilization and irrigation, is important in lowering Fe and Mn levels in alluvial groundwaters underneath a paddy field. This study was performed to investigate the processes regulating Fe and Mn levels in groundwaters of a point bar area, which has been intensively used for flood cultivation. Four multilevel-groundwater samplers were installed to examine the relationship between geology and the vertical changes in water chemistry. The results show that Fe and Mn levels are regulated by the presence of NO 3 at shallow depths and by SO 4 reduction at the greater depths. Isotopic and mass balance analyses revealed that NO 3 and SO 4 in groundwater are mostly supplied from the paddy field, suggesting that the Fe-and Mn-rich zone of the study area is confined by the agricultural activities. For this reason, the geologic conditions controlling the infiltration of agrochemicals are also important for the occurrence of Fe/Mn-rich groundwaters in the paddy field area
1. Preparing students for higher education and careers in agriculture and related fields: An ethnography of an urban charter school
Science.gov (United States)
Henry, Kesha Atasha
This study explored the preparation of students for higher education and careers in agriculturally-related fields at an urban charter high school. The data were collected through interviews, observations, and field notes. The data were analyzed by qualitative methodology with phenomenology as the theoretical framework. Findings indicated that administrators thought it was important to incorporate agricultural science courses into urban school curricula. They stated that agricultural science courses gave urban students a different way of looking at science and helped to enhance the science and technology focus of the school. Further, agricultural science courses helped to break urban students' stereotypes about agriculture and helped to bring in more state funding for educational programs. However they thought that it was more challenging to teach agricultural science in urban versus rural schools and they focused more on Science, Technology, Engineering, and Mathematics (STEM) related careers. The students had mixed views about higher education and careers in agriculture. This was based on their limited knowledge and stereotypes about agricultural majors and career options. The students highlighted several key reasons why they chose to enroll in agricultural science courses. This included the benefits of dual science credits and the ability to earn an associate degree upon successful completion of their program. Students also loved science and appreciated the science intensive nature of the agricultural courses. Additionally, they thought that the agricultural science courses were better than the other optional courses. The results also showed that electronic media such as radio and TV had a negative impact on students' perceptions about higher education and careers in agriculturally-related fields. Conclusions and recommendations are presented.
2. Utilization of radiation in industrial, agricultural and medical fields and its perspective
International Nuclear Information System (INIS)
Shibata, Tokushi
2008-01-01
The current status for the utilization of radiation in Japan was given from the view point of the economic scale. The topics which will be developed in near future such as lithography, radiation processing, radiation analysis in the industry, mutation breeding, sterile insect technique, food irradiation in agriculture, and radiation diagnosis, radiation therapy in medical field were presented. The important techniques for the further development of utilization of radiation will be the techniques related to the fabrication of semiconductor, developments of small accelerators and compact neutron generators. (author)
3. Mercury contamination in soil, tailing and plants on agricultural fields near closed gold mine in Buru Island, Maluku
Directory of Open Access Journals (Sweden)
Reginawanti Hindersah
2018-01-01
Full Text Available Agricultural productivity in Buru Island, Maluku is threatened by tailings which are generated from formerly gold mine in Botak Mountain in Wamsait Village. Gold that extracted by using mercury was carried out in mining area as well agricultural field. High content of mercury in tailings and agricultural field pose a serious problem of food production and quality; and further endangers human health. The purpose of this research was to determine the contaminant level of mercury in tailing, soil and its accumulation in edible part of some food crops. Soil, tailing and plant samples for Hg testing were taken by purposive method based on mining activities in Waelata, Waeapo and Namlea sub district. Six soil samples had been analyzed for their chemical properties. Total mercury levels in tailings and plants were measured by Atomic Adsorption Spectrophotometer. This study showed that agricultural field where tailings were deposited contained Hg above the threshold but agricultural area which is far from hot spot did not. Most edible parts of food crops accumulated mercury more than Indonesian threshold for mercury content in food. This evidence explained that tailings deposited on the surface of agricultural field had an impact on soil quality and crop quality. Tailing accumulated on soil will decreased soil quality since naturally soil fertility in agricultural field in Buru is low.
4. A novel application for concentrator photovoltaic in the field of agriculture photovoltaics
Science.gov (United States)
Liu, Luqing; Guan, Chenggang; Zhang, Fangxin; Li, Ming; Lv, Hui; Liu, Yang; Yao, Peijun; Ingenhoff, Jan; Liu, Wen
2017-09-01
Agriculture photovoltaics is a trend setting area which has already led to a new industrial revolution. Shortage of land in some countries and desertification of land where regular solar panels are deployed are some of the major problems in the photovoltaic industry. Concentrator photovoltaics experienced a decline in applicability after the cost erosion of regular solar panels at the end of the last decade. We demonstrate a novel and unique application for concentrator photovoltaics tackling at a same time the issue of conventional photovoltaics preventing the land being used for agricultural purpose where ever solar panels are installed. We leverage the principle of diffractive and interference technology to split the sun light into transmitted wavelengths necessary for plant growth and reflected wavelengths useful for solar energy generation. The technology has been successfully implemented in field trials and sophisticated scientific studies have been undertaken to evaluate the suitability of this technology for competitive solar power generation and simultaneous high-quality plant growth. The average efficiency of the agriculture photovoltaic system has reached more than 8% and the average efficiency of the CPV system is 6.80%.
5. Importance of the Decompensative Correction of the Gravity Field for Study of the Upper Crust: Application to the Arabian Plate and Surroundings
Science.gov (United States)
Kaban, Mikhail K.; El Khrepy, Sami; Al-Arifi, Nassir
2017-01-01
The isostatic correction represents one of the most useful "geological" reduction methods of the gravity field. With this correction it is possible to remove a significant part of the effect of deep density heterogeneity, which dominates in the Bouguer gravity anomalies. However, even this reduction does not show the full gravity effect of unknown anomalies in the upper crust since their impact is substantially reduced by the isostatic compensation. We analyze a so-called decompensative correction of the isostatic anomalies, which provides a possibility to separate these effects. It was demonstrated that this correction is very significant at the mid-range wavelengths and may exceed 100 m/s2 (mGal), therefore ignoring this effect would lead to wrong conclusions about the upper crust structure. At the same time, the decompensative correction is very sensitive to the compensation depth and effective elastic thickness of the lithosphere. Therefore, these parameters should be properly determined based on other studies. Based on this technique, we estimate the decompensative correction for the Arabian plate and surrounding regions. The amplitude of the decompensative anomalies reaches ±250 m/s2 10-5 (mGal), evidencing for both, large density anomalies of the upper crust (including sediments) and strong isostatic disturbances of the lithosphere. These results improve the knowledge about the crustal structure in the Middle East.
6. Analysis of specific absorption rate and internal electric field in human biological tissues surrounding an air-core coil-type transcutaneous energy transmission transformer.
Science.gov (United States)
Shiba, Kenji; Zulkifli, Nur Elina Binti; Ishioka, Yuji
2017-06-01
In this study, we analyzed the internal electric field E and specific absorption rate (SAR) of human biological tissues surrounding an air-core coil transcutaneous energy transmission transformer. Using an electromagnetic simulator, we created a model of human biological tissues consisting of a dry skin, wet skin, fat, muscle, and cortical bone. A primary coil was placed on the surface of the skin, and a secondary coil was located subcutaneously inside the body. The E and SAR values for the model representing a 34-year-old male subject were analyzed using electrical frequencies of 0.3-1.5 MHz. The transmitting power was 15 W, and the load resistance was 38.4 Ω. The results showed that the E values were below the International Commission on Non-ionizing Radiation Protection (ICNIRP) limit for the general public exposure between the frequencies of 0.9 and 1.5 MHz, and SAR values were well below the limit prescribed by the ICNIRP for the general public exposure between the frequencies of 0.3 and 1.2 MHz.
7. Trichoderma Biodiversity of Agricultural Fields in East China Reveals a Gradient Distribution of Species.
Science.gov (United States)
Jiang, Yuan; Wang, Jin-Liang; Chen, Jing; Mao, Li-Juan; Feng, Xiao-Xiao; Zhang, Chu-Long; Lin, Fu-Cheng
2016-01-01
We surveyed the Trichoderma (Hypocreales, Ascomycota) biodiversity in agricultural fields in four major agricultural provinces of East China. Trichoderma strains were identified based on molecular approaches and morphological characteristics. In three sampled seasons (spring, summer and autumn), 2078 strains were isolated and identified to 17 known species: T. harzianum (429 isolates), T. asperellum (425), T. hamatum (397), T. virens (340), T. koningiopsis (248), T. brevicompactum (73), T. atroviride (73), T. fertile (26), T. longibrachiatum (22), T. pleuroticola (16), T. erinaceum (16), T. oblongisporum (2), T. polysporum (2), T. spirale (2), T. capillare (2), T. velutinum (2), and T. saturnisporum (1). T. harzianum, T. asperellum, T. hamatum, and T. virens were identified as the dominant species with dominance (Y) values of 0.057, 0.052, 0.048, and 0.039, respectively. The species amount, isolate numbers and the dominant species of Trichoderma varied between provinces. Zhejiang Province has shown the highest diversity, which was reflected in the highest species amount (14) and the highest Shannon-Wiener diversity index of Trichoderma haplotypes (1.46). We observed that relative frequencies of T. hamatum and T. koningiopsis under rice soil were higher than those under wheat and maize soil, indicating the preference of Trichoderma to different crops. Remarkable seasonal variation was shown, with summer exhibiting the highest biodiversity of the studied seasons. These results show that Trichoderma biodiversity in agricultural fields varies by region, crop, and season. Zhejiang Province (the southernmost province in the investigated area) had more T. hamatum than Shandong Province (the northernmost province), not only in isolate amounts but also in haplotype amounts. Furthermore, at haplotype level, only T. hamatum showed a gradient distribution from south to north in correspondence analysis among the four dominant species. The above results would contribute to the
8. Trichoderma Biodiversity of Agricultural Fields in East China Reveals a Gradient Distribution of Species
Science.gov (United States)
Chen, Jing; Mao, Li-Juan; Feng, Xiao-Xiao; Zhang, Chu-Long; Lin, Fu-Cheng
2016-01-01
We surveyed the Trichoderma (Hypocreales, Ascomycota) biodiversity in agricultural fields in four major agricultural provinces of East China. Trichoderma strains were identified based on molecular approaches and morphological characteristics. In three sampled seasons (spring, summer and autumn), 2078 strains were isolated and identified to 17 known species: T. harzianum (429 isolates), T. asperellum (425), T. hamatum (397), T. virens (340), T. koningiopsis (248), T. brevicompactum (73), T. atroviride (73), T. fertile (26), T. longibrachiatum (22), T. pleuroticola (16), T. erinaceum (16), T. oblongisporum (2), T. polysporum (2), T. spirale (2), T. capillare (2), T. velutinum (2), and T. saturnisporum (1). T. harzianum, T. asperellum, T. hamatum, and T. virens were identified as the dominant species with dominance (Y) values of 0.057, 0.052, 0.048, and 0.039, respectively. The species amount, isolate numbers and the dominant species of Trichoderma varied between provinces. Zhejiang Province has shown the highest diversity, which was reflected in the highest species amount (14) and the highest Shannon–Wiener diversity index of Trichoderma haplotypes (1.46). We observed that relative frequencies of T. hamatum and T. koningiopsis under rice soil were higher than those under wheat and maize soil, indicating the preference of Trichoderma to different crops. Remarkable seasonal variation was shown, with summer exhibiting the highest biodiversity of the studied seasons. These results show that Trichoderma biodiversity in agricultural fields varies by region, crop, and season. Zhejiang Province (the southernmost province in the investigated area) had more T. hamatum than Shandong Province (the northernmost province), not only in isolate amounts but also in haplotype amounts. Furthermore, at haplotype level, only T. hamatum showed a gradient distribution from south to north in correspondence analysis among the four dominant species. The above results would contribute to the
9. Trichoderma Biodiversity of Agricultural Fields in East China Reveals a Gradient Distribution of Species.
Directory of Open Access Journals (Sweden)
Yuan Jiang
Full Text Available We surveyed the Trichoderma (Hypocreales, Ascomycota biodiversity in agricultural fields in four major agricultural provinces of East China. Trichoderma strains were identified based on molecular approaches and morphological characteristics. In three sampled seasons (spring, summer and autumn, 2078 strains were isolated and identified to 17 known species: T. harzianum (429 isolates, T. asperellum (425, T. hamatum (397, T. virens (340, T. koningiopsis (248, T. brevicompactum (73, T. atroviride (73, T. fertile (26, T. longibrachiatum (22, T. pleuroticola (16, T. erinaceum (16, T. oblongisporum (2, T. polysporum (2, T. spirale (2, T. capillare (2, T. velutinum (2, and T. saturnisporum (1. T. harzianum, T. asperellum, T. hamatum, and T. virens were identified as the dominant species with dominance (Y values of 0.057, 0.052, 0.048, and 0.039, respectively. The species amount, isolate numbers and the dominant species of Trichoderma varied between provinces. Zhejiang Province has shown the highest diversity, which was reflected in the highest species amount (14 and the highest Shannon-Wiener diversity index of Trichoderma haplotypes (1.46. We observed that relative frequencies of T. hamatum and T. koningiopsis under rice soil were higher than those under wheat and maize soil, indicating the preference of Trichoderma to different crops. Remarkable seasonal variation was shown, with summer exhibiting the highest biodiversity of the studied seasons. These results show that Trichoderma biodiversity in agricultural fields varies by region, crop, and season. Zhejiang Province (the southernmost province in the investigated area had more T. hamatum than Shandong Province (the northernmost province, not only in isolate amounts but also in haplotype amounts. Furthermore, at haplotype level, only T. hamatum showed a gradient distribution from south to north in correspondence analysis among the four dominant species. The above results would contribute to the
10. The floristic changes on excluded from agricultural production field after single Roundup spraying
Directory of Open Access Journals (Sweden)
Wojciech Jabłoński
2013-12-01
Full Text Available The purpose of experiment conducting on the field, weedy by Agropyron repens (L. P. B. was established what is the degree of elimination of Agropyron repens plants from experimental plots by single Roundup spraying. The changes of the species composition on the fields with different clover-grass mixtures or with Phacelia tanacaetifolia Benth. were studied as well. The stand tables have been made in the first year of the conducting experiment, to determination the density of weeds, after different agricultural practices. It has been found the great elimination of Agropyron repens (L. P. B. plants after Roundup spraying and the great density of Echinochloa crus-galli (L. P. B. plants. It has been found the great density of Chenopodium album L. at VII treatment and Galinsoga parviflora Cav. at III, V, VII and VIII treatments as well (Table I.
11. Designing and Testing a UAV Mapping System for Agricultural Field Surveying
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Martin Peter Christiansen
2017-11-01
Full Text Available A Light Detection and Ranging (LiDAR sensor mounted on an Unmanned Aerial Vehicle (UAV can map the overflown environment in point clouds. Mapped canopy heights allow for the estimation of crop biomass in agriculture. The work presented in this paper contributes to sensory UAV setup design for mapping and textual analysis of agricultural fields. LiDAR data are combined with data from Global Navigation Satellite System (GNSS and Inertial Measurement Unit (IMU sensors to conduct environment mapping for point clouds. The proposed method facilitates LiDAR recordings in an experimental winter wheat field. Crop height estimates ranging from 0.35–0.58 m are correlated to the applied nitrogen treatments of 0–300 kg N ha . The LiDAR point clouds are recorded, mapped, and analysed using the functionalities of the Robot Operating System (ROS and the Point Cloud Library (PCL. Crop volume estimation is based on a voxel grid with a spatial resolution of 0.04 × 0.04 × 0.001 m. Two different flight patterns are evaluated at an altitude of 6 m to determine the impacts of the mapped LiDAR measurements on crop volume estimations.
12. Designing and Testing a UAV Mapping System for Agricultural Field Surveying.
Science.gov (United States)
Christiansen, Martin Peter; Laursen, Morten Stigaard; Jørgensen, Rasmus Nyholm; Skovsen, Søren; Gislum, René
2017-11-23
A Light Detection and Ranging (LiDAR) sensor mounted on an Unmanned Aerial Vehicle (UAV) can map the overflown environment in point clouds. Mapped canopy heights allow for the estimation of crop biomass in agriculture. The work presented in this paper contributes to sensory UAV setup design for mapping and textual analysis of agricultural fields. LiDAR data are combined with data from Global Navigation Satellite System (GNSS) and Inertial Measurement Unit (IMU) sensors to conduct environment mapping for point clouds. The proposed method facilitates LiDAR recordings in an experimental winter wheat field. Crop height estimates ranging from 0.35-0.58 m are correlated to the applied nitrogen treatments of 0-300 kg N ha . The LiDAR point clouds are recorded, mapped, and analysed using the functionalities of the Robot Operating System (ROS) and the Point Cloud Library (PCL). Crop volume estimation is based on a voxel grid with a spatial resolution of 0.04 × 0.04 × 0.001 m. Two different flight patterns are evaluated at an altitude of 6 m to determine the impacts of the mapped LiDAR measurements on crop volume estimations.
13. Energy Savings from Optimised In-Field Route Planning for Agricultural Machinery
Directory of Open Access Journals (Sweden)
Efthymios Rodias
2017-10-01
Full Text Available Various types of sensors technologies, such as machine vision and global positioning system (GPS have been implemented in navigation of agricultural vehicles. Automated navigation systems have proved the potential for the execution of optimised route plans for field area coverage. This paper presents an assessment of the reduction of the energy requirements derived from the implementation of optimised field area coverage planning. The assessment regards the analysis of the energy requirements and the comparison between the non-optimised and optimised plans for field area coverage in the whole sequence of operations required in two different cropping systems: Miscanthus and Switchgrass production. An algorithmic approach for the simulation of the executed field operations by following both non-optimised and optimised field-work patterns was developed. As a result, the corresponding time requirements were estimated as the basis of the subsequent energy cost analysis. Based on the results, the optimised routes reduce the fuel energy consumption up to 8%, the embodied energy consumption up to 7%, and the total energy consumption from 3% up to 8%.
14. Hubble Space Telescope-NICMOS Observations of M31'S Metal-Rich Globular Clusters and Their Surrounding Fields. I. Techniques
Science.gov (United States)
Stephens, Andrew W.; Frogel, Jay A.; Freedman, Wendy; Gallart, Carme; Jablonka, Pascale; Ortolani, Sergio; Renzini, Alvio; Rich, R. Michael; Davies, Roger
2001-05-01
Astronomers are always anxious to push their observations to the limit-basing results on objects at the detection threshold, spectral features barely stronger than the noise, or photometry in very crowded regions. In this paper we present a careful analysis of photometry in crowded regions and show how image blending affects the results and interpretation of such data. Although this analysis is specifically for our NICMOS observations in M31, the techniques we develop can be applied to any imaging data taken in crowded fields; we show how the effects of image blending will limit even the Next Generation Space Telescope. We have obtained HST-NICMOS observations of five of M31's most metal-rich globular clusters. These data allow photometry of individual stars in the clusters and their surrounding fields. However, to achieve our goals-obtain accurate luminosity functions to compare with their Galactic counterparts, determine metallicities from the slope of the giant branch, identify long-period variables, and estimate ages from the AGB tip luminosity-we must be able to disentangle the true properties of the population from the observational effects associated with measurements made in very crowded fields. We thus use three different techniques to analyze the effects of crowding on our data, including the insertion of artificial stars (traditional completeness tests) and the creation of completely artificial clusters. These computer simulations are used to derive threshold- and critical-blending radii for each cluster, which determine how close to the cluster center reliable photometry can be achieved. The simulations also allow us to quantify and correct for the effects of blending on the slope and width of the RGB at different surface brightness levels. We then use these results to estimate the limits blending will place on future space-based observations. Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science
15. Carbon Stock in Integrated Field Laboratory Faculty of Agriculture University of Lampung
Directory of Open Access Journals (Sweden)
Irwan Sukri Banuwa
2016-05-01
Full Text Available This study aimed to determine the amount of carbon stock and CO2 plant uptake in the Integrated Field Laboratory (IFL Faculty of Agriculture University of Lampung. The research was conducted from April to November 2015. The study was arranged in a completely randomized block design (CRBD, consisting of five land units as treatment with four replications for each treatment. Biomass of woody plants was estimated using allometric equation, biomass of understorey plants was estimated using plant dry weight equation, and organic C content in plants and soils were analyzed using a Walkey and Black method. The results showed that land unit consisting of densely woody plants significantly affects total biomass of woody plants, organic C content in woody plants and total carbon content (above and below ground. The highest amount of woody plant biomass was observed in land unit 5, i.e. 1,196.88 Mg ha-1, and above ground total carbon was 437.19 Mg ha-1. IFL Faculty of Agriculture University of Lampung has a total carbon stock of 2,051.90 Mg and capacity to take up total CO2 of 6,656.88 Mg.
16. Monitoring soil moisture dynamics via ground-penetrating radar survey of agriculture fields after irrigation
Science.gov (United States)
Muro, G.
2015-12-01
It is possible to examine the quality of ground-penetrating radar (GPR) as a measure of soil moisture content in the shallow vadose zone, where roots are most abundant and water conservation best management practices are critical in active agricultural fields. By analyzing temporal samplings of 100 Mhz reflection profiles and common-midpoint (CMP) soundings over a full growing season, the variability of vertical soil moisture distribution directly after irrigation events are characterized throughout the lifecycle of a production crop. Reflection profiles produce high-resolution travel time data and summed results of CMP sounding data provide sampling depth estimates for the weak, but coherent reflections amid strong point scatterers. The high ratio of clay in the soil limits the resolution of downward propagation of infiltrating moisture after irrigation; synthetic data analysis compared against soil moisture lysimeter logs throughout the profile allow identification of the discrete soil moisture content variation in the measured GPR data. The nature of short duration irrigation events, evapotranspiration, and drainage behavior in relation to root depths observed in the GPR temporal data allow further examination and comparison with the variable saturation model HYDRUS-1D. After retrieving soil hydraulic properties derived from laboratory measured soil samples and simplified assumptions about boundary conditions, the project aims to achieve good agreement between simulated and measured soil moisture profiles without the need for excessive model calibration for GPR-derived soil moisture estimates in an agricultural setting.
17. Study on the manganese distribution in the soil of an agricultural field using neutron activation analysis method
International Nuclear Information System (INIS)
Souza, Marcos P. de; Armelin, Maria J.A.; Cruvinel, Paulo E.
1997-01-01
Manganese distribution in the soil of an agricultural field was evaluated by neutron activation analysis. The accuracy and precision of the method were verified by the analysis of two Standard Reference Materials with different manganese concentration in the experimental field, through one schematic diagram. (author). 7 refs., 1 fig., 2 tabs
18. Pretreatment of agriculture field water for improving membrane flux during pesticide removal
Science.gov (United States)
Mehta, Romil; Saha, N. K.; Bhattacharya, A.
2017-10-01
Pretreatment of feed water to improve membrane flux during filtration of agriculture field water containing substituted phenyl urea pesticide diuron has been reported. Laboratory-made reverse osmosis membrane was used for filtration. Preliminary experiments were conducted with model solution containing natural organic matter extracted from commercial humic acids, divalent ions Ca2+, Mg2+. Membrane fouling was characterized by pure water flux decline, change in membrane hydrophilicity and infrared spectroscopy. Natural organic matter present in field water causes severe membrane fouling. The presence of divalent cations further aggravated fouling. Use of ethylenediaminetetraacetic acid (EDTA) and polyacrylic acids (PAA) in feed resulted in the decrease in membrane fouling. Pretreatment of field water is a must if it is contaminated with micro-organism having membrane fouling potential. Feed water pretreatment and use of PAA restricted membrane fouling to 16 % after 60 h of filtration. Membrane permeate flux decline was maximum at the first 12 h and thereafter remained steady at around 45-46 lm-2h-1 till the end of 60 h. Diuron rejection remained consistently greater than 93 % throughout the experiment. Diuron rejection was found to be unaffected by membrane fouling.
19. Agricultural and Management Practices and Bacterial Contamination in Greenhouse versus Open Field Lettuce Production
Science.gov (United States)
Holvoet, Kevin; Sampers, Imca; Seynnaeve, Marleen; Jacxsens, Liesbeth; Uyttendaele, Mieke
2014-01-01
The aim of this study was to gain insight into potential differences in risk factors for microbial contamination in greenhouse versus open field lettuce production. Information was collected on sources, testing, and monitoring and if applicable, treatment of irrigation and harvest rinsing water. These data were combined with results of analysis on the levels of Escherichia coli as a fecal indicator organism and the presence of enteric bacterial pathogens on both lettuce crops and environmental samples. Enterohemorragic Escherichia coli (EHEC) PCR signals (vt1 or vt2 positive and eae positive), Campylobacter spp., and Salmonella spp. isolates were more often obtained from irrigation water sampled from open field farms (21/45, 46.7%) versus from greenhouse production (9/75, 12.0%). The open field production was shown to be more prone to fecal contamination as the number of lettuce samples and irrigation water with elevated E. coli was significantly higher. Farmers comply with generic guidelines on good agricultural practices available at the national level, but monitoring of microbial quality, and if applicable appropriateness of water treatment, or water used for irrigation or at harvest is restricted. These results indicate the need for further elaboration of specific guidelines and control measures for leafy greens with regard to microbial hazards. PMID:25546272
20. Use of Airborne Hyperspectral Imagery to Map Soil Properties in Tilled Agricultural Fields
International Nuclear Information System (INIS)
Hively, W.D; McCarty, G.W; Reeves, J.B; Lang, M.W; Oesterling, R.A; Delwiche, S.R
2011-01-01
Soil hyperspectral reflectance imagery was obtained for six tilled (soil) agricultural fields using an airborne imaging spectrometer (400-2450 nm, -10 nm resolution, 2.5 m spatial resolution). Surface soil samples (n=315) were analyzed for carbon content, particle size distribution, and 15 agronomically important elements (Mehlich-III extraction). When partial least squares (PLS) regression of imagery-derived reflectance spectra was used to predict analyte concentrations, 13 of the 19 analytes were predicted with R 2 >0.50, including carbon (0.65), aluminum (0.76), iron (0.75), and silt content (0.79). Comparison of 15 spectral math preprocessing treatments showed that a simple first derivative worked well for nearly all analytes. The resulting PLS factors were exported as a vector of coefficients and used to calculate predicted maps of soil properties for each field. Image smoothing with a 3 x 3 low-pass filter prior to spectral data extraction improved prediction accuracy. The resulting raster maps showed variation associated with topographic factors, indicating the effect of soil redistribution and moisture regime on in-field spatial variability. High-resolution maps of soil analyte concentrations can be used to improve precision environmental management of farmlands.
1. Evaluation of Three Models for Simulating Pesticide Runoff from Irrigated Agricultural Fields.
Science.gov (United States)
Zhang, Xuyang; Goh, Kean S
2015-11-01
Three models were evaluated for their accuracy in simulating pesticide runoff at the edge of agricultural fields: Pesticide Root Zone Model (PRZM), Root Zone Water Quality Model (RZWQM), and OpusCZ. Modeling results on runoff volume, sediment erosion, and pesticide loss were compared with measurements taken from field studies. Models were also compared on their theoretical foundations and ease of use. For runoff events generated by sprinkler irrigation and rainfall, all models performed equally well with small errors in simulating water, sediment, and pesticide runoff. The mean absolute percentage errors (MAPEs) were between 3 and 161%. For flood irrigation, OpusCZ simulated runoff and pesticide mass with the highest accuracy, followed by RZWQM and PRZM, likely owning to its unique hydrological algorithm for runoff simulations during flood irrigation. Simulation results from cold model runs by OpusCZ and RZWQM using measured values for model inputs matched closely to the observed values. The MAPE ranged from 28 to 384 and 42 to 168% for OpusCZ and RZWQM, respectively. These satisfactory model outputs showed the models' abilities in mimicking reality. Theoretical evaluations indicated that OpusCZ and RZWQM use mechanistic approaches for hydrology simulation, output data on a subdaily time-step, and were able to simulate management practices and subsurface flow via tile drainage. In contrast, PRZM operates at daily time-step and simulates surface runoff using the USDA Soil Conservation Service's curve number method. Among the three models, OpusCZ and RZWQM were suitable for simulating pesticide runoff in semiarid areas where agriculture is heavily dependent on irrigation. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc.
2. Natural regeneration in abandoned fields following intensive agricultural land use in an Atlantic Forest Island, Brazil
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Milene Silvestrini
2012-08-01
Full Text Available The time required to regrowth a forest in degraded areas depends on how the forest is removed and on the type of land use following removal. Natural regeneration was studied in abandoned old fields after intensive agricultural land use in areas originally covered by Brazilian Atlantic Forests of the Anchieta Island, Brazil in order to understand how plant communities reassemble following human disturbances as well as to determine suitable strategies of forest restoration. The fields were classified into three vegetation types according to the dominant plant species in: 1 Miconia albicans (Sw. Triana (Melastomataceae fields, 2 Dicranopteris flexuosa (Schrader Underw. (Gleicheniaceae thickets, and 3 Gleichenella pectinata (Willd. Ching. (Gleicheniaceae thickets. Both composition and structure of natural regeneration were compared among the three dominant vegetation types by establishing randomly three plots of 1 x 3 m in five sites of the island. A gradient in composition and abundance of species in natural regeneration could be observed along vegetation types from Dicranopteris fern thickets to Miconia fields. The gradient did not accurately follow the pattern of spatial distribution of the three dominant vegetation types in the island regarding their proximity of the remnant forests. A complex association of biotic and abiotic factors seems to be affecting the seedling recruitment and establishment in the study plots. The lowest plant regeneration found in Dicranopteris and Gleichenella thickets suggests that the ferns inhibit the recruitment of woody and herbaceous species. Otherwise, we could not distinguish different patterns of tree regeneration among the three vegetation types. Our results showed that forest recovery following severe anthropogenic disturbances is not direct, predictable or even achievable on its own. Appropriated actions and methods such as fern removal, planting ground covers, and enrichment planting with tree species were
3. Nitrate concentration-drainage flow (C-Q) relationship for a drained agricultural field in Eastern North Carolina Plain
Science.gov (United States)
Liu, W.; Youssef, M.; Birgand, F.; Chescheir, G. M.; Maxwell, B.; Tian, S.
2017-12-01
Agricultural drainage is a practice used to artificially enhance drainage characteristics of naturally poorly drained soils via subsurface drain tubing or open-ditch systems. Approximately 25% of the U.S. agricultural land requires improved drainage for economic crop production. However, drainage increases the transport of dissolved agricultural chemicals, particularly nitrates to downstream surface waters. Nutrient export from artificially drained agricultural landscapes has been identified as the leading source of elevated nutrient levels in major surface water bodies in the U.S. Controlled drainage has long been practiced to reduce nitrogen export from agricultural fields to downstream receiving waters. It has been hypothesized that controlled drainage reduces nitrogen losses by promoting denitrification, reducing drainage outflow from the field, and increasing plant uptake. The documented performance of the practice was widely variable as it depends on several site-specific factors. The goal of this research was to utilize high frequency measurements to investigate the effect of agricultural drainage and related management practices on nitrate fate and transport for an artificially drained agricultural field in eastern North Carolina. We deployed a field spectrophotometer to measure nitrate concentration every 45 minutes and measured drainage flow rate using a V-notch weir every 15 minutes. Furthermore, we measured groundwater level, precipitation, irrigation amount, temperature to characterize antecedent conditions for each event. Nitrate concentration-drainage flow (C-Q) relationships generated from the high frequency measurements illustrated anti-clockwise hysteresis loops and nitrate flushing mechanism in response to most precipitation and irrigation events. Statistical evaluation will be carried out for the C-Q relationships. The results of our analysis, combined with numerical modeling, will provide a better understanding of hydrological and
4. Identifying diffused nitrate sources in a stream in an agricultural field using a dual isotopic approach
International Nuclear Information System (INIS)
Ding, Jingtao; Xi, Beidou; Gao, Rutai; He, Liansheng; Liu, Hongliang; Dai, Xuanli; Yu, Yijun
2014-01-01
Nitrate (NO 3 − ) pollution is a severe problem in aquatic systems in Taihu Lake Basin in China. A dual isotope approach (δ 15 N-NO 3 − and δ 18 O-NO 3 − ) was applied to identify diffused NO 3 − inputs in a stream in an agricultural field at the basin in 2013. The site-specific isotopic characteristics of five NO 3 − sources (atmospheric deposition, AD; NO 3 − derived from soil organic matter nitrification, NS; NO 3 − derived from chemical fertilizer nitrification, NF; groundwater, GW; and manure and sewage, M and S) were identified. NO 3 − concentrations in the stream during the rainy season [mean ± standard deviation (SD) = 2.5 ± 0.4 mg/L] were lower than those during the dry season (mean ± SD = 4.0 ± 0.5 mg/L), whereas the δ 18 O-NO 3 − values during the rainy season (mean ± SD = + 12.3 ± 3.6‰) were higher than those during the dry season (mean ± SD = + 0.9 ± 1.9‰). Both chemical and isotopic characteristics indicated that mixing with atmospheric NO 3 − resulted in the high δ 18 O values during the rainy season, whereas NS and M and S were the dominant NO 3 − sources during the dry season. A Bayesian model was used to determine the contribution of each NO 3 − source to total stream NO 3 − . Results showed that reduced N nitrification in soil zones (including soil organic matter and fertilizer) was the main NO 3 − source throughout the year. M and S contributed more NO 3 − during the dry season (22.4%) than during the rainy season (17.8%). AD generated substantial amounts of NO 3 − in May (18.4%), June (29.8%), and July (24.5%). With the assessment of temporal variation of diffused NO 3 − sources in agricultural field, improved agricultural management practices can be implemented to protect the water resource and avoid further water quality deterioration in Taihu Lake Basin. - Highlights: • The isotopic characteristics of potential NO 3 − sources were identified. • Mixing with atmospheric NO 3 − resulted
5. Use of hyperspectral remote sensing to estimate the gross photosynthesis of agricultural fields
International Nuclear Information System (INIS)
Strachan, I.B.; Pattey, E.; Salustro, C.; Miller, J.R.
2008-01-01
Optimization of crop growth and yield is achieved through the use of effective management practices. However, transient weather conditions will modify crop growth and yield. To assess crop development it is therefore essential to understand the current crop ecophysiological status. Such information can be monitored continuously using micrometeorological instrumented towers over agricultural surfaces. The spatial coverage of this approach is limited to the upwind area contributing to the flux. Remote sensing becomes key in deriving carbon exchanges and crop vigour over larger spatial areas. Derived from ground-based hyperspectral reflectance measurements from five growing seasons, a relationship between the eddy covariance estimates of gross photosynthesis and the product of the standardized photochemical reflectance index and the integrated modified triangular index was expanded to the field scale through the use of Compact Airborne Spectrographic Imager (CASI) data for corn and wheat over two consecutive seasons in the same field. Imagery-derived maps of gross photosynthesis successfully identified areas of potential stress that were known to be correlated with lower yield. Results were further verified using an independent flux dataset. This approach, modified from previous attempts in natural ecosystems, offers additional promise for managed systems. (author)
6. Accuracy of topographic index models at identifying ephemeral gully trajectories on agricultural fields
Science.gov (United States)
Sheshukov, Aleksey Y.; Sekaluvu, Lawrence; Hutchinson, Stacy L.
2018-04-01
Topographic index (TI) models have been widely used to predict trajectories and initiation points of ephemeral gullies (EGs) in agricultural landscapes. Prediction of EGs strongly relies on the selected value of critical TI threshold, and the accuracy depends on topographic features, agricultural management, and datasets of observed EGs. This study statistically evaluated the predictions by TI models in two paired watersheds in Central Kansas that had different levels of structural disturbances due to implemented conservation practices. Four TI models with sole dependency on topographic factors of slope, contributing area, and planform curvature were used in this study. The observed EGs were obtained by field reconnaissance and through the process of hydrological reconditioning of digital elevation models (DEMs). The Kernel Density Estimation analysis was used to evaluate TI distribution within a 10-m buffer of the observed EG trajectories. The EG occurrence within catchments was analyzed using kappa statistics of the error matrix approach, while the lengths of predicted EGs were compared with the observed dataset using the Nash-Sutcliffe Efficiency (NSE) statistics. The TI frequency analysis produced bi-modal distribution of topographic indexes with the pixels within the EG trajectory having a higher peak. The graphs of kappa and NSE versus critical TI threshold showed similar profile for all four TI models and both watersheds with the maximum value representing the best comparison with the observed data. The Compound Topographic Index (CTI) model presented the overall best accuracy with NSE of 0.55 and kappa of 0.32. The statistics for the disturbed watershed showed higher best critical TI threshold values than for the undisturbed watershed. Structural conservation practices implemented in the disturbed watershed reduced ephemeral channels in headwater catchments, thus producing less variability in catchments with EGs. The variation in critical thresholds for all
7. Extracurricular Activities Targeted towards Increasing the Number of Engineers Working in the Field of Precision Agriculture
DEFF Research Database (Denmark)
Larsen, Leon Bonde; Stark Olsen, Kent; Ahrenkiel, Linda
SERVICE ROBOTS in precision agriculture have the potential to ensure a more competitive and sustainable production, but the lack of skilled engineers within this area is limiting the industry’s ability to develop new and innovative agricultural technology products. Part of the reason...... is that engineers and scientists have little knowledge about agricultural technology, and they therefore choose to work in other domains. It is hypothesised that introducing engineering students to precision agriculture through practical work with small-scale service robots will increase their interest...... in agriculture and agricultural technology. This article presents the results of an interdisciplinary extracurricular activity for first year engineering students carried out in the Fall 2012 at the University of Southern Denmark. The case was based on practical group-work centered around an agricultural mobile...
8. Agricultural terraces montoring and modeling: a field survey in Chianti region, Firenze, Italy - First part
Science.gov (United States)
Preti, Federico; Caruso, Marco; Dani, Andrea; Errico, Alessandro; Guastini, Enrico; Trucchi, Paolo
2015-04-01
The two abstracts present the design and set-up of an experimental field plant whose aim is the study and modeling of water circulation in a terraced slope together with its influence on the stability of the retaining dry stone walls. The pilot plant is located at "Fattoria di Lamole" (Greve in Chianti, Firenze, Italy) where both ancient and recently restored or rebuilt dry stone retaining walls are present. The intense vineyards cultivation makes it very representative in terms of range of external stresses that affect both hillslopes and walls. The research is developed within a bigger framework of landscape preservation as a way to prevent hydrogeological instabilities and landslide risks. First Part A first/preliminary field survey was carried out in order to estimate the hydraulic and mechanical soil characteristics. Field saturated hydraulic conductivity measurements with the Simplified Falling Head (SFH) method on a terrace along an alignment were performed. Infiltrometer tests with a double ring device and soil texture determinations with both fine particle-size and skeleton fraction distributions were also performed. The Direct shear test on undisturbed and reconstituted soil samples will offer an estimation of the Mohr-Coulomb failure envelope parameters (friction angle and cohesion). A reference portion of a dry stone wall will be also monitored. Lateral earth pressure at backfill-retaining wall interface (compared to temperature and air pressure measured values), backfill volumetric water content (both in saturated and unsaturated states) and ground-water level are measured. Acknowledgements Italian Research Project of Relevant Interest (PRIN2010-2011), prot. 20104ALME4, National network for monitoring, modeling, and sustainable management of erosion processes in agricultural land and hilly-mountainous area
9. Linking field observations, Landsat and MODIS data to estimate agricultural change in European Russia.
Science.gov (United States)
de Beurs, K. M.; Ioffe, G.
2011-12-01
Agricultural reform has been one of the most important anthropogenic change processes in European Russia that has been unfolding since the formal collapse of the Soviet Union at the end of 1991. Widespread land abandonment is perhaps the most vivid side effect of the reform, even visible in synoptic imagery. Currently, Russia is transitioning into a country with an internal "archipelago" of islands of productive agriculture around cities embedded in a matrix of unproductive, abandoned lands. This heterogeneous spatial pattern is mainly driven by depopulation of the least favorable parts of the countryside, where "least favorable" is a function of fertility, remoteness, and their interaction. In this work we provide a satellite, GIS and field based overview of the current agricultural developments in Russia and look beyond the unstable period immediately following the collapse of the Soviet Union. We apply Landsat images in one of Russia's oblasts to create a detailed land cover map. We then use a logistic model to link the Landsat land cover map with the inter-annual variability in key phenological parameters calculated from MODIS to derive the percent of cropland per 500m MODIS pixel. By evaluating the phenological characteristics of the MODIS curves for each year we determine whether a pixel was actually cropped or left fallow. A comparison of satellite-estimated cropped areas with regional statistics (by rayon) revealed that the satellite estimates are highly correlated with the regional statistics for both arable lands and successfully cropped areas. We use the crop maps to determine the number of times a particular area was cropped between 2002 and 2009 by summing all the years with crops per pixel. This variable provides a good indication about the intensification and de-intensification of the Russian croplands over the last decade. We have visited several rural areas in Russia and we link the satellite data with information acquired through field interviews
10. Maize production and land degradation: a Portuguese agriculture field case study
Science.gov (United States)
Ferreira, Carla S. S.; Pato, João V.; Moreira, Pedro M.; Valério, Luís M.; Guilherme, Rosa; Casau, Fernando J.; Santos, Daniela; Keizer, Jacob J.; Ferreira, António J. D.
2016-04-01
While food security is a main challenge faced by human kind, intensive agriculture often leads to soil degradation which then can threaten productivity. Maize is one of the most important crops across the world, with 869 million tons produced worldwide in 2012/2013 (IGC 2015), of which 929.5 thousand tons in Portugal (INE 2014). In Portugal, maize is sown in April/May and harvest occurs generally in October. Conventional maize production requires high inputs of water and fertilizers to achieve higher yields. As Portuguese farmers are typically rather old (on average, 63 years) and typically have a low education level (INE 2014), sustainability of their land management practises is often not a principal concern. This could explain why, in 2009, only 4% of the Portuguese temporary crops were under no-tillage, why only 8% of the farmers performed soil analyses in the previous three years, and why many soils have a low organic matter content (INE 2014). Nonetheless, sustainable land management practices are generally accepted to be the key to reducing agricultural soil degradation, preventing water pollution, and assuring long-term crop production objectives and food security. Sustainable land management should therefore not only be a concern for policy makers but also for farmers, since land degradation will have negative repercussions on the productivity, thus, on their economical income. This paper aims to assess the impact of maize production on soil properties. The study focusses on an 8 ha maize field located in central Portugal, with a Mediterranean climate on a gently sloping terrain (<3%) and with a soil classified as Eutric Fluvisol. On the field, several experiments were carried out with different maize varieties as well as with different fertilizers (solid, liquid and both). Centre pivot irrigation was largely used. Data is available from 2003, and concerns crop yield, fertilization and irrigation practices, as well as soil properties assessed through
11. Nanotechnologies in agriculture and food - an overview of different fields of application, risk assessment and public perception.
Science.gov (United States)
Grobe, Antje; Rissanen, Mikko E
2012-12-01
Nanomaterials in agriculture and food are key issues of public and regulatory interest. Over the past ten years, patents for nanotechnological applications in the field of food and agriculture have become abundant. Uncertainty prevails however regarding their current development status and presence in the consumer market. Thus, the discussion on nanotechnologies in the food sector with its specific public perception of benefits and risks and the patterns of communication are becoming similar to the debate on genetically modified organisms. The food industry's silence in communication increased mistrust of consumer organisations and policy makers. The article discusses the background of the current regulatory debates, starting with the EU recommendation for defining nanomaterials, provides an overview of possible fields of application in agriculture and food industries and discusses risk assessment and the public debate on benefits and risks. Communicative recommendations are directed at researchers, the food industry and regulators in order to increase trust both in stakeholders, risk management and regulatory processes.
12. Spatial probability of soil water repellency in an abandoned agricultural field in Lithuania
Science.gov (United States)
Pereira, Paulo; Misiūnė, Ieva
2015-04-01
Water repellency is a natural soil property with implications on infiltration, erosion and plant growth. It depends on soil texture, type and amount of organic matter, fungi, microorganisms, and vegetation cover (Doerr et al., 2000). Human activities as agriculture can have implications on soil water repellency (SWR) due tillage and addition of organic compounds and fertilizers (Blanco-Canqui and Lal, 2009; Gonzalez-Penaloza et al., 2012). It is also assumed that SWR has a high small-scale variability (Doerr et al., 2000). The aim of this work is to study the spatial probability of SWR in an abandoned field testing several geostatistical methods, Organic Kriging (OK), Simple Kriging (SK), Indicator Kriging (IK), Probability Kriging (PK) and Disjunctive Kriging (DK). The study area it is located near Vilnius urban area at (54 49' N, 25 22', 104 masl) in Lithuania (Pereira and Oliva, 2013). It was designed a experimental plot with 21 m2 (07x03 m). Inside this area it was measured SWR was measured every 50 cm using the water drop penetration time (WDPT) (Wessel, 1998). A total of 105 points were measured. The probability of SWR was classified in 0 (No probability) to 1 (High probability). The methods accuracy was assessed with the cross validation method. The best interpolation method was the one with the lowest Root Mean Square Error (RMSE). The results showed that the most accurate probability method was SK (RMSE=0.436), followed by DK (RMSE=0.437), IK (RMSE=0.448), PK (RMSE=0.452) and OK (RMSE=0.537). Significant differences were identified among probability tests (Kruskal-Wallis test =199.7597 ptested technique. Simple Kriging, DK, IK and PK methods identified the high SWR probabilities in the northeast and central part of the plot, while OK observed mainly in the south-western part of the plot. In conclusion, before predict the spatial probability of SWR it is important to test several methods in order to identify the most accurate. Acknowledgments COST action ES
13. A statistical approach to estimating soil-to-plant transfer factor of strontium in agricultural fields
International Nuclear Information System (INIS)
Ishikawa, Nao; Tagami, Keiko; Uchida, Shigeo
2009-01-01
Soil-to-plant transfer factor (TF) is one of the important parameters in radiation dose assessment models for the environmental transfer of radionuclides. Since TFs are affected by several factors, including radionuclides, plant species and soil properties, development of a method for estimation of TF using some soil and plant properties would be useful. In this study, we took a statistical approach to estimating the TF of stable strontium (TF Sr ) from selected soil properties and element concentrations in plants, which was used as an analogue of 90 Sr. We collected the plant and soil samples used for the study from 142 agricultural fields throughout Japan. We applied a multiple linear regression analysis in order to get an empirical equation to estimate TF Sr . TF Sr could be estimated from the Sr concentration in soil (C Sr soil ) and Ca concentration in crop (C Ca crop ) using the following equation: log TF Sr =-0.88·log C Sr soil +0.93·log C Ca crop -2.53. Then, we replaced our data with Ca concentrations in crops from a food composition database compiled by the Japanese government. Finally, we predicted TF Sr using Sr concentration in soil from our data and Ca concentration in crops from the database of food composition. (author)
14. FATE OF ATRAZINE IN THE AGRICULTURAL SOIL OF CORN FIELDS IN FARS PROVINCE OF IRAN
Directory of Open Access Journals (Sweden)
S. Nasseri ، M. Dehghani ، S. Amin ، K. Naddafi ، Z. Zamanian
2009-10-01
Full Text Available Atrazine, a herbicide widely used in corn production, is frequently detected as pesticide in water resources. In this research, four agricultural fields with a long history of atrazine application in Shiraz and its vicinity in Fars province of Iran, have been studied to determine the fate of atrazine through the passage of time. These four farms were cultivated under a crop rotation (corn-wheat during the past 10 years. Samples were collected from four soil profiles of 0-10, 10-20, 20-40, and 40-60 cm soil depth at different times. The time intervals for soil sampling started before atrazine application and continued until no atrazine was detected. According to the general linear model, there was no significant difference between atrazine residual concentrations and the soil moisture and depth (p≥0.05. But, significant difference between atrazine residual concentrations and the sampling regions was observed (p<0.001. Based on the data, atrazine leaching and dissipation rate in different soil profiles in the four sampling regions were high and significant. Therefore, there is a high risk of atrazine pollution in groundwater resources of the region.
15. Fluxes of Nitrous Acid (HONO) above an Agricultural Field Side near Paris
Science.gov (United States)
Laufs, S.; Cazaunau, M.; Stella, P.; Loubet, B.; Kurtenbach, R.; Cellier, P.; Mellouki, W.; Kleffmann, J.
2012-04-01
HONO is an important precursor of the OH radical, the detergent of the atmosphere. Field measurements show high diurnal HONO mixing ratios that cannot be explained by chemical models with known gas phase chemistry. Therefore, daytime sources of HONO are still under discussion. During the last decade many experimental investigation were performed to study heterogeneous production of HONO like the photo enhanced reduction of NO2 on humic acids or photolysis of HNO3 on surfaces. Recently, nitrite produced by bacteria, present in soil, was discussed as a source of HONO as well. In addition gas phase sources like the photolysis of nitrophenols, or the reaction of excited NO2 are discussed. Gradient measurements show high mixing ratios of HONO even above the boundary layer. However, beside intensive investigations on the sources of HONO, it is still an open question whether heterogeneous or gas phase sources are more important in the atmosphere. Flux measurements could represent a method to find the origin of missing sources of HONO. Until now instruments are not sensitive and fast enough to do Eddy correlation measurements for HONO. Alternatively, HONO fluxes are estimated by the Aerodynamic Gradient (AGM), or Relaxed Eddy Accumulation (REA) methods. Here we present HONO fluxes estimated by AGM and the LOPAP technique (Long Path Absorption Photometer) above an agricultural field in Grignon, Paris (48°51'N, 1°58'E). Fluxes during different seasons and different types of vegetations including bare soil will be presented and compared with chemical corrected fluxes of NO, NO2 and O3, or other parameters.
16. Fast phosphorus loss by sediment resuspension in a re-established shallow lake on former agricultural fields
DEFF Research Database (Denmark)
Kragh, Theis; Sand-Jensen, Kaj; Petersen, Kathrine
2017-01-01
Lake restoration on fertilized agricultural fields can lead to extensive nutrient release from flooded soils which can maintain a poor ecological quality in the new lake. The period with high sediment release is poorly understood due to few detailed lake restorations studies. We conducted such a ...
17. Estimation of decay rates for fecal indicator bacteria and bacterial pathogens in agricultural field-applied manure
Science.gov (United States)
Field-applied manure is an important source of pathogenic exposure in surface water bodies for humans and ecological receptors. We analyzed the persistence and decay of fecal indicator bacteria and bacterial pathogens from three sources (cattle, poultry, swine) for agricultural f...
18. Fast phosphorus loss by sediment resuspension in a re-established shallow lake on former agricultural fields
DEFF Research Database (Denmark)
Kragh, Theis; Sand-Jensen, Kaj; Petersen, Kathrine
2017-01-01
Lake restoration on fertilized agricultural fields can lead to extensive nutrient release from flooded soils which can maintain a poor ecological quality in the new lake. The period with high sediment release is poorly understood due to few detailed lake restorations studies. We conducted...
19. THE USE OF CHEMICALS IN THE FIELD OF FARM ANIMAL HEALTH (NUTRITION, ENTOMOLOGY, PATHOLOGY). AGRICULTURAL CHEMICALS TECHNOLOGY, NUMBER 7.
Science.gov (United States)
Ohio State Univ., Columbus. Center for Vocational and Technical Education.
DEVELOPED BY A NATIONAL TASK FORCE ON THE BASIS OF STATE STUDIES, THIS MODULE IS ONE OF A SERIES DESIGNED TO ASSIST TEACHERS IN PREPARING POST-SECONDARY STUDENTS FOR AGRICULTURAL CHEMICAL OCCUPATIONS. THE SPECIFIC OBJECTIVE OF THIS MODULE IS TO PREPARE TECHNICIANS IN THE FIELD OF THE USE OF CHEMICALS FOR ANIMAL HEALTH. SECTIONS INCLUDE -- (1)…
20. Bringing diversity back to agriculture: Smaller fields and non-crop elements enhance biodiversity in intensively managed arable farmlands
Czech Academy of Sciences Publication Activity Database
Šálek, Martin; Hula, V.; Kipson, M.; Daňková, R.; Niedobová, J.; Gamero, A.
2018-01-01
Roč. 90, July (2018), s. 65-73 ISSN 1470-160X Institutional support: RVO:68081766 Keywords : Common Agricultural Policy * Conservation measures * Field size * Habitat heterogeneity * Species richness * Abundance * Biodiversity indicators Subject RIV: EH - Ecology, Behaviour OBOR OECD: Ecology Impact factor: 3.898, year: 2016
1. Economic feasibility of surface flow constructed (SFCW) wetlands for reduction of water pollution from agricultural fields in Denmark
DEFF Research Database (Denmark)
Gachango, Florence Gathoni; Pedersen, Søren Marcus; Kjaergaard, Charlotte
2014-01-01
Constructed wetlands have been proposed as cost effective and more targeted technologies in the reduction of nitrogen and phosphorous water pollution in drainage losses from agricultural fields in Denmark. Using two pig farms and one dairy farm situated in a pumped lowland catchment as study cases...
2. Use of agricultural fields by ruffs staging in southwest Friesland in 2003–2013
NARCIS (Netherlands)
Schmaltz, Lucie E.; Vega, Marta L.; Verkuil, Yvonne I.; Hooijmeijer, Joslyn; Piersma, Theunis
2016-01-01
Intensive dairy farming has changed the agricultural grassland areas of The Netherlands profoundly, with negative impacts on the reproduction of the shorebirds breeding there. This modern agricultural landscape also forms a staging site for migrating shorebirds, where they moult and replenish fuel
3. Changes in water budgets and sediment yields from a hypothetical agricultural field as a function of landscape and management characteristics--A unit field modeling approach
Science.gov (United States)
Roth, Jason L.; Capel, Paul D.
2012-01-01
Crop agriculture occupies 13 percent of the conterminous United States. Agricultural management practices, such as crop and tillage types, affect the hydrologic flow paths through the landscape. Some agricultural practices, such as drainage and irrigation, create entirely new hydrologic flow paths upon the landscapes where they are implemented. These hydrologic changes can affect the magnitude and partitioning of water budgets and sediment erosion. Given the wide degree of variability amongst agricultural settings, changes in the magnitudes of hydrologic flow paths and sediment erosion induced by agricultural management practices commonly are difficult to characterize, quantify, and compare using only field observations. The Water Erosion Prediction Project (WEPP) model was used to simulate two landscape characteristics (slope and soil texture) and three agricultural management practices (land cover/crop type, tillage type, and selected agricultural land management practices) to evaluate their effects on the water budgets of and sediment yield from agricultural lands. An array of sixty-eight 60-year simulations were run, each representing a distinct natural or agricultural scenario with various slopes, soil textures, crop or land cover types, tillage types, and select agricultural management practices on an isolated 16.2-hectare field. Simulations were made to represent two common agricultural climate regimes: arid with sprinkler irrigation and humid. These climate regimes were constructed with actual climate and irrigation data. The results of these simulations demonstrate the magnitudes of potential changes in water budgets and sediment yields from lands as a result of landscape characteristics and agricultural practices adopted on them. These simulations showed that variations in landscape characteristics, such as slope and soil type, had appreciable effects on water budgets and sediment yields. As slopes increased, sediment yields increased in both the arid and
4. Field studies on the behaviour of radiocaesium in agricultural environments after the Chernobyl accident
Energy Technology Data Exchange (ETDEWEB)
Rosen, K
1996-05-01
This thesis deals with the occurrence of Chernobyl {sup 137}Cs and {sup 134}Cs in cultivated, semi-natural and natural agricultural areas of five Swedish counties. The investigations were carried out under field conditions 1986 to 1995 on farms where transfer to grass and milk during the first years were high. Vertical migration rate in soil profiles, the practical value of countermeasures to reduce transfer to feed and food and the impact of passing time were important aims for the study. The transfer of Cs was higher on permanent pasture than on temporary grassland and much lower to barley grain. Stubble and grass swards kept Cs available for transfer to grass. High organic matter contents in the surface soil also caused high transfer during a lag period of some years. Soil texture, grass sward, K-fertilization and growth dilution explained the variation in Cs transfer and its reduction rate. A case study on transfer of Cs to vegetation and to grazing lambs was made on a mountain farm. High transfer to vegetation was found, 510-2260 Bq/kg d.w.. Mean transfer soil to plant (TFg,m{sup 2}/kg) was 67 and plant to muscle 0.7 during 1990-1993. The effect of K-fertilization on soil-plant transfer was studied on 15 soils. A dose of 100 to 200 kg/ha K decreased the transfer on sandy soils with a factor of up to 10. Liming was effective on soils that were originally low in pH. Adding zeolite on the surface of pastures did not reduce the root uptake of Cs. Ploughing down the contaminated surface was effective in reducing the transfer. Downward migration of Cs was usually less on mineral soils than or organic or podsolized soils. 68 refs, 9 figs, 13 tabs.
5. Field studies on the behaviour of radiocaesium in agricultural environments after the Chernobyl accident
International Nuclear Information System (INIS)
Rosen, K.
1996-05-01
This thesis deals with the occurrence of Chernobyl 137 Cs and 134 Cs in cultivated, semi-natural and natural agricultural areas of five Swedish counties. The investigations were carried out under field conditions 1986 to 1995 on farms where transfer to grass and milk during the first years were high. Vertical migration rate in soil profiles, the practical value of countermeasures to reduce transfer to feed and food and the impact of passing time were important aims for the study. The transfer of Cs was higher on permanent pasture than on temporary grassland and much lower to barley grain. Stubble and grass swards kept Cs available for transfer to grass. High organic matter contents in the surface soil also caused high transfer during a lag period of some years. Soil texture, grass sward, K-fertilization and growth dilution explained the variation in Cs transfer and its reduction rate. A case study on transfer of Cs to vegetation and to grazing lambs was made on a mountain farm. High transfer to vegetation was found, 510-2260 Bq/kg d.w.. Mean transfer soil to plant (TFg,m 2 /kg) was 67 and plant to muscle 0.7 during 1990-1993. The effect of K-fertilization on soil-plant transfer was studied on 15 soils. A dose of 100 to 200 kg/ha K decreased the transfer on sandy soils with a factor of up to 10. Liming was effective on soils that were originally low in pH. Adding zeolite on the surface of pastures did not reduce the root uptake of Cs. Ploughing down the contaminated surface was effective in reducing the transfer. Downward migration of Cs was usually less on mineral soils than or organic or podsolized soils. 68 refs, 9 figs, 13 tabs
6. Effects of Mechanical Site Preparation on Growth of Oaks Planted on Former Agricultural Fields
Directory of Open Access Journals (Sweden)
John D. Hodges
2011-12-01
Full Text Available Mechanical site preparation is frequently proposed to alleviate problematic soil conditions when afforesting retired agricultural fields. Without management of soil problems, any seedlings planted in these areas may exhibit poor growth and survival. While mechanical site preparation methods currently employed in hardwood afforestation are proven, there is a substantial void in research comparing subsoiling, bedding, and combination plowing treatments. A total of 4,320 bare-root Nuttall oak (Quercus texana Buckley, Shumard oak (Quercus shumardii Buckley, and swamp chestnut oak (Quercus michauxii Nutt. seedlings were planted in February 2008 on three Mississippi sites. All sites were of comparable soils and received above average precipitation throughout the three-year duration of the study. Four site preparation treatments were replicated at each site, with 480 seedlings planted in each of nine replications, and a total of 1,440 seedlings per species planted across all sites. Mechanical treatments were installed using 3.1 m row centers, with treatments as follows: control, subsoiling, bedding, and combination plowing. Treatment effects on seedling height, groundline diameter (GLD, and survival were analyzed. Seedlings exhibited greater height in bedded and combination plowed areas (79.7 cm to 102.7 cm and 82.6 cm to 100.1 cm, respectively compared to subsoiled or control areas (70.4 cm to 84.6 cm and 71.4 cm to 86.9 cm, respectively. Greater GLD was observed in bedded and combination plowed areas (11.9 mm to 18.4 mm and 12.2 mm to 18.3 mm, respectively compared to subsoiled or control areas (10.2 mm to 14.6 mm and 10.5 mm to 15.6 mm, respectively. Survival was high for this study (94.%, and no differences were detected among treatments.
7. Multi-parameter approximation of the stress field in a cracked body in the more distant surroundings of the crack tip
Czech Academy of Sciences Publication Activity Database
Veselý, V.; Sobek, J.; Frantík, P.; Seitl, Stanislav
2016-01-01
Roč. 89, AUG (2016), s. 20-35 ISSN 0142-1123. [International Conference on Characterisation of Crack Tip Fields /3./. Urbino, 20.04.2015-22.04.2015] Institutional support: RVO:68081723 Keywords : Crack-tip fields * Williams power series * Higher order terms * Stress field reconstruction * Multi-parameter approximation accuracy Subject RIV: JL - Materials Fatigue, Friction Mechanics Impact factor: 2.899, year: 2016
8. Overview of the Bushland Evapotranspiration and Agricultural Remote sensing EXperiment 2008 (BEAREX08): A field experiment evaluating methods for quantifying ET at multiple scales
Science.gov (United States)
Evett, Steven R.; Kustas, William P.; Gowda, Prasanna H.; Anderson, Martha C.; Prueger, John H.; Howell, Terry A.
2012-12-01
In 2008, scientists from seven federal and state institutions worked together to investigate temporal and spatial variations of evapotranspiration (ET) and surface energy balance in a semi-arid irrigated and dryland agricultural region of the Southern High Plains in the Texas Panhandle. This Bushland Evapotranspiration and Agricultural Remote sensing EXperiment 2008 (BEAREX08) involved determination of micrometeorological fluxes (surface energy balance) in four weighing lysimeter fields (each 4.7 ha) containing irrigated and dryland cotton and in nearby bare soil, wheat stubble and rangeland fields using nine eddy covariance stations, three large aperture scintillometers, and three Bowen ratio systems. In coordination with satellite overpasses, flux and remote sensing aircraft flew transects over the surrounding fields and region encompassing an area contributing fluxes from 10 to 30 km upwind of the USDA-ARS lysimeter site. Tethered balloon soundings were conducted over the irrigated fields to investigate the effect of advection on local boundary layer development. Local ET was measured using four large weighing lysimeters, while field scale estimates were made by soil water balance with a network of neutron probe profile water sites and from the stationary flux systems. Aircraft and satellite imagery were obtained at different spatial and temporal resolutions. Plot-scale experiments dealt with row orientation and crop height effects on spatial and temporal patterns of soil surface temperature, soil water content, soil heat flux, evaporation from soil in the interrow, plant transpiration and canopy and soil radiation fluxes. The BEAREX08 field experiment was unique in its assessment of ET fluxes over a broad range in spatial scales; comparing direct and indirect methods at local scales with remote sensing based methods and models using aircraft and satellite imagery at local to regional scales, and comparing mass balance-based ET ground truth with eddy covariance
9. Accidental Strangulation Due to Entrapment of Saree in Crop Thrasher Machine in an Elderly Women Working at Agricultural Field.
Science.gov (United States)
Parchake, Manoj Bhausaheb; Kumre, Vikas; Kachare, Rajesh V
2016-09-01
Strangulation is generally considered as homicidal death and in accidental strangulation circumstantial evidence alone can point toward the accidental nature of incidence. In present case, a 71-year-old woman, wearing a saree (garment worn by traditional women in India) working in agricultural field, got entangled in the crop thrasher machine and got strangled. Immediately, she was taken to the nearest hospital, where she survived for 6 to 8 hours and then died. The autopsy reveals cross ribbon-shaped ligature mark on neck and anterior chest along with 1 puncture wound at the right lateral aspect of the neck. A lack of proper precaution and safety measures at agricultural field are other contributing factors. Accidental strangulation by saree is extremely rare, hence, this case is presented for its rarity and pattern of injury.
10. Mitigation of dimethazone residues in soil and runoff water from agricultural field.
Science.gov (United States)
Antonious, George F
2011-01-01
Dimethazone, also known as clomazone [2-[(2-chlorophenyl) methyl]- 4,4-dimethyl-3-isoxaolidinone] is a pre-emergent nonionic herbicide commonly used in agriculture. A field study was conducted on a silty-loam soil of 10 % slope to monitor off-site movement and persistence of dimethazone in soil under three management practices. Eighteen plots of 22 x 3.7 m each were separated using stainless steel metal borders and the soil in six plots was mixed with municipal sewage sludge (MSS) and yard waste (YW) compost (MSS+YW) at 15 t acre⁻¹ on dry weight basis, six plots were mixed with MSS at 15 t acre⁻¹, and six unamended plots (NM) were used for comparison purposes. The objectives of this investigation were to: (i) monitor the dissipation and half-life (T₁/₂) of dimethazone in soil under three management practices; (ii) determine the concentration of dimethazone residues in runoff and infiltration water following natural rainfall events; and (iii) assess the impact of soil amendments on the transport of NO₃, NH₄, and P into surface and subsurface water. Gas chromatography/mass spectrometery (GC/MS) analyses of soil extracts indicated the presence of ion fragments at m/z 125 and 204 that can be used for identification of dimethazone residues. Intitial deposits of dimethazone varied from 1.3 μg g⁻¹ dry native soil to 3.2 and 11.8 μg g⁻¹ dry soil in MSS and MSS+YW amended soil, respectively. Decline of dimethazone residues in the top 15 cm native soil and soil incorporated with amendments revealed half-life (T₁/₂) values of 18.8, 25.1, and 43.0 days in MSS+YW, MSS, and NM treatments, respectively. Addition of MSS+YW mix and MSS alone to native soil increased water infiltration, lowering surface runoff water volume and dimethazone residues in runoff following natural rainfall events.
11. Evaluation of the APEX Model to Simulate Runoff Quality from Agricultural Fields in the Southern Region of the United States.
Science.gov (United States)
Ramirez-Avila, John J; Radcliffe, David E; Osmond, Deanna; Bolster, Carl; Sharpley, Andrew; Ortega-Achury, Sandra L; Forsberg, Adam; Oldham, J Larry
2017-11-01
The Agricultural Policy Environmental eXtender (APEX) model has been widely applied to assess phosphorus (P) loss in runoff water and has been proposed as a model to support practical decisions regarding agricultural P management, as well as a model to evaluate tools such as the P Index. The aim of this study is to evaluate the performance of APEX to simulate P losses from agricultural systems to determine its potential use for refinement or replacement of the P Index in the southern region of the United States. Uncalibrated and calibrated APEX model predictions were compared against measured water quality data from row crop fields in North Carolina and Mississippi and pasture fields in Arkansas and Georgia. Calibrated models satisfactorily predicted event-based surface runoff volumes at all sites (Nash-Sutcliffe efficiency [NSE] > 0.47, |percent bias [PBIAS]| < 34) except Arkansas (NSE < 0.11, |PBIAS| < 50) but did not satisfactory simulate sediment, dissolved P, or total P losses in runoff water. The APEX model tended to underestimate dissolved and total P losses from fields where manure was surface applied. The model also overestimated sediments and total P loads during irrigation events. We conclude that the capability of APEX to predict sediment and P losses is limited, and consequently so is the potential for using APEX to make P management recommendations to improve P Indices in the southern United States. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc.
12. Low field pulsed NMR- a mass screening tool in agricultural research
International Nuclear Information System (INIS)
Tiwari, P.N.
1994-01-01
One of the main requirements in agricultural research is to analyse large number of samples for their one or more chemical constituents and physical properties. In plant breeding programmes and germplasm evaluation, it is necessary that the analysis is fast as many samples are to be analysed. Pulsed nuclear magnetic resonance (NMR) is a potential tool for developing rapid and nondestructive method of analysis. Various applications of low resolution pulsed NMR in agricultural research, which are generally used as screening method are briefly described. 25 refs., 2 figs., 2 tabs
13. Monitoring and Analysis of Nonpoint Source Pollution - Case study on terraced paddy fields in an agricultural watershed
Science.gov (United States)
Chen, Shih-Kai; Jang, Cheng-Shin; Yeh, Chun-Lin
2013-04-01
The intensive use of chemical fertilizer has negatively impacted environments in recent decades, mainly through water pollution by nitrogen (N) and phosphate (P) originating from agricultural activities. As a main crop with the largest cultivation area about 0.25 million ha per year in Taiwan, rice paddies account for a significant share of fertilizer consumption among agriculture crops. This study evaluated the fertilization of paddy fields impacting return flow water quality in an agricultural watershed located at Hsinchu County, northern Taiwan. Water quality monitoring continued for two crop-periods in 2012, around subject to different water bodies, including the irrigation water, drainage water, and shallow groundwater. The results indicated that obviously increasing of ammonium-N, nitrate-N and TP concentrations in the surface drainage water were observed immediately following three times of fertilizer applications (including basal, tillering, and panicle fertilizer application), but reduced to relatively low concentrations after 7-10 days after each fertilizer application. Groundwater quality monitoring showed that the observation wells with the more shallow water depth, the more significant variation of concentrations of ammonium-N, nitrate-N and TP could be observed, which means that the contamination potential of nutrient of groundwater is related not only to the impermeable plow sole layer but also to the length of percolation route in this area. The study also showed that the potential pollution load of nutrient could be further reduced by well drainage water control and rational fertilizer management, such as deep-water irrigation, reuse of return flow, the rational application of fertilizers, and the SRI (The System of Rice Intensification) method. The results of this study can provide as an evaluation basis to formulate effective measures for agricultural non-point source pollution control and the reuse of agricultural return flow. Keywords
14. Mass balance and swath displacement evaluations from agricultural application field trials
Science.gov (United States)
Spray drift is on an ongoing concern for any agricultural application and continues to be the focus for new developments and research efforts dealing with drift reduction technologies, best management application practices and the development of new decision support systems for applicators. Typical...
15. Celtic field agriculture and Early Anthropogenic Environmental change in the Meuse-Demer-Scheldt region, NW Europe
Science.gov (United States)
Van der Sanden, Germaine; Kluiving, Sjoerd; Roymans, Nico
2016-04-01
The field of Archaeology remains focused on historical issues while underexploring its potential contribution on currently existing societal problems, e.g. climate change. The aim of this paper is to show the relevance of archeological studies for the research of the 'human species as a significant moving agent' in terms of the changing natural environment during a much earlier time frame. This research is based on the study area of the Meuse-Demer-Scheldt region in the Netherlands and Belgium and exhibits the period from the Late Bronze Age to the Early Roman period. This period is characterized by the widespread introduction and use of an agricultural system, often referred to as the Celtic Field system that served as one of the most modifying systems in terms of anthropogenic-environmental change during this period. Emphasis in this research is given to results generated by the use of the remote sensing technology, LiDAR. New information is reported considering a correlation between singular field size and the overall surface of the agricultural complexes and secondly, the presentation of newly identified Celtic field systems in the Meuse-Demer-Scheldt region are presented. The study of the dynamics of the Celtic Field agricultural system provides evidence for a significant anthropogenic footprint on the natural environment due to land cover dominance, soil degeneration, increased soil acidification and forest clearance. Soil exhaustion forced the inhabitants to re-establish their relationship with the landscape in terms of fundamental changes in the habitation pattern and the agrarian exploitations of the land.
16. Two new field measurements for D ampersand D: rapid Th-230 determinations and detection of rad waste in and surrounding sewer or process lines
International Nuclear Information System (INIS)
Duray, J.R.
1988-01-01
The Technical Measurements Center has developed a rapid thorium-230 field measurement method. The field method is much faster than the conventional practice of sending soil samples to a laboratory for analysis. Including the time to take a soil sample, the method yields a result in about one hour. Miniature gamma-ray and beta detectors have been coupled to a portable scaler through a long, flexible adaptation of a plumber's snake. Both detector assemblies and, in particular the gamma detector, are state-of-the-art in miniaturization and durability. The detector assemblies are small enough to easily pass through a three-inch sewer trap. Future proposed work will add a surface unit to locate the detector in the buried line. Other applications of the gamma unit are logging shallow boreholes and probing for radiometric contamination under slabs instead of drilling through the slab
17. Selection of flooded agricultural fields and other landscapes by female northern pintails wintering in Tulare Basin, California
Science.gov (United States)
Fleskes, Joseph P.; Jarvis, Robert L.; Gilmer, David S.
2003-01-01
Habitat selection and use are measures of relative importance of habitats to wildlife and necessary information for effective wildlife conservation. To measure the relative importance of flooded agricultural fields and other landscapes to northern pintails (Anas acuta) wintering in Tulare Basin (TB), California, we radiotagged female pintails during late August-early October, 1991-1993 in TB and other San Joaquin Valley areas and determined use and selection of these TB landscapes through March each year. Availability of landscape and field types in TB changed within and among years. Pintail use and selection (based upon use-to-availability log ratios) of landscape and field types differed among seasons, years, and diel periods. Fields flooded after harvest and before planting (i.e., pre-irrigated) were the most available, used, and selected landscape type before the hunting season (Prehunt). Safflower was the most available, used, and-except in 1993, when pre-irrigated fallow was available-selected pre-irrigated field type during Prehunt. Pre-irrigated barley-wheat received 19-22% of use before hunting season, but selection varied greatly among years and diel periods. During and after hunting season, managed marsh was the most available, used, and, along with floodwater areas, selected landscape type; pre-irrigated cotton and alfalfa were the least selected field types and accounted for <13% of pintail use. Agricultural drainwater evaporation ponds, sewage treatment ponds, and reservoirs accounted for 42-48% of flooded landscape available but were little used and least selected. Exodus of pintails from TB coincided with drying of pre-irrigated fallow, safflower, and barley-wheat fields early in winter, indicating that preferred habitats were lacking in TB during late winter. Agriculture conservation programs could improve TB for pintails by increasing flooding of fallow and harvested safflower and grain fields. Conservation of remaining wetlands should concentrate
18. Importance of the Decompensative Correction of the Gravity Field for Study of the Upper Crust: Application to the Arabian Plate and Surroundings
OpenAIRE
M. K. Kaban; Sami El Khrepy; Nassir Al-Arifi
2017-01-01
The isostatic correction represents one of the most useful “geological” reduction methods of the gravity field. With this correction it is possible to remove a significant part of the effect of deep density heterogeneity, which dominates in the Bouguer gravity anomalies. However, even this reduction does not show the full gravity effect of unknown anomalies in the upper crust since their impact is substantially reduced by the isostatic compensation. We analyze a so-called decompensative corre...
19. Distribution of uranium in soil components of agricultural fields after long-term application of phosphate fertilizers
International Nuclear Information System (INIS)
Yamaguchi, N.; Kawasaki, A.; Iiyama, I.
2009-01-01
Long-term application of phosphate fertilizers causes accumulation of U in the surface soil of agricultural fields. We investigated the soil constituents that contribute to the accumulation of U by using chemical extraction methods. Surface soil samples were obtained from upland fields, pastures, and paddy fields cultivated without any phosphate fertilizer (control site), with NPK fertilizer (NPK site), and with both NPK fertilizer and compost (NPK + compost site) for more than 20 years. In addition to the total U (U t ) concentration in soil, the concentrations of pyrophosphate- and acid oxalate-extractable U were determined as a measure of U associated with soil organic matter and poorly crystalline Fe/Al minerals in soil, respectively. The total, pyrophosphate-extractable, and acid oxalate-extractable U concentrations were higher in the soil obtained from the NPK and NPK + compost sites than in that obtained from the control site. The difference in the U concentrations between the NPK or NPK + compost site and the control site corresponded with the increased U concentration observed after the application of the phosphate fertilizer or both the fertilizer and compost. In the upland field and pasture soil, the increase in pyrophosphate-extractable U was 83-94% of that in U t . On the other hand, the increase in acid oxalate-extractable U was 44-58% of that in U t in the upland field and pasture soil, but it was almost equivalent to the increase in U t in the paddy soil with NPK. In conclusion, most of the phosphate fertilizer-derived U was either incorporated into the soil organic matter or poorly crystalline Fe/Al minerals in the surface soil of agricultural fields. Thus, soil organic matter is an important pool of U in upland field and pasture soil, whereas poorly crystalline Fe/Al minerals are important pools of U in paddy soil experiencing alternating changes in redox conditions
20. A field method for soil erosion measurements in agricultural and natural lands
Science.gov (United States)
Y.P. Hsieh; K.T. Grant; G.C. Bugna
2009-01-01
Soil erosion is one of the most important watershed processes in nature, yet quantifying it under field conditions remains a challenge. The lack of soil erosion field data is a major factor hindering our ability to predict soil erosion in a watershed. We present here the development of a simple and sensitive field method that quantifies soil erosion and the resulting...
1. Education and Training Needs in the Field of Agriculture and Rural Development in the Lower Danube Region
Directory of Open Access Journals (Sweden)
Nicolae Istudor
2010-11-01
Full Text Available Given the conditions of European Strategy for Labour which was ratified also by Romania, that states an intensifying implementation at national level of labour policies and especially those regarding young person labour market integration, and taking into consideration the great human and agricultural potential of Lower Danube Region, we consider the implementation of national and regional programmes in order to train agriculture and rural development specialists to be very necessary. This article inquires the necessity of training agriculture and rural development specialists within Lower Danube Region in the context of cross-border cooperation between Romania and Bulgaria. This research starts by analysing the European and national legal framework of adult training in those two fields. Subsequently, the main premises and advantages of those activities were emphasized. It is good to mention that the Academy of Economic Studies in Bucharest, Romania, and the D. Tsenov Academy of Economics in Svishtov, Bulgaria, proposed themselves to cooperate in the field of “human resources development – common development of skills and knowledge”. The legal base exists as the Romania-Bulgaria Cross-border Cooperation Programme 2007-2013 is enforced. Furthermore, a four years comparative study of the number of persons trained for the main jobs in rural area, including farmer, in Lower Danube Region was conducted. All these led to the idea that it is necessary to continue and to stress adult training of farmers and rural specialists as a solution for rural economy development and social welfare. Also, comparative analysis of supply and demand of professionals in the field of agriculture was elaborated. The main educational programs in training agriculture and rural development specialists were identified and some problems and perspectives were worked out. This research can be considered as a first step of future deeper and profound collaboration of Tsenov
2. Environmental Fate of the Herbicide Fluazifop-P-butyl and Its Degradation Products in Two Loamy Agricultural Soils: A Combined Laboratory and Field Study
DEFF Research Database (Denmark)
Badawi, Nora; Rosenbom, Anette E.; Olsen, Preben
2015-01-01
The herbicide fluazifop-P-butyl (FPB) is used against grasses in agricultural crops such as potato, oilseed rape and sugar beet. Limited information is available in Scientific literature on its environmental fate, therefore extensive monitoring at two agricultural test fields was combined...
3. Effects of agricultural fungicides on microorganisms associated with floral nectar: susceptibility assays and field experiments.
Science.gov (United States)
Bartlewicz, Jacek; Pozo, María I; Honnay, Olivier; Lievens, Bart; Jacquemyn, Hans
2016-10-01
Pesticides have become an inseparable element of agricultural intensification. While the direct impact of pesticides on non-target organisms, such as pollinators, has recently received much attention, less consideration has been given to the microorganisms that are associated with them. Specialist yeasts and bacteria are known to commonly inhabit floral nectar and change its chemical characteristics in numerous ways, possibly influencing pollinator attraction. In this study, we investigated the in vitro susceptibility of nectar yeasts Metschnikowia gruessi, Metschnikowia reukaufii, and Candida bombi to six widely used agricultural fungicides (prothioconazole, tebuconazole, azoxystrobin, fenamidone, boscalid, and fluopyram). Next, a commercial antifungal mixture containing tebuconazole and trifloxystrobin was applied to natural populations of the plant Linaria vulgaris and the occurrence, abundance, and diversity of nectar-inhabiting yeasts and bacteria was compared between treated and untreated plants. The results showed that prothioconazole and tebuconazole were highly toxic to nectar yeasts, inhibiting their growth at concentrations varying between 0.06 and 0.5 mg/L. Azoxystrobin, fenamidone, boscalid, and fluopyram on the other hand exhibited considerably lower toxicity, inhibiting yeast growth at concentrations between 1 and 32 mg/L or in many cases not inhibiting microbial growth at all. The application of the antifungal mixture in natural plant populations resulted in a significant decrease in the occurrence and abundance of yeasts in individual flowers, but this did not translate into noticeable changes in bacterial incidence and abundance. Yeast and bacterial species richness and distribution did not also differ between treated and untreated plants. We conclude that the application of fungicides may have negative effects on the abundance of nectar yeasts in floral nectar. The consequences of these effects on plant pollination processes in agricultural
4. Application of radioisotopes and radiation in the field of agricultural engineering in Japan
International Nuclear Information System (INIS)
Ochiai, T.
1974-01-01
Data have been published about the application of radioisotopes and radiation in Japan agricultural engineering. The radioisotopes have been used : 1 for measuring the humidity of the ground in the development of the irrigation and canalization of the cultivated areas; 2 for measuring i. the circulation rate of the ground water, ii. the porosity and the storing capacity of the water-carrier layers. iii. the drift and sand-transporting speed of the open canals; 3, for the control of the dam leaking in the ground water hydrology. (K.A.)
5. PestLCI - a model for estimating field emissions of pesticides in agricultural LCA
DEFF Research Database (Denmark)
Birkved, Morten; Hauschild, Michael Zwicky
2006-01-01
of a product or service is a specific element of LCA termed life cycle inventory (LCI). Estimation of chemical emissions in agricultural LCA is typically based on standard emission factors which at best are determined by a few physical-chemical substance properties and the use scenario of the chemical compound...... to the different environmental compartments. It estimates the fractions of the applied quantity which is emitted to the air, surface water, and groundwater compartment based on information which will normally be available to the model user about: type and time of application, crop species and development stage...... for other regions of the world. (c) 2006 Elsevier B.V. All rights reserved....
6. What is trust?: perspectives from farmers and other experts in the field of agriculture in Africa
Directory of Open Access Journals (Sweden)
Ezezika Obidimma C
2012-11-01
Full Text Available Abstract Background Agricultural biotechnology public-private partnerships (PPPs have been recognized as necessary for improving agricultural productivity and increasing food production in sub-Saharan Africa. However, there are issues of public trust uniquely associated with PPPs involved in the development of genetically modified (GM crops. Insight into how trust is understood by agbiotech stakeholders is needed to be able to promote and improve trust among actors comprising agbiotech PPPs. This study aimed to explore how stakeholders from the agricultural sector in sub-Saharan Africa understood the concept of trust in general as well as in the context of agbiotech PPPs. Methods Our data collection relied on sixty-one semi-structured, face-to-face interviews conducted with agbiotech stakeholders as part of a larger study investigating the role of trust in eight agbiotech projects across Africa. Interview transcripts were analyzed to create a narrative on how trust is understood by the study’s participants. Results Responses to the question “what is trust?” were diverse. However, across interviewees’ responses we identified six themes. In order to build and foster trust in a partnership, partners reported that one must practice integrity and honesty; deliver results in an accountable manner; be capable and competent; share the same objectives and interests; be transparent about actions and intentions through clear communication; and target services toward the interests of the public. Conclusions Participants reported that trust is either a very important factor or the most important factor in the making or breaking of success in agbiotech PPPs. The six themes that emerged from the interview data form a concept of trust. We thereby propose the following definition of trust in the context of agricultural biotechnology: an expectation held by an individual that the performance and behaviour of another will be supported by tangible results
7. Spatial variability of soil magnetic susceptibility in an agricultural field located in Eastern Ukraine
Science.gov (United States)
Menshov, Oleksandr; Pereira, Paulo; Kruglov, Oleksandr
2015-04-01
Magnetic susceptibility (MS) have been used to characterize soil properties. It gives an indirect information about heavy metals content and degree of human impacts on soil contamination derived from atmospheric pollution (Girault et al., 2011). This method is inexpensive in relation to chemical analysis and very useful to track soil pollution, since several toxic components deposited on soil surface are rich in particulates produced by oxidation processes (Boyko et al., 2004; Morton-Bernea et al., 2009). Thus, identify the spatial distribution of MS is of major importance, since can give an indirect information of high metals content (Dankoub et al., 2012). This allows also to distinguish the pedogenic and technogenic origin magnetic signal. For example Ukraine chernozems contain fine-grained oxidized magnetite and maghemite of pedogenic origin formed by weathering of the parent material (Jeleńska et al., 2004). However, to a correct understanding of variables distribution, the identification of the most accurate interpolation method is fundamental for a better interpretation of map information (Pereira et al., 2013). The objective of this work is to study the spatial variability of soil MS in an agricultural fields located in the Tcherkascy Tishki area (50.11°N, 36.43 °E, 162 m a.s.l), Ukraine. Soil MS was measured in 77 sampling points in a north facing slope. To estimate the best interpolation method, several interpolation methods were tested, as inverse distance to a weight (IDW) with the power of 1,2,3,4 and 5, Local Polynomial (LP) with the power of 1 and 2, Global Polynomial (GP), radial basis functions - spline with tension (SPT), completely regularized spline (CRS), multiquatratic (MTQ), inverse multiquatratic (IMTQ), and thin plate spline (TPS) - and some geostatistical methods as, ordinary kriging (OK), Simple Kriging (SK) and Universal Kriging (UK), used in previous works (Pereira et al., 2014). On average, the soil MS of the studied plot had 686
8. Areas to explore surrounding the Cerro Prieto geothermal field, BC; Areas para exploracion en los alrededores del campo geotermico de Cerro Prieto, BC
Energy Technology Data Exchange (ETDEWEB)
Aguilar Dumas, Alvaro [Comision Federal de Electricidad, Gerencia de Proyectos Geotermoelectricos, Residencia General de Cerro Prieto, Mexicali, Baja California (Mexico)]. E-mail: [email protected]
2009-07-15
Exploration plays an important role in tapping underground natural resources-whether water, oil, natural gas or minerals. Exploratory data allow us to learn reservoir conditions, increasing probable reserves and reservoir life span. Around the Cerro Prieto geothermal field, BC, and in the Mexicali Valley in general, exploration had almost stopped but recently was resumed by the Studies Division of Comision Federal de ELectricidad (CFE)'s Gerencia de Proyectos Geotermoelectricos. The division sent technical personnel to structurally map the northern and eastern portions of Laguna Salada. The paper offers a general outline of the main zones undergoing exploratory studies-studies perhaps culminating in siting exploratory wells to locate more geothermal resources (and ultimately producing them using binary power plants). CFE also wants to site injection wells west of the current production zone, and this is covered, as well. All activities are meant to increase the productive lifespan of the geothermal reservoir. [Spanish] Cuando se trata de la explotacion de recursos naturales del subsuelo, sea agua, gas, petroleo o minerales, la exploracion juega un papel muy importante, ya que permite conocer las condiciones del yacimiento que pudieran llevar a incrementar las reservas de los recursos explotados y extender su vida util. En las zonas aledanas al campo geotermico de Cerro Prieto, BC, y en general en el Valle de Mexicali, la exploracion estaba practicamente detenida habiendose reactivado a raiz de que la Subgerencia de Estudios de la Gerencia de Proyectos Geotermoelectricos de la Comision Federal de Electricidad (CFE) envio personal para realizar mapeos estructurales en las porciones norte y oriente de la Laguna Salada. Este trabajo presenta un panorama general de las areas prioritarias para realizar estudios exploratorios y poder programar, con mas bases, pozos exploratorios enfocados a localizar mas recursos geotermicos, inclusive para generar energia por medio
9. Field, Laboratory and Imaging spectroscopic Analysis of Landslide, Debris Flow and Flood Hazards in Lacustrine, Aeolian and Alluvial Fan Deposits Surrounding the Salton Sea, Southern California
Science.gov (United States)
Hubbard, B. E.; Hooper, D. M.; Mars, J. C.
2015-12-01
High resolution satellite imagery, field spectral measurements using a portable ASD spectrometer, and 2013 hyperspectral AVIRIS imagery were used to evaluate the age of the Martinez Mountain Landslide (MML) near the Salton Sea, in order to determine the relative ages of adjacent alluvial fan surfaces and the potential for additional landslides, debris flows, and floods. The Salton Sea (SS) occupies a pluvial lake basin, with ancient shorelines ranging from 81 meters to 113 meters above the modern lake level. The highest shoreline overlaps the toe of the 0.24 - 0.38 km3 MML deposit derived from hydrothermally altered granites exposed near the summit of Martinez Mountain. The MML was originally believed to be of early Holocene age. However, AVIRIS mineral maps show abundant desert varnish on the top and toe of the landslide. Desert varnish can provide a means of relative dating of alluvial fan (AF) or landslide surfaces, as it accumulates at determinable rates over time. Based on the 1) highest levels of desert varnish accumulation mapped within the basin, 2) abundant evaporite playa minerals on top of the toe of the landslide, and 3) the highest shoreline of the ancestral lake overtopping the toe of the landslide with gastropod and bivalve shells, we conclude that the MML predates the oldest alluvial fan terraces and lake sediments exposed in the Coachella and Imperial valleys and must be older than early Holocene (i.e. Late Pleistocene?). Thus, the MML landslide has the potential to be used as a spectral endmember for desert varnish thickness and thus proxy for age discrimination of active AF washes versus desert pavements. Given the older age of the MML landslide and low water levels in the modern SS, the risk from future rockslides of this size and related seiches is rather low. However, catastrophic floods and debris flows do occur along the most active AF channels; and the aftermath of such flows can be identified spectrally by montmorillonite crusts forming in
10. "Green technology": Bio-stimulation by an electric field for textile reactive dye contaminated agricultural soil.
Science.gov (United States)
Annamalai, Sivasankar; Santhanam, Manikandan; Selvaraj, Subbulakshmi; Sundaram, Maruthamuthu; Pandian, Kannan; Pazos, Marta
2018-05-15
The aim of the study is to degrade pollutants as well as to increase the fertility of agricultural soil by starch enhancing electrokinetic (EKA) and electro-bio-stimulation (EBS) processes. Starch solution was used as an anolyte and voltage gradient was about 0.5V/cm. The influence of bacterial mediated process was evaluated in real contaminated farming soil followed by pilot scale experiment. The in-situ formation of β-cyclodextrin from starch in the treatments had also influence on the significant removal of the pollutants from the farming soil. The conductivity of the soil was effectively reduced from 15.5dS/m to 1.5dS/m which corroborates well with the agricultural norms. The bio-stimulation was confirmed by the increase of the phosphorus content in the treated soil. Finally, phytotoxicity assays demonstrated the viability of the developed technique for soil remediation because plant germination percentage was higher in the treated soil in comparison to untreated soil. Copyright © 2017 Elsevier B.V. All rights reserved.
11. The Utilization of Edge-of-Field Monitoring of Agricultural Runoff in Addressing Nonpoint Source Pollution
Science.gov (United States)
While basin-scale studies and modeling are important tools in relating land uses to water quality concerns, edge-of-field monitoring (EOFM) provides the necessary resolution to spatially target, design, and evaluate in-field conservation practices for reducing nutrient and sediment loading from agri...
12. Towards the Development of a Smart Flying Sensor: Illustration in the Field of Precision Agriculture
Directory of Open Access Journals (Sweden)
Andres Hernandez
2015-07-01
Full Text Available Sensing is an important element to quantify productivity, product quality and to make decisions. Applications, such as mapping, surveillance, exploration and precision agriculture, require a reliable platform for remote sensing. This paper presents the first steps towards the development of a smart flying sensor based on an unmanned aerial vehicle (UAV. The concept of smart remote sensing is illustrated and its performance tested for the task of mapping the volume of grain inside a trailer during forage harvesting. Novelty lies in: (1 the development of a position-estimation method with time delay compensation based on inertial measurement unit (IMU sensors and image processing; (2 a method to build a 3D map using information obtained from a regular camera; and (3 the design and implementation of a path-following control algorithm using model predictive control (MPC. Experimental results on a lab-scale system validate the effectiveness of the proposed methodology.
13. Towards the Development of a Smart Flying Sensor: Illustration in the Field of Precision Agriculture.
Science.gov (United States)
Hernandez, Andres; Murcia, Harold; Copot, Cosmin; De Keyser, Robin
2015-07-10
Sensing is an important element to quantify productivity, product quality and to make decisions. Applications, such as mapping, surveillance, exploration and precision agriculture, require a reliable platform for remote sensing. This paper presents the first steps towards the development of a smart flying sensor based on an unmanned aerial vehicle (UAV). The concept of smart remote sensing is illustrated and its performance tested for the task of mapping the volume of grain inside a trailer during forage harvesting. Novelty lies in: (1) the development of a position-estimation method with time delay compensation based on inertial measurement unit (IMU) sensors and image processing; (2) a method to build a 3D map using information obtained from a regular camera; and (3) the design and implementation of a path-following control algorithm using model predictive control (MPC). Experimental results on a lab-scale system validate the effectiveness of the proposed methodology.
14. Investigating summer flow paths in a Dutch agricultural field using high frequency direct measurements
Science.gov (United States)
Delsman, J. R.; Waterloo, M. J.; Groen, M. M. A.; Groen, J.; Stuyfzand, P. J.
2014-11-01
The search for management strategies to cope with projected water scarcity and water quality deterioration calls for a better understanding of the complex interaction between groundwater and surface water in agricultural catchments. We separately measured flow routes to tile drains and an agricultural ditch in a deep polder in the coastal region of the Netherlands, characterized by exfiltration of brackish regional groundwater flow and intake of diverted river water for irrigation and water quality improvement purposes. We simultaneously measured discharge, electrical conductivity and temperature of these separate flow routes at hourly frequencies, disclosing the complex and time-varying patterns and origins of tile drain and ditch exfiltration. Tile drainage could be characterized as a shallow flow system, showing a non-linear response to groundwater level changes. Tile drainage was fed primarily by meteoric water, but still transported the majority (80%) of groundwater-derived salt to surface water. In contrast, deep brackish groundwater exfiltrating directly in the ditch responded linearly to groundwater level variations and is part of a regional groundwater flow system. We could explain the observed salinity of exfiltrating drain and ditch water from the interaction between the fast-responding pressure distribution in the subsurface that determined groundwater flow paths (wave celerity), and the slow-responding groundwater salinity distribution (water velocity). We found water demand for maintaining water levels and diluting salinity through flushing to greatly exceed the actual sprinkling demand. Counterintuitively, flushing demand was found to be largest during precipitation events, suggesting the possibility of water savings by operational flushing control.
15. Recent advancement on chemical arsenal of Bt toxin and its application in pest management system in agricultural field.
Science.gov (United States)
2018-04-01
Bacillus thuringiensis ( Bt ) is a Gram-positive, spore-forming, soil bacterium, which is very popular bio-control agent in agricultural and forestry. In general, B. thuringiensis secretes an array of insecticidal proteins including toxins produced during vegetative growth phase (such as secreted insecticidal protein, Sip; vegetative insecticidal proteins, Vip), parasporal crystalline δ-endotoxins produced during vegetative stationary phase (such as cytolytic toxin, Cyt; and crystal toxin, Cry), and β-exotoxins. Till date, a wide spectrum of Cry proteins has been reported and most of them belong to three-domain-Cry toxins, Bin-like toxin, and Etx_Mtx2-like toxins. To the best of our knowledge, neither Bt insecticidal toxins are exclusive to Bt nor all the strains of Bt are capable of producing insecticidal Bt toxins. The lacuna in their latest classification has also been discussed. In this review, the updated information regarding the insecticidal Bt toxins and their different mode of actions were summarized. Before applying the Bt toxins on agricultural field, the non-specific effects of toxins should be investigated. We also have summarized the problem of insect resistance and the strategies to combat with this problem. We strongly believe that this information will help a lot to the budding researchers in the field of modern pest control biotechnology.
16. Assessment of soil redistribution rates by (137)Cs and (210)Pbex in a typical Malagasy agricultural field.
Science.gov (United States)
Rabesiranana, N; Rasolonirina, M; Solonjara, A F; Ravoson, H N; Raoelina Andriambololona; Mabit, L
2016-02-01
17. Development of the ClearSky smoke dispersion forecast system for agricultural field burning in the Pacific Northwest
Science.gov (United States)
Jain, Rahul; Vaughan, Joseph; Heitkamp, Kyle; Ramos, Charleston; Claiborn, Candis; Schreuder, Maarten; Schaaf, Mark; Lamb, Brian
The post-harvest burning of agricultural fields is commonly used to dispose of crop residue and provide other desired services such as pest control. Despite careful regulation of burning, smoke plumes from field burning in the Pacific Northwest commonly degrade air quality, particularly for rural populations. In this paper, ClearSky, a numerical smoke dispersion forecast system for agricultural field burning that was developed to support smoke management in the Inland Pacific Northwest, is described. ClearSky began operation during the summer through fall burn season of 2002 and continues to the present. ClearSky utilizes Mesoscale Meteorological Model version 5 (MM5v3) forecasts from the University of Washington, data on agricultural fields, a web-based user interface for defining burn scenarios, the Lagrangian CALPUFF dispersion model and web-served animations of plume forecasts. The ClearSky system employs a unique hybrid source configuration, which treats the flaming portion of a field as a buoyant line source and the smoldering portion of the field as a buoyant area source. Limited field observations show that this hybrid approach yields reasonable plume rise estimates using source parameters derived from recent field burning emission field studies. The performance of this modeling system was evaluated for 2003 by comparing forecast meteorology against meteorological observations, and comparing model-predicted hourly averaged PM 2.5 concentrations against observations. Examples from this evaluation illustrate that while the ClearSky system can accurately predict PM 2.5 surface concentrations due to field burning, the overall model performance depends strongly on meteorological forecast error. Statistical evaluation of the meteorological forecast at seven surface stations indicates a strong relationship between topographical complexity near the station and absolute wind direction error with wind direction errors increasing from approximately 20° for sites in
18. Infecciones parasitarias del coyote, Canis latrans (Carnivora: Canidae en un Parque Nacional y una zona agrícola en Costa Rica Parasitic infections of coyote, Canis latrans (Carnivora: Canidae in a Costa Rican National Park and a surrounding agricultural area
Directory of Open Access Journals (Sweden)
Carmen Niehaus
2012-06-01
disseminators of infectious diseases (including parasites, coyotes (Canis latrans may also serve as indicators of ecological health. In Costa Rica, little information exists on coyote parasites, making research necessary to identify potential zoonotic interactions. For this reason, a survey of the coyote parasites was performed in a mixed area of protected woodland and agricultural land, surrounding Irazu Volcano National Park (IVNP in Cartago, Costa Rica. Over a one-year period, 209 fecal samples were collected directly from the ground. Collection took place on a monthly basis in a trail sectioned into three sub-areas named Irazú (closest to the volcano, potato fields (where potatoes were cultivated, and Prusia (a protected sector of IVNP. Sectioning the trail allowed separate collection and analysis of the samples, where 99 were obtained from Irazú, 11 from potato fields and 99 from Prusia. Using direct examination and mechanical concentration 36.84% positive samples containing at least one helminth were found. The presence of parasites was similar for both woodland areas (33.3% in Prusia and 37.4% in Irazú, but differed from the 63.6% observed in the potato fields. Hookworm parasites (probably Ancylostoma caninum, threadworms (possibly Strongyloides sp., Toxocara canis, Trichuris sp. and Taenia pisiformis were identified, as well as Hymenolepis diminuta, possible spurious parasite resulting from the ingestion of rodents by coyotes. Seasonal details are discussed, concluding that wet and dry seasons affect presence of parasites. Some remarks are made on the importance of these first findings for Costa Rica, especially considering the systematic way in which the collection of samples was carried out. Rev. Biol. Trop. 60 (2: 799-808. Epub 2012 June 01.
19. Polarization signatures for abandoned agricultural fields in the Manix Basin area of the Mojave Desert
Science.gov (United States)
Ray, Terrill W.; Farr, Tom G.; Vanzyl, Jakob J.
1991-01-01
Polarimetric signatures from abandoned circular alfalfa fields in the Manix Basin area of the Mojave desert show systematic changes with length of abandonment. The obliteration of circular planting rows by surface processes could account for the disappearance of bright 'spokes', which seems to be reflection patterns from remnants of the planting rows, with increasing length of abandonment. An observed shift in the location of the maximum L-band copolarization return away from VV, as well as an increase in surface roughness, both occurring with increasing age of abandonment, seems to be attributable to the formation of wind ripple on the relatively vegetationless fields. A Late Pleistocene/Holocene sand bar deposit, which can be identified in the radar images, is probably responsible for the failure of three fields to match the age sequence patterns in roughness and peak shift.
20. Long-term monitoring of nitrate-N transport to drainage from three agricultural clayey till fields
Science.gov (United States)
Ernstsen, V.; Olsen, P.; Rosenbom, A. E.
2015-01-01
The application of nitrogen (N) fertilisers to crops grown on tile-drained fields is necessary to sustain most modern crop production, but poses a risk to the aquatic environment since tile drains facilitate rapid transport pathways with no significant reduction in nitrate. To maintain the water quality of the aquatic environment and the provision of food from highly efficient agriculture in line with the EU's Water Framework Directive and Nitrates Directive, field-scale knowledge is imperative if there is to be differentiated N-regulation in future. This study describes nitrate-N leaching to drainage based on coherent monitoring of nitrate-N concentrations, the climate, the groundwater table and crop-specific parameters obtained over eleven years (2001-2011) at three subsurface-drained clayey till fields (1.3-2.3 ha). The monitoring results showed significant field differences in nitrate-N transport to drainage. Not only were these caused by periods of bare soil after short-season crops and N-fixing crops (pea), which have been shown to generate high nitrate-N concentrations in drainage, but by the hydrogeological field conditions that were shown to be the controlling factor of nitrate-N transport to drainage. The fields had the following characteristics: (A) the lowest mass transport (13 kg N ha-1) and fertiliser input had short-term and low-intensity drainage with the highest nitrate-N concentrations detected, representing 40% of net precipitation (226 mm) combined with low air temperatures, (B) the medium mass transport (14 kg N ha-1) had medium-term and medium-intensity drainage, representing 42% of net precipitation (471 mm) combined with periods of both low and higher air temperatures, (C) the highest mass transport (19 kg N ha-1) had long-term drainage, representing 68% of net precipitation (617 mm), but had the highest potential for in-situ soil denitrification and post-treatment (e.g. constructed wetlands) due to long periods with both high water
1. Some results from a temperature evaluation of a cotton field with infrared thermometer for agricultural use
International Nuclear Information System (INIS)
Ovcharova, A.; Kolev, N.; Nedkov, N.
2005-01-01
The aims of the present study were connected with evaluation of the basic soil properties, distribution of thermal, hydrological and electronic soil properties and criteria for minimization of the measurement points, obtained in the cotton non-irrigated field of the Institute of durum wheat and cotton near Chirpan. It were measured crop temperature of cotton field and soil surface temperature distribution during the main vegetative stages. Using the energy balance equation and soil water balance equation was calculated the intensity of evapotranspiration during the days of measurements
2. Field tracer investigation of unsaturated zone flow paths and mechanisms in agricultural soils of northwestern Mississippi, USA
Science.gov (United States)
Perkins, K.S.; Nimmo, J.R.; Rose, C.E.; Coupe, R.H.
2011-01-01
In many farmed areas, intensive application of agricultural chemicals and withdrawal of groundwater for irrigation have led to water quality and supply issues. Unsaturated-zone processes, including preferential flow, play a major role in these effects but are not well understood. In the Bogue Phalia basin, an intensely agricultural area in the Delta region of northwestern Mississippi, the fine-textured soils often exhibit surface ponding and runoff after irrigation and rainfall as well as extensive surface cracking during prolonged dry periods. Fields are typically land-formed to promote surface flow into drainage ditches and streams that feed into larger river ecosystems. Downward flow of water below the root zone is considered minimal; regional groundwater models predict only 5% or less of precipitation recharges the heavily used alluvial aquifer. In this study transport mechanisms within and below the root zone of a fallow soybean field were assessed by performing a 2-m ring infiltration test with tracers and subsurface monitoring instruments. Seven months after tracer application, 48 continuous cores were collected for tracer extraction to define the extent of water movement and quantify preferential flow using a mass-balance approach. Vertical water movement was rapid below the pond indicating the importance of vertical preferential flow paths in the shallow unsaturated zone, especially to depths where agricultural disturbance occurs. Lateral flow of water at shallow depths was extensive and spatially non-uniform, reaching up to 10. m from the pond within 2. months. Within 1. month, the wetting front reached a textural boundary at 4-5. m between the fine-textured soil and sandy alluvium, now a potential capillary barrier which, prior to extensive irrigation withdrawals, was below the water table. Within 10. weeks, tracer was detectable at the water table which is presently about 12. m below land surface. Results indicate that 43% of percolation may be through
3. Ionizing radiation in the field of hydrogels used for agriculture and medicine
International Nuclear Information System (INIS)
Radoiu, M.; Martin, D.; Oproiu, C.; Indreias, I; Toma, M.; Dragusin, M.; Moraru, R.; Manea, A.
1998-01-01
The hydrogels, such as homopolymers of acrylamide (AHH type), co-polymers of acrylamide-sodium acrylate (ANACH type) and homopolymers of sodium acrylate (NAHH type), obtained by gamma ray and accelerated electron beam are presented. The effects of the solution chemical composition, swelling medium nature, radiation absorbed dose and radiation absorbed dose rate upon the swelling degree and mechanical strength of these hydrogel types are discussed. Distilled water, physiological serum and 4 N NaCl aqueous solution were used as swelling medium. Radiation absorbed dose has an important effect upon the swelling degree of AHH and ANACH types especially when distilled water is used as swelling medium while the NAHH swelling degree presents a small dependence versus absorbed dose for all swelling medium types. Usually, the swelling degree for all hydrogel types decreases versus absorbed dose and absorbed dose rate and exhibits the higher values for distilled water as swelling medium. The hydrogels mechanical strength exhibits a maximum value versus absorbed dose. The best values for mechanical strength depend on hydrogel type and swelling medium. The used range for absorbed dose was from 2 kGy to 16 kGy. Our types of hydrogels were developed for some applications such as in agriculture (AHH and ANACH types) to maintain soil humidity and in medicine as absorption material for dressing (NAHH types). (author)
4. Evaluation of Physic-chemical Parameters of Water Quality on Agricultural Fields of Western Bahia
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Enoc Lima do Rego
2017-06-01
Full Text Available For the diagnosis of the quality of water it is necessary to execute a set of analyzes (physical and chemical of the body of water that will provide information that integrate biotic and abiotic factors that govern the functioning of the ecosystem. The objective of this study is to evaluate the quality of water from wells and rivers of Urucuia aquifer region for investigation of contamination or contamination risks. Were realize collections in nine (9 areas of western Bahia, which were collect in each area, two points of well water samples and a river, and determining the electrical conductivity, pH, dissolved ions and metals. The results were compare with the maximum permissible values (MPV for human consumption by Ordinance No. 2914/11 of the Ministry of Health and National Environment Counsel - CONAMA (Resolution 357 and supplementary resolutions. The quantitative results of the analysis showed that the surface and well waters that are part of the aquifer Urucuia within the parameters investigated are below the values recommended by the legislation showing that the agricultural activities in the region has not affected to the evaluated parameters, the quality of water for human consumption. However, it is necessary a monitoring of surface and groundwater in the region with expansion parameters evaluated. DOI: http://dx.doi.org/10.17807/orbital.v9i2.880
5. Soil organic carbon mapping of partially vegetated agricultural fields with imaging spectroscopy
NARCIS (Netherlands)
Bartholomeus, H.; Kooistra, L.; Stevens, A.; Leeuwen, van M.; Wesemael, van B.; Ben-Dor, E.; Tychon, B.
2011-01-01
Soil Organic Carbon (SOC) is one of the key soil properties, but the large spatial variation makes continuous mapping a complex task. Imaging spectroscopy has proven to be an useful technique for mapping of soil properties, but the applicability decreases rapidly when fields are partially covered
6. FroboMind, proposing a conceptual architecture for agricultural field robot navigation
DEFF Research Database (Denmark)
Jensen, Kjeld; Bøgild, Anders; Nielsen, Søren Hundevadt
2011-01-01
The aim of this work is to propose a conceptual system architecture Field Robot Cognitive System Architecture (FroboMind). which can provide the flexibility and extend ability required for further research and development within cognition based navigation of plant nursing robots....
7. Entomopathogenic fungi in predatory beetles (Col: Carabidae and Staphylinidae) from agricultural fields
DEFF Research Database (Denmark)
Steenberg, T; Langer, V; Esbjerg, P
1995-01-01
Prevalence of entomopathogenic fungi was studied in overwintering ground beetles (Col.: Carabidae) and rove beetles (Col.: Staphylinidae) collected from fields of lucerne, white cabbage and white cabbage undersown with white clover. In general infection levels in adult ground beetles and rove bee...
8. ANALYSIS OF ELECTROMAGNETIC FIELDS AND NOISE IN THE AREA OF AGRICUL-TURAL BIOGAS PLANT
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Paweł A. Mazurek
2016-12-01
Full Text Available Electro-magnetic and acoustic fields were analysed at the bioenergy and biogas production plant of 0.999 MW operational power, localized in Piaski. Measured values were compared with valid national norms and did not exceed limiting values in zones of people’s permanent residence.
9. Emissions from Prescribed Burning of Agricultural Fields in the Pacific Northwest
Science.gov (United States)
Prescribed burns of winter wheat stubble and Kentucky bluegrass fields in northern Idaho and eastern Washington states (U.S.A.) were sampled using ground-, aerostat-, airplane-, and laboratory-based measurement platforms to determine emission factors, compare methods, and provide...
10. Tetracyclines and tetracycline resistance in agricultural soils: microcosm and field studies.
NARCIS (Netherlands)
Schmitt, Heike; Stoob, Krispin; Hamscher, Gerd; Smit, Eric; Seinen, Willem
2006-01-01
The influence of the use of antibiotics on the prevalence of resistance genes in the environment is still poorly understood. We studied the diversity of tetracycline and sulfonamide resistance genes as influenced by fertilization with pig manure in soil microcosms and at two field locations. Manure
11. Standardization of doctoral study in agricultural and extension education: is the field of study mature enough for achievement of the optimum degree of order?
Science.gov (United States)
Briers, G E; Lindner, J R; Shinn, G C; Wingenbach, G W; Baker, M T
2010-01-01
Agricultural and extension education--or some derivative name--is a field of study leading to the doctoral degree in universities around the world. Is there are body of knowledge or a taxonomy of the knowledge--e.g., a knowledge domain--that one should possess with a doctorate in agricultural and extension education? The purpose of this paper was to synthesize the work of researchers who attempted to define the field of study, with a taxonomy comprising the knowledge domains (standards) and knowledge objects--structured interrelated sets of data, knowledge, and wisdom--of the field of study. Doctoral study in agricultural and extension education needs a document that provides for rules and guidelines--rules and guidelines that in turn provide for common and repeated use--all leading to achievement of an optimum degree of order in the context of academic, scholarly, and professional practice in agricultural and extension education. Thus, one would know in broad categories the knowledge, skills, and abilities possessed by one who holds a doctoral degree in agricultural and extension education. That is, there would exist a standard for doctoral degrees in agricultural and extension education. A content analysis of three previous attempts to categorize knowledge in agricultural and extension education served as the primary technique to create a new taxonomy--or to confirm an existing taxonomy--for doctoral study in agricultural and extension education. The following coalesced as nine essential knowledge domains for a doctorate in agricultural and extension education: (1) history, philosophy, ethics, and policy; (2) agricultural/rural development; (3) organizational development and change management; (4) planning, needs assessment, and evaluation; (5) learning theory; (6) curriculum development and instructional design; (7) teaching methods and delivery strategies; (8) research methods and tools; and, (9) scholarship and communications.
12. Assessment of soil erosion and deposition rates in a Moroccan agricultural field using fallout 137Cs and 210Pbex.
Science.gov (United States)
Benmansour, M; Mabit, L; Nouira, A; Moussadek, R; Bouksirate, H; Duchemin, M; Benkdad, A
2013-01-01
13. Long-term field-scale experiment on using lime filters in an agricultural catchment.
Science.gov (United States)
Kirkkala, Teija; Ventelä, Anne-Mari; Tarvainen, Marjo
2012-01-01
The River Yläneenjoki catchment in southwest Finland is an area with a high agricultural nutrient load. We report here on the nutrient removal performance of three on-site lime-sand filters (F1, F2, and F3), established within or on the edge of the buffer zones. The filters contain burnt lime (CaO) or spent lime [CaO, Ca(OH), and CaCO]. Easily soluble lime results in a high pH level (>11) and leads to an efficient precipitation of soluble phosphorus (P) from the runoff. Water samples were taken from the inflow and outflow of each site in different hydrological situations. The length of the monitoring period was 4 yr for F1, 6 yr for F2, and 1.5 yr for F3. F1 and F2 significantly reduced the suspended solids (SS), total P (PTOT), and dissolved reactive P (DRP) in the treated water. The proportional reduction (%) varied but was usually clearly positive. Filter F3 was divided into two equal parts, one containing burnt lime and the other spent lime. Both filter parts removed PTOT and SS efficiently from the water; the burnt-lime part also removed DRP. The mixed-lime part removed DRP for a year, but then the efficiency decreased. The effect of filters on nitrogen compounds varied. We conclude that sand filters incorporating lime can be used together with buffer zones to reduce both P and SS load to watercourses. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc.
14. Agricultural terraces montoring and modeling: a field survey in Chianti region, Firenze, Italy – Second part
Science.gov (United States)
Preti, Federico; Caruso, Marco; Dani, Andrea; Cassiani, Giorgio; Romano, Nunzio; Tarolli, Paolo
2015-04-01
sustainable management of erosion processes in agricultural land and hilly-mountainous area
15. Wind dispersal of alien plant species into remnant natural vegetation from adjacent agricultural fields
Directory of Open Access Journals (Sweden)
Chika Egawa
2017-07-01
Full Text Available Knowledge regarding the seed dispersal of alien species is crucial to manage invasion risk in fragmented natural habitats. Focusing on wind dispersal, this study assessed the spatial and quantitative extents to which a remnant natural fen receives the seeds of alien species dispersed from adjacent hay meadows in Hokkaido, northern Japan. I established a total of 80 funnel seed traps in the fen at distances of 1, 2, 5, 10, 20, 30, 50, and 100 m from the meadows. The proportion of alien species in the seed rain at each distance was quantified, and the 99th-percentile dispersal distance from the meadows was estimated for each alien species by constructing dispersal kernels. Despite the presence of a marginal ditch and an elevational difference between the fen and the meadows, five alien species, including four grasses that do not have modified seed structures for wind dispersal, dispersed their seeds into the fen. These alien species accounted for up to 65.9% of the seed rain in terms of quantity. The 99th-percentile dispersal distances of the alien species ranged from 3.8 m to 309.3 m, and these distances were longer than the values predicted on the basis of their functional traits, such as terminal velocity. The results of this study demonstrated that numerous seeds of farmland-derived alien species were transported into the remnant vegetation via wind dispersal, and that simple predictions of dispersal distance based on functional traits could underestimate the potential area that alien species can reach. Continuous management both in farmland (to reduce seed escape and in remnant vegetation (to prevent the establishment of alien species is necessary to protect native vegetation from biological invasion in agricultural landscapes.
16. Tetracyclines and tetracycline resistance in agricultural soils: microcosm and field studies.
OpenAIRE
Schmitt, Heike; Stoob, Krispin; Hamscher, Gerd; Smit, Eric; Seinen, Willem
2006-01-01
The influence of the use of antibiotics on the prevalence of resistance genes in the environment is still poorly understood. We studied the diversity of tetracycline and sulfonamide resistance genes as influenced by fertilization with pig manure in soil microcosms and at two field locations. Manure contained a high diversity of resistance genes, regardless of whether it stemmed from a farm operation with low or regular use of antibiotics. In the microcosm soils, the influence of fertilization...
17. Chemical and biological characterization of products of incomplete combustion from the simulated field burning of agricultural plastic.
Science.gov (United States)
Linak, W P; Ryan, J V; Perry, E; Williams, R W; DeMarini, D M
1989-06-01
Chemical and biological analyses were performed to characterize products of incomplete combustion emitted during the simulated open field burning of agricultural plastic. A small utility shed equipped with an air delivery system was used to simulate pile burning and forced-air-curtain incineration of a nonhalogenated agricultural plastic that reportedly consisted of polyethylene and carbon black. Emissions were analyzed for combustion gases; volatile, semi-volatile, and particulate organics; and toxic and mutagenic properties. Emission samples, as well as samples of the used (possibly pesticide-contaminated) plastic, were analyzed for the presence of several pesticides to which the plastic may have been exposed. Although a variety of alkanes, alkenes, and aromatic and polycyclic aromatic hydrocarbon (PAH) compounds were identified in the volatile, semi-volatile, and particulate fractions of these emissions, a substantial fraction of higher molecular weight organic material was not identified. No pesticides were identified in either combustion emission samples or dichloromethane washes of the used plastic. When mutagenicity was evaluated by exposing Salmonella bacteria (Ames assay) to whole vapor and vapor/particulate emissions, no toxic or mutagenic effects were observed. However, organic extracts of the particulate samples were moderately mutagenic. This mutagenicity compares approximately to that measured from residential wood heating on a revertant per unit heat release basis. Compared to pile burning, forced air slightly decreased the time necessary to burn a charge of plastic. There was not a substantial difference, however, in the variety or concentrations of organic compounds identified in samples from these two burn conditions. This study highlights the benefits of a combined chemical/biological approach to the characterization of complex, multi-component combustion emissions. These results may not reflect those of other types of plastic that may be used
18. Geospatial field applications within United States Department of Agriculture, Veterinary Services.
Science.gov (United States)
FitzMaurice, Priscilla L; Freier, Jerome E; Geter, Kenneth D
2007-01-01
Epidemiologists, veterinary medical officers and animal health technicians within Veterinary Services (VS) are actively utilising global positioning system (GPS) technology to obtain positional data on livestock and poultry operations throughout the United States. Geospatial data, if acquired for monitoring and surveillance purposes, are stored within the VS Generic Database (GDB). If the information is collected in response to an animal disease outbreak, the data are entered into the Emergency Management Response System (EMRS). The Spatial Epidemiology group within the Centers for Epidemiology and Animal Health (CEAH) has established minimum data accuracy standards for geodata acquisition. To ensure that field-collected geographic coordinates meet these minimum standards, field personnel are trained in proper data collection procedures. Positional accuracy is validated with digital atlases, aerial photographs, Web-based parcel maps, or address geocoding. Several geospatial methods and technologies are under investigation for future use within VS. These include the direct transfer of coordinates from GPS receivers to computers, GPS-enabled digital cameras, tablet PCs, and GPS receivers preloaded with custom ArcGIS maps - all with the objective of reducing transcription and data entry errors and improving the ease of data collection in the field.
19. Nutrient uptake by agricultural crops from biochar-amended soils: results from two field experiments in Austria
Science.gov (United States)
Karer, Jasmin; Zehetner, Franz; Kloss, Stefanie; Wimmer, Bernhard; Soja, Gerhard
2013-04-01
The use of biochar as soil amendment is considered as a promising agricultural soil management technique, combining carbon sequestration and soil fertility improvements. These expectations are largely founded on positive experiences with biochar applications to impoverished or degraded tropical soils. The validity of these results for soils in temperate climates needs confirmation from field experiments with typical soils representative for intensive agricultural production areas. Frequently biochar is mixed with other organic additives like compost. As these two materials interact with each other and each one may vary considerably in its basic characteristics, it is difficult to attribute the effects of the combined additive to one of its components and to a specific physico-chemical parameter. Therefore investigations of the amendment efficacy require the study of the pure components to characterize their specific behavior in soil. This is especially important for adsorption behavior of biochar for macro- and micronutrients because in soil there are multiple nutrient sinks that compete with plant roots for vital elements. Therefore this contribution presents results from a field amendment study with pure biochar that had the objective to characterize the macro- and microelement uptake of crops from different soils in two typical Austrian areas of agricultural production. At two locations in North and South-East Austria, two identical field experiments on different soils (Chernozem and Cambisol) were installed in 2011 with varying biochar additions (0, 30 and 90 t/ha) and two nitrogen levels. The biochar was a product from slow pyrolysis of wood (SC Romchar SRL). During the installation of the experiments, the biochar fraction of corn). An omission of biochar addition at the same nitrogen addition rate resulted in a yield decrease of 10 % for barley although the total N uptake was 11 % higher but P and K uptake decreased by 14 and 6 %. This indicates that the
20. Earthworms influenced by reduced tillage, conventional tillage and energy forest in Swedish agricultural field experiments
Energy Technology Data Exchange (ETDEWEB)
Lagerloef, Jan (SLU, Department of Ecology, Swedish University of Agricultural Sciences, Uppsala (Sweden)), Email: [email protected]; Paalsson, Olof; Arvidsson, Johan (SLU, Department of Soil and Environment, Swedish University of Agricultural Sciences, Uppsala (Sweden))
2012-03-15
We compared earthworm density, depth distribution and species composition in three soil cultivation experiments including the treatments ploughless tillage and mouldboard ploughing. Sampling was done in September 2005 and for one experiment also in 1994. By yearly sampling 1995-2005, earthworms in an energy forest of Salix viminalis were compared with those in an adjacent arable field. Sampling method was digging of soil blocks and hand sorting and formalin sampling in one cultivation experiment. Both methods were used in the energy forest and arable land comparison. In two soil cultivation experiments, highest abundances or biomass were found in ploughless tillage. Earthworm density was higher in the upper 10 cm, especially in the ploughless tillage. Earthworm density was significantly higher in the energy forest than in the arable field. Formalin sampling revealed c. 36% of the earthworm numbers found by digging in the energy forest and gave almost no earthworms in the arable field. In all treatments with soil cultivation, species living and feeding in the rhizosphere and soil dominated. One such species, Allolobophora chlorotica, was more abundant under mouldboard ploughing than ploughless tillage. Lumbricus terrestris, browsing on the surface and producing deep vertical burrows, was more common in the ploughless tillage. Species living and feeding close to the soil surface were almost only found in the energy forest, which had not been soil cultivated since 1984. The findings support earlier studies pointing out possibilities to encourage earthworms by reduced soil cultivation. This is one of the first published studies that followed earthworm populations in an energy forest plantation during several years. Explanation of earthworm reactions to management and environmental impacts should be done with consideration of the ecology of species or species groups. Earthworm sampling by formalin must always be interpreted with caution and calibrated by digging and
1. Statistical analysis of nitrous oxide emission factors from pastoral agriculture field trials conducted in New Zealand
International Nuclear Information System (INIS)
Kelliher, F.M.; Cox, N.; Weerden, T.J. van der; Klein, C.A.M. de; Luo, J.; Cameron, K.C.; Di, H.J.; Giltrap, D.; Rys, G.
2014-01-01
Between 11 May 2000 and 31 January 2013, 185 field trials were conducted across New Zealand to measure the direct nitrous oxide (N 2 O) emission factors (EF) from nitrogen (N) sources applied to pastoral soils. The log(EF) data were analysed statistically using a restricted maximum likelihood (REML) method. To estimate mean EF values for each N source, best linear unbiased predictors (BLUPs) were calculated. For lowland soils, mean EFs for dairy cattle urine and dung, sheep urine and dung and urea fertiliser were 1.16 ± 0.19% and 0.23 ± 0.05%, 0.55 ± 0.19% and 0.08 ± 0.02% and 0.48 ± 0.13%, respectively, each significantly different from one another (p 12°, mean EFs were significantly lower. Thus, urine and dung EFs should be disaggregated for sheep and cattle as well as accounting for terrain. -- Highlights: • Nitrous oxide emission factors (EFs) for pastoral soils measured in 185 field trials. • For lowland, the mean (±standard error) urea nitrogen fertiliser EF was 0.5 ± 0.1%. • For lowland, mean dairy cattle urine and dung EFs were 1.2 and 0.2%, respectively. • For lowland, mean sheep urine and dung EFs were 0.6 and 0.1%, respectively. • For pastoral soils in terrain with slopes >12°, mean EFs were significantly lower. -- From 185 field trials, mean nitrous oxide emission factors for pastoral soils were 0.1% for sheep dung up to 1.2% for dairy cattle urine, while that for urea fertiliser was 0.5%
2. Temporal Patterns of Glyphosate Leaching at a Loamy Agricultural Field in Denmark
DEFF Research Database (Denmark)
Nørgaard, Trine; Møldrup, Per; Olsen, Preben
2013-01-01
applications in combination with the effect of precipitation events, drain water runoff, soil water content at 25 cm soil depth, management, and particle leaching patterns, and compares this with monitored field-scale glyphosate and AMPA leaching to a tile drainage system. Preliminary findings indicate...... that there is an accumulation of glyphosate and AMPA in the soil after the successive applications of glyphosate, as the level of the peaking concentrations right after applications increases. Furthermore, large precipitation events with subsequent high drain water runoff together with management, especially plowing...
3. Assessment of soil redistribution rates by 137Cs and 210Pbex in a typical Malagasy agricultural field
International Nuclear Information System (INIS)
Rabesiranana, N.; Rasolonirina, M.; Solonjara, A.F.; Ravoson, H.N.; Raoelina Andriambololona; Mabit, L.
2016-01-01
4. Controlling factors of nitrous oxide (N2O) emissions at the field-scale in an agricultural slope
Science.gov (United States)
Vilain, Guillaume; Garnier, Josette; Tallec, Gaëlle; Tournebize, Julien; Cellier, Pierre; Flipo, Nicolas
2010-05-01
Agricultural practices widely contribute to the atmospheric nitrous oxide (N2O) concentration increase and are the major source of N2O which account for 24% of the global annual emission (IPCC, 2007). Soil nitrification and denitrification are the microbial processes responsible for the production of N2O, which also depends on soil characteristics and management. Besides their control by various factors, such as climate, soil conditions and management (content of NO3- and NH4+, soil water content, presence of degradable organic material…), the role of topography is less known although it can play an important role on N2O emissions (Izaurralde et al., 2004). Due to the scarcity of data on N2O direct vs. indirect emission rate from agriculture in the Seine Basin (Garnier et al., 2009), one of the objectives of the study conducted here was to determine the N2O emission rates of the various land use representative for the Seine Basin, in order to better assess the direct N2O emissions, and to explore controlling factor such as meteorology, topography, soil properties and crop successions. The main objective of this study was at the same time to characterize N2O fluxes variability along a transect from an agricultural plateau to a river and to analyze the influence of landscape position on these emissions. We conducted this study in the Orgeval catchment (Seine basin, France; between 48°47' and 48°55' N, and 03°00' and 03°55' E) from May 2008 to August 2009 on two agricultural fields cropped with wheat, barley, oats, corn. N2O fluxes were monitored from weekly to bimonthly using static manual chambers placed along the chosen transect in five different landscape positions from the plateau to the River. This study has shown that soil moisture (expressed as Water Filled Pore Space) and NO3- soil concentrations explained most of the N2O flux variability during the sampling period. Most of N2O was emitted directly after N fertilization application during a relatively
5. Measurements of the effectiveness of conservation agriculture at the field scale using radioisotopic techniques and runoff plots
Science.gov (United States)
Mabit, L.; Klik, A.; Toloza, A.; Benmansour, M.; Geisler, A.; Gerstmann, U. C.
2009-04-01
Growing evidence of the cost of soil erosion on agricultural land and off site impact of associated processes has emphasized the needs for quantitative assessment of erosion rates to develop and assess erosion control technology and to allocate conservation resources and development of conservation regulation, policies and programmes. Our main study goal was to assess the magnitude of deposition rates using Fallout Radionuclides ‘FRNs' (137-Cs and 210-Pb) and the mid-term (13 years) erosion rates using conventional runoff plot measurements in a small agricultural watershed under conventional and conservation tillage practices. The tillage treatments were conventional tillage system (CT), mechanical plough to 30 cm depth (the most common tillage system within the watershed); conservation tillage (CS) with cover crops during winter; and direct seeding (DS) no tillage with cover crops during winter. The experimental design - located in Mistelbach watershed 60 km north of Vienna/Austria - consists of one 3-metre-wide and 15-metre-long runoff plot (silt loam - slope of 14%) for each tillage system (CT, CS and DS) with the plots placed in the upper part of an agricultural field. 76 soil samples were collected to evaluate the initial fallout of 137-Cs and 210-Pb in a small forested area close to the experimental field, along a systematic multi-grid design,. In the sedimentation area of the watershed and down slope the agricultural field, 2 additional soil profiles were collected to 1 m depth. All soil samples were air dried, sieved to 2mm and analysed for their 137-Cs and 210-Pb contents using gamma detector. The main results and conclusion can be summarised as following: i) The initial 137-Cs fallout as measured in the 76 forested soil samples ranged from 1123 to 3354 Bq/m2 for an average of 1954 Bq/m2 with a coefficient of variation of 20.4 %. ii) Long-term erosion measurements (1994-2006) from runoff plots located in the upper part of the agricultural field just up
6. Soil-to-crop transfer factors of radium in Japanese agricultural fields
International Nuclear Information System (INIS)
Uchida, S.; Tagami, K.
2007-01-01
The concentrations of 226 Ra in upland field crops (e.g., cabbage, leek, onion, potato, and so on) and associated soils collected from 45 locations throughout Japan were determined in order to obtain soil-to-crop transfer factors (TFs). Concentrations of 226 Ra in the soils collected in southwestern Japan were higher than those in northeastern Japan; however, no correlations between 226 Ra concentrations in crops and soils were observed. The TFs ranged from -3 to 5.8 x 10 -2 with a geometric mean of 6.4 x 10 -3 . These data were within the 95% confidential range of TF-Ra for several crops as reported in the IAEA Technical Reports Series No.364. Among the alkaline earth metals. TF-Ba was similar to TF-Ra. (author)
7. Mapping Soil Physical Structure of Loamy Agricultural Fields for Assessing Localised Potential Leaching Risks
DEFF Research Database (Denmark)
Nørgaard, Trine; Vendelboe, Anders Lindblad; Olsen, Preben
in Silstrup was evaluated based on soil texture, structural parameters, tritium breakthrough curves, and colloid- and phosphorus leaching to investigate the link between the leaching of pesticides such as TFMP and soil structure. Bulk soil was sampled from the A-horizon in a 15 x 15 m grid across the field......, and according to soil texture analyses the clay content was ranging from 14.2 to 18.9%, whereas the organic carbon (OC) content was ranging between 1.7 and 2.2%. Clay content increased to the North and OC content to the South. It was found that there is a risk for pronounced leaching to take place from......During the last decades detection of pesticides and their metabolites in groundwater has increased, forcing several drinking water wells to shut down. The Danish Pesticide Leaching Assessment Programme (PLAP), initiated in 1998, evaluates the leaching risk of pesticides and their metabolites...
8. Assessment of soil erosion and deposition rates in a Moroccan agricultural field using fallout 137Cs and 210Pbex
International Nuclear Information System (INIS)
Benmansour, M.; Mabit, L.; Nouira, A.; Moussadek, R.; Bouksirate, H.; Duchemin, M.; Benkdad, A.
2013-01-01
In Morocco land degradation – mainly caused by soil erosion – is one of the most serious agroenvironmental threats encountered. However, only limited data are available on the actual magnitude of soil erosion. The study site investigated was an agricultural field located in Marchouch (6°42′ W, 33° 47′ N) at 68 km south east from Rabat. This work demonstrates the potential of the combined use of 137 Cs, 210 Pb ex as radioisotopic soil tracers to estimate mid and long term erosion and deposition rates under Mediterranean agricultural areas. The net soil erosion rates obtained were comparable, 14.3 t ha −1 yr −1 and 12.1 ha −1 yr −1 for 137 Cs and 210 Pb ex respectively, resulting in a similar sediment delivery ratio of about 92%. Soil redistribution patterns of the study field were established using a simple spatialisation approach. The resulting maps generated by the use of both radionuclides were similar, indicating that the soil erosion processes has not changed significantly over the last 100 years. Over the previous 10 year period, the additional results provided by the test of the prediction model RUSLE 2 provided results of the same order of magnitude. Based on the 137 Cs dataset established, the contribution of the tillage erosion impact has been evaluated with the Mass Balance Model 3 and compared to the result obtained with the Mass Balance Model 2. The findings highlighted that water erosion is the leading process in this Moroccan cultivated field, tillage erosion under the experimental condition being the main translocation process within the site without a significant and major impact on the net erosion. - Highlights: ► Net erosion rates estimated by 137 Cs and 210 Pb ex techniques were found comparable. ► The water erosion is the leading process in this Moroccan cultivated field. ► Soil erosion process has not changed significantly over the last 100 years. ► The prediction model RUSLE 2 provided results of the same order of
9. Comparative metagenomic analysis of the microbial communities in the surroundings of Iheya north and Iheya ridge hydrothermal fields reveals insights into the survival strategy of microorganisms in deep-sea environments
Science.gov (United States)
Wang, Hai-liang; Sun, Li
2018-04-01
In this study, metagenomic analysis was performed to investigate the taxonomic compositions and metabolic profiles of the microbial communities inhabiting the sediments in the surroundings of Iheya North and Iheya Ridge hydrothermal fields. The microbial communities in four different samples were found to be dominated by bacteria and, to a much lesser extent, archaea belonging to the phyla Proteobacteria, Actinobacteria, Planctomycetes, Firmicutes, Deinococcus-Thermus, and Nitrospirae, which play important roles in the cycling of carbon, nitrogen, and sulfur. All four microbial communities (i) contained chemoautotrophs and heterotrophs, the former probably fixed CO2 via various carbon fixation pathways, and the latter may degrade organic matters using nitrate and sulfate as electron acceptors, (ii) exhibited an abundance of DNA repair genes and bacterial sulfur oxidation mediated by reverse sulfate reduction, and (iii) harbored bacteria and archaea involved in anaerobic methane oxidation via intra-aerobic denitrification and reverse methanogenesis, which were found for the first time in hydrothermal areas. Furthermore, genes involved in DNA repair, reductive acetyl-CoA pathway, and ammonia metabolism were possibly affected by distance to the vent fields. These findings facilitate our understanding of the strategies of the microbial communities to adapt to the environments in deep sea areas associated with hydrothermal vents.
10. Using possibilities of some agricultural wastes in open-field banana cultivation
Directory of Open Access Journals (Sweden)
Mehmet ÖTEN
2016-06-01
Full Text Available Usage of farmyard manure is the one of the major factors to increase production cost in banana cultivation. Besides increasing the production costs, other disadvantages of farmyard manure are playing active role on carrying diseases and pests and also difficulty in obtaining. Due to the stated disadvantages, the use farmyard manure of banana farmers is decreasing. Therefore, we need alternative ways to increase the organic matter capacity of the soil. The effects of alternative applications to farmyard manure, namely banana waste and mushroom compost were investigated. The objective of the study was to evaluate effects of these applications on some morphological properties (plant height, plant circumference and number of leaves, yield (number of hands, number of fingers, bunch weight, finger weight and length and quality properties (flesh/skin ratio, total soluble solids matter, sugars etc. under open-field banana cultivation. The experiment was conducted in Kargıcak location of Alanya in randomized complete block design (RCBD with 3 replications. Experimental results revealed that using of farmyard manure and waste treatments positively affected the yield parameters like the number of hands and fingers, finger length, finger weight and bunch weight. On the other hand, treatments did not have a statistically significant effect on fruit quality parameters like soluble solids content, titratable acidity, pH and ash.
11. Celtic field agriculture and Early Anthropogenic Environmental change in soil records of the Meuse-Demer-Scheldt region, NW Europe.
Science.gov (United States)
Van der Sanden, Germaine; Kluiving, Sjoerd; Roymans, Nico
2017-04-01
Archaeological research is fundamental in the process of obtaining a greater understanding on the intricate dynamics between the human species and the 'natural' environment. Deep historical processes can evaluate the complex interactions that eventually led to the human species as the dominating agent, in terms of the Earth's biotic and abiotic processes. Regional landscape studies can determine whether the human species can be evaluated as a formative element in soil formation processes during the Holocene. This study is directed to examine early anthropogenic land cover change (ALCC) in the Meuse-Demer-Scheldt region, in the southern Netherlands and northern Belgium, between the Late Bronze Age and Early Roman Period (1050-200 AD). The introduction of an extensive agricultural system, the Celtic field system, in co-relation with demographic rise, led to increased anthropogenic pressure on the MDS landscape. Throughout the Holocene, demographic rise pressured farmers to develop increasingly efficient and innovative methods of extracting more yields per unit area farmed resulting in a decrease in land use per capita over time (Kaplan et al. 2010; Boserup, 1965,1981)). The land use per capita under Celtic field technology was relatively high compared to contemporary numbers, based on the assumption that land use per capita did not remain constant. The MDS region is a clear example of early Holocene ALCC and modification of terrestrial ecosystems due to excessive clearance of vegetation. Early Holocene ALCC resulted in ecological deficiencies in the landscape, e.g. deforestation, acceleration of podzolisation and a decrease in terrestrial carbon storage as well as water retention capacity. ALCC can impact climate through biogeophysical and biogeochemical feedbacks to the atmosphere, and result in regional negative radiative forcing. Here we hypothesize that the previously presumed fundamental restructuring that led to a structural bipartition in the landscape due to
12. Field-based evidence for consistent responses of bacterial communities to copper contamination in two contrasting agricultural soils
Directory of Open Access Journals (Sweden)
Jing eLi
2015-02-01
Full Text Available Copper contamination on China’s arable land could pose severe economic, ecological and healthy consequences in the coming decades. As the drivers in maintaining ecosystem functioning, the responses of soil microorganisms to long-term copper contamination in different soil ecosystems are still debated. This study investigated the impacts of copper gradients on soil bacterial communities in two agricultural fields with contrasting soil properties. Our results revealed consistent reduction in soil microbial biomass carbon (SMBC with increasing copper levels in both soils, coupled by significant declines in bacterial abundance in most cases. Despite of contrasting bacterial community structures between the two soils, the bacterial diversity in the copper-contaminated soils showed considerably decreasing patterns when copper levels elevated. High-throughput sequencing revealed copper selection for major bacterial guilds, in particular, Actinobacteria showed tolerance, while Acidobacteria and Chloroflexi were highly sensitive to copper. The thresholds that bacterial communities changed sharply were 800 and 200 added copper mg kg-1 in the fluvo-aquic soil and red soil, respectively, which were similar to the toxicity thresholds (EC50 values characterized by SMBC. Structural equation model (SEM analysis ascertained that the shifts of bacterial community composition and diversity were closely related with the changes of SMBC in both soils. Our results provide field-based evidence that copper contamination exhibits consistently negative impacts on soil bacterial communities, and the shifts of bacterial communities could have largely determined the variations of the microbial biomass.
13. DeepAnomaly: Combining Background Subtraction and Deep Learning for Detecting Obstacles and Anomalies in an Agricultural Field
Directory of Open Access Journals (Sweden)
Peter Christiansen
2016-11-01
Full Text Available Convolutional neural network (CNN-based systems are increasingly used in autonomous vehicles for detecting obstacles. CNN-based object detection and per-pixel classification (semantic segmentation algorithms are trained for detecting and classifying a predefined set of object types. These algorithms have difficulties in detecting distant and heavily occluded objects and are, by definition, not capable of detecting unknown object types or unusual scenarios. The visual characteristics of an agriculture field is homogeneous, and obstacles, like people, animals and other obstacles, occur rarely and are of distinct appearance compared to the field. This paper introduces DeepAnomaly, an algorithm combining deep learning and anomaly detection to exploit the homogenous characteristics of a field to perform anomaly detection. We demonstrate DeepAnomaly as a fast state-of-the-art detector for obstacles that are distant, heavily occluded and unknown. DeepAnomaly is compared to state-of-the-art obstacle detectors including “Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks” (RCNN. In a human detector test case, we demonstrate that DeepAnomaly detects humans at longer ranges (45–90 m than RCNN. RCNN has a similar performance at a short range (0–30 m. However, DeepAnomaly has much fewer model parameters and (182 ms/25 ms = a 7.28-times faster processing time per image. Unlike most CNN-based methods, the high accuracy, the low computation time and the low memory footprint make it suitable for a real-time system running on a embedded GPU (Graphics Processing Unit.
14. Demonstration and validation of automated agricultural field extraction from multi-temporal Landsat data for the majority of United States harvested cropland
Science.gov (United States)
Yan, L.; Roy, D. P.
2014-12-01
The spatial distribution of agricultural fields is a fundamental description of rural landscapes and the location and extent of fields is important to establish the area of land utilized for agricultural yield prediction, resource allocation, and for economic planning, and may be indicative of the degree of agricultural capital investment, mechanization, and labor intensity. To date, field objects have not been extracted from satellite data over large areas because of computational constraints, the complexity of the extraction task, and because consistently processed appropriate resolution data have not been available or affordable. A recently published automated methodology to extract agricultural crop fields from weekly 30 m Web Enabled Landsat data (WELD) time series was refined and applied to 14 states that cover 70% of harvested U.S. cropland (USDA 2012 Census). The methodology was applied to 2010 combined weekly Landsat 5 and 7 WELD data. The field extraction and quantitative validation results are presented for the following 14 states: Iowa, North Dakota, Illinois, Kansas, Minnesota, Nebraska, Texas, South Dakota, Missouri, Indiana, Ohio, Wisconsin, Oklahoma and Michigan (sorted by area of harvested cropland). These states include the top 11 U.S states by harvested cropland area. Implications and recommendations for systematic application to global coverage Landsat data are discussed.
15. Transfer of 137Cs, essential and trace elements from soil to potato plants in an agricultural field
International Nuclear Information System (INIS)
2000-01-01
The concentrations of 137 Cs, essential and trace elements were measured in soils and potato tubers collected from 26 agricultural fields in Aomori, Japan, and soil-to-potato transfer factors were determined. The elements were divided into two groups. The first group (Cl, K, Ca, etc.) showed an inverse correlation between the transfer factors and the concentrations of the elements in the soils, while for the second group (Sc, Co, etc.) the transfer factors were independent of the soil concentrations of the elements. The transfer factors of 137 Cs (0.0037-0.16), derived from global fallout, were well correlated with those of naturally stable Cs (0.00052-0.080). These transfer factors showed a negative correlation with the soil concentrations of K and Cs, but they were independent of the organic material contents in the soils. These results suggest that the transfer of stable Cs could serve as a natural analog to predict the behavior of radiocesium in the soil-plant pathway. The distributions of these elements were determined for the entire potato plant. The concentrations of the elements were lower in the tubers than in leaves, petioles and stems. During the harvesting of potatoes the elements in the non-edible portions of the potato plants are returned to the soil, where they may again be utilized in the soil-potato pathways. Therefore, the distributions of elements in plant components can provide useful information for understanding the transfer of radionuclides and elements from the soil to plants in agricultural fields. The concentration ratios for Sr/Ca in potato plant components showed relatively constant values while those for Cs/K varied. These findings suggest that the translocation rates of both Ca and Sr were similar within a potato plant, whereas those of K and Cs were different. Consequently, the transfers of both Ca and Sr may predict the behavior of radiostrontium. The transfer of Cs could be used to predict the behavior of radiocesium, whereas the
16. Study on the quantitative relationship between Agricultural water and fertilization process and non-point source pollution based on field experiments
Science.gov (United States)
Wang, H.; Chen, K.; Wu, Z.; Guan, X.
2017-12-01
17. Enhancement of Afterimage Colors by Surrounding Contours
Directory of Open Access Journals (Sweden)
Takao Sato
2011-05-01
Full Text Available Presenting luminance contours surrounding the adapted areas in test phase enhances color afterimages in both duration and color appearance. The presence of surrounding contour is crucial to some color phenomenon such as van Lier's afterimage, but the contour-effect itself has not been seriously examined. In this paper, we compared the contour-effect to color afterimages and to actually colored patches to examine the nature of color information subserving color-aftereffect. In the experiment, observers were adapted for 1 sec to a small colored square (red, green, yellow, or blue presented on a gray background. Then, a test field either with or without surrounding contour was presented. Observers matched the color of a test-patch located near the afterimage to the color of afterimage. It was found that the saturation of negative afterimage was almost doubled by the presence of surrounding contours. There was no effect of luminance contrast or polarity of contours. In contrast, no enhancement of saturation by surrounding contours was observed for actually colored patches even though the colors of patches were equalized to that of afterimage without contours. This dissociation in the contour-effect demonstrates the crucial difference between the color information for aftereffects and for ordinary bottom-up color perception.
18. A ' SELECTED AGRICULTURAL FIELDS
African Journals Online (AJOL)
collected from four in'igation sites were used in the evaluation. The soils particle .... comparing the model simulated outputs with measured/observed state variables the model ... The soils of the study area are classified as alfisols based on the USDA (1975). classification. .... under predict measured values. “A positive value ...
19. Agricultural methanization
International Nuclear Information System (INIS)
2011-01-01
After having briefly outlined the interest of the development of methanization of agricultural by-products in the context of struggle against climate change, and noticed that France is only now developing this sector as some other countries already did, this publication describes the methanization process also called anaerobic digestion, which produces a digestate and biogas. Advantages for the agriculture sector are outlined, as well as drawbacks and recommendations (required specific technical abilities, an attention to the use of energetic crops, an improved economic balance which still depends on public subsidies, competition in the field of waste processing). Actions undertaken by the ADEME are briefly evoked
20. Pesticidal activity of Rivina humilis L. (Phytolaccaceae against important agricultural polyphagous field pest, Spodoptera litura (Fab. (Lepidoptera: Noctuidae
Directory of Open Access Journals (Sweden)
Elumalai Arumugam
2015-05-01
Full Text Available Objective: To evaluate the pesticidal activity of antifeedant, oviposition deterrent, ovicidal and larvicidal activities of benzene, dichloromethane, diethylether, ethylacetate and methanol extracts of Rivina humilis at different concentrations against agricultural polyphagous pest Spodoptera litura (Lepidoptera: Noctuidae (S. litura. Methods: Antifeedant activities of the selected plant extract were studied as described by Isman et al. (1990, with slight modifications. For oviposition deterrent activity, ten pairs of (adult moths S. litura were subjected in five replicates. After 48 h, the numbers of eggs masses laid on treated and control leaves were recorded and the percentage of oviposition deterrence was calculated. The ovicidal activity was determined against the eggs of S. litura. Twenty five early fourth instar larvae of S. litura were exposed to various concentrations and was assayed by using the protocol of Abbott’s formula (1925; the 24 h LC50 values of the Rivina humilis leaf extract was determined by probit analysis. Results: All the extracts showed moderate antifeedant activitiy; however, significant antifeedant, ovicidal, oviposition deterrent and larvicidal activities were observed in methanol extract. Conclusions: This study showed that the selected plant can be a potent source of natural antifeedant, oviposition deterrent, ovicidal and larvicidal activities against field pest S. litura.
1. Shifts in soil fungal communities in Tuber melanosporum plantations over a 20-year transition from agriculture fields to oak woodlands
Energy Technology Data Exchange (ETDEWEB)
Bing, L.; Fischer, C.R.; Bonet, J.A.; Castaño, C.; Colinas, C.
2016-07-01
Aim of study: To explore the diversity of soil fungi found in black truffle (Tuber melanosporum) plantations following the introduction of the mycorrhizal-colonized host tree, (Quercus ilex), through the development of the brûlé and production of mature sporocarps. Area of study: This research was carried out province of Teruel, Aragon (central eastern Spain). Material and Methods: Soil samples from 6 plantations were collected beneath Q. ilex trees inoculated with T. melanosporum, of 3, 5, 7, 10, 14 and 20 years after out planting in truffle plantations. Soil DNA was extracted, PCR-amplified and sequenced to compare soil fungi present at different ages. Main results: As tree age increased, we observed an increased frequency of T. melanosporum (from 8% to 71% of sequenced colonies) and concomitant decrease in the combined frequency of Fusarium spp. and Phoma spp. (from 64% to 3%). Research highlights: There are important shifts in species richness and in functional groups in the soil fungal communities in maturing black truffle-oak woodland plantations. The observed inverse relationship between the frequency of soil endophytic and/or pathogenic fungi and that of the mycorrhizal mutualist T. melanosporum provides support to continue a deeper analysis of shifts in fungal communities and functional groups where there is a transition from agriculture fields to woodlands. (Author)
2. A Combined Approach of Sensor Data Fusion and Multivariate Geostatistics for Delineation of Homogeneous Zones in an Agricultural Field
Directory of Open Access Journals (Sweden)
Annamaria Castrignanò
2017-12-01
Full Text Available To assess spatial variability at the very fine scale required by Precision Agriculture, different proximal and remote sensors have been used. They provide large amounts and different types of data which need to be combined. An integrated approach, using multivariate geostatistical data-fusion techniques and multi-source geophysical sensor data to determine simple summary scale-dependent indices, is described here. These indices can be used to delineate management zones to be submitted to differential management. Such a data fusion approach with geophysical sensors was applied in a soil of an agronomic field cropped with tomato. The synthetic regionalized factors determined, contributed to split the 3D edaphic environment into two main horizontal structures with different hydraulic properties and to disclose two main horizons in the 0–1.0-m depth with a discontinuity probably occurring between 0.40 m and 0.70 m. Comparing this partition with the soil properties measured with a shallow sampling, it was possible to verify the coherence in the topsoil between the dielectric properties and other properties more directly related to agronomic management. These results confirm the advantages of using proximal sensing as a preliminary step in the application of site-specific management. Combining disparate spatial data (data fusion is not at all a naive problem and novel and powerful methods need to be developed.
3. Impact of Brick Kilns’ Emission on Soil Quality of Agriculture Fields in the Vicinity of Selected Bhaktapur Area of Nepal
Directory of Open Access Journals (Sweden)
Gunjan Bisht
2015-01-01
Full Text Available The study was conducted to evaluate soil quality and impact of brick kiln on different physicochemical parameters of soils of agricultural field, located in the vicinity of Bhaktapur, Nepal. The study was carried out by determining the physicochemical characteristics of soil, soil fertility, and heavy metal contamination of soil. During the entire study period, water absorptivity of soil ranged from 2.4 to 3.3 mg/L, pH varies from 5.885 to 7.64, and organic carbon content and organic matter varied from 0.277 to 0.93%, from 0.477% to 1.603%, respectively. Nutrient content, that is, sulfate and nitrate concentration, in the soil ranged from 0.829 to 3.764 mol/L and from 0.984 to 29.99 mol/L, respectively. The findings revealed that concentrations of heavy metals (chromium and lead were within permissible limit, although the levels were higher in soil at 50 m and decrease farther from brick kiln. However, the physical parameters and nutrient content were deficient in soil at 50 m while increasing gradually at distances of 100 m and 150 m. The variation of result obtained for physical parameters supports the fact that quality of soil in terms of heavy metal content and nutrient content was directly proportional to the distance from the kiln; that is, the quality of soil increased with increasing distance.
4. Impact of dicyandiamide on emissions of nitrous oxide, nitric oxide and ammonia from agricultural field in the North China Plain.
Science.gov (United States)
Zhou, Yizhen; Zhang, Yuanyuan; Tian, Di; Mu, Yujing
2016-02-01
Nitrous oxide (N2O), nitric oxide (NO) and ammonia (NH3) emissions from an agricultural field in the North China Plain were compared for three treatments during a whole maize growing period from 26 June to 11 October, 2012. Compared with the control treatment (without fertilization, designated as CK), remarkable pulse emissions of N2O, NO and NH3 were observed from the normal fertilization treatment (designated as NP) just after fertilization, whereas only N2O and NH3 pulse emissions were evident from the nitrification inhibitor treatment (designated as ND). The reduction proportions of N2O and NO emissions from the ND treatment compared to those from the NP treatment during the whole maize growing period were 31% and 100%, respectively. A measurable increase of NH3 emission from the ND treatment was found with a cumulative NH3 emission of 3.8 ± 1.2 kg N/ha, which was 1.4 times greater than that from the NP treatment (2.7 ± 0.7 kg N/ha). Copyright © 2015. Published by Elsevier B.V.
5. Identification, measurement, and assessment of water cycle of unhusked rice agricultural phases: Case study at Tangerang paddy field, Indonesia
Science.gov (United States)
Hartono, N.; Laurence; Johannes, H. P.
2017-11-01
According to one of UN reports, water scarcity has happened all around the world, including Indonesia. Irrigation sector takes up 70% of world water consumption and potentially increases 20% due to the population explosion. Rice is accounted for 69% of agricultural products contributions in Indonesia’s water footprint. Therefore, evaluation of water cycle was essential to raise awareness among practitioners. Data collections were conducted in the functional unit of one-hectare rice field located in Tangerang. This study used CropWat 8.0 and SimaPro software. Identification involved data such as climate, crop, and soil. Nursery became the highest water consumed phase, requiring 419 mm in height. Measurement through water footprint resulted in consumption of green water footprint for 8,183,618.5 liters (62.9%), followed by grey for 4,805,733.2 liters (36.9%) and blue for 23,902.36 liters (0.2%). The grey consumption was exceeding the average, which indicated high doses of pesticides. Life Cycle Assessment showed negative impacts of fertilizers that caused damages like fossil depletion, respiratory health, and eutrophication.
6. Shifts in soil fungal communities in Tuber melanosporum plantations over a 20-year transition from agriculture fields to oak woodlands
Directory of Open Access Journals (Sweden)
Liu Bing
2016-04-01
Full Text Available Aim of study: To explore the diversity of soil fungi found in black truffle (Tuber melanosporum plantations following the introduction of the mycorrhizal-colonized host tree, (Quercus ilex, through the development of the brûlé and production of mature sporocarps.Area of study: This research was carried out province of Teruel, Aragon (central eastern Spain.Material and Methods: Soil samples from 6 plantations were collected beneath Q. ilex trees inoculated with T. melanosporum, of 3, 5, 7, 10, 14 and 20 years after out planting in truffle plantations. Soil DNA was extracted, PCR-amplified and sequenced to compare soil fungi present at different ages.Main results: As tree age increased, we observed an increased frequency of T. melanosporum (from 8% to 71% of sequenced colonies and concomitant decrease in the combined frequency of Fusarium spp. and Phoma spp. (from 64% to 3%.Research highlights: There are important shifts in species richness and in functional groups in the soil fungal communities in maturing black truffle-oak woodland plantations. The observed inverse relationship between the frequency of soil endophytic and/or pathogenic fungi and that of the mycorrhizal mutualist T. melanosporum provides support to continue a deeper analysis of shifts in fungal communities and functional groups where there is a transition from agriculture fields to woodlands.Abbreviations used: Ectomycorrhiza (ECM fungus; Vesicular arbuscular mycorrhiza (VAM; Operational taxonomic unit (OTU.
7. A Combined Approach of Sensor Data Fusion and Multivariate Geostatistics for Delineation of Homogeneous Zones in an Agricultural Field.
Science.gov (United States)
Castrignanò, Annamaria; Buttafuoco, Gabriele; Quarto, Ruggiero; Vitti, Carolina; Langella, Giuliano; Terribile, Fabio; Venezia, Accursio
2017-12-03
To assess spatial variability at the very fine scale required by Precision Agriculture, different proximal and remote sensors have been used. They provide large amounts and different types of data which need to be combined. An integrated approach, using multivariate geostatistical data-fusion techniques and multi-source geophysical sensor data to determine simple summary scale-dependent indices, is described here. These indices can be used to delineate management zones to be submitted to differential management. Such a data fusion approach with geophysical sensors was applied in a soil of an agronomic field cropped with tomato. The synthetic regionalized factors determined, contributed to split the 3D edaphic environment into two main horizontal structures with different hydraulic properties and to disclose two main horizons in the 0-1.0-m depth with a discontinuity probably occurring between 0.40 m and 0.70 m. Comparing this partition with the soil properties measured with a shallow sampling, it was possible to verify the coherence in the topsoil between the dielectric properties and other properties more directly related to agronomic management. These results confirm the advantages of using proximal sensing as a preliminary step in the application of site-specific management. Combining disparate spatial data (data fusion) is not at all a naive problem and novel and powerful methods need to be developed.
8. Root-collar diameter and third-year survival of three bottomland hardwoods planted on former agricultural fields in the Lower Mississippi Alluvial Valley
Science.gov (United States)
Emile S. Gardiner; Douglass F. Jacobs; Ronald P. Overton; George Hernandez
2009-01-01
Athough the Lower Mississippi Alluvial Valley (LMAV) has experienced substantial afforestation of former agricultural fields during the past 2 decades, seedling standards that support satisfactory outplanting performance of bottomland hardwood tree species are not available. A series of experimental plantations, established on three afforestation sites in the LMAV,...
9. Third cycle university studies in Europe in the field of agricultural engineering and in the emerging discipline of biosystems engineering.
Science.gov (United States)
Ayuga, F; Briassoulis, D; Aguado, P; Farkas, I; Griepentrog, H; Lorencowicz, E
2010-01-01
The main objectives of European Thematic Network entitled 'Education and Research in Agricultural for Biosystems Engineering in Europe (ERABEE-TN)' is to initiate and contribute to the structural development and the assurance of the quality assessment of the emerging discipline of Biosystems Engineering in Europe. ERABEE is co-financed by the European Community in the framework of the LLP Programme. The partnership consists of 35 participants from 27 Erasmus countries, out of which 33 are Higher Education Area Institutions (EDU) and 2 are Student Associations (ASS). 13 Erasmus participants (e.g. Thematic Networks, Professional Associations, and Institutions from Brazil, Croatia, Russia and Serbia) are also involved in the Thematic Network through synergies. To date, very few Biosystems Engineering programs exist in Europe and those that are initiated are at a very primitive stage of development. The innovative and novel goal of the Thematic Network is to promote this critical transition, which requires major restructuring in Europe, exploiting along this direction the outcomes accomplished by its predecessor; the USAEE-TN (University Studies in Agricultural Engineering in Europe). It also aims at enhancing the compatibility among the new programmes of Biosystems Engineering, aiding their recognition and accreditation at European and International level and facilitating greater mobility of skilled personnel, researchers and students. One of the technical objectives of ERABEE is dealing with mapping and promoting the third cycle studies (including European PhDs) and supporting the integration of research at the 1st and 2nd cycle regarding European Biosystems Engineering university studies. During the winter 2008 - spring 2009 period, members of ERABEE conducted a survey on the contemporary status of doctoral studies in Europe, and on a possible scheme for promotion of cooperation and synergies in the framework of the third cycle of studies and the European Doctorate
10. Future trends in agricultural engineering.
NARCIS (Netherlands)
Jongebreur, A.A.; Speelman, L.
1997-01-01
Beside traditional mechanical engineering, other engineering branches such as electronics, control engineering and physics play their specific role within the agricultural engineering field. Agricultural engineering has affected and stimulated major changes in agriculture. In the last decades
11. Polyoxyethylene Tallow Amine, a Glyphosate Formulation Adjuvant: Soil Adsorption Characteristics, Degradation Profile, and Occurrence on Selected Soils from Agricultural Fields in Iowa, Illinois, Indiana, Kansas, Mississippi, and Missouri.
Science.gov (United States)
Tush, Daniel; Meyer, Michael T
2016-06-07
Polyoxyethylene tallow amine (POEA) is an inert ingredient added to formulations of glyphosate, the most widely applied agricultural herbicide. POEA has been shown to have toxic effects to some aquatic organisms making the potential transport of POEA from the application site into the environment an important concern. This study characterized the adsorption of POEA to soils and assessed its occurrence and homologue distribution in agricultural soils from six states. Adsorption experiments of POEA to selected soils showed that POEA adsorbed much stronger than glyphosate; calcium chloride increased the binding of POEA; and the binding of POEA was stronger in low pH conditions. POEA was detected on a soil sample from an agricultural field near Lawrence, Kansas, but with a loss of homologues that contain alkenes. POEA was also detected on soil samples collected between February and early March from corn and soybean fields from ten different sites in five other states (Iowa, Illinois, Indiana, Missouri, Mississippi). This is the first study to characterize the adsorption of POEA to soil, the potential widespread occurrence of POEA on agricultural soils, and the persistence of the POEA homologues on agricultural soils into the following growing season.
12. Using a Mobile Device “App” and Proximal Remote Sensing Technologies to Assess Soil Cover Fractions on Agricultural Fields
Directory of Open Access Journals (Sweden)
Ahmed Laamrani
2018-02-01
Full Text Available Quantifying the amount of crop residue left in the field after harvest is a key issue for sustainability. Conventional assessment approaches (e.g., line-transect are labor intensive, time-consuming and costly. Many proximal remote sensing devices and systems have been developed for agricultural applications such as cover crop and residue mapping. For instance, current mobile devices (smartphones & tablets are usually equipped with digital cameras and global positioning systems and use applications (apps for in-field data collection and analysis. In this study, we assess the feasibility and strength of a mobile device app developed to estimate crop residue cover. The performance of this novel technique (from here on referred to as “app” method was compared against two point counting approaches: an established digital photograph-grid method and a new automated residue counting script developed in MATLAB at the University of Guelph. Both photograph-grid and script methods were used to count residue under 100 grid points. Residue percent cover was estimated using the app, script and photograph-grid methods on 54 vertical digital photographs (images of the ground taken from above at a height of 1.5 m collected from eighteen fields (9 corn and 9 soybean, 3 samples each located in southern Ontario. Results showed that residue estimates from the app method were in good agreement with those obtained from both photograph–grid and script methods (R2 = 0.86 and 0.84, respectively. This study has found that the app underestimates the residue coverage by −6.3% and −10.8% when compared to the photograph-grid and script methods, respectively. With regards to residue type, soybean has a slightly lower bias than corn (i.e., −5.3% vs. −7.4%. For photos with residue <30%, the app derived residue measurements are within ±5% difference (bias of both photograph-grid- and script-derived residue measurements. These methods could therefore be used to track
13. Using a Mobile Device "App" and Proximal Remote Sensing Technologies to Assess Soil Cover Fractions on Agricultural Fields.
Science.gov (United States)
Laamrani, Ahmed; Pardo Lara, Renato; Berg, Aaron A; Branson, Dave; Joosse, Pamela
2018-02-27
Quantifying the amount of crop residue left in the field after harvest is a key issue for sustainability. Conventional assessment approaches (e.g., line-transect) are labor intensive, time-consuming and costly. Many proximal remote sensing devices and systems have been developed for agricultural applications such as cover crop and residue mapping. For instance, current mobile devices (smartphones & tablets) are usually equipped with digital cameras and global positioning systems and use applications (apps) for in-field data collection and analysis. In this study, we assess the feasibility and strength of a mobile device app developed to estimate crop residue cover. The performance of this novel technique (from here on referred to as "app" method) was compared against two point counting approaches: an established digital photograph-grid method and a new automated residue counting script developed in MATLAB at the University of Guelph. Both photograph-grid and script methods were used to count residue under 100 grid points. Residue percent cover was estimated using the app, script and photograph-grid methods on 54 vertical digital photographs (images of the ground taken from above at a height of 1.5 m) collected from eighteen fields (9 corn and 9 soybean, 3 samples each) located in southern Ontario. Results showed that residue estimates from the app method were in good agreement with those obtained from both photograph-grid and script methods (R² = 0.86 and 0.84, respectively). This study has found that the app underestimates the residue coverage by -6.3% and -10.8% when compared to the photograph-grid and script methods, respectively. With regards to residue type, soybean has a slightly lower bias than corn (i.e., -5.3% vs. -7.4%). For photos with residue <30%, the app derived residue measurements are within ±5% difference (bias) of both photograph-grid- and script-derived residue measurements. These methods could therefore be used to track the recommended minimum
14. Multifunctional landscapes: Site characterization and field-scale design to incorporate biomass production into an agricultural system
International Nuclear Information System (INIS)
Ssegane, Herbert; Negri, M. Cristina; Quinn, John; Urgun-Demirtas, Meltem
2015-01-01
Current and future demand for food, feed, fiber, and energy require novel approaches to land management, which demands that multifunctional landscapes are created to integrate various ecosystem functions into a sustainable land use. We developed an approach to design such landscapes at a field scale to minimize concerns of land use change, water quality, and greenhouse gas emissions associated with production of food and bioenergy. This study leverages concepts of nutrient recovery and phytoremediation to place bioenergy crops on the landscape to recover nutrients released to watersheds by commodity crops. Crop placement is determined by evaluating spatial variability of: 1) soils, 2) surface flow pathways, 3) shallow groundwater flow gradients, 4) subsurface nitrate concentrations, and 5) primary crop yield. A 0.8 ha bioenergy buffer was designed within a 6.5 ha field to intercept concentrated surface flow, capture and use nitrate leachate, and minimize use of productive areas. Denitrification-Decomposition (DNDC) simulations show that on average, a switchgrass (Panicum Virgatum L.) or willow (Salix spp.) buffer within this catchment according to this design could reduce annual leached NO 3 by 61 or 59% and N 2 O emission by 5.5 or 10.8%, respectively, produce 8.7 or 9.7 Mg ha −1 of biomass respectively, and displace 6.7 Mg ha −1 of corn (Zea mays L.) grain. Therefore, placement of bioenergy crops has the potential to increase environmental sustainability when the pairing of location and crop type result in minimal disruption of current food production systems and provides additional environmental benefits. - Highlights: • Design of a multifunctional landscape by integrating cellulosic biofuel production into an existing agricultural system. • The design does not adversely offset current grain production for bioenergy crops. • Maps of concentrated flow paths, subsurface flow direction, NO 3 –N hotspots, and intra-field corn yield variability.
15. Estimation of Soil Erosion by Using Magnetic Method: A Case Study of an Agricultural Field in Southern Moravia (Czech Republic)
Science.gov (United States)
Petrovsky, E.; Grison, H.; Kapicka, A.; Dlouha, S.; Kodesova, R.; Jaksik, O.
2013-05-01
In this study we have applied magnetism of soils for estimation of erosion at an agricultural land. The testing site is situated in loess region in Southern Moravia (in Central Europe). The approach is based on well-established method of differentiation of magnetic parameters of the topsoil and the subsoil horizons as a result of in situ formation of strongly magnetic iron oxides. Our founding is established on a simple tillage homogenization model described by Royall (2001) using magnetic susceptibility and its frequency dependence to estimate soil loss caused by the tillage and subsequent erosion. The original dominant Soil Unit in the investigated area is Haplic Chernozem, which is due to intensive erosion progressively transformed into different Soil Units. The site is characterized by a flat upper part while the middle part, formed by a substantive side valley, is steeper (up to 15°). The side valley represents a major line of concentrated runoff emptying into a colluvial fan. Field measurements of the topsoil volume magnetic susceptibility were carried out by the Bartington MS2D probe. Data are resulting in regular grid of 101 data points, where the bulk soil material was gathered for further laboratory investigations. Moreover, vertical distribution of magnetic susceptibility (deep to 40 cm) was measured on selected transects using the SM400 kappameter. In the laboratory, after drying and sieving of collected soil samples, mass-specific magnetic susceptibility and its frequency-dependent susceptibility was measured. In order to identify magnetic minerals the thermomagnetic analyses were performed using the AGICO KLY-4S Kappabridge with CS-3 furnace. Hysteresis loops were carried out on vibrating magnetometer ADE EV9 to assess the grain-size distribution of ferrimagnetic particles. Hereafter, the isothermal remanent magnetization acqusition followed by D.C. demagnetization were done. All these laboratory magnetic measurements were performed in order to
16. Variation on the magnetic field profiles of transmission lines for various surrounding conditions calculated by the finite element method; Variacion de los perfiles de campo magnetico en lineas de transmision en diversas condiciones del entorno calculadas mediante el metodo de elementos finitos
Energy Technology Data Exchange (ETDEWEB)
Ponta, Fernando; Ferreira, Fabiana
2001-07-01
This paper applies the finite element method for the calculation of line magnetic field transversal profile using own routine calculation. Using a real case, simulations were performed under various conditions gathering distortion elements, obtaining the field profile. By analysing these results conclusions are drawing related to the changes produced by the distortions on the magnetic field configuration and evaluations of the surrounding elements influence are evaluated.
17. Digital soil mapping as a basis for climatically oriented agriculture a thematic on the territory of the national crop testing fields of the Republic of Tatarstan, Russia
Science.gov (United States)
Sahabiev, I. A.; Giniyatullin, K. G.; Ryazanov, S. S.
2018-01-01
The concept of climate-optimized agriculture (COA) of the UN FAO implies the transformation of agriculture techniques in conditions of changing climate. It is important to implement a timely transition to the concept of COA and sustainable development of soil resources, accurate digital maps of spatial distribution of soils and soil properties are needed. Digital mapping of soil humus content was carried out on the territory of the national crop testing fields (NCTF) of the Republic of Tatarstan (Russian Federation) and the accuracy of the maps obtained was estimated.
18. Evaluation of the leucine incorporation technique for detection of pollution-induced community tolerance to copper in a long-term agricultural field trial with urban waste fertilizers
DEFF Research Database (Denmark)
Lekfeldt, Jonas Duus Stevens; Magid, Jakob; Holm, Peter Engelund
2014-01-01
increased bacterial community tolerance to Cu was observed for soils amended with organic waste fertilizers and was positively correlated with total soil Cu. However, metal speciation and whole-cell bacterial biosensor analysis demonstrated that the observed PICT responses could be explained entirely by Cu......Copper (Cu) is known to accumulate in agricultural soils receiving urban waste products as fertilizers. We here report the use of the leucine incorporation technique to determine pollution-induced community tolerance (Leu-PICT) to Cu in a long-term agricultural field trial. A significantly...
19. SOME NORMATIVE AND INSTITUTIONAL DEVELOPMENTS IN THE FIELD OF COMMON AGRICULTURAL POLICY AND THEIR CONSEQUENCES ON THE PROTECTION OF THE EUROPEAN CITIZENS’ INTERESTS
Directory of Open Access Journals (Sweden)
Gabriela Alexandra Oanta
2007-07-01
Full Text Available This paper intends to briefly comment on some changes in the field of Common Agricultural Policy, especially regarding the safety of agricultural products and foodstuff. Within the framework of the CAP the food safety has managed to progressively constitute its third pillar, currently boasting an outstanding place in the attainment of its objectives. CAP has been progressing in its mechanisms and legal instruments towards a more relevant integration of the concerns relative to the consumer’s health protection and to the food safety in the objectives to be reached.
20. Fate of synthetic musks in a domestic wastewater treatment plant and in an agricultural field amended with biosolids
International Nuclear Information System (INIS)
Yang, J.-J.; Metcalfe, Chris D.
2006-01-01
Synthetic musks are widely used as fragrance ingredients in personal care products, and they enter domestic wastewater treatment plants (WWTPs) through discharges into municipal sewage systems. Samples of aqueous sewage and biosolids collected from the Peterborough Wastewater Treatment Plant (WWTP), Ontario, Canada were analyzed for 11 synthetic musk compounds using GC/MS. The results showed that 1,3,4,6,7,8-hexahydro-4,6,6,7,8,8-hexamethyl-cyclopenta[g]-2-benzopyrane (HHCB, 173.1 ± 43.4 ng/L) and 7-acetyl-1,1,3,4,4,6-hexamethyl-tetrahydronaphthalene (AHTN, 41.6 ± 15.8 ng/L) were the dominant fragrances in sewage, but other polycyclic musks and nitro musks were present at lower concentrations. The concentrations of HHCB and AHTN in the aqueous phase of the sewage were highly correlated with both BOD 5 and TOC. The overall removal efficiency of synthetic musks from the aqueous sewage in the WWTP ranged from 43.3% to 56.9%, but removal occurred mainly by partitioning into the biosolids. Based on a mass balance model, the daily input and output of HHCB and AHTN in the Peterborough WWTP were 47 g and 46 g, respectively. In an agricultural field amended with biosolids from the Peterborough WWTP, HHCB and AHTN were detected in soil immediately after application at mean concentrations of 1.0 and 1.3 μg/kg, respectively, but concentrations declined relatively rapidly over the next 6 weeks, post-application
1. Response of ground-nesting farmland birds to agricultural intensification across Europe: Landscape and field level management factors
NARCIS (Netherlands)
Guerrero, I.; Morales, M.B.; Onate, J.J.; Geiger, F.; Berendse, F.; Snoo, de G.R.
2012-01-01
European farmland bird populations have decreased dramatically in recent decades and agricultural intensification has been identified as the main cause contributing to these declines. Identifying which specific intensification pressures are driving those population trends seems vital for bird
2. Enhanced levels of atmospheric low-molecular weight monocarboxylic acids in gas and particulates over Mt. Tai, North China, during field burning of agricultural wastes
Science.gov (United States)
Mochizuki, Tomoki; Kawamura, Kimitaka; Nakamura, Shinnosuke; Kanaya, Yugo; Wang, Zifa
2017-12-01
To understand the source and atmospheric behaviour of low molecular weight monocarboxylic acids (monoacids), gaseous (G) and particulate (P) organic acids were collected at the summit of Mt. Tai in the North China Plain (NCP) during field burning of agricultural waste (wheat straw). Particulate organic acids were collected with neutral quartz filter whereas gaseous organic acids were collected with KOH-impregnated quartz filter. Normal (C1-C10), branched (iC4-iC6), hydroxy (lactic and glycolic), and aromatic (benzoic) monoacids were determined with a capillary gas chromatography employing p-bromophenacyl esters. We found acetic acid as the most abundant gas-phase species whereas formic acid is the dominant particle-phase species. Concentrations of formic (G/P 1 570/1 410 ng m-3) and acetic (3 960/1 120 ng m-3) acids significantly increased during the enhanced field burning of agricultural wastes. Concentrations of formic and acetic acids in daytime were found to increase in both G and P phases with those of K+, a field-burning tracer (r = 0.32-0.64). Primary emission and secondary formation of acetic acid is linked with field burning of agricultural wastes. In addition, we found that particle-phase fractions (Fp = P/(G + P)) of formic (0.50) and acetic (0.31) acids are significantly high, indicating that semi-volatile organic acids largely exist as particles. Field burning of agricultural wastes may play an important role in the formation of particulate monoacids in the NCP. High levels (917 ng m-3) of particle-phase lactic acid, which is characteristic of microorganisms, suggest that microbial activity associated with terrestrial ecosystem significantly contributes to the formation of organic aerosols.
3. Circumstances surrounding aneurysmal subarachnoid hemorrhage
NARCIS (Netherlands)
Schievink, W. I.; Karemaker, J. M.; Hageman, L. M.; van der Werf, D. J.
1989-01-01
The circumstances surrounding aneurysmal subarachnoid hemorrhage were investigated in a group of 500 consecutive patients admitted to a neurosurgical center. Subarachnoid hemorrhage occurred during stressful events in 42.8% of the patients, during nonstrenuous activities in 34.4%, and during rest or
4. Are BVOC exchanges in agricultural ecosystems overestimated? Insights from fluxes measured in a maize field over a whole growing season
Science.gov (United States)
Bachy, Aurélie; Aubinet, Marc; Schoon, Niels; Amelynck, Crist; Bodson, Bernard; Moureaux, Christine; Heinesch, Bernard
2016-04-01
Maize is the most important C4 crop worldwide. It is also the second most important crop worldwide (C3 and C4 mixed), and is a dominant crop in some world regions. Therefore, it can potentially influence local climate and air quality through its exchanges of gases with the atmosphere. Among others, biogenic volatile organic compounds (BVOC) are known to influence the atmospheric composition and thereby modify greenhouse gases lifetime and pollutant formation in the atmosphere. However, so far, only two studies have dealt with BVOC exchanges from maize. Moreover, these studies were conducted on a limited range of meteorological and phenological conditions, so that the knowledge of BVOC exchanges by this crop remains poor. Here, we present the first BVOC measurement campaign performed at ecosystem-scale on a maize field during a whole growing season. It was carried out in the Lonzée Terrestrial Observatory (LTO), an ICOS site. BVOC fluxes were measured by the disjunct by mass-scanning eddy covariance technique with a proton transfer reaction mass spectrometer for BVOC mixing ratios measurements. Outstanding results are (i) BVOC exchanges from soil were as important as BVOC exchanges from maize itself; (ii) BVOC exchanges observed on our site were much lower than exchanges observed by other maize studies, even under normalized temperature and light conditions, (iii) they were also lower than those observed on other crops grown in Europe. Lastly (iv), BVOC exchanges observed on our site under standard environmental conditions, i.e., standard emission factors SEF, were much lower than those currently considered by BVOC exchange up-scaling models. From those observations, we deduced that (i) soil BVOC exchanges should be better understood and should be incorporated in terrestrial BVOC exchanges models, and that (ii) SEF for the C4 crop plant functional type cannot be evaluated at global scale but should be determined for each important agronomic and pedo-climatic region
5. Agricultural Markets Instability
NARCIS (Netherlands)
Garrido, A.; Brümmer, B.; M'Barek, R.; Gielen-Meuwissen, M.P.M.; Morales-Opazo, C.
2016-01-01
Since the financial and food price crises of 2007, market instability has been a topic of major concern to agricultural economists and policy professionals. This volume provides an overview of the key issues surrounding food prices volatility, focusing primarily on drivers, long-term implications of
6. Nitrous oxide emissions from European agriculture - an analysis of variability and drivers of emissions from field experiments
DEFF Research Database (Denmark)
Rees, R M; Agustin, J; Alberti, G
2013-01-01
Nitrous oxide emissions from a network of agricultural experiments in Europe were used to explore the relative importance of site and management controls of emissions. At each site, a selection of management interventions were compared within replicated experimental designs in plot-based experime......Nitrous oxide emissions from a network of agricultural experiments in Europe were used to explore the relative importance of site and management controls of emissions. At each site, a selection of management interventions were compared within replicated experimental designs in plot...
7. Agricultural Education: Key to Providing Broader Opportunities for Third World Women in Production Agriculture.
Science.gov (United States)
Lelle, Mark A.; Holt, Barbara A.
1987-01-01
The authors focus on providing opportunities for women in Third World countries in agriculture. A review of the body of knowledge in agricultural development and of the issues surrounding current world food crises is included. (CH)
8. Dynamics of soil carbon, nitrogen and soil respiration in farmer’s field with conservation agriculture Siem Reap, Cambodia
Science.gov (United States)
The years of intensive tillage in many countries, including Cambodia, have caused significant decline in agriculture’s natural resources that could threaten the future of agricultural production and sustainability worldwide. Long-term tillage system and site-specific crop management can affect chang...
9. Rainwater lens dynamics and mixing between infiltrating rainwater and upward saline groundwater seepage beneath a tile-drained agricultural field
NARCIS (Netherlands)
Louw, de P.G.B.; Eeman, S.; Oude Essink, G.H.P.; Vermue, E.; Post, V.E.A.
2013-01-01
Thin rainwater lenses (RW-lenses) near the land surface are often the only source of freshwater in agricultural areas with regionally-extensive brackish to saline groundwater. The seasonal and inter-annual dynamics of these lenses are poorly known. Here this knowledge gap is addressed by
10. Evaluation of the APEX model to simulate runoff quality from agricultural fields in the southern region of the US
Science.gov (United States)
The phosphorus (P) Index (PI) is the risk assessment tool approved in the NRCS 590 standard used to target critical source areas and practices to reduce P losses. A revision of the 590 standard, suggested using the Agricultural Policy/Environmental eXtender (APEX) model to assess the risk of nitroge...
11. Harmonization of customs policy of the Republic of Serbia in the field of agriculture as a condition for accession to the European Union
Directory of Open Access Journals (Sweden)
Nikolić Đurica
2016-01-01
Full Text Available The European Union wants to expand its market in order to qualify their products, and one way is to carry out the admission of new member states into the European Union. Some Balkan countries that are also used to be the former Yugoslav Republic want to become a full member of the European Union. In order to become an inclusive member, the Republic of Serbia must adjust economic, foreign trade, customs, security and other policies. The aim is to indicate how and in which way to harmonize customs policy of the European Union and of the Republic of Serbia. Comparing the tariff policy in the field of Agriculture of the Republic of Serbia and the European Union we want to point out the similarities and differences in the measures of protection of domestic agriculture in the Republic of Serbia and in the European Union, with the desire the Republic of Serbia, as far as possible, harmonize customs policies in the field of agriculture with policy of the European Union, in order to, among other conditions, allow for accession to the European Union. The process of harmonization is time consuming, requires knowledge, skill and expertise of the people at the Ministry of Finance and the Customs Administration. It is very important that all the recommendations given by the competent bodies of the European Union are implemented in a timely manner by the Republic of Serbia.
12. Opportunity's Surroundings on Sol 1818
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this full-circle view of the rover's surroundings during the 1,818th Martian day, or sol, of Opportunity's surface mission (March 5, 2009). South is at the center; north at both ends. The rover had driven 80.3 meters (263 feet) southward earlier on that sol. Tracks from the drive recede northward in this view. The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and lighter-toned bedrock. This view is presented as a cylindrical projection with geometric seam correction.
13. Climate Information and Agricultural Practice in Adaptation to Climate Variability: The Case of Climate Field Schools in Indramayu, Indonesia
NARCIS (Netherlands)
Crane, T.A.; Siregar, P.R.
2011-01-01
Inspired by the Farmer Field School methodology, a “Climate Field School” was conducted with farmers in the Indramayu region of Indonesia in 2003 to promote adaptive application of climate forecasts to crop selection decisions. However, five years after the Climate Field School, use of the forecasts
14. Application of swine manure on agricultural fields contributes to extended-spectrum β-lactamase-producing Escherichia coli spread in Tai’an, China
Directory of Open Access Journals (Sweden)
Lili eGao
2015-04-01
Full Text Available The prevalence of extended-spectrum beta-lactamase (ESBL-producing Escherichia coli (E. coli is increasing rapidly in both hospital environments and animal farms. A lot of animal manure has been directly applied into arable fields in the developing countries. But the impact of ESBL-positive bacteria from animal manure on the agricultural fields is sparse, especially in the rural regions of Tai’an, China. Here, we collected 29, 3, and 10 ESBL-producing E. coli from pig manure, compost, and soil samples, respectively. To track ESBL-harboring E. coli from agricultural soil, these isolates of different sources were analyzed with regard to antibiotic resistance profiles, ESBL genes, plasmid replicons, and enterobacterial repetitive intergenic consensus (ERIC-polymerase chain reaction (PCR typing. The results showed that all the isolates exhibited multi-drug resistance. CTX-M gene was the predominant ESBL gene in the isolates from pig farm samples (30/32, 93.8% and soil samples (7/10, 70.0%, but no SHV gene was detected. 25 isolates contained the IncF-type replicon of plasmid, including 18 strains (18/32, 56.3% from the pig farm and 7 (7/10, 70.0% from the soil samples. ERIC-PCR demonstrated that 3 isolates from the soil had above 90% genetic similarity with strains from pig farm samples. In conclusion, application of animal manure carrying drug-resistant bacteria on agricultural fields is a likely contributor to antibiotic resistance gene spread.
15. Opportunity's Surroundings on Sol 1687
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this 360-degree view of the rover's surroundings on the 1,687th Martian day, or sol, of its surface mission (Oct. 22, 2008). Opportunity had driven 133 meters (436 feet) that sol, crossing sand ripples up to about 10 centimeters (4 inches) tall. The tracks visible in the foreground are in the east-northeast direction. Opportunity's position on Sol 1687 was about 300 meters southwest of Victoria Crater. The rover was beginning a long trek toward a much larger crater, Endeavour, about 12 kilometers (7 miles) to the southeast. This view is presented as a cylindrical projection with geometric seam correction.
16. Opportunity's Surroundings on Sol 1798
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this 180-degree view of the rover's surroundings during the 1,798th Martian day, or sol, of Opportunity's surface mission (Feb. 13, 2009). North is on top. The rover had driven 111 meters (364 feet) southward on the preceding sol. Tracks from that drive recede northward in this view. For scale, the distance between the parallel wheel tracks is about 1 meter (about 40 inches). The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and lighter-toned bedrock. This view is presented as a cylindrical projection with geometric seam correction.
17. Monitoring program of surrounding of the NPP SE-EBO
International Nuclear Information System (INIS)
Dobis, L.; Kostial, J.
1997-01-01
The paper dealt with monitoring program of radiation control of surrounding of the NPP Bohunice, which has the aim: (1) to ensure the control of influence of work of the NPP Bohunice on the environment in their surrounding; (2) to ensure the back-ground for regular brief of control and supervisory organs about condition of the environment in surrounding of the NPP Bohunice; (3) to maintain the expected technical level of control of the NPP Bohunice and to exploit optimally the technical means; (4) to solicit permanently the data about the radioactivity of environment in surrounding of the NPP Bohunice for forming of files of the data; (5) to exploit purposefully the technical equipment, technical workers and to maintain their in permanent emergency and technical eligibility for the case of the breakdown; (6) to obtain permanently the files of the values for qualification of the reference levels. This program of monitoring includes the radiation control of surrounding of the NPP Bohunice, in the time of normal work of power-station's blocks, inclusively of all types of trouble-shooting and repairer works in surrounding of the NPP Bohunice, up to distance 20 km from power-station. The monitoring includes: outlets from the NPP Bohunice, monitoring of radiation characteristics in surrounding of the NPP Bohunice, (aerosols, fall-outs, soil), the links of food chains: (grass and fodder, milk, agriculture products), hydrosphere in surrounding (surface waters, drink water, bores of radiation control in complex of the NPP Bohunice, components of the hydrosphere), measurement of radiation from external sources (measurement of the dose rates, measurement of the doses [sk
18. Agriculture: Agriculture and Air Quality
Science.gov (United States)
Information on air emissions from agricultural practices, types of agricultural burning, air programs that may apply to agriculture, reporting requirements, and links to state and other federal air-quality information.
19. Mapping daily evapotranspiration at field scales over rainfed and irrigated agricultural areas using remote sensing data fusion
Science.gov (United States)
A continuous monitoring of daily evapotranspiration (ET) at field scale can be achieved by combining thermal infrared remote sensing data information from multiple satellite platforms. Here, an integrated approach to field scale ET mapping is described, combining multi-scale surface energy balance e...
20. Depth profiles of radioactive cesium and iodine released from the Fukushima Daiichi nuclear power plant in different agricultural fields and forests
International Nuclear Information System (INIS)
Ohno, Takeshi; Muramatsu, Yasuyuki; Oda, Kazumasa; Inagawa, Naoya; Ogawa, Hiromu; Yamazaki, Atsuko; Toyama, Chiaki; Miura, Yoshinori; Sato, Mutsuto
2012-01-01
1. Mercury cycling in agricultural and managed wetlands: a synthesis of methylmercury production, hydrologic export, and bioaccumulation from an integrated field study
Science.gov (United States)
Windham-Myers, Lisamarie; Fleck, Jacob A.; Ackerman, Joshua T.; Marvin-DiPasquale, Mark C.; Stricker, Craig A.; Heim, Wesley A.; Bachand, Philip A.M.; Eagles-Smith, Collin A.; Gill, Gary; Stephenson, Mark; Alpers, Charles N.
2014-01-01
With seasonal wetting and drying, and high biological productivity, agricultural wetlands (rice paddies) may enhance the conversion of inorganic mercury (Hg(II)) to methylmercury (MeHg), the more toxic, organic form that biomagnifies through food webs. Yet, the net balance of MeHg sources and sinks in seasonal wetland environments is poorly understood because it requires an annual, integrated assessment across biota, sediment, and water components. We examined a suite of wetlands managed for rice crops or wildlife during 2007–2008 in California's Central Valley, in an area affected by Hg contamination from historic mining practices. Hydrologic management of agricultural wetlands for rice, wild rice, or fallowed — drying for field preparation and harvest, and flooding for crop growth and post-harvest rice straw decay — led to pronounced seasonality in sediment and aqueous MeHg concentrations that were up to 95-fold higher than those measured concurrently in adjacent, non-agricultural permanently-flooded and seasonally-flooded wetlands. Flooding promoted microbial MeHg production in surface sediment of all wetlands, but extended water residence time appeared to preferentially enhance MeHg degradation and storage. When incoming MeHg loads were elevated, individual fields often served as a MeHg sink, rather than a source. Slow, horizontal flow of shallow water in the agricultural wetlands led to increased importance of vertical hydrologic fluxes, including evapoconcentration of surface water MeHg and transpiration-driven advection into the root zone, promoting temporary soil storage of MeHg. Although this hydrology limited MeHg export from wetlands, it also increased MeHg exposure to resident fish via greater in situ aqueous MeHg concentrations. Our results suggest that the combined traits of agricultural wetlands — slow-moving shallow water, manipulated flooding and drying, abundant labile plant matter, and management for wildlife — may enhance microbial
2. A regional field-based assessment of organic C sequestration and GHG balances in irrigated agriculture in Mediterranean semi-arid land
Science.gov (United States)
Virto, Inigo; Antón, Rodrigo; Arias, Nerea; Orcaray, Luis; Enrique, Alberto; Bescansa, Paloma
2016-04-01
In a context of global change and increasing food demand, agriculture faces the challenge of ensuring food security making a sustainable use of resources, especially arable land and water. This implies in many areas a transition towards agricultural systems with increased and stable productivity and a more efficient use of inputs. The introduction of irrigation is, within this framework, a widespread strategy. However, the C cycle and the net GHG emissions can be significantly affected by irrigation. The net effect of this change needs to be quantified at a regional scale. In the region of Navarra (NE Spain) more than 22,300 ha of rainfed agricultural land have been converted to irrigation in the last years, adding to the previous existing irrigated area of 70,000 ha. In this framework the project Life+ Regadiox (LIFE12 ENV/ES/000426, http://life-regadiox.es/) has the objective of evaluating the net GHG balances and atmospheric CO2 fixation rates of different management strategies in irrigated agriculture in the region. The project involved the identification of areas representative of the different pedocllimatic conditions in the region. This required soil and climate characterizations, and the design of a network of agricultural fields representative of the most common dryland and irrigation managements in these areas. This was done from available public datasets on climate and soil, and from soil pits especially sampled for this study. Two areas were then delimited, mostly based on their degree of aridity. Within each of those areas, fields were selected to allow for comparisons at three levels: (i) dryland vs irrigation, (ii) soil and crop management systems for non-permanent crops, and (iii) soil management strategies for permanent crops (namely olive orchards and vineyards). In a second step, the objective of this work was to quantify net SOC variations and GHG balances corresponding to the different managements identified in the previous step. These
3. Soil maps, field knowledge, forest inventory and Ecological-Economic Zoning as a basis for agricultural suitability of lands in Minas Gerais elaborated in GIS
Directory of Open Access Journals (Sweden)
2013-12-01
Full Text Available Lands (broader concept than soils, including all elements of the environment: soils, geology, topography, climate, water resources, flora and fauna, and the effects of anthropogenic activities of the state of Minas Gerais are in different soil, climate and socio-economics conditions and suitability for the production of agricultural goods is therefore distinct and mapping of agricultural suitability of the state lands is crucial for planning guided sustainability. Geoprocessing uses geographic information treatment techniques and GIS allows to evaluate geographic phenomena and their interrelationships using digital maps. To evaluate the agricultural suitability of state lands, we used soil maps, field knowledge, forest inventories and databases related to Ecological-Economic Zoning (EEZ of Minas Gerais, to develop a map of land suitability in GIS. To do this, we have combined the maps of soil fertility, water stress, oxygen deficiency, vulnerability to erosion and impediments to mechanization. In terms of geographical expression, the main limiting factor of lands is soil fertility, followed by lack of water, impediments to mechanization and vulnerability to erosion. Regarding agricultural suitability, the group 2 (regular suitability for crops is the most comprehensive, representing 45.13% of the state. For management levels A and B, low and moderate technological level, respectively, the most expressive suitability class is the regular, followed by the restricted class and last, the adequate class, while for the management level C (high technological level the predominant class is the restricted. The predominant most intensive use type is for crops, whose area increases substantially with capital investment and technology (management levels B and C.
4. Ground beetles (Coleoptera: Carabidae) of rice field banks and restored habitats in an agricultural area of the Po Plain (Lombardy, Italy).
Science.gov (United States)
Pilon, Nicola; Cardarelli, Elisa; Bogliani, Giuseppe
2013-01-01
An entomological investigation was carried out in an agricultural area, mainly rice fields, of the Po river plain, located in the municipalities of Lacchiarella (MI) and Giussago (PV) (Lombardy, Italy). In 2009 and 2010, ground beetles (Coleoptera: Carabidae) were sampled along rice field banks and in restored habitats, by means of pitfall traps. The area appeared as species-rich, compared to other anthropogenic habitats in the Po river pain. Most of the collected Carabids were species with a wide distribution in the Paleartic region, eurytopic and common in European agroecosystems. The assemblages were dominated by small-medium, macropterous species, with summer larvae. No endemic species were found. Species with southern distribution, rarely found north of the Po river, were also sampled. Amaralittorea is recorded for the first time in Italy.
5. Ground beetles (Coleoptera: Carabidae of rice field banks and restored habitats in an agricultural area of the Po Plain (Lombardy, Italy
Directory of Open Access Journals (Sweden)
Nicola Pilon
2013-11-01
Full Text Available An entomological investigation was carried out in an agricultural area, mainly rice fields, of the Po river plain, located in the municipalities of Lacchiarella (MI and Giussago (PV (Lombardy, Italy. In 2009 and 2010, ground beetles (Coleoptera: Carabidae were sampled along rice field banks and in restored habitats, by means of pitfall traps. The area appeared as species-rich, compared to other anthropogenic habitats in the Po river pain. Most of the collected Carabids were species with a wide distribution in the Paleartic region, eurytopic and common in European agroecosystems. The assemblages were dominated by small-medium, macropterous species, with summer larvae. No endemic species were found. Species with southern distribution, rarely found north of the Po river, were also sampled. Amara littorea is recorded for the first time in Italy.
6. Binaural Rendering in MPEG Surround
Directory of Open Access Journals (Sweden)
Kristofer Kjörling
2008-04-01
Full Text Available This paper describes novel methods for evoking a multichannel audio experience over stereo headphones. In contrast to the conventional convolution-based approach where, for example, five input channels are filtered using ten head-related transfer functions, the current approach is based on a parametric representation of the multichannel signal, along with either a parametric representation of the head-related transfer functions or a reduced set of head-related transfer functions. An audio scene with multiple virtual sound sources is represented by a mono or a stereo downmix signal of all sound source signals, accompanied by certain statistical (spatial properties. These statistical properties of the sound sources are either combined with statistical properties of head-related transfer functions to estimate “binaural parameters†that represent the perceptually relevant aspects of the auditory scene or used to create a limited set of combined head-related transfer functions that can be applied directly on the downmix signal. Subsequently, a binaural rendering stage reinstates the statistical properties of the sound sources by applying the estimated binaural parameters or the reduced set of combined head-related transfer functions directly on the downmix. If combined with parametric multichannel audio coders such as MPEG Surround, the proposed methods are advantageous over conventional methods in terms of perceived quality and computational complexity.
7. Lovelock black holes surrounded by quintessence
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Sushant G. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa); Centre for Theoretical Physics, Multidisciplinary Centre for Advanced Research and Studies (MCARS), New Delhi (India); Maharaj, Sunil D.; Baboolal, Dharmanand; Lee, Tae-Hun [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)
2018-02-15
Lovelock gravity consisting of the dimensionally continued Euler densities is a natural generalization of general relativity to higher dimensions such that equations of motion are still second order, and the theory is free of ghosts. A scalar field with a positive potential that yields an accelerating universe has been termed quintessence. We present exact black hole solutions in D-dimensional Lovelock gravity surrounded by quintessence matter and also perform a detailed thermodynamical study. Further, we find that the mass, entropy and temperature of the black hole are corrected due to the quintessence background. In particular, we find that a phase transition occurs with a divergence of the heat capacity at the critical horizon radius, and that specific heat becomes positive for r{sub h} < r{sub c} allowing the black hole to become thermodynamically stable. (orig.)
8. Lovelock black holes surrounded by quintessence
Science.gov (United States)
Ghosh, Sushant G.; Maharaj, Sunil D.; Baboolal, Dharmanand; Lee, Tae-Hun
2018-02-01
Lovelock gravity consisting of the dimensionally continued Euler densities is a natural generalization of general relativity to higher dimensions such that equations of motion are still second order, and the theory is free of ghosts. A scalar field with a positive potential that yields an accelerating universe has been termed quintessence. We present exact black hole solutions in D-dimensional Lovelock gravity surrounded by quintessence matter and also perform a detailed thermodynamical study. Further, we find that the mass, entropy and temperature of the black hole are corrected due to the quintessence background. In particular, we find that a phase transition occurs with a divergence of the heat capacity at the critical horizon radius, and that specific heat becomes positive for r_h
9. Polarization signatures for abandoned agricultural fields in the Manix Basin area of the Mojave Desert - Can polarimetric SAR detect desertification?
Science.gov (United States)
Ray, Terrill W.; Farr, Tom G.; Van Zyl, Jakob J.
1992-01-01
Radar backscatter from abandoned circular alfalfa fields in the Manix Basin area of the Mojave desert shows systematic changes with length of abandonment. The obliteration of circular planting rows by surface processes could account for the disappearance of bright spokes, which seem to be reflection patterns from remnants of the planting rows, with increasing length of abandonment. An observed shift in the location of the maximum L-band copolarization return away from VV, as well as an increase in surface roughness, both occurring with increasing age of abandonment, seems to be attributable to the formation of wind ripples on the relatively vegetationless fields.
10. Evaluation of a model framework to estimate soil and soil organic carbon redistribution by water and tillage using 137Cs in two U.S. Midwest agricultural fields
Science.gov (United States)
Young, Claudia J.; Liu, Shuguang; Schumacher, Joseph A.; Schumacher, Thomas E.; Kaspar, Thomas C.; McCarty, Gregory W.; Napton, Darrell; Jaynes, Dan B.
2014-01-01
Cultivated lands in the U.S. Midwest have been affected by soil erosion, causing soil organic carbon (SOC) redistribution in the landscape and other environmental and agricultural problems. The importance of SOC redistribution on soil productivity and crop yield, however, is still uncertain. In this study, we used a model framework, which includes the Unit Stream Power-based Erosion Deposition (USPED) and the Tillage Erosion Prediction (TEP) models, to understand the soil and SOC redistribution caused by water and tillage erosion in two agricultural fields in the U.S. Midwest. This model framework was evaluated for different digital elevation model (DEM) spatial resolutions (10-m, 24-m, 30-m, and 56-m) and topographic exponents (m = 1.0–1.6 and n = 1.0–1.3) using soil redistribution rates from 137Cs measurements. The results showed that the aggregated 24-m DEM, m = 1.4 and n = 1.0 for rill erosion, and m = 1.0 and n = 1.0 for sheet erosion, provided the best fit with the observation data at both sites. Moreover, estimated average SOC redistributions were 1.3 ± 9.8 g C m− 2 yr− 1 in field site 1 and 3.6 ± 14.3 g C m− 2 yr− 1 in field site 2. Spatial distribution patterns showed SOC loss (negative values) in the eroded areas and SOC gain (positive value) in the deposition areas. This study demonstrated the importance of the spatial resolution and the topographic exponents to estimate and map soil redistribution and the SOC dynamics throughout the landscape, helping to identify places where erosion and deposition from water and tillage are occurring at high rates. Additional research is needed to improve the application of the model framework for use in local and regional studies where rainfall erosivity and cover management factors vary. Therefore, using this model framework can help to improve the information about the spatial distribution of soil erosion across agricultural landscapes and to gain a better understanding of SOC
11. Reduced persistence of the macrolide antibiotics erythromycin, clarithromycin and azithromycin in agricultural soil following several years of exposure in the field
Energy Technology Data Exchange (ETDEWEB)
Topp, Edward, E-mail: [email protected]; Renaud, Justin; Sumarah, Mark; Sabourin, Lyne
2016-08-15
The macrolide antibiotics erythromycin, clarithromycin and azithromycin are very important in human and animal medicine, and can be entrained onto agricultural ground through application of sewage sludge or manures. In the present study, a series of replicated field plots were left untreated or received up to five annual spring applications of a mixture of three drugs to achieve a nominal concentration for each of 10 or 0.1 mg kg{sup −1} soil; the latter an environmentally relevant concentration. Soil samples were incubated in the laboratory, and supplemented with antibiotics to establish the dissipation kinetics of erythromycin and clarithromycin using radioisotope methods, and azithromycin using HPLC-MS/MS. All three drugs were dissipated significantly more rapidly in soils with a history of field exposure to 10 mg kg{sup −1} macrolides, and erythromycin and clarithromycin were also degraded more rapidly in field soil exposed to 0.1 mg kg{sup −1} macrolides. Rapid mineralization of {sup 14}C-labelled erythromycin and clarithromycin are consistent with biodegradation. Analysis of field soils revealed no carryover of parent compound from year to year. Azithromycin transformation products were detected consistent with removal of the desosamine and cladinose moieties. Overall, these results have revealed that following several years of exposure to macrolide antibiotics these are amenable to accelerated degradation. The potential accelerated degradation of these drugs in soils amended with manure and sewage sludge should be investigated as this phenomenon would attenuate environmental exposure and selection pressure for clinically relevant resistance. - Highlights: • The impact of field exposure on persistence of macrolide antibiotics was evaluated. • Soil samples were incubated in the laboratory with macrolides. • Field exposure resulted in more rapid dissipation of all macrolides. • Radiolabelled erythromycin and clarithromycin were rapidly mineralized
12. Reduced persistence of the macrolide antibiotics erythromycin, clarithromycin and azithromycin in agricultural soil following several years of exposure in the field
International Nuclear Information System (INIS)
Topp, Edward; Renaud, Justin; Sumarah, Mark; Sabourin, Lyne
2016-01-01
The macrolide antibiotics erythromycin, clarithromycin and azithromycin are very important in human and animal medicine, and can be entrained onto agricultural ground through application of sewage sludge or manures. In the present study, a series of replicated field plots were left untreated or received up to five annual spring applications of a mixture of three drugs to achieve a nominal concentration for each of 10 or 0.1 mg kg"−"1 soil; the latter an environmentally relevant concentration. Soil samples were incubated in the laboratory, and supplemented with antibiotics to establish the dissipation kinetics of erythromycin and clarithromycin using radioisotope methods, and azithromycin using HPLC-MS/MS. All three drugs were dissipated significantly more rapidly in soils with a history of field exposure to 10 mg kg"−"1 macrolides, and erythromycin and clarithromycin were also degraded more rapidly in field soil exposed to 0.1 mg kg"−"1 macrolides. Rapid mineralization of "1"4C-labelled erythromycin and clarithromycin are consistent with biodegradation. Analysis of field soils revealed no carryover of parent compound from year to year. Azithromycin transformation products were detected consistent with removal of the desosamine and cladinose moieties. Overall, these results have revealed that following several years of exposure to macrolide antibiotics these are amenable to accelerated degradation. The potential accelerated degradation of these drugs in soils amended with manure and sewage sludge should be investigated as this phenomenon would attenuate environmental exposure and selection pressure for clinically relevant resistance. - Highlights: • The impact of field exposure on persistence of macrolide antibiotics was evaluated. • Soil samples were incubated in the laboratory with macrolides. • Field exposure resulted in more rapid dissipation of all macrolides. • Radiolabelled erythromycin and clarithromycin were rapidly mineralized. • Macrolides
13. Nitrous oxide emissions from European agriculture – an analysis of variability and drivers of emissions from field experiments
Directory of Open Access Journals (Sweden)
R. M. Rees
2013-04-01
Full Text Available Nitrous oxide emissions from a network of agricultural experiments in Europe were used to explore the relative importance of site and management controls of emissions. At each site, a selection of management interventions were compared within replicated experimental designs in plot-based experiments. Arable experiments were conducted at Beano in Italy, El Encin in Spain, Foulum in Denmark, Logården in Sweden, Maulde in Belgium, Paulinenaue in Germany, and Tulloch in the UK. Grassland experiments were conducted at Crichton, Nafferton and Peaknaze in the UK, Gödöllö in Hungary, Rzecin in Poland, Zarnekow in Germany and Theix in France. Nitrous oxide emissions were measured at each site over a period of at least two years using static chambers. Emissions varied widely between sites and as a result of manipulation treatments. Average site emissions (throughout the study period varied between 0.04 and 21.21 kg N2O-N ha−1 yr−1, with the largest fluxes and variability associated with the grassland sites. Total nitrogen addition was found to be the single most important determinant of emissions, accounting for 15% of the variance (using linear regression in the data from the arable sites (p 2O emissions within sites that occurred as a result of manipulation treatments was greater than that resulting from site-to-site and year-to-year variation, highlighting the importance of management interventions in contributing to greenhouse gas mitigation.
14. Per-field crop classification in irrigated agricultural regions in middle Asia using random forest and support vector machine ensemble
Science.gov (United States)
Löw, Fabian; Schorcht, Gunther; Michel, Ulrich; Dech, Stefan; Conrad, Christopher
2012-10-01
Accurate crop identification and crop area estimation are important for studies on irrigated agricultural systems, yield and water demand modeling, and agrarian policy development. In this study a novel combination of Random Forest (RF) and Support Vector Machine (SVM) classifiers is presented that (i) enhances crop classification accuracy and (ii) provides spatial information on map uncertainty. The methodology was implemented over four distinct irrigated sites in Middle Asia using RapidEye time series data. The RF feature importance statistics was used as feature-selection strategy for the SVM to assess possible negative effects on classification accuracy caused by an oversized feature space. The results of the individual RF and SVM classifications were combined with rules based on posterior classification probability and estimates of classification probability entropy. SVM classification performance was increased by feature selection through RF. Further experimental results indicate that the hybrid classifier improves overall classification accuracy in comparison to the single classifiers as well as useŕs and produceŕs accuracy.
15. Stabilization of Cd-, Pb-, Cu- and Zn-contaminated calcareous agricultural soil using red mud: a field experiment.
Science.gov (United States)
Wang, Yangyang; Li, Fangfang; Song, Jian; Xiao, Ruiyang; Luo, Lin; Yang, Zhihui; Chai, Liyuan
2018-04-12
Red mud (RM) was used to remediate heavy metal-contaminated soils. Experiments with two different dosages of RM added to soils were carried out in this study. It was found that soil pH increased 0.3 and 0.5 unit with the dosage of 3 and 5% (wt%), respectively. At the dosage of 5%, the highest stabilization efficiencies for Cd, Pb, Cu and Zn reached 67.95, 64.21, 43.73 and 63.73%, respectively. The addition of RM obviously transferred Cd from the exchangeable fraction to the residual fraction. Meanwhile, in comparison with the control (no RM added), it reduced 24.38, 49.20, 19.42 and 8.89% of Cd, Pb, Cu and Zn in wheat grains at the RM addition dosage of 5%, respectively. At the same time, the yield of wheat grains increased 17.81 and 24.66% at the RM addition dosage of 3 and 5%, respectively. Finally, the addition of RM did not change the soil bacterial community. These results indicate that RM has a great potential in stabilizing heavy metals in calcareous agricultural soils.
16. Chitin amendment increases soil suppressiveness toward plant pathogens and modulates the actinobacterial and oxalobacteraceal communities in an experimental agricultural field
NARCIS (Netherlands)
Cretoiu, Mariana Silvia; Korthals, Gerard W.; Visser, Johnny H. M.; van Elsas, Jan Dirk
A long-term experiment on the effect of chitin addition to soil on the suppression of soilborne pathogens was set up and monitored for 8 years in an experimental field, Vredepeel, The Netherlands. Chitinous matter obtained from shrimps was added to soil top layers on two different occasions, and the
17. Chromatic induction from surrounding stimuli under perceptual suppression.
Science.gov (United States)
Horiuchi, Koji; Kuriki, Ichiro; Tokunaga, Rumi; Matsumiya, Kazumichi; Shioiri, Satoshi
2014-11-01
The appearance of colors can be affected by their spatiotemporal context. The shift in color appearance according to the surrounding colors is called color induction or chromatic induction; in particular, the shift in opponent color of the surround is called chromatic contrast. To investigate whether chromatic induction occurs even when the chromatic surround is imperceptible, we measured chromatic induction during interocular suppression. A multicolor or uniform color field was presented as the surround stimulus, and a colored continuous flash suppression (CFS) stimulus was presented to the dominant eye of each subject. The subjects were asked to report the appearance of the test field only when the stationary surround stimulus is invisible by interocular suppression with CFS. The resulting shifts in color appearance due to chromatic induction were significant even under the conditions of interocular suppression for all surround stimuli. The magnitude of chromatic induction differed with the surround conditions, and this difference was preserved regardless of the viewing conditions. The chromatic induction effect was reduced by CFS, in proportion to the magnitude of chromatic induction under natural (i.e., no-CFS) viewing conditions. According to an analysis with linear model fitting, we revealed the presence of at least two kinds of subprocesses for chromatic induction that reside at higher and lower levels than the site of interocular suppression. One mechanism yields different degrees of chromatic induction based on the complexity of the surround, which is unaffected by interocular suppression, while the other mechanism changes its output with interocular suppression acting as a gain control. Our results imply that the total chromatic induction effect is achieved via a linear summation of outputs from mechanisms that reside at different levels of visual processing.
18. A Field-Scale Sensor Network Data Set for Monitoring and Modeling the Spatial and Temporal Variation of Soil Water Content in a Dryland Agricultural Field
Science.gov (United States)
Gasch, C. K.; Brown, D. J.; Campbell, C. S.; Cobos, D. R.; Brooks, E. S.; Chahal, M.; Poggio, M.
2017-12-01
We describe a soil water content monitoring data set and auxiliary data collected at a 37 ha experimental no-till farm in the Northwestern United States. Water content measurements have been compiled hourly since 2007 by ECH2O-TE and 5TE sensors installed at 42 locations and five depths (0.3, 0.6, 0.9, 1.2, and 1.5 m, 210 sensors total) across the R.J. Cook Agronomy Farm, a Long-Term Agro-Ecosystem Research Site stationed on complex terrain in a Mediterranean climate. In addition to soil water content readings, the data set includes hourly and daily soil temperature readings, annual crop histories, a digital elevation model, Bt horizon maps, seasonal apparent electrical conductivity, soil texture, and soil bulk density. Meteorological records are also available for this location. We discuss the unique challenges of maintaining the network on an operating farm and demonstrate the nature and complexity of the soil water content data. This data set is accessible online through the National Agriculture Library, has been assigned a DOI, and will be maintained for the long term.
19. Stepping-stones to improve upon functioning of participatory agricultural extension programmes : farmer field schools in Uganda
NARCIS (Netherlands)
Isubikalu, P.
2007-01-01
This thesis deals with Farmer Field Schools (FFS) inUganda.FFSis a grassroots learning and application device for
20. Forest Fragments Surrounded by Sugar Cane Are More Inhospitable to Terrestrial Amphibian Abundance Than Fragments Surrounded by Pasture
Directory of Open Access Journals (Sweden)
Paula Eveline Ribeiro D’Anunciação
2013-01-01
Full Text Available In recent years, there has been increasing interest in matrix-type influence on forest fragments. Terrestrial amphibians are good bioindicators for this kind of research because of low vagility and high philopatry. This study compared richness, abundance, and species composition of terrestrial amphibians through pitfall traps in two sets of semideciduous seasonal forest fragments in southeastern Brazil, according to the predominant surrounding matrix (sugar cane and pasture. There were no differences in richness, but fragments surrounded by sugar cane had the lowest abundance of amphibians, whereas fragments surrounded by pastures had greater abundance. The most abundant species, Rhinella ornata, showed no biometric differences between fragment groups but like many other amphibians sampled showed very low numbers of individuals in fragments dominated by sugar cane fields. Our data indicate that the sugar cane matrix negatively influences the community of amphibians present in fragments surrounded by this type of land use.
1. Agriculture: Climate
Science.gov (United States)
Climate change affects agricultural producers because agriculture and fisheries depend on specific climate conditions. Temperature changes can cause crop planting dates to shift. Droughts and floods due to climate change may hinder farming practices.
2. Agricultural Overpopulation
OpenAIRE
Bičanić, Rudolf
2003-01-01
The author discusses three different approaches to agricultural overpopulation: from the consumption side, from the production side and from the aspect of immobility of agricultural population. In the first approach agrarian overpopulation is defined from the consumption point of viewas the number of people living from agriculture that can live from aggregate agricultural income at a certain standard of consumption. In this connection the problem of measuring total agricultu...
3. Cost-Effectiveness Analysis of Surface Flow Constructed Wetlands (SFCW) for Nutrient Reduction in Drainage Discharge from Agricultural Fields in Denmark.
Science.gov (United States)
Gachango, F G; Pedersen, S M; Kjaergaard, C
2015-12-01
Constructed wetlands have been proposed as cost-effective and more targeted technologies in the reduction of nitrogen and phosphorous water pollution in drainage losses from agricultural fields in Denmark. Using two pig farms and one dairy farm situated in a pumped lowland catchment as case studies, this paper explores the feasibility of implementing surface flow constructed wetlands (SFCW) based on their cost effectiveness. Sensitivity analysis is conducted by varying the cost elements of the wetlands in order to establish the most cost-effective scenario and a comparison with the existing nutrients reduction measures carried out. The analyses show that the cost effectiveness of the SFCW is higher in the drainage catchments with higher nutrient loads. The range of the cost effectiveness ratio on nitrogen reduction differs distinctively with that of catch crop measure. The study concludes that SFCW could be a better optimal nutrients reduction measure in drainage catchments characterized with higher nutrient loads.
4. Cost-effectiveness analysis of surface flow constructed wetlands (SFCW) for nutrient reduction in drainage discharge from agricultural fields in Denmark
DEFF Research Database (Denmark)
Gachango, Florence Gathoni; Pedersen, Søren Marcus; Kjærgaard, Charlotte
2015-01-01
Constructed wetlands have been proposed as cost-effective and more targeted technologies in the reduction of nitrogen and phosphorous water pollution in drainage losses from agricultural fields in Denmark. Using two pig farms and one dairy farm situated in a pumped lowland catchment as case studies......, this paper explores the feasibility of implementing surface flow constructed wetlands (SFCW) based on their cost effectiveness. Sensitivity analysis is conducted by varying the cost elements of the wetlands in order to establish the most cost-effective scenario and a comparison with the existing nutrients...... reduction measures carried out. The analyses show that the cost effectiveness of the SFCW is higher in the drainage catchments with higher nutrient loads. The range of the cost effectiveness ratio on nitrogen reduction differs distinctively with that of catch crop measure. The study concludes that SFCW...
5. LONG TERM EFFECTS OF AMELIORATIVE WORKS ON SOME SOIL QUALITY PARAMETERS FROM BAIA –MOLDOVA EXPERIMENTAL AGRICULTURAL DRAINAGE FIELD
Directory of Open Access Journals (Sweden)
V. Moca
2009-10-01
Full Text Available The soil-climatic conditions from Baia Depression – the hydrographical basin from the extra-Carpathian area of the Moldova River - have frequently determined the presence, under different forms, intensities and periods, of temporary water excess from soil. The underground drainage, as a measure of water excess control, with stagnant character, caused mainly by rainfall amounts registered for 1-5 consecutive days, was firstly arranged in pilot-experimental fields during 1972-1978. We followed the behaviour in exploitation of underground drainage technical solutions, as concerns the functional efficiency of the means of water excess removal and of the improved soil favourableness and/or suitability for crop growing.In order to assess the long-term effects of ameliorating works, applied in 1978 in the drainage field of Baia, on an area of 3.50 ha, we have qualitatively classified and estimated the albic stagnic glossic Luvosoil (S.R.T.S. – 2003, improved and unimproved. Based on this study, we have estimated the present favourableness for crops of the improved soil, as compared to unimproved soil, used as natural grassland, after an exploitation cycle of 30 years (1978- 2008.
6. Multi-scale variation in spatial heterogeneity for microbial community structure in an eastern Virginia agricultural field
Science.gov (United States)
Franklin, Rima B.; Mills, Aaron L.
2003-01-01
To better understand the distribution of soil microbial communities at multiple spatial scales, a survey was conducted to examine the spatial organization of community structure in a wheat field in eastern Virginia (USA). Nearly 200 soil samples were collected at a variety of separation distances ranging from 2.5 cm to 11 m. Whole-community DNA was extracted from each sample, and community structure was compared using amplified fragment length polymorphism (AFLP) DNA fingerprinting. Relative similarity was calculated between each pair of samples and compared using geostatistical variogram analysis to study autocorrelation as a function of separation distance. Spatial autocorrelation was found at scales ranging from 30 cm to more than 6 m, depending on the sampling extent considered. In some locations, up to four different correlation length scales were detected. The presence of nested scales of variability suggests that the environmental factors regulating the development of the communities in this soil may operate at different scales. Kriging was used to generate maps of the spatial organization of communities across the plot, and the results demonstrated that bacterial distributions can be highly structured, even within a habitat that appears relatively homogeneous at the plot and field scale. Different subsets of the microbial community were distributed differently across the plot, and this is thought to be due to the variable response of individual populations to spatial heterogeneity associated with soil properties. c2003 Federation of European Microbiological Societies. Published by Elsevier Science B.V. All rights reserved.
7. Remediation of contaminated agricultural soils near a former Pb/Zn smelter in Austria: Batch, pot and field experiments
International Nuclear Information System (INIS)
Friesl, W.; Friedl, J.; Platzer, K.; Horak, O.; Gerzabek, M.H.
2006-01-01
Metal contaminated crops from contaminated soils are possible hazards for the food chain. The aim of this study was to find practical and cost-effective measures to reduce metal uptake in crops grown on metal contaminated soils near a former metal smelter in Austria. Metal-inefficient cultivars of crop plants commonly grown in the area were investigated in combination with in-situ soil amendments. A laboratory batch experiment using 15 potential amendments was used to select 5 amendments to treat contaminated soil in a pot study using two Barley (Hordeum vulgare L.) cultivars that differed in their ability to accumulate cadmium. Results from this experiment identified 3 of these amendments for use in a field trial. In the pot experiment a reduction in ammonium nitrate extractable Cd (<41%) and Pb (<49%) compared to the controls was measured, with a concurrent reduction of uptake into barley grain (Cd < 62%, Pb < 68%). In the field extractable fractions of Cd, Pb, and Zn were reduced by up to 96%, 99%, and 99%, respectively in amended soils. - Gravel sludge and red mud, combined with metal-excluding cultivars, can improve contaminated land
8. Spatial variability of isoproturon mineralizing activity within an agricultural field: Geostatistical analysis of simple physicochemical and microbiological soil parameters
Energy Technology Data Exchange (ETDEWEB)
El Sebai, T. [UMR Microbiologie et Geochimie des Sols, INRA/CMSE, 17 Rue Sully, BP 86510, 21065 Dijon Cedex (France); Lagacherie, B. [UMR Microbiologie et Geochimie des Sols, INRA/CMSE, 17 Rue Sully, BP 86510, 21065 Dijon Cedex (France); Soulas, G. [UMR Microbiologie et Geochimie des Sols, INRA/CMSE, 17 Rue Sully, BP 86510, 21065 Dijon Cedex (France); Martin-Laurent, F. [UMR Microbiologie et Geochimie des Sols, INRA/CMSE, 17 Rue Sully, BP 86510, 21065 Dijon Cedex (France)]. E-mail: [email protected]
2007-02-15
We assessed the spatial variability of isoproturon mineralization in relation to that of physicochemical and biological parameters in fifty soil samples regularly collected along a sampling grid delimited across a 0.36 ha field plot (40 x 90 m). Only faint relationships were observed between isoproturon mineralization and the soil pH, microbial C biomass, and organic nitrogen. Considerable spatial variability was observed for six of the nine parameters tested (isoproturon mineralization rates, organic nitrogen, genetic structure of the microbial communities, soil pH, microbial biomass and equivalent humidity). The map of isoproturon mineralization rates distribution was similar to that of soil pH, microbial biomass, and organic nitrogen but different from those of structure of the microbial communities and equivalent humidity. Geostatistics revealed that the spatial heterogeneity in the rate of degradation of isoproturon corresponded to that of soil pH and microbial biomass. - In field spatial variation of isoproturon mineralization mainly results from the spatial heterogeneity of soil pH and microbial C biomass.
9. Spatial variability of isoproturon mineralizing activity within an agricultural field: Geostatistical analysis of simple physicochemical and microbiological soil parameters
International Nuclear Information System (INIS)
El Sebai, T.; Lagacherie, B.; Soulas, G.; Martin-Laurent, F.
2007-01-01
We assessed the spatial variability of isoproturon mineralization in relation to that of physicochemical and biological parameters in fifty soil samples regularly collected along a sampling grid delimited across a 0.36 ha field plot (40 x 90 m). Only faint relationships were observed between isoproturon mineralization and the soil pH, microbial C biomass, and organic nitrogen. Considerable spatial variability was observed for six of the nine parameters tested (isoproturon mineralization rates, organic nitrogen, genetic structure of the microbial communities, soil pH, microbial biomass and equivalent humidity). The map of isoproturon mineralization rates distribution was similar to that of soil pH, microbial biomass, and organic nitrogen but different from those of structure of the microbial communities and equivalent humidity. Geostatistics revealed that the spatial heterogeneity in the rate of degradation of isoproturon corresponded to that of soil pH and microbial biomass. - In field spatial variation of isoproturon mineralization mainly results from the spatial heterogeneity of soil pH and microbial C biomass
10. Evapotranspiration from selected fallowed agricultural fields on the Tule Lake National Wildlife Refuge, California, during May to October 2000
Science.gov (United States)
Bidlake, W.R.
2002-01-01
An investigation of evapotranspiration, vegetation quantity and composition, and depth to the water table below the land surface was made at three sites in two fallowed agricultural lots on the 15,800-hectare Tule Lake National Wildlife Refuge in northern California during the 2000 growing season. All three sites had been farmed during 1999, but were not irrigated since the 1999 growing season. Vegetation at the lot C1B and lot 6 stubble sites included weedy species and small grain plants. The lot 6 cover crop site supported a crop of cereal rye that had been planted during the previous winter. Percentage of coverage by live vegetation ranged from 0 to 43.2 percent at the lot C1B site, from approximately 0 to 63.2 percent at the lot 6 stubble site, and it was estimated to range from 0 to greater than 90 percent at the lot 6 cover crop site. Evapotranspiration was measured using the Bowen ratio energy balance technique and it was estimated using a model that was based on the Priestley-Taylor equation and a model that was based on reference evapotranspiration with grass as the reference crop. Total evapotranspiration during May to October varied little among the three evapotranspiration measurement sites, although the timing of evapotranspiration losses did vary among the sites. Total evapotranspiration from the lot C1B site was 426 millimeters, total evapotranspiration from the lot 6 stubble site was 444 millimeters, and total evapotranspiration from the lot 6 cover crop site was 435 millimeters. The months of May to July accounted for approximately 78 percent of the total evapotranspiration from the lot C1B site, approximately 63 percent of the evapotranspiration from the lot 6 stubble site, and approximately 86 percent of the total evapotranspiration from the lot 6 cover crop site. Estimated growing season precipitation accounted for 16 percent of the growing-season evapotranspiration at the lot C1B site and for 17 percent of the growing-season evapotranspiration
11. Field populations of native Indian honey bees from pesticide intensive agricultural landscape show signs of impaired olfaction
Science.gov (United States)
Chakrabarti, Priyadarshini; Rana, Santanu; Bandopadhyay, Sreejata; Naik, Dattatraya G.; Sarkar, Sagartirtha; Basu, Parthiba
2015-07-01
Little information is available regarding the adverse effects of pesticides on natural honey bee populations. This study highlights the detrimental effects of pesticides on honey bee olfaction through behavioural studies, scanning electron microscopic imaging of antennal sensillae and confocal microscopic studies of honey bee brains for calcium ions on Apis cerana, a native Indian honey bee species. There was a significant decrease in proboscis extension response and biologically active free calcium ions and adverse changes in antennal sensillae in pesticide exposed field honey bee populations compared to morphometrically similar honey bees sampled from low/no pesticide sites. Controlled laboratory experiments corroborated these findings. This study reports for the first time the changes in antennal sensillae, expression of Calpain 1(an important calcium binding protein) and resting state free calcium in brains of honey bees exposed to pesticide stress.
12. Spatial variability of isoproturon mineralizing activity within an agricultural field: geostatistical analysis of simple physicochemical and microbiological soil parameters.
Science.gov (United States)
El Sebai, T; Lagacherie, B; Soulas, G; Martin-Laurent, F
2007-02-01
We assessed the spatial variability of isoproturon mineralization in relation to that of physicochemical and biological parameters in fifty soil samples regularly collected along a sampling grid delimited across a 0.36 ha field plot (40 x 90 m). Only faint relationships were observed between isoproturon mineralization and the soil pH, microbial C biomass, and organic nitrogen. Considerable spatial variability was observed for six of the nine parameters tested (isoproturon mineralization rates, organic nitrogen, genetic structure of the microbial communities, soil pH, microbial biomass and equivalent humidity). The map of isoproturon mineralization rates distribution was similar to that of soil pH, microbial biomass, and organic nitrogen but different from those of structure of the microbial communities and equivalent humidity. Geostatistics revealed that the spatial heterogeneity in the rate of degradation of isoproturon corresponded to that of soil pH and microbial biomass.
13. Multifunctional landscapes: Site characterization and field-scale design to incorporate biomass production into an agricultural system
Energy Technology Data Exchange (ETDEWEB)
Ssegane, Herbert; Negri, M. Cristina; Quinn, John; Urgun-Demirtas, Meltem
2015-09-01
Current and future demand for food, feed, fiber, and energy require novel approaches to land management, which demands that multifunctional landscapes are created to integrate various ecosystem functions into a sustainable land use. We developed an approach to design such landscapes at a field scale to minimize concerns of land use change, water quality, and greenhouse gas emissions associated with production of food and bioenergy. This study leverages concepts of nutrient recovery and phytoremediation to place bioenergy crops on the landscape to recover nutrients released to watersheds by commodity crops. Crop placement is determined by evaluating spatial variability of: 1) soils, 2) surface flow pathways, 3) shallow groundwater flow gradients, 4) subsurface nitrate concentrations, and 5) primary crop yield. A 0.8 ha bioenergy buffer was designed within a 6.5 ha field to intercept concentrated surface flow, capture and use nitrate leachate, and minimize use of productive areas. Denitrification-Decomposition (DNDC) simulations show that on average, a switchgrass (Panicum Virgatum L.) or willow (Salix spp.) buffer within this catchment according to this design could reduce annual leached NO3 by 61 or 59% and N2O emission by 5.5 or 10.8%, respectively, produce 8.7 or 9.7 Mg ha-1 of biomass respectively, and displace 6.7 Mg ha-1 of corn (Zea mays L.) grain. Therefore, placement of bioenergy crops has the potential to increase environmental sustainability when the pairing of location and crop type result in minimal disruption of current food production systems and provides additional environmental benefits.
14. Comparison of water soil erosion on Spanish Mediterannean abandoned land and agricultural fields under vine, almond, olives and citrus
Science.gov (United States)
Rodrigo-Comino, Jesús; Martínez-Hernández, Carlos; Iserloh, Thomas; Cerdà, Artemi
2017-04-01
The abandonment of agricultural lands is considered as a global dynamic with on- and off-site consequences on the soil mostly ignored (Vanmaercke et al., 2011), which enhance land degradation processes by increasing water soil erosion (Cammeraat et al., 2010; Keesstra et al., 2012) and by decreasing biodiversity (Brevik et al., 2015; Smith et al., 2015). However, there is a lack of information at pedon scale about the assessment and quantification of which environmental elements activate or avoid water soil erosion after its respective abandonment. Small portable rainfall simulators are considered as useful tool for measuring interrelated soil erosion processes such as splash, initial rainfall-runoff processes, infiltration, sediment yield, water turbidity or nutrient suspensions (Cerdà, 1999; Iserloh et al., 2013; Rodrigo Comino et al., 2016). 105 experiments were conducted with a small portable rainfall simulator (rainfall intensity of 40 mm h-1 in 30 minutes) in four different land uses and their respective abandoned land: i) citrus and olives (Valencia), almonds (Murcia) and vines (Málaga). We studied the main environmental factors that may determine water soil erosion during the performed experiments: slope, vegetation cover, rock fragment cover, soil properties (texture) and hydrological responses (time to runoff and infiltration generation). REFERENCES Brevik, E.C., Cerdà, A., Mataix-Solera, J., Pereg, L., Quinton, J.N., Six, J., Van Oost, K., 2015. The interdisciplinary nature of SOIL. SOIL 1, 117-129. doi:10.5194/soil-1-117-2015 Cammeraat, E.L.H., Cerdà, A., Imeson, A.C., 2010. Ecohydrological adaptation of soils following land abandonment in a semi-arid environment. Ecohydrology 3, 421-430. doi:10.1002/eco.161 Cerdà, A., 1999. Simuladores de lluvia y su aplicación a la Geomorfología: Estado de la cuestión. Cuad. Investig. Geográfica 45-84. Iserloh, T., Ries, J.B., Arnáez, J., Boix-Fayos, C., Butzen, V., Cerdà, A., Echeverría, M.T., Fern
15. Determination for regional differences of agriculture using satellite data
Science.gov (United States)
Saito, G.
2006-12-01
Remote Sensing Laboratory, Field Science Center, Graduate School of Agriculture Science, Tohoku University starts at April 2004. For studies and education at the laboratory we are now developing the system of remote sensing and GIS. Earth Remote Sensing Data Analysis Center (ERSDAC) made the Home Pages of Terra/ASTER Image Web Library 3 "The Major Airport of the World." http://www.Ersdac.or.jp/ASTERimage3/library_E.html. First, we check the Airport Data to use agricultural understanding for the world. Almost major airport is located in rural area and surrounded with agriculture field. To survey the agriculture field adjacent to the major airport has almost the same condition of human activities. The images are same size and display about 18km X 14km. We can easily understand field size and surrounding conditions. We study seven airports as follows, 1. Tokyo Narita Airport (NRT), Japan, 2. Taipei Chiang kai Shek International Airport (TPE), Taiwan, 3. Bangkok International Airport (BKK), Thailand, 4. Riyadh King Khalid International Airport (RUH), Saudi Arabia, 5. Charles de Gaulle Airport (CDG), Paris, France, 6. Vienna International Airport (VIE), Austria, 7. Denver International Airport (DEN), CO, USA. At the area of Tokyo Narita Airport, there are many golf courses, big urban area and small size of agricultural fields. At Taipei Airport area are almost same as Tokyo Narita Airport area and there are many ponds for irrigations. Bangkok Airport area also has golf courses and many ponds for irrigation water. Riyadh Airport area is quite different from others, and there are large bare soils and small agriculture fields with irrigation and circle shape. Paris Airport area and Vienna Airport area are almost agricultural fields and there are vegetated field and bare soil fields because of crop rotation. Denver Airport area consists of almost agriculture fields and each field size is very large. The advantages of ASTER data are as follows, 1. High-resolution and large
International Nuclear Information System (INIS)
D'Souza, S.F.
2013-01-01
The Department of Atomic Energy through its research, development and deployment activities in nuclear science and technology, has been contributing towards enhancing the production of agricultural commodities and their preservation. Radiations and radioisotopes are used in agricultural research to induce genetic variability in crop plants to develop improved varieties, to manage insect pests, monitor fate and persistence of pesticides, to study fertilizer use efficiency and plant micronutrient uptake and also to preserve agricultural produce. Use of radiation and radioisotopes in agriculture which is often referred to as nuclear agriculture is one of the important fields of peaceful applications of atomic energy for societal benefit and BARC has contributed significantly in this area. 41 new crop varieties developed at BARC have been released and Gazette notified by the MoA, GOI for commercial cultivation and are popular among the farming community and grown through out the country
17. Robust spatialization of soil water content at the scale of an agricultural field using geophysical and geostatistical methods
Science.gov (United States)
Henine, Hocine; Tournebize, Julien; Laurent, Gourdol; Christophe, Hissler; Cournede, Paul-Henry; Clement, Remi
2017-04-01
Research on the Critical Zone (CZ) is a prerequisite for undertaking issues related to ecosystemic services that human societies rely on (nutrient cycles, water supply and quality). However, while the upper part of CZ (vegetation, soil, surface water) is readily accessible, knowledge of the subsurface remains limited, due to the point-scale character of conventional direct observations. While the potential for geophysical methods to overcome this limitation is recognized, the translation of the geophysical information into physical properties or states of interest remains a challenge (e.g. the translation of soil electrical resistivity into soil water content). In this study, we propose a geostatistical framework using the Bayesian Maximum Entropy (BME) approach to assimilate geophysical and point-scale data. We especially focus on the prediction of the spatial distribution of soil water content using (1) TDR point-scale measurements of soil water content, which are considered as accurate data, and (2) soil water content data derived from electrical resistivity measurements, which are uncertain data but spatially dense. We used a synthetic dataset obtained with a vertical 2D domain to evaluate the performance of this geostatistical approach. Spatio-temporal simulations of soil water content were carried out using Hydrus-software for different scenarios: homogeneous or heterogeneous hydraulic conductivity distribution, and continuous or punctual infiltration pattern. From the simulations of soil water content, conceptual soil resistivity models were built using a forward modeling approach and point sampling of water content values, vertically ranged, were done. These two datasets are similar to field measurements of soil electrical resistivity (using electrical resistivity tomography, ERT) and soil water content (using TDR probes) obtained at the Boissy-le-Chatel site, in Orgeval catchment (East of Paris, France). We then integrated them into a specialization
18. Nitrogen Fertilizer Rate and Crop Management Effects on Nitrate Leaching from an Agricultural Field in Central Pennsylvania
Directory of Open Access Journals (Sweden)
Richard H. Fox
2001-01-01
Full Text Available Eighteen pan lysimeters were installed at a depth of 1.2 m in a Hagerstown silt loam soil in a corn field in central Pennsylvania in 1988. In 1995, wick lysimeters were also installed at 1.2 m depth in the same access pits. Treatments have included N fertilizer rates, use of manure, crop rotation (continuous corn, corn-soybean, alfalfa-corn, and tillage (chisel plow-disk, no-till. The leachate data were used to evaluate a number of nitrate leaching models. Some of the highlights of the 11 years of results include the following: 1 growing corn without organic N inputs at the economic optimum N rate (EON resulted in NO3–-N concentrations of 15 to 20 mg l-1 in leachate; 2 use of manure or previous alfalfa crop as partial source of N also resulted in 15 to 20 mg l-1 of NO3–-N in leachate below corn at EON; 3 NO3–-N concentration in leachate below alfalfa was approximately 4 mg l-1; 4 NO3–-N concentration in leachate below soybeans following corn was influenced by fertilizer N rate applied to corn; 5 the mass of NO3–-N leached below corn at the EON rate averaged 90 kg N ha-1 (approx. 40% of fertilizer N applied at EON; 6 wick lysimeters collected approximately 100% of leachate vs. 40–50% collected by pan lysimeters. Coefficients of variation of the collected leachate volumes for both lysimeter types were similar; 7 tillage did not markedly affect nitrate leaching losses; 8 tested leaching models could accurately predict leachate volumes and could be calibrated to match nitrate leaching losses in calibration years, but only one model (SOILN accurately predicted nitrate leaching losses in the majority of validation treatment years. Apparent problems with tested models: there was difficulty estimating sizes of organic N pools and their transformation rates, and the models either did not include a macropore flow component or did not handle macropore flow well.
19. Effects of remedial measures on long term transfer of radiocaesium from soil to agricultural products as calculated from Swedish field experimental data
International Nuclear Information System (INIS)
Loensjoe, H.; Rosen, K.; Haak, E.
1990-01-01
Extensive studies on the transfer of radiocaesium from soil to agricultural products under long term field conditions have been performed in Sweden since 1961. Effects of various remedial measures to be taken after farm land contamination have been studied in long term microplot experiments, in ploughing experiments and in conventional field experiments in Chernobyl fallout areas. Furthermore, the transfer of radiocaesium in various farm ecosystems, as influenced by farm management practices and the line of production applied, has been calculated. Fertilization with potassium has been found to effectively reduce the transfer of radiocaesium from the soil to various crops. The best effects were found on peat and sandy soils in the Chernobyl fallout areas, where a reduction by a factor of 2-5 or more has been recorded. Also, on clay soils heavy K application was found to depress the Cs transfer appreciably. Placement of the nuclide below the normal ploughing depth reduced the Cs transfer by a factor of 2-3 as compared with the effect of a homogeneous distribution in the plough layer. With a combination of deep placement and K fertilization a reduction by a factor of 10 or more has been obtained. It seems possible to reduce the caesium transfer from soil to food by a factor of 5-10 by changing the line of production on a farm in various ways. (author). 12 refs, 5 tabs
20. Impact of agronomy practices on the effects of reduced tillage systems on CH4 and N2O emissions from agricultural fields: A global meta-analysis.
Science.gov (United States)
Feng, Jinfei; Li, Fengbo; Zhou, Xiyue; Xu, Chunchun; Ji, Long; Chen, Zhongdu; Fang, Fuping
2018-01-01
The effect of no- and reduced tillage (NT/RT) on greenhouse gas (GHG) emission was highly variable and may depend on other agronomy practices. However, how the other practices affect the effect of NT/RT on GHG emission remains elusive. Therefore, we conducted a global meta-analysis (including 49 papers with 196 comparisons) to assess the effect of five options (i.e. cropping system, crop residue management, split application of N fertilizer, irrigation, and tillage duration) on the effect of NT/RT on CH4 and N2O emissions from agricultural fields. The results showed that NT/RT significantly mitigated the overall global warming potential (GWP) of CH4 and N2O emissions by 6.6% as compared with conventional tillage (CT). Rotation cropping systems and crop straw remove facilitated no-tillage (NT) to reduce the CH4, N2O, or overall GWP both in upland and paddy field. NT significantly mitigated the overall GWP when the percentage of basal N fertilizer (PBN) >50%, when tillage duration > 10 years or rainfed in upland, while when PBN agronomy practices and land use type.
1. The agricultural impact of pesticides on Physalaemus cuvieri tadpoles (Amphibia: Anura ascertained by comet assay
Directory of Open Access Journals (Sweden)
Macks W. Gonçalves
2017-10-01
Full Text Available ABSTRACT Amphibians inhabiting agricultural areas are constantly exposed to large amounts of chemicals, which reach the aquatic environment during the rainy season through runoff, drainage, and leaching. We performed a comet assay on the erythrocytes of tadpoles found in the surroundings of agricultural fields (soybean and corn crops, where there is an intense release of several kinds of pesticides in different quantities. We aimed to detect differences in the genotoxic parameters between populations collected from soybeans and cornfields, and between them and tadpoles sampled from non-agricultural areas (control group. Tadpoles collected from ponds located at soybean fields had significantly more DNA damage, followed by tadpoles collected from cornfields. In contrast, animals sampled from non-agricultural areas had the lowest incidence of DNA damage. In addition, we found a negative correlation between the parameters of the comet assay and the area of the ponds surrounding soybean. This correlation indicates a possible dilution effect in the concentration of pesticides. Finally, Physalaemus cuvieri Fitzinger, 1826 seems to be a good bioindicator for detecting the genotoxic effects of field agricultural insecticides; therefore, we suggest that this species should be used in environmental biomonitoring studies, since it is common and abundant where it occurs.
2. Chemical and isotopic characteristics of rainwater at Los Humeros geothermal field, Puebla, Mexico and surrounding areas; Caracteristicas quimicas e isotopicas del agua de lluvia en el campo geotermico de Los Humeros, Puebla, Mexico y zonas aledanas
Energy Technology Data Exchange (ETDEWEB)
Tovar Aguado, Rigoberto; Cruz Grajales, Irma [Comision Federal de Electricidad, Los Humeros, Puebla (Mexico)
2000-12-01
A study of chemical and isotopic characteristics of rainwater at Los Humeros geothermal field was undertaken for the second consecutive year. Samples were collected in seven stations-two inside the field and five on the periphery. In 1996, a total of 99 samples were collected and 104 were collected in 1997. Of these, 19-18.26% of the total-had a negative alkalinity. The Atempan (No.5) and Campamento (No.1) stations showed the highest number of anomalous samples (31.25 and 27.8%, respectively). Anomalous samples in Perote station were not observed a result that we attribute to the predominant wind direction. The results for the Campamento station are attributed to the thermal inversion phenomena occurring when the samples with negative alkalinity were obtained. Concentrations of cations in some samples were relatively high, with the maximum concentration of calcium in the Los Humeros station (79.7 ppm) . Other significantly high values were found in the Texcal station (34.8 ppm) and Perote (33.8 ppm) due to the presence of dust particles scattered in the air and because of the lack of pavement where the sampling stations are located. Another factor affecting these figures could be the presence of block and lime factories in the neighborhood. Although measured concentrations may seem high, reports exist with similar concentrations in nongeothermal areas. Oxygen-18 and deuterium contents were determined for each stations, mixing anomalous samples. The results show that the most enriched samples correspond to the San Juan Xiutetelco, Puebla (No. 6) station and the minimum to the Perote Veracruz (No. 7) station. The concentration of SO{sub 4} has marine and industrial origins, with a contribution of the first source ranging between 10 and 25 percent. [Spanish] En el campo geotermico de Los Humeros, Puebla se realizo, por segundo ano consecutivo, la caracterizacion quimica e isotopica de agua de lluvia en muestras colectadas en siete estaciones, dos localizadas dentro
3. Vegetative and structural characteristics of agricultural drainages in the Mississippi Delta landscapes
International Nuclear Information System (INIS)
Bouldin, J.L.; Farris, J.L.; Moore, M.T.; Cooper, C.M.
2004-01-01
Agricultural drainage ditches in the Mississippi Alluvial Delta landscape vary from edge-of-field waterways to sizeable drainages. Ditch attributes vary with size, location and maintenance and may aid in mitigation of contaminants from agricultural fields. The goal of this study was to better understand how vegetative characteristics affect water quality in conveyance structures in the context of ditch class and surrounding land use. Characterization of 36 agricultural ditches included presence of riparian buffer strips, water depth, surrounding land use, vegetative cover, and associated aqueous physicochemical parameters. Vegetation was assessed quantitatively, obtaining stem counts in a sub-sample of ditch sites, using random quadrat method. Physical features varied with ditch size and vegetative diversity was higher in larger structures. Polygonum sp. was the dominant bed vegetation and was ubiquitous among site sizes. Macrophytes varied from aquatic to upland species, and included Leersia sp. and upland grasses (Poaceae family) in all drainage size classes. Percent cover of bed and bank varied from 0 to 100% and 70 to 100%, respectively, and highest nutrient values were measured in sites with no buffer strips. These conveyance structures and surrounding buffer zones are being ranked for their ability to reduce excess nutrients, suspended solids, and pesticides associated with runoff. - Capsule: Vegetated buffer areas provide effective mitigation for non-point source pollution from agriculture
4. Agriculture. Sector 4
International Nuclear Information System (INIS)
1994-01-01
In Lebanon, emissions of greenhouse gases from agricultural activities occur through the following processes: -enteric fermentation and manure management of the domestic livestock emits methane and nitrous oxide. -agricultural burning of crop residues is of minor importance since field burning of crop residue is not a common practice in Lebanon -agricultural soils are a source of nitrous oxide directly from the soils and from animal production, and indirectly from the nitrogen added to the soils. The following results were obtained for the inventory year 1994: 7.60955 Gg of methane, 3.01478 Gg of nitrous oxide, 0.00146 Gg of nitrogen oxides and 0.04306 Gg of carbon monoxide
5. Surrounding rock stress analysis of underground high level waste repository
International Nuclear Information System (INIS)
Liu Wengang; Wang Ju; Wang Guangdi
2006-01-01
During decay of nuclear waste, enormous energy was released, which results in temperature change of surrounding rock of depository. Thermal stress was produced because thermal expansion of rock was controlled. Internal structure of surrounding rock was damaged and strength of rock was weakened. So, variation of stress was a dynamic process with the variation of temperature. BeiShan region of Gansu province was determined to be the depository field in the future, it is essential to make research on granite in this region. In the process of experiment, basic physical parameters of granite were analyzed preliminary with MTS. Long range temperature and stress filed was simulated considering the damage effect of surrounding rock, and rules of temperature and stress was achieved. (authors)
6. Sustainable agricultural development in inland valleys
NARCIS (Netherlands)
Zwart, S.J.
2018-01-01
The inland valley in Africa are common landscapes that have favorable conditions for agricultural production. Compared to the surrounding uplands they are characterized by a relatively high and secure water availability and high soil fertility levels. Inland valleys thus have a high agricultural
7. Addressing Issues of Malnutrition in Children through Public Nutrition using Local Resources of Agriculture and Land Use: Evidence from the Field Based Evaluation Study in Uttar Pradesh
Directory of Open Access Journals (Sweden)
Nemthianngai Guite
2014-12-01
Full Text Available Introduction: Public Nutrition refers to work in the interest of the public; with the participation of the public; and with all sectors involved in society, not just the health sector, nor mainly the health sector, though for the benefit of population health and nutrition. Action outside of the health sector, particularly with regard to food systems is required, such as capacitating women in agriculture and land use for increased vegetable production. Rationale: Adopting public health approach, an evidence from a field project wherein the evaluation study was conducted by Oxfam India (a leading non-profit organization, and where the authors coordinated and documented field evidence through conducting end line evaluation study is discussed in this paper, in order to highlight the achievement of women farmers in ensuring food and nutrition security by strengthening low cost vegetable production in Shaharanpur and Pilibhit, Uttar Pradesh. Objective of the study: To assess the success and impact of measures adopted under the project in order to enhance the capacity and skills of women vegetable farmers in sustainable farming practices. Materials and Methods: Purposive Non Probability Sampling adopted to include key set of stakeholders, which includes 100 women vegetable farmers, 8 NGO and 5 government officials respectively drawn from Shahjahanpur and Pilibhit district of Uttar Pradesh. The methods which were used to gather quantitative and qualitative data for the study were: In-depth Interview, Focused Group Discussion (FGD, Case Studies. Results: Child nutrition is positively and independently associated with increased vegetable production through agriculture and land use by women in the villages. It enhanced the nutritional status of women and improved the health status of their family members as well. Conclusion: The public nutrition approach will make it possible to increase the impact of current initiatives which aim to reverse
8. Photochemistry in Power Plant and Urban Plumes over Forested and Agricultural Regions during SOS (1990s) and SENEX (2013) field intensives (Invited)
Science.gov (United States)
Trainer, M.; Frost, G. J.; Kim, S.; Ryerson, T. B.; Pollack, I. B.; Roberts, J. M.; Veres, P. R.; Flocke, F. M.; Neuman, J. A.; Nowak, J. B.; Nenes, A.; Warneke, C.; Graus, M.; Gilman, J.; Lerner, B. M.; Kuster, W.; Atlas, E. L.; Hanisco, T. F.; Wolfe, G. M.; Keutsch, F. N.; Kaiser, J.; Lee, Y.; Brock, C. A.; Middlebrook, A. M.; Liao, J.; Welti, A.; Parrish, D. D.; Fehsenfeld, F. C.; De Gouw, J. A.
2013-12-01
Extensive forested regions of the southeastern United States show high emissions of biogenic reactive hydrocarbons such as isoprene, while emissions of these compounds are typically much lower from agricultural areas. The Southern Oxidant Study (SOS) field intensives during the 1990s contributed to an improved understanding of ozone (O3) formation resulting from nitrogen oxides (NOx) emitted from urban areas and power plants in the presence and absence of the biogenic hydrocarbons. Decreases in NOx emissions from power plants and urban areas have contributed to the widespread reduction of ambient O3 over the southeastern US during the past two decades. Measurements of Volatile Organic Compounds (VOCs), NOx, and their reaction products made at successive distances downwind of emission sources during the SOS (1999) and the Southeast Nexus (SENEX, 2013) campaigns reflect the modulation of the photochemical processing of biogenic VOCs by ambient NOx concentrations. The results constrain the ambient levels of HOx radicals as a function of NOx, and they reflect the mechanisms of the coupling between anthropogenic and biogenic emissions that form species such as ozone, formaldehyde, PeroxyAcetic Nitric anhydride (PAN), nitric acid, as well as, inorganic and organic aerosols.
9. On the use of Indium ({sup 115}In) activation foils for the study of neutron radiation field surrounding a not shielded cyclotron; Sobre o uso de folhas de ativacao de Indio ({sup 115}In) para o estudo do campo de radiacao neutronica ao redor de um ciclotron nao blindado
Energy Technology Data Exchange (ETDEWEB)
Guimaraes, Adriana, E-mail: [email protected] [Centro de Desenvolvimento da Tecnologia Nuclear (CDTN/CNEN-MG), Belo Horizonte, MG (Brazil). Programa de Pos-Graduacao em Ciencia e Tecnologia das Radiacoes, Minerais e Materiais; Rodrigues, Sergio Luiz Moreira; Andrade, Ricardo Severino [Centro de Desenvolvimento da Tecnologia Nuclear (SECPRA/CDTN/CNEN-MG), Belo Horizonte, MG (Brazil). Servico de Pesquisa e Producao de Radiofarmacos; Lacerda, Marco Aurelio de Sousa [Centro de Desenvolvimento da Tecnologia Nuclear (SEPRA/CDTN/CNEN-MG), Belo Horizonte, MG (Brazil). Servico de Protecao Radiologica; Silva, Teogenes Augusto da [Centro de Desenvolvimento da Tecnologia Nuclear (SERAS/CDTN/CNEN-MG), Belo Horizonte, MG (Brazil). Servico das Radiacoes Aplicadas a Saude
2011-10-26
Use activation foils of {sup 115}In were evaluated for study of neutron radiation field surrounding a non shielded 16.5 MeV cyclotron, during the production of fluorine-18. Two foils of {sup 115}In were used which were exposed to the neutron flux of target-chamber of the GEPETtrace-8 of CDTN/CNEN, Brazil. The first foil were positioned in front of cyclotron beam, and the second one in the diametral opposed position to the beam. It was possible to distinguish for the first foil the 417 keV photo peaks, attributed to the thermal and the 417 keV neutrons attributed to the fast neutrons. On the second foil it was only distinguished the 417 keV photopeak. The results had shown that it is possible to evaluate the fast and thermal neutron fraction surrounding the cyclotron by using indium foils. However, the short half life of the {sup 115}In makes unviable the simultaneous irradiation of a great number of foils
10. Agricultural experts’ attitude towards precision agriculture: Evidence from Guilan Agricultural Organization, Northern Iran
Directory of Open Access Journals (Sweden)
2016-09-01
Full Text Available Identifying factors that influence the attitudes of agricultural experts regarding precision agriculture plays an important role in developing, promoting and establishing precision agriculture. The aim of this study was to identify factors affecting the attitudes of agricultural experts regarding the implementation of precision agriculture. A descriptive research design was employed as the research method. A research-made questionnaire was used to examine the agricultural experts’ attitude toward precision agriculture. Internal consistency was demonstrated with a coefficient alpha of 0.87, and the content and face validity of the instrument was confirmed by a panel of experts. The results show that technical, economic and accessibility factors accounted for 55% of the changes in attitudes towards precision agriculture. The findings revealed that there were no significant differences between participants in terms of gender, field of study, extension education, age, experience, organizational position and attitudes, while education levels had a significant effect on the respondent’s attitudes.
11. Religion's relationship with social boundaries surrounding gender ...
African Journals Online (AJOL)
Religion's relationship with social boundaries surrounding gender. ... is associated with segregation, marginalization and differentiation between men and women. ... are necessary in the society it should not be mistaken for gender inequality.
12. A study of the flow field surrounding interacting line fires
Science.gov (United States)
Trevor Maynard; Marko Princevac; David R. Weise
2016-01-01
The interaction of converging fires often leads to significant changes in fire behavior, including increased flame length, angle, and intensity. In this paper, the fluid mechanics of two adjacent line fires are studied both theoretically and experimentally. A simple potential flow model is used to explain the tilting of interacting flames towards each other, which...
13. Agriculture Sectors
Science.gov (United States)
The Agriculture sectors comprise establishments primarily engaged in growing crops, raising animals, and harvesting fish and other animals. Find information on compliance, enforcement and guidance on EPA laws and regulations on the NAICS 111 & 112 sectors.
14. Presentation of a Modified Boustrophedon Decomposition Algorithm for Optimal Configuration of Flat Fields to use in Path Planning Systems of Agricultural Vehicles
Directory of Open Access Journals (Sweden)
R Goudarzi
2018-03-01
Full Text Available Introduction The demand of pre-determined optimal coverage paths in agricultural environments have been increased due to the growing application of field robots and autonomous field machines. Also coverage path planning problem (CPP has been extensively studied in robotics and many algorithms have been provided in many topics, but differences and limitations in agriculture lead to several different heuristic and modified adaptive methods from robotics. In this paper, a modified and enhanced version of currently used decomposition algorithm in robotics (boustrophedon cellular decomposition has been presented as a main part of path planning systems of agricultural vehicles. Developed algorithm is based on the parallelization of the edges of the polygon representing the environment to satisfy the requirements of the problem as far as possible. This idea is based on "minimum facing to the cost making condition" in turn, it is derived from encounter concept as a basis of cost making factors. Materials and Methods Generally, a line termed as a slice in boustrophedon cellular decomposition (BCD, sweeps an area in a pre-determined direction and decomposes the area only at critical points (where two segments can be extended to top and bottom of the point. Furthermore, sweep line direction does not change until the decomposition finish. To implement the BCD for parallelization method, two modifications were applied in order to provide a modified version of the boustrophedon cellular decomposition (M-BCD. In the first modification, the longest edge (base edge is targeted, and sweep line direction is set in line with the base edge direction (sweep direction is set perpendicular to the sweep line direction. Then Sweep line moves through the environment and stops at the first (nearest critical point. Next sweep direction will be the same as previous, If the length of those polygon's newly added edges, during the decomposition, are less than or equal to the
15. Identifying the characteristic of SundaParahiyangan landscape for a model of sustainable agricultural landscape
Science.gov (United States)
Dahlan, M. Z.; Nurhayati, H. S. A.; Mugnisjah, W. Q.
2017-10-01
This study was an explorative study of the various forms of traditional ecological knowledge (TEK) of Sundanese people in the context of sustainable agriculture. The qualitative method was used to identify SundaParahiyangan landscape by using Rapid Participatory Rural Appraisal throughsemi-structured interviews, focus group discussions, and field survey. The Landscape Characteristic Assessment and Community Sustainability Assessment were used to analyze the characteristic of landscape to achieve the sustainable agricultural landscape criteria proposed by US Department of Agriculture. The results revealed that the SundaParahiyangan agricultural landscape has a unique characteristic as a result of the long-term adaptation of agricultural society to theirlandscape through a learning process for generations. In general, this character was reflected in the typical of Sundanese’s agroecosystems such as forest garden, mixed garden, paddy field, and home garden. In addition, concept of kabuyutan is one of the TEKs related to understanding and utilization of landscape has been adapted on revitalizing the role of landscape surrounding the agroecosystem as the buffer zone by calculating and designating protected areas. To support the sustainability of production area, integrated practices of agroforestry with low-external-input and sustainable agriculture (LEISA) system can be applied in utilizing and managing agricultural resources.
16. Agriculture: About EPA's National Agriculture Center
Science.gov (United States)
EPA's National Agriculture Center (Ag Center), with the support of the United States Department of Agriculture, serves growers, livestock producers, other agribusinesses, and agricultural information/education providers.
17. Pharmaceutical and personal care products in tile drainage following surface spreading and injection of dewatered municipal biosolids to an agricultural field.
Science.gov (United States)
Edwards, M; Topp, E; Metcalfe, C D; Li, H; Gottschall, N; Bolton, P; Curnoe, W; Payne, M; Beck, A; Kleywegt, S; Lapen, D R
2009-07-01
Land application of municipal biosolids can be a source of environmental contamination by pharmaceutical and personal care products (PPCPs). This study examined PPCP concentrations/temporally discrete mass loads in agricultural tile drainage systems where two applications of biosolids had previously taken place. The field plots received liquid municipal biosolids (LMB) in the fall of 2005 at an application rate of approximately 93,500 L ha (-1), and a second land application was conducted using dewatered municipal biosolids (DMB) applied at a rate of approximately 8Mg dw ha (-1) in the summer of 2006 [corrected].The DMB land application treatments consisted of direct injection (DI) of the DMB beneath the soil surface at a nominal depth of approximately 0.11 m, and surface spreading (SS) plus subsequent tillage incorporation of DMB in the topsoil (approximately 0.10 m depth). The PPCPs examined included eight pharmaceuticals (acetaminophen, fluoxetine, ibuprofen, gemfibrozil, naproxen, carbamazepine, atenolol, sulfamethoxazole), the nicotine metabolite cotinine, and two antibacterial personal care products triclosan and triclocarban. Residues of naproxen, cotinine, atenolol and triclosan originating from the fall 2005 LMB application were detected in tile water nearly nine months after application (triclocarban was not measured in 2005). There were no significant differences (p>0.05) in PPCP mass loads among the two DMB land application treatments (i.e., SS vs. DI); although, average PPCP mass loads late in the study season (>100 days after application) were consistently higher for the DI treatment relative to the SS treatment. While the concentration of triclosan (approximately 14,000 ng g(-1) dw) in DMB was about twice that of triclocarban (approximately 8000 ng g(-1) dw), the average tile water concentrations for triclosan were much higher (43+/-5 ng L(-1)) than they were for triclocarban (0.73+/-0.14 ng L(-1)). Triclosan concentrations (maximum observed in 2006
18. Nanotechnology in Agriculture
Science.gov (United States)
An overview is given of the application of nanotechnology to agriculture. This is an active field of R&D, where a large number of findings and innovations have been reported. For example, in soil management, applications reported include nanofertilizers, soil binders, water retention aids, and nut...
19. Advancing agricultural greenhouse gas quantification*
Science.gov (United States)
Olander, Lydia; Wollenberg, Eva; Tubiello, Francesco; Herold, Martin
2013-03-01
Agricultural Research Service 2011), which aim to improve consistency of field measurement and data collection for soil carbon sequestration and soil nitrous oxide fluxes. Often these national-level activity data and emissions factors are the basis for regional and smaller-scale applications. Such data are used for model-based estimates of changes in GHGs at a project or regional level (Olander et al 2011). To complement national data for regional-, landscape-, or field-level applications, new data are often collected through farmer knowledge or records and field sampling. Ideally such data could be collected in a standardized manner, perhaps through some type of crowd sourcing model to improve regional—and national—level data, as well as to improve consistency of locally collected data. Data can also be collected by companies working with agricultural suppliers and in country networks, within efforts aimed at understanding firm and product (supply-chain) sustainability and risks (FAO 2009). Such data may feed into various certification processes or reporting requirements from buyers. Unfortunately, this data is likely proprietary. A new process is needed to aggregate and share private data in a way that would not be a competitive concern so such data could complement or supplement national data and add value. A number of papers in this focus issue discuss issues surrounding quantification methods and systems at large scales, global and national levels, while others explore landscape- and field-scale approaches. A few explore the intersection of top-down and bottom-up data measurement and modeling approaches. 5. The agricultural greenhouse gas quantification project and ERL focus issue Important land management decisions are often made with poor or few data, especially in developing countries. Current systems for quantifying GHG emissions are inadequate in most low-income countries, due to a lack of funding, human resources, and infrastructure. Most non-Annex 1 countries
20. Dynamic-energetic balance of agricultural tractors: active systems for the measurement of the power requirements in static tests and under field conditions
Directory of Open Access Journals (Sweden)
Daniele Pochi
2013-09-01
power take off, their combination. The system simulates such operations by applying to the tractor, by means of a system of sensors and actuators operated by feedback signals, work cycles combining force of traction, p.t.o. torque, hydraulic power, derived from data recorded during real field test with agricultural machines.
1. Explaining preferences for home surroundings and locations
DEFF Research Database (Denmark)
Andersen, Hans Skifter
2011-01-01
This article is based on a survey carried out in Denmark that asked a random sample of the population about their preferences for home surroundings and locations. It shows that the characteristics of social surroundings are very important and can be divided into three independent dimensions......: avoiding social nuisances, preferring social homogeneity and living close to one’s social network and place of origin. The study shows that most people have many detailed preferences, whereas some have very few. This confirms an earlier theory that some people are very connected to certain places...... with given characteristics and thus do not have priorities regarding home surroundings and locations. For others, mostly young people and singles, home is just a place to sleep and relax, whereas life is lived elsewhere. For this group, there are only preferences for location and there are few specific...
2. Remote sensing and GIS-based integrated analysis of land cover change in Duzce plain and its surroundings (north western Turkey).
Science.gov (United States)
Ikiel, Cercis; Ustaoglu, Beyza; Dutucu, Ayse Atalay; Kilic, Derya Evrim
2013-02-01
The aim of this study is to research natural land cover change caused by the permanent effects of human activities in Duzce plain and its surroundings, and to determine the current status of the land cover. For this purpose, two Landsat TM images were used in the study for the years 1987 and 2010. These images are analysed by using data image processing techniques in ERDAS Imagine©10.0 and ArcGIS©10.0 software. Land cover change nomenclature is classified according to the Coordination of Information on the Environment Level 2 Classification (1--urban fabric, 2--industrial, commercial and transport units, 3--heterogeneous agricultural areas, 4--forests, and 5--inland wetlands). Furthermore, the image analysis results are confirmed by the field research. According to the results, a decrease of 33.5 % was recorded in forest areas from 24,840.7 to 16,529.0 ha; an increase of 11.2 % was recorded in heterogeneous agricultural areas from 47,702.7 to 53,051.7 ha. Natural vegetation, which is the large part of land cover in the research area, has been changing rapidly because of rapid urbanisation and agricultural activities. As a result, it is concluded that significant changes have occurred on the natural land cover between the years 1987 and 2010 in the Duzce plain and its surroundings.
3. Modeling the effect of soil structure on water flow and isoproturon dynamics in an agricultural field receiving repeated urban waste compost application.
Science.gov (United States)
Filipović, Vilim; Coquet, Yves; Pot, Valérie; Houot, Sabine; Benoit, Pierre
2014-11-15
Transport processes in soils are strongly affected by heterogeneity of soil hydraulic properties. Tillage practices and compost amendments can modify soil structure and create heterogeneity at the local scale within agricultural fields. The long-term field experiment QualiAgro (INRA-Veolia partnership 1998-2013) explores the impact of heterogeneity in soil structure created by tillage practices and compost application on transport processes. A modeling study was performed to evaluate how the presence of heterogeneity due to soil tillage and compost application affects water flow and pesticide dynamics in soil during a long-term period. The study was done on a plot receiving a co-compost of green wastes and sewage sludge (SGW) applied once every 2 years since 1998. The plot was cultivated with a biannual rotation of winter wheat-maize (except 1 year of barley) and a four-furrow moldboard plow was used for tillage. In each plot, wick lysimeter outflow and TDR probe data were collected at different depths from 2004, while tensiometer measurements were also conducted during 2007/2008. Isoproturon concentration was measured in lysimeter outflow since 2004. Detailed profile description was used to locate different soil structures in the profile, which was then implemented in the HYDRUS-2D model. Four zones were identified in the plowed layer: compacted clods with no visible macropores (Δ), non-compacted soil with visible macroporosity (Γ), interfurrows created by moldboard plowing containing crop residues and applied compost (IF), and the plow pan (PP) created by plowing repeatedly to the same depth. Isoproturon retention and degradation parameters were estimated from laboratory batch sorption and incubation experiments, respectively, for each structure independently. Water retention parameters were estimated from pressure plate laboratory measurements and hydraulic conductivity parameters were obtained from field tension infiltrometer experiments. Soil hydraulic
4. Modifications of center-surround, spot detection and dot-pattern selective operators
NARCIS (Netherlands)
Petkov, Nicolai; Visser, Wicher T.
2005-01-01
This paper describes modifications of the models of center-surround and dot-pattern selective cells proposed previously. These modifications concern mainly the normalization of the difference of Gaussians (DoG) function used to model center-surround receptive fields, the normalization of
5. Agriculture applications
International Nuclear Information System (INIS)
Bastidas O, G.; Obando D, R.; Alvarez F, A.
1989-01-01
Since its beginnings, the Agricultural Area had a selected research team involved in the development of different agricultural techniques. Currently, there are two main branches engaged in the solution of agricultural problems: Soil fertility and induced mutations. Soil fertility: Within this branch, studies on soil nutrients and availability of water and light resources, have been made by using isotope methods. In the near future studies on nitrogen and potassium content in potato, rice and wheat plantations will be held. Induced mutations: The main objective of this team is to obtain through radioinduced mutations, as well as in vitro growth, improved rice and other cereal seeds to be used under hostile environmental conditions. The further goal will be to develop new genotypes straight from the mutants or by utilization of this material as breeding materials in interchange programs
6. Agricultural sector
International Nuclear Information System (INIS)
Ainul Hayati Daud; Hazmimi Kasim
2010-01-01
The applications of nuclear technology in agriculture sector cover the use of the technology at every aspects of agricultural activity, starting from the seed to harvesting as well as the management of plantations itself. In this sector, a total of 55 entities comprising 17 public agencies and 38 private companies were selected for the study. Almost all, 91 % of them are located in Peninsular Malaysia; the rest operates in Sabah and Sarawak. The findings of the study in the public agencies and private companies are presented in the next sections. (author)
7. Enhanced sources of acoustic power surrounding AR 11429
International Nuclear Information System (INIS)
Donea, Alina; Hanson, Christopher
2013-01-01
Multi-frequency power maps of the local acoustic oscillations show acoustic enhancements (''acoustic-power halos'') at high frequencies surrounding large active region. Computational seismic holography reveals a high-frequency ''acoustic-emission halo'', or ''seismic glory'' surrounding large active regions. In this study, we have applied computational seismic holography to map the seismic seismic source density surrounding AR 11429. Studies of HMI/SDO Doppler data, shows that the ''acoustic halos'' and the ''seismic glories'' are prominent at high frequencies 5–8 mHz. We investigate morphological properties of acoustic-power and acoustic emission halos around an active region to see if they are spatially correlated. Details about the local magnetic field from vectormagnetograms of AR 11429 are included. We identify a 15'' region of seismic deficit power (dark moat) shielding the white-light boundary of the active region. The size of the seismic moat is related to region of intermediate magnetic field strength. The acoustic moat is circled by the halo of enhanced seismic amplitude as well as enhanced seismic emission. Overall, the results suggest that features are related. However, if we narrow the frequency band to 5.5 – 6.5 mHz, we find that the seismic source density dominates over the local acoustic power, suggesting the existence of sources that emit more energy downward into the solar interior than upward toward the solar surface.
8. Isotopes in tropical agriculture
Energy Technology Data Exchange (ETDEWEB)
NONE
1962-04-15
Ways in which the use of radioisotopes and radiation can help to improve the agriculture of tropical Africa were discussed by a panel of experts. The panel included scientists from Africa, Europe, and the United States, most of whom had had actual experience dealing with agricultural problems in various parts of tropical Africa. The experts agreed that radioisotopes and radiation might now be employed to particular advantage in tropical Africa to improve crop nutrition and combat insect pests. Other applications discussed were in the fields of hydrology, plant breeding and food preservation
9. Isotopes in tropical agriculture
International Nuclear Information System (INIS)
1962-01-01
Ways in which the use of radioisotopes and radiation can help to improve the agriculture of tropical Africa were discussed by a panel of experts. The panel included scientists from Africa, Europe, and the United States, most of whom had had actual experience dealing with agricultural problems in various parts of tropical Africa. The experts agreed that radioisotopes and radiation might now be employed to particular advantage in tropical Africa to improve crop nutrition and combat insect pests. Other applications discussed were in the fields of hydrology, plant breeding and food preservation
10. Smart Chips for Smart Surroundings -- 4S
NARCIS (Netherlands)
Schuler, Eberhard; König, Ralf; Becker, Jürgen; Rauwerda, G.K.; van de Burgwal, M.D.; Smit, Gerardus Johannes Maria; Cardoso, João M.P.; Hübner, Michael
2011-01-01
The overall mission of the 4S project (Smart Chips for Smart Surroundings) was to define and develop efficient flexible, reconfigurable core building blocks, including the supporting tools, for future Ambient System Devices. Reconfigurability offers the needed flexibility and adaptability, it
11. Childhood Suicide and Myths Surrounding It.
Science.gov (United States)
Greene, Dorothea B.
1994-01-01
Dispels five misconceptions surrounding the suicide of children: that children under the age of six do not commit suicide; that suicide in latency years is extremely rare; that psychodynamically and developmentally true depression is not possible in childhood; that child cannot understand finality of death; and that children are cognitively and…
12. Runoff experiment and adapted SfM photogrammetry to assess rill erosion in Mediterranean agricultural fields from a holistic point of view
Science.gov (United States)
Gronz, Oliver; Rodrigo-Comino, Jesús; Seeger, Manuel
2017-04-01
In Mediterranean agricultural fields, more research is needed to quantify soil loss and to assess runoff generation caused by unsuitable land management strategies (García-Díaz et al., 2017; Keesstra et al., 2016). Nowadays, farmers are increasing the generation of rills and, consequently, enhancing several sub-processes related to soil erosion by water such as headcut retreats, piping or cracks joint to mass movements (Marzolff and Poesen, 2009; Poesen et al., 2003; Rodrigo Comino et al., 2015). This complex problem under different spatiotemporal scales hinders a reliable forecasting of its final consequences (Prasuhn, 2011; Salome et al., 2014). Several researchers pay more attention to point observations, but no to general and connected overviews of processes related to forms and the quantitative functioning of all elements. Therefore, the main goal of this study is to characterize and quantify the rill erosion generated by these degradation processes. To achieve this goal, two runoff experiments were carried out with two repetitions (dry and wet conditions) under extreme conditions (Wirtz et al., 2013, 2012, 2010): a motor driven pump discharged a water inflow up to ˜4.2 l s-1 maintained during between 4 and 6 minutes (≈1000 litres). Additionally, a 3D-captation of the rill by an adapted SfM photogrammetry was performed to assess: i) clear visible zonation of geomorphological (structural) connectivity features; ii) runoff and sediment productions close to the catchment outlet under actual conditions; iii) topsoil-subsoil interaction and crusting crucial for runoff generation; and, iv) the area with evidence of (former) high erosion intensity now stable, but with remnant. García-Díaz, A., Bienes, R., Sastre, B., Novara, A., Gristina, L., Cerdà, A., 2017. Nitrogen losses in vineyards under different types of soil groundcover. A field runoff simulator approach in central Spain. Agric. Ecosyst. Environ. 236, 256-267. doi:10.1016/j.agee.2016.12.013 Keesstra
13. Identification of β-SiC surrounded by relatable surrounding diamond ...
β-SiC is identified in the presence of a relatable surrounding diamond medium using subtle, but discernible Raman ... Change in the nature of the surrounding material structure and its .... intensity implies very low graphite content in thin film. In.
14. Emerging Agricultural Biotechnologies for Sustainable Agriculture and Food Security.
Science.gov (United States)
Anderson, Jennifer A; Gipmans, Martijn; Hurst, Susan; Layton, Raymond; Nehra, Narender; Pickett, John; Shah, Dilip M; Souza, Thiago Lívio P O; Tripathi, Leena
2016-01-20
As global populations continue to increase, agricultural productivity will be challenged to keep pace without overtaxing important environmental resources. A dynamic and integrated approach will be required to solve global food insecurity and position agriculture on a trajectory toward sustainability. Genetically modified (GM) crops enhanced through modern biotechnology represent an important set of tools that can promote sustainable agriculture and improve food security. Several emerging biotechnology approaches were discussed in a recent symposium organized at the 13th IUPAC International Congress of Pesticide Chemistry meeting in San Francisco, CA, USA. This paper summarizes the innovative research and several of the new and emerging technologies within the field of agricultural biotechnology that were presented during the symposium. This discussion highlights how agricultural biotechnology fits within the context of sustainable agriculture and improved food security and can be used in support of further development and adoption of beneficial GM crops.
15. Journal of Agricultural Extension Vol.17 (2) December, 2013 ISSN ...
African Journals Online (AJOL)
ONIKOYI
management staff (head of department agriculture) and five (5) field staff from other cadres were ..... Inadequate budget allocation to agricultural departments. 3.47*. 0.724 ... Lack of quick or immediate cash return from most agricultural projects.
16. Data mining in agriculture
CERN Document Server
Mucherino, Antonio; Pardalos, Panos M
2009-01-01
Data Mining in Agriculture represents a comprehensive effort to provide graduate students and researchers with an analytical text on data mining techniques applied to agriculture and environmental related fields. This book presents both theoretical and practical insights with a focus on presenting the context of each data mining technique rather intuitively with ample concrete examples represented graphically and with algorithms written in MATLAB®. Examples and exercises with solutions are provided at the end of each chapter to facilitate the comprehension of the material. For each data mining technique described in the book variants and improvements of the basic algorithm are also given. Also by P.J. Papajorgji and P.M. Pardalos: Advances in Modeling Agricultural Systems, 'Springer Optimization and its Applications' vol. 25, ©2009.
17. Sustainable agriculture and nitrogen reduction: an open field experiment using natural zeolitites in silty-clay reclaimed soil at Codigoro (Po River Delta, Ferrara, Italy)
Science.gov (United States)
Faccini, Barbara; Di Giuseppe, Dario; Mastrocicco, Micòl; Coltorti, Massimo; Colombani, Nicolò; Ferretti, Giacomo
2014-05-01
Following the guidelines of Nitrate and Water Framework Directives (91/676/CEE, 200/60/CE) an innovative integrated zeolitite cycle is being tested on a reclaimed clayey-silt soil in the Po Delta area (Ferrara Province, Italy), in the framework of the EU-funded ZeoLIFE project (LIFE+10 ENV/IT/000321). Natural zeolitites are pyroclastic rocks containing more than 50% of zeolites, a kind of hydrous minerals with peculiar physical and chemical properties, like high and selective cation exchange capacity (CEC), molecular adsorption and reversible dehydration. Zeolitites can trap NH4+ from solutions and release it gradually to the plant roots once they have been mixed in agricultural soils, allowing both fertilization and irrigation reduction and improvement of the yield. The fertilization reduction can result in a decrease of the nitrate content in groundwater and surface waters, ultimately leading to a mitigation of nutrient excess in the environment. Similarly, reduction of irrigation water means a minor exploitation of the water resource. The selected material used in the project is a chabazite zeolitite coming from a quarry near Sorano in Central Italy (Bolsena volcanic district). The open-field experimentation foresees two year of cultivation. A surface of about 6 ha has been divided into six parcels: three control parcels are cultivated and irrigated in traditional way; two parcels have been added with coarse-grained (ø = 3- 6 mm) natural zeolitite at different zeolitite/soil ratios (5 kg/m2 and 15 kg/m2) and one has been mixed with fine-grained (ø tests, and the ammonium enriched material is obtained by cation exchange with swine manure in a specifically conceived prototype. The environmental quality of soil and water in each parcel is monitored by periodic soil, groundwater and porewater analyses. Soil EC, temperature and volumetric water content are continuously measured with probes at different depth (5-30-50-100-150 cm). The quality of surface water is
18. Agricultural problems
International Nuclear Information System (INIS)
Bickerton, George E.
1997-01-01
Although there were not reasons to deplore against major activity release from any of the 110 industrial reactors authorized to operate in US, the nuclear incident that occurred at the Three Mile Island Plant in 1979 urged the public conscience toward the necessity of readiness to cope with events of this type. The personnel of the Emergency Planning Office functioning in the frame of US Department of Agriculture has already participated in around 600 intervention drillings on a federal, local or state scale to plan, test or asses radiological emergency plans or to intervene locally. These exercises allowed acquiring a significant experience in elaborating emergency plans, planning the drillings, working out scenarios and evaluation of the potential impact of accidents from the agricultural point of view. We have also taken part in different international drillings among which the most recent are INEX 1 and RADEX 94. We have found on these occasions that the agricultural problems are essential preoccupations in most of the cases no matter if the context is international, national, local or of state level. The paper poses problems specifically related to milk, fruits and vegetables, soils, meat and meat products. Finally the paper discusses issues like drilling planning, alarm and notification, sampling strategy, access authorizations for farmers, removing of contamination wastes. A number of social, political and economical relating problems are also mentioned
19. Making Conventional Agriculture Environmentally Friendly: Moving beyond the Glorification of Organic Agriculture and the Demonization of Conventional Agriculture
OpenAIRE
Alon Tal
2018-01-01
The article reviews the most recent research surrounding the potential role of organic agriculture in providing food for the planet. It challenges the claims of organic agriculture’s environmental superiority compared to well-managed, conventional agriculture. The relative advantages of these contrasting approaches to farming in areas such as aggregate land requirements, biodiversity/habitat loss, water quality, land degradation and climate change are considered. Legitimate concerns abo...
20. 3-D Imaging Systems for Agricultural Applications—A Review
Directory of Open Access Journals (Sweden)
Manuel Vázquez-Arellano
2016-04-01
Full Text Available Efficiency increase of resources through automation of agriculture requires more information about the production process, as well as process and machinery status. Sensors are necessary for monitoring the status and condition of production by recognizing the surrounding structures such as objects, field structures, natural or artificial markers, and obstacles. Currently, three dimensional (3-D sensors are economically affordable and technologically advanced to a great extent, so a breakthrough is already possible if enough research projects are commercialized. The aim of this review paper is to investigate the state-of-the-art of 3-D vision systems in agriculture, and the role and value that only 3-D data can have to provide information about environmental structures based on the recent progress in optical 3-D sensors. The structure of this research consists of an overview of the different optical 3-D vision techniques, based on the basic principles. Afterwards, their application in agriculture are reviewed. The main focus lays on vehicle navigation, and crop and animal husbandry. The depth dimension brought by 3-D sensors provides key information that greatly facilitates the implementation of automation and robotics in agriculture.
1. Using Pesticides: Commercial Applicator Manual, Texas. Agricultural Pest Control - Field Crop Pest Control, Fruit and Vegetable Pest Control, Weed and Brush Control.
Science.gov (United States)
Texas A and M Univ., College Station. Texas Agricultural Extension Service.
This document is designed to provide commercial pesticide applicators with practical information and regulations required by the Texas Department of Agriculture. The manual includes two major sections. The first section discusses labels and labeling, pesticides, aerial application, ground application, pesticide safety, pests and pest damage,…
2. The yield gap of major food crops in family agriculture in the tropics: Assessment and analysis through field surveys and modelling
NARCIS (Netherlands)
Affholder, F.; Poeydebat, C.; Corbeels, M.; Scopel, E.; Tittonell, P.A.
2013-01-01
Yield gaps of major food crops are wide under rainfed family agriculture in the tropics. Their magnitude and causes vary substantially across agro-ecological, demographic and market situations. Methods to assess yield gaps should cope with spatio-temporal variability of bio-physical conditions,
3. Atrazine transport within a coastal zone in Southeastern Puerto Rico: a sensitivity analysis of an agricultural field model and riparian zone management model
Science.gov (United States)
Water quality models are used to predict effects of conservation practices to mitigate the transport of herbicides to water bodies. We used two models - the Agricultural Policy/Environmental eXtender (APEX) and the Riparian Ecosystem Management Model (REMM) to predict the movement of atrazine from ...
4. High trees increase sunflower seed predation by birds in an agricultural landscape of Israel
Directory of Open Access Journals (Sweden)
Jessica eSchäckermann
2014-07-01
Full Text Available Natural habitats in agricultural landscapes promote agro-ecosystem services but little is known about negative effects (dis-services derived by natural habitats such as crop seed predation. Birds are important seed predators and use high landscape structures to perch and hide. High trees in agricultural landscapes may therefore drive seed predation. We examined if the presence, the distance and the percentages of high trees (tree height >5 m and the percentages of natural habitat surrounding sunflower fields, increased seed predation by birds in Israel. At the field scale, we assessed seed predation across a sample grid of an entire field. At the landscape scale, we assessed seed predation at the field margins and interiors of 20 sunflower fields. Seed predation was estimated as the percentage of removed seeds from sunflower heads. Distances of sample points to the closest high tree and percentage of natural habitat and of high trees in a 1km radius surrounding the fields were measured.We found that seed predation increased with decreasing distance to the closest high tree at the field and landscape scale. At the landscape scale, the percentage of high trees and natural habitat did not increase seed predation. Seed predation in the fields increased by 37 %, with a maximum seed predation of 92 %, when a high tree was available within zero to 50 m to the sunflower fields. If the closest high tree was further away, seed predation was less than 5 %. Sunflower seed predation by birds can be reduced, when avoiding sowing sunflowers within a radius of 50 m to high trees. Farmers should plan to grow crops, not sensitive to bird seed predation, closer to trees to eventually benefit from ecosystem services provided by birds, such as predation of pest insects, while avoiding these locations for growing crops sensitive to bird seed predation. Such management recommendations are directing towards sustainable agricultural landscapes.
5. Polybrominated diphenyl ethers, perfluorinated alkylated substances, and metals in tile drainage and groundwater following applications of municipal biosolids to agricultural fields.
Science.gov (United States)
Gottschall, N; Topp, E; Edwards, M; Russell, P; Payne, M; Kleywegt, S; Curnoe, W; Lapen, D R
2010-01-15
Polybrominated diphenyl ethers (PBDEs), perfluorinated alkylated substances (PFAS), and metals were monitored in tile drainage and groundwater following liquid (LMB) and dewatered municipal biosolid (DMB) applications to silty-clay loam agricultural field plots. LMB was applied (93,500 L ha(-1)) in late fall 2005 via surface spreading on un-tilled soil (SS(LMB)), and a one-pass aerator-based pre-tillage prior to surface spreading (AerWay SSD) (A). The DMB was applied (8 Mg d wha(-1)) in early summer 2006 on the same plots by injecting DMB beneath the soil surface (DI), and surface spreading on un-tilled soil (SS(DMB)). Key PBDE congeners (BDE-47, -99, -100, -153, -154, -183, -209) comprising 97% of total PBDE in LMB, had maximum tile effluent concentrations ranging from 6 to 320 ng L(-1) during application-induced tile flow. SS(LMB) application-induced tile mass loads for these PBDE congeners were significantly higher than those for control (C) plots (no LMB) (p0.05). PBDE mass loss via tile (0-2h post-application) as a percent of mass applied was approximately 0.04-0.1% and approximately 0.8-1.7% for A and SS(LMB), respectively. Total PBDE loading to soil via LMB and DMB application was 0.0018 and 0.02 kg total PBDE ha(-1)yr(-1), respectively. Total PBDE concentration in soil (0-0.2m) after both applications was 115 ng g(-1)dw, (sampled 599 days and 340 days post LMB and DMB applications respectively). Of all the PFAS compounds, only PFOS (max concentration=17 ng L(-1)) and PFOA (12 ng L(-1)) were found above detectable limits in tile drainage from the application plots. Mass loads of metals in tile for the LMB application-induced tile hydrograph event, and post-application concentrations of metals in groundwater, showed significant (pA>C for tile and SS(LMB) and A>C for groundwater for most results). Following DMB application, no significant differences in metal mass loads in tile were found between SS(DMB) and DI treatments (PBDE/PFAS were not measured). But for
6. Cholinergic enhancement reduces orientation-specific surround suppression but not visual crowding
Directory of Open Access Journals (Sweden)
Anna A. Kosovicheva
2012-09-01
Full Text Available Acetylcholine (ACh reduces the spatial spread of excitatory fMRI responses in early visual cortex and the receptive field sizes of V1 neurons. We investigated the perceptual consequences of these physiological effects of ACh with surround suppression and crowding, two tasks that involve spatial interactions between visual field locations. Surround suppression refers to the reduction in perceived stimulus contrast by a high-contrast surround stimulus. For grating stimuli, surround suppression is selective for the relative orientations of the center and surround, suggesting that it results from inhibitory interactions in early visual cortex. Crowding refers to impaired identification of a peripheral stimulus in the presence of flankers and is thought to result from excessive integration of visual features. We increased synaptic ACh levels by administering the cholinesterase inhibitor donepezil to healthy human subjects in a placebo-controlled, double-blind design. In Exp. 1, we measured surround suppression of a central grating using a contrast discrimination task with three conditions: 1 surround grating with the same orientation as the center (parallel, 2 surround orthogonal to the center, or 3 no surround. Contrast discrimination thresholds were higher in the parallel than in the orthogonal condition, demonstrating orientation-specific surround suppression (OSSS. Cholinergic enhancement reduced thresholds only in the parallel condition, thereby reducing OSSS. In Exp. 2, subjects performed a crowding task in which they reported the identity of a peripheral letter flanked by letters on either side. We measured the critical spacing between the target and flanking letters that allowed reliable identification. Cholinergic enhancement had no effect on critical spacing. Our findings suggest that ACh reduces spatial interactions in tasks involving segmentation of visual field locations but that these effects may be limited to early visual cortical
7. Impacts of Intensified Agriculture Developments on Marsh Wetlands
Directory of Open Access Journals (Sweden)
Zhaoqing Luan
2013-01-01
Full Text Available A spatiotemporal analysis on the changes in the marsh landscape in the Honghe National Nature Reserve, a Ramsar reserve, and the surrounding farms in the core area of the Sanjiang Plain during the past 30 years was conducted by integrating field survey work with remote sensing techniques. The results indicated that intensified agricultural development had transformed a unique natural marsh landscape into an agricultural landscape during the past 30 years. Ninety percent of the natural marsh wetlands have been lost, and the areas of the other natural landscapes have decreased very rapidly. Most dry farmland had been replaced by paddy fields during the progressive change of the natural landscape to a farm landscape. Attempts of current Chinese institutions in preserving natural wetlands have achieved limited success. Few marsh wetlands have remained healthy, even after the establishment of the nature reserve. Their ecological qualities have been declining in response to the increasing threats to the remaining wetland habitats. Irrigation projects play a key role in such threats. Therefore, the sustainability of the natural wetland ecosystems is being threatened by increased regional agricultural development which reduced the number of wetland ecotypes and damaged the ecological quality.
8. fields
Directory of Open Access Journals (Sweden)
2014-07-01
Full Text Available Surface irrigation, such as flood or furrow, is the predominant form of irrigation in California for agronomic crops. Compared to other irrigation methods, however, it is inefficient in terms of water use; large quantities of water, instead of being used for crop production, are lost to excess deep percolation and tail runoff. In surface-irrigated fields, irrigators commonly cut off the inflow of water when the water advance reaches a familiar or convenient location downfield, but this experience-based strategy has not been very successful in reducing the tail runoff water. Our study compared conventional cutoff practices to a retroactively applied model-based cutoff method in four commercially producing alfalfa fields in Northern California, and evaluated the model using a simple sensor system for practical application in typical alfalfa fields. These field tests illustrated that the model can be used to reduce tail runoff in typical surface-irrigated fields, and using it with a wireless sensor system saves time and labor as well as water.
9. Agricultural utilization of industrial thermal effluents
International Nuclear Information System (INIS)
Guillermin, P.; Delmas, J.; Grauby, A.
1976-01-01
An assessment is made of the utilization of thermal effluent for agricultural purpose (viz. early vegetables, cereals, trees). Heated waters are being used in field experiments on soil heating, improvement of agricultural procedures and crop yields. Thermal pollution cannot be removed yet it is reduced to acceptable limits. New prospects are open to traditional agriculture, leading towards a more competitive industrial model [fr
10. Opportunity's Surroundings on Sol 1818 (Vertical)
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this full-circle view of the rover's surroundings during the 1,818th Martian day, or sol, of Opportunity's surface mission (March 5, 2009). South is at the center; north at both ends. This view is presented as a vertical projection with geometric seam correction. North is at the top. The rover had driven 80.3 meters (263 feet) southward earlier on that sol. Tracks from the drive recede northward in this view. The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and lighter-toned bedrock.
11. Opportunity's Surroundings on Sol 1818 (Polar)
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this full-circle view of the rover's surroundings during the 1,818th Martian day, or sol, of Opportunity's surface mission (March 5, 2009). South is at the center; north at both ends. This view is presented as a polar projection with geometric seam correction. North is at the top. The rover had driven 80.3 meters (263 feet) southward earlier on that sol. Tracks from the drive recede northward in this view. The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and lighter-toned bedrock.
12. Crust Structure Data of Seas Surrounding Turkey
International Nuclear Information System (INIS)
2007-01-01
Black Sea, Aegean, Mediterranean and Marmara Sea, which surround the Turkey, have not been examined with respect to the Geological, Geophysical and other natural sciences sufficiently. In fact, it is not attach importance the Turkish seas adequately and abandoned with respect to the scientific researches. The most important reason of this situation is the lack of the education of the Marine Sciences in the Turkish Universities. In this study, it is tried to construct a crustal structure data base of the surrounding seas of the Turkey by collecting crustal structure data sets done by different authors in different times so far. The data acquired in the base are collected from different data base sources by dragging. The Moho depth in the eastern and western basin of the Black sea is 22 km and 19 km, respectively. In the Marmara Sea the Moho depth is 24 km. The moho value in the southern Aegean is 20 km, in the northern Aegean the moho depth is 30 km. on the other hand, the moho depth value in the eastern and western basin of the Mediterranean Sea are 15-20 km and 25-30 km, respectively
13. Perceived agricultural runoff impact on drinking water.
Science.gov (United States)
Crampton, Andrea; Ragusa, Angela T
2014-09-01
Agricultural runoff into surface water is a problem in Australia, as it is in arguably all agriculturally active countries. While farm practices and resource management measures are employed to reduce downstream effects, they are often either technically insufficient or practically unsustainable. Therefore, consumers may still be exposed to agrichemicals whenever they turn on the tap. For rural residents surrounded by agriculture, the link between agriculture and water quality is easy to make and thus informed decisions about water consumption are possible. Urban residents, however, are removed from agricultural activity and indeed drinking water sources. Urban and rural residents were interviewed to identify perceptions of agriculture's impact on drinking water. Rural residents thought agriculture could impact their water quality and, in many cases, actively avoided it, often preferring tank to surface water sources. Urban residents generally did not perceive agriculture to pose health risks to their drinking water. Although there are more agricultural contaminants recognised in the latest Australian Drinking Water Guidelines than previously, we argue this is insufficient to enhance consumer protection. Health authorities may better serve the public by improving their proactivity and providing communities and water utilities with the capacity to effectively monitor and address agricultural runoff.
14. Remote sensing based evapotranspiration and runoff modeling of agricultural, forest and urban flux sites in Denmark: From field to macro-scale
DEFF Research Database (Denmark)
Bøgh, E.; Poulsen, R.N.; Butts, M.
2009-01-01
representing agricultural, forest and urban land surfaces in physically based hydrological modeling makes it possible to reproduce much of the observed variability (48–73%) in stream flow (Q − Qb) when data and modeling is applied at an effective spatial resolution capable of representing land surface...... variability in eddy covariance latent heat fluxes. The “effective” spatial resolution needed to adopt local-scale model parameters for spatial-deterministic hydrological modeling was assessed using a high-spatial resolution (30 m) variogram analysis of the NDVI. The use of the NDVI variogram to evaluate land...
15. Description of relevant scenarios in the field of agricultural, environmental and climate policy and energy prices for the preliminary study on a Roadmap for the 'SuikerUnie'
International Nuclear Information System (INIS)
Plomp, A.J.
2011-11-01
In the Dutch Long Term Agreements on energy efficiency (MJA3 and MEE)the Dutch government and industry agreed to strive for a 30% energy efficiency improvement in 2020 compared to 2005. To reach more than 30%, it is not enough to optimize; instead larger process changes will be needed. An important instrument is the realization of preliminary studies and roadmaps, which are supported by the government. This memo offers an overview of relevant developments and scenarios from Agricultural, climate and environmental policy and energy prices for the Dutch sugar industry. This memo serves as input for the Preliminary study Roadmap SuikerUnie. [nl
16. Opportunity's Surroundings on Sol 1798 (Polar)
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this 180-degree view of the rover's surroundings during the 1,798th Martian day, or sol, of Opportunity's surface mission (Feb. 13, 2009). North is on top. This view is presented as a polar projection with geometric seam correction. The rover had driven 111 meters (364 feet) southward on the preceding sol. Tracks from that drive recede northward in this view. For scale, the distance between the parallel wheel tracks is about 1 meter (about 40 inches). The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and lighter-toned bedrock.
17. Opportunity's Surroundings After Sol 1820 Drive (Polar)
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this full-circle view of the rover's surroundings during the 1,820th to 1,822nd Martian days, or sols, of Opportunity's surface mission (March 7 to 9, 2009). This view is presented as a polar projection with geometric seam correction. North is at the top. The rover had driven 20.6 meters toward the northwest on Sol 1820 before beginning to take the frames in this view. Tracks from that drive recede southwestward. For scale, the distance between the parallel wheel tracks is about 1 meter (about 40 inches). The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and small exposures of lighter-toned bedrock.
18. Opportunity's Surroundings on Sol 1798 (Vertical)
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this 180-degree view of the rover's surroundings during the 1,798th Martian day, or sol, of Opportunity's surface mission (Feb. 13, 2009). North is on top. This view is presented as a vertical projection with geometric seam correction. The rover had driven 111 meters (364 feet) southward on the preceding sol. Tracks from that drive recede northward in this view. For scale, the distance between the parallel wheel tracks is about 1 meter (about 40 inches). The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and lighter-toned bedrock.
19. Opportunity's Surroundings on Sol 1687 (Vertical)
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this 360-degree view of the rover's surroundings on the 1,687th Martian day, or sol, of its surface mission (Oct. 22, 2008). Opportunity had driven 133 meters (436 feet) that sol, crossing sand ripples up to about 10 centimeters (4 inches) tall. The tracks visible in the foreground are in the east-northeast direction. Opportunity's position on Sol 1687 was about 300 meters southwest of Victoria Crater. The rover was beginning a long trek toward a much larger crater, Endeavour, about 12 kilometers (7 miles) to the southeast. This view is presented as a vertical projection with geometric seam correction.
20. Opportunity's Surroundings After Sol 1820 Drive (Vertical)
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this full-circle view of the rover's surroundings during the 1,820th to 1,822nd Martian days, or sols, of Opportunity's surface mission (March 7 to 9, 2009). This view is presented as a vertical projection with geometric seam correction. North is at the top. The rover had driven 20.6 meters toward the northwest on Sol 1820 before beginning to take the frames in this view. Tracks from that drive recede southwestward. For scale, the distance between the parallel wheel tracks is about 1 meter (about 40 inches). The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and small exposures of lighter-toned bedrock.
1. Opportunity's Surroundings on Sol 1687 (Polar)
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this 360-degree view of the rover's surroundings on the 1,687th Martian day, or sol, of its surface mission (Oct. 22, 2008). Opportunity had driven 133 meters (436 feet) that sol, crossing sand ripples up to about 10 centimeters (4 inches) tall. The tracks visible in the foreground are in the east-northeast direction. Opportunity's position on Sol 1687 was about 300 meters southwest of Victoria Crater. The rover was beginning a long trek toward a much larger crater, Endeavour, about 12 kilometers (7 miles) to the southeast. This view is presented as a polar projection with geometric seam correction.
2. Opportunity's Surroundings After Sol 1820 Drive
Science.gov (United States)
2009-01-01
NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this full-circle view of the rover's surroundings during the 1,820th to 1,822nd Martian days, or sols, of Opportunity's surface mission (March 7 to 9, 2009). South is at the center; north at both ends. The rover had driven 20.6 meters toward the northwest on Sol 1820 before beginning to take the frames in this view. Tracks from that drive recede southwestward. For scale, the distance between the parallel wheel tracks is about 1 meter (about 40 inches). The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and small exposures of lighter-toned bedrock. This view is presented as a cylindrical projection with geometric seam correction.
3. Towards Semantic Understanding of Surrounding Vehicular Maneuvers
DEFF Research Database (Denmark)
Kristoffersen, Miklas Strøm; Dueholm, Jacob Velling; Satzoda, Ravi K.
2016-01-01
This paper proposes the use of multiple low-cost visual sensors to obtain a surround view of the ego-vehicle for semantic understanding. A multi-perspective view will assist the analysis of naturalistic driving studies (NDS), by automating the task of data reduction of the observed sequences...... into events. A user-centric vision-based framework is presented using a vehicle detector and tracker in each separate perspective. Multi-perspective trajectories are estimated and analyzed to extract 14 different events, including potential dangerous behaviors such as overtakes and cut-ins. The system...... is tested on ten sequences of real-world data collected on U. S. highways. The results show the potential use of multiple low-cost visual sensors for semantic understanding around the ego-vehicle....
4. Estimation of the degree of soil P saturation from Brazilian Mehlich-1 P data and field investigations on P losses from agricultural sites in Minas Gerais.
Science.gov (United States)
Fischer, P; Pöthig, R; Gücker, B; Venohr, M
The degree of phosphorus saturation (DPS) of agricultural soils is studied worldwide for risk assessment of phosphorus (P) losses. In previous studies, DPS could be reliably estimated from water-soluble P (WSP) for European and Brazilian soils. In the present study, we correlated measured WSP and Mehlich-1 P (M1P) from soils of Minas Gerais (MG) and Pernambuco (PE) (R(2) = 0.94, n = 59) to create a DPS map from monitoring data. The resulting DPS map showed high spatial variability and low values of DPS (54 ± 22%, mean and standard deviation; n = 1,827). Measured soil DPS values amounted to 63 ± 14% and resulted in relatively low dissolved P concentrations measured in a surface runoff study in MG. However, fertilizer grains on the soil surface led to high WSP values (>30 mg/kg) indicating high risks of dissolved P losses. We suppose that small Oxisol particles with Fe and Al hydroxides sorbed most of the dissolved fertilizer P in runoff so that P was mainly exported in particulate form. In soils with lower contents of P sorption and binding partners, e.g. Entisols in PE, this effect may be less dominant. Consequently, superficial fertilizer effects have to be considered in addition to DPS in risk assessment of P losses from agricultural areas in Brazil.
5. Blooming Trees: Substructures and Surrounding Groups of Galaxy Clusters
Science.gov (United States)
Yu, Heng; Diaferio, Antonaldo; Serra, Ana Laura; Baldi, Marco
2018-06-01
We develop the Blooming Tree Algorithm, a new technique that uses spectroscopic redshift data alone to identify the substructures and the surrounding groups of galaxy clusters, along with their member galaxies. Based on the estimated binding energy of galaxy pairs, the algorithm builds a binary tree that hierarchically arranges all of the galaxies in the field of view. The algorithm searches for buds, corresponding to gravitational potential minima on the binary tree branches; for each bud, the algorithm combines the number of galaxies, their velocity dispersion, and their average pairwise distance into a parameter that discriminates between the buds that do not correspond to any substructure or group, and thus eventually die, and the buds that correspond to substructures and groups, and thus bloom into the identified structures. We test our new algorithm with a sample of 300 mock redshift surveys of clusters in different dynamical states; the clusters are extracted from a large cosmological N-body simulation of a ΛCDM model. We limit our analysis to substructures and surrounding groups identified in the simulation with mass larger than 1013 h ‑1 M ⊙. With mock redshift surveys with 200 galaxies within 6 h ‑1 Mpc from the cluster center, the technique recovers 80% of the real substructures and 60% of the surrounding groups; in 57% of the identified structures, at least 60% of the member galaxies of the substructures and groups belong to the same real structure. These results improve by roughly a factor of two the performance of the best substructure identification algorithm currently available, the σ plateau algorithm, and suggest that our Blooming Tree Algorithm can be an invaluable tool for detecting substructures of galaxy clusters and investigating their complex dynamics.
6. Experimental and theoretical basis of agricultural plant immunostimulation with regard to pathogenic fungi by magnetic field and He-Ne laser irradiation
Science.gov (United States)
Belski, Alexey I.; Chivanov, Vadym D.
1996-09-01
Spring barley, winter wheat and maize seeds were subjected to the action of He-Ne laser irradiation having a low intensity in the visible region of the spectrum (628-640 nm) in conjunction with magnetic fields. The following results were obtained: laser irradiation with magnetic fields induced activation of the natural plant defence/immune systems gave the harvest crop level increased to about 50- 300 percent; a correlation was established between the rate of the fungal pathogens growth and the stimulation of plant immunity after the seeds had been treated with laser irradiation and magnetic field.
7. Arthropods Biodiversity in Agricultural Landscapes: Effects of Land Use and Anthropization
Directory of Open Access Journals (Sweden)
Enrico Previati
2007-06-01
Full Text Available The greatest proportion of Po river plain is occupied by arable lands. Negative effects of modern intensive agriculture on biodiversity can derive from various phenomena operating at different spatial scales, from local to regional ones. If agricultural fields are subjected to periodical disturbances by farming practices, also landscape structure can influence community structure in the fields providing refugial areas or alternative trophic resources. In the same way in perennial habitats, such as strips and meadows, community structure and composition may be linked to both local factors and surrounding land use, that can influence organism persistence and dispersal mechanisms. We studied some natural and anthropized habitats in a wide agricultural area in the province of Ferrara (conventional annual and perennial fields, herbaceous strips, hedgerows and meadows to investigate relationships between arthropod community structure and both local impact factors (habitat type, management and surronding landscape structure and use. Results from uni and multivariate analysis showed a great influence on trophic and taxonomic structure of habitat type and quality.A less complex landscape had only slightly influence on trophic structure, leading to higher abundance and richness of generalist taxa. In conclusion we emphasize the importance of maintaining high-quality habitats to enhance arthopod diversity in agricultural landscapes.
8. Nitrogen turnover, crop use efficiency and soil fertility in a long-term field experiment amended with different qualities of urban and agricultural waste
DEFF Research Database (Denmark)
Gomez Muñoz, Beatriz; Magid, Jakob; Jensen, Lars Stoumann
2017-01-01
manure and deep litter) have been applied annually for 11 years (at normal and accelerated rates), were used to estimate the effects of the different qualities of organic wastes on soil fertility, N turnover and crop N availability. Soil physical fertility parameters, such as water retention and total......Organic wastes contain significant amounts of organic matter and nutrients and their recycling into agriculture can potentially contribute to closing the natural ecological cycle. The aim of this study was to evaluate the improvement in overall soil fertility and soil nitrogen (N) supply capacity...... carbon, improved with the application of organic wastes. Cattle manure, sewage sludge and composted household waste in single or accelerated rates of application increased soil total N by 13–131% compared to the mineral fertiliser NPK treatment. The highest net N mineralisation capacity was observed...
9. Self-control of insect pests: a nuclear application that is friendly to the environment in the field of combat and eradicate of agricultural pests
International Nuclear Information System (INIS)
Mansour, M.
2014-01-01
For decades, insect control methods depend primarily on insecticides, and the world consumption of insecticides is increasing by about 5% every year. Unfortunately, however, these chemicals pollute the environment, leave residues on agricultural products, and kill beneficial organisms leading to secondary pest problems and insecticide resistance. Ecological and environmental concerns have lead to new tactics in insect pest control. These tactics put more emphasis on cultural, physical and biological control methods including autocidal control where insects are used to destroy their own natural population. This article discusses the subject of autocidal control, its history, philosophy, basics, advantages, how to use it and where. It also gives an idea about its current use and future outlook. (author)
10. Status and developmental strategy of nuclear agricultural sciences in researches of eco-environmental sciences in agriculture
International Nuclear Information System (INIS)
Hua Luo; Wang Xunqing
2001-01-01
The concept, research scopes, research progress and achievement of nuclear agricultural sciences in past several decades in China, as well as the relationship between nuclear agriculture research and eco-environmental sciences were described. The disciplinary frontier, major research fields and priority developmental fields of nuclear agriculture in eco-environmental sciences was displayed. Suggestions were made to improve and strengthen nuclear agriculture research. Those provided basic source materials and consideration for application developmental strategy of nuclear agriculture in eco-environmental sciences
11. [Veterinary issues in the proceedings of the Amsterdam Agricultural Society, 1776-1832].
Science.gov (United States)
Mathijsen, A H H M
2006-01-01
The Amsterdam Agricultural Society, founded in 1776, was created by six wealthy gentlemen, well known for the important positions in society held by them. They invested the money earned through trade among others in the acquisition of land, partially newly reclaimed in the surroundings of Amsterdam. As a consequence of the expansion of the population the profitability of agriculture had increased. The merchants and regents knew how to combine business with pleasure. In the second half of the 17th and the first half of the 18th century, they have built about 500 country estates in the surroundings of Amsterdam. Besides the pleasures of country-life, the owners gained a practical interest in agriculture and animal husbandry. Missing practical knowledge in these fields themselves, they felt the moral obligation to contribute to the general welfare of the society by the promotion of new ideas or experiences gained by others. In the first volume of the Proceedings is stated: 'It is beyond question that chemistry, botany, meteorology and the Ars veterinaria are to be considered as the true fundaments of agricultural knowledge'. Inspired by the ideas of the Enlightenment and, quite in conformity with the spirit of the time, the establishment of a society was thought to be the answer in order to bring agricultural and thus economical reform. The method used was copied from the learned societies. The members proposed subjects for prize competitions and judged the answers sent in. The crowned answers were the main, but not the only, contents of the Society's Proceedings. The paper analyses the membership (the number of ordinary members decreased from 70 at the start to 56; that of honorary members was stable at about 20; further there were a few orrespondents), and quantifies the distribution of articles in the Proceedings, devoted respectively to agricultural, veterinary and zootechnical subjects. In addition, a detailed list with commentary, of the veterinary and
12. Effects of Agricultural Management Policies on the Exposure of Black-Winged Stilts (Himantopus himantopus Chicks to Cholinesterase-Inhibiting Pesticides in Rice Fields.
Directory of Open Access Journals (Sweden)
Gregorio M Toral
Full Text Available Levels of exposure to pesticides in rice fields can be significant depending on the environmental policies practiced. The aim of European Union integrated management policy is to reduce pesticide use and impact on environment. Rice fields provide an alternative breeding habitat for many waterbirds that are exposed to the pesticides used and therefore can be valuable indicators of their risk for wildlife. To evaluate integrated management success we examined exposure of Black-winged Stilts (Himantopus himantopus to cholinesterase-inhibiting pesticides in rice fields under different types of management by measuring plasma cholinesterase activity. Cholinesterase activity was lower in birds sampled in (a 2008 after a period of intense pesticide application, than in (b 2005-2007 and 2011 in rice fields subject to integrated management in Doñana (SW Spain and (c in control natural wetlands in Spain and Morocco. During 2009 and 2010, cholinesterase activity was lower in rice fields in Doñana than in rice fields in Larache and Sidi Allal Tazi (NW Morocco. Our results suggest that integrated management successfully reduced the exposure of Black-winged Stilts to pesticides in most of the years. Care should be taken to implement mosquito and pest crop controls on time and with environmentally friendly products in order to reduce its impact on wildlife.
13. Cytoplasmic movement profiles of mouse surrounding nucleolus and not-surrounding nucleolus antral oocytes during meiotic resumption.
Science.gov (United States)
Bui, Thi Thu Hien; Belli, Martina; Fassina, Lorenzo; Vigone, Giulia; Merico, Valeria; Garagna, Silvia; Zuccotti, Maurizio
2017-05-01
Full-grown mouse antral oocytes are classified as surrounding nucleolus (SN) or not-surrounding nucleolus (NSN), depending on the respective presence or absence of a ring of Hoechst-positive chromatin surrounding the nucleolus. In culture, both types of oocytes resume meiosis and reach the metaphase II (MII) stage, but following insemination, NSN oocytes arrest at the two-cell stage whereas SN oocytes may develop to term. By coupling time-lapse bright-field microscopy with image analysis based on particle image velocimetry, we provide the first systematic measure of the changes to the cytoplasmic movement velocity (CMV) occurring during the germinal vesicle-to-MII (GV-to-MII) transition of these two types of oocytes. Compared to SN oocytes, NSN oocytes display a delayed GV-to-MII transition, which can be mostly explained by retarded germinal vesicle break down and first polar body extrusion. SN and NSN oocytes also exhibit significantly different CMV profiles at four main time-lapse intervals, although this difference was not predictive of SN or NSN oocyte origin because of the high variability in CMV. When CMV profile was analyzed through a trained artificial neural network, however, each single SN or NSN oocyte was blindly identified with a probability of 92.2% and 88.7%, respectively. Thus, the CMV profile recorded during meiotic resumption may be exploited as a cytological signature for the non-invasive assessment of the oocyte developmental potential, and could be informative for the analysis of the GV-to-MII transition of oocytes of other species. © 2017 Wiley Periodicals, Inc.
14. Results of an experimental campaign of monitoring of agricultural practice of field combustion of rice straw; Risultati di una campagna sperimentale di monitoraggio della pratica di combustione allaperto della paglia di riso
Energy Technology Data Exchange (ETDEWEB)
Spezzano, P.; Cerea, E.; Massironi, L.; Nocente, M.; Olivetta, A. [ENEA, Centro Ricerche Saluggia, Vercelli (Italy). Dipt. Ambiente; Castellani, C. M.; De Zaiacomo, T. [ENEA, centro Ricerche Ezio Clementel`, Bologna (Italy). Dipt. Ambiente
1997-09-01
For the evaluation of environmental impact of agricultural practice of field combustion of rice straw following harvest an experimental campaign was performed in a field situated near Rive Vercellese (Vercelli, Italy) by burning the amount of rice straw in a 1.2 hectare piece of ground. Four sampling positions were operated, each one composed of a miniaturized impactor and a battery-powered pump, and an optical monitor was also used to measure aerosuspended aerosol concentration continuously. Experimental results show that after field combustion, resulting ash is depleted in cadmium, copper, lead and zinc while manganese and silica remaining almost quantitatively in the ash. Manganese and silica were the only components attributable to field combustion of rice straw in the atmospheric aerosol collected during this monitoring survey. Aerosuspended mass concentration values obtained by means of both optical measurements and gravimetric determinations are presented. Aerosol granulometric distribution, measured in the vicinity of the experimental field and the parameter values of the log-normal distribution obtained with experimental data are also indicated. Finally, a comparison is made between aerosol granulometric data and respirable fraction as defined by international standards.
15. Opportunity's Surroundings on Sol 1798 (Stereo)
Science.gov (United States)
2009-01-01
[figure removed for brevity, see original site] Left-eye view of a color stereo pair for PIA11850 [figure removed for brevity, see original site] Right-eye view of a color stereo pair for PIA11850 NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this stereo 180-degree view of the rover's surroundings during the 1,798th Martian day, or sol, of Opportunity's surface mission (Feb. 13, 2009). North is on top. This view combines images from the left-eye and right-eye sides of the navigation camera. It appears three-dimensional when viewed through red-blue glasses with the red lens on the left. The rover had driven 111 meters (364 feet) southward on the preceding sol. Tracks from that drive recede northward in this view. For scale, the distance between the parallel wheel tracks is about 1 meter (about 40 inches). The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and lighter-toned bedrock. This view is presented as a cylindrical-perspective projection with geometric seam correction.
16. Opportunity's Surroundings on Sol 1818 (Stereo)
Science.gov (United States)
2009-01-01
[figure removed for brevity, see original site] Left-eye view of a color stereo pair for PIA11846 [figure removed for brevity, see original site] Right-eye view of a color stereo pair for PIA11846 NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this full-circle view of the rover's surroundings during the 1,818th Martian day, or sol, of Opportunity's surface mission (March 5, 2009). South is at the center; north at both ends. This view combines images from the left-eye and right-eye sides of the navigation camera. It appears three-dimensional when viewed through red-blue glasses with the red lens on the left. The rover had driven 80.3 meters (263 feet) southward earlier on that sol. Tracks from the drive recede northward in this view. The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and lighter-toned bedrock. This view is presented as a cylindrical-perspective projection with geometric seam correction.
17. Opportunity's Surroundings on Sol 1687 (Stereo)
Science.gov (United States)
2009-01-01
[figure removed for brevity, see original site] Left-eye view of a color stereo pair for PIA11739 [figure removed for brevity, see original site] Right-eye view of a color stereo pair for PIA11739 NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this stereo, 360-degree view of the rover's surroundings on the 1,687th Martian day, or sol, of its surface mission (Oct. 22, 2008). The view appears three-dimensional when viewed through red-blue glasses. Opportunity had driven 133 meters (436 feet) that sol, crossing sand ripples up to about 10 centimeters (4 inches) tall. The tracks visible in the foreground are in the east-northeast direction. Opportunity's position on Sol 1687 was about 300 meters southwest of Victoria Crater. The rover was beginning a long trek toward a much larger crater, Endeavour, about 12 kilometers (7 miles) to the southeast. This panorama combines right-eye and left-eye views presented as cylindrical-perspective projections with geometric seam correction.
18. Opportunity's Surroundings After Sol 1820 Drive (Stereo)
Science.gov (United States)
2009-01-01
[figure removed for brevity, see original site] Left-eye view of a color stereo pair for PIA11841 [figure removed for brevity, see original site] Right-eye view of a color stereo pair for PIA11841 NASA's Mars Exploration Rover Opportunity used its navigation camera to take the images combined into this full-circle view of the rover's surroundings during the 1,820th to 1,822nd Martian days, or sols, of Opportunity's surface mission (March 7 to 9, 2009). This view combines images from the left-eye and right-eye sides of the navigation camera. It appears three-dimensional when viewed through red-blue glasses with the red lens on the left. The rover had driven 20.6 meters toward the northwest on Sol 1820 before beginning to take the frames in this view. Tracks from that drive recede southwestward. For scale, the distance between the parallel wheel tracks is about 1 meter (about 40 inches). The terrain in this portion of Mars' Meridiani Planum region includes dark-toned sand ripples and small exposures of lighter-toned bedrock. This view is presented as a cylindrical-perspective projection with geometric seam correction.
19. The lithosphere-asthenosphere: Italy and surroundings
International Nuclear Information System (INIS)
Panza, G.F.; Aoudia, A.; Pontevivo, A.; Chimera, G.; Raykova, R.
2003-02-01
The velocity-depth distribution of the lithosphere-asthenosphere in the Italian region and surroundings is imaged, with a lateral resolution of about 100 km, by surface wave velocity tomography and non-linear inversion. Maps of the Moho depth, of the thickness of the lithosphere and of the shear-wave velocities, down to depths of 200 km and more, are constructed. A mantle wedge, identified in the uppermost mantle along the Apennines and the Calabrian Arc, underlies the principal recent volcanoes, and partial melting can be relevant in this part of the uppermost mantle. In Calabria a lithospheric doubling is seen, in connection with the subduction of the Ionian lithosphere. The asthenosphere is shallow in the Southern Tyrrhenian Sea. High velocity bodies, cutting the asthenosphere, outline the Adria-lonian subduction in the Tyrrhenian Sea and the deep-reaching lithospheric root in the Western Alps. Less deep lithospheric roots are seen in the Central Apennines. The lithosphere-asthenosphere properties delineate a differentiation between the northern and the southern sectors of the Adriatic Sea, likely attesting the fragmentation of Adria. (author)
20. The lithosphere-asthenosphere Italy and surroundings
CERN Document Server
Panza, G F; Chimera, G; Pontevivo, A; Raykova, R
2003-01-01
The velocity-depth distribution of the lithosphere-asthenosphere in the Italian region and surroundings is imaged, with a lateral resolution of about 100 km, by surface wave velocity tomography and non-linear inversion. Maps of the Moho depth, of the thickness of the lithosphere and of the shear-wave velocities, down to depths of 200 km and more, are constructed. A mantle wedge, identified in the uppermost mantle along the Apennines and the Calabrian Arc, underlies the principal recent volcanoes, and partial melting can be relevant in this part of the uppermost mantle. In Calabria a lithospheric doubling is seen, in connection with the subduction of the Ionian lithosphere. The asthenosphere is shallow in the Southern Tyrrhenian Sea. High velocity bodies, cutting the asthenosphere, outline the Adria-lonian subduction in the Tyrrhenian Sea and the deep-reaching lithospheric root in the Western Alps. Less deep lithospheric roots are seen in the Central Apennines. The lithosphere-asthenosphere properties delineat...
1. Attitudes of students at College of Food and Agricultural Sciences toward agriculture
Directory of Open Access Journals (Sweden)
Mohammed Saleh Shenaifi
2013-06-01
Full Text Available The primary purpose of the study was to determine the attitudes of students at the College of Agriculture toward agriculture programs and the field of agriculture in an effort to better identify, recruit, and retain students in the College of Agriculture. The population of the study was 110 students from the College of Agriculture freshmen enrolling in course 203 Ag. ext. Communication skills in 2009 and 60 students who transferred from the College of Agriculture to another College. Questionnaire was reviewed for content and face validity by a panel of experts from the department of Agricultural Extension at the College of Agriculture, King Saud University. A five-point Likert-type scale was used. Cronbach’s alpha coefficient was found to be 0.89, which indicated the internal consistency of the scale. Ninety-six of the students were from cities and do not have a farm background. Many of them indicated that they were not happy in the College of Agriculture. Only 31.18% of the respondents (53 indicated that more students should be encouraged to enroll in the College of Agriculture, whereas nearly 69 disagreed or were uncertain. The attitudes of students toward the field of Agriculture were positive. Seventy-one of respondents viewed Agriculture as a scientific area of study, nearly 66% of respondents viewed the field of Agriculture as a blend of scientific principles and agricultural practices. Significant differences at the level of 0.01 were detected, in means of students who had been enrolled in Agricultural program and those students who had not. Students who had enrolled in Agriculture program displayed different attitudes toward the field of Agriculture than did students who were in non-Agriculture program. Generally, students who were studying Agriculture programs possessed attitudes, which were supportive of Agriculture as a career field. Freshmen of the College of Agriculture viewed agriculture as being both scientific and technical. It
2. Teacher Leadership: Everyday Practices Surrounding Work- Related Stress
Directory of Open Access Journals (Sweden)
Chiweshe Nigel
2015-06-01
Full Text Available This interpretivist study contributes to our scholarly understanding of how everyday practices surrounding work-related stress in education affect teacher leadership and successful learning outcomes. Insights are drawn from our long-standing engagement in the field where we observed how teaching staff, students, and management interacted. These observations were supplemented by in-depth interviews with 20 teaching staff. Our findings reveal competing demands and practices across the individual intrapersonal environment and the work related environment. There were three key themes that emerged in answer to the core research question: 1 the role of relational practices in managing teacher burnout, 2 the role of surveillance practices in education and 3 the role of assimilating practices in education. Drawing insights from these practices, we develop a conceptual framework that will help us to see relations at work anew, and develop a deeper understanding of ‘sickies’, motivation, learning outcomes and teacher leadership opportunities in education
3. BIODYNAMIC AGRICULTURE - ECO-FRIENDLY AGRICULTURAL PRACTICE
Directory of Open Access Journals (Sweden)
Veselka Vlahova
2015-06-01
Full Text Available Biodynamic agriculture is undoubtedly the oldest organized agricultural movement in the world. It is considered as an organic agricultural farming approach and determined as the oldest organized alternative agricultural movement in the world. In 1924 Rudolf Steiner – an Austrian natural scientist and philosopher, carried out a series of eight lectures in Koberwitz, currently Kobierzyce- Poland, where he formulated his visions on changes in agriculture and revealed his spiritual and scientific concepts about the connection between nature and agriculture by determining the important role of agriculture for the future of humanity and thus he became known as “the father of anthroposophy”. The great ecological effect of the application of the biodynamic agriculture is expressed in soil preservation and preservation of the living organisms in the soil, as well as maintenance of the natural balance in the vegetable and animal kingdom.
4. Understanding community norms surrounding tobacco sales.
Directory of Open Access Journals (Sweden)
Patricia A McDaniel
Full Text Available In the US, denormalizing tobacco use is key to tobacco control; less attention has been paid to denormalizing tobacco sales. However, some localities have placed limits on the number and type of retailers who may sell tobacco, and some retailers have abandoned tobacco sales voluntarily. Understanding community norms surrounding tobacco sales may help accelerate tobacco denormalization.We conducted 15 focus groups with customers of California, New York, and Ohio retailers who had voluntarily discontinued tobacco sales to examine normative assumptions about where cigarettes should or should not be sold, voluntary decisions to discontinue tobacco sales, and government limits on such sales.Groups in all three states generally agreed that grocery stores that sold healthy products should not sell tobacco; California groups saw pharmacies similarly, while this was a minority opinion in the other two states. Convenience stores were regarded as a natural place to sell tobacco. In each state, it was regarded as normal and commendable for some stores to want to stop selling tobacco, although few participants could imagine convenience stores doing so. Views on government's role in setting limits on tobacco sales varied, with California and New York participants generally expressing support for restrictions, and Ohio participants expressing opposition. However, even those who expressed opposition did not approve of tobacco sales in all possible venues. Banning tobacco sales entirely was not yet normative.Limiting the ubiquitous availability of tobacco sales is key to ending the tobacco epidemic. Some limits on tobacco sales appear to be normative from the perspective of community members; it may be possible to shift norms further by problematizing the ubiquitous presence of cigarettes and drawing connections to other products already subject to restrictions.
5. Understanding community norms surrounding tobacco sales.
Science.gov (United States)
McDaniel, Patricia A; Malone, Ruth E
2014-01-01
In the US, denormalizing tobacco use is key to tobacco control; less attention has been paid to denormalizing tobacco sales. However, some localities have placed limits on the number and type of retailers who may sell tobacco, and some retailers have abandoned tobacco sales voluntarily. Understanding community norms surrounding tobacco sales may help accelerate tobacco denormalization. We conducted 15 focus groups with customers of California, New York, and Ohio retailers who had voluntarily discontinued tobacco sales to examine normative assumptions about where cigarettes should or should not be sold, voluntary decisions to discontinue tobacco sales, and government limits on such sales. Groups in all three states generally agreed that grocery stores that sold healthy products should not sell tobacco; California groups saw pharmacies similarly, while this was a minority opinion in the other two states. Convenience stores were regarded as a natural place to sell tobacco. In each state, it was regarded as normal and commendable for some stores to want to stop selling tobacco, although few participants could imagine convenience stores doing so. Views on government's role in setting limits on tobacco sales varied, with California and New York participants generally expressing support for restrictions, and Ohio participants expressing opposition. However, even those who expressed opposition did not approve of tobacco sales in all possible venues. Banning tobacco sales entirely was not yet normative. Limiting the ubiquitous availability of tobacco sales is key to ending the tobacco epidemic. Some limits on tobacco sales appear to be normative from the perspective of community members; it may be possible to shift norms further by problematizing the ubiquitous presence of cigarettes and drawing connections to other products already subject to restrictions.
6. Four myths surrounding U.S. biofuels
International Nuclear Information System (INIS)
Wetzstein, M.; Wetzstein, H.
2011-01-01
The rapid growth of biofuels has elicited claims and predictions concerning the current and future role of these fuels in the U.S. vehicle-fuel portfolio. These assertions are at times based on a false set of assumptions concerning the biofuel's market related to the petroleum and agricultural commodities markets, and the nonmarket consequences of our automobile driving. As an aid in clarifying these market relations, the following four biofuel myths are presented: (1) biofuels will be adopted because we will soon run out of oil, (2) biofuels will solve the major external costs associated with our automobile driving, (3) biofuels cause food price inflation (the food before fuel issue), and (4) biofuels will become a major vehicle fuel. - Highlights: → Biofuels will be adopted because we will soon run out of oil. → Biofuels will solve the major external costs associated with our automobile driving. → Biofuels cause food price inflation (the food before fuel issue). → Biofuels will become a major vehicle fuel.
7. Practices surrounding children's photos in homes
NARCIS (Netherlands)
Vyas, Dhaval; van der Veer, Gerrit C.; Nijholt, Antinus; Grassel, Guido; Chi, E.H.; Höök, K,
2012-01-01
New parents cherish photos of their children. In their homes one can observe a varied set of arrangements of their young ones' photos. We studied eight families with young children to learn about their practices related to photos. We provide preliminary results from the field study and elaborate on
8. Assessment of MODIS-EVI, MODIS-NDVI and VEGETATION-NDVI composite data using agricultural measurements: an example at corn fields in western Mexico.
Science.gov (United States)
Chen, Pei-Yu; Fedosejevs, Gunar; Tiscareño-López, Mario; Arnold, Jeffrey G
2006-08-01
Although several types of satellite data provide temporal information of the land use at no cost, digital satellite data applications for agricultural studies are limited compared to applications for forest management. This study assessed the suitability of vegetation indices derived from the TERRA-Moderate Resolution Imaging Spectroradiometer (MODIS) sensor and SPOT-VEGETATION (VGT) sensor for identifying corn growth in western Mexico. Overall, the Normalized Difference Vegetation Index (NDVI) composites from the VGT sensor based on bi-directional compositing method produced vegetation information most closely resembling actual crop conditions. The NDVI composites from the MODIS sensor exhibited saturated signals starting 30 days after planting, but corresponded to green leaf senescence in April. The temporal NDVI composites from the VGT sensor based on the maximum value method had a maximum plateau for 80 days, which masked the important crop transformation from vegetative stage to reproductive stage. The Enhanced Vegetation Index (EVI) composites from the MODIS sensor reached a maximum plateau 40 days earlier than the occurrence of maximum leaf area index (LAI) and maximum intercepted fraction of photosynthetic active radiation (fPAR) derived from in-situ measurements. The results of this study showed that the 250-m resolution MODIS data did not provide more accurate vegetation information for corn growth description than the 500-m and 1000-m resolution MODIS data.
9. Promoting Pollinating Insects in Intensive Agricultural Matrices: Field-Scale Experimental Manipulation of Hay-Meadow Mowing Regimes and Its Effects on Bees
Science.gov (United States)
Buri, Pierrick; Humbert, Jean-Yves; Arlettaz, Raphaël
2014-01-01
Bees are a key component of biodiversity as they ensure a crucial ecosystem service: pollination. This ecosystem service is nowadays threatened, because bees suffer from agricultural intensification. Yet, bees rarely benefit from the measures established to promote biodiversity in farmland, such as agri-environment schemes (AES). We experimentally tested if the spatio-temporal modification of mowing regimes within extensively managed hay meadows, a widespread AES, can promote bees. We applied a randomized block design, replicated 12 times across the Swiss lowlands, that consisted of three different mowing treatments: 1) first cut not before 15 June (conventional regime for meadows within Swiss AES); 2) first cut not before 15 June, as treatment 1 but with 15% of area left uncut serving as a refuge; 3) first cut not before 15 July. Bees were collected with pan traps, twice during the vegetation season (before and after mowing). Wild bee abundance and species richness significantly increased in meadows where uncut refuges were left, in comparison to meadows without refuges: there was both an immediate (within year) and cumulative (from one year to the following) positive effect of the uncut refuge treatment. An immediate positive effect of delayed mowing was also evidenced in both wild bees and honey bees. Conventional AES could easily accommodate such a simple management prescription that promotes farmland biodiversity and is likely to enhance pollination services. PMID:24416434
10. Promoting pollinating insects in intensive agricultural matrices: field-scale experimental manipulation of hay-meadow mowing regimes and its effects on bees.
Science.gov (United States)
Buri, Pierrick; Humbert, Jean-Yves; Arlettaz, Raphaël
2014-01-01
Bees are a key component of biodiversity as they ensure a crucial ecosystem service: pollination. This ecosystem service is nowadays threatened, because bees suffer from agricultural intensification. Yet, bees rarely benefit from the measures established to promote biodiversity in farmland, such as agri-environment schemes (AES). We experimentally tested if the spatio-temporal modification of mowing regimes within extensively managed hay meadows, a widespread AES, can promote bees. We applied a randomized block design, replicated 12 times across the Swiss lowlands, that consisted of three different mowing treatments: 1) first cut not before 15 June (conventional regime for meadows within Swiss AES); 2) first cut not before 15 June, as treatment 1 but with 15% of area left uncut serving as a refuge; 3) first cut not before 15 July. Bees were collected with pan traps, twice during the vegetation season (before and after mowing). Wild bee abundance and species richness significantly increased in meadows where uncut refuges were left, in comparison to meadows without refuges: there was both an immediate (within year) and cumulative (from one year to the following) positive effect of the uncut refuge treatment. An immediate positive effect of delayed mowing was also evidenced in both wild bees and honey bees. Conventional AES could easily accommodate such a simple management prescription that promotes farmland biodiversity and is likely to enhance pollination services.
11. Promoting pollinating insects in intensive agricultural matrices: field-scale experimental manipulation of hay-meadow mowing regimes and its effects on bees.
Directory of Open Access Journals (Sweden)
Pierrick Buri
Full Text Available Bees are a key component of biodiversity as they ensure a crucial ecosystem service: pollination. This ecosystem service is nowadays threatened, because bees suffer from agricultural intensification. Yet, bees rarely benefit from the measures established to promote biodiversity in farmland, such as agri-environment schemes (AES. We experimentally tested if the spatio-temporal modification of mowing regimes within extensively managed hay meadows, a widespread AES, can promote bees. We applied a randomized block design, replicated 12 times across the Swiss lowlands, that consisted of three different mowing treatments: 1 first cut not before 15 June (conventional regime for meadows within Swiss AES; 2 first cut not before 15 June, as treatment 1 but with 15% of area left uncut serving as a refuge; 3 first cut not before 15 July. Bees were collected with pan traps, twice during the vegetation season (before and after mowing. Wild bee abundance and species richness significantly increased in meadows where uncut refuges were left, in comparison to meadows without refuges: there was both an immediate (within year and cumulative (from one year to the following positive effect of the uncut refuge treatment. An immediate positive effect of delayed mowing was also evidenced in both wild bees and honey bees. Conventional AES could easily accommodate such a simple management prescription that promotes farmland biodiversity and is likely to enhance pollination services.
12. Danish emission inventories for agriculture
DEFF Research Database (Denmark)
Mikkelsen, Mette Hjorth; Albrektsen, Rikke; Gyldenkærne, Steen
. This report contains a description of the emissions from the agricultural sector from 1985 to 2009. Furthermore, the report includes a detailed description of methods and data used to calculate the emissions, which is based on national methodologies as well as international guidelines. For the Danish...... emissions calculations and data management an Integrated Database model for Agricultural emissions (IDA) is used. The emission from the agricultural sector includes emission of the greenhouse gases methane (CH4), nitrous oxide (N2O), ammonia (NH3), particulate matter (PM), non-methane volatile organic...... compounds (NMVOC) and other pollutants related to the field burning of agricultural residue such as NOx, CO2, CO, SO2, heavy metals, dioxin and PAH. The ammonia emission from 1985 to 2009 has decreased from 119 300 tonnes of NH3 to 73 800 tonnes NH3, corresponding to a 38 % reduction. The emission...
13. Distribution and characteristic of nitrite-dependent anaerobic methane oxidation bacteria by comparative analysis of wastewater treatment plants and agriculture fields in northern China
Directory of Open Access Journals (Sweden)
Zhen Hu
2016-12-01
Full Text Available Nitrite-dependent anaerobic methane oxidation (n-damo is a recently discovered biological process which has been arousing global attention because of its potential in minimizing greenhouse gases emissions. In this study, molecular biological techniques and potential n-damo activity batch experiments were conducted to investigate the presence and diversity of M. oxyfera bacteria in paddy field, corn field, and wastewater treatment plant (WWTP sites in northern China, as well as lab-scale n-damo enrichment culture. N-damo enrichment culture showed the highest abundance of M. oxyfera bacteria, and positive correlation was observed between potential n-damo rate and abundance of M. oxyfera bacteria. Both paddy field and corn field sites were believed to be better inoculum than WWTP for the enrichment of M. oxyfera bacteria due to their higher abundance and the diversity of M. oxyfera bacteria. Comparative analysis revealed that long biomass retention time, low NH ${}_{4}^{+}$ 4 + and high NO ${}_{2}^{-}$ 2 − content were suitable for the growth of M. oxyfera bacteria.
14. Urban Agriculture Guide
NARCIS (Netherlands)
Visser, A.J.; Jansma, J.E.; Dekking, A.J.G.; Klieverik, M.J.M.
2007-01-01
The Urban Agriculture Guide describes the experiences, learning moments, tips and tricks of those involved in the initiatives of urban agriculture and an indication is provided of what is required to develop urban agriculture further in the Netherlands
15. Agricultural SWOT analysis and wisdom agriculture design of chengdu
Science.gov (United States)
Zhang, Qian; Chen, Xiangyu; Du, Shaoming; Yin, Guowei; Yu, Feng; Liu, Guicai; Gong, Jin; Han, Fujun
2017-08-01
According to the status of agricultural information, this paper analyzed the advantages, opportunities and challenges of developing wisdom agriculture in Chengdu. By analyzed the local characteristics of Chengdu agriculture, the construction program of Chengdu wisdom agriculture was designed, which was based on the existing agricultural informatization. The positioning and development theme of Chengdu agriculture is leisure agriculture, urban agriculture and quality agriculture.
16. Integrated emergy, energy and economic evaluation of rice and vegetable production systems in alluvial paddy fields: implications for agricultural policy in China.
Science.gov (United States)
Lu, Hongfang; Bai, Yu; Ren, Hai; Campbell, Daniel E
2010-12-01
China is the largest rice producing and consuming country in the world, but rice production has given way to the production of vegetables during the past twenty years. The government has been trying to stop this land-use conversion and increase the area in rice-vegetable rotation. Important questions that must be answered to determine what strategy is best for society are, "What is the reason behind this conversion?"; "Which system is more productive and which is more sustainable?"; and "How can economic policy be used to adjust the pattern of farmland use to attain sustainable development?" To answer these questions, a combined evaluation of these agricultural production systems was done using emergy, energy and economic methods. An economic analysis clearly showed that the reason for this conversion was simply that the economic output/input ratio and the benefit density of the vegetable production system were greater than that of rice. However, both energy and emergy evaluations showed that long-term rice was the best choice for sustainable development, followed by rotation systems. The current price of rice is lower than the em-value of rice produced from the long-term rice system, but higher than that of rice produced from the rotation system. Scenario analysis showed that if the government increases the price of rice to the em-value of rice produced from the long-term rice system, US$0.4/kg, and takes the value of soil organic matter into account, the economic output/input ratios of both the rice and rotation systems will be higher than that of the vegetable system. The three methods, energy, emergy and economics, are different but complementary, each revealing a different aspect of the same system. Their combined use shows not only the reasons behind a system's current state or condition, but also the way to adjust these systems to move toward more sustainable states. Copyright © 2010 Elsevier Ltd. All rights reserved. 17. Impacts of Artificial Reefs on Surrounding Ecosystems Science.gov (United States) Manoukian, Sarine Artificial reefs are becoming a popular biological and management component in shallow water environments characterized by soft seabed, representing both important marine habitats and tools to manage coastal fisheries and resources. An artificial reef in the marine environment acts as an open system with exchange of material and energy, altering the physical and biological characteristics of the surrounding area. Reef stability will depend on the balance of scour, settlement, and burial resulting from ocean conditions over time. Because of the unstable nature of sediments, they require a detailed and systematic investigation. Acoustic systems like high-frequency multibeam sonar are efficient tools in monitoring the environmental evolution around artificial reefs, whereas water turbidity can limit visual dive and ROV inspections. A high-frequency multibeam echo sounder offers the potential of detecting fine-scale distribution of reef units, providing an unprecedented level of resolution, coverage, and spatial definition. How do artificial reefs change over time in relation to the coastal processes? How accurately does multibeam technology map different typologies of artificial modules of known size and shape? How do artificial reefs affect fish school behavior? What are the limitations of multibeam technology for investigating fish school distribution as well as spatial and temporal changes? This study addresses the above questions and presents results of a new approach for artificial reef seafloor mapping over time, based upon an integrated analysis of multibeam swath bathymetry data and geoscientific information (backscatter data analysis, SCUBA observations, physical oceanographic data, and previous findings on the geology and sedimentation processes, integrated with unpublished data) from Senigallia artificial reef, northwestern Adriatic Sea (Italy) and St. Petersburg Beach Reef, west-central Florida continental shelf. A new approach for observation of fish 18. Multi-Modal Detection and Mapping of Static and Dynamic Obstacles in Agriculture for Process Evaluation Directory of Open Access Journals (Sweden) Timo Korthals 2018-03-01 Full Text Available Today, agricultural vehicles are available that can automatically perform tasks such as weed detection and spraying, mowing, and sowing while being steered automatically. However, for such systems to be fully autonomous and self-driven, not only their specific agricultural tasks must be automated. An accurate and robust perception system automatically detecting and avoiding all obstacles must also be realized to ensure safety of humans, animals, and other surroundings. In this paper, we present a multi-modal obstacle and environment detection and recognition approach for process evaluation in agricultural fields. The proposed pipeline detects and maps static and dynamic obstacles globally, while providing process-relevant information along the traversed trajectory. Detection algorithms are introduced for a variety of sensor technologies, including range sensors (lidar and radar and cameras (stereo and thermal. Detection information is mapped globally into semantical occupancy grid maps and fused across all sensors with late fusion, resulting in accurate traversability assessment and semantical mapping of process-relevant categories (e.g., crop, ground, and obstacles. Finally, a decoding step uses a Hidden Markov model to extract relevant process-specific parameters along the trajectory of the vehicle, thus informing a potential control system of unexpected structures in the planned path. The method is evaluated on a public dataset for multi-modal obstacle detection in agricultural fields. Results show that a combination of multiple sensor modalities increases detection performance and that different fusion strategies must be applied between algorithms detecting similar and dissimilar classes. 19. Controversies Surrounding Exercise in Genetic Cardiomyopathies. Science.gov (United States) Atteya, Gourg; Lampert, Rachel 2018-04-01 Exercise and sports are an integral part of daily life for millions of Americans, with 16% of the US population older than age 15 years engaged in sports or exercise activities (Bureau of Labor statistics). The physical and psychological benefits of exercise are well-recognized. However, high-profile cases of athletes dying suddenly on the field, often due to undiagnosed genetic cardiomyopathies, raise questions about the risks and benefits of exercise for those with cardiomyopathy. Copyright © 2018 Elsevier Inc. All rights reserved. 20. What happens when crops are turned on? Simulating constitutive volatiles for tritrophic pest suppression across an agricultural landscape. Science.gov (United States) Kaplan, Ian; Lewis, Danny 2015-01-01 Herbivore-induced plant volatiles, or HIPVs, are increasingly considered as a biocontrol enhancement tool by constitutively emitting these carnivore-attracting chemicals from agricultural fields. While ample data substantiate the olfactory preference of predators for HIPVs in laboratory environments, little is understood about the consequences of 'turning crops on' in the field. To explore the ramifications for arthropod pest management, a spatially explicit predator-prey population model was constructed that simulated a crop field releasing signals to recruit natural enemies from the surrounding landscape. Field size had an overriding influence on model outcome, both isolated as a single factor and interactively shaping responses to other parameters (e.g. habituation, foraging efficiency). Predator recruitment exponentially declined with increasing field size from nearly double the baseline density in small fields (225 individuals m(-2)) to a mere 4% increase (130 individuals m(-2)) in large fields. Correspondingly, HIPVs enhanced pest consumption in small fields (ca 50% fewer prey), while generating virtually no impact in large fields. Collectively, the model suggests that reducing the perimeter/core area ratio will ultimately constrain the utility of predator retention as a pest control tactic in commercial-sized fields and illustrates potential consequences of the widespread commercialization of this technology in agriculture. © 2014 Society of Chemical Industry. 1. Vocational Agriculture Computer Handbook. Science.gov (United States) Kentucky State Dept. of Education, Frankfort. This document is a catalog of reviews of computer software suitable for use in vocational agriculture programs. The reviews were made by vocational agriculture teachers in Kentucky. The reviews cover software on the following topics: farm management, crop production, livestock production, horticulture, agricultural mechanics, general agriculture,… 2. Agro-Science Journal of Tropical Agriculture, Food, Environment ... African Journals Online (AJOL) PC USER Agro-Science Journal of Tropical Agriculture, Food, Environment and Extension. Volume 12 Number 3 ... agricultural field one could maintain a high level of soil fertility. ..... Journal of Applied Biosciences. 7: 202-206. ... International Journal of. 3. On the transition to the normal phase for superconductors surrounded by normal conductors DEFF Research Database (Denmark) Fournais, Søren; Kachmar, Ayman 2009-01-01 For a cylindrical superconductor surrounded by a normal material, we discuss transition to the normal phase of stable, locally stable and critical configurations. Associated with those phase transitions, we define critical magnetic fields and we provide a sufficient condition for which those... 4. Recoil of the pion-surrounded nucleon bag and axial form factors International Nuclear Information System (INIS) Klabucar, D.; Picek, I. 1984-03-01 A recent method of boosting the bag is extended to the pion-surrounded nucleon bag and developed for the calculation of low-energy nucleon form factors. The usefulness of the method is illustrated by the induced pseudoscalar form factor where both the inclusion of the pion field and the non-vanishing momentum transfer are necessary. (Auth.) 5. Soil Erosion and Agricultural Sustainability Science.gov (United States) Montgomery, D. R. 2009-04-01 Data drawn from a global compilation of studies support the long articulated contention that erosion rates from conventionally plowed agricultural fields greatly exceed rates of soil production, erosion under native vegetation, and long-term geological erosion. Whereas data compiled from around the world show that soil erosion under conventional agriculture exceeds both rates of soil production and geological erosion rates by up to several orders of magnitude, similar global distributions of soil production and geological erosion rates suggest an approximate balance. Net soil erosion rates in conventionally plowed fields on the order of 1 mm/yr can erode typical hillslope soil profiles over centuries to millennia, time-scales comparable to the longevity of major civilizations. Well-documented episodes of soil loss associated with agricultural activities date back to the introduction of erosive agricultural methods in regions around the world, and stratigraphic records of accelerated anthropogenic soil erosion have been recovered from lake, fluvial, and colluvial stratigraphy, as well as truncation of soil stratigraphy (such as truncated A horizons). A broad convergence in the results from studies based on various approaches employed to study ancient soil loss and rates of downstream sedimentation implies that widespread soil loss has accompanied human agricultural intensification in examples drawn from around the world. While a broad range of factors, including climate variability and society-specific social and economic contexts — such as wars or colonial relationships — all naturally influence the longevity of human societies, the ongoing loss of topsoil inferred from studies of soil erosion rates in conventional agricultural systems has obvious long-term implications for agricultural sustainability. Consequently, modern agriculture — and therefore global society — faces a fundamental question over the upcoming centuries. Can an agricultural system 6. P1-13: Color Induction from Surround Color under Interocular Suppression Directory of Open Access Journals (Sweden) Ichiro Kuriki 2012-10-01 Full Text Available The effect of surround colors on color appearance is known to subserve color constancy in humans, but how multiple mechanisms in the visual system are involved in this effect is controversial. We used an interocular-suppression technique to examine how the effect occurs at the level higher than the interaction of binocular information. A test color chip (1.7 × 1.7 deg visual angle was presented in a static surround either with continuous-flash suppression in the dominant eye (CFS condition to make the surround inperceptible or without the suppression (no-CFS condition. The surround stimulus was either a Mondrian or a uniform field of the same mean chromaticity. Stimuli were simulated OSA color chips under red, white (D65, or green illuminant color and were presented on a CRT display. Unique yellows were measured by asking the subjects to judge whether the test stimulus appeared reddish or greenish. Two sizes of the surround stimuli (widths of 1 deg and 4 deg were used. Results showed significant shifts in unique yellow even under the CFS conditions, except for the 1 deg uniform-surround condition. Under the no-CFS condition, the shifts showed remarkable difference between subjects, except for the 4 deg Mondrian-surround condition. Interestingly, trends of the shifts showed high consistency within each subject, across conditions. These results indicate that mechanisms at both higher and lower levels than the neuronal site of interocular suppression are involved, and that the color shifts follow each subject's strategy in the higher-order mechanisms when only insufficient clues are available in the surround to estimate illuminant color. 7. Agricultural crops and soil treatment impacts on the daily and seasonal dynamics of CO2 fluxes in the field agroecosystems at the Central region of Russia Science.gov (United States) Mazirov, Ilya; Vasenev, Ivan; Meshalkina, Joulia; Yaroslavtsev, Alexis; Berezovskiy, Egor; Djancharov, Turmusbek 2015-04-01 The problem of greenhouse gases' concentrations increasing becomes more and more important due to global changes issues. The main component of greenhouse gases is carbon dioxide. The researches focused on its fluxes in natural and anthropogenic modified landscapes can help in this problem solution. Our research has been done with support of the RF Government grants # 11.G34.31.0079 and # 14.120.14.4266 and of FP7 Grant # 603542 LUC4C in the representative for Central Region of Russia field agroecosystems at the Precision Farming Experimental Field of Russian Timiryazev State Agrarian University with cultivated sod podzoluvisols, barley and oats - vetch grass mix (Moscow station of the RusFluxNet). The daily and seasonal dynamics of the carbon dioxide have been studied at the ecosystem level by the Eddy covariance method (2 stations) and at the soil level by the exposition chamber method (40 chambers) with mobile infra red gas analyzer (Li-Cor 820). The primary Eddy covariance monitoring data on CO2 fluxes and water vapor have been processed by EddyPro software developed by LI-COR Biosciences. According to the two-year monitoring data the daily CO2 sink during the vegetation season is usually approximately two times higher than its emission at night. Seasonal CO2 fluxes comparative stabilization has been fixed in case the plants height around 10-12 cm and it usually persist until the wax ripeness phase. There is strong dependence between the soil CO2 emission and the air temperature with the correlation coefficient 0.86 in average (due to strong input of the soil thin top functional subhorizon), but it drops essentially at the end of the season - till 0.38. The soil moisture impact on CO2 fluxes dynamics was less, with negative correlation at the end of the season. High daily dynamics of CO2 fluxes determines the protocol requirements for seasonal soil monitoring investigation with less limitation at the end of the season. The accumulated monitoring data will be 8. Gender in crop agriculture OpenAIRE Food and Agriculture Organization; The World Bank; IFAD 2008-01-01 Metadata only record This is a module in the "Gender in Agriculture Sourcebook" published by the World Bank, UN Food and Agriculture Organization, and International Fund for Agricultural Development. This module examines the role of gender in crop agriculture as an essential component of development and poverty reduction. Gender is an integral aspect of crop agriculture because women's roles in crop production and household subsistence, as well as their knowledge of complex production syst... 9. EXPERT SYSTEMS - DEVELOPMENT OF AGRICULTURAL INSURANCE TOOL Directory of Open Access Journals (Sweden) NAN Anca-Petruţa 2013-07-01 Full Text Available Because of the fact that specialty agricultural assistance is not always available when the farmers need it, we identified expert systems as a strong instrument with an extended potential in agriculture. This started to grow in scale recently, including all socially-economic activity fields, having the role of collecting data regarding different aspects from human experts with the purpose of assisting the user in the necessary steps for solving problems, at the performance level of the expert, making his acquired knowledge and experience available. We opted for a general presentation of the expert systems as well as their necessity, because, the solution to develop the agricultural system can come from artificial intelligence by implementing the expert systems in the field of agricultural insurance, promoting existing insurance products, farmers finding options in depending on their necessities and possibilities. The objective of this article consists of collecting data about different aspects about specific areas of interest of agricultural insurance, preparing the database, a conceptual presentation of a pilot version which will become constantly richer depending on the answers received from agricultural producers, with the clearest exposure of knowledgebase possible. We can justify picking this theme with the fact that even while agricultural insurance plays a very important role in agricultural development, the registered result got from them are modest, reason why solutions need to be found in the scope of developing the agricultural sector. The importance of this consists in the proposal of an immediate viable solution to correspond with the current necessities of agricultural producers and in the proposal of an innovative solution, namely the implementation of expert system in agricultural insurance as a way of promoting insurance products. Our research, even though it treats the subject at an conceptual level, it wants to undertake an 10. Bird community in an Araucaria forest fragment in relation to changes in the surrounding landscape in Southern Brazil Directory of Open Access Journals (Sweden) Pedro Scherer-Neto 2012-12-01 Full Text Available The dynamics of the bird community in a small forest fragment was evaluated along seven years in relation to changes in the surrounding landscape. The study area is an Araucaria forest fragment in Southern Brazil (state of Paraná. The sampling period covered the years 1988 through 1994 and the mark-release-recapture method was utilized. The landscape analysis was based on Landsat TM images, and changes in exotic tree plantations, native forest, open areas (agriculture, pasture, bare soil, and abandoned field, and "capoeira"(native vegetation < 2 m were quantified. The relationship between landscape changes and changes in abundance diversity of forest birds, open-area birds, forest-edge birds, and bamboo specialists was evaluated. Richness estimates were run for each year studied. The richness recorded in the study area comprised 96 species. The richness estimates were 114, 118 and 110 species for Chao 1, Jackknife 1 and Bootstrap, respectively. The bird community varied in species richness, abundance and diversity from year to year. As for species diversity, 1991, 1993 and 1994 were significantly different from the other years. Changes in the landscape contributed to the increase in abundance and richness for the groups of forest, open-area and bamboo-specialist species. An important factor discussed was the effect of the flowering of "taquara" (Poaceae, which contributed significantly to increasing richness of bamboo seed eaters, mainly in 1992 and 1993. In general, the results showed that landscape changes affected the dynamics and structure of the bird community of this forest fragment over time, and proved to have an important role in conservation of the avian community in areas of intensive forestry and agricultural activities. 11. Use of the soil and water assessment tool to scale sediment delivery from field to watershed in an agricultural landscape with topographic depressions. Science.gov (United States) Almendinger, James E; Murphy, Marylee S; Ulrich, Jason S 2014-01-01 For two watersheds in the northern Midwest United States, we show that landscape depressions have a significant impact on watershed hydrology and sediment yields and that the Soil and Water Assessment Tool (SWAT) has appropriate features to simulate these depressions. In our SWAT models of the Willow River in Wisconsin and the Sunrise River in Minnesota, we used Pond and Wetland features to capture runoff from about 40% of the area in each watershed. These depressions trapped considerable sediment, yet further reductions in sediment yield were required for calibration and achieved by reducing the Universal Soil Loss Equation (USLE) cropping-practice (P) factor to 0.40 to 0.45. We suggest terminology to describe annual sediment yields at different conceptual spatial scales and show how SWAT output can be partitioned to extract data at each of these scales. These scales range from plot-scale yields calculated with the USLE to watershed-scale yields measured at the outlet. Intermediate scales include field, upland, pre-riverine, and riverine scales, in descending order along the conceptual flow path from plot to outlet. Sediment delivery ratios, when defined as watershed-scale yields as a percentage of plot-scale yields, ranged from 1% for the Willow watershed (717 km) to 7% for the Sunrise watershed (991 km). Sediment delivery ratios calculated from published relations based on watershed area alone were about 5 to 6%, closer to pre-riverine-scale yields in our watersheds. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc. 12. Communication and surrounding of Asco and Vandellos II nuclear power plants International Nuclear Information System (INIS) 2004-01-01 The Asco and Vandellos-II power plants have always been integrated into the regions where they are located, and they take an active part in the development of surrounding towns through quality employment provided by our facilities, social and cultural support and aid to development promoted by regional councils. Communication to media is a corporate priority defined in our strategic plant, to ensure openness, rigour and punctuality. We also attend to the visitors who want to learn more about our facilities in the visitor center, and we have agreements with agrarian institutions in the area so that students can de practical training in the farms we own for agricultural production. (Author) 13. Biology: An Important Agricultural Engineering Mechanism Science.gov (United States) Henderson, S. M. 1974-01-01 Describes the field of bioengineering with particular emphasis on agricultural engineering, and presents the results of a survey of schools that combine biology and engineering in their curricula. (JR) 14. Joint IAEA/FAO evaluation the Agency's activities in some sectors of agriculture in Sub-Saharan Africa. Based on field evaluation in Kenya, Senegal, United Republic of Tanzania and Zambia. Special evaluation review International Nuclear Information System (INIS) 1996-11-01 A desk review was completed in 1995 of the Agency's activities in the Sub-Saharan region during the previous ten years, covering soil science, irrigation and plant nutrition, plant breeding and genetics, and agricultural biochemistry. As a follow-up of the recommendations of this review, a field evaluation covering activities in Kenya, Senegal, Tanzania and Zambia, as four of the six participants in the first phase of the ongoing regional project ''Increasing Food Security in Sub-Saharan Africa'', was conducted in 1996 jointly with the FAO Programme and Budget Evaluation. Ethiopia and Niger were not included in the field evaluation. To date, total disbursement during the last ten years in the 19 projects considered in this evaluation amounted to$2.5 million, evenly distributed in the four countries, plus about \$500,000 for training funded outside the projects. Agency inputs included isotope analysers, sample preparation equipment, moisture and density gauges, labelled fertilizers, isotopes and supporting soil laboratory equipment, training of researchers and technicians and expert advice on research trials and on-the-job training on the use of laboratory equipment. Figs, tabs
15. Weather extremes could affect agriculture
Science.gov (United States)
Balcerak, Ernie
2012-05-01
As Earth's climate warms, agricultural producers will need to adapt. Changes, especially increases in extreme events, are already having an impact on food production, according to speakers at a 1 May session on agriculture and food security at the AGU Science Policy Conference. Christopher Field, director of the Department of Global Ecology at the Carnegie Institution for Science of Washington, D. C., pointed out the complex factors that come into play in understanding food security, including spatially varying controls and stresses, incomplete models, and the potential for threshold responses. Factors that are likely to cause problems include increasing population; increasing preference for meat, which needs more land and energy inputs to produce; climate change; and increasing use of agricultural lands for biomass energy.
16. How A Black Hole Lights Up Its Surroundings
Science.gov (United States)
Kohler, Susanna
2017-10-01
How do the supermassive black holes that live at the centers of galaxies influence their environments? New observations of a distant active galaxy offer clues about this interaction.Signs of CoevolutionPlot demonstrating the m-sigma relation, the empirical correlation between the stellar velocity dispersion of a galactic bulge and the mass of the supermassive black hole at its center. [Msigma]We know that the centers of active galaxies host supermassive black holes with masses of millions to billions of suns. One mystery surrounding these beasts is that they are observed to evolve simultaneously with their host galaxies for instance, an empirical relationship is seen between the growth of a black hole and the growth of its host galaxys bulge. This suggests that there must be a feedback mechanism through which the evolution of a black hole is linked to that of its host galaxy.One proposed source of this coupling is the powerful jets emitted from the poles of these supermassive black holes. These jets are thought to be produced as some of the material accreting onto the black hole is flung out, confined by surrounding gas and magnetic fields. Because the jets of hot gas and radiation extend outward through the host galaxy, they provide a means for the black hole to influence the gas and dust of its surroundings.In our current model of a radio-loud active galactic nuclei,a region of hot, ionized gas the narrow-line region lies beyond the sphere of influence of the supermassive black hole. [C.M. Urry and P. Padovani]Clues in the Narrow-Line RegionThe region of gas thought to sit just outside of the black holes sphere of influence (at a distance of perhaps a thousand to a few thousand light-years) is known as the narrow line region so named because we observe narrow emission lines from this gas. Given its hot, ionized state, this gas must somehow be being pummeled with energy. In the canonical picture, radiation from the black hole heats the gas directly in a process
17. Agricultural drainage water quality
International Nuclear Information System (INIS)
2002-01-01
'Full text:' Agricultural drainage systems have been identified as potential contributors of non-point source pollution. Two of the major concerns have been with nitrate-nitrogen (NO3 - -N) concentrations and bacteria levels exceeding the Maximum Acceptable Concentration in drainage water. Heightened public awareness of environmental issues has led to greater pressure to maintain the environmental quality of water systems. In an ongoing field study, three experiment sites, each with own soil properties and characteristics, are divided into drainage plots and being monitored for NO3 - -N and fecal coliforms contamination. The first site is being used to determine the impact of the rate of manure application on subsurface drainage water quality. The second site is being used to determine the difference between hog manure and inorganic fertilizer in relation to fecal coliforms and NO3-N leaching losses under a carrot rotation system. The third site examines the effect of timing of manure application on water quality, and is the only site equipped with a surface drainage system, as well as a subsurface drainage system. Each of the drains from these fields lead to heated outflow buildings to allow for year-round measurements of flow rates and water samples. Tipping buckets wired to data-loggers record the outflow from each outlet pipe on an hourly basis. Water samples, collected from the flowing drains, are analyzed for NO3 - -N concentrations using the colorimetric method, and fecal coliforms using the Most Probable Number (MPN) method. Based on this information, we will be able better positioned to assess agricultural impacts on water resources which will help towards the development on industry accepted farming practices. (author)
18. A nebula of gases from Io surrounding Jupiter.
Science.gov (United States)
Krimigis, Stamatios M; Mitchell, Donald G; Hamilton, Douglas C; Dandouras, Jannis; Armstrong, Thomas P; Bolton, Scott J; Cheng, Andrew F; Gloeckler, George; Hsieh, K C; Keath, Edwin P; Krupp, Norbert; Lagg, Andreas; Lanzerotti, Louis J; Livi, Stefano; Mauk, Barry H; McEntire, Richard W; Roelof, Edmond C; Wilken, Berend; Williams, Donald J
2002-02-28
Several planetary missions have reported the presence of substantial numbers of energetic ions and electrons surrounding Jupiter; relativistic electrons are observable up to several astronomical units (au) from the planet. A population of energetic (>30[?]keV) neutral particles also has been reported, but the instrumentation was not able to determine the mass or charge state of the particles, which were subsequently labelled energetic neutral atoms. Although images showing the presence of the trace element sodium were obtained, the source and identity of the neutral atoms---and their overall significance relative to the loss of charged particles from Jupiter's magnetosphere---were unknown. Here we report the discovery by the Cassini spacecraft of a fast (>103[?]km[?]s-1) and hot magnetospheric neutral wind extending more than 0.5[?]au from Jupiter, and the presence of energetic neutral atoms (both hot and cold) that have been accelerated by the electric field in the solar wind. We suggest that these atoms originate in volcanic gases from Io, undergo significant evolution through various electromagnetic interactions, escape Jupiter's magnetosphere and then populate the environment around the planet. Thus a 'nebula' is created that extends outwards over hundreds of jovian radii.
19. What can offer us reclaimed landscape surrounding future lake Medard
Energy Technology Data Exchange (ETDEWEB)
Hrajnohova-Gillarova, H.; Kazmierski, T.; Martis, M. [Czech Univ. of Life Sciences, Prague (Czech Republic); Pecharova, E. [Czech Univ. of Life Sciences, Prague (Czech Republic); South-Bohemian Univ., Ceske Budejovice (Czech Republic)
2010-07-01
Soon after closing down a mine, the landscape that had been systematically disturbed by mining, should start to serve people from neighbouring towns and villages. This study characterized the Medard site located in the western part of the Czech Republic. The future Lake Medard includes the area of the former Medard-Libik Mine. Medard was an opencast brown coal mine, where mining finished in 2000 and reclamation plans involve its flooding until the year 2013. Forestry reclamation was also in progress. This paper presented a survey that was designed to help determine what the reclaimed landscape surrounding the future Lake Medard could offer. The paper provided background information on Medard Lake and outlined the methodology and results of the study. The methodology involved use of recent orthophotomaps, a study of the future lake Medard and data from the field survey. The study examined the long-term impacts on the social and environmental situation in the area. It was concluded that, once the reclamations are finished, there should be natural trails with information and educational infrastructure so that visitors to the area can learn about the places of interest. 17 refs., 6 figs.
20. Agricultural policy schemes
DEFF Research Database (Denmark)
Hansen, Henning Otte
2016-01-01
Agricultural support is a very important element in agricultural policy in many countries. Agricultural support is basically an instrument to meet the overall objectives of the agricultural policy – objectives set by society. There are a great number of instruments and ways of intervention...... in agricultural policy and they have different functions and impacts. Market price support and deficiency payments are two very important instruments in agricultural policy; however, they belong to two different support regimes or support systems. Market price support operates in the so-called high price system...
1. HIV behavioural surveillance among refugees and surrounding host ...
African Journals Online (AJOL)
We used a standardised behavioural surveillance survey (BSS), modified to be directly relevant to populations in conflict and post-conflict settings as well as to their surrounding host populations, to survey the populations of a refugee settlement in south-western Uganda and its surrounding area. Two-stage probability ...
2. Investigation of the readout electronics of DELPHI surround muon chamber
International Nuclear Information System (INIS)
Khovanskij, N.; Krumshtejn, Z.; Ol'shevskij, A.; Sadovskij, A.; Sedykh, Yu.; Molnar, J.; Sicho, P.; Tomsa, Z.
1995-01-01
The characteristics of the readout electronics of the DELPHI surround muon chambers with various AMPLEX chips (AMPLEX 16 and AMPLEX-SICAL) are presented. This electronics is studied in a cosmic rays test of the real surround muon chamber model. 4 refs., 6 figs., 1 tab
3. Surrounding land cover types as predictors of palustrine wetland vegetation quality in conterminous USA
Science.gov (United States)
Stapanian, Martin A.; Gara, Brian; Schumacher, William
2018-01-01
The loss of wetland habitats and their often-unique biological communities is a major environmental concern. We examined vegetation data obtained from 380 wetlands sampled in a statistical survey of wetlands in the USA. Our goal was to identify which surrounding land cover types best predict two indices of vegetation quality in wetlands at the regional scale. We considered palustrine wetlands in four regions (Coastal Plains, North Central East, Interior Plains, and West) in which the dominant vegetation was emergent, forested, or scrub-shrub. For each wetland, we calculated weighted proportions of eight land cover types surrounding the area in which vegetation was assessed, in four zones radiating from the edge of the assessment area to 2 km. Using Akaike's Information Criterion, we determined the best 1-, 2- and 3-predictor models of the two indices, using the weighted proportions of the land cover types as potential predictors. Mean values of the two indices were generally higher in the North Central East and Coastal Plains than the other regions for forested and emergent wetlands. In nearly all cases, the best predictors of the indices were not the dominant surrounding land cover types. Overall, proportions of forest (positive effect) and agriculture (negative effect) surrounding the assessment area were the best predictors of the two indices. One or both of these variables were included as predictors in 65 of the 72 models supported by the data. Wetlands surrounding the assessment area had a positive effect on the indices, and ranked third (33%) among the predictors included in supported models. Development had a negative effect on the indices and was included in only 28% of supported models. These results can be used to develop regional management plans for wetlands, such as creating forest buffers around wetlands, or to conserve zones between wetlands to increase habitat connectivity.
4. Stimulus size dependence of hue changes induced by chromatic surrounds.
Science.gov (United States)
Kellner, Christian Johannes; Wachtler, Thomas
2016-03-01
A chromatic surround induces a change in the perceived hue of a stimulus. This shift in hue depends on the chromatic difference between the stimulus and the surround. We investigated how chromatic induction varies with stimulus size and whether the size dependence depends on the surround hue. Subjects performed asymmetric matching of color stimuli with different sizes in surrounds of different chromaticities. Generally, induced hue shifts decreased with increasing stimulus size. This decrease was quantitatively different for different surround hues. However, when size effects were normalized to an overall induction strength, the chromatic specificity was largely reduced. The separability of inducer chromaticity and stimulus size suggests that these effects are mediated by different neural mechanisms.
5. Priority of areas for agricultural countermeasure assessment
International Nuclear Information System (INIS)
Rochedo, E.R.R.; Barboza, A.E.; Igreja, E.; Silva, D.N.G. da; Wasserman, A.E.
2015-01-01
Within the overall preparedness related to nuclear and/or radiological accidents that lead to the release of radionuclides to the environment with the consequent contamination of agricultural areas, the priority of research for agricultural areas should then focus on the surrounding areas of nuclear power plants that have higher probability of public exposure through the ingestion pathway. The objective of this work was to create a rank order of priority of agricultural products to be considered in assessing the effects of countermeasures, based on both economic value and doses to the public. Additionally, the study describes relevant needs of radioecological studies to improve short and long-terms dose assessments. . Sixteen municipalities surrounding the Brazilian Nuclear Power Central were analyzed for a contamination with 137 Cs, considering seasonal aspects related to agricultural practices in the Southeastern Brazil. Rank order provided by considering economical aspects shows that there is a need for radioecological research for some high value products, such as palmetto and sugar cane, and the need to include in the current model more detailed description for some food items, such as eggs. Combined rank criteria shows that main product within the considered area is milk. As so, the study of countermeasures for the ingestion of milk should be prioritized. (authors)
6. APPLICATION OF CONVOLUTIONAL NEURAL NETWORK IN CLASSIFICATION OF HIGH RESOLUTION AGRICULTURAL REMOTE SENSING IMAGES
Directory of Open Access Journals (Sweden)
C. Yao
2017-09-01
Full Text Available With the rapid development of Precision Agriculture (PA promoted by high-resolution remote sensing, it makes significant sense in management and estimation of agriculture through crop classification of high-resolution remote sensing image. Due to the complex and fragmentation of the features and the surroundings in the circumstance of high-resolution, the accuracy of the traditional classification methods has not been able to meet the standard of agricultural problems. In this case, this paper proposed a classification method for high-resolution agricultural remote sensing images based on convolution neural networks(CNN. For training, a large number of training samples were produced by panchromatic images of GF-1 high-resolution satellite of China. In the experiment, through training and testing on the CNN under the toolbox of deep learning by MATLAB, the crop classification finally got the correct rate of 99.66 % after the gradual optimization of adjusting parameter during training. Through improving the accuracy of image classification and image recognition, the applications of CNN provide a reference value for the field of remote sensing in PA.
7. Organic matter composition of soil macropore surfaces under different agricultural management practices
Science.gov (United States)
Glæsner, Nadia; Leue, Marin; Magid, Jacob; Gerke, Horst H.
2016-04-01
Understanding the heterogeneous nature of soil, i.e. properties and processes occurring specifically at local scales is essential for best managing our soil resources for agricultural production. Examination of intact soil structures in order to obtain an increased understanding of how soil systems operate from small to large scale represents a large gap within soil science research. Dissolved chemicals, nutrients and particles are transported through the disturbed plow layer of agricultural soil, where after flow through the lower soil layers occur by preferential flow via macropores. Rapid movement of water through macropores limit the contact between the preferentially moving water and the surrounding soil matrix, therefore contact and exchange of solutes in the water is largely restricted to the surface area of the macropores. Organomineral complex coated surfaces control sorption and exchange properties of solutes, as well as availability of essential nutrients to plant roots and to the preferentially flowing water. DRIFT (Diffuse Reflectance infrared Fourier Transform) Mapping has been developed to examine composition of organic matter coated macropores. In this study macropore surfaces structures will be determined for organic matter composition using DRIFT from a long-term field experiment on waste application to agricultural soil (CRUCIAL, close to Copenhagen, Denmark). Parcels with 5 treatments; accelerated household waste, accelerated sewage sludge, accelerated cattle manure, NPK and unfertilized, will be examined in order to study whether agricultural management have an impact on the organic matter composition of intact structures.
8. Agriculture: Land Use
Science.gov (United States)
Land Use and agriculture. Information about land use restrictions and incentive programs.Agricultural operations sometimes involve activities regulated by laws designed to protect water supplies, threatened or endangered plants and animals, or wetlands.
9. Agricultural Health and Safety
Science.gov (United States)
... that occur while living, working, or visiting agricultural work environments (primarily farms) are considered agricultural injuries, whether or ... of Labor's Occupational Safety & Health Administration (OSHA) supports safe and healthful working conditions by setting and enforcing standards and by ...
10. Innovations in urban agriculture
NARCIS (Netherlands)
Schans, van der J.W.; Renting, Henk; Veenhuizen, Van René
2014-01-01
This issuehighlights innovations in urban agriculture. Innovation and the various forms of innovations are of particular importance because urban agriculture is adapted to specific urban challenges and opportunities. Innovation is taking place continuously, exploring the multiple fundions of urban
11. Agricultural Research Service
Science.gov (United States)
... Menu United States Department of Agriculture Agricultural Research Service Research Research Home National Programs Research Projects Scientific Manuscripts International Programs Scientific Software/Models Databases and Datasets Office of Scientific Quality ...
12. Agricultural science policy
OpenAIRE
Alston, Julian M.; Pardey, Philip G.; Taylor, Michael J.
2001-01-01
Technological advances developed through R&D have supplied the world with not only more food, but better food. This report looks at issues raised by this changing environment for agricultural productivity, agricultural R&D, and natural resource management.
13. Priority of areas for agricultural radiovulnerability mapping
Energy Technology Data Exchange (ETDEWEB)
Rochedo, Elaine R.R.; Igreja, Eduardo, E-mail: [email protected], E-mail: [email protected] [Instituto Militar de Engenharia (IME), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Wasserman, Maria Angelica V., E-mail: [email protected] [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil); Perez, Daniel V., E-mail: [email protected] [Empresa Brasileira de Pesquisa Agropecuaria (EMBRAPA), Rio de Janeiro, RJ (Brazil). Centro Nacional de Pesquisa de Solos; Rochedo, Pedro R.R., E-mail: [email protected] [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Programa de Planejamento Energetico; Silva, Diogo N.G., E-mail: [email protected] [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Instituto de Biofisica Carlos Chagas Filho
2013-07-01
The methodology for classifying areas according to soil properties for the vulnerability to a {sup 137}Cs contamination is of high importance to the preparedness related to nuclear and/or radiological accidents that lead to release of radionuclides to the environment with the consequent contamination of agricultural areas. The priority of research for agricultural areas should then focus on the surrounding areas of nuclear power plant that have higher probability of public exposure through the ingestion pathway. The objective of this work was to create a rank order for priority of areas to be mapped based on EMBRAPA database on soil properties. The 16 municipalities previously selected to define parameters for dose assessment simulations related to the Brazilian Nuclear Power Plants, located in the district of Angra dos Reis, Rio de Janeiro, have been investigated in order to create this rank order to direct the research on radio vulnerability mapping, considering their relevance to public exposure based on their agricultural productivity. The two aspects selected in this study account for the maximum loss of income and to the collective doses that can be averted due to the banning of agricultural products. These quantities are inputs to optimization analysis. The priority defined shall then guide research on both the adequate values for the transfer factors and on the agricultural countermeasures suitable to each area according to the cause(s) of their vulnerability and their typical agricultural crops. (author)
14. Priority of areas for agricultural radiovulnerability mapping
International Nuclear Information System (INIS)
Rochedo, Elaine R.R.; Igreja, Eduardo; Perez, Daniel V.; Rochedo, Pedro R.R.; Silva, Diogo N.G.
2013-01-01
The methodology for classifying areas according to soil properties for the vulnerability to a 137 Cs contamination is of high importance to the preparedness related to nuclear and/or radiological accidents that lead to release of radionuclides to the environment with the consequent contamination of agricultural areas. The priority of research for agricultural areas should then focus on the surrounding areas of nuclear power plant that have higher probability of public exposure through the ingestion pathway. The objective of this work was to create a rank order for priority of areas to be mapped based on EMBRAPA database on soil properties. The 16 municipalities previously selected to define parameters for dose assessment simulations related to the Brazilian Nuclear Power Plants, located in the district of Angra dos Reis, Rio de Janeiro, have been investigated in order to create this rank order to direct the research on radio vulnerability mapping, considering their relevance to public exposure based on their agricultural productivity. The two aspects selected in this study account for the maximum loss of income and to the collective doses that can be averted due to the banning of agricultural products. These quantities are inputs to optimization analysis. The priority defined shall then guide research on both the adequate values for the transfer factors and on the agricultural countermeasures suitable to each area according to the cause(s) of their vulnerability and their typical agricultural crops. (author)
15. Gender and agricultural markets
OpenAIRE
Food and Agriculture Organization; The World Bank; IFAD
2008-01-01
Metadata only record This is a module in the "Gender in Agriculture Sourcebook" published by the World Bank, UN Food and Agriculture Organization, and International Fund for Agricultural Development. This module examines the traditional division of labor within agricultural markets, where women farmers are primarily responsible for subsistence and household crop production while male farmers dominate the commercial sector. Challenging these gendered roles by increasing women farmers' acces...
16. The Danish technology foresight on environmentally friendly agriculture
DEFF Research Database (Denmark)
Borch, Kristian
2013-01-01
A premise that is necessary for agriculture to develop into an environmentally friendly direction is that research is undertaken into environmentally friendly technologies and methods and how they can be brought into use. There is a need for a prioritised research effort that focuses on those...... without any plan or with some thought. Therefore the National Forest and Nature Agency in Denmark initiated the Green Technological foresight on environmentally friendly agriculture with the aim of examining the agricultural environmental challenges and suggesting technological and structural solutions....... problems which are related to minimising environmental problems affected by the agricultural production’s negative influence on the surroundings, improving animal welfare and finding new ways and products for agriculture. Future directions of agriculture can derive with or without dialogue; it can occur...
17. Division of Agriculture
Science.gov (United States)
Department of Natural Resources logo, color scheme Department of Natural Resources Division of Agriculture Search Search DNR's site DNR State of Alaska Toggle main menu visibility Agriculture Home Programs Asset Disposals Alaska Caps Progam Board of Agriculture & Conservation Farm To School Program Grants
18. Gender in Agriculture Sourcebook
OpenAIRE
World Bank; Food and Agriculture Organization; International Fund for Agricultural Development
2009-01-01
Three out of every four poor people in developing countries live in rural areas, and most of them depend directly or indirectly on agriculture for their livelihoods. In many parts of the world, women are the main farmers or producers, but their roles remain largely unrecognized. The 2008 World development report: agriculture for development highlights the vital role of agriculture in susta...
19. Nigeria Agricultural Journal: Submissions
African Journals Online (AJOL)
Author Guidelines. NATURE OF PAPERS. Papers should be of agricultural interest and include: full reports of original research not previously elsewhere, research notes which consist of brief or new findings; techniques and equipment of importance to agricultural workers; evaluations of problems and trends in agricultural ...
20. Biotechnology and Agriculture.
Science.gov (United States)
Kenney, Martin
Even at this early date in the application of biotechnology to agriculture, it is clear that agriculture may provide the largest market for new or less expensive biotechnologically manufactured products. The chemical and pharmaceutical industries that hold important positions in agricultural inputs are consolidating their positions by purchasing…
1. Achieving production and conservation simultaneously in tropical agricultural landscapes
DEFF Research Database (Denmark)
Renwick, Anna R.; Vickery, Juliet A.; Potts, Simon G.
2014-01-01
Increasing population size and demand for food in the developing world is driving the intensification of agriculture, often threatening the biodiversity within the farmland itself and in the surrounding landscape. This paper quantifies bird and tree species richness, tree carbon and farmer's gross...... for the rural populations, and ensuring ‘sustained agricultural growth’ within such systems while minimising negative impacts on biodiversity and other key ecosystem services will be a major future challenge....
2. Changes in unique hues induced by chromatic surrounds.
Science.gov (United States)
Klauke, Susanne; Wachtler, Thomas
2016-03-01
A chromatic surround can have a strong influence on the perceived hue of a stimulus. We investigated whether chromatic induction has similar effects on the perception of colors that appear pure and unmixed (unique red, green, blue, and yellow) as on other colors. Subjects performed unique hue settings of stimuli in isoluminant surrounds of different chromaticities. Compared with the settings in a neutral gray surround, unique hue settings altered systematically with chromatic surrounds. The amount of induced hue shift depended on the difference between stimulus and surround hues, and was similar for unique hue settings as for settings of nonunique hues. Intraindividual variability in unique hue settings was roughly twice as high as for settings obtained in asymmetric matching experiments, which may reflect the presence of a reference stimulus in the matching task. Variabilities were also larger with chromatic surrounds than with neutral gray surrounds, for both unique hue settings and matching of nonunique hues. The results suggest that the neural representations underlying unique hue percepts are influenced by the same neural processing mechanisms as the percepts of other colors.
3. Isotopes in agriculture
International Nuclear Information System (INIS)
1983-01-01
Part 1: The stable isotope of nitrogen 15N has become widely used as tracer in agriculture, medicine and biology research. The film gives an overview of the sample preparation and analytical procedures followed in the analysis of the nitrogen isotopic composition (14N/15N ratio) by optical emission spectrometry at the Seibersdorf Laboratory. The subsampling of plant material and the several steps of chemical pretreatment such as Kjeldahl digestion, distillation, titration and adjustment of the proper N concentration in the extract are demonstrated. The preparation of the discharge tubes is shown in detail. Final measurement of the 14N/15N ratio is carried out with the NOI-5 and JASCO emission spectrometers. Part 2: This training film deals with the use of 32P-labelled materials in field and greenhouse experimentation in soil-plant relationships studies. All technical aspects, including safe handling and radiation protection procedures to be considered in the layout and harvesting of field experiments are documented in detail. Procedures followed up in the evaluation of P fertilizers such as rock phosphates under greenhouse conditions are described. Several soil injection techniques available for determination of the root activity pattern of trees are shown
4. Scalar QNMs for higher dimensional black holes surrounded by quintessence in Rastall gravity
Energy Technology Data Exchange (ETDEWEB)
Graca, J.P.M.; Lobo, Iarley P. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil)
2018-02-15
The spacetime solution for a black hole, surrounded by an exotic matter field, in Rastall gravity, is calculated in an arbitrary d-dimensional spacetime. After this, we calculate the scalar quasinormal modes of such solution, and study the shift on the modes caused by the modification of the theory of gravity, i.e., by the introduction of a new term due to Rastall. We conclude that the shift strongly depends on the kind of exotic field one is studying, but for a low density matter that supposedly pervades the universe, it is unlikely that Rastall gravity will cause an instability for the probe field. (orig.)
5. Radiation pattern of open ended waveguide in air core surrounded by annular plasma column
International Nuclear Information System (INIS)
Sharma, D.R.; Verma, J.S.
1977-01-01
Radiation pattern of open ended waveguide excited in circular symmetric mode (TM 01 ) in an air core having central conductor and surrounded by an annular plasma column is studied. The field distribution at the open end of the waveguide is considered to be equivalent to the vector sum of magnetic current rings of various radii, ranging from the outer radius of the inner conductor to the inner radius of the outer conductor of the waveguide at the open end. The radiation field is obtained as a vector sum of field components due to individual rings of current. Such a configuration gives rise to multiple narrow radiation beams away from the critical angle. (author)
6. AGRICULTURAL POLICIES AND COMPETITION IN WORLD AGRICULTURE
Directory of Open Access Journals (Sweden)
Raluca Duma
2011-04-01
Full Text Available Agricultural policies have had a guiding role inagriculture development and implicitly in their marketing. Usually they belongto each state and government and are issued in accordance with their specificclimate, social-economic and cultural background which includes food andgastronomic traditions. Agricultural policies have in view home and foreignmarket demand, as well as the socio-demographic, political and military contextat a certain point in the socio-economic development
7. Determination of the pollution with lead in the batteries factory in Al-Saffera (Aleppo) and surrounding area
International Nuclear Information System (INIS)
Al-Oudat, M.; Al-Kharfan, K.; Al-Shamali, K.
2007-10-01
The study aimed to determine the lead concentrations in the ecosystem surrounding the batteries factory in Al-Saffera. The results showed that the lead levels were very high in both factory area and the surrounding agricultural area. Lead levels in air varied between 12 and 34 μg/m3 in the area outside the factory. The same trends were in both soil and plant samples, and normal washing does not decrease the lead level in plant samples to acceptable levels. Mean lead levels in blood was also high and ranged between 55 and 28 μg /dl for factory workers and village inhabitants respectively. In conclusion the authorities administration must take all necessary procedures to reduce the lead levels in the factory area and in the surrounding area.(Author)
8. Determination of the pollution with lead in the batteries factory in Al-Saffera (Aleppo) and surrounding area
Energy Technology Data Exchange (ETDEWEB)
Al-Oudat, M; Al-Kharfan, K; Al-Shamali, K [Atomic Energy Commission, Damascus (Syrian Arab Republic), Dept. of Protection and Safety
2007-10-15
The study aimed to determine the lead concentrations in the ecosystem surrounding the batteries factory in Al-Saffera. The results showed that the lead levels were very high in both factory area and the surrounding agricultural area. Lead levels in air varied between 12 and 34 {mu}g/m3 in the area outside the factory. The same trends were in both soil and plant samples, and normal washing does not decrease the lead level in plant samples to acceptable levels. Mean lead levels in blood was also high and ranged between 55 and 28 {mu}g /dl for factory workers and village inhabitants respectively. In conclusion the authorities administration must take all necessary procedures to reduce the lead levels in the factory area and in the surrounding area.(Author)
9. 7. Food and agriculture
International Nuclear Information System (INIS)
Livernash, R.
1992-01-01
Global food production has increased substantially over the past two decades, but factors such as population pressures and environmental degradation are undermining agriculture's current condition and future prospects. This chapter discusses the following: global trends; production trends (livestock and fisheries); per capita production trends (population density and agriculture); environmental trends (soil degradation, inputs of fertilizers, pesticides, and freshwater); economic trends (agricultural commodity prices, declining investment in irrigation, World Bank lending); trade liberalization and the Gatt negotiations; conventional agriculture and alternative agriculture; problems with the conventional model (on-farm impacts, off-farm impacts); agricultural policies - creating a new environment; policy impacts - distorted price structures; new policy options (reducing input subsidies, land conservation programs, management agreements, taxes, fees, and tax incentives, strengthening regulations, subsidizing conversion); the economics of alternative agriculture
10. Impacts of Agricultural Practices and Tourism Activities on the Sustainability of Telaga Warna and Telaga Pengilon Lakes, Dieng Plateau, Central Java
Science.gov (United States)
2018-02-01
Telaga Warna and Telaga Pengilon are two volcanic lakes in the Dieng Plateau offer some unique phenomena which are interested for tourists to visit. Telaga Warna and Telaga Pengilon are located side by side in the Dieng Palteau. Those two lakes also have specific ecosystem which differ to other lakes. However as land use in the surrounding area is now gradually changing, the lake is now facing to environmental degradation. The land use in the surrounding area is for intensive agricultural which main crops are vegetable, especially potatoes. Meanwhile, the number of tourist visiting those two lakes is increasing; it may also give some impact to the lake environment. This research aims to study the impacts of agricultural practices and tourism activities to the lake environmental which lead to the environment sustainability of the lakes. The field survey was conducted to collect some data on lakes characteristics, agricultural and tourism activities. Some interviews to local people and tourists were also conducted. Some water and sediment samples were collected followed by laboratory analyses. Some secondary data from previous study was also collected. Data analysis was conducted based on qualitative and quantitative techniques. The study found that agricultural practices of potatoes plantation uses water from the Telaga Pengilon to irrigate the plant by pumping out the water using water pump and distributes the water over the plantation area. Agricultural practices lead to soil erosion, which contribute sediment to the lake carried by surface runoff. Therefore, the volume of lakes is gradually decreasing. The use of fertilizer in the agricultural practice contribute nutrient into the lake carried by surface runoff, leading to the eutrophication, due to the excess used of fertilizer. The study concludes that agricultural practices and tourism activities have some positive economic impacts to the local community, however it also give some adverse affects on the lakes
11. A synchronous surround increases the motion strength gain of motion.
Science.gov (United States)
Linares, Daniel; Nishida, Shin'ya
2013-11-12
Coherent motion detection is greatly enhanced by the synchronous presentation of a static surround (Linares, Motoyoshi, & Nishida, 2012). To further understand this contextual enhancement, here we measured the sensitivity to discriminate motion strength for several pedestal strengths with and without a surround. We found that the surround improved discrimination of low and medium motion strengths, but did not improve or even impaired discrimination of high motion strengths. We used motion strength discriminability to estimate the perceptual response function assuming additive noise and found that the surround increased the motion strength gain, rather than the response gain. Given that eye and body movements continuously introduce transients in the retinal image, it is possible that this strength gain occurs in natural vision.
12. Surrounding Moving Obstacle Detection for Autonomous Driving Using Stereo Vision
Directory of Open Access Journals (Sweden)
Hao Sun
2013-06-01
Full Text Available Detection and tracking surrounding moving obstacles such as vehicles and pedestrians are crucial for the safety of mobile robotics and autonomous vehicles. This is especially the case in urban driving scenarios. This paper presents a novel framework for surrounding moving obstacles detection using binocular stereo vision. The contributions of our work are threefold. Firstly, a multiview feature matching scheme is presented for simultaneous stereo correspondence and motion correspondence searching. Secondly, the multiview geometry constraint derived from the relative camera positions in pairs of consecutive stereo views is exploited for surrounding moving obstacles detection. Thirdly, an adaptive particle filter is proposed for tracking of multiple moving obstacles in surrounding areas. Experimental results from real-world driving sequences demonstrate the effectiveness and robustness of the proposed framework.
13. Contamination of nebulisers and surrounding air at the bedside of ...
African Journals Online (AJOL)
An air sampler was used to collect air samples from the surrounding bedside environment. .... individualised resealable plastic bags and stored upside down in a cooler .... conventional and mesh technology nebulisers used at home by adults.
14. Glow phenomenon surrounding the vertical stabilizer and OMS pods
Science.gov (United States)
1994-01-01
This 35mm frame, photographed as the Space Shuttle Columbia was orbiting Earth during a 'night' pass, documents the glow phenomenon surrounding the vertical stabilizer and the Orbital Maneuvering System (OMS) pods of the spacecraft.
15. Rain Simulation for the Test of Automotive Surround Sensors
Science.gov (United States)
Hasirlioglu, Sinan; Riener, Andreas; Doric, Igor
2017-04-01
The WHO Global Health Observatory data indicates that over 1.25 million people die in traffic accidents annually. To save lives, car manufacturers spend lot of efforts on the development of novel safety systems aiming to avoid or mitigate accidents and provide maximum protection for vehicle occupants as well as vulnerable road users. All the safety features mainly rely on data from surround sensors such as radar, lidar and camera and intelligent vehicles today use these environmental data for instant decision making and vehicle control. As already small errors in sensor data measurements could lead to catastrophes like major injuries or road traffic fatalities, it is of utmost importance to ensure high reliability and accuracy of sensors and safety systems. This work focuses on the influence of environmental factors such as rain conditions, as it is known that rain drops scatter the electromagnetic waves. The result is incorrect measurements with a direct negative impact on environment detection. To identify potential problems of sensors under varying environmental conditions, systems are today tested in real-world settings with two main problems: First, tests are time-consuming and second, environmental conditions are not reproducible. Our approach to test the influence of weather on automotive sensors is to use an indoor rain simulator. Our artificial rain maker, installed at CARISSMA (Center of Automotive Research on Integrated Safety Systems and Measurement Area), is parametrized with rain characteristics measured in the field using a standard disdrometer. System behavior on artificial rain is compared and validated with natural rainfall. With this simulator it is finally possible to test environmental influence at various levels and under reproducible conditions. This saves lot of efforts required for the test process itself and furthermore has a positive impact on the reliability of sensor systems due to the fact that test driven development is enabled.
16. Camouflaging in a complex environment--octopuses use specific features of their surroundings for background matching.
Directory of Open Access Journals (Sweden)
Noam Josef
Full Text Available Living under intense predation pressure, octopuses evolved an effective and impressive camouflaging ability that exploits features of their surroundings to enable them to "blend in." To achieve such background matching, an animal may use general resemblance and reproduce characteristics of its entire surroundings, or it may imitate a specific object in its immediate environment. Using image analysis algorithms, we examined correlations between octopuses and their backgrounds. Field experiments show that when camouflaging, Octopus cyanea and O. vulgaris base their body patterns on selected features of nearby objects rather than attempting to match a large field of view. Such an approach enables the octopus to camouflage in partly occluded environments and to solve the problem of differences in appearance as a function of the viewing inclination of the observer.
17. Partner Selection Optimization Model of Agricultural Enterprises in Supply Chain
OpenAIRE
Feipeng Guo; Qibei Lu
2013-01-01
With more and more importance of correctly selecting partners in supply chain of agricultural enterprises, a large number of partner evaluation techniques are widely used in the field of agricultural science research. This study established a partner selection model to optimize the issue of agricultural supply chain partner selection. Firstly, it constructed a comprehensive evaluation index system after analyzing the real characteristics of agricultural supply chain. Secondly, a heuristic met...
18. Chemical and microbiological water quality of subsurface agricultural drains during a field trial of liquid dairy manure effluent application rate and varying tillage practices, Upper Tiffin Watershed, southeastern Michigan
Science.gov (United States)
Haack, Sheridan Kidd; Duris, Joseph W.
2008-01-01
A field trial was done in the Upper Tiffin River Watershed, in southeastern Michigan, to determine the influence of liquid dairy manure effluent (LDME) management practices on the quality of agricultural subsurface-drain water. Samples from subsurface drains were analyzed for nutrients, fecal-coliform and Escherichia coli (E. coli) bacteria, antibiotics, chemicals typically detected in wastewater, and the occurrence of genes indicating the presence of shiga-toxin-producing E. coli, or of bovine-specific Bacteroidetes bacteria. Samples were collected from November 2, 2006, to March 20, 2007, from eight subsurface drains under field plots that received no LDME and no tillage (controls) or received 4,000 or 8,000 gallons per acre (gal/acre) of LDME and either no tillage or two different types of tillage. The two types of tillage tested were (1) ground-driven, rotary, subsurface cultivation and (2) rolling-tine aeration. Samples were collected before LDME application and at 4 hours, and 1, 2, 6, 7, and 14 days post-application. Nutrient concentrations were high in subsurface-drain water throughout the field-trial period and could not be attributed to the field-trial LDME application. Of the 59 drain-water samples, including those collected before LDME application and control samples for each date, 56 had concentrations greater than the U.S. Environmental Protection Agency (USEPA), Ecoregion VI recommended surface-water criterion for total phosphorus, and all samples had concentrations greater than the recommended total nitrogen criterion. Nitrate + nitrite nitrogen concentration exceeded 20 milligrams per liter for every sample and contributed most to the total nitrogen concentrations. Substantial increases in drain-water concentrations of organic and ammonia nitrogen and total phosphorus were found for all treatments, including controls, at 14 days post-application after 0.84 inch of rainfall over 2 days. E. coli concentrations exceeded the USEPA recreational
19. Phase-specific Surround suppression in Mouse Primary Visual Cortex Correlates with Figure Detection Behavior Based on Phase Discontinuity.
Science.gov (United States)
Li, Fengling; Jiang, Weiqian; Wang, Tian-Yi; Xie, Taorong; Yao, Haishan
2018-05-21
In the primary visual cortex (V1), neuronal responses to stimuli within the receptive field (RF) are modulated by stimuli in the RF surround. A common effect of surround modulation is surround suppression, which is dependent on the feature difference between stimuli within and surround the RF and is suggested to be involved in the perceptual phenomenon of figure-ground segregation. In this study, we examined the relationship between feature-specific surround suppression of V1 neurons and figure detection behavior based on figure-ground feature difference. We trained freely moving mice to perform a figure detection task using figure and ground gratings that differed in spatial phase. The performance of figure detection increased with the figure-ground phase difference, and was modulated by stimulus contrast. Electrophysiological recordings from V1 in head-fixed mice showed that the increase in phase difference between stimuli within and surround the RF caused a reduction in surround suppression, which was associated with an increase in V1 neural discrimination between stimuli with and without RF-surround phase difference. Consistent with the behavioral performance, the sensitivity of V1 neurons to RF-surround phase difference could be influenced by stimulus contrast. Furthermore, inhibiting V1 by optogenetically activating either parvalbumin (PV)- or somatostatin (SOM)-expressing inhibitory neurons both decreased the behavioral performance of figure detection. Thus, the phase-specific surround suppression in V1 represents a neural correlate of figure detection behavior based on figure-ground phase discontinuity. Copyright © 2018 IBRO. Published by Elsevier Ltd. All rights reserved.
20. Health hazards to children in agriculture.
Science.gov (United States)
Wilk, V A
1993-09-01
Children comprise a significant portion of the agricultural workforce and are exposed to many workplace hazards, including farm machinery, pesticides, poor field sanitation, unsafe transportation, and fatigue from doing physically demanding work for long periods. Migrant farmworker children face the additional hazard of substandard or nonexistent housing in the fields. Children account for a disproportionate share of agricultural workplace fatalities and disabling injuries, with more than 300 deaths and 27,000 injuries per year. The most common cause of fatal and nonfatal injury among children in agriculture is farm machinery, with tractors accounting for the greatest number. Remedies to the problems of child labor must take into account family economics and the need for child care. Labor law reform and rigorous enforcement of existing laws and of workplace health and safety requirements are vital to better protect the children and adults working in agriculture.
1. Agriculture and environmental pollution
International Nuclear Information System (INIS)
Iqbal, M.M.; Idris, M.; Shah, S.M.
1997-01-01
Agriculture is a profession which is open both to natural conditions and intense human activity. This has brought it in direct interface with the environment. The activities related to agriculture can have favorable as well as unfavorable influence on environment. Pressure of burgeoning population in demanding increased production from agriculture to feed and clothe the teeming millions. This has resulted in excessive use of soil, fertilizers and pesticides. The paper describes the effect of these productive resources on environment and human health. (author)
2. Trichoderma for climate resilient agriculture.
Science.gov (United States)
Kashyap, Prem Lal; Rai, Pallavi; Srivastava, Alok Kumar; Kumar, Sudheer
2017-08-01
Climate change is one of the biggest challenges of the twenty-first century for sustainable agricultural production. Several reports highlighted the need for better agricultural practices and use of eco-friendly methods for sustainable crop production under such situations. In this context, Trichoderma species could be a model fungus to sustain crop productivity. Currently, these are widely used as inoculants for biocontrol, biofertilization, and phytostimulation. They are reported to improve photosynthetic efficiency, enhance nutrient uptake and increase nitrogen use efficiency in crops. Moreover, they can be used to produce bio-energy, facilitate plants for adaptation and mitigate adverse effect of climate change. The technological advancement in high throughput DNA sequencing and biotechnology provided deep insight into the complex and diverse biotic interactions established in nature by Trichoderma spp. and efforts are being made to translate this knowledge to enhance crop growth, resistance to disease and tolerance to abiotic stresses under field conditions. The discovery of several traits and genes that are involved in the beneficial effects of Trichoderma spp. has resulted in better understanding of the performance of bioinoculants in the field, and will lead to more efficient use of these strains and possibly to their improvement by genetic modification. The present mini-review is an effort to elucidate the molecular basis of plant growth promotion and defence activation by Trichoderma spp. to garner broad perspectives regarding their functioning and applicability for climate resilient agriculture.
3. Malawi - Conservation Agriculture
Data.gov (United States)
Millennium Challenge Corporation — The randomized control trial impact evaluation tests different strategies for communicating information about agricultural technologies to smallholder maize farmers...
4. Energy in agriculture
Energy Technology Data Exchange (ETDEWEB)
Le Roux, E J
1980-02-01
Agriculture is an important component of Canadian energy policy. There are many opportunities for both the production of energy from agricultural processes and the conservation of energy in agricultural production. These opportunities, as well as current practices and research in progress, are outlined in this report. Energy sources in agriculture include biomass (straw and other residues), methane production from manure, and oil and alcohol from crops. Alternate energy sources such as solar and wind power conserve conventional resources, and additional conservation opportunities exist in the use of greenhouses, waste heat and energy-efficient farming processes. Research programs and possible trends are outlined. 10 figs., 3 tabs.
5. Agriculture - reconciling ancient tensions
Directory of Open Access Journals (Sweden)
David Atkinson
2002-09-01
Full Text Available Decision-making in agriculture has tended to be driven by factors other than environmental concerns. This may be changing, and perhaps the emphases of the two creation accounts in Genesis (responsible management or 'dominion', and active care may become more important. The paper examines a number of current developments in agriculture (synthetic fertilizers and pesticides, genetic manipulation, and organic versus industrial methodologies and discusses the issues they raise for agricultural productivity and the human communities dependent on farming. The questions raised are complex; we are faced with establishing a new paradigm for agricultural practice.
6. Agriculture. Pt. 2
International Nuclear Information System (INIS)
1994-01-01
The climatic effects of agriculture and nutritional habits of the West German population are investigated. Changes in solar UV-B radiation and methods of measuring them are described. The climatic relevance of ecological and conventional agricultural techniques are compared. The agricultural policy of the European Communities is presented and discussed. The climatic effects of the totality of agricultural production techniques and processing stages of the food industry, as well as of transport and trade, are analyzed. Sociological investigations are made of the nutritional habits of the population, and the consequences for the global climate are compared. (SR) [de
7. NANOTECHNOLOGY APPLICATIONS IN AGRICULTURE: AN UPDATE
OpenAIRE
Tejpal Dhewa
2015-01-01
Although the scientific studies on the applications of nanotechnology in the agriculture are less than a decade old yet the prospects of nanotechnology in this field has been considerable. The rapid developments in the nanosciences have a great impact on agricultural practices and food manufacturing industries. Nanotechnology has an enormous potential to offer smarter, stronger, cost-effective packaging materials, biosensors for the rapid detection of the food pathogens, toxins and other cont...
8. The agricultural policy of Serbia and common agricultural policy
Directory of Open Access Journals (Sweden)
Stanković Milica
2012-01-01
Full Text Available The agricultural sector has a relatively high importance in the economic structure of Serbia. The Common Agricultural Policy (CAP, Common Agricultural Policy is one of the main policies of the European Union. It is very important to point out the fundamental principles and objectives of the Common Agricultural Policy. Harmonization of the national agricultural policy of Serbia with the Common Agricultural Policy and acceptance of its mechanisms is crucial for the development of the agricultural sector as a whole.
9. Clustering of agricultural enterprises
Directory of Open Access Journals (Sweden)
Michaela Beranová
2013-01-01
Full Text Available Agricultural business is a very specific branch which is characterized by very low financial performance while this characteristic is given mainly by external factors as market pricing of agricultural commodities on one side, and production costs of agricultural commodities on the other side. This way, agricultural enterprises recognize negative values of gross margin in the Profit and Loss Statement but positive value of operating profit after even there are items of costs which are deducted. These results are derived from agricultural production subsidies which are recognized as income in the P/L Statement. In connection with this fact, the government subsidies are a substantial component of financial performance of agricultural enterprises.Primary research proceeded on the statistical sample of one hundred agricultural companies, has shown that also other specifics influencing financial performance of these businesses exist here. In order to determine the influences, the cluster analysis has been applied at using more than 10 variables. This approach has led to construction of clusters (groups of agricultural business entities with different characteristics of the group. The objective of this paper is to identify the main determinants of financial performance of agricultural enterprises and to determine their influences under different economic characteristics of these business entities. For this purpose, the regression analysis has been subsequently applied on the groups of companies coming out from the cluster analysis. Besides the operating profit which is the main driving force of financial performance measured with the economic value added (EVA in agricultural enterprises, also capital structure and cost of capital have been observed as very strong influences on financial performance but these factors have different directions of their influence on the economic value added under different financial characteristics of agricultural
10. Vocational Agriculture Education: Agricultural Livestock Skills.
Science.gov (United States)
Pierce, Greg
Ten units of instruction are provided in this curriculum guide on agricultural livestock skills. Unit topics are as follow: (1) restraining, (2) vaccination, (3) livestock castration, (4) dehorning, (5) docking, (6) growth stimulants, (7) identification, (8) shearing, (9) hoof trimming, and (10) birth assistance. Each instructional unit generally…
11. Placental vascular responses are dependent on surrounding tissue
DEFF Research Database (Denmark)
Brøgger, Torbjørn Halle
-depth understanding of the mechanism regulating blood flow and perfusion is necessary if we are to come up with new ideas for intervention and treatment. Method: From fresh born placentas stem villi arteries were carefully dissected. The artery branches were divided. The surrounding tissue was removed from one end...... and was left untouched in the other end. Then using wire myography they were investigated in terms of contractility and sensitivity to physiological relevant human-like agonists. Results: Sensitivity to PGF2α, Tx-analog, 5-HT and endothelin-1 was significantly lower in arteries with intact surrounding tissue...... compared to arteries stripped of the tissue. The maximal force development was also significantly lower in arteries with surrounding tissue, when they were depolarized high extracellular [K+] or stimulated with PGF2α or endotheline-1. Conclusion: The perivascular tissue significantly alters stem villi...
12. Placental vascular responses are dependent on surrounding tissue
DEFF Research Database (Denmark)
Brøgger, Torbjørn Halle
. Materials and methods. From fresh born placentas, stem villi arteries were carefully dissected. The artery branches were divided. The surrounding tissue was removed from one end and was left untouched in the other end.Then, using wire myography, they were investigated in terms of contractility...... and sensitivity to physiological relevant human-like agonists. Results. Sensitivity to PGF2α, Tx-analog, 5-HT and endothelin-1 was significantly lower in arteries with intact surrounding tissue compared to arteries stripped of the tissue. The maximal force development was also significantly lower in arteries...... with surrounding tissue when they were depolarized high extracellular [K+] or stimulated with PGF2α or endotheline-1. Conclusion. The perivascular tissue significantly alters stem villi arteries' sensitivity and force development in a suppressive way. This implicates a new aspect of blood flow regulation...
13. Journal of Agricultural Extension
African Journals Online (AJOL)
Scope of journal The Journal of Agricultural Extension" is devoted to the advancement of knowledge of agricultural extension services and practice through the publication of original and empirically based research, ... Vol 22, No 1 (2018) ... Symbol recognition and interpretation of HIV/AIDS pictorial messages among rural ...
14. Sustainable Agriculture: Cover Cropping
Science.gov (United States)
Webster, Megan
2018-01-01
Sustainable agriculture practices are increasingly being used by farmers to maintain soil quality, increase biodiversity, and promote production of food that is environmentally safe. There are several types of sustainable agriculture practices such as organic farming, crop rotation, and aquaculture. This lesson plan focuses on the sustainable…
15. The Urban Agriculture Circle
NARCIS (Netherlands)
Jansma, J.E.; Chambers, Joe; Sabas, Eva; Veen, E.J.
2015-01-01
The lack of inclusion of urban agriculture in city planning directly affects the success of initiatives in this sector, which subsequently could impede fu-ture innovations. The poor representation of urban agriculture in planning can be attributed to a lack of understanding about its
16. Theme: Urban Agriculture.
Science.gov (United States)
Ellibee, Margaret; And Others
1990-01-01
On the theme of secondary agricultural education in urban areas, this issue includes articles on opportunities, future directions, and implications for the profession; creative supervised experiences for horticulture students; floral marketing, multicultural education; and cultural diversity in urban agricultural education. (JOW)
17. AGRICULTURE IN THE CITY
International Development Research Centre (IDRC) Digital Library (Canada)
The target audience of this book, then, is not only researchers and high-level ...... given the current higher availability of food traded in agricultural markets and in ... recyclable materials as containers for the organic matter and agricultural soil ...
18. Conservation Agriculture in Europe
Directory of Open Access Journals (Sweden)
Á. Kertész
2014-03-01
Yield performance and stability, operating costs, environmental policies and programs of the Common Agricultural Policy (CAP, and climate change will likely be the major driving forces defining the direction and for the extension of CA in Europe. The role of agriculture in climate change mitigation in the EU is discussed in the paper.
19. Agriculture. Pt. 1
International Nuclear Information System (INIS)
1994-01-01
The study investigates the impact of agriculture on the earth's atmosphere. It describes the natural carbon cycle, the socioeconomic factors that influence it, and the climate effects. The climatic relevance of gaseous sulphur and nitrogen compounds, methane and other hydrocarbons, and ammonia emissions from biological and agricultural process is discussed. (SR) [de
20. Glossary on agricultural landscapes.
NARCIS (Netherlands)
Kruse, A.; Centeri, C.; Renes, J.; Roth, M.; Printsman, A.; Palang, H.; Benito Jorda, M.-D.; Verlarde, M.D.; Kruckenberg, H.
2010-01-01
T he following glossary of terms related to the European agricultural landscape shall serve as a common basis for all parties, working in or on agricultural landscapes. Some of the terms are quite common and sometimes used in our every day language, but they often have different meanings in | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5247271656990051, "perplexity": 7400.305720530487}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221217951.76/warc/CC-MAIN-20180821034002-20180821054002-00311.warc.gz"} |
https://pressbooks.online.ucf.edu/algphysics/chapter/applications-of-electrostatics/ | Chapter 18 Electric Charge and Electric Field
# 18.8 Applications of Electrostatics
### Summary
• Name several real-world applications of the study of electrostatics.
The study of electrostatics has proven useful in many areas. This module covers just a few of the many applications of electrostatics.
# The Van de Graaff Generator
Van de Graaff generators (or Van de Graaffs) are not only spectacular devices used to demonstrate high voltage due to static electricity—they are also used for serious research. The first was built by Robert Van de Graaff in 1931 (based on original suggestions by Lord Kelvin) for use in nuclear physics research. Figure 1 shows a schematic of a large research version. Van de Graaffs utilize both smooth and pointed surfaces, and conductors and insulators to generate large static charges and, hence, large voltages.
A very large excess charge can be deposited on the sphere, because it moves quickly to the outer surface. Practical limits arise because the large electric fields polarize and eventually ionize surrounding materials, creating free charges that neutralize excess charge or allow it to escape. Nevertheless, voltages of 15 million volts are well within practical limits.
### Take-Home Experiment: Electrostatics and Humidity
Rub a comb through your hair and use it to lift pieces of paper. It may help to tear the pieces of paper rather than cut them neatly. Repeat the exercise in your bathroom after you have had a long shower and the air in the bathroom is moist. Is it easier to get electrostatic effects in dry or moist air? Why would torn paper be more attractive to the comb than cut paper? Explain your observations.
# Xerography
Most copy machines use an electrostatic process called xerography—a word coined from the Greek words xeros for dry and graphos for writing. The heart of the process is shown in simplified form in Figure 2.
A selenium-coated aluminum drum is sprayed with positive charge from points on a device called a corotron. Selenium is a substance with an interesting property—it is a photoconductor. That is, selenium is an insulator when in the dark and a conductor when exposed to light.
In the first stage of the xerography process, the conducting aluminum drum is grounded so that a negative charge is induced under the thin layer of uniformly positively charged selenium. In the second stage, the surface of the drum is exposed to the image of whatever is to be copied. Where the image is light, the selenium becomes conducting, and the positive charge is neutralized. In dark areas, the positive charge remains, and so the image has been transferred to the drum.
The third stage takes a dry black powder, called toner, and sprays it with a negative charge so that it will be attracted to the positive regions of the drum. Next, a blank piece of paper is given a greater positive charge than on the drum so that it will pull the toner from the drum. Finally, the paper and electrostatically held toner are passed through heated pressure rollers, which melt and permanently adhere the toner within the fibers of the paper.
# Laser Printers
Laser printers use the xerographic process to make high-quality images on paper, employing a laser to produce an image on the photoconducting drum as shown in Figure 3. In its most common application, the laser printer receives output from a computer, and it can achieve high-quality output because of the precision with which laser light can be controlled. Many laser printers do significant information processing, such as making sophisticated letters or fonts, and may contain a computer more powerful than the one giving them the raw data to be printed.
# Ink Jet Printers and Electrostatic Painting
The ink jet printer, commonly used to print computer-generated text and graphics, also employs electrostatics. A nozzle makes a fine spray of tiny ink droplets, which are then given an electrostatic charge. (See Figure 4.)
Once charged, the droplets can be directed, using pairs of charged plates, with great precision to form letters and images on paper. Ink jet printers can produce color images by using a black jet and three other jets with primary colors, usually cyan, magenta, and yellow, much as a color television produces color. (This is more difficult with xerography, requiring multiple drums and toners.)
Electrostatic painting employs electrostatic charge to spray paint onto odd-shaped surfaces. Mutual repulsion of like charges causes the paint to fly away from its source. Surface tension forms drops, which are then attracted by unlike charges to the surface to be painted. Electrostatic painting can reach those hard-to-get at places, applying an even coat in a controlled manner. If the object is a conductor, the electric field is perpendicular to the surface, tending to bring the drops in perpendicularly. Corners and points on conductors will receive extra paint. Felt can similarly be applied.
# Smoke Precipitators and Electrostatic Air Cleaning
Another important application of electrostatics is found in air cleaners, both large and small. The electrostatic part of the process places excess (usually positive) charge on smoke, dust, pollen, and other particles in the air and then passes the air through an oppositely charged grid that attracts and retains the charged particles. (See Figure 5.)
Large electrostatic precipitators are used industrially to remove over 99% of the particles from stack gas emissions associated with the burning of coal and oil. Home precipitators, often in conjunction with the home heating and air conditioning system, are very effective in removing polluting particles, irritants, and allergens.
### Problem-Solving Strategies for Electrostatics
1. Examine the situation to determine if static electricity is involved. This may concern separated stationary charges, the forces among them, and the electric fields they create.
2. Identify the system of interest. This includes noting the number, locations, and types of charges involved.
3. Identify exactly what needs to be determined in the problem (identify the unknowns). A written list is useful. Determine whether the Coulomb force is to be considered directly—if so, it may be useful to draw a free-body diagram, using electric field lines.
4. Make a list of what is given or can be inferred from the problem as stated (identify the knowns). It is important to distinguish the Coulomb force ${F}$ from the electric field ${E}$, for example.
5. Solve the appropriate equation for the quantity to be determined (the unknown) or draw the field lines as requested.
6. Examine the answer to see if it is reasonable: Does it make sense? Are units correct and the numbers involved reasonable?
# Integrated Concepts
The Integrated Concepts exercises for this module involve concepts such as electric charges, electric fields, and several other topics. Physics is most interesting when applied to general situations involving more than a narrow set of physical principles. The electric field exerts force on charges, for example, and hence the relevance of Chapter 4 Dynamics: Force and Newton’s Laws of Motion. The following topics are involved in some or all of the problems labeled “Integrated Concepts”:
The following worked example illustrates how this strategy is applied to an Integrated Concept problem:
### Example 1: Acceleration of a Charged Drop of Gasoline
If steps are not taken to ground a gasoline pump, static electricity can be placed on gasoline when filling your car’s tank. Suppose a tiny drop of gasoline has a mass of ${4.00 \times 10^{-15} \;\text{kg}}$ and is given a positive charge of ${3.20 \times 10^{-19} \;\text{C}}$. (a) Find the weight of the drop. (b) Calculate the electric force on the drop if there is an upward electric field of strength ${3.00 \times 10^5 \;\text{N} / \text{C}}$ due to other static electricity in the vicinity. (c) Calculate the drop’s acceleration.
Strategy
To solve an integrated concept problem, we must first identify the physical principles involved and identify the chapters in which they are found. Part (a) of this example asks for weight. This is a topic of dynamics and is defined in Chapter 4 Dynamics: Force and Newton’s Laws of Motion. Part (b) deals with electric force on a charge, a topic of Chapter 18 Electric Charge and Electric Field. Part (c) asks for acceleration, knowing forces and mass. These are part of Newton’s laws, also found in Chapter 4 Dynamics: Force and Newton’s Laws of Motion.
The following solutions to each part of the example illustrate how the specific problem-solving strategies are applied. These involve identifying knowns and unknowns, checking to see if the answer is reasonable, and so on.
Solution for (a)
Weight is mass times the acceleration due to gravity, as first expressed in
${w = mg.}$
Entering the given mass and the average acceleration due to gravity yields
${w = (4.00 \times 10^{-15} \;\text{kg})(9.80 \;\text{m} / \text{s}^2) = 3.92 \times 10^{-14} \;\text{N}. }$
Discussion for (a)
This is a small weight, consistent with the small mass of the drop.
Solution for (b)
The force an electric field exerts on a charge is given by rearranging the following equation:
${F = qE.}$
Here we are given the charge (${3.20 \times 10^{-19} \;\text{C}}$ is twice the fundamental unit of charge) and the electric field strength, and so the electric force is found to be
${F=(3.20 \times 10^{-19} \;\text{C})(3.00 \times 10^5 \;\text{N} / \text{C}) = 9.60 \times 10^{-14} \;\text{N}.}$
Discussion for (b)
While this is a small force, it is greater than the weight of the drop.
Solution for (c)
The acceleration can be found using Newton’s second law, provided we can identify all of the external forces acting on the drop. We assume only the drop’s weight and the electric force are significant. Since the drop has a positive charge and the electric field is given to be upward, the electric force is upward. We thus have a one-dimensional (vertical direction) problem, and we can state Newton’s second law as
${a =}$ ${\frac{F_{net}}{m}}$.
where ${F_{net} = F - w}$. Entering this and the known values into the expression for Newton’s second law yields
$\begin{array}{r @{{}={}}l} {a}= & {\frac{F - w}{m}} \\[1em]= & {\frac{9.60 \times 10^{-14} \;\text{N} - 3.92 \times 10^{-14} \;\text{N}}{4.00 \times 10^{-15} \;\text{kg}}} \\[1em]= & {14.2 \;\text{m} / \text{s}^2}. \end{array}$
Discussion for (c)
This is an upward acceleration great enough to carry the drop to places where you might not wish to have gasoline.
This worked example illustrates how to apply problem-solving strategies to situations that include topics in different chapters. The first step is to identify the physical principles involved in the problem. The second step is to solve for the unknown using familiar problem-solving strategies. These are found throughout the text, and many worked examples show how to use them for single topics. In this integrated concepts example, you can see how to apply them across several topics. You will find these techniques useful in applications of physics outside a physics course, such as in your profession, in other science disciplines, and in everyday life. The following problems will build your skills in the broad application of physical principles.
### Unreasonable Results
The Unreasonable Results exercises for this module have results that are unreasonable because some premise is unreasonable or because certain of the premises are inconsistent with one another. Physical principles applied correctly then produce unreasonable results. The purpose of these problems is to give practice in assessing whether nature is being accurately described, and if it is not to trace the source of difficulty.
Problem-Solving Strategy
To determine if an answer is reasonable, and to determine the cause if it is not, do the following.
1. Solve the problem using strategies as outlined above. Use the format followed in the worked examples in the text to solve the problem as usual.
2. Check to see if the answer is reasonable. Is it too large or too small, or does it have the wrong sign, improper units, and so on?
3. If the answer is unreasonable, look for what specifically could cause the identified difficulty. Usually, the manner in which the answer is unreasonable is an indication of the difficulty. For example, an extremely large Coulomb force could be due to the assumption of an excessively large separated charge.
# Section Summary
• Electrostatics is the study of electric fields in static equilibrium.
• In addition to research using equipment such as a Van de Graaff generator, many practical applications of electrostatics exist, including photocopiers, laser printers, ink-jet printers and electrostatic air filters.
### Problems & Exercises
1: (a) What is the electric field 5.00 m from the center of the terminal of a Van de Graaff with a 3.00 mC charge, noting that the field is equivalent to that of a point charge at the center of the terminal? (b) At this distance, what force does the field exert on a ${2.00 \;\mu \text{C}}$ charge on the Van de Graaff’s belt?
2: (a) What is the direction and magnitude of an electric field that supports the weight of a free electron near the surface of Earth? (b) Discuss what the small value for this field implies regarding the relative strength of the gravitational and electrostatic forces.
3: A simple and common technique for accelerating electrons is shown in Figure 6, where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to continue moving. (a) Calculate the acceleration of the electron if the field strength is ${2.50 \times 10^4 \;\text{N} / \text{C}}$. (b) Explain why the electron will not be pulled back to the positive plate once it moves through the hole.
4: Earth has a net charge that produces an electric field of approximately 150 N/C downward at its surface. (a) What is the magnitude and sign of the excess charge, noting the electric field of a conducting sphere is equivalent to a point charge at its center? (b) What acceleration will the field produce on a free electron near Earth’s surface? (c) What mass object with a single extra electron will have its weight supported by this field?
5: Point charges of ${25.0 \;\mu \text{C}}$ and ${45.0 \;\mu \text{C}}$ are placed 0.500 m apart. (a) At what point along the line between them is the electric field zero? (b) What is the electric field halfway between them?
6: What can you say about two charges q1 and q2, if the electric field one-fourth of the way from q1 to q2 is zero?
### Problems & Exercises
Integrated Concepts
1: Calculate the angular velocity $\omega$ of an electron orbiting a proton in the hydrogen atom, given the radius of the orbit is ${0.530 \times 10^{-10} \;\text{m}}$. You may assume that the proton is stationary and the centripetal force is supplied by Coulomb attraction.
2: An electron has an initial velocity of ${5.00 \times 10^{6} \;\text{m} / \text{s}}$ in a uniform ${2.00 \times 10^5 \;\text{N} / \text{C}}$ strength electric field. The field accelerates the electron in the direction opposite to its initial velocity. (a) What is the direction of the electric field? (b) How far does the electron travel before coming to rest? (c) How long does it take the electron to come to rest? (d) What is the electron’s velocity when it returns to its starting point?
3: The practical limit to an electric field in air is about ${3.00 \times 10^6 \;\text{N} / \text{C}}$. Above this strength, sparking takes place because air begins to ionize and charges flow, reducing the field. (a) Calculate the distance a free proton must travel in this field to reach 3.00% of the speed of light, starting from rest. (b) Is this practical in air, or must it occur in a vacuum?
4: A 5.00 g charged insulating ball hangs on a 30.0 cm long string in a uniform horizontal electric field as shown in Figure 7. Given the charge on the ball is ${1.00 \;\mu \text{C}}$, find the strength of the field.
5: Figure 8 shows an electron passing between two charged metal plates that create an 100 N/C vertical electric field perpendicular to the electron’s original horizontal velocity. (These can be used to change the electron’s direction, such as in an oscilloscope.) The initial speed of the electron is ${3.00 \times 10^6 \;\text{m} / \text{s}}$, and the horizontal distance it travels in the uniform field is 4.00 cm. (a) What is its vertical deflection? (b) What is the vertical component of its final velocity? (c) At what angle does it exit? Neglect any edge effects.
6: The classic Millikan oil drop experiment was the first to obtain an accurate measurement of the charge on an electron. In it, oil drops were suspended against the gravitational force by a vertical electric field. (See Figure 9.) Given the oil drop to be ${1.00 \;\mu \text{m}}$ in radius and have a density of 920 kg/m3: (a) Find the weight of the drop. (b) If the drop has a single excess electron, find the electric field strength needed to balance its weight.
7: (a) In Figure 10, four equal charges q lie on the corners of a square. A fifth charge Q is on a mass mm directly above the center of the square, at a height equal to the length d of one side of the square. Determine the magnitude of q in terms of Q, m, and d, if the Coulomb force is to equal the weight of m. (b) Is this equilibrium stable or unstable? Discuss.
### Unreasonable Results
1: (a) Calculate the electric field strength near a 10.0 cm diameter conducting sphere that has 1.00 C of excess charge on it. (b) What is unreasonable about this result? (c) Which assumptions are responsible?
2: (a) Two 0.500 g raindrops in a thunderhead are 1.00 cm apart when they each acquire 1.00 mC charges. Find their acceleration. (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?
3: A wrecking yard inventor wants to pick up cars by charging a 0.400 m diameter ball and inducing an equal and opposite charge on the car. If a car has a 1000 kg mass and the ball is to be able to lift it from a distance of 1.00 m: (a) What minimum charge must be used? (b) What is the electric field near the surface of the ball? (c) Why are these results unreasonable? (d) Which premise or assumption is responsible?
1: Consider two insulating balls with evenly distributed equal and opposite charges on their surfaces, held with a certain distance between the centers of the balls. Construct a problem in which you calculate the electric field (magnitude and direction) due to the balls at various points along a line running through the centers of the balls and extending to infinity on either side. Choose interesting points and comment on the meaning of the field at those points. For example, at what points might the field be just that due to one ball and where does the field become negligibly small? Among the things to be considered are the magnitudes of the charges and the distance between the centers of the balls. Your instructor may wish for you to consider the electric field off axis or for a more complex array of charges, such as those in a water molecule.
2: Consider identical spherical conducting space ships in deep space where gravitational fields from other bodies are negligible compared to the gravitational attraction between the ships. Construct a problem in which you place identical excess charges on the space ships to exactly counter their gravitational attraction. Calculate the amount of excess charge needed. Examine whether that charge depends on the distance between the centers of the ships, the masses of the ships, or any other factors. Discuss whether this would be an easy, difficult, or even impossible thing to do in practice.
## Glossary
Van de Graaff generator
a machine that produces a large amount of excess charge, used for experiments with high voltage
electrostatics
the study of electric forces that are static or slow-moving
photoconductor
a substance that is an insulator until it is exposed to light, when it becomes a conductor
xerography
a dry copying process based on electrostatics
grounded
connected to the ground with a conductor, so that charge flows freely to and from the Earth to the grounded object
laser printer
uses a laser to create a photoconductive image on a drum, which attracts dry ink particles that are then rolled onto a sheet of paper to print a high-quality copy of the image
ink-jet printer
small ink droplets sprayed with an electric charge are controlled by electrostatic plates to create images on paper
electrostatic precipitators
filters that apply charges to particles in the air, then attract those charges to a filter, removing them from the airstream
### Solutions
Problems & Exercises
2: (a) ${5.58 \times 10^{-11} \;\text{N} / \text{C}}$
(b)the coulomb force is extraordinarily stronger than gravity
4: (a) ${-6.76 \times 10^5 \;\text{C}}$
(b) ${2.63 \times 10^{13} \;\text{m} / \text{s}^2 \;\text{(upward)}}$
(c) ${2.45 \times 10^{-18} \;\text{kg}}$
6: The charge q2 is 9 times greater than q1. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8304648399353027, "perplexity": 593.7712591172957}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991537.32/warc/CC-MAIN-20210513045934-20210513075934-00599.warc.gz"} |
https://en.wikipedia.org/wiki/Secant_method | # Secant method
The first two iterations of the secant method. The red curve shows the function f and the blue lines are the secants. For this particular case, the secant method will not converge.
In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite difference approximation of Newton's method. However, the method was developed independently of Newton's method, and predated the latter by over 3,000 years.[1]
## The method
The secant method is defined by the recurrence relation
$x_n =x_{n-1}-f(x_{n-1})\frac{x_{n-1}-x_{n-2}}{f(x_{n-1})-f(x_{n-2})} =\frac{x_{n-2}f(x_{n-1})-x_{n-1}f(x_{n-2})}{f(x_{n-1})-f(x_{n-2})}$
As can be seen from the recurrence relation, the secant method requires two initial values, x0 and x1, which should ideally be chosen to lie close to the root.
## Derivation of the method
Starting with initial values x0 and x1, we construct a line through the points (x0, f(x0)) and (x1, f(x1)), as demonstrated in the picture on the right. In point-slope form, this line has the equation
$y = \frac{f(x_1)-f(x_0)}{x_1-x_0}(x-x_1) + f(x_1)$
We find the root of this line – the value of x such that y = 0 – by solving the following equation for x:
$0 = \frac{f(x_1)-f(x_0)}{x_1-x_0}(x-x_1) + f(x_1)$
The solution is
$x = x_1 - f(x_1)\frac{x_1-x_0}{f(x_1)-f(x_0)}$
We then use this new value of x as x2 and repeat the process using x1 and x2 instead of x0 and x1. We continue this process, solving for x3, x4, etc., until we reach a sufficiently high level of precision (a sufficiently small difference between xn and xn - 1).
$x_2 = x_1 - f(x_1)\frac{x_1-x_0}{f(x_1)-f(x_0)}$
$x_3 = x_2 - f(x_2)\frac{x_2-x_1}{f(x_2)-f(x_1)}$
$x_n = x_{n-1} - f(x_{n-1})\frac{x_{n-1}-x_{n-2}}{f(x_{n-1})-f(x_{n-2})}$
## Convergence
The iterates $x_n$ of the secant method converge to a root of $f$, if the initial values $x_0$ and $x_1$ are sufficiently close to the root. The order of convergence is α, where
$\alpha = \frac{1+\sqrt{5}}{2} \approx 1.618$
is the golden ratio. In particular, the convergence is superlinear, but not quite quadratic.
This result only holds under some technical conditions, namely that $f$ be twice continuously differentiable and the root in question be simple (i.e., with multiplicity 1).
If the initial values are not close enough to the root, then there is no guarantee that the secant method converges. There is no general definition of "close enough", but the criterion has to do with how "wiggly" the function is on the interval $[~x_0,~x_1~]$. For example, if $f$ is differentiable on that interval and there is a point where $f^\prime = 0$ on the interval, then the algorithm may not converge.
## Comparison with other root-finding methods
The secant method does not require that the root remain bracketed like the bisection method does, and hence it does not always converge. The false position method (or regula falsi) uses the same formula as the secant method. However, it does not apply the formula on $x_{n-1}$ and $x_{n-2}$, like the secant method, but on $x_{n-1}$ and on the last iterate $x_k$ such that $f(x_k)$ and $f(x_{n-1})$ have a different sign. This means that the false position method always converges.
The recurrence formula of the secant method can be derived from the formula for Newton's method
$x_{n} = x_{n-1} - \frac{f(x_{n-1})}{f^\prime(x_{n-1})}$
by using the finite difference approximation
$f^\prime(x_{n-1}) \approx \frac{f(x_{n-1}) - f(x_{n-2})}{x_{n-1} - x_{n-2}}$.
The secant method can be interpreted as a method in which the derivative is replaced by an approximation and is thus a Quasi-Newton method. If we compare Newton's method with the secant method, we see that Newton's method converges faster (order 2 against α ≈ 1.6). However, Newton's method requires the evaluation of both $f$ and its derivative $f^\prime$ at every step, while the secant method only requires the evaluation of $f$. Therefore, the secant method may occasionally be faster in practice. For instance, if we assume that evaluating $f$ takes as much time as evaluating its derivative and we neglect all other costs, we can do two steps of the secant method (decreasing the logarithm of the error by a factor α² ≈ 2.6) for the same cost as one step of Newton's method (decreasing the logarithm of the error by a factor 2), so the secant method is faster. If however we consider parallel processing for the evaluation of the derivative, Newton's method proves its worth, being faster in time, though still spending more steps.
## Generalizations
Broyden's method is a generalization of the secant method to more than one dimension.
The following graph shows the function f in red and the last secant line in bold blue. In the graph, the x-intercept of the secant line seems to be a good approximation of the root of f.
## A computational example
The Secant method is applied to find a root of the function f(x) = x2 − 612. Here is an implementation in the Matlab language. (From calculation, we expect that the iteration converges at x = 24.7386)
f=@(x) x^2 - 612;
x(1)=10;
x(2)=30;
for i=3:7
x(i) = x(i-1) - (f(x(i-1)))*((x(i-1) - x(i-2))/(f(x(i-1)) - f(x(i-2))));
end
root=x(7)
## Notes
1. ^ Papakonstantinou, J., The Historical Development of the Secant Method in 1-D, retrieved 2011-06-29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 28, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.899657666683197, "perplexity": 231.37258156952706}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398459214.39/warc/CC-MAIN-20151124205419-00206-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.gamedev.net/forums/topic/385288-data-structures/ | # Data structures
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I want to speed up collision detection between units so I've divided my map into squares and want each square to hold information about all of the units in the square, then each unit checks collision only with the units in his square. Also, the units should be able to put themselves into the square's memory and then remove itself. I though about having each square hold a stl vector of pointers to the units in it's square, but then how would a unit be able to remove himself from one square and put himself in another (if it's moveing for example) ? Thanks.
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You could use a quadtree/octree (2d vs. 3d), a kd-tree or a combination of both or another kind. There's lots of spatial dividing/separation (it's called someting else but cannot quite remember the last word) methods like the one you've made available around the net.
But a simple solution for your problem would probably be to let the objects register themselves in a manager, and let that manager decide when and where they should go (eg. in what the squares they should be placed).
That's the solution I've made for my quadtree and it works like a charm (and the whole thing is lighting fast too, for my needs at least :D).
http://www.cs.berkeley.edu/~demmel/cs267/lecture26/lecture26.html
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By letting the unit have a pointer back to the "square" (and hence indirectly to the vector) being in. Moreover, by granting access to the square, the unit is able to get pointers to the surrounding squares.
However, please notice that collisions between units in neighboured squares may occur. So either you have to overlap the squares by an amount of maximal unit extent, or else check collision also with the units of the neighboured squares if the unit is close enough to te squares border.
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nife: that sounds like a good idea, but how is the manager built, and how does it place and remove the units?
haegarr: I don't understand how a pointer to the square would help?
I'm rather new to data structures so any clarification would be appreciated.
Thanks.
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Quote:
Original post by daniel_i_lnife: that sounds like a good idea, but how is the manager built, and how does it place and remove the units?haegarr: I don't understand how a pointer to the square would help?I'm rather new to data structures so any clarification would be appreciated.Thanks.
You use the pointer in order to "know about" the containing Square, so that the unit can communicate with that square. It looks something like:
class Unit { Square* holder; // other stuff public: void move(int dx, int dy) { x += dx; y += dy; // other checking logic holder = holder->notifyMoved(this, dx, dy); }};class Square { vector<Unit> contained; Square* left, right, up, down; // other stuff public: Square* notifyMoved(Unit* u, int dx, int dy) { if (u is no longer within my bounds) { remove u from contained; Square* target = (left/right/up/down, as appropriate); target->add(u); return target; } return this; // otherwise } void add(Unit* u) { add u to contained; }}
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A nice overview of a common grid-based method for broad phase collision detection is at:
http://www.harveycartel.org/metanet/tutorials/tutorialB.html
We did something similar in a commercial game currently under development. It works pretty well.
If you really want to delve into the nitty gritty details, have a look at "Real-Time Collision Detection" by Christer Ericson. His section on Uniform Grids is really good.
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Thanks, I just dont understand how to do: remove u from contained;
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Zahlman's pseudocode really shows you how to accomplish that. However, if you explicitly want to know how to remove something from a std::vector it is very easy.
// lets say this is in Zahlman's Square class...bool removeUnit( Unit* unit ){ size_t const unit_count = contained.size( ); bool unit_found = false; for( size_t i=0; i < unit_count; ++i ){ if( unit == contained ){ contained.erase( contained.begin( ) + i ); unit_found = true break; } } return unit_found;} | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.219201922416687, "perplexity": 2237.216867819173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891816068.93/warc/CC-MAIN-20180224231522-20180225011522-00382.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-2-solving-equations-2-8-proportions-and-similar-figures-standardized-test-prep-page-136/33 | ## Algebra 1
The associative property of addition says that any pair of addends can be summed first without changing the total. This is shown below: $(a+b)+c=(b+c)+a$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8608261942863464, "perplexity": 558.6791350667661}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313747.38/warc/CC-MAIN-20190818083417-20190818105417-00392.warc.gz"} |
https://www.transtutors.com/questions/the-stop-decay-company-sells-an-electric-toothbrush-for-25-its-sales-have-averaged-8-5144771.htm | # The Stop Decay Company sells an electric toothbrush for $25. Its sales have averaged 8,000 units... 1 answer below » Question 1 The Stop Decay Company sells an electric toothbrush for$25. Its sales have averaged
8,000 units per month over the last year. Recently, its closest competitor Decay Fighter
reduced the price of its electric toothbrush from $35 to$30. As a result, Stop Decay’s sales
declined by 1,500 units per month.
(i) What is the cross price elasticity of demand between Stop Decay’s toothbrush and Decay
Fighter’s tooth brush? Use the averaging formula. What does this indicate about the
relationship between the two products? (3 marks)
(ii) If Stop Decay knows that the price elasticity of demand for its toothbrush is -1.5, what
price would Stop Decay have to charge to sell the same number of units as it did before the
Decay Fighter price cut? Assume that Decay Fighter holds its price of its toothbrush constant
at \$30 Use the averaging formula. (3 marks).
(iii)What is Stop Decay’s average monthly total revenue from the sale of its electric
toothbrushes before and after the price change determined in part (ii)? (2 marks)
(iv) Is the result in part (iii) necessarily desirable? What other factors would have to be taken
into consideration? (2 marks)
Question 2
(a) Explain the differences between accounting profit, economic profit and normal profit
(3 marks).
(b) Suppose that due to changing tastes there is a sudden increase in demand for emu
meat.
(i) Assuming the costs of emu meat production remain unchanged, what would you expect
to happen to profits in the emu meat industry? (2 marks)
(ii) Assuming that there are low barriers to entry into the emu meat industry, explain why
resources would move into this industry? (2 marks).
(iii)In the long run, what would you expect to happen to profits in this industry? (1 mark).
(iv) Will normal profits occur in this industry in the long run? If so, explain why?
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https://brilliant.org/problems/blah-blah/ | # A calculus problem by Joel Yip
Calculus Level 3
What is $$\int _{ -\infty }^{ \infty }{ { e }^{ -{ x }^{ 2 } } } \, dx$$ to two decimal places.
× | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6937459707260132, "perplexity": 7709.035051783391}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934804680.40/warc/CC-MAIN-20171118075712-20171118095712-00011.warc.gz"} |
https://puzzling.stackexchange.com/questions/45078/what-is-a-cb-number/45084 | # What is a CB Number™?
This puzzle is based off the What is a Word™, What is a Phrase™ and What is a Number™ series started by JLee.
If a number conforms to a certain rule, I call it a CB Number™. Use the following examples to find the rule:
Here is a CSV:
CB Numbers™,Non-CB Numbers™
383,384
1412,1214
7557,8557
49537,43579
84286,86420
310222,420333
629218,639318
1234511,5432111
4762129,4763239
22222530,33333520
63655555,36355555
89899898,89898989
The puzzle relies on the series' inbuilt assumption, that each number can be tested for whether it is a CB Number™ own its own. In particular, a number's relationship to other numbers in the sequence is irrelevant.
These are not the only examples of CB Numbers™, more can be found.
The only reason the Non-CB Numbers™ are not in ascending order is because I have tried to make them look similar to the corresponding CB Numbers™ to their left. Note that this doesn't change the puzzle.
• CB Numbers™ aren't reliant on an obscure property of numbers like my previous question on weird numbers. – boboquack Oct 27 '16 at 21:10
• are the letter's 'CB' significant, or are they arbitrary? – Pat Oct 27 '16 at 21:32
• If they're arbitrary, I think they'd be the first puzzle of this sort in which the name had no significance at all. – Gareth McCaughan Oct 27 '16 at 21:39
• @Pat They aren't arbitrary - they are of some significance, though they probably won't allow you to easily solve the puzzle. More that if you solve the puzzle in the way I intended, you would have a second point of conformation. – boboquack Oct 27 '16 at 21:46
CB Numbers are numbers that
If you treat each digit as weights, the whole number balances on the midpoint of the scale.
For example,
in the number 1412, let us visualise as 1-4^1-2 where ^ indicates the midpoint. It can be observed that the distance-to-center of an outer digit is 3 times that of the inner digit.
We have,
the sum of weight times distance-to-center (left) = 1*3 + 4*1 = 7
the sum of weight times distance-to-center (right) = 1*1 + 2*3 = 7
Hence, 1412 balances on the midpoint.
CB probably stands for
Centrally balanced. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4295746982097626, "perplexity": 1386.5594820294796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141733122.72/warc/CC-MAIN-20201204040803-20201204070803-00136.warc.gz"} |
https://www.physicsforums.com/threads/calculate-the-change-in-the-boxs-kinetic-energy.152380/ | # Calculate the change in the box's kinetic energy
1. Jan 21, 2007
### lzh
1. The problem statement, all variables and given/known data
An 72.4 N box of clothes is pulled 28.8 m up
a 21.8degrees ramp by a force of 117 N that points
along the ramp.
The acceleration of gravity is 9.81 m/s2 :
If the coefficient of kinetic friction between
the box and ramp is 0.27, calculate the change
in the box's kinetic energy. Answer in units
of J.
3. The attempt at a solution
I have already figured out everything, but i'd like to know if the change here is the sum of both the diss. energy from friction and gravitational potential. Since, all the kinetic gets converted to grav. potential and diss in the end.
2. Jan 21, 2007
### radou
The work of all forces equals the change of kinetic energy. That's all you need to know.
3. Jan 21, 2007
### lzh
so what i said was right?
4. Jan 21, 2007
### radou
Forget about conservative forces, potential changes, etc. The work of all forces equals the change in kinetic energy, as stated, independent of the nature of these forces.
5. Jan 21, 2007
### lzh
oh, i see. So i would just use W=F*displacemnt= 3369.6J?
6. Jan 21, 2007
### lzh
so essentially, the work of all forces is the sum of the work of mgh and F(diss)*displacement?
7. Jan 21, 2007
### radou
There are three forces. You named two of them, and the third one is the force which pulls the crate up.
8. Jan 21, 2007
### lzh
oh i see! ty
9. Jan 21, 2007
### lzh
i tried adding it all up, but my hw service keeps saying that i'm wrong.
heres what i found:
mgh+Fdeltax+117:
->72.4*(10.69539)=774.3465J
10.695(height) was founded with:
28.8sin21.8=10.6954
Fdeltax-energy of friction:
first i founded the normal force:
72.4cos21.8=67.22
so force of friction is:
67.22*.27=18.15N
->18.15*(28.8)=522.72J
774.3465J+522.72J+117=1414J
but this isn't correct!
I tried this same step on a friend's version(same quesition w/ different numbers), and it ended up being right.
what did i do wrong?
10. Jan 21, 2007
### lzh
ok i figured it out
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Similar Discussions: Calculate the change in the box's kinetic energy | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8266851305961609, "perplexity": 2682.6369514875146}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171166.18/warc/CC-MAIN-20170219104611-00543-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://ohsu.pure.elsevier.com/en/publications/roles-of-the-subfornical-organ-and-area-postrema-in-arterial-pres | # Roles of the subfornical organ and area postrema in arterial pressure increases induced by 48-h water deprivation in normal rats
John P. Collister, David B. Nahey, Michael D. Hendel, Virginia L. Brooks
Research output: Contribution to journalArticlepeer-review
3 Scopus citations
## Abstract
In rats, water deprivation (WD) increases arterial blood pressure (BP) in part due to actions of elevated osmolality in the brain to increase vasopressin levels and sympathetic activity. However, the osmoreceptors that mediate this response have not been identified. To test the hypothesis that osmoregulatory circumventricular organs are involved, BP and heart rate (HR) were continuously recorded telemetrically during 48 h of WD in normal rats with lesions (x) or sham lesions (sham) of the subfornical organ (SFO) or area postrema (AP). Although WD increased BP in SFOx and SFOsham rats, no significant difference in the hypertensive response was observed between groups. HR decreased transiently but similarly in SFOx and SFOsham rats during the first 24 h of WD. When water was reintroduced, BP and HR decreased rapidly and similarly in both groups. BP (during lights off) and HR were both lower in APx rats before WD compared to APsham. WD increased BP less in APx rats, and the transient bradycardia was eliminated. Upon reintroduction of drinking water, smaller falls in both BP and HR were observed in APx rats compared to APsham rats. WD increased plasma osmolality and vasopressin levels similarly in APx and APsham rats, and acute blockade of systemic V1 vasopressin receptors elicited similar depressor responses, suggesting that the attenuated BP response is not due to smaller increases in vasopressin or osmolality. In conclusion, the AP, but not the SFO, is required for the maximal hypertensive effect induced by WD in rats.
Original language English (US) e00191 Physiological reports 2 1 https://doi.org/10.1002/phy2.191 Published - Jan 2014
## Keywords
• Area postrema
• Blood pressure
• Heart rate
• Subfornical organ
• Water deprivation
## ASJC Scopus subject areas
• Physiology
• Physiology (medical)
## Fingerprint
Dive into the research topics of 'Roles of the subfornical organ and area postrema in arterial pressure increases induced by 48-h water deprivation in normal rats'. Together they form a unique fingerprint. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8137332797050476, "perplexity": 29706.249393611986}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711151.22/warc/CC-MAIN-20221207085208-20221207115208-00540.warc.gz"} |
https://repository.upenn.edu/edissertations/3005/ | ## Publicly Accessible Penn Dissertations
2017
Dissertation
#### Degree Name
Doctor of Philosophy (PhD)
Mechanical Engineering & Applied Mechanics
Pedro Ponte Castañeda
#### Abstract
\noindent Porosity can have a significant effect on the overall constitutive behavior of many materials, especially when it serves to relax kinematic constraints imposed by the underlying matrix behavior. In this study, we investigate the multiscale, finite-strain response of viscoplastic porous single crystals and porous polycrystals. For these materials, the presence of voids leads to highly nonlinear dilatational behavior for loads with a large hydrostatic component, even though the matrix material itself is essentially incompressible.
\vspace*{15pt}
\noindent In this study, we employ the recently developed fully optimized second-order" homogenization approach, along with an iterated homogenization procedure, to obtain accurate estimates for the effective behavior of porous single crystals and porous polycrystals with fixed states of the microstructure. The method makes use of the effective properties of a linear comparison composite," whose local properties are chosen according to a suitably designed variational principle, to generate the corresponding estimates for the actual nonlinear porous materials. Additionally, consistent homogenization estimates for the average strain-rate and spin fields in the phases are used to develop approximate evolution equations for the microstructures. The model is quite general, and applies for viscoplastic porous single crystals and polycrystals with general crystallographic texture, general ellipsoidal voids, and general ellipsoidal grains, which are subjected to general loading conditions. The model is used to study both the instantaneous response and the evolution of the microstructure for porous FCC and HCP single crystals and polycrystals. It is found that the intrinsic anisotropy of the matrix phase---either due to the local crystallography in single crystals or to the texture of polycrystals---has significant effects on the porosity evolution, as well as on the overall hardening/softening behavior of the porous materials. In particular, the predictions of the model for porous single crystals are found to be in fairly good agreement with the full-field, numerical results available in the literature. The results for porous polycrystals suggest that the macroscopic behavior is controlled by porosity growth at high stress triaxialities, while it is controlled by texture evolution of the underlying matrix at low triaxialities.
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COinS | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6624671816825867, "perplexity": 1359.2409723411718}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662552994.41/warc/CC-MAIN-20220523011006-20220523041006-00682.warc.gz"} |
https://blog.listcomp.com/c++/2015/03/14/cpp-including-headers | Yao Yao on March 14, 2015
• Published in category
• C++
A header file is a file containing the external declarations for a library.
The #include preprocessor directive tells the preprocessor to open the named header file and insert its contents where the #include statement appears.
#include <header> // search in some systematic paths
#include "local.h" // typically search relative to the current directory. If not found, reprocessed as <local.h>
The libraries that have been inherited from C are still available with the traditional ‘.h’ extension. However, you can also use them with the more modern C++ include style by prepending a “c” before the name. Thus:
#include <stdio.h>
#include <stdlib.h>
become:
#include <cstdio>
#include <cstdlib>
And so on, for all the Standard C headers. This provides a nice distinction to the reader indicating when you’re using C versus C++ libraries.
## How the linker searches a library
When you make an external reference to a function or variable in C or C++, the linker, upon encountering this reference, can do one of two things. If it has not already encountered the definition for the function or variable, it adds the identifier to its list of “unresolved references.” If the linker has already encountered the definition, the reference is resolved.
If the linker cannot find the definition in the list of object modules, it searches the libraries. Libraries have some sort of indexing so the linker doesn’t need to look through all the object modules in the library–-it just looks in the index. When the linker finds a definition in a library, the entire object module, not just the function definition, is linked into the executable program.
If you want to minimize executable program size, you might consider putting a single function in each source code file when you build your own libraries. This requires more editing3, but it can be helpful to the user. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4218330681324005, "perplexity": 2043.9089635539945}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039503725.80/warc/CC-MAIN-20210421004512-20210421034512-00102.warc.gz"} |
http://fredrikj.net/math/hurwitz_zeta.html | # Rigorous high-precision computation of the Hurwitz zeta function and its derivatives
Author: Fredrik Johansson
Final submitted version (PDF)
In Numerical Algorithms, DOI: 10.1007/s11075-014-9893-1
arXiv preprint: http://arxiv.org/abs/1309.2877, published September 11, 2013.
## Abstract
We study the use of the Euler-Maclaurin formula to numerically evaluate the Hurwitz zeta function $\zeta(s,a)$ for $s, a \in \mathbb{C}$, along with an arbitrary number of derivatives with respect to $s$, to arbitrary precision with rigorous error bounds. Techniques that lead to a fast implementation are discussed. We present new record computations of Stieltjes constants, Keiper-Li coefficients and the first nontrivial zero of the Riemann zeta function, obtained using an open source implementation of the algorithms described in this paper.
## Implementation
The implementation of the Hurwitz zeta function is available as part of the open source Arb library.
## Computational data
Small files:
• The imaginary part of the Riemann zeta zero $\rho_1$ to over 303000 digits, decimal representation [txt, 0.3 MB]
• The imaginary part of the Riemann zeta zero $\rho_1$ to over 303000 digits, internal representation $a2^b \pm c2^d$ [txt, 0.3 MB]
• The Stieltjes constants $\gamma_0 \ldots \gamma_{100000}$ rounded to 20 decimal digits [txt, 2.8 MB]
• The Keiper-Li coefficients $\lambda_0 \ldots \lambda_{100000}$ rounded to 20 decimal digits [txt, 2.1 MB]
Huge files (each line contains five integers n a b c d, separated by single spaces, such that $\gamma_n$ (respectively $\lambda_n$) is contained in the ball $a2^b \pm c2^d$):
• The Stieltjes constants $\gamma_0 \ldots \gamma_{100000}$ with accuracy between roughly 37000 and 10000 digits, internal representation [txt.tar.bz2, 902 MB compressed, 2.0 GB decompressed]
• The Keiper-Li coefficients $\lambda_0 \ldots \lambda_{100000}$ with accuracy between roughly 33000 and 2900 digits, internal representation [txt.tar.bz2, 741 MB compressed, 1.7 GB decompressed]
Last updated July 31, 2014. Contact: [email protected].
Back to fredrikj.net | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7434515953063965, "perplexity": 1558.7551820971778}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323604.1/warc/CC-MAIN-20170628101910-20170628121910-00230.warc.gz"} |
http://quant.stackexchange.com/questions/9652/examples-of-non-increasing-variance-of-a-time-homogeneous-markovian-process | # Examples of non-increasing variance of a time homogeneous Markovian process
This is an edit to the previous question, on stationary process, which was answered by Richard below.
Let $x_t$ be a zero mean, time homogeneous Markovian process over time $t$ starting from $x_0=0$. What are the examples of $x_t$ where the variance at $t$ does not increase over $t$?
1) In discrete time and discrete state, the followig is a very simple example where the variance periodically oscillates over time.
$$x_{t+1} = \eta(1-|x_t|),\, x_0=0;\, \eta\in\{-1,1\},\mbox{ with probability of } \frac{1}{2} \mbox{ on each value of }\eta.$$
2) In continuous time, but discontinuous path setting, is the following jump diffusion process a correct example?
$$dx_t = -\alpha x_t dt+dz_t+ y\eta dN_t,\, x_0 = 0,$$ where $\alpha\gg 0$, $z_t$ is the standard brownian motion with mean $0$ and standard deviation $t$, $N_t$ is the Poisson process with frequency $0<\lambda\ll 1$, $\eta$ takes on values $-1$ or $1$ with $0.5$ probability each, $z_{t_1}$, $N_{t_2}$ and $\eta$ are independent of each other at arbitrary $t_1$ and $t_2$, and constant $y\gg 1$.
On second thought, this is not a correct example. One can solve this equation and one will find the variance of this process is the sum of the variance from $dz_t$ and that from $dN_t$ due their independence. We will have to make the jumps negatively correlated to $z_t$.
A better setup is to shift $x_t$ beyond a barrier directly back to the $x=0$ line. So the process resides on the topology of two cylinders touched along a longitude. However, it seems to me, even this set up with $x_t$ being either a standard Browniam motion or mean reverting one without any jump process still has its variance increasing with time.
Therefore, I am still without a valid example in this setup.
3) What are the examples for continuous path? I suspect it is not possible. Can anyone prove this if it is indeed impossible?
-
"variance periodically oscillates over time"...that doesn't sound time homogeneous to me – quasi Dec 9 '13 at 21:58
Check out my example. – Hans Dec 9 '13 at 22:23
gotcha, get it now – quasi Dec 9 '13 at 23:19
en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process; start it from its steady state distribution. note this has mean-reverting behavior, similar to your example. oops, doesn't start at 0 though – quasi Dec 9 '13 at 23:22
This does not work. The variance of the mean-reverting Ornstein-Uhlenbeck process strictly increases over time. – Hans Dec 10 '13 at 3:04
In the literature it is often dealt with the covariance function. For a stationary time series, the covariance between $X_t$ and $X_s$ only depends on the time span $|t-s|$. For the varianace of $X_t$ we have $t-s=0$.
why is $t-a=0$? Also the autocovariance is to be a function of the time difference not necessarily a constant. – Hans Dec 7 '13 at 21:40
If we want to apply the formulation of covariance to the simple variance case, then $t=s$ and thus $t-s=0$. The ACF is a function of the time difference, true. But this is zero for the variance. A random walk e.g. is not stationary. The variance increases with the square-root of time. An white noise on the other hand is stationary - the variance at each point in time is the same. – Richard Dec 7 '13 at 22:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9501467347145081, "perplexity": 329.43950977593863}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936461332.16/warc/CC-MAIN-20150226074101-00190-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://www.iacr.org/cryptodb/data/paper.php?pubkey=23137 | ## CryptoDB
### Paper: Accountability: Definition and Relationship to Verifiability
Authors: Ralf Küsters Tomasz Truderung Andreas Vogt URL: http://eprint.iacr.org/2010/236 Search ePrint Search Google Many cryptographic tasks and protocols, such as non-repudiation, contract-signing, voting, auction, identity-based encryption, and certain forms of secure multi-party computation, involve the use of (semi-)trusted parties, such as notaries and authorities. It is crucial that such parties can be held accountable in case they misbehave as this is a strong incentive for such parties to follow the protocol. Unfortunately, there does not exist a general and convincing definition of accountability that would allow to assess the level of accountability a protocol provides. In this paper, we therefore propose a new, widely applicable definition of accountability, with interpretations both in symbolic and computational models. Our definition reveals that accountability is closely related to verifiability, for which we also propose a new definition. We prove that verifiability can be interpreted as a restricted form of accountability. Our findings on verifiability are of independent interest. As a proof of concept, we apply our definitions to the analysis of protocols for three different tasks: contract-signing, voting, and auctions. Our analysis unveils some subtleties and unexpected weaknesses, showing in one case that the protocol is unusable in practice. However, for this protocol we propose a fix to establish a reasonable level of accountability.
##### BibTeX
@misc{eprint-2010-23137,
title={Accountability: Definition and Relationship to Verifiability},
booktitle={IACR Eprint archive},
keywords={cryptographic protocols / Accountability, Verifiability, Protocol Analysis, E-Voting, Auction, Contract Signing},
url={http://eprint.iacr.org/2010/236},
note={ [email protected] 14726 received 27 Apr 2010},
author={Ralf Küsters and Tomasz Truderung and Andreas Vogt},
year=2010
} | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7779639363288879, "perplexity": 3424.634739210395}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363437.15/warc/CC-MAIN-20211208022710-20211208052710-00610.warc.gz"} |
https://www.mindstick.com/forum/1223/vbscript-skipline-and-cr-line-endings | #### vbscript skipline and cr line endings
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Hi Expert,
For some reason when I use the objFile.ReadLine method to read my text file, the entire file is returned as one long line. The file I'm opening is using CR line endings instead of CRLF or LF line endings. Does anyone know how I can read this file line by line in vbscript if ReadLine does not recognize CR line endings? Code is below:
Set objFSO = CreateObject("Scripting.FileSystemObject")Set txsInput = objFSO.OpenTextFile("C:\Path\To\My\File.csv",1)'Read lines one by one Do While txsInput.AtEndOfStream <> True strTemp = txsInput.ReadLine msgbox strTempLoop
Instead of alerting for each line, I get one alert with the entire file. Any help is appreciated.
1. ##### Re: vbscript skipline and cr line endings
Hi Pravesh,
.ReadLine won't work in your case, because it depends on the existence of a vbLf character. If you don't want to re-encode the line breaks or read the entire file and split it at vbCr (if the file is not-so-large):
For Each line In Split(text, vbCr)
MsgBox line
Next
Re-encoding the file can be done like this:
Set fso = CreateObject("Scripting.FileSystemObject")
filename = "C:\path\to\your.csv"
Set infile = fso.OpenTextFile(filename)
Set outfile = fso.OpenTextFile(filename & ".tmp", 2)
Do Until infile.AtEndOfStream
If c = vbCr Then
outfile.Write vbCrLf
Else
outfile.Write c
End If
Loop
infile.Close
outfile.Close
fso.DeleteFile filename, True
fso.MoveFile filename & ".tmp", filename
Or you could use something like recode for the conversion. Most text editors (e.g. Vim, Notepad++, SciTE, UltraEdit, …) can do this kind of conversion, too. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5178794264793396, "perplexity": 13514.448880054877}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514571506.61/warc/CC-MAIN-20190915134729-20190915160729-00077.warc.gz"} |
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