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https://www.physicsforums.com/threads/area-of-a-dome.57784/	# Area of a dome 1. Dec 25, 2004 ### DaveC426913 Trying to figure out the answer to another thread. What is formula for the surface area of a dome? Googling got me $$2\pi r h$$ (where $$h$$ is the height of the dome above its slice through the sphere). Is that right? Ultimately, I'm trying to figure out how the area changes as a function of the slice through the sphere. i.e.: When the slice goes through the centre of the sphere, the area is X (in fact, exactly half of the sphere's area). OK. Now, if I move the slice out to $$1/2 r$$, what does that do to the area of the dome? Does the area halve? or quarter? 2. Dec 25, 2004 ### dextercioby I advise u draw a picture.Explain the geometry of the drawing.Which is the sphere,which is the paraboloid,is it a revolution paraboloid,are they coaxial,what is "h",what is "r",or simply give the link to the webpage where u got that result. If you're asking for help,at least do it in a proper way. Daniel. 3. Dec 25, 2004 ### DaveC426913 Guess I didn't get the memo on "the proper way". (Don't know why this gpt posted twice...) Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook Have something to add? Similar Discussions: Area of a dome	{"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": 0.842997133731842, "perplexity": 1808.9589964448883}, "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-2017-04/segments/1484560285001.96/warc/CC-MAIN-20170116095125-00127-ip-10-171-10-70.ec2.internal.warc.gz"}
https://brilliant.org/problems/a-classical-mechanics-problem-by-aniket-sanghi/	# Curly waves Equation of two waves are $$y = A \sin(wt - kx)$$ $$y=A \sin(wt - kx + 90)$$ 90 denotes 90 degrees, A is amplitude,w is angular frequency, $$k$$ is wave number; Now the equation of the resulting wave can be represented as $$y = A\sqrt [ 2 ]{ a } \sin(wt - kx + b)$$ where $$a$$ is an integer, and $$b$$ is in degrees Find $$(b2)/(a5)$$. ×	{"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": 0.9982691407203674, "perplexity": 2002.093108795851}, "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/1547583728901.52/warc/CC-MAIN-20190120163942-20190120185942-00605.warc.gz"}
http://mathhelpforum.com/calculus/107749-differentiation-sinh-function.html	# Thread: differentiation of sinh function 1. ## differentiation of sinh function I'm trying to differentiate sinh^(-1) (KL). (so arsinh(KL)) with respect to K and also with respect to L. Can some one point me in the right direction? Thanks 2. Hello, willowtree! Differentiate: . $y \:=\:\sinh^{-1}(kx)$ with respect to $x.$ Take $\sinh$ of both sides: . $\sinh (y) \;=\;kx$ Differentiate implicitly: . $\cosh(y)\,\frac{dy}{dx} \:=\:k \quad\Rightarrow\quad \frac{dy}{dx} \:=\:\frac{k}{\cosh(y)}$ We have: . $\cosh^2(y) - \sinh^2(y) \:=\:1 \quad\Rightarrow\quad \cos^2(y) \:=\:1 + \sin^2(y) \;=\;1 + (kx)^2$ . . Hence: . $\cos(y) \:=\:\sqrt{1+k^2x^2}$ Therefore: . $\frac{dy}{dx} \;=\;\frac{k}{\sqrt{1+k^2x^2}}$	{"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": 8, "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": 0.977262556552887, "perplexity": 3013.946321913707}, "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-2017-13/segments/1490218187744.59/warc/CC-MAIN-20170322212947-00274-ip-10-233-31-227.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/damped-oscillator-problem-very-hard.270446/	# Damped Oscillator Problem - Very Hard 1. Nov 8, 2008 ### Dillio 1. The problem statement, all variables and given/known data I have read the chapter twice and I have read through the notes several times to help me with the homework assignment. It deals with damped Harmonic Oscillations. Problem: You have a mass submerged horizontally in oil and a spring with a k of 85 N/m pulls on a mass of 250g in oil with a b = 0.07 Kg/s 1. What is the period of oscillation? I found the angular frequency of the system and then used the 2(pi) / omega to find the period. I found this to be around 0.3407 seconds. Is this correct? 2. How long does it take for the amplitude to die down to 0.5 amplitude of the max? There seems to be nothing in the book or the notes that helps with solving this unless I am missing something. I do not know a distance (or position), Amplitude, or phase angle to use the equation found in the book. I found an answer of 4.95 seconds but I am not sure if that is correct since no equation in the book solves something like this. I took the Amplitude term of the damped harmonic oscillator equation and set it equal to 0.5A and solved for t. 3. How long until the total energy is 0.5 the initial value? The book just gives the rate of energy loss in terms of a velocity value and a b value, which was not given. Absolutely no clue here.... I appreciate ANY help! Thanks. 2. Nov 9, 2008 ### alphysicist Hi Dillio, That looks right to me. That looks right to me. In #2 you found the time for the amplitude to reach half of its starting value. For #3, when the energy is half of its value, what is the amplitude (compared to the original amplitude)? Once you answer that you can follow the same procedure you used in #2. 3. Nov 9, 2008 ### Dillio I used E = 0.5kA^2 and found A to be equal to sqrt([2E]/k). To solve for the energy when it is one half of its original value. I made the second energy equation: 05E = 0.5kA^2. I solved for this amplitude and found sqrt(E/k). That means the second amplitude is related to the initial energy by: E/sqrt(2) I solved this for t in the amplitude equation and actually found 2.4 seconds, which is about half the time value I found in part 2. Does this make sense? Similar Discussions: Damped Oscillator Problem - Very Hard	{"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": 0.8543029427528381, "perplexity": 419.107197738967}, "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/1508187825812.89/warc/CC-MAIN-20171023073607-20171023093607-00839.warc.gz"}
http://wiki.math.toronto.edu/TorontoMathWiki/index.php?title=Topology_of_Algebraic_Varieties_Learning_Seminar&oldid=3953	# Topology of Algebraic Varieties Learning Seminar (diff) ← Older revision \| Latest revision (diff) \| Newer revision → (diff) A learning seminar on topology of algebraic varieties. We meet on Tuesdays 9:30-11:00 in BA 6180. Topics We will cover some subset of the following topics: Lefschetz theorems, Hodge decomposition, intersection homology, decomposition theorem, perverse sheaves, mixed Hodge structures, with applications to toric varieties, geometric Satake correspondence, and Ngo's proof of the fundamental Lemma. References 1. Our main reference is the survey paper "The decomposition theorem, perverse sheaves, and the topology of algebraic maps" by Cataldo and Migliorini, recently published in the Bulletin of the AMS and available here: http://front.math.ucdavis.edu/0712.0349 2. "Intersection homology theory" by Goresky and MacPherson. 3. Introduction to intersection homology theory by Kirwan. 4. Notes on Perverse Sheaves and Vanishing Cycles by David B. Massey http://arxiv.org/abs/math/9908107v2 5. Algebraic Geometry over the complex numbers by Arapura http://www.math.purdue.edu/~dvb/book.html 6. Intersection homology II, by Goresky and MacPherson. Schedule 1. Jan 12, Smooth projective varieties, cohomology, and Lefschetz theorems (1.1), Joel 2. Jan 19, Families of projective varieties, monodromy, and degeneration of Leray-Serre spectral sequence (1.2) Stephen 3. Jan 26, Intersection homology (topological approach), decomposition and examples (1.3, 1.4) Misha M 4. Feb 2, Intersection homology (topological approach), decomposition and examples #2 (1.3, 1.4) Misha M 5. Feb 9, Cohomology of Sheaves and Derived Categories (1.5) Arthur 6. Feb 23, Cohomology of Sheaves and Derived Categories / IC Sheaves + Perverse Sheaves - Arthur/Omar 7. Mar 2, IC Sheaves + Perverse Sheaves (2.1, 2.2) Omar 8. Mar 9, Perverse Sheaves + Decomposition theorem - Omar/Chris (1.6, 1.8) 9. Mar 16, Decomposition theorem examples - Chris 10. Mar 23, Semismall maps and Springer theory I (4.2) Sergey 11. Mar 30, Semismall maps and Springer theory II (4.2) Sergey 12. April 13, Sheaf to functions and Kazhdan-Lusztig polynomial (4.3,4.4) Brad 13. April 15, Geometric Satake isomorphism (4.5) Bruce 14. April 20, Riemann-Hilbert Correspondence, Dan Also it would be nice to have a couple of talks on Hodge theory at some point.	{"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": 0.8784677982330322, "perplexity": 4033.164972127705}, "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-2013-20/segments/1368704253666/warc/CC-MAIN-20130516113733-00010-ip-10-60-113-184.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/commutator-of-4-momentum-and-position.263707/	# Commutator of 4-momentum and position 1. Oct 12, 2008 ### kilokhan Is there a commutation relation between $x^{\mu}$ and $\partial^{\nu}$ if you treat them as operators? I think I will need that to prove this $[J J^{\mu \nu}, J^{\rho \sigma}] = i (g^{\nu \rho} J^{\mu \sigma} - g^{\mu \rho} J^{\nu \sigma} - g^{\nu \sigma} J^{\mu \rho} + g^{\mu \sigma} J^{\nu \rho})$ Where the generators are defined as $J J^{\mu \nu} = i (x^{\mu} \partial^{\nu} - x^{\nu} \partial^{\mu})$ Last edited: Oct 12, 2008 2. Oct 12, 2008 ### kilokhan Never mind, I found the appropriate relation, $\partial_{\mu}x^{\nu}=g^{\mu \nu}$ But I'm not entirely sure why this is true. If someone could explain that would be great.	{"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": 0.9837374687194824, "perplexity": 648.4650176813099}, "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-2016-44/segments/1476988719564.4/warc/CC-MAIN-20161020183839-00357-ip-10-171-6-4.ec2.internal.warc.gz"}
http://mathoverflow.net/questions/98993/torsion-in-cuspidal-cohomology	# Torsion in cuspidal cohomology Following Lemma 2.7 from Vogtmann's Rational Homology of Bianchi Groups, I want to define cuspidal cohomology as $$H_{\mathrm{cusp}}(M)=\frac{H_1(M)}{i_(H_1(\partial M))}$$ where $i:\partial M\to M$ is the inclusion and I take integral coefficients. The motivation is that Abelian covering spaces such that the preimage of a cusp consists of disjoint copies of the same cusp are corresponding to exactly those holonomies $\pi_1(M)\to G$ that factor through the cuspidal cohomology. I verified for all hyperbolic cusped 3-manifolds in the SnapPea census that if $H_1(M)=\mathbb{Z}^n\oplus T$ where $T$ is torsion, then $H_\mathrm{cusp}(M)=\mathbb{Z}^{n-\mbox{number of cusps}}\oplus T$. This is to be expected rationally by half-lives-half-dies. It seems to also hold integrally for hyperbolic 3-manifolds. Is there an argument that this holds for all hyperbolic cusped 3-manifolds? (And maybe a counterexample if you take a non-hyperbolic manifold) - Vogtmann's name is spelled with two n's. – Jim Conant Jun 6 '12 at 23:11 Consider the long exact sequence on homology (coefficients in $\mathbb{Z}$) $$\to H_1(\partial M)\overset{i}{\to} H_1(M)\to H_1(M,\partial M) \to H_0(\partial M) \to$$ You are looking for $H_1(M)/i_\ast(H_1(\partial M)) \cong im\{ H_1(M)\to H_1(M,\partial M)\} \cong ker \{ H_1(M,\partial M)\to H_0(\partial M)\}$ by the exactness of the sequence. If $H_1(M)\cong \mathbb{Z}^n\oplus T$, $T$ torsion, then $H_2(M)\cong \mathbb{Z}^{n-1}$ (the rank $n-1$ follows from Euler characteristic). By universal coefficients, we have a short exact sequence $$0\to Ext(H_1(M),\mathbb{Z})\to H^2(M) \to Hom(H_2(M),\mathbb{Z})\to 0.$$ One computes $Ext(H_1(M),\mathbb{Z})\cong T$, $Hom(H_2(M),\mathbb{Z})\cong \mathbb{Z}^{n-1}$ (see p. 195 of Hatcher), so that $H^2(M)\cong \mathbb{Z}^{n-1} \oplus T$. By Lefschetz duality, $H^2(M)\cong H_1(M,\partial M) \cong \mathbb{Z}^{n-1}\oplus T$. So you are looking for the torsion in $$ker\{ H_1(M,\partial M)\to H_0(\partial M) \} \cong ker\{ \mathbb{Z}^{n-1}\oplus T \to \mathbb{Z}^c\},$$ which is clearly isomorphic to $T$. - One can make some progress on this by using half-lives--half-dies with coefficients in $\mathbb{F}_p$. Suppose the cuspidal homology is $\mathbb{Z}^{n - c} \oplus S$. If $p$ is coprime to the order of $T$, then the dimension of $H_1(M; \mathbb{F}_p)$ is just $n$ and the mod $p$ cuspidal homology has dimension $n - c$; hence the order of $S$ must also be coprime to $p$. Indeed, this argument shows that if the order of $T$ is square-free then your claim holds. Perhaps some more sophisticated argument with universal coefficients is enough to prove it in general? (If this is true, it's surely not because the manifolds are hyperbolic but rather a general fact about 3-manifolds with torus boundary.) - I can't vote my own answer down, but Ian's answer (currently below this one) is complete. – Nathan Dunfield Jun 12 '12 at 13:18 It is worth pointing out that $T$ may lie in the image of $i_$: There is an $M$ such that $H_1(M) \cong \mathbb{Z}^{n} \oplus T$ and $H_{\mathrm{cusp}}(M) \cong \mathbb{Z}^{n-\mathrm{number\ of\ cusps}} \oplus T$ but $T$ dies under the quotient map $H_1(M) \to H_\mathrm{cusp}(M)$. Let $N$ be an orientable $I$-bundle over the Klein bottle. Then the "cuspidal homology" of $N$ is $\mathbb{Z}/2\mathbb{Z}$, but the torsion in $H_1(M)$ dies under $H_1(M) \to H_\mathrm {cusp}(M)$. To find a hyperbolic example, note that a theorem of R. Myers (Excellent 1-manifolds in compact 3-manifolds. Topology Appl., 49(2):115–127, 1993.) produces a null-homotopic hyperbolic knot $K$ in $N$. Thurston's Hyperbolic Dehn Surgery Theorem allows us to perform surgery on $K$ to obtain a hyperbolic $M$ where all the maps on homology are as above. - @Richard, it seems you are saying A and not A in your answer. – Misha Jun 7 '12 at 16:30 @Misha: The answer is an attempt to emphasize the difference between isomorphism and equality. As the question asks for equality, I think this is relevant. – Richard Kent Jun 7 '12 at 16:41 Edited to clarify. – Richard Kent Jun 7 '12 at 16:54 @Richard, I understand what you are saying now. However, it seems to me that in the context of the question, equality would not make much sense since $H_{cusp}$ is the quotient of $H_1$, not a subgroup. I think the equality sign in question is just the (common) abuse of notation. Nevertheless, you have a very nice example which shows that torsion part of $H_1$ could lie in the image of $i_*$. It also suggests that one should check what happens in the case of other Seifert manifolds. – Misha Jun 7 '12 at 17:15 @Misha: Yeah, my interpretation of equality as meaning that T survives is psychological, I guess. One more edit to further clarify. – Richard Kent Jun 7 '12 at 17:27	{"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": 0.9742176532745361, "perplexity": 307.3061981933337}, "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/1432207928780.77/warc/CC-MAIN-20150521113208-00247-ip-10-180-206-219.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/279465/how-to-evaluate-the-following-integral-using-hypergeometric-function	# How to evaluate the following integral using hypergeometric function? May I know how this integral was evaluated using hypergeometric function? $$\int \sin^n x\ dx$$ Wolframalpha showed this result but with no steps - You can prove using integration by parts that these integrals (as a sequence of functions) satisfy a recurrence relation. Similarly, hypergeometric series satisfy lots of similar relations (which is one of the main reasons they are special, actually). This is why they often pop up when doing integrals. – Marek Jan 15 '13 at 20:28 @Marek, thanks for your highlights. – Tariq Jan 16 '13 at 17:47 Assuming $n$ is a non-negative integer, you could use binomial theorem: $$\begin{eqnarray} \sin^n(x) &=& \left( \frac{\exp(i x) - \exp(-i x)}{2i}\right)^n = \frac{1}{2^n i^n} \sum_{m=0}^n \binom{n}{m} (-1)^m \exp\left( i \left(n-2m\right)x \right) \\ &=& \frac{1}{2^n i^n} \sum_{m=0}^n \binom{n}{m} (-1)^m \left(\cos\left(\left(n-2m\right)x \right) + i \sin\left( \left(n-2m\right)x \right) \right) \end{eqnarray}$$ Since the left-hand-side is real we only keep cosines for even $n$: $$\begin{eqnarray} \sin^{2n}(x) &=& \frac{1}{2^{2n}} \sum_{m=0}^{2n} \binom{2n}{m}\left(-1\right)^{n-m} \cos\left(\left(2n-2m\right)x\right) \\ &\stackrel{\text{symmetry}}{=}& \frac{1}{2^{2n}} \binom{2n}{n} + \frac{1}{2^{2n-1}} \sum_{m=0}^{n-1} \binom{2n}{m}\left(-1\right)^{n-m} \cos\left(2 \left(n-m\right)x\right) \\ &\stackrel{m\to n-m} =& \frac{1}{2^{2n}} \binom{2n}{n} + \frac{1}{2^{2n-1}} \sum_{m=1}^n \binom{2n}{n+m} (-1)^n \cos(2 m x) \tag{1} \end{eqnarray}$$ and, likewise, only sines for odd $n$: $$\sin^{2n+1}(x) = \frac{1}{2^{2n}} \sum_{m=0}^n \binom{2n+1}{n+1+m} (-1)^m \sin\left((2m+1)x\right) \tag{2}$$ We can now integrate element-wise: $$\int \sin^{2n}(x) \, \mathrm{d}x = \frac{1}{2^{2n}} \binom{2n}{n} x + \frac{1}{2^{2n-1}} \sum_{m=1}^n \binom{2n}{n+m} (-1)^n \frac{\sin(2 m x)}{2m} + \text{const.}$$ $$\int \sin^{2n+1}(x) \, \mathrm{d}x = -\frac{1}{2^{2n}} \sum_{m=0}^n \binom{2n+1}{n+1+m} (-1)^m \frac{\cos\left((2m+1)x\right)}{2m+1} + \text{const.}$$ To obtain a hypergeometric function, let $u = \sin(x)$. Then $$\int \sin^n(x)\, \mathrm{d}x = \int \frac{u^n}{\sqrt{1-u^2}} \mathrm{d}u$$ Now see this answer of mine on how to find the anti-derivative of $\int u^a (1-u)^b \mathrm{d} u$. Applying the same principles, we find: $$\int \frac{u^n}{\sqrt{1-u^2}} \mathrm{d}u =\int u^n \cdot {}_1F_0\left(\left.\begin{array}{c} \frac{1}{2} \\ - \end{array} \right\| u^2 \right) \mathrm{d} u = \int \frac{\mathrm{d}}{\mathrm{d}u} \left( \frac{u^{n+1}}{n+1} \cdot {}_2F_1\left(\left.\begin{array}{cc} \frac{1}{2} & \frac{n+1}{2} \\ & \frac{n+3}{2} \end{array} \right\| u^2 \right) \right) \mathrm{d} u$$ Thus, we have: $$\int \sin^n(x) \, \mathrm{d}x = \frac{\sin^{n+1}(x)}{n+1} \cdot {}_2F_1\left(\left.\begin{array}{cc} \frac{1}{2} & \frac{n+1}{2} \\ & \frac{n+3}{2} \end{array} \right\| \sin^2(x) \right) + \text{const.} \tag{3}$$ This works where $u = \sin(x)$ is invertible. To extend validity of the answer, differentiate it. We would get $$\frac{\mathrm{d}}{\mathrm{d}x} \left( \frac{\sin^{n+1}(x)}{n+1} \cdot {}_2F_1\left(\left.\begin{array}{cc} \frac{1}{2} & \frac{n+1}{2} \\ & \frac{n+3}{2} \end{array} \right\| \sin^2(x) \right) \right) = \frac{\sqrt{\cos^2(x)}}{\cos(x)} \sin^{n} (x)$$ and since the pre-factor $\frac{\sqrt{\cos^2(x)}}{\cos(x)}$ is a differential constant, i.e. its derivative is zero, we arrive at: $$\int \sin^n(x) \, \mathrm{d}x = \frac{\cos(x)}{\sqrt{\cos^2(x)}} \frac{\sin^{n+1}(x)}{n+1} \cdot {}_2F_1\left(\left.\begin{array}{cc} \frac{1}{2} & \frac{n+1}{2} \\ & \frac{n+3}{2} \end{array} \right\| \sin^2(x) \right) + \text{const.} \tag{4}$$ This can be related to the answer provided by Wolfram\|Alpha, and thus by Mathematica, using Kummer's relations. @J.M. Thanks! $\ \$ – Sasha Jan 16 '13 at 17:53	{"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": 0.980557918548584, "perplexity": 316.2933593555279}, "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-2014-23/segments/1404776435465.20/warc/CC-MAIN-20140707234035-00077-ip-10-180-212-248.ec2.internal.warc.gz"}
https://physics.stackexchange.com/questions/41439/when-we-define-the-s-matrix-what-are-in-and-out-states	# When we define the S-matrix, what are “in” and “out” states? I have seen the scattering matrix defined using initial ("in") and final ("out") eigenstates of the free hamiltonian, with $$\left\| \vec{p}_1 \cdots \vec{p}_n \; \text{out} \right\rangle = S^{-1} \left\| \vec{p}_1 \cdots \vec{p}_n \; \text{in} \right\rangle$$ so that $$\left\langle \vec{p}_1 \cdots \vec{p}_n \; \text{out} \mid \vec{q}_1 \cdots \vec{q}_m \; \text{in} \right\rangle = \left\langle \vec{p}_1 \cdots \vec{p}_n \; \text{in} \mid S \mid \vec{q}_1 \cdots \vec{q}_m \; \text{in} \right\rangle.$$ 1) What are "in" and "out" states? 2) Are they Fock states? 3) In Schrödinger or Heisenberg or interaction representation? 4) How are they related? (I believe that I see what they handwavily represent physically, but not formally.) My main issue is that, if "in" and "out" states are one-particle eigenstates of the free hamiltonian, i.e. if $\left\| \vec{p}_1 \text{out} \right\rangle$ describes a free particle with momentum $\vec{p}_1$, and $\left\| \vec{p}_1 \text{in} \right\rangle$ also describes a free particle with momentum $\vec{p}_1$, then $\left\| \vec{p}_1 \text{out} \right\rangle = \left\| \vec{p}_1 \text{in} \right\rangle$ ... which is false. Still, books (some at least) describe these "in" and "out" states like that. Moreover, I have seen (e.g. in Wikipedia, but also on this answer) that the scattering matrix is a map between two different Fock states, and I don't understand that. 5) Do states of the interacting system live in the same Fock space that asymptotic free states? 6) And if not, where do they live? Understandable references would be appreciated. 1/2. In and out states (of massive theories) are joint energy-momentum eigenstates (spanning asymptotic in and out Fock spaces) of asymptotic, free Hamiltonians (and momentum operators) associated with the bound states of a theory. These Hamiltonians are not identical with the Hamiltonian defining the finite-time dynamics of the theory; in simple cases (ordinary quantum mechanics without bound states) they are just the Hamiltonians obtained by discarding the interaction terms. (For a rigorous discussion of this well understood situation see Chapter 3 in Volume 3 of Thirring's treatise on mathematical physics.) 3. The representation (Schrödinger or Heisenberg or interaction) doesn't change the meaning of the states; it just changes where the dynamics is recorded. 4. In and out states are related by the S-matrix, through the formula in your original question. For a single particle in an external potential (which is equivalent to two particles with a translation-invariant interaction, viewed in the rest frame of their center of mass), this is usually handled via the Lippman-Schwinger equation, treated in most textbooks. The relation $\|p_1,in\rangle=\|p_1,out\rangle$ (which you believe to be false) is in fact true, as single bound states do not scatter. The S-matrix is the identity on (dressed) single-particle states of a translation invartiant theory. Things get interesting when there are at least two particles around. Since only the total momentum is conserved, there is typically an exchange of momentum, and the amount is determined by the S-matrix. (The classical analogue is the change of direction when playing a golf ball across an uneven lawn - in the analogy the unevenness would be due to the influence of the second particle.) 5. In a relativistic quantum field theory, the asymptotic Fock spaces are not equivalent to the Hilbert space in which the dynamics happens. The latter is never a Fock space (which means that the commutation relations are realized in an inequivalent manner). This is called Haag's theorem, and is the main reason for the UV divergences in perturbative QFT, where one tries to ignore this fact. See, e.g., Haag's theorem and practical QFT computations Renormalization scheme independence of beta function *6. The asymptotic spaces are obtained by a limiting procedure from the space where the finite-time dynamics happens, via Haag-Ruelle theory. In the nonrelativistic case, there is a somewhat less technical construction due to Sandhas http://projecteuclid.org/euclid.cmp/1103839514 • Thanks ! I have lots of things to read, but a first more question : for (4), I am tempted to say that n free particles with momenta $p_1$ ... $p_n$ long before or long after interaction are the same thing, so that $\left\| p_1, p_2, \cdots p_n \; \text{in} \right\rangle = \left\| p_1, p_2, \cdots p_n \; \text{out} \right\rangle$, thus leading to $S = \mathbb{I}$ without additional terms ... This is probably false, and I fail to see why it is. Perhaps after understanding what you said it will be more clear. – A. Zerkof Oct 22 '12 at 20:01 • @A.Zerkof: I added something to 4. – Arnold Neumaier Oct 22 '12 at 20:28 • Another time, thanks for your answer. I'll allow myself one more naive question : is it correct to say that we begin form asymptotic Fock states $\left\|p_1, p_2, \cdots \right\rangle$ and somehow map them to interacting states in an Hilbert space where they evolve (with some evolution operator $U$), and "after" the interaction, we map them back to Fock states $\left\|p_1, p_2, \cdots \right\rangle$, so that, at the end, we have something like $B U A \left\|p_1, p_2, \cdots \right\rangle$, with $B$ and $A$ the operators that map between asymptotic and interacting spaces. [cf. next comment] – A. Zerkof Nov 12 '12 at 14:07 • @A.Zerkof: The asymptotic plane-wave states are already smeared out over infinite volume and are "noninteracting" in the sense that the scattering is a subleading correction to their behavior. This is why the Fock space is already in the theory. – Ron Maimon Aug 29 '14 at 17:14 • @ArnordNeumaier Accroding to Bjorken and Drell, if I understand correctly, they show that in and out states are eigenstates of the full Hamiltonian of the interacting theory. They show that in and out states are eigenstates of $P^mu$ of the full theory. Peskin and Schroeder, too, tend to say something similar. But I'm throughly confused. – SRS Jun 1 '17 at 4:24	{"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": 0.8850976228713989, "perplexity": 458.5123865679382}, "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-2019-22/segments/1558232256887.36/warc/CC-MAIN-20190522163302-20190522185302-00025.warc.gz"}
https://socratic.org/questions/how-do-you-find-the-square-root-of-52	Algebra Topics # How do you find the square root of 52? Sep 12, 2015 $\sqrt{52} = 2 \sqrt{13} \approx 7.21110$ #### Explanation: If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$, so: $\sqrt{52} = \sqrt{{2}^{2} \cdot 13} = \sqrt{{2}^{2}} \sqrt{13} = 2 \sqrt{13}$ If you want to calculate an approximation by hand, you could follow the advice I gave for $\sqrt{28}$ in http://socratic.org/questions/how-do-you-find-the-square-root-28 Using the method described there: Let $n = 52$, ${p}_{0} = 7$, ${q}_{0} = 1$ Then: ${p}_{1} = {7}^{2} + 52 \cdot {1}^{2} = 49 + 52 = 101$ ${q}_{1} = 2 \cdot 7 \cdot 1 = 14$ ${p}_{2} = {101}^{2} + 52 \cdot {14}^{2} = 10201 + 10192 = 20393$ ${q}_{2} = 2 \cdot 101 \cdot 14 = 2828$ Stopping at this point, we get a result accurate to $5$ decimal places: $\sqrt{52} \approx \frac{20393}{2828} \approx 7.21110$ ##### Impact of this question 4671 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": 14, "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": 0.9348986744880676, "perplexity": 901.351219630923}, "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-2019-51/segments/1575540499439.6/warc/CC-MAIN-20191207132817-20191207160817-00456.warc.gz"}
https://events.berkeley.edu/?event_ID=111591&date=2017-09-25&tab=academic	## Arithmetic Geometry and Number Theory RTG Seminar: Rational motivic path spaces Seminar \| September 25 \| 3:10-5 p.m. \| 891 Evans Hall Ishai Dan-Cohen, Ben-Gurion University Department of Mathematics A central ingredient in Kim's work on integral points of hyperbolic curves is the “unipotent Kummer map” which goes from integral points to certain torsors for the prounipotent completion of the fundamental group, and which, roughly speaking, sends an integral point to the torsor of homotopy classes of paths connecting it to a fixed base-point. In joint work with Tomer Schlank, we introduce a space Ω of rational motivic loops, and we construct a double factorization of the unipotent Kummer map which may be summarized schematically as $\mbox {points} \to \mbox {rational motivic points} \to \Omega \mbox {-torsors} \to \pi _1\mbox {-torsors}.$ Our “connectedness theorem” says that any two motivic points are connected by a non-empty torsor. Our “concentration theorem” says that for an affine curve, Ω is actually equal to $\pi _1$. Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students. [email protected]	{"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": 0.9021678566932678, "perplexity": 2468.483519870456}, "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-2019-39/segments/1568514573052.26/warc/CC-MAIN-20190917040727-20190917062727-00057.warc.gz"}
https://www.ias.ac.in/describe/article/sadh/045/0076	• Optimizing warehouse network reliability under intentional disruption by increasing network ambiguity: a multi objective optimization model • # Keywords Network reliability; warehouse location; ambiguity; intentional disruption; interdiction • # Abstract In today’s world, intentional disruptions in networks are expanding and the impacts are seen in many parts of the world. An effective approach for reducing the impact of such disruptions is to confuse invaders. Increasing ambiguity in the network is one of the effective ways which may confuse the invaders. Toattain this goal, dummy facilities are added to the network. Dummy facilities are the facilities which are exactly the same as the real ones thus making it hard for the invader to make the distinction. In this paper, a new multiobjectivemathematical model is presented to suitably design a network consisting of real and dummy warehouses. One objective is to minimize the total cost and the other is set to maximize reliability. An index for assessing network reliability is also introduced and used. The model is solved using AUGMECON and NSGAII.Results demonstrate that establishing dummy facilities in the network will increase reliability while no significant cost is imposed.	{"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": 0.9198442697525024, "perplexity": 1666.003995648978}, "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-2021-04/segments/1610703519600.31/warc/CC-MAIN-20210119170058-20210119200058-00693.warc.gz"}
https://www.encyclopediaofmath.org/index.php?title=Witt_vector&oldid=14729	# Witt vector (diff) ← Older revision \| Latest revision (diff) \| Newer revision → (diff) An element of an algebraic construct, first proposed by E. Witt [1] in 1936 in the context of the description of unramified extensions of -adic number fields. Witt vectors were subsequently utilized in the study of algebraic varieties over a field of positive characteristic [3], in the theory of commutative algebraic groups [4], [5], and in the theory of formal groups [6]. Let be an associative, commutative ring with unit element. Witt vectors with components in are infinite sequences , , which are added and multiplied in accordance with the following rules: where , are polynomials in the variables , with integer coefficients, uniquely defined by the conditions where are polynomials, and is a prime number. In particular, The Witt vectors with the operations introduced above form a ring, called the ring of Witt vectors and denoted by . For any natural number there also exists a definition of the ring of truncated Witt vectors of length . The elements of this ring are finite tuples , , with the addition and multiplication operations described above. The canonical mappings are homomorphisms. The rule (or ) defines a covariant functor from the category of commutative rings with unit element into the category of rings. This functor may be represented by the ring of polynomials (or ) on which the structure of a ring object has been defined. The spectrum (or ) is known as a Witt scheme (or a truncated Witt scheme) and is a ring scheme [3]. Each element defines a Witt vector called the Teichmüller representative of the element . If is a perfect field of characteristic , is a complete discrete valuation ring of zero characteristic with field of residues and maximal ideal . Each element can be uniquely represented as where . Conversely, each such ring with field of residues is canonically isomorphic to the ring . The Teichmüller representation makes it possible to construct a canonical multiplicative homomorphism , splitting the mapping If is the prime field of elements, is the ring of integral -adic numbers . #### References [1] E. Witt, "Zyklische Körper und Algebren der characteristik vom Grad . Struktur diskret bewerteter perfekter Körper mit vollkommenem Restklassen-körper der Charakteristik " J. Reine Angew. Math. , 176 (1936) pp. 126–140 [2] S. Lang, "Algebra" , Addison-Wesley (1974) [3] D. Mumford, "Lectures on curves on an algebraic surface" , Princeton Univ. Press (1966) [4] J.-P. Serre, "Groupes algébrique et corps des classes" , Hermann (1959) [5] M. Demazure, P. Gabriel, "Groupes algébriques" , 1 , North-Holland (1971) [6] J. Dieudonné, "Groupes de Lie et hyperalgèbres de Lie sur un corps de charactéristique VII" Math. Ann. , 134 (1957) pp. 114–133 There is a generalization of the construction above which works for all primes simultaneously, [a3]: a functor called the big Witt vector. Here, is the category of commutative, associative rings with unit element. The functor described above, of Witt vectors of infinite length associated to the prime , is a quotient of which can be conveniently denoted by . For each , let be the polynomial Then there is the following characterization theorem for the Witt vectors. There is a unique functor satisfying the following properties: 1) as a functor , and for any ring homomorphism ; 2) , is a functorial homomorphism of rings for every and . The functor admits functorial ring endomorphisms , for every , that are uniquely characterized by for all . Finally, there is a functorial homomorphism that is uniquely characterized by the property for all , . To construct , define polynomials ; ; by the requirements The and are polynomials in ; and the are polynomials in the and they all have integer coefficients. is now defined as the set with addition, multiplication and "minus" : The zero of is and the unit element is . The Frobenius endomorphisms and the Artin–Hasse exponential are constructed by means of similar considerations, i.e. they are also given by certain universal polynomials. In addition there are the Verschiebung morphisms , which are characterized by The are group endomorphisms of but not ring endomorphisms. The ideals define a topology on making a separated complete topological ring. For each , let be the Abelian group under multiplication of power series; defines a functional isomorphism of Abelian groups, and using the isomorphism there is a commutative ring structure on . Using the Artin–Hasse exponential defines a functorial homomorphism of rings making a functorial special -ring. The Artin–Hasse exponential defines a cotriple structure on and the co-algebras for this co-triple are precisely the special -rings (cf. also Category and Triple). On the Frobenius and Verschiebung endomorphisms satisfy and are completely determined by this (plus functoriality and additivity in the case of ). For each supernatural number , , one defines , where is the -adic valuation of , i.e. the number of prime factors in . Let Then is an ideal in and for each supernatural a corresponding ring of Witt vectors is defined by In particular, one thus finds , the ring of infinite-length Witt vectors for the prime , discussed in the main article above, as a quotient of the ring of big Witt vectors . The Artin–Hasse exponential is compatible in a certain sense with the formation of these quotients, and using also the isomorphism one thus finds a mapping where denotes the -adic integers and the field of elements, which can be identified with the classical morphism defined by Artin and Hasse [a1], [a2], [a3]. As an Abelian group is isomorphic to the group of curves of curves in the one-dimensional multiplicative formal group . In this way there is a Witt-vector-like Abelian-group-valued functor associated to every one-dimensional formal group. For special cases, such as the Lubin–Tate formal groups, this gives rise to ring-valued functors called ramified Witt vectors, [a3], [a4]. Let be the sequence of polynomials with coefficients in defined by The Cartier ring is the ring of all formal expressions () with the calculation rules Commutative formal groups over are classified by certain modules over . In case is a -algebra, a simpler ring can be used for this purpose. It consists of all expressions () where now the only run over the powers of the prime . The calculation rules are the analogous ones. In case is a perfect field of characteristic and denotes the Frobenius endomorphism of (which in this case is given by ), then can be described as the ring of all expressions in two symbols and and with coefficients in , with the extra condition and the calculation rules This ring, and also its subring of all expressions is known as the Dieudonné ring and certain modules (called Dieudonné modules) over it classify unipotent commutative affine group schemes over , cf. [a5]. #### References [a1] E. Artin, H. Hasse, "Die beide Ergänzungssätze zum Reciprozitätsgesetz der -ten Potenzreste im Körper der -ten Einheitswurzeln" Abh. Math. Sem. Univ. Hamburg , 6 (1928) pp. 146–162 [a2] G. Whaples, "Generalized local class field theory III: Second form of the existence theorem, structure of analytic groups" Duke Math. J. , 21 (1954) pp. 575–581 [a3] M. Hazewinkel, "Twisted Lubin–Tate formal group laws, ramified Witt vectors and (ramified) Artin–Hasse exponentials" Trans. Amer. Math. Soc. , 259 (1980) pp. 47–63 [a4] M. Hazewinkel, "Formal group laws and applications" , Acad. Press (1978) [a5] M. Demazure, P. Gabriel, "Groupes algébriques" , 1 , North-Holland (1971) How to Cite This Entry: Witt vector. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Witt_vector&oldid=14729 This article was adapted from an original article by I.V. Dolgachev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article	{"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": 0.9785118103027344, "perplexity": 790.8868197426008}, "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-2019-30/segments/1563195526931.25/warc/CC-MAIN-20190721061720-20190721083720-00543.warc.gz"}
https://core.ac.uk/display/52411500	slides oai:okina.univ-angers.fr:10344 # Inverse statistical learning ## Abstract Let (X,Y)∈X×Y be a random couple with unknown distribution P. Let G be a class of measurable functions and ℓ a loss function. The problem of statistical learning deals with the estimation of the Bayes: g∗=arg ming∈ GEPℓ(g,(X,Y)). In this paper, we study this problem when we deal with a contaminated sample (Z1,Y1),…,(Zn,Yn) of i.i.d. indirect observations. Each input Zi, i=1,…,n is distributed from a density Af, where A is a known compact linear operator and f is the density of the direct input X. We derive fast rates of convergence for the excess risk of empirical risk minimizers based on regularization methods, such as deconvolution kernel density estimators or spectral cut-off. These results are comparable to the existing fast rates in Koltchinskii (2006) for the direct case. It gives some insights into the effect of indirect measurements in the presence of fast rates of convergence ## Full text ### Okina Provided a free PDF oai:okina.univ-angers.fr:10344Last time updated on 11/11/2016View original full text link This paper was published in Okina. # Having an issue? Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.	{"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": 0.9033160209655762, "perplexity": 1221.3459672868637}, "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/1679296945288.47/warc/CC-MAIN-20230324180032-20230324210032-00535.warc.gz"}
https://www.shaalaa.com/question-bank-solutions/concept-elements-compounds-mixture-tick-most-appropriate-answer-constituents-mixture-are-present-fixed-ratio-variable-ratio-ratio-2-1-none-these_31426	Share # Tick the Most Appropriate Answer. the Constituents of a Mixture Are Present in a Fixed Ratio a Variable Ratio, the Ratio of 2: 1 None of These - Chemistry Course ConceptConcept of Elements, Compounds and Mixture #### Question The constituents of a mixture are present in 1. a fixed ratio 2. a variable ratio, 3. the ratio of 2: 1 4. none of these #### Solution a variable ratio, Is there an error in this question or solution? Solution Tick the Most Appropriate Answer. the Constituents of a Mixture Are Present in a Fixed Ratio a Variable Ratio, the Ratio of 2: 1 None of These Concept: Concept of Elements, Compounds and Mixture. S	{"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": 0.8964951634407043, "perplexity": 2029.6475010904621}, "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/1585370507738.45/warc/CC-MAIN-20200402173940-20200402203940-00221.warc.gz"}
https://byjus.com/square-foot-to-square-meter-calculator/	# Square Foot To Square Meter Calculator Square foot (foot)2= Square meter (meter)2= Square Foot To Square Meter Calculator is a free online tool that displays the conversion. BYJU’S online Square foot to Square meter calculator tool makes the calculation faster, and it shows the result in a fraction of seconds. ## How to Use the Square Foot To Square Meter Calculator? The procedure to use the square foot to square meter calculator is as follows: Step 1: Enter the number of square foot in the input field Step 2: Now click the button “Solve” to get the result Step 3: Finally, the value of number of square meters will be displayed in the output field ### What is Meant by the Square Foot To Square Meter Conversion? Square foot is a measurement derived from the area of a square with a side length measured in feet. Similarly, the square meter can also be defined as the area of a square with side measures of one meter. One square foot is equal to 0.09290304 square meters. Hence, to convert the area from square foot (sq.ft) to square meters (sq.m), multiply the number of square foot by 0.09290304. A few conversion of units from square foot to square meters are given below: 1 sq.ft = 0.09290304 sq.m (or = 0.093 approx.) 2 sq.ft = 0.18580608 sq.m (or = 0.186 approx.) 50 sq.ft = 4.645152 sq.m (or = 4.645 approx.)	{"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": 0.9062486886978149, "perplexity": 1419.9221694090209}, "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/1623488268274.66/warc/CC-MAIN-20210621055537-20210621085537-00225.warc.gz"}
https://www.physicsforums.com/threads/resetting-the-affine-transformation-matrix.564716/	# Resetting the Affine Transformation matrix 1. Jan 3, 2012 ### Avinash Raj Affine Transformation Matrix is said to be formed by initializing it using a learned projection matrix from a conventional algorithm like Eigenfaces or Fisherfaces; then it is reset by using the singular value decomposition T=UAV', where T is the transformation matrix. Could somebody explain how the decomposition is obtained and what it is? 2. Jan 3, 2012 ### Avinash Raj I didnt go into details of initialising the tranformation matrix as well as the "resetting". I presumed that those in the forum are learned enough to know the basics of affine transformation. Do let me know if somebody wants more data from me to be able to explain the concept to me. 3. Jan 3, 2012 ### Avinash Raj It is obvious that SVD of the matrix T is shown. An IEEE paper (Face Verification With Balanced Thresholds) that I read few days back says "the right orthogonal matrix of SVD of a transformation matrix does not affect the similarity measure if based on Euclidean distance." I drew blanks in my attempts to understand how it is so and wikipedia wasnt a help at all. Could you tell me why the measure is invariant to the right orthogonal matrix? Note - The right unitary matrix becomes orthogonal as only real matrices are considered in the problem.	{"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": 0.9112241268157959, "perplexity": 873.4760270339194}, "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-2018-47/segments/1542039747215.81/warc/CC-MAIN-20181121052254-20181121074254-00107.warc.gz"}
https://usq.edu.au/academic-success-planner/trigonometry/trigonometric-ratios/step1	Contact The Learning Centre Basic Trigonometric Ratios Trigonometric relationships • There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent. • These six trigonometric ratios are abbreviated as $$\sin$$, $$\cos$$, $$\tan$$, $$\csc$$, $$\sec$$, $$\cot$$. • These are referred to as ratios since they can be expressed in terms of the sides of a right-angled triangle for a specific angle $$\theta$$. • Using the triangle above: \begin{eqnarray*} \sin\theta &=& \frac{\mbox{Opposite}}{\mbox{Hypothenuse}}\\	{"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": 0.9993444085121155, "perplexity": 757.5380672518227}, "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-2021-21/segments/1620243991870.70/warc/CC-MAIN-20210517211550-20210518001550-00018.warc.gz"}
https://www.physicsforums.com/threads/alternating-series-help.210243/	# Alternating series help 1. Jan 22, 2008 ### rcmango 1. The problem statement, all variables and given/known data Determine wheter the series is convergent or divergent. If it convergent, approximate the sum of the series correct to four decimal places. heres the equation: http://img251.imageshack.us/img251/2261/46755781zg9.png [Broken] 2. Relevant equations 3. The attempt at a solution This appears to be an alternating geometric series, Would it be okay to move the exponent k over everything? in other words: ( (-1)/k) )^k So then it looks alot like a geometric series, so then It converges by the rules of an alernating series, it is decreasing and it is approaching zero. So then to find its sum, i would do so by geometric series right? first term would be starting at k = 2, so: 1/2? then use 1/2 divided by 1 -r Am i on the right track? what is r??? is it also, 1/2? Last edited by a moderator: May 3, 2017 2. Jan 22, 2008 ### Pyrrhus Yes you can use k as the exponent of the whole because of the distributive property of exponentiation. 3. Jan 22, 2008 ### rcmango how about the rest of what i'm doing here, this was my best hypothesis to approach the problem. I need help with the common ratio. i'm not sure what to use if its k^k ? 4. Jan 22, 2008 ### dynamicsolo It isn't a geometric series because such series has a constant ratio between successive terms. However, that gives you a clue to the proof of its convergence. (Try a comparison test.) As for the estimate of the sum, do they want an analytical proof of some sort or just something carried out on a calculator (how many terms do you need to get to a precision of 10^-4 ?) Last edited by a moderator: May 3, 2017 Similar Discussions: Alternating series help	{"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": 0.9277750253677368, "perplexity": 861.386882830066}, "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/1502886117519.92/warc/CC-MAIN-20170823035753-20170823055753-00514.warc.gz"}
https://www.physicsforums.com/threads/calculating-a-in-shm-from-x-v-a.229932/	# Homework Help: Calculating A in SHM from x, v & a 1. Apr 19, 2008 ### mudkip9001 how can you work out the amplitude knowing only displacement, velocity and acceleration? I have been able to work out angular velocity, frequency and period, but I can't work out amplitude without knowing either the spring constant, the mass or the phase angle. 2. Apr 19, 2008 ### Hootenanny Staff Emeritus Welcome to PF, Why don't you post what you have thus far? HINT: What is the velocity of the particle when it is at it's amplitude? 3. Apr 19, 2008 ### mudkip9001 Thank you, it seems like a nice place :) I have these equations x=Acos($$\omega$$t+$$\phi$$) v=-A$$\omega$$sin($$\omega$$t + $$\phi$$) a=-$$\omega$$$$^{2}$$cos($$\omega$$t+$$\phi$$) =$$\omega$$x I could work out $$\omega$$ by re arranging the equation for a. It's 0, but I'm still left with two unknown variables, $$\phi$$ and A, am I not? edit: why does omega keep showing up as superscript? 4. Apr 19, 2008 ### Hootenanny Staff Emeritus Have you any initial conditions, such as whether it starts from x=A or x=0? 5. Apr 19, 2008 ### mudkip9001 Sorry, I should have typed up the question from the start: I struggled with this for hours and concluded that the question must be wrong, but I went to the homepage of the textbook and downloaded the errata and didn't find anything. 6. Apr 19, 2008 ### Hootenanny Staff Emeritus It seems to me that you have a system of simultaneous equations. Which values of $\left(\omega t + \phi\right)$ correspond to the particle being at x=A? Last edited: Apr 19, 2008 7. Apr 20, 2008 ### mudkip9001 when x=A, $\left(\omega t + \phi\right)$=0 I still can't solve it though, I just end up with division of 0, can you confirm that it really is solvable? 8. Apr 20, 2008 ### alphysicist Hi mudkip9001, Try conservation of energy. Equate the energy at the given point to the energy at the amplitude. What do you get? 9. Apr 20, 2008 ### mudkip9001 but I don't know neither k nor m 10. Apr 20, 2008 ### alphysicist You'll be able to get rid of them by using what you know about the acceleration. 11. Apr 20, 2008 ### alphysicist What I mean is that although you don't know either k or m, you can find the value of (k/m). 12. Apr 20, 2008 ### mudkip9001 I just wrote all this, and then figured it out myself just as I finished. But I guess I might as well post t anyway. Thanks for all your help, I'm very relieved now (but I also feel a bit dumb, since I was so sure there was something wrong with the question:grumpy:). where I went wrong was that the question is how much further it would go, not the amplitude. 13. Dec 3, 2009 ### LawnNinja What you were missing is squaring the quantity m/k (i.e., A = \sqrt((x^2+v^2)/(x/a)^2) (Sorry I couldn't write this in pretty-print. I'm new here.)	{"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": 0.9432597756385803, "perplexity": 1354.1981598726318}, "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-2018-30/segments/1531676591332.73/warc/CC-MAIN-20180719222958-20180720002958-00491.warc.gz"}
https://scholarworks.iu.edu/dspace/handle/2022/14128?show=full	# Indiana University dc.contributor.author Park, Joon Y. dc.contributor.author Chang, Yonsoon dc.date.accessioned 2012-01-23T02:36:25Z dc.date.available 2012-01-23T02:36:25Z dc.date.issued 2010-12-22 dc.identifier.citation Chang, Yonsoon and Joon Y. Park. Endogeneity in Nonlinear Regressions with Integrated Time Series, Econometric Reviews 30, 51-87, 2011. en dc.identifier.uri http://www.tandfonline.com/doi/abs/10.1080/07474938.2011.520567 en dc.identifier.uri http://hdl.handle.net/2022/14128 dc.description JEL Classification: C13, C22. en dc.description.abstract This article considers the nonlinear regression with integrated regressors that are contemporaneously correlated with the regression error. We, in particular, establish the consistency and derive the limit distribution of the nonlinear least squares estimator under such endogeneity. For the regressions with various types of regression functions, it is shown that the estimator is consistent and has the same rate of convergence as for the case of the regressions with no endogeneity. Whether or not the limit distribution is affected by the presence of endogeneity, however, depends upon the functional type of the parameter derivative of regression function. If it is asymptotically homogeneous, the limit distribution of the nonlinear least squares estimator has an additional bias term reflecting the presence of endogeneity. On the other hand, the endogeneity does not have any effect on the nonlinear least squares limit theory, if the parameter derivative of regression function is integrable. Regardless of the presence of endogeneity, the en least squares estimator has the same limit distribution in this case. To illustrate our theory, we consider the nonlinear regressions with logistic and power regression functions with integrated regressors that have contemporaneous correlations with the regression error. dc.language.iso en_US en dc.publisher Taylor and Francis en dc.subject nonlinear regression, integrated time series, endogeneity, consistency, limit distributions. en dc.title Endogeneity in Nonlinear Regressions with Integrated Time Series en dc.type Article en	{"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": 0.9397717118263245, "perplexity": 2232.7986152197414}, "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-2016-44/segments/1476988722459.85/warc/CC-MAIN-20161020183842-00037-ip-10-171-6-4.ec2.internal.warc.gz"}
https://proceedings.mlr.press/v108/azizian20a.html	# Accelerating Smooth Games by Manipulating Spectral Shapes Waïss Azizian, Damien Scieur, Ioannis Mitliagkas, Simon Lacoste-Julien, Gauthier Gidel Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:1705-1715, 2020. #### Abstract We use matrix iteration theory to characterize acceleration in smooth games. We define the spectral shape of a family of games as the set containing all eigenvalues of the Jacobians of standard gradient dynamics in the family. Shapes restricted to the real line represent well-understood classes of problems, like minimization. Shapes spanning the complex plane capture the added numerical challenges in solving smooth games. In this framework, we describe gradient-based methods, such as extragradient, as transformations on the spectral shape. Using this perspective, we propose an optimal algorithm for bilinear games. For smooth and strongly monotone operators, we identify a continuum between convex minimization, where acceleration is possible using Polyak’s momentum, and the worst case where gradient descent is optimal. Finally, going beyond first-order methods, we propose an accelerated version of consensus optimization.	{"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": 0.8259731531143188, "perplexity": 727.2260055699852}, "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/1637964363337.27/warc/CC-MAIN-20211207075308-20211207105308-00124.warc.gz"}
https://brilliant.org/problems/without-using-lhopitals-rule-1/	# Without using l'hopital's rule 1 Calculus Level 1 $\large \lim_{x\to0} \dfrac{1-\cos x}x = \ ?$ Bonus: Solve this question without using L'Hôpital's rule. ×	{"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": 0.9993969202041626, "perplexity": 4697.390763057264}, "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-2018-51/segments/1544376823236.2/warc/CC-MAIN-20181210013115-20181210034615-00043.warc.gz"}
http://mathhelpforum.com/calculus/98151-nth-derivative-function.html	# Math Help - nth derivative of a function 1. ## nth derivative of a function I need to find that $n^{th}$ derivative of the function $f(x)=\frac{1}{(2-x)^2}$. I'm not really sure how to proceed. I wrote down a few derivatives, but I can't find a pattern. Is their a general method or formula for $n^{th}$ derivatives? Thanks. I need to find that $n^{th}$ derivative of the function $f(x)=\frac{1}{(2-x)^2}$. I'm not really sure how to proceed. I wrote down a few derivatives, but I can't find a pattern. Is their a general method or formula for $n^{th}$ derivatives? Thanks. $f^{\prime}(x)=\frac{2}{(2-x)^3}$ $f^{\prime\prime}(x)=\frac{6}{(2-x)^4}$ $f^{\prime\prime\prime}(x)=\frac{24}{(2-x)^5}$ ... So it follows that $f^{(n)}(x)=\frac{(n+1)!}{(2-x)^{n+2}}$. 3. Originally Posted by skeeter Chris forgot a (-1) factor ... easy fix. $f^{\prime}(x)=\frac{-2}{(2-x)^3}$ $f^{\prime\prime}(x)=\frac{6}{(2-x)^4}$ $f^{\prime\prime\prime}(x)=\frac{-24}{(2-x)^5}$ ... $f^{(n)}(x)=\frac{(-1)^n(n+1)!}{(2-x)^{n+2}}$. Don't forget to chain the denominator! $\frac{\,d}{\,dx}(2-x)=-1$! Hence, all the negatives are cancelled! So $f^{\prime}(x)=\frac{-2}{(2-x)^3}(-1)=\frac{2}{(2-x)^3}$ $f^{\prime}(x)=\frac{-6}{(2-x)^{4}}(-1)=\frac{6}{(2-x)^4}$ etc... 4. my error ... sorry. 5. Originally Posted by skeeter my error ... sorry. However, I see your point since $(2-x)^2=(x-2)^2$... If we rewrote the function as $f(x)=\frac{1}{(x-2)^2}$, then you would be correct.... 6. Originally Posted by Chris L T521 However, I see your point since $(2-x)^2=(x-2)^2$... If we rewrote the function as $f(x)=\frac{1}{(x-2)^2}$, then you would be correct.... Ok, that's why I was having difficulty find a pattern. I didn't notice $(2-x)^2=(x-2)^2$. Ok, that's why I was having difficulty find a pattern. I didn't notice $(2-x)^2=(x-2)^2$. It would also make this easier to recognize that $f(x)= \frac{1}{(2-x)^2}= \frac{1}{(x-2)^2}= (x- 2)^{-2}$. $f'(x)= -2(x-2)^{-3}$ $f"(x)= 6(x-2)^{-4}= (-1)^2(2+1)!)(x-2)^{-(2+2)}$ $f"'(x)= -12(x-2)^{-5}= (-1)^3(3+1)!)(x-2)^{-(3+2)}$ $f""(x)= 60(x-2)^{-6}= (-1)^4(4+1)!(x-2)^{-(4+2)}$	{"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": 28, "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": 0.9158022999763489, "perplexity": 399.5466451937401}, "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-2015-18/segments/1429246644200.21/warc/CC-MAIN-20150417045724-00236-ip-10-235-10-82.ec2.internal.warc.gz"}
http://alekskleyn.blogspot.com/2011_01_01_archive.html	Friday, January 21, 2011 Representation of Universal Algebra I published my new book: Representation Theory: Representation of Universal Algebra. In this book I consider morphism of representation, consept of generating set and basis of representation. This allows me to consider basis manifold of representation, active and passive transformations, concept of geometrical object in representation of universal algebra. Similar way I consider tower of representations.	{"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": 0.9946915507316589, "perplexity": 1279.8200575413734}, "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-2017-22/segments/1495463609837.56/warc/CC-MAIN-20170528141209-20170528161209-00070.warc.gz"}
https://www.expii.com/t/inverse-powers-and-radical-functions-4938	Expii # Inverse Powers and Radical Functions - Expii The inverse of a power function of exponent n is a nth root radical function. For example, the inverse of y = 10x^2 is y = √(x/10) (at least for positive values of x and y).	{"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": 0.9374158978462219, "perplexity": 656.0119366039182}, "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-2022-49/segments/1669446711126.30/warc/CC-MAIN-20221207021130-20221207051130-00374.warc.gz"}
https://adityam.github.io/context-blog/post/correct-math-escape-in-t-vim/	# Correct math escape in t-vim Posted on July 22, 2017 There is a feature in t-vim module that allows the use of TeX code in comments, which is useful when typeset math in comments. For example: \definevimtyping[C][syntax=c, escape=on] \startC /* The following function computes the roots of \m{ax^2+bx+c=0} * using the determinant \m{\Delta=\frac{-b\pm\sqrt{b^2-2ac}}{2a}} / double root (double a, double b, double c) {....} \stopC The escape=on option activates this feature. Only \, {, and } have their usual meaning inside the Comment region, so I use \m{...} to enter math mode. The above code get typeset as: Gerion Entrup reported on the context mailing list that the spacing inside the math mode is not always correct. The incorrect behavior is not visit in the above example, because there was no blank space inside the math mode. As soon as we add space in the math mode, the output is too spaced out. For example, \definevimtyping[C][syntax=c, escape=on] \startC / The following function computes the roots of \m{ax^2 + bx + c = 0} * using the determinant \m{\Delta = \frac{-b \pm \sqrt{b^2 - 2ac}}{2a}} */ double root (double a, double b, double c) {....} \stopC Spacing inside math mode should not affect the output. What is happening here? After a bit of sleuthing, I found the culprit. As I had ranted in an old blog post, I want syntax highlighting programs to generate clean TeX output. Therefore, I do not escape space and newline characters. After all, it is easy enough to tell ConTeXt to honor spaces and newlines by using \obeyspaces and \obeylines. By themselves, \obeyspaces and \obeylines are okay. \bgroup \obeylines\obeyspaces\tttf The following function computes the roots of \m{ax^2 + bx + c = 0} using the determinant \m{\Delta = \frac{-b \pm \sqrt{b^2 - 2ac}}{2a}} \egroup In t-vim, I wanted to control how to wrap long lines. The default option is not to do anything and let the user figure out how to wrap the source code. There is also an option to split a long line at a space. (For other options on splitting long lines, see the documentation). To control whether a long line should be split at a space or not, I redefined \obeyedspace. For those who are not familiar with ConTeXt internals, whenever \obeyspaces is active, space is mapped to \obeyedspace. This makes it possible, for example, to visualize spaces. For example, \bgroup \obeylines\obeyspaces\tttf\def\obeyedspace{-} The following function computes the roots \egroup So, to allow a line to break at a space, I use \def\obeyedspace{\hskip\interwordspace\relax} and to prevent lines from breaking at a space, I use \def\obeyedspace{\kern\interwordspace\relax} However, this definition creates a wreck inside math mode. \bgroup \obeylines\obeyspaces\tttf \def\obeyedspace{\hskip\interwordspace\relax} The following function computes the roots of \m{ax^2 + bx + c = 0} using the determinant \m{\Delta = \frac{-b \pm \sqrt{b^2 - 2ac}}{2a}} \egroup Now, that we know what is going on, it is an easy fix (suggested by Henri Menke). Define \obeyedspace to \def\obeyedspace{\mathortext\normalspace{\hskip\interwordspace\relax}} Let’s test this. \bgroup \obeylines\obeyspaces\tttf \def\obeyedspace{\mathortext\normalspace{\hskip\interwordspace\relax}} The following function computes the roots of \m{ax^2 + bx + c = 0} using the determinant \m{\Delta = \frac{-b \pm \sqrt{b^2 - 2ac}}{2a}} \egroup This bug has been fixed in t-vim version 2017.07.29 This entry was posted in Formatting and tagged t-vim, math, horizontal spacing, code formatting.	{"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": 0.9370803833007812, "perplexity": 1899.934953978574}, "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-2018-39/segments/1537267159561.37/warc/CC-MAIN-20180923153915-20180923174315-00119.warc.gz"}
https://www.physicsforums.com/threads/vectors-problem.50088/	# Vectors problem 1. Oct 28, 2004 ### Chen It's given that vector c is perpendicular to both vectors a and b. Which of the following is true: 1) http://phstudy.technion.ac.il/~wn114071/physweb/question/1_4_01.gif [Broken] (a x b) x c 2) http://phstudy.technion.ac.il/~wn114071/physweb/question/1_4_02.gif [Broken] (a x c) dot b 3) http://phstudy.technion.ac.il/~wn114071/physweb/question/1_4_03.gif [Broken] (a x c) x b 4) http://phstudy.technion.ac.il/~wn114071/physweb/question/1_4_04.gif [Broken] (a x b) dot c Can someone please just confirm the answer is (1) because I have only one attempt left at submitting an answer for this question. Thanks Last edited by a moderator: May 1, 2017 2. Oct 28, 2004 ### Galileo I can't open the files. You need authorization for that... 3. Oct 28, 2004 ### Chen I knew that might happen, so I wrote the expression in each link below. (1) is (a x b) x c, i.e (a cross b) cross c. Thanks. 4. Oct 28, 2004 ### Tom Mattson Staff Emeritus It's impossible to say which one is true, because those are all expressions, not equations. 5. Oct 28, 2004 ### BobG Answers 2 and 4 give you a scalar number. The absolute value is the same for both, but the sign changes. Answer 1 gives you a null vector (all components equal to 0) since the cross product of A and B is either in the same direction as C or the exact opposite direction of C. Answer 3 gives you a vector. Similar Discussions: Vectors problem	{"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": 0.9034833312034607, "perplexity": 2358.2228107464803}, "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/1502886110792.29/warc/CC-MAIN-20170822143101-20170822163101-00086.warc.gz"}
http://www.computer.org/csdl/trans/tc/1992/09/t1176-abs.html	Subscribe Issue No.09 - September (1992 vol.41) pp: 1176-1180 ABSTRACT <p>An algorithm for exact parametric analysis of stochastic Petri nets is presented. The algorithm is derived from the theory of decomposition and aggregation of Markov chains. The transition rate of interest is confined into a diagonal submatrix of the associated Markov chain by row and column permutations. Every time a new value is assigned to the transition, a smaller Markov chain is analyzed. As a result, the computational cost is greatly reduced.</p> INDEX TERMS row permutations; stochastic Petri nets; exact parametric analysis; decomposition; aggregation; Markov chains; transition rate of interest; diagonal submatrix; column permutations; Markov processes; matrix algebra; Petri nets. CITATION M. Li, N.D. Georganas, "Exact Parametric Analysis of Stochastic Petri Nets", IEEE Transactions on Computers, vol.41, no. 9, pp. 1176-1180, September 1992, doi:10.1109/12.165403	{"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": 0.9348911643028259, "perplexity": 2467.899357362971}, "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-2015-27/segments/1435375097204.8/warc/CC-MAIN-20150627031817-00009-ip-10-179-60-89.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/chargedistribution-from-a-given-potential.329973/	# Chargedistribution from a given potential 1. Aug 10, 2009 ### eXorikos The following potential is given The question is what the charge distribution is. The middle part is a charged dielectric. The two discontinuous points are the result of a charge accumulated in one point. And after that point the potential doesn't vary. So my thoughts are that the physical situation is a charged dielectric between two charged plated, with the charges of the dielectric oposite to the charge on the plate it faces. I think I'm right so far. But now I want to calculate the charge distribution. The hint was to use delta-function and I can see why, but I don't know how. Can any of you help me? PS: My paint skills suck, but I hope it's clear that the middle parabolic and the left potential is higher than the right one. 2. Aug 10, 2009 ### Bob_for_short Use the equation ∆φ ~ ρ. In a 1D case the second derivative of your potential will give the charge density. 3. Aug 10, 2009 ### eXorikos But what is the equation for such a potential? 4. Aug 10, 2009 ### Bob_for_short Sorry, I should have written it as ρ ~ ∆φ (Gauss law) or ρ(x) ~ (d²/dx²)φ(x) in your case. ρ is a charge density and φ is the electrostatic potential. Depending on units, the equation may contain 4π, etc. 5. Aug 10, 2009 ### eXorikos I know how to solve a laplacian, but I can't find the equation for the potential. 6. Aug 10, 2009 ### Bob_for_short The equation is the following: ρ(x) ~ (d²/dx²)φ(x) in your case. All you have to do is to differentiate twice your potential given in your figure. 7. Aug 10, 2009 ### eXorikos I know all that. I've studied my book (Introduction to Electrodynamics), but I need the equation for the potential. That's my problem... 8. Aug 10, 2009 ### Bob_for_short You mean an analytical formula for your curve in the figure? Approximate it with something differentiable and you will obtain an approximate charge density. The differential equation for a potential is the Gauss law ∆φ ~ ρ. If the charge density ρ is given, you have to integrate this differential equation to find the potential φ. If the potential φ is given, you have to differentiate it to find the density ρ. Similar Discussions: Chargedistribution from a given potential	{"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": 0.9577791094779968, "perplexity": 924.4879406167271}, "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-2017-43/segments/1508187825399.73/warc/CC-MAIN-20171022165927-20171022185927-00642.warc.gz"}
https://baylor-ir.tdl.org/baylor-ir/browse?value=Dugas%2C+Manfred.&type=author	Now showing items 1-3 of 3 • #### Finitary incidence algebras. (, 2014-06-11) Let P be an arbitrary partially ordered set and I(P) its incidence space. Then F(P) is the finitary incidence algebra and I(P) is a bimodule over it. Consequently we can form D(P) = FI(P) ⊕ I(P) the idealization of I(P). ... • #### On a ring associated to F[x]. (, 2013-09-24) For a ﬁeld F and the polynomial ring F [x] in a single indeterminate, we deﬁne Ḟ [x] = {α ∈ End_F(F [x]) : α(ƒ) ∈ ƒF [x] for all ƒ ∈ F [x]}. Then Ḟ [x] is naturally isomorphic to F [x] if and only if F is inﬁnite. If F ... • #### On rings with distinguished ideals and their modules. (2007-05-23) Let S be an integral domain, R an S algebra, and F a family of left ideals of R. Define End(R, F) = {φ ∈ End(R+) : φ(X ) ⊆ X for all X ∈ F }. In 1967, H. Zassenhaus proved that if R is a ring such that R+ is free of finite ...	{"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": 0.8294748067855835, "perplexity": 3498.848047146957}, "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-2016-44/segments/1476988719843.44/warc/CC-MAIN-20161020183839-00504-ip-10-171-6-4.ec2.internal.warc.gz"}
https://proceedings.neurips.cc/paper/2019/hash/a34bacf839b923770b2c360eefa26748-Abstract.html	#### Authors Kamil Ciosek, Quan Vuong, Robert Loftin, Katja Hofmann #### Abstract <p>Actor-critic methods, a type of model-free Reinforcement Learning, have been successfully applied to challenging tasks in continuous control, often achieving state-of-the art performance. However, wide-scale adoption of these methods in real-world domains is made difficult by their poor sample efficiency. We address this problem both theoretically and empirically. On the theoretical side, we identify two phenomena preventing efficient exploration in existing state-of-the-art algorithms such as Soft Actor Critic. First, combining a greedy actor update with a pessimistic estimate of the critic leads to the avoidance of actions that the agent does not know about, a phenomenon we call pessimistic underexploration. Second, current algorithms are directionally uninformed, sampling actions with equal probability in opposite directions from the current mean. This is wasteful, since we typically need actions taken along certain directions much more than others. To address both of these phenomena, we introduce a new algorithm, Optimistic Actor Critic, which approximates a lower and upper confidence bound on the state-action value function. This allows us to apply the principle of optimism in the face of uncertainty to perform directed exploration using the upper bound while still using the lower bound to avoid overestimation. We evaluate OAC in several challenging continuous control tasks, achieving state-of the art sample efficiency.</p>	{"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": 0.8284317851066589, "perplexity": 1220.5282939438148}, "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/1614178364027.59/warc/CC-MAIN-20210302160319-20210302190319-00291.warc.gz"}
http://www.mathematicalfoodforthought.com/2007/02/return-of-triangle-topic_11.html	Sunday, February 11, 2007 Return Of The Triangle. Topic: Geometry/Inequalities/Trigonometry. Level: AIME. Problem: (1961 IMO - #2) Let $a, b, c$ be the sides of a triangle, and $T$ its area. Prove: $a^2+b^2+c^2 \ge 4T\sqrt{3}$. In what case does equality hold? Solution: We begin with the trivial inequality, $(a-b)^2 \ge 0$, which has equality at $a = b$. Rearrange to get $a^2+b^2 \ge 2ab$. Let $\theta$ be the angle between the sides with lengths $a, b$. Since $2 \ge \cos{\theta}+\sqrt{3}\sin{\theta}$ (can be proved by combining RHS) with equality at $\theta = \frac{\pi}{3}$, we know $a^2+b^2 \ge ab(\cos{\theta}+\sqrt{3}\sin{\theta})$ $2(a^2+b^2) \ge 2ab(\cos{\theta}+\sqrt{3}\sin{\theta})$ $a^2+b^2+(a^2+b^2-2ab\cos{\theta}) \ge 2\sqrt{3} \cdot ab\sin{\theta}$. Recalling the Law of Cosines, we know $c^2 = a^2+b^2-2ab\cos{\theta}$. Also, $T = \frac{1}{2}ab\sin{\theta}$, so substituting we obtain $a^2+b^2+c^2 \ge 4T\sqrt{3}$ as desired. Equality holds when $a = b$ and $\theta = \frac{\pi}{3}$, which means the triangle must be equilateral. QED. -------------------- Comment: There are lots of ways to prove this, but this is one of the more elementary ones, requiring only basic knowledge of inequalities and trigonometry. Which is always good because I don't know any geometry. We see that this inequality is in general pretty weak, with equality only when the triangle is equilateral - there is a stronger version that states $a^2+b^2+c^2 \ge 4T\sqrt{3}+(a-b)^2+(b-c)^2+(c-a)^2$. See if you can prove that... -------------------- Practice Problem: Let $a, b, c$ be the sides of a triangle, and $T$ its area. Prove: $a^2+b^2+c^2 \ge 4T\sqrt{3}+(a-b)^2+(b-c)^2+(c-a)^2$.	{"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": 0.9637899994850159, "perplexity": 306.86866823420837}, "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-2021-43/segments/1634323585196.73/warc/CC-MAIN-20211018031901-20211018061901-00334.warc.gz"}
https://open.kattis.com/problems/luhnchecksum	Kattis # Luhn's Checksum Algorithm In 1954, Hans Peter Luhn, a researcher at IBM, filed a patent describing a simple checksum algorithm for numbers written as strings of base-$10$ digits. If a number is chosen according to Luhn’s technique, the algorithm provides a basic integrity check. This means that with reasonably high probability it can detect whether one or more digits have been accidentally modified. (On the other hand, it provides essentially no protection against intentional modifications.) Most credit card and bank card numbers can be validated using Luhn’s checksum algorithm, as can the national identification numbers of several countries (including Canada). Given a number $n = d_ k d_{k-1} \ldots d_2 d_1$, where each $d_ i$ is a base-$10$ digit, here is how to apply Luhn’s checksum test: 1. Starting at the right end of $n$, transform every second digit $d_ i$ (i.e., $d_2, d_4, d_6, \ldots$) as follows: • multiply $d_ i$ by $2$ • if $2 \cdot d_ i$ consists of more than one digit, i.e., is greater than 9, add these digits together; this will always produce a single-digit number 2. Add up all the digits of $n$ after the transformation step. If the resulting sum is divisible by $10$, $n$ passes the Luhn checksum test. Otherwise, $n$ fails the Luhn checksum test. For example, consider the number $n = 1234567890123411$ from Sample Input 1. The first row of Figure 1 gives the original digits of $n$, and the second row contains the digits of $n$ after the transformation step, with transformed digits shown in bold. The sum of the digits in the second row is $2+2+6+4+1+6+5+8+9+0+2+2+6+4+2+1=60$ and since $60$ is divisible by $10$, $n$ passes the Luhn checksum test. $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $0$ $1$ $2$ $3$ $4$ $1$ $1$ $\mathbf{2}$ $2$ $\mathbf{6}$ $4$ $\mathbf{1}$ $6$ $\mathbf{5}$ $8$ $\mathbf{9}$ $0$ $\mathbf{2}$ $2$ $\mathbf{6}$ $4$ $\mathbf{2}$ $1$ Figure 1: Application of Luhn’s algorithm to $n = 1234567890123411$ ## Input The first line of input contains a single integer $T$ $(1 \leq T \leq 100)$, the number of test cases. Each of the following $T$ lines contains a single test case consisting of a number given as a string of base-$10$ digits (09). The length of each string is between $2$ and $50$, inclusive, and numbers may have leading (leftmost) zeros. ## Output For each test case, output a single line containing “PASS” if the number passes the Luhn checksum test, or “FAIL” if the number fails the Luhn checksum test. Sample Input 1 Sample Output 1 3 00554 999 1234567890123411 PASS FAIL PASS	{"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": 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": 0.8434697985649109, "perplexity": 579.5285556176115}, "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/1585370496669.0/warc/CC-MAIN-20200330054217-20200330084217-00037.warc.gz"}
https://www.physicsforums.com/threads/dynamic-suspension-emergency.256448/	# Dynamic Suspension Emergency! 1. Sep 15, 2008 ### blue-steel Hi all, (see the attached images) working on a dynamics project about the suspension system in a bike, we have been given a 4 bar linkage - dynamic system, and im trying to find the velocity of POINT C and POINT F, but given in terms of the angular velocity of bar AB in the STATIC POSITION the solid grey position, the other 'shadow' image is the linkage at it's deflected image, the 2 images attached show a diagram of the system, Point C represents the centre of the back wheel, all black circles are pivot points, the second gives the coordinates of the points in the two positions what im workin on so far is the relative velocity relationship, Vc = Vb + Vc/b to find Vc, only problem is this (ultimately) involves omega_BC when the final value for Vc should only involve omega_AB should look something like this anyone familiar with similar problem or have any advice on how to go about it would greatly appreciate it Cheers blue steel #### Attached Files: File size: 30.1 KB Views: 52 • ###### bicyclecoordinates.JPG File size: 33.2 KB Views: 46 2. Sep 16, 2008 ### MikeLizzi I suppose there are lots of ways to approach this problem. Here's mine. I would start by redrawing the picture. Leave out the spring and E-G. Redraw B-C-D as a straight bar B-D. (You loose point C but that can be added later.) Now you have four unequal bars pined at their four corners. A-E is vertical. A-B is horizontal. Now consider a small rotation of bar A-B while holding A-E fixed. Can you calcualte the required rotation of E-D? Its messy geometry but you should be able to get that angule of E-D as a function of the angle of A-E. Once you’ve done that you can calculate the angular velocity of E-D as a function of the angular velocity of A-E. Then you can calculate the linear velocity of any point in bar E-D. That gives you the velocity of point F and D. Now replace bar B-D with the original B-C-D. You know the velocity at points B and D. Do you know how to use that info to calculate the velocity at C? 3. Sep 16, 2008 ### blue-steel Thanks a lot, the thing I was getting confused with most was the 'bent link' BCD but since all points on it travel with the same angular velocity the simplification BD worked Cheers	{"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": 0.8353976011276245, "perplexity": 1393.200500880797}, "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/1508187823229.49/warc/CC-MAIN-20171019050401-20171019070401-00611.warc.gz"}
https://tex.stackexchange.com/questions/277933/beginlanguage-causes-unwanted-vertical-space-e-g-in-tabular	# \begin{language} causes unwanted vertical space e.g. in tabular The \begin{language} environment in polyglossia seems to create an extra vertical space which misaligns text, for example in a table. Here is an example. I have tabular with 2 columns of type p{} , English on the left, and Arabic on the right. When the mainlanguage is Arabic, I need to specify \begin{english} for the left column. But this then creates extra vertical space (moves the English text downwards) and misaligns the table. I can 'patch' this by redundantly specifying \begin{Arabic} for the left column, which then creates a matching vertical space, aligning the texts. The results are shown here: Why is this vertical space being caused by any \begin{language} command? Is it common to other environments? The MWE below has got the two single-row tables, one with the problem, and the next with the problem patched by using a redundant begin{Arabic} command. By the way, I drew the horizontal rule manually. Is there a way I could have done this in Latex, given the tabular environment? \documentclass[11pt,oneside]{article} \usepackage{polyglossia} \setmainlanguage[numerals=mashriq]{arabic} \setotherlanguage{english} \newfontfamily\englishfont[Script=Latin, Scale = 1]{Times New Roman} \begin{document} \begin{tabular}[t]{p{0.45\linewidth}p{0.45\linewidth}} ااا ببب ااا & \begin{english} aaa bbb \end{english} \end{tabular} \begin{tabular}[t]{p{0.45\linewidth}p{0.45\linewidth}} \begin{Arabic} ااا ببب ااا \end{Arabic} & \begin{english} aaa bbb \end{english} \end{tabular} \end{document} • I can't compile your example (I've got an incomplete installation) but I would try to guess: does a \leavevmode just before \begin{english} help? – campa Nov 12 '15 at 14:11 • unfortunately this kills the left-to-right direction of the English text, so it appears backwards. – Tim Nov 12 '15 at 19:46	{"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": 0.9566370844841003, "perplexity": 3173.191527971702}, "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-2019-35/segments/1566027315865.44/warc/CC-MAIN-20190821085942-20190821111942-00229.warc.gz"}
https://mathhelpboards.com/threads/2-questions-regarding-initial-values-and-verifying-solutions.6377/	# 2 questions regarding initial values and verifying solutions #### nathancurtis11 ##### New member Sep 3, 2013 10 I want to start out with a quick disclaimer, we had a 75 question homework packet assigned a few weeks ago with a few questions from every lecture and this first one is due tomorrow. I missed a lecture, so am completely lost on 3 questions from that lecture. Just dont want it to seem like I'm dumping my whole homework assignment on here so I don't have to do it myself! Just so close to finishing this monstrous packet and need some guidance! Here are the first 2 questions: Question 1: The function f: (all real) -> (all real) is defined by the set { y''+(pi)2y=0 S: { y(1/3) = (3).5 { y'(1/3) = -pi Find two numbers (c1 and c2) such that c1cos((pi)x) + c2 sin((pi(x)) Question 2: Let f: I -> (all real) be a solution of the diff eq y''-xy'+y=0 a) is f 3 times differentiable? b) is f smooth? #### Chris L T521 ##### Well-known member Staff member Jan 26, 2012 995 I want to start out with a quick disclaimer, we had a 75 question homework packet assigned a few weeks ago with a few questions from every lecture and this first one is due tomorrow. I missed a lecture, so am completely lost on 3 questions from that lecture. Just dont want it to seem like I'm dumping my whole homework assignment on here so I don't have to do it myself! Just so close to finishing this monstrous packet and need some guidance! Here are the first 2 questions: Question 1: The function f: (all real) -> (all real) is defined by the set { y''+(pi)2y=0 S: { y(1/3) = (3).5 { y'(1/3) = -pi Find two numbers (c1 and c2) such that c1cos((pi)x) + c2 sin((pi(x)) Since the general solution of $y^{\prime\prime}+\pi^2 y=0$ is $y=c_1\cos(\pi x)+c_2\sin(\pi x)$, it follows that $y^{\prime}=-\pi c_1\sin(\pi x) + \pi c_2\cos(\pi x)$. At this point, you would want to plug in the initial conditions $y(1/3)=\sqrt{3}$ and $y^{\prime}(1/3)=-\pi$ to get the system of equations \left\{\begin{aligned} c_1\cos\left(\frac{\pi}{3}\right) + c_2\sin\left(\frac{\pi}{3}\right) &= \sqrt{3} \\ -\pi c_1\sin\left(\frac{\pi}{3}\right) + \pi c_2\cos\left(\frac{\pi}{3}\right) &= -\pi\end{aligned}\right. I'll leave simplifying the system of equations to you, as well as solving the system. All in all, it shouldn't be too difficult to finish off the problem from here. Question 2: Let f: I -> (all real) be a solution of the diff eq y''-xy'+y=0 a) is f 3 times differentiable? b) is f smooth? If $f:I\rightarrow \mathbb{R}$ is a solution to $y^{\prime\prime}-xy^{\prime}+y=0$, then we know for sure it's at least two times differentiable; in particular, if $y=f(x)$ is the solution, then we know that $f^{\prime\prime}(x)= xf^{\prime}(x) - f(x)$. Now, $x$, $f(x)$ are at least twice differentiable and $f^{\prime}(x)$ is at least once differentiable; thus, it follows that $\frac{d}{dx}\left(xf^{\prime}(x)-f(x)\right)= f^{\prime}(x) + xf^{\prime\prime}(x) - f^{\prime}(x) = xf^{\prime\prime}(x) = x^2f^{\prime}(x)-xf(x).$ Thus, we've expressed the third derivative of $f$ in terms of functions that are at least once and twice differentiable. To me, this is good enough to show that $f$ is at least three times differentiable. You can extend this argument to showing that $f(x)$ is smooth (i.e. infinitely times differentiable) by showing that the higher order derivatives can be defined in terms of the lower order derivatives. If you have any follow-up questions, don't hesitate to post them! I hope this makes sense! #### nathancurtis11 ##### New member Sep 3, 2013 10 Thank you Chris! Once explained I realized how easy they actually were, just was frustrated never seeing anything of the sort before that wasn't quite sure how to get started. #### Jester ##### Well-known member MHB Math Helper Jan 26, 2012 183 Let me add a bit. As Chris mentioned differentiating both sides gives $f''' = x f''$ This you can integrate to find $f$ explicitly! #### chisigma ##### Well-known member Feb 13, 2012 1,704 Question 2: Let f: I -> (all real) be a solution of the diff eq y''-xy'+y=0 a) is f 3 times differentiable? b) is f smooth? The solving procedure for a second order incomplete linear ODE ... $\displaystyle y^{\ ''} - x\ y^{\ '} + y =0\ (1)$ ... has been illustrated in... http://mathhelpboards.com/different...inear-variable-coefficient-2089.html#post9571 If u and v are solution of (1), then is... $\displaystyle u^{\ ''} - x\ u^{\ '} + u = 0$ $\displaystyle v^{\ ''} - x\ v^{\ '} + v = 0\ (2)$ ... and multiplying the first equation by v and the second by u a computing the difference we have... $\displaystyle v\ u^{\ ''} - u\ v^{\ ''} - x\ (v\ u^{\ '} - u\ v^{\ '}) = 0\ (3)$ ... and taking $\displaystyle z= v\ u^{\ '} - u\ v^{\ '}$ we have the first order ODE... $\displaystyle z^{\ '} = x\ z\ (4)$ ... the solution of which is... $\displaystyle z= c_{2}\ e^{\frac{x^{2}}{2}}\ (5)$ From (5) we3 derive... $\displaystyle \frac{z}{v^{2}} = \frac{d}{dx} (\frac{u}{v}) = c_{2}\ \frac{e^{\frac{x^{2}}{2}}}{v^{2}} \implies u = c_{1}\ v + c_{2}\ v\ \int \frac{e^{\frac{x^{2}}{2}}}{v^{2}}\ dx\ (6)$ It is easy to verify that $\displaystyle v=x$ is solution of (1) and that means that from (6) we derive that $\displaystyle u = x\ \int \frac{e^{\frac{x^{2}}{2}}}{x^{2}}\ dx$ is also solution and the general solution of (1) is... $\displaystyle y = c_{1}\ x + c_{2}\ x\ \int \frac{e^{\frac{x^{2}}{2}}}{x^{2}}\ dx\ (7)$ A precise characterization of the u(x) has to be made before to answer the points 1 and 2... Kind regards $\chi$ $\sigma$ #### chisigma ##### Well-known member Feb 13, 2012 1,704 The solving procedure for a second order incomplete linear ODE ... $\displaystyle y^{\ ''} - x\ y^{\ '} + y =0\ (1)$ ... has been illustrated in... http://mathhelpboards.com/different...inear-variable-coefficient-2089.html#post9571 If u and v are solution of (1), then is... $\displaystyle u^{\ ''} - x\ u^{\ '} + u = 0$ $\displaystyle v^{\ ''} - x\ v^{\ '} + v = 0\ (2)$ ... and multiplying the first equation by v and the second by u a computing the difference we have... $\displaystyle v\ u^{\ ''} - u\ v^{\ ''} - x\ (v\ u^{\ '} - u\ v^{\ '}) = 0\ (3)$ ... and taking $\displaystyle z= v\ u^{\ '} - u\ v^{\ '}$ we have the first order ODE... $\displaystyle z^{\ '} = x\ z\ (4)$ ... the solution of which is... $\displaystyle z= c_{2}\ e^{\frac{x^{2}}{2}}\ (5)$ From (5) we3 derive... $\displaystyle \frac{z}{v^{2}} = \frac{d}{dx} (\frac{u}{v}) = c_{2}\ \frac{e^{\frac{x^{2}}{2}}}{v^{2}} \implies u = c_{1}\ v + c_{2}\ v\ \int \frac{e^{\frac{x^{2}}{2}}}{v^{2}}\ dx\ (6)$ It is easy to verify that $\displaystyle v=x$ is solution of (1) and that means that from (6) we derive that $\displaystyle u = x\ \int \frac{e^{\frac{x^{2}}{2}}}{x^{2}}\ dx$ is also solution and the general solution of (1) is... $\displaystyle y = c_{1}\ x + c_{2}\ x\ \int \frac{e^{\frac{x^{2}}{2}}}{x^{2}}\ dx\ (7)$ A precise characterization of the u(x) has to be made before to answer the points 1 and 2... If we analyse the function... $\displaystyle u(x) = x\ \int \frac{e^{\frac{x^{2}}{2}}}{x^{2}}\ d x\ (1)$ ... using the series expansion... $\displaystyle e^{\frac{x^{2}}{2}} = 1 + \frac{x^{2}}{2} + \frac{x^{4}}{8} + \frac{x^{6}}{48} + ...\ (2)$ ... with symple steps we obtain... $\displaystyle u(x) = -1 + \frac{x^{2}}{2} + \frac{x^{4}}{24} + \frac{x^{6}}{240} + ...\ (3)$ ... and the series (3) converges for any real [and complex...] x... Kind regards $\chi$ $\sigma$	{"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": 0.9097170829772949, "perplexity": 894.8918916211122}, "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/1623487620971.25/warc/CC-MAIN-20210615084235-20210615114235-00611.warc.gz"}
https://www.math.princeton.edu/events/some-recent-work-conformal-biharmonic-maps-2017-09-28t203009	# Some recent work on conformal biharmonic maps - Yelin Ou, Texas A&M University-Commerce Fine Hall 401 Biharmonic maps are generalizations of harmonic maps and biharmonic functions. As solutions of a system of 4th order PDEs, examples and the general properties of biharmonic maps are hard to reveal. In this talk, we will talk about some recent work on the study of biharmonic maps among conformal maps. These include examples and classifications of biharmonic conformal immersions of surfaces, biharmonic conformal maps between manifolds of the same dimension, and the links between conformal biharmonicity and the notion of $f$-biharmonic maps and the equations of Yamabe type.	{"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": 0.9237281084060669, "perplexity": 580.6343446076625}, "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-2017-51/segments/1512948577018.52/warc/CC-MAIN-20171215172833-20171215194833-00181.warc.gz"}
https://worldwidescience.org/topicpages/s/susy+mass+scales.html	#### Sample records for susy mass scales 1. Neutrino masses from SUSY breaking in radiative seesaw models International Nuclear Information System (INIS) Figueiredo, Antonio J.R. 2015-01-01 Radiatively generated neutrino masses (m ν ) are proportional to supersymmetry (SUSY) breaking, as a result of the SUSY non-renormalisation theorem. In this work, we investigate the space of SUSY radiative seesaw models with regard to their dependence on SUSY breaking (SUSY). In addition to contributions from sources of SUSY that are involved in electroweak symmetry breaking (SUSY EWSB contributions), and which are manifest from left angle F H † right angle = μ left angle anti H right angle ≠ 0 and left angle D right angle = g sum H left angle H † x H H right angle ≠ 0, radiatively generated m ν can also receive contributions from SUSY sources that are unrelated to EWSB (SUSY EWS contributions). We point out that recent literature overlooks pure-SUSY EWSB contributions (∝ μ/M) that can arise at the same order of perturbation theory as the leading order contribution from SUSY EWS . We show that there exist realistic radiative seesaw models in which the leading order contribution to m ν is proportional to SUSY EWS . To our knowledge no model with such a feature exists in the literature. We give a complete description of the simplest model topologies and their leading dependence on SUSY. We show that in one-loop realisations LLHH operators are suppressed by at least μ m soft /M 3 or m soft 2 /M 3 . We construct a model example based on a oneloop type-II seesaw. An interesting aspect of these models lies in the fact that the scale of soft-SUSY effects generating the leading order m ν can be quite small without conflicting with lower limits on the mass of new particles. (orig.) 2. Soft see-saw: Radiative origin of neutrino masses in SUSY theories Directory of Open Access Journals (Sweden) Luka Megrelidze 2017-01-01 Full Text Available Radiative neutrino mass generation within supersymmetric (SUSY construction is studied. The mechanism is considered where the lepton number violation is originating from the soft SUSY breaking terms. This requires MSSM extensions with states around the TeV scale. We present several explicit realizations based on extensions either by MSSM singlet or SU(2w triplet states. Besides some novelties of the proposed scenarios, various phenomenological implications are also discussed. 3. Cosmological constant in SUGRA models with Planck scale SUSY breaking and degenerate vacua International Nuclear Information System (INIS) Froggatt, C.D.; Nevzorov, R.; Nielsen, H.B.; Thomas, A.W. 2014-01-01 The empirical mass of the Higgs boson suggests small to vanishing values of the quartic Higgs self-coupling and the corresponding beta function at the Planck scale, leading to degenerate vacua. This leads us to suggest that the measured value of the cosmological constant can originate from supergravity (SUGRA) models with degenerate vacua. This scenario is realised if there are at least three exactly degenerate vacua. In the first vacuum, associated with the physical one, local supersymmetry (SUSY) is broken near the Planck scale while the breakdown of the SU(2) W ×U(1) Y symmetry takes place at the electroweak (EW) scale. In the second vacuum local SUSY breaking is induced by gaugino condensation at a scale which is just slightly lower than Λ QCD in the physical vacuum. Finally, in the third vacuum local SUSY and EW symmetry are broken near the Planck scale 4. Searches for SUSY at LHC International Nuclear Information System (INIS) Kharchilava, A. 1997-01-01 One of the main motivations of experiments at the LHC is to search for SUSY particles. The talk is based on recent analyses, performed by CMS Collaboration, within the framework of the Supergravity motivated minimal SUSY extension of the Standard Model. The emphasis is put on leptonic channels. The strategies for obtaining experimental signatures for strongly and weakly interacting sparticles productions, as well as examples of determination of SUSY masses and model parameters are discussed. The domain of parameter space where SUSY can be discovered is investigated. Results show, that if SUSY is of relevance at Electro-Weak scale it could hardly escape detection at LHC. (author) 5. Naturalness in low-scale SUSY models and "non-linear" MSSM CERN Document Server 2014-01-01 In MSSM models with various boundary conditions for the soft breaking terms (m_{soft}) and for a higgs mass of 126 GeV, there is a (minimal) electroweak fine-tuning Delta\\approx 800 to 1000 for the constrained MSSM and Delta\\approx 500 for non-universal gaugino masses. These values, often regarded as unacceptably large, may indicate a problem of supersymmetry (SUSY) breaking, rather than of SUSY itself. A minimal modification of these models is to lower the SUSY breaking scale in the hidden sector (\\sqrt f) to few TeV, which we show to restore naturalness to more acceptable levels Delta\\approx 80 for the most conservative case of low tan_beta and ultraviolet boundary conditions as in the constrained MSSM. This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce Delta. In the present case Delta is reduced due to additional (effective) quartic higgs couplings proportional to the ratio m_{soft}/(\\sqrt f) of the visible to the hidden sector SUSY breaking... 6. Probing the Higgs sector of high-scale SUSY-breaking models at the Tevatron International Nuclear Information System (INIS) Carena, Marcela; Liu, Tao 2010-12-01 A canonical signature of the Minimal Supersymmetric Standard Model (MSSM) is the presence of a neutral Higgs boson with mass bounded from above by about 135 GeV and Standard Model (SM)-like couplings to the electroweak gauge bosons. In this note we investigate the reach of the Tevatron collider for the MSSM Higgs sector parameter space associated with a variety of high-scale minimal models of supersymmetry (SUSY)-breaking, including the Constrained MSSM (CMSSM), minimal Gauge Mediated SUSY-breaking (mGMSB), and minimal Anomaly Mediated SUSY-breaking (mAMSB). We find that the Tevatron can provide strong constraints on these models via Higgs boson searches. Considering a simple projection for the efficiency improvements in the Tevatron analyses, we find that with an integrated luminosity of 16 fb -1 per detector and an efficiency improvement of 20% compared to the present situation, these models could be probed essentially over their entire ranges of validity. With 40% analysis improvements and 16 fb -1 , our projection shows that evidence at the 3σ level for the light Higgs boson could be expected in extended regions of parameter space. (orig.) 7. Probing the Higgs sector of high-scale SUSY-breaking models at the Tevatron Energy Technology Data Exchange (ETDEWEB) Carena, Marcela [Fermi National Accelerator Laboratory, Batavia, IL (United States); Chicago Univ., Chicago, IL (United States). Enrico Fermi Inst.; Draper, Patrick [Chicago Univ., Chicago, IL (United States). Enrico Fermi Inst.; Heinemeyer, Sven [Instituto de Fisica de Cantabria (CSIC-UC), Santander (Spain); Liu, Tao [Chicago Univ., Chicago, IL (United States). Enrico Fermi Inst.; California Univ., Santa Barbara, CA (United States). Dept. of Physics; Wagner, Carlos E.M. [Chicago Univ., Chicago, IL (United States). Enrico Fermi Inst.; Argonne National Laboratory, Argonne, IL (United States). HEP Div.; Chicago Univ., Chicago, IL (United States). KICP and Dept. of Physics; Weiglein, Georg [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2010-12-15 A canonical signature of the Minimal Supersymmetric Standard Model (MSSM) is the presence of a neutral Higgs boson with mass bounded from above by about 135 GeV and Standard Model (SM)-like couplings to the electroweak gauge bosons. In this note we investigate the reach of the Tevatron collider for the MSSM Higgs sector parameter space associated with a variety of high-scale minimal models of supersymmetry (SUSY)-breaking, including the Constrained MSSM (CMSSM), minimal Gauge Mediated SUSY-breaking (mGMSB), and minimal Anomaly Mediated SUSY-breaking (mAMSB). We find that the Tevatron can provide strong constraints on these models via Higgs boson searches. Considering a simple projection for the efficiency improvements in the Tevatron analyses, we find that with an integrated luminosity of 16 fb{sup -1} per detector and an efficiency improvement of 20% compared to the present situation, these models could be probed essentially over their entire ranges of validity. With 40% analysis improvements and 16 fb{sup -1}, our projection shows that evidence at the 3{sigma} level for the light Higgs boson could be expected in extended regions of parameter space. (orig.) 8. The Higgs boson mass and SUSY spectra in 10D SYM theory with magnetized extra dimensions Directory of Open Access Journals (Sweden) Hiroyuki Abe 2014-11-01 Full Text Available We study the Higgs boson mass and the spectrum of supersymmetric (SUSY particles in the well-motivated particle physics model derived from a ten-dimensional supersymmetric Yang–Mills theory compactified on three factorizable tori with magnetic fluxes. This model was proposed in a previous work, where the flavor structures of the standard model including the realistic Yukawa hierarchies are obtained from non-hierarchical input parameters on the magnetized background. Assuming moduli- and anomaly-mediated contributions dominate the soft SUSY breaking terms, we study the precise SUSY spectra and analyze the Higgs boson mass in this mode, which are compared with the latest experimental data. 9. Low-scale SUSY breaking and the (s)goldstino physics CERN Document Server 2013-01-01 For a 4D N=1 supersymmetric model with a low SUSY breaking scale (f) and general Kahler potential K(Phi^i,Phi_j^) and superpotential W(Phi^i) we study, in an effective theory approach, the relation of the goldstino superfield to the (Ferrara-Zumino) superconformal symmetry breaking chiral superfield X. In the presence of more sources of supersymmetry breaking, we verify the conjecture that the goldstino superfield is the (infrared) limit of X for zero-momentum and Lambda->\\infty. (Lambda is the effective cut-off scale). We then study the constraint X^2=0, which in the one-field case is known to decouple a massive sgoldstino and thus provide an effective superfield description of the Akulov-Volkov action for the goldstino. In the presence of additional fields that contribute to SUSY breaking we identify conditions for which X^2=0 remains valid, in the effective theory below a large but finite sgoldstino mass. The conditions ensure that the effective expansion (in 1/Lambda) of the initial Lagrangian is not in ... 10. Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events Science.gov (United States) Debnath, Dipsikha; Gainer, James S.; Kilic, Can; Kim, Doojin; Matchev, Konstantin T.; Yang, Yuan-Pao 2017-06-01 We critically examine the classic endpoint method for particle mass determination, focusing on difficult corners of parameter space, where some of the measurements are not independent, while others are adversely affected by the experimental resolution. In such scenarios, mass differences can be measured relatively well, but the overall mass scale remains poorly constrained. Using the example of the standard SUSY decay chain \\tilde{q}\\to {\\tilde{χ}}_2^0\\to \\tilde{ℓ}\\to {\\tilde{χ}}_1^0 , we demonstrate that sensitivity to the remaining mass scale parameter can be recovered by measuring the two-dimensional kinematical boundary in the relevant three-dimensional phase space of invariant masses squared. We develop an algorithm for detecting this boundary, which uses the geometric properties of the Voronoi tessellation of the data, and in particular, the relative standard deviation (RSD) of the volumes of the neighbors for each Voronoi cell in the tessellation. We propose a new observable, \\overline{Σ} , which is the average RSD per unit area, calculated over the hypothesized boundary. We show that the location of the \\overline{Σ} maximum correlates very well with the true values of the new particle masses. Our approach represents the natural extension of the one-dimensional kinematic endpoint method to the relevant three dimensions of invariant mass phase space. 11. Stability of neutrino parameters and self-complementarity relation with varying SUSY breaking scale Science.gov (United States) Singh, K. Sashikanta; Roy, Subhankar; Singh, N. Nimai 2018-03-01 The scale at which supersymmetry (SUSY) breaks (ms) is still unknown. The present article, following a top-down approach, endeavors to study the effect of varying ms on the radiative stability of the observational parameters associated with the neutrino mixing. These parameters get additional contributions in the minimal supersymmetric model (MSSM). A variation in ms will influence the bounds for which the Standard Model (SM) and MSSM work and hence, will account for the different radiative contributions received from both sectors, respectively, while running the renormalization group equations (RGE). The present work establishes the invariance of the self complementarity relation among the three mixing angles, θ13+θ12≈θ23 against the radiative evolution. A similar result concerning the mass ratio, m2:m1 is also found to be valid. In addition to varying ms, the work incorporates a range of different seesaw (SS) scales and tries to see how the latter affects the parameters. 12. Detecting kinematic boundary surfaces in phase space and particle mass measurements in SUSY-like events CERN Document Server Debnath, Dipsikha; Kilic, Can; Kim, Doojin; Matchev, Konstantin T.; Yang, Yuan-Pao 2017-06-19 We critically examine the classic endpoint method for particle mass determination, focusing on difficult corners of parameter space, where some of the measurements are not independent, while others are adversely affected by the experimental resolution. In such scenarios, mass differences can be measured relatively well, but the overall mass scale remains poorly constrained. Using the example of the standard SUSY decay chain $\\tilde q\\to \\tilde\\chi^0_2\\to \\tilde \\ell \\to \\tilde \\chi^0_1$, we demonstrate that sensitivity to the remaining mass scale parameter can be recovered by measuring the two-dimensional kinematical boundary in the relevant three-dimensional phase space of invariant masses squared. We develop an algorithm for detecting this boundary, which uses the geometric properties of the Voronoi tessellation of the data, and in particular, the relative standard deviation (RSD) of the volumes of the neighbors for each Voronoi cell in the tessellation. We propose a new observable, $\\bar\\Sigma$, which is ... 13. SUSY Searches at ATLAS and CMS CERN Document Server Urquijo, P; The ATLAS collaboration 2009-01-01 We review the current strategies to search for Supersymmetry (SUSY) with the ATLAS and CMS detectors at the LHC. The early data discovery potential will be presented for search channels based on missing transverse momentum from undetected neutralinos and multiple high transverse momentum jets. We describe the search for models of gauge-mediated SUSY breaking for which the next to lightest SUSY particle is a neutralino that decays into a photon and gravitino. Examples of measurement techniques that probe the SUSY mass scale in the first data, through reconstruction of kinematic endpoints, are also shown. 14. SUSY method for the three-dimensional Schrödinger equation with effective mass International Nuclear Information System (INIS) Ioffe, M.V.; Kolevatova, E.V.; Nishnianidze, D.N. 2016-01-01 Highlights: • SUSY intertwining relations for the 3-dim Schrödinger equation with effective mass were studied. • The general solution of these intertwining relations with first order supercharges was obtained. • Four different options for parameters values were considered separately to find the mass functions and partner potentials. - Abstract: The three-dimensional Schrödinger equation with a position-dependent (effective) mass is studied in the framework of Supersymmetrical (SUSY) Quantum Mechanics. The general solution of SUSY intertwining relations with first order supercharges is obtained without any preliminary constraints. Several forms of coefficient functions of the supercharges are investigated and analytical expressions for the mass function and partner potentials are found. As usual for SUSY Quantum Mechanics with nonsingular superpotentials, the spectra of intertwined Hamiltonians coincide up to zero modes of supercharges, and the corresponding wave functions are connected by intertwining relations. All models are partially integrable by construction: each of them has at least one second order symmetry operator. 15. High scale parity invariance as a solution to the SUSY CP problem ... scale SUSY ДК model provides a solution to the CP problems of the MSSM. A minimal version of this .... the renormalizable seesaw model so that К-parity conservation remains automatic. Pramana – J. Phys., Vol ... from the Planck scale to ЪК in the squark sector is to split the third generation squarks slightly from the first two ... International Nuclear Information System (INIS) Ross, G.G. 2014-01-01 Given that there is currently no direct evidence for supersymmetric particles at the LHC it is timely to re-evaluate the need for low scale supersymmetry and to ask whether it is likely to be discoverable by the LHC running at its full energy. We review the status of simple SUSY extensions of the Standard Model in the light of the Higgs discovery and the non-observation of evidence for SUSY at the LHC. The need for large radiative corrections to drive the Higgs mass up to 126 GeV and for the coloured SUSY states to be heavy to explain their non-observation introduces a little hierarchy problem and we discuss how to quantify the associated fine tuning. The requirement of low fine tuning requires non-minimal SUSY extensions and we discuss the nature and phenomenology of models which still have perfectly acceptable low fine tuning. A brief discussion of SUSY flavour-changing and CP-violation problems and their resolution is presented. (orig.) 17. Non-universal gaugino masses and fine tuning implications for SUSY searches in the MSSM and the GNMSSM Energy Technology Data Exchange (ETDEWEB) Kaminska, Anna [Oxford Univ. (United Kingdom). Centre for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Ross, Graham G. [Oxford Univ. (United Kingdom). Centre for Theoretical Physics; Schmidt-Hoberg, Kai [European Lab. for Particle Physics (CERN), Geneva (Switzerland) 2013-08-15 For the case of the MSSM and the most general form of the NMSSM (GNMSSM) we determine the reduction in the fine tuning that follows from allowing gaugino masses to be non-degenerate at the unification scale, taking account of the LHC8 bounds on SUSY masses, the Higgs mass bound, gauge coupling unification and the requirement of an acceptable dark matter density. We show that low-fine tuned points fall in the region of gaugino mass ratios predicted by specific unified and string models. For the case of the MSSM the minimum fine tuning is still large, approximately 1:60 allowing for a 3 GeV uncertainty in the Higgs mass (1:500 for the central value), but for the GNMSSM it is below 1:20. We find that the spectrum of SUSY states corresponding to the low-fine tuned points in the GNMSSM is often compressed, weakening the LHC bounds on coloured states. The prospect for testing the remaining low-fine-tuned regions at LHC14 is discussed. 18. Non-universal gaugino masses and fine tuning implications for SUSY searches in the MSSM and the GNMSSM CERN Document Server Kaminska, Anna; Schmidt-Hoberg, Kai 2013-01-01 For the case of the MSSM and the most general form of the NMSSM (GNMSSM) we determine the reduction in the fine tuning that follows from allowing gaugino masses to be non-degenerate at the unification scale, taking account of the LHC8 bounds on SUSY masses, the Higgs mass bound, gauge coupling unification and the requirement of an acceptable dark matter density. We show that low-fine tuned points fall in the region of gaugino mass ratios predicted by specific unified and string models. For the case of the MSSM the minimum fine tuning is still large, approximately 1:60 allowing for a 3 GeV uncertainty in the Higgs mass (1:500 for the central value), but for the GNMSSM it is below 1:20. We find that the spectrum of SUSY states corresponding to the low-fine tuned points in the GNMSSM is often compressed, weakening the LHC bounds on coloured states. The prospect for testing the remaining low-fine-tuned regions at LHC14 is discussed. 19. Combining high-scale inflation with low-energy SUSY Energy Technology Data Exchange (ETDEWEB) Antusch, Stefan [Basel Univ. (Switzerland). Dept. of Physics; Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut; Dutta, Koushik [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Halter, Sebastian [Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut 2011-12-15 We propose a general scenario for moduli stabilization where low-energy supersymmetry can be accommodated with a high scale of inflation. The key ingredient is that the stabilization of the modulus field during and after inflation is not associated with a single, common scale, but relies on two different mechanisms. We illustrate this general scenario in a simple example, where during inflation the modulus is stabilized with a large mass by a Kaehler potential coupling to the field which provides the inflationary vacuum energy via its F-term. After inflation, the modulus is stabilized, for instance, by a KKLT superpotential. (orig.) 20. Symmetric neutrino mass matrix with two zeros in SUSY SO(10) GUT International Nuclear Information System (INIS) Bando, Masako; Kaneko, Satoru; Obara, Midori; Tanimoto, Morimitsu 2004-01-01 We study the symmetric 2-zero texture of lepton and quark mass matrix, for the SUSY SO(10) GUT model including the Pati-Salam symmetry. We show that our model can simultaneously explain the current neutrino experimental data, predicted rate of lepton flavor violating processes are safely below the experimental bounds and baryon asymmetry of the universe can be obtained through thermal leptogenesis. (author) 1. Fermion Masses and Mixing in SUSY Grand Unified Gauge Models with Extended Gut Gauge Groups Energy Technology Data Exchange (ETDEWEB) Chou, Chih-Lung 2005-04-05 The authors discuss a class of supersymmetric (SUSY) grand unified gauge (GUT) models based on the GUT symmetry G x G or G x G x G, where G denotes the GUT group that has the Standard Model symmetry (SU(3){sub c} x SU(2){sub L} x U(1){sub Y}) embedded as a subgroup. As motivated from string theory, these models are constructed without introducing any Higgs field of rani two or higher. Thus all the Higgs fields are in the fundamental representations of the extended GUT symmetry or, when G = SO(10), in the spinorial representation. These Higgs fields, when acquiring their vacuum expectation values, would break the extended GUT symmetry down to the Standard Model symmetry. In this dissertation, they argue that the features required of unified models, such as the Higgs doublet-triplet splitting, proton stability, and the hierarchy of fermion masses and mixing angles, could have natural explanations in the framework of the extended SUSY GUTs. Furthermore, they argue that the frameworks used previously to construct SO(10) GUT models using adjoint Higgs fields can naturally arise from the SO(10) x SO(10) and SO(10) x SO(10) x SO(10) models by integrating out heavy fermions. This observation thus suggests that the traditional SUSY GUT SO(10) theories can be viewed as the low energy effective theories generated by breaking the extended GUT symmetry down to the SO(10) symmetry. 2. SUSY particles CERN Document Server Nath, Pran 1994-01-01 Analysis of the SUSY spectrum in supergravity unified models is given under the naturalness criterion that the universal scalar mass (m_0) and the gluino mass (m_{\\tilde g}) satisfy the constraint m_0, m_{\\tilde g} less than or equal to 1 TeV. The SUSY spectrum is analysed in four different scenarios: (1) minimal supergravity models ignoring proton decay from dimension five operators, (2) imposing proton stability constraint in supergravity models with SU(5) type embedding which allow proton decay via dimension five operators, (3) with inclusion of dark matter constraints in models of type (1), and (4) with inclusion of dark matter constraint in models of type (2). It is found that there is a very strong upper limit on the light chargino mass in models of type (4), i.e., the light chargino mass is less than or equals 120 GeV. 3. Global fits of GUT-scale SUSY models with GAMBIT Science.gov (United States) Athron, Peter; Balázs, Csaba; Bringmann, Torsten; Buckley, Andy; Chrząszcz, Marcin; Conrad, Jan; Cornell, Jonathan M.; Dal, Lars A.; Edsjö, Joakim; Farmer, Ben; Jackson, Paul; Krislock, Abram; Kvellestad, Anders; Mahmoudi, Farvah; Martinez, Gregory D.; Putze, Antje; Raklev, Are; Rogan, Christopher; de Austri, Roberto Ruiz; Saavedra, Aldo; Savage, Christopher; Scott, Pat; Serra, Nicola; Weniger, Christoph; White, Martin 2017-12-01 We present the most comprehensive global fits to date of three supersymmetric models motivated by grand unification: the constrained minimal supersymmetric standard model (CMSSM), and its Non-Universal Higgs Mass generalisations NUHM1 and NUHM2. We include likelihoods from a number of direct and indirect dark matter searches, a large collection of electroweak precision and flavour observables, direct searches for supersymmetry at LEP and Runs I and II of the LHC, and constraints from Higgs observables. Our analysis improves on existing results not only in terms of the number of included observables, but also in the level of detail with which we treat them, our sampling techniques for scanning the parameter space, and our treatment of nuisance parameters. We show that stau co-annihilation is now ruled out in the CMSSM at more than 95% confidence. Stop co-annihilation turns out to be one of the most promising mechanisms for achieving an appropriate relic density of dark matter in all three models, whilst avoiding all other constraints. We find high-likelihood regions of parameter space featuring light stops and charginos, making them potentially detectable in the near future at the LHC. We also show that tonne-scale direct detection will play a largely complementary role, probing large parts of the remaining viable parameter space, including essentially all models with multi-TeV neutralinos. 4. Global fits of GUT-scale SUSY models with GAMBIT Energy Technology Data Exchange (ETDEWEB) Athron, Peter [Monash University, School of Physics and Astronomy, Melbourne, VIC (Australia); Australian Research Council Centre of Excellence for Particle Physics at the Tera-scale (Australia); Balazs, Csaba [Monash University, School of Physics and Astronomy, Melbourne, VIC (Australia); Australian Research Council Centre of Excellence for Particle Physics at the Tera-scale (Australia); Bringmann, Torsten; Dal, Lars A.; Krislock, Abram; Raklev, Are [University of Oslo, Department of Physics, Oslo (Norway); Buckley, Andy [University of Glasgow, SUPA, School of Physics and Astronomy, Glasgow (United Kingdom); Chrzaszcz, Marcin [Universitaet Zuerich, Physik-Institut, Zurich (Switzerland); H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Krakow (Poland); Conrad, Jan; Edsjoe, Joakim; Farmer, Ben [AlbaNova University Centre, Oskar Klein Centre for Cosmoparticle Physics, Stockholm (Sweden); Stockholm University, Department of Physics, Stockholm (Sweden); Cornell, Jonathan M. [McGill University, Department of Physics, Montreal, QC (Canada); Jackson, Paul; White, Martin [Australian Research Council Centre of Excellence for Particle Physics at the Tera-scale (Australia); University of Adelaide, Department of Physics, Adelaide, SA (Australia); Kvellestad, Anders; Savage, Christopher [NORDITA, Stockholm (Sweden); Mahmoudi, Farvah [Univ Lyon, Univ Lyon 1, CNRS, ENS de Lyon, Centre de Recherche Astrophysique de Lyon UMR5574, Saint-Genis-Laval (France); Theoretical Physics Department, CERN, Geneva (Switzerland); Martinez, Gregory D. [University of California, Physics and Astronomy Department, Los Angeles, CA (United States); Putze, Antje [LAPTh, Universite de Savoie, CNRS, Annecy-le-Vieux (France); Rogan, Christopher [Harvard University, Department of Physics, Cambridge, MA (United States); Ruiz de Austri, Roberto [IFIC-UV/CSIC, Instituto de Fisica Corpuscular, Valencia (Spain); Saavedra, Aldo [Australian Research Council Centre of Excellence for Particle Physics at the Tera-scale (Australia); The University of Sydney, Faculty of Engineering and Information Technologies, Centre for Translational Data Science, School of Physics, Camperdown, NSW (Australia); Scott, Pat [Imperial College London, Department of Physics, Blackett Laboratory, London (United Kingdom); Serra, Nicola [Universitaet Zuerich, Physik-Institut, Zurich (Switzerland); Weniger, Christoph [University of Amsterdam, GRAPPA, Institute of Physics, Amsterdam (Netherlands); Collaboration: The GAMBIT Collaboration 2017-12-15 We present the most comprehensive global fits to date of three supersymmetric models motivated by grand unification: the constrained minimal supersymmetric standard model (CMSSM), and its Non-Universal Higgs Mass generalisations NUHM1 and NUHM2. We include likelihoods from a number of direct and indirect dark matter searches, a large collection of electroweak precision and flavour observables, direct searches for supersymmetry at LEP and Runs I and II of the LHC, and constraints from Higgs observables. Our analysis improves on existing results not only in terms of the number of included observables, but also in the level of detail with which we treat them, our sampling techniques for scanning the parameter space, and our treatment of nuisance parameters. We show that stau co-annihilation is now ruled out in the CMSSM at more than 95% confidence. Stop co-annihilation turns out to be one of the most promising mechanisms for achieving an appropriate relic density of dark matter in all three models, whilst avoiding all other constraints. We find high-likelihood regions of parameter space featuring light stops and charginos, making them potentially detectable in the near future at the LHC. We also show that tonne-scale direct detection will play a largely complementary role, probing large parts of the remaining viable parameter space, including essentially all models with multi-TeV neutralinos. (orig.) 5. Predicting the sparticle spectrum from GUTs via SUSY threshold corrections with SusyTC Energy Technology Data Exchange (ETDEWEB) Antusch, Stefan [Department of Physics, University of Basel,Klingelbergstr. 82, CH-4056 Basel (Switzerland); Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),Föhringer Ring 6, D-80805 München (Germany); Sluka, Constantin [Department of Physics, University of Basel,Klingelbergstr. 82, CH-4056 Basel (Switzerland) 2016-07-21 Grand Unified Theories (GUTs) can feature predictions for the ratios of quark and lepton Yukawa couplings at high energy, which can be tested with the increasingly precise results for the fermion masses, given at low energies. To perform such tests, the renormalization group (RG) running has to be performed with sufficient accuracy. In supersymmetric (SUSY) theories, the one-loop threshold corrections (TC) are of particular importance and, since they affect the quark-lepton mass relations, link a given GUT flavour model to the sparticle spectrum. To accurately study such predictions, we extend and generalize various formulas in the literature which are needed for a precision analysis of SUSY flavour GUT models. We introduce the new software tool SusyTC, a major extension to the Mathematica package REAP http://dx.doi.org/10.1088/1126-6708/2005/03/024, where these formulas are implemented. SusyTC extends the functionality of REAP by a full inclusion of the (complex) MSSM SUSY sector and a careful calculation of the one-loop SUSY threshold corrections for the full down-type quark, up-type quark and charged lepton Yukawa coupling matrices in the electroweak-unbroken phase. Among other useful features, SusyTC calculates the one-loop corrected pole mass of the charged (or the CP-odd) Higgs boson as well as provides output in SLHA conventions, i.e. the necessary input for external software, e.g. for performing a two-loop Higgs mass calculation. We apply SusyTC to study the predictions for the parameters of the CMSSM (mSUGRA) SUSY scenario from the set of GUT scale Yukawa relations ((y{sub e})/(y{sub d}))=−(1/2), ((y{sub μ})/(y{sub s}))=6, and ((y{sub τ})/(y{sub b}))=−(3/2), which has been proposed recently in the context of SUSY GUT flavour models. 6. Where is SUSY? CERN Multimedia Antonella Del Rosso 2012-01-01 Recent information from the LHC experiments, the relatively low mass of the new boson and other data coming from experiments looking for dark matter worldwide are placing new constraints on the existence of supersymmetry (SUSY). However, there is a large community of scientists that still believes that SUSY particles are out there. Like lost keys at night, perhaps we have been looking for SUSY under the wrong lamp-posts… Can you work out this rebus? Source: Caroline Duc. So far, SUSY is “just” a theoretical physics model, which could solve problems beyond the Standard Model by accounting for dark matter and other phenomena in the Universe. However, SUSY has not been spotted so far, and might be hiding because of features different from what physicists previously expected. “Currently, there is no evidence for SUSY, but neither has any experimental data ruled it out. Many searches have focused on simplified versions of the theory but, given the recen... 7. Testing SUSY CERN Document Server Cassel, S; Ross, G G 2010-01-01 If SUSY provides a solution to the hierarchy problem then supersymmetric states should not be too heavy. This requirement is quantified by the Barbieri-Giudice fine tuning measure that provides a quantitative test of SUSY as a solution to the hierarchy problem. The measure is useful in correlating the impact of the various experimental measurements relevant to the search for supersymmetry and also in identifying the most sensitive measurements for testing SUSY. In this paper we apply the measure to the CMSSM, computing it to two-loop order and taking account of current experimental limits and the constraint on dark matter abundance. Using this we determine the present limits on the CMSSM parameter space and identify the measurements at the LHC that are most significant in covering the remaining parameter space. Without imposing the LEP Higgs mass bound we show that the smallest fine tuning (1:14.5) consistent with a saturation of the relic density within the 1$\\sigma$ WMAP bounds corresponds to a Higgs mass o... 8. Sparticle mass hierarchies, simplified models from SUGRA unification, and benchmarks for LHC Run-II SUSY searches International Nuclear Information System (INIS) Francescone, David; Akula, Sujeet; Altunkaynak, Baris; Nath, Pran 2015-01-01 Sparticle mass hierarchies contain significant information regarding the origin and nature of supersymmetry breaking. The hierarchical patterns are severely constrained by electroweak symmetry breaking as well as by the astrophysical and particle physics data. They are further constrained by the Higgs boson mass measurement. The sparticle mass hierarchies can be used to generate simplified models consistent with the high scale models. In this work we consider supergravity models with universal boundary conditions for soft parameters at the unification scale as well as supergravity models with nonuniversalities and delineate the list of sparticle mass hierarchies for the five lightest sparticles. Simplified models can be obtained by a truncation of these, retaining a smaller set of lightest particles. The mass hierarchies and their truncated versions enlarge significantly the list of simplified models currently being used in the literature. Benchmarks for a variety of supergravity unified models appropriate for SUSY searches at future colliders are also presented. The signature analysis of two benchmark models has been carried out and a discussion of the searches needed for their discovery at LHC Run-II is given. An analysis of the spin-independent neutralino-proton cross section exhibiting the Higgs boson mass dependence and the hierarchical patterns is also carried out. It is seen that a knowledge of the spin-independent neutralino-proton cross section and the neutralino mass will narrow down the list of the allowed sparticle mass hierarchies. Thus dark matter experiments along with analyses for the LHC Run-II will provide strong clues to the nature of symmetry breaking at the unification scale. 9. Search for Higgs Bosons in SUSY Cascades in CMS and Dark Matter with Non-universal Gaugino Masses CERN Document Server Huitu, Katri; Laamanen, Jari; Lehti, Sami; Roy, Sourov; Salminen, Tapio 2008-01-01 In grand unified theories (GUT), non-universal boundary conditions for the gaugino masses may arise at the unification scale, and affect the observability of the neutral MSSM Higgs bosons (h/H/A) at the LHC. The implications of such non-universal gaugino masses are investigated for the Higgs boson production in the SUSY cascade decay chain gluino --> squark quark, squark --> neutralino_2 quark, neutralino_2 --> neutralino_1 h/H/A, h/H/A --> b b-bar produced in pp interactions. In the singlet representation with universal gaugino masses only the light Higgs boson can be produced in this cascade with the parameter region of interest for us, while with non-universal gaugino masses heavy neutral MSSM Higgs boson production may dominate. The allowed parameter space in the light of the WMAP constraints on the cold dark matter relic density is investigated in the above scenarios for gaugino mass parameters. We also demonstrate that combination of representations can give the required amount of dark matter in any poi... 10. Naturalness, SUSY heavy higgses and flavor constraints CERN Multimedia CERN. Geneva 2014-01-01 I will demonstrate that supersymmetric (SUSY) higgses provide an important diagnostic for electroweak naturalness in the SUSY paradigm. I first review the naturalness problem of the Standard Model (SM) and SUSY as one of its most promising solutions. I study the masses of heavy Higgses in SUSY theories under broad assumptions, and show how they are constrained by their role in Electroweak symmetry breaking. I then show how Flavor Physics severely constrains large parts of SUSY parameter space, otherwise favored by naturalness. If SUSY Higgses are not discovered at relatively low mass during the next LHC run, this tension will further increase, disfavoring naturalness from SUSY. 11. SUSY Unparticle and Conformal Sequestering Energy Technology Data Exchange (ETDEWEB) Nakayama, Yu; Nakayama, Yu 2007-07-17 We investigate unparticle physics with supersymmetry (SUSY). The SUSY breaking effects due to the gravity mediation induce soft masses for the SUSY unparticles and hence break the conformal invariance. The unparticle physics observable in near future experiments is only consistent if the SUSY breakingeffects from the hidden sector to the standard model sector are dominated by the gauge mediation, or if the SUSY breaking effects to the unparticle sector are sufficiently sequestered. We argue that the natural realization of the latter possibility is the conformal sequestering scenario. 12. Soft SUSY breaking parameters and RG running of squark and slepton masses in large volume Swiss Cheese compactifications International Nuclear Information System (INIS) Misra, Aalok; Shukla, Pramod 2010-01-01 We consider type IIB large volume compactifications involving orientifolds of the Swiss Cheese Calabi-Yau WCP 4 [1,1,1,6,9] with a single mobile space-time filling D3-brane and stacks of D7-branes wrapping the 'big' divisor Σ B (as opposed to the 'small' divisor usually done in the literature thus far) as well as supporting D7-brane fluxes. After reviewing our proposal of (Misra and Shukla, 2010) for resolving a long-standing tension between large volume cosmology and phenomenology pertaining to obtaining a 10 12 GeV gravitino in the inflationary era and a TeV gravitino in the present era, and summarizing our results of (Misra and Shukla, 2010) on soft supersymmetry breaking terms and open-string moduli masses, we discuss the one-loop RG running of the squark and slepton masses in mSUGRA-like models (using the running of the gaugino masses) to the EW scale in the large volume limit. Phenomenological constraints and some of the calculated soft SUSY parameters identify the D7-brane Wilson line moduli as the first two generations/families of squarks and sleptons and the D3-brane (restricted to the big divisor) position moduli as the two Higgses for MSSM-like models at TeV scale. We also discuss how the obtained open-string/matter moduli make it easier to impose FCNC constraints, as well as RG flow of off-diagonal squark mass(-squared) matrix elements. 13. Soft SUSY breaking parameters and RG running of squark and slepton masses in large volume Swiss Cheese compactifications Science.gov (United States) Misra, Aalok; Shukla, Pramod 2010-03-01 We consider type IIB large volume compactifications involving orientifolds of the Swiss Cheese Calabi-Yau WCP[1,1,1,6,9] with a single mobile space-time filling D3-brane and stacks of D7-branes wrapping the “big” divisor ΣB (as opposed to the “small” divisor usually done in the literature thus far) as well as supporting D7-brane fluxes. After reviewing our proposal of [1] (Misra and Shukla, 2010) for resolving a long-standing tension between large volume cosmology and phenomenology pertaining to obtaining a 10 GeV gravitino in the inflationary era and a TeV gravitino in the present era, and summarizing our results of [1] (Misra and Shukla, 2010) on soft supersymmetry breaking terms and open-string moduli masses, we discuss the one-loop RG running of the squark and slepton masses in mSUGRA-like models (using the running of the gaugino masses) to the EW scale in the large volume limit. Phenomenological constraints and some of the calculated soft SUSY parameters identify the D7-brane Wilson line moduli as the first two generations/families of squarks and sleptons and the D3-brane (restricted to the big divisor) position moduli as the two Higgses for MSSM-like models at TeV scale. We also discuss how the obtained open-string/matter moduli make it easier to impose FCNC constraints, as well as RG flow of off-diagonal squark mass(-squared) matrix elements. 14. SUSY Searches at ATLAS CERN Document Server Mamuzic, Judita; The ATLAS collaboration 2017-01-01 Supersymmetry (SUSY) is considered one of the best motivated extensions of the Standard Model. It postulates a fundamental symmetry between fermions and bosons, and introduces a set of new supersymmetric particles at the electroweak scale. It addresses the hierarchy and naturalness problem, gives a solution to the gauge coupling unification, and offers a cold dark matter candidate. Different aspects of SUSY searches, using strong, electroweak, third generation production, and R-parity violation and long lived particles are being studied at the LHC. An overview of most recent SUSY searches results using the 13 TeV ATLAS RUN2 data will be presented. 15. Gluino reach and mass extraction at the LHC in radiatively-driven natural SUSY Energy Technology Data Exchange (ETDEWEB) Baer, Howard; Savoy, Michael; Sengupta, Dibyashree [University of Oklahoma, Department of Physics and Astronomy, Norman, OK (United States); Barger, Vernon [University of Wisconsin, Department of Physics, Madison, WI (United States); Gainer, James S.; Tata, Xerxes [University of Hawaii, Department of Physics and Astronomy, Honolulu, HI (United States); Huang, Peisi [University of Chicago, Enrico Fermi Institute, Chicago, IL (United States); HEP Division, Argonne National Laboratory, Argonne, IL (United States); Texas A and M University, Mitchell Institute for Fundamental Physics and Astronomy, College Station, TX (United States) 2017-07-15 Radiatively-driven natural SUSY (RNS) models enjoy electroweak naturalness at the 10% level while respecting LHC sparticle and Higgs mass constraints. Gluino and top-squark masses can range up to several TeV (with other squarks even heavier) but a set of light Higgsinos are required with mass not too far above m{sub h} ∝ 125 GeV. Within the RNS framework, gluinos dominantly decay via g → tt{sub 1}{sup }, anti tt{sub 1} → t anti tZ{sub 1,2} or t anti bW{sub 1}{sup -} + c.c., where the decay products of the higgsino-like W{sub 1} and Z{sub 2} are very soft. Gluino pair production is, therefore, signaled by events with up to four hard b-jets and large E{sub T}. We devise a set of cuts to isolate a relatively pure gluino sample at the (high-luminosity) LHC and show that in the RNS model with very heavy squarks, the gluino signal will be accessible for m{sub g} < 2400 (2800) GeV for an integrated luminosity of 300 (3000) fb{sup -1}. We also show that the measurement of the rate of gluino events in the clean sample mentioned above allows for a determination of m{sub g} with a statistical precision of 2-5% (depending on the integrated luminosity and the gluino mass) over the range of gluino masses where a 5σ discovery is possible at the LHC. (orig.) 16. Precise Higgs mass calculations in (non-)minimal supersymmetry at both high and low scales Energy Technology Data Exchange (ETDEWEB) Athron, Peter [Monash Univ., Victoria (Australia). School of Physics and Astronomy; Park, Jae-hyeon [Korea Institute for Advanced Study, Seoul (Korea, Republic of). Quantum Universe Center; Steudtner, Tom; Stoeckinger, Dominik [TU Dresden (Germany). Inst. fuer Kern- und Teilchenphysik; Voigt, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2016-09-15 We present FlexibleEFTHiggs, a method for calculating the SM-like Higgs pole mass in SUSY (and even non-SUSY) models, which combines an effective field theory approach with a diagrammatic calculation. It thus achieves an all order resummation of leading logarithms together with the inclusion of all non-logarithmic 1-loop contributions. We implement this method into FlexibleSUSY and study its properties in the MSSM, NMSSM, E{sub 6}SSM and MRSSM. In the MSSM, it correctly interpolates between the known results of effective field theory calculations in the literature for a high SUSY scale and fixed-order calculations in the full theory for a sub-TeV SUSY scale. We compare our MSSM results to those from public codes and identify the origin of the most significant deviations between the DR programs. We then perform a similar comparison in the remaining three non-minimal models. For all four models we estimate the theoretical uncertainty of FlexibleEFTHiggs and the fixed-order DR programs thereby finding that the former becomes more precise than the latter for a SUSY scale above a few TeV. Even for sub-TeV SUSY scales, FlexibleEFTHiggs maintains the uncertainty estimate around 2-3 GeV, remaining a competitive alternative to existing fixed-order computations. 17. Precise Higgs mass calculations in (non-)minimal supersymmetry at both high and low scales Energy Technology Data Exchange (ETDEWEB) Athron, Peter [ARC Centre of Excellence for Particle Physics at the Terascale,School of Physics and Astronomy, Monash University,Melbourne, Victoria 3800 (Australia); Park, Jae-hyeon [Quantum Universe Center, Korea Institute for Advanced Study,85 Hoegiro Dongdaemungu, Seoul 02455 (Korea, Republic of); Steudtner, Tom; Stöckinger, Dominik [Institut für Kern- und Teilchenphysik, TU Dresden,Zellescher Weg 19, 01069 Dresden (Germany); Voigt, Alexander [Deutsches Elektronen-Synchrotron DESY,Notkestraße 85, 22607 Hamburg (Germany) 2017-01-18 We present FlexibleEFTHiggs, a method for calculating the SM-like Higgs pole mass in SUSY (and even non-SUSY) models, which combines an effective field theory approach with a diagrammatic calculation. It thus achieves an all order resummation of leading logarithms together with the inclusion of all non-logarithmic 1-loop contributions. We implement this method into FlexibleSUSY and study its properties in the MSSM, NMSSM, E{sub 6}SSM and MRSSM. In the MSSM, it correctly interpolates between the known results of effective field theory calculations in the literature for a high SUSY scale and fixed-order calculations in the full theory for a sub-TeV SUSY scale. We compare our MSSM results to those from public codes and identify the origin of the most significant deviations between the (DR)-bar programs. We then perform a similar comparison in the remaining three non-minimal models. For all four models we estimate the theoretical uncertainty of FlexibleEFTHiggs and the fixed-order (DR)-bar programs thereby finding that the former becomes more precise than the latter for a SUSY scale above a few TeV. Even for sub-TeV SUSY scales, FlexibleEFTHiggs maintains the uncertainty estimate around 2–3 GeV, remaining a competitive alternative to existing fixed-order computations. 18. SUSY searches with the ATLAS detector CERN Document Server Ventura, Andrea; The ATLAS collaboration 2016-01-01 Despite the absence of experimental evidence, weak scale supersymmetry remains one of the best motivated and studied Standard Model extensions. This talk summarises recent ATLAS results for searches for supersymmetric (SUSY) particles, with focus on those obtained using proton-proton collisions at a centre of mass energy of 13 TeV. Strong production in both R-Parity conserving and R-Parity violating SUSY scenarios are considered. The searches involved final states including jets, missing transverse momentum, light leptons, as well as long-lived particle signatures. 19. Interplay of LFV and slepton mass splittings at the LHC as a probe of the SUSY seesaw CERN Document Server Abada, A; Romao, J C; Teixeira, A M 2010-01-01 We study the impact of a type-I SUSY seesaw concerning lepton flavour violation (LFV) both at low-energies and at the LHC. The study of the di-lepton invariant mass distribution at the LHC allows to reconstruct some of the masses of the different sparticles involved in a decay chain. In particular, the combination with other observables renders feasible the reconstruction of the masses of the intermediate sleptons involved in $\\chi_2^0\\to \\tilde \\ell \\,\\ell \\to \\ell \\,\\ell\\,\\chi_1^0$ decays. Slepton mass splittings can be either interpreted as a signal of non-universality in the SUSY soft breaking-terms (signalling a deviation from constrained scenarios as the cMSSM) or as being due to the violation of lepton flavour. In the latter case, in addition to these high-energy processes, one expects further low-energy manifestations of LFV such as radiative and three-body lepton decays. Under the assumption of a type-I seesaw as the source of neutrino masses and mixings, all these LFV observables are related. Worki... 20. Implications for new physics from fine-tuning arguments 1. Application to SUSY and seesaw cases International Nuclear Information System (INIS) Alberto Casas, J.; Hidalgo, Irene; Espinosa, Jose R. 2004-01-01 We revisit the standard argument to estimate the scale of new physics (NP) beyond the SM, based on the sensitivity of the Higgs mass to quadratic divergences. Although this argument is arguably naive, the corresponding estimate, Λ SM SM . One can obtain more precise implications from fine-tuning arguments in specific examples of NP. Here we consider SUSY and right-handed (seesaw) neutrinos. SUSY is a typical example for which the previous general estimate is indeed conservative: the MSSM is fine-tuned a few %, even for soft masses of a few hundred GeV. In contrast, other SUSY scenarios, in particular those with low-scale SUSY breaking, can easily saturate the general bound on Λ SM . The seesaw mechanism requires large fine-tuning if M R > or approx.10 7 GeV, unless there is additional NP (SUSY being a favourite option). (author) 1. Reach of the Fermilab Tevatron and CERN LHC for gaugino mediated SUSY breaking models International Nuclear Information System (INIS) Baer, Howard; Belyaev, Alexander; Krupovnickas, Tadas; Tata, Xerxes 2002-01-01 In supersymmetric models with gaugino mediated SUSY breaking (gMSB), it is assumed that SUSY breaking on a hidden brane is communicated to the visible brane via gauge superfields which propagate in the bulk. This leads to GUT models where the common gaugino mass m 1/2 is the only soft SUSY breaking term to receive contributions at the tree level. To obtain a viable phenomenology, it is assumed that the gaugino mass is induced at some scale M c beyond the GUT scale, and that additional renormalization group running takes place between M c and M GUT as in a SUSY GUT. We assume an SU(5) SUSY GUT above the GUT scale, and compute the SUSY particle spectrum expected in models with gMSB. We use the Monte Carlo program ISAJET to simulate signals within the gMSB model, and compute the SUSY reach including cuts and triggers appropriate to Fermilab Tevatron and CERN LHC experiments. We find no reach for SUSY by the Tevatron collider in the trilepton channel. At the CERN LHC, values of m 1/2 =1000 (1160) GeV can be probed with 10 (100) fb -1 of integrated luminosity, corresponding to a reach in terms of m g-tilde of 2150 (2500) GeV. The gMSB model and MSUGRA can likely only be differentiated at a linear e + e - collider with sufficient energy to produce sleptons and charginos 2. Electroweak SUSY production searches at ATLAS and CMS CERN Document Server Flowerdew, M; The ATLAS collaboration 2014-01-01 The discovery of weak-scale supersymmetric (SUSY) particles is one of the primary goals of the Large Hadron Collider experiments. Depending on the mechanism of SUSY breaking, it could be that strongly interacting squarks and gluinos are too massive to produce at the LHC. In this case, the primary SUSY production mode is of charginos, neutralinos and sleptons, mediated by electroweak interactions. However, the experimental signatures for discovery vary widely, depending on the mass hierarchy, SUSY particle mixing parameters and conservation/violation of R-parity, necessitating a large and complex suite of experimental search strategies. These strategies include searching for events with multiple charged leptons, photons, reconstructed higgs bosons or new long-lived particles. In this presentation, the latest ATLAS and CMS search results in these channels are presented, based mainly on $20~$fb$^{-1}$ of $pp$ collisions at $\\sqrt{s} = 8~$TeV collected in 2012. The resulting constraints on the parameter spaces of... 3. EW SUSY production searches at ATLAS and CMS CERN Document Server Flowerdew, MJ; The ATLAS collaboration 2014-01-01 The discovery of weak-scale supersymmetric (SUSY) particles is one of the primary goals of the Large Hadron Collider experiments. Depending on the mechanism of SUSY breaking, it could be that strongly interacting squarks and gluinos are too massive to produce at the LHC. In this case, the primary SUSY production mode is of charginos, neutralinos and sleptons, mediated by electroweak interactions. However, the experimental signatures for discovery vary widely, depending on the mass hierarchy, SUSY particle mixing parameters and conservation/violation of R-parity, necessitating a large and complex suite of experimental search strategies. These strategies include searching for events with multiple charged leptons, photons, reconstructed higgs bosons or new long-lived particles. In this presentation, the latest ATLAS and CMS search results in these channels are presented, based mainly on 20 fb$^{-1}$ of pp collisions at $\\sqrt{s} = 8$ TeV collected in 2012. The resulting constraints on the parameter spaces of var... 4. SUSY Without Prejudice International Nuclear Information System (INIS) Berger, C. 2008-01-01 We begin an exploration of the physics associated with the general CP-conserving MSSM with Minimal Flavor Violation, the pMSSM. The 19 soft SUSY breaking parameters in this scenario are chosen so as to satisfy all existing experimental and theoretical constraints assuming that the WIMP is a thermal relic, i.e., the lightest neutralino. We scan this parameter space twice using both flat and log priors for the soft SUSY breaking mass parameters and compare the results which yield similar conclusions. Detailed constraints from both LEP and the Tevatron searches play a particularly important role in obtaining our final model samples. We find that the pMSSM leads to a much broader set of predictions for the properties of the SUSY partners as well as for a number of experimental observables than those found in any of the conventional SUSY breaking scenarios such as mSUGRA. This set of models can easily lead to atypical expectations for SUSY signals at the LHC 5. SUSY Search at LHC CERN Document Server Xu, Da; The ATLAS collaboration 2018-01-01 Despite the absence of experimental evidence, weak scale supersymmetry remains one of the best motivated and studied Standard Model extensions. This talk gives an overview of the most recent SUSY searches in ATLAS and CMS experiments using 13 TeV ATLAS Run2 data. 6. Non-universal SUSY breaking, hierarchy and squark degeneracty International Nuclear Information System (INIS) Murayama, Hitoshi. 1995-01-01 I discuss non-trivial effects in the soft SUSY breaking terms which appear when one integrates out heavy fields. The effects exist only when the SUSY breaking terms are non-universal. They may spoil (1) the hierarchy between the weak and high-energy scales, or (2) degeneracy among the squark masses even in the presense of a horizontal symmetry. I argue, in the end, that such new effects may be useful in probing physics at high-energy scales from TeV-scale experiments 7. Initial conditions for inflation and the energy scale of SUSY-breaking from the (nearly) gaussian sky CERN Document Server Álvarez-Gaumé, Luis; Jimenez, Raul We show how general initial conditions for small field inflation can be obtained in multi-field models. This is provided by non-linear angular friction terms in the inflaton that provide a phase of non-slow-roll inflation before the slow-roll inflation phase. This in turn provides a natural mechanism to star small-field slow-roll at nearly zero velocity for arbitrary initial conditions. We also show that there is a relation between the scale of SUSY breaking sqrt (f) and the amount of non-gaussian fluctuations generated by the inflaton. In particular, we show that in the local non-gaussian shape there exists the relation sqrt (f) = 10^{13} GeV sqrt (f_NL). With current observational limits from Planck, and adopting the minimum amount of non-gaussian fluctuations allowed by single-field inflation, this provides a very tight constraint for the SUSY breaking energy scale sqrt (f) = 3-7 x 10^{13} GeV at 95% confidence. Further limits, or detection, from next year's Planck polarisation data will further tighten th... 8. Improved GUT and SUSY breaking by the same field International Nuclear Information System (INIS) Agashe, Kaustubh 2000-01-01 In a previous paper [hep-ph/9809421; Phys. Lett. B 444 (1998) 61], we presented a model in which the same modulus field breaks SUSY and a simple GUT gauge group, and which has dynamical origins for both SUSY breaking and GUT scales. In this model, the supergravity (SUGRA) and gauge mediated contributions to MSSM scalar and gaugino masses are comparable -- this enables a realistic spectrum to be attained since the gauge mediated contribution to the right-handed (RH) slepton (mass) 2 (at the weak scale) by itself (i.e., neglecting SUGRA contribution to sfermion and gaugino masses) is negative. But, in general, the SUGRA contribution to sfermion masses (from non-renormalizable contact Kaehler terms) leads to flavor violation. In this paper, we use the recently proposed idea of gaugino mediated SUSY breaking ( g-tilde MSB) to improve the above model. With MSSM matter and SUSY breaking fields localized on separate branes in an extra dimension of size R∼5M -1 Pl (in which gauge fields propagate), the SUGRA contribution to sfermion masses (which violates flavor) is suppressed. As in 4 dimensions, MSSM gauginos acquire non-universal masses from both SUGRA and gauge mediation - gaugino masses (in particular the SUGRA contribution to gaugino masses), in turn, generate acceptable sfermion masses through renormalization group evolution; the phenomenology is discussed briefly. We also point out that (a) in models where SUSY is broken by a GUT non-singlet field, there is, in general, a contribution to MSSM gaugino (and scalar) masses from the coupling to heavy gauge multiplet which might be comparable to the SUGRA contribution and (b) models of gauge mediation proposed earlier which also have negative RH slepton (mass) 2 can be rendered viable using the g-tilde MSB idea 9. Quark and lepton masses at the GUT scale including supersymmetric threshold corrections International Nuclear Information System (INIS) Antusch, S.; Spinrath, M. 2008-01-01 We investigate the effect of supersymmetric (SUSY) threshold corrections on the values of the running quark and charged lepton masses at the grand unified theory (GUT) scale within the large tanβ regime of the minimal supersymmetric standard model. In addition to the typically dominant SUSY QCD contributions for the quarks, we also include the electroweak contributions for quarks and leptons and show that they can have significant effects. We provide the GUT scale ranges of quark and charged lepton Yukawa couplings as well as of the ratios m μ /m s , m e /m d , y τ /y b and y t /y b for three example ranges of SUSY parameters. We discuss how the enlarged ranges due to threshold effects might open up new possibilities for constructing GUT models of fermion masses and mixings. 10. Lifshitz-sector mediated SUSY breaking International Nuclear Information System (INIS) Pospelov, Maxim; Tamarit, Carlos 2014-01-01 We propose a novel mechanism of SUSY breaking by coupling a Lorentz-invariant supersymmetric matter sector to non-supersymmetric gravitational interactions with Lifshitz scaling. The improved UV properties of Lifshitz propagators moderate the otherwise uncontrollable ultraviolet divergences induced by gravitational loops. This ensures that both the amount of induced Lorentz violation and SUSY breaking in the matter sector are controlled by Λ HL 2 /M P 2 , the ratio of the Hořava-Lifshitz cross-over scale Λ HL to the Planck scale M P . This ratio can be kept very small, providing a novel way of explicitly breaking supersymmetry without reintroducing fine-tuning. We illustrate our idea by considering a model of scalar gravity with Hořava-Lifshitz scaling coupled to a supersymmetric Wess-Zumino matter sector, in which we compute the two-loop SUSY breaking corrections to the masses of the light scalars due to the gravitational interactions and the heavy fields 11. FlexibleSUSY-A spectrum generator generator for supersymmetric models Science.gov (United States) Athron, Peter; Park, Jae-hyeon; Stöckinger, Dominik; Voigt, Alexander 2015-05-01 We introduce FlexibleSUSY, a Mathematica and C++ package, which generates a fast, precise C++ spectrum generator for any SUSY model specified by the user. The generated code is designed with both speed and modularity in mind, making it easy to adapt and extend with new features. The model is specified by supplying the superpotential, gauge structure and particle content in a SARAH model file; specific boundary conditions e.g. at the GUT, weak or intermediate scales are defined in a separate FlexibleSUSY model file. From these model files, FlexibleSUSY generates C++ code for self-energies, tadpole corrections, renormalization group equations (RGEs) and electroweak symmetry breaking (EWSB) conditions and combines them with numerical routines for solving the RGEs and EWSB conditions simultaneously. The resulting spectrum generator is then able to solve for the spectrum of the model, including loop-corrected pole masses, consistent with user specified boundary conditions. The modular structure of the generated code allows for individual components to be replaced with an alternative if available. FlexibleSUSY has been carefully designed to grow as alternative solvers and calculators are added. Predefined models include the MSSM, NMSSM, E6SSM, USSM, R-symmetric models and models with right-handed neutrinos. 12. Simplified SUSY at the ILC Energy Technology Data Exchange (ETDEWEB) Berggren, Mikael 2013-08-15 At the ILC, one has the possibility to search for SUSY in an model-independent way: The corner-stone of SUSY is that sparticles couple as particles. This is independent of the mechanism responsible for SUSY breaking. Any model will have one Lightest SUSY Particle (LSP), and one Next to Lightest SUSY Particle (NLSP). In models with conserved R-parity, the NLSP must decay solely to the LSP and the SM partner of the NLSP. Therefore, studying NLSP production and decay can be regarded as a ''simplified model without simplification'': Any SUSY model will have such a process. The NLSP could be any sparticle: a slepton, an electroweak-ino, or even a squark. However, since there are only a finite number of sparticles, one can systematically search for signals of all possible NLSP:s. This way, the entire space of models that have a kinematically reachable NLSP can be covered. For any NLSP, the ''worst case'' can be determined, since the SUSY principle allows to calculate the cross-section once the NLSP nature and mass are given. The region in the LSP-NLSP mass-plane where the ''worst case'' could be discovered or excluded experimentally can be found by estimating background and efficiency at each point in the plane. From experience at LEP, it is expected that the lower signal-to background ratio will indeed be found for models with conserved R-parity. In this document, we show that at the ILC, such a program is possible, as it was at LEP. No loop-holes are left, even for difficult or non-standard cases: whatever the NLSP is it will be detectable. 13. Simplified SUSY at the ILC International Nuclear Information System (INIS) Berggren, Mikael 2013-08-01 At the ILC, one has the possibility to search for SUSY in an model-independent way: The corner-stone of SUSY is that sparticles couple as particles. This is independent of the mechanism responsible for SUSY breaking. Any model will have one Lightest SUSY Particle (LSP), and one Next to Lightest SUSY Particle (NLSP). In models with conserved R-parity, the NLSP must decay solely to the LSP and the SM partner of the NLSP. Therefore, studying NLSP production and decay can be regarded as a ''simplified model without simplification'': Any SUSY model will have such a process. The NLSP could be any sparticle: a slepton, an electroweak-ino, or even a squark. However, since there are only a finite number of sparticles, one can systematically search for signals of all possible NLSP:s. This way, the entire space of models that have a kinematically reachable NLSP can be covered. For any NLSP, the ''worst case'' can be determined, since the SUSY principle allows to calculate the cross-section once the NLSP nature and mass are given. The region in the LSP-NLSP mass-plane where the ''worst case'' could be discovered or excluded experimentally can be found by estimating background and efficiency at each point in the plane. From experience at LEP, it is expected that the lower signal-to background ratio will indeed be found for models with conserved R-parity. In this document, we show that at the ILC, such a program is possible, as it was at LEP. No loop-holes are left, even for difficult or non-standard cases: whatever the NLSP is it will be detectable. 14. Natural SUSY endures Energy Technology Data Exchange (ETDEWEB) Papucci, Michele; Ruderman, Joshua T. [Lawrence Berkeley National Laboratory, CA (United States). Theoretical Physics Group; California Univ., Berkeley, CA (United States). Dept. of Physics; Weiler, Andreas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); European Organization for Nuclear Research, Geneva (Switzerland). Theoretical Physics Div. 2011-10-31 The first 1 fb{sup -1} of LHC searches have set impressive limits on new colored particles decaying to missing energy. We address the implication of these searches for naturalness in supersymmetry (SUSY). General bottom-up considerations of natural electroweak symmetry breaking show that higgsinos, stops, and the gluino should not be too far above the weak scale. The rest of the spectrum, including the squarks of the first two generations, can be heavier and beyond the current LHC reach. We have used collider simulations to determine the limits that all of the 1 fb{sup -1} searches pose on higgsinos, stops, and the gluino. We find that stops and the left-handed sbottom are starting to be constrained and must be heavier than about 200-300 GeV when decaying to higgsinos. The gluino must be heavier than about 600-800 GeV when it decays to stops and sbottoms. While these findings point toward scenarios with a lighter third generation split from the other squarks, we do find that moderately-tuned regions remain, where the gluino is just above 1 TeV and all the squarks are degenerate and light. Among all the searches, jets plus missing energy and same-sign dileptons often provide the most powerful probes of natural SUSY. Overall, our results indicate that natural SUSY has survived the first 1 fb{sup -1} of data. The LHC is now on the brink of exploring the most interesting region of SUSY parameter space. (orig.) 15. SUSY long-lived massive particles. Detection and physics at the LHC International Nuclear Information System (INIS) Ambrosiano, S.; Mele, B.; Nisati, A.; Petrarca, S.; Polesello, G.; Rimoldi, A.; Salvini, G. 2001-01-01 It was drawn a possible scenario for the observation of massive long-lived charged particles at the LHC detector ATLAS. The required flexibility of the detector triggers and of the identification and reconstruction systems are discussed. As an example, it was focused on the measurement of the mass and lifetime of long-lived charged sleptons predicted in the framework of supersymmetric models with gauge-mediated supersymmetry (SUSY) breaking. In this case the next-to-lightest SUSY particle can be the light scalar partner of the tau lepton (τ 1 ), possibly decaying slowly into a gravitino. A wide region of the SUSY parameters space was explored. The accessible range and precision on the measurement of the SUSY breaking scale parameter of √ F achievable with a counting method are assessed [it 16. Mass quantization in quantum and susy cosmological models with matter content International Nuclear Information System (INIS) Ortiz, C; Socorro, J; Tkach, V I; Torres, J; Rosales, J 2005-01-01 We present the study of the quantum closed Friedmann-Robertson-Walker (FRW) cosmological model with a matter content given by a perfect fluid with barotropic state equation p = γρ The Wheeler-DeWitt equation is viewed as the Schroedinger equation for the linear harmonic oscillator with energy E. Such type of Universe has quantized masses of the order of the Planck mass and harmonic oscillator wave functions. Then, we consider the n = 2 supersymmetric superfield approach for the same model and obtain a normalizable wave function (at zero energy) of the universe. Besides, the mass parameter spectrum is found in the Schroedinger picture, being similar to those obtained by other methods, using a black hole system 17. Recent SUSY results in ATLAS CERN Document Server Mamuzic, Judita; The ATLAS collaboration 2018-01-01 Supersymmetry (SUSY) is considered one of the best motivated extensions of the Standard Model. It postulates a fundamental symmetry between fermions and bosons, and introduces a set of new supersymmetric particles at the electroweak scale. It addresses the hierarchy and natu- ralness problem, gives a solution to the gauge couplings unification, and offers a cold dark matter candidate. Different aspects of SUSY searches, using strong, electroweak, third generation production, R-parity violation models, and long lived particles are being studied at the LHC. An overview of most recent results in SUSY searches using Run 2 ATLAS data, at 13 TeV with 36.1 fb−1 of integrated luminosity, was presented. 18. What is a natural SUSY scenario? Energy Technology Data Exchange (ETDEWEB) Casas, J. Alberto; Moreno, Jesús M.; Robles, Sandra; Rolbiecki, Krzysztof [Instituto de Física Teórica, IFT-UAM/CSIC, Universidad Autónoma de Madrid,Cantoblanco, 28049 Madrid (Spain); Zaldívar, Bryan [Service de Physique Théorique, Université Libre de Bruxelles,Boulevard du Triomphe, CP225, 1050 Brussels (Belgium) 2015-06-11 The idea of “Natural SUSY', understood as a supersymmetric scenario where the fine-tuning is as mild as possible, is a reasonable guide to explore supersymmetric phenomenology. In this paper, we re-examine this issue in the context of the MSSM including several improvements, such as the mixing of the fine-tuning conditions for different soft terms and the presence of potential extra fine-tunings that must be combined with the electroweak one. We give tables and plots that allow to easily evaluate the fine-tuning and the corresponding naturalness bounds for any theoretical model defined at any high-energy (HE) scale. Then, we analyze in detail the complete fine-tuning bounds for the unconstrained MSSM, defined at any HE scale. We show that Natural SUSY does not demand light stops. Actually, an average stop mass below 800 GeV is disfavored, though one of the stops might be very light. Regarding phenomenology, the most stringent upper bound from naturalness is the one on the gluino mass, which typically sets the present level fine-tuning at O(1%). However, this result presents a strong dependence on the HE scale. E.g. if the latter is 10{sup 7} GeV the level of fine-tuning is ∼ four times less severe. Finally, the most robust result of Natural SUSY is by far that Higgsinos should be rather light, certainly below 700 GeV for a fine-tuning of O(1%) or milder. Incidentally, this upper bound is not far from ≃1 TeV, which is the value required if dark matter is made of Higgsinos. 19. SUSY signals at DESY HERA in the no-scale flipped SU(5) supergravity model Energy Technology Data Exchange (ETDEWEB) Lopez, J.L.; Nanopoulos, D.V.; Wang, X.; Zichichi, A. (Center for Theoretical Physics, Department of Physics, Texas A M University, College Station, Texas 77843-4242 (United States) Astroparticle Physics Group, Houston Advanced Research Center (HARC), The Woodlands, Texas 77381 (United States) CERN, Geneva (Switzerland)) 1993-11-01 Sparticle production and detection at DESY HERA are studied within the recently proposed no-scale flipped SU(5) supergravity model. Among the various reaction channels that could lead to sparticle production at HERA, only the following are within its limit of sensitivity in this model: [ital e][sup [minus 20. High scale parity invariance as a solution to the SUSY CP problem ... It is shown that if the supersymmetric Standard Model (MSSM) emerges as the low energy limit of a high scale left–right symmetric gauge structure, the number of uncontrollable CP violating phases of MSSM are drastically reduced. In particular it guarantees the vanishing of the dangerous phases that were at the root of the ... 1. Constraints of chromoelectric dipole moments to natural SUSY type sfermion spectrum Science.gov (United States) Maekawa, Nobuhiro; Muramatsu, Yu; Shigekami, Yoshihiro 2017-06-01 We investigate the lower bounds of sfermion masses from the constraints of chromoelectric dipole moments (CEDMs) in the natural SUSY-type sfermion mass spectrum, in which stop mass mt ˜ is much smaller than the other sfermion masses m0. The natural SUSY-type sfermion mass spectrum has been studied since the supersymmetric (SUSY) flavor-changing neutral currents (FCNC) are suppressed because of large sfermion masses of the first two generations, and the weak scale is stabilized because of the light stop. However, this type of sfermion mass spectrum is severely constrained by CEDM, because the light stop contributions to the up quark CEDM are not decoupled in the limit m0→∞ , while the down quark CEDM is decoupled in the limit. It is important that the constraints are severe even if SUSY-breaking parameters (and Higgsino mass) are taken to be real because complex diagonalizing matrices of Yukawa matrices, which are from complex Yukawa couplings, generate nonvanishing C P phases in off-diagonal elements of sfermion mass matrices. We calculate the CEDM of up and down quarks numerically in the minimal SUSY standard model, and give the lower bounds for stop mass and the other sfermion masses. We show that the lower bound of stop mass becomes 7 TeV to satisfy the CEDM constraints from Hg EDM. The result is not acceptable if the weak scale stability is considered seriously. We show that if the up-type Yukawa couplings are taken to be real at the grand unification scale, the CEDM constraints are satisfied even if mt ˜˜1 TeV . 2. Prospects for axion detection in natural SUSY with mixed axion-higgsino dark matter: back to invisible? Energy Technology Data Exchange (ETDEWEB) Bae, Kyu Jung [Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon 34051 (Korea, Republic of); Baer, Howard; Serce, Hasan, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019 (United States) 2017-06-01 Under the expectation that nature is natural, we extend the Standard Model to include SUSY to stabilize the electroweak sector and PQ symmetry to stabilize the QCD sector. Then natural SUSY arises from a Kim-Nilles solution to the SUSY μ problem which allows for a little hierarchy where μ∼ f {sub a} {sup 2}/ M {sub P} {sub ∼} 100−300 GeV while the SUSY particle mass scale m {sub SUSY}∼ 1−10 TeV >> μ. Dark matter then consists of two particles: a higgsino-like WIMP and a SUSY DFSZ axion. The range of allowed axion mass values m {sub a} depends on the mixed axion-higgsino relic density. The range of m {sub a} is actually restricted in this case by limits on WIMPs from direct and indirect detection experiments. We plot the expected axion detection rate at microwave cavity experiments. The axion-photon-photon coupling is severely diminished by charged higgsino contributions to the anomalous coupling. In this case, the axion may retreat, at least temporarily, back into the regime of near invisibility. From our results, we urge new ideas for techniques which probe both deeper and more broadly into axion coupling versus axion mass parameter space. 3. D-term contributions and CEDM constraints in E6 × SU(2)F × U(1)A SUSY GUT model Science.gov (United States) Shigekami, Yoshihiro 2017-11-01 We focus on E6 × SU(2)F × U(1)A supersymmetric (SUSY) grand unified theory (GUT) model. In this model, realistic Yukawa hierarchies and mixings are realized by introducing all allowed interactions with 𝓞(1) coefficients. Moreover, we can take stop mass is smaller than the other sfermion masses. This type of spectrum called by natural SUSY type sfermion mass spectrum can suppress the SUSY contributions to flavor changing neutral current (FCNC) and stabilize weak scale at the same time. However, light stop predicts large up quark CEDM and stop contributions are not decoupled. Since there is Kobayashi-Maskawa phase, stop contributions to the up quark CEDM is severely constrained even if all SUSY breaking parameters and Higgsino mass parameter μ are real. In this model, real up Yukawa couplings are realized at the GUT scale because of spontaneous CP violation. Therefore CEDM bounds are satisfied, although up Yukawa couplings are complex at the SUSY scale through the renormalization equation group effects. We calculated the CEDMs and found that EDM constraints can be satisfied even if stop mass is 𝓞(1) TeV. In addition, we investigate the size of D-terms in this model. Since these D-term contributions is flavor dependent, the degeneracy of sfermion mass spectrum is destroyed and the size of D-term is strongly constrained by FCNCs when SUSY breaking scale is the weak scale. However, SUSY breaking scale is larger than 1 TeV in order to obtain 125 GeV Higgs mass, and therefore sizable D-term contribution is allowed. Furthermore, we obtained the non-trivial prediction for the difference of squared sfermion mass. 4. Lifshitz-sector mediated SUSY breaking OpenAIRE Pospelov, MaximDepartment of Physics and Astronomy, University of Victoria, Victoria, BC, V8P 5C2, Canada; Tamarit, Carlos(Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada) 2014-01-01 We propose a novel mechanism of SUSY breaking by coupling a Lorentz-invariant supersymmetric matter sector to non-supersymmetric gravitational interactions with Lifshitz scaling. The improved UV properties of Lifshitz propagators moderate the otherwise uncontrollable ultraviolet divergences induced by gravitational loops. This ensures that both the amount of induced Lorentz violation and SUSY breaking in the matter sector are controlled by ${{{\\Lambda_{\\mathrm{HL}}^2}} \\left/ {{M_P^2}} \\righ... 5. B-L mediated SUSY breaking with radiative B-L symmetry breaking International Nuclear Information System (INIS) Kikuchi, Tatsuru; Kubo, Takayuki 2008-01-01 We explore a mechanism of radiative B-L symmetry breaking in analogous to the radiative electroweak symmetry breaking. The breaking scale of B-L symmetry is related to the neutrino masses through the see-saw mechanism. Once we incorporate the U(1) B-L gauge symmetry in SUSY models, the U(1) B-L gaugino, Z-tilde B-L appears, and it can mediate the SUSY breaking (Z-prime mediated SUSY breaking) at around the scale of 10 6 GeV. Then we find a links between the neutrino mass (more precisly the see-saw or B-L scale of order 10 6 GeV) and the Z-prime mediated SUSY breaking scale. It is also very interesting that the gluino at the weak scale becomes relatively light, and almost compressed mass spectra for the gaugino sector can be realized in this scenario, which is very interesting in scope of the LHC. 6. Peccei-Quinn invariant singlet extended SUSY with anomalous U(1) gauge symmetry Energy Technology Data Exchange (ETDEWEB) Im, Sang Hui; Seo, Min-Seok [Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS),Daejeon 305-811 (Korea, Republic of) 2015-05-13 Recent discovery of the SM-like Higgs boson with m{sub h}≃125 GeV motivates an extension of the minimal supersymmetric standard model (MSSM), which involves a singlet Higgs superfield with a sizable Yukawa coupling to the doublet Higgs superfields. We examine such singlet-extended SUSY models with a Peccei-Quinn (PQ) symmetry that originates from an anomalous U(1){sub A} gauge symmetry. We focus on the specific scheme that the PQ symmetry is spontaneously broken at an intermediate scale v{sub PQ}∼√(m{sub SUSY}M{sub Pl}) by an interplay between Planck scale suppressed operators and tachyonic soft scalar mass m{sub SUSY}∼√(D{sub A}) induced dominantly by the U(1){sub A}D-term D{sub A}. This scheme also results in spontaneous SUSY breaking in the PQ sector, generating the gaugino masses M{sub 1/2}∼√(D{sub A}) when it is transmitted to the MSSM sector by the conventional gauge mediation mechanism. As a result, the MSSM soft parameters in this scheme are induced mostly by the U(1){sub A}D-term and the gauge mediated SUSY breaking from the PQ sector, so that the sparticle masses can be near the present experimental bounds without causing the SUSY flavor problem. The scheme is severely constrained by the condition that a phenomenologically viable form of the low energy operators of the singlet and doublet Higgs superfields is generated by the PQ breaking sector in a way similar to the Kim-Nilles solution of the μ problem, and the resulting Higgs mass parameters allow the electroweak symmetry breaking with small tan β. We find two minimal models with two singlet Higgs superfields, satisfying this condition with a relatively simple form of the PQ breaking sector, and briefly discuss some phenomenological aspects of the model. 7. Determining SUSY model parameters and masses at the LHC using cross sections, kinematic edges and other observables CERN Document Server White, M J; Parker, M A 2005-01-01 We address the problem of mass measurements of supersymmetric particles at the Large Hadron Collider, using the ATLAS detector as an example. By using Markov Chain sampling techniques to combine standard measurements of kinematic edges in the invariant mass distributions of decay products with a measurement of a missing$p_T$cross-section, we show that the precision of mass measurements at the LHC can be dramatically improved, even when we do not assume that we have measured the kinematic endpoints precisely, or that we have identified exactly which particles are involved in the decay chain causing the endpoints. The generality of the technique is demonstrated in a preliminary investigation of a non-universal SUGRA model, in which we relax the requirements of mSUGRA by breaking the degeneracy of the GUT scale gaugino masses. The model studied is compatible with the WMAP limits on dark matter relic density. 8. Higgs, Binos and Gluinos: Split Susy within Reach Energy Technology Data Exchange (ETDEWEB) Alves, Daniele S.M.; Izaguirre, Eder; /SLAC /Stanford U., Phys. Dept.; Wacker, Jay G.; /SLAC /Stanford U., ITP 2012-09-14 Recent results from the LHC for the Higgs boson with mass between 142 GeV {approx}< m{sub h{sup 0}} {approx}< 147 GeV points to PeV-scale Split Supersymmetry. This article explores the consequences of a Higgs mass in this range and possible discovery modes for Split Susy. Moderate lifetime gluinos, with decay lengths in the 25 {micro}m to 10 yr range, are its imminent smoking gun signature. The 7TeV LHC will be sensitive to the moderately lived gluinos and trilepton signatures from direct electroweakino production. Moreover, the dark matter abundance may be obtained from annihilation through an s-channel Higgs resonance, with the LSP almost purely bino and mass m{sub {chi}{sub 1}{sup 0}} {approx_equal} 70 GeV. The Higgs resonance region of Split Susy has visible signatures in dark matter direct and indirect detection and electric dipole moment experiments. If the anomalies go away, the majority of Split Susy parameter space will be excluded. 9. RPV SUSY searches at ATLAS and CMS CERN Document Server Pettersson, Nora Emilia; The ATLAS collaboration 2015-01-01 Experimental searches for Supersymmetry (SUSY) at the Large Hadronic Collider (LHC) often assume R-Parity Conservation (RPC) to avoid proton decay. A consequence RPC is that it implies a stable SUSY-particle that cannot decay. The search strategies are strongly based on the hypothesize of weakly interacting massive particles escaping without detection - yielding missing transverse energy (MET) to the collision events. It is vital to explore all possibilities considering that no observation of SUSY has been made and that strong exclusions already have been placed on RPC-SUSY scenarios. Introducing individually baryon- and lepton-number violating couplings in R-Parity Violating (RPV) models would avoid rapid proton decay. The strong mass and cross-section exclusion set for RPC-SUSY are weaken if RPV couplings are allowed in the SUSY Lagrangian - as these standard searches lose sensitivity due to less expected MET. This talk aims to summarise a few of the experimental searches for both prompt and long-lived RPV ... 10. SUSY meets her twin Energy Technology Data Exchange (ETDEWEB) Katz, Andrey [Theory Division, CERN,CH-1211 Geneva 23 (Switzerland); Département de Physique Théorique and Center for Astroparticle Physics (CAP),Université de Genève,24 quai Ansermet, CH-1211 Genève 4 (Switzerland); Mariotti, Alberto [Theoretische Natuurkunde and IIHE/ELEM, Vrije Universiteit Brussel,and International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Pokorski, Stefan [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,ul. Pasteura 5, PL-02-093 Warsaw (Poland); Redigolo, Diego [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University,Tel-Aviv 69978 (Israel); Department of Particle Physics and Astrophysics, Weizmann Institute of Science,Rehovot 7610001 (Israel); Ziegler, Robert [Institute for Theoretical Particle Physics (TTP), Karlsruhe Institute of Technology,Engesserstraße 7, D-76128 Karlsruhe (Germany) 2017-01-31 We investigate the general structure of mirror symmetry breaking in the Twin Higgs scenario. We show, using the IR effective theory, that a significant gain in fine tuning can be achieved if the symmetry is broken hardly. We emphasize that weakly coupled UV completions can naturally accommodate this scenario. We analyze SUSY UV completions and present a simple Twin SUSY model with a tuning of around 10% and colored superpartners as heavy as 2 TeV. The collider signatures of general Twin SUSY models are discussed with a focus on the extended Higgs sectors. 11. A continuous family of realistic SUSY SU(5) GUTs Energy Technology Data Exchange (ETDEWEB) Bajc, Borut, E-mail: [email protected] [J. Stefan Institute, Jamova cesta 39, 1000, Ljubljana (Slovenia) 2016-06-21 It is shown that the minimal renormalizable supersymmetric SU(5) is still realistic providing the supersymmetric scale is at least few tens of TeV or large R-parity violating terms are considered. In the first case the vacuum is metastable, and different consistency constraints can give a bounded allowed region in the tan β − m{sub susy} plane. In the second case the mass eigenstate electron (down quark) is a linear combination of the original electron (down quark) and Higgsino (heavy colour triplet), and the mass ratio of bino and wino is determined. Both limits lead to light gravitino dark matter. 12. Searches for Electroweak SUSY by ATLAS and CMS CERN Document Server Khoo, Teng Jian; The ATLAS collaboration 2018-01-01 While strongly-produced SUSY and third-generation squark searches have already breached the TeV mass range, direct production of electroweak gauginos is less tightly constrained. New searches are presented, showcasing novel strategies for filling in the gaps in sensitivity to electroweak SUSY at ATLAS and CMS. 13. Susy and Such International Nuclear Information System (INIS) Dawson, S. 1997-01-01 In these lectures, the author discusses the theoretical motivation for supersymmetric theories and introduce the minimal low energy effective supersymmetric theory, (MSSM). I consider only the MSSM and its simplest grand unified extension here. Some of the other possible low-energy SUSY models are summarized. The particles and their interactions are examined in detail in the next sections and a grand unified SUSY model presented which gives additional motivation for pursuing supersymmetric theories 14. SUSY naturalness without prejudice CERN Document Server Ghilencea, D M 2014-01-01 Unlike the Standard Model (SM), supersymmetric models stabilize the electroweak (EW) scale$v$at the quantum level and {\\it predict} that$v$is a function of the TeV-valued SUSY parameters ($\\gamma_\\alpha$) of the UV Lagrangian. We show that the (inverse of the) covariance matrix of the model in the basis of these parameters and the usual deviation$\\delta\\chi^2$(from$\\chi^2_{min}$of a model) automatically encode information about the "traditional" EW fine-tuning measuring this stability, {\\it provided that} the EW scale$v\\sim m_Z$is indeed regarded as a function$v=v(\\gamma)$. It is known that large EW fine-tuning may signal an incomplete theory of soft terms and can be reduced when relations among$\\gamma_\\alpha$exist (due to GUT symmetries, etc). The global correlation coefficient of this matrix can help one investigate if such relations are present. An upper bound on the usual EW fine-tuning measure ("in quadrature") emerges from the analysis of the$\\delta\\chi^2$and the s-standard deviation conf... 15. SUSY naturalness without prejudice Science.gov (United States) Ghilencea, D. M. 2014-05-01 Unlike the Standard Model (SM), supersymmetric models stabilize the electroweak (EW) scale v at the quantum level and predict that v is a function of the TeV-valued SUSY parameters (γα) of the UV Lagrangian. We show that the (inverse of the) covariance matrix of the model in the basis of these parameters and the usual deviation δχ2 (from χmin2 of a model) automatically encode information about the "traditional" EW fine-tuning measuring this stability, provided that the EW scale v ˜mZ is indeed regarded as a function v =v(γ). It is known that large EW fine-tuning may signal an incomplete theory of soft terms and can be reduced when relations among γα exist (due to GUT symmetries, etc.). The global correlation coefficient of this matrix can help one investigate if such relations are present. An upper bound on the usual EW fine-tuning measure ("in quadrature") emerges from the analysis of the δχ2 and the s-standard deviation confidence interval by using v =v(γ) and the theoretical approximation (loop order) considered for the calculation of the observables. This upper bound avoids subjective criteria for the "acceptable" level of EW fine-tuning for which the model is still "natural." 16. Yukawa unification in moduli-dominant SUSY breaking International Nuclear Information System (INIS) Khalil, S.; Tatsuo Kobayashi 1997-07-01 We study Yukawa in string models with moduli-dominant SUSY breaking. This type of SUSY breaking in general leads to non-universal soft masses, i.e. soft scalar masses and gaugino masses. Such non-universality is important for phenomenological aspects of Yukawa unification, i.e., successful electroweak breaking, SUSY corrections to the bottom mass and the branching ratio of b → sγ. We show three regions in the whole parameter space which lead to successful electroweak breaking and allow small SUSY corrections to the bottom mass. For these three regions we investigated the b → sγ decay and mass spectra. (author). 26 refs, 6 figs 17. Heavy quark hadron mass scale International Nuclear Information System (INIS) Anderson, J.T. 1994-01-01 Without the spin interactions the hardron masses within a multiplet are degenerate. The light quark hadron degenerate mulitplet mass spectrum is extended from the 3 quark ground state multiplets at J P =0 - , 1/2 + , 1 - to include the excited states which follow the spinorial decomposition of SU(2)xSU(2). The mass scales for the 4, 5, 6, .. quark hadrons are obtained from the degenerate multiplet mass m 0 /M=n 2 /α with n=4, 5, 6, .. The 4, 5, 6, .. quark hadron degenerate multiplet masses follow by splitting of the heavy quark mass scales according to the spinorial decomposition of SU(2)xSU(2). (orig.) 18. Cosmological origin of mass scales International Nuclear Information System (INIS) Terazawa, H. 1981-01-01 We discuss the possibility that spontaneous breakdown of conformal invariance due to the very existence of our universe originates all the mass (or length) scales ranging from the Planck mass (approx. 10 19 GeV) to the Hubble constant (approx. 10 -42 GeV) and suggest that the photon may have a curvature-dependent mass which is as small as 10 -42 GeV. We also present a possible clue to Dirac's large number hypothesis. (orig.) 19. Cosmological origin of mass scales International Nuclear Information System (INIS) Terazawa, Hidezumi. 1981-02-01 We discuss the possibility that spontaneous breakdown of conformal invariance due to the very existence of our universe originates all the mass (or length) scales ranging from the Planck mass (--10 19 GeV) to the Hubble constant (--10 -42 GeV) and suggest that the photon may have a curvature-dependent mass which is as small as 10 -42 GeV. We also present a possible clue to the Dirac's large number hypothesis. (author) 20. Spontaneous SUSY breaking without R symmetry in supergravity Science.gov (United States) Maekawa, Nobuhiro; Omura, Yuji; Shigekami, Yoshihiro; Yoshida, Manabu 2018-03-01 We discuss spontaneous supersymmetry (SUSY) breaking in a model with an anomalous U (1 )A symmetry. In this model, the size of the each term in the superpotential is controlled by the U (1 )A charge assignment and SUSY is spontaneously broken via the Fayet-Iliopoulos of U (1 )A at the metastable vacuum. In the global SUSY analysis, the gaugino masses become much smaller than the sfermion masses, because an approximate R symmetry appears at the SUSY breaking vacuum. In this paper, we show that gaugino masses can be as large as gravitino mass, taking the supergravity effect into consideration. This is because the R symmetry is not imposed so that the constant term in the superpotential, which is irrelevant to the global SUSY analysis, largely contributes to the soft SUSY breaking terms in the supergravity. As the mediation mechanism, we introduce the contributions of the field not charged under U (1 )A and the moduli field to cancel the anomaly of U (1 )A. We comment on the application of our SUSY breaking scenario to the grand unified theory. 1. Minimal SUSY SO(10) and Yukawa unification International Nuclear Information System (INIS) Okada, Nobuchika 2013-01-01 The minimal supersymmetric (SUSY) SO(10) model, where only two Higgs multiplets {10⊕126-bar} are utilized for Yukawa couplings with matter fields, can nicely fit the neutrino oscillation parameters as well as charged fermion masses and mixing angles. In the fitting of the fermion mass matrix data, the largest element in the Yukawa coupling with the 126-bar -plet Higgs (Y 126 ) is found to be of order one, so that the right see-saw scale should be provided by Higgs vacuum expectation values (VEVs) of β(10 14 GeV). This fact causes a serious problem, namely, the gauge coupling unification is spoiled because of the presence of many exotic Higgs multiples emerging at the see-saw scale. In order to solve this problem, we consider a unification between bottom-quark and tau Yukawa couplings (b - τ Yukawa coupling unification) at the grand unified theory (GUT) scale, due to threshold corrections of superpartners to the Yukawa couplings at the 1 TeV scale. When the b - τ Yukawa coupling unification is very accurate, the largest element in Y 126 can become β(0.01), so that the right see-saw scale is realized by the GUT scale VEV and the usual gauge coupling unification is maintained. Since the b - τ Yukawa unification alters the Yukawa coupling data at the GUT scale, we re-analyze the fitting of the fermion mass matrix data by taking all the relevant free parameters into account. Unfortunately, we find that no parameter region shows up to give a nice fit for the current neutrino oscillation data and therefore, the usual picture of the gauge coupling unification cannot accommodate the fermion mass matrix data fitting in our procedure. 2. Susy seesaw inflation and NMSO(10)GUT International Nuclear Information System (INIS) Aulakh, Charanjit S. 2013-01-01 We show that Supersymmetric models with Type I seesaw neutrino masses support slow roll inflection point inflation. The inflaton is the D-flat direction labelled by the chiral invariant HLN composed of the Higgs(H), slepton(L) and conjugate sneutrino(N) superfields. The scale of inflation and fine tuning is set by the conjugate neutrino Majorana mass M ν c ∼ 10 6 - 10 12 GeV. The cubic term in the (quartic) inflaton potential is dominantly from superpotential (not soft Susy breaking) couplings. The tuning conditions are thus insensitive to soft supersymmetry breaking parameters and are generically much less stringent than for previous 'A-term' inflation scenarios controlled by mass scales ∼TeV. WMAP limits on the ratio of tensor to scalar perturbations limit the scale M controlling inflection point inflation: M 13 GeV. 'Instant preheating' is operative and dumps the inflaton energy into MSSM modes giving a high reheat temperature: T rh ≈M ν c (3/4) 10 6 GeV ∼ 10 11 - 10 15 GeV. A large gravitino mass > 50 TeV is therefore required to avoid over closure by reheat produced gravitinos. 'Instant preheating' and NLH inflaton facilitate production of right handed neutrinos during inflaton decay and thus non-thermal leptogenesis in addition to thermal leptogenesis. We show that the embedding in the fully realistic New Minimal Supersymmetric SO(10) GUT requires use of the heaviest righthanded neutrino mass as the controlling scale but the possibility of a measurable tensor scalar perturbation ratio seems marginal. We examine the parametric difficulties remaining. 3. We still love SUSY Energy Technology Data Exchange (ETDEWEB) Anon. 1992-11-15 Supersymmetry, affectionately known as SUSY, is still the darling of theoretical particle physics. Invented some 20 years ago, the charismatic idea really took off at the beginning of the 1980s. At the time, a workshop at CERN reflected the youthful enthusiasm for these new ideas. 4. SUSY GUT Model Building International Nuclear Information System (INIS) Raby, Stuart 2008-01-01 In this talk I discuss the evolution of SUSY GUT model building as I see it. Starting with 4 dimensional model building, I then consider orbifold GUTs in 5 dimensions and finally orbifold GUTs embedded into the E 8 xE 8 heterotic string. 5. We still love SUSY International Nuclear Information System (INIS) Anon. 1992-01-01 Supersymmetry, affectionately known as SUSY, is still the darling of theoretical particle physics. Invented some 20 years ago, the charismatic idea really took off at the beginning of the 1980s. At the time, a workshop at CERN reflected the youthful enthusiasm for these new ideas 6. Natural Higgs mass in supersymmetry from nondecoupling effects. Science.gov (United States) Lu, Xiaochuan; Murayama, Hitoshi; Ruderman, Joshua T; Tobioka, Kohsaku 2014-05-16 The Higgs mass implies fine-tuning for minimal theories of weak-scale supersymmetry (SUSY). Nondecoupling effects can boost the Higgs mass when new states interact with the Higgs boson, but new sources of SUSY breaking that accompany such extensions threaten naturalness. We show that two singlets with a Dirac mass can increase the Higgs mass while maintaining naturalness in the presence of large SUSY breaking in the singlet sector. We explore the modified Higgs phenomenology of this scenario, which we call the "Dirac next-to-minimal supersymmetric standard model." 7. Natural SUSY dark matter model International Nuclear Information System (INIS) Mohanty, Subhendra; Rao, Soumya; Roy, D.P. 2013-01-01 The most natural region of cosmologically compatible dark matter relic density in terms of low fine-tuning in a minimal supersymmetric standard model with nonuniversal gaugino masses is the so called bulk annihilation region. We study this region in a simple and predictive SUSY- GUT model of nonuniversal gaugino masses, where the latter transform as a combination of singlet plus a nonsinglet representation of the GUTgroup SU(5). The model prediction for the direct dark matter detection rates is well below the present CDMS and XENON100 limits, but within the reach of a future 1Ton XENON experiment. The most interesting and robust model prediction is an indirect detection signal of hard positron events, which resembles closely the shape of the observed positron spectrum from the PAMELA experiment. (author) 8. GUT Scale Fermion Mass Ratios International Nuclear Information System (INIS) Spinrath, Martin 2014-01-01 We present a series of recent works related to group theoretical factors from GUT symmetry breaking which lead to predictions for the ratios of quark and lepton Yukawa couplings at the unification scale. New predictions for the GUT scale ratios y μ /y s , y τ /y b and y t /y b in particular are shown and compared to experimental data. For this comparison it is important to include possibly large supersymmetric threshold corrections. Due to this reason the structure of the fermion masses at the GUT scale depends on TeV scale physics and makes GUT scale physics testable at the LHC. We also discuss how this new predictions might lead to predictions for mixing angles by discussing the example of the recently measured last missing leptonic mixing angle θ 13 making this new class of GUT models also testable in neutrino experiments 9. Overview of SUSY results from the ATLAS experiment Directory of Open Access Journals (Sweden) Federico Brazzale Simone 2014-04-01 Full Text Available The search for Supersymmetric extensions of the Standard Model (SUSY remains a hot topic in high energy phisycs in the light of the discovery of the Higgs boson with mass of 125 GeV. Supersymmetric particles can cancel out the quadratically-divergent loop corrections to the Higgs boson mass and can explain presence of Dark Matter in the Universe. Moreover, SUSY can unify the gauge couplings of the Standard Model at high energy scales. Under certain theoretical assumptions, some of the super-symmetric particles are preferred to be lighter than one TeV and their discovery can thus be accessible at the LHC. The recent results from searches for Supersymmetry with the ATLAS experiment which utilized up to 21 fb−1 of proton-proton collisions at a center of mass energy of 8 TeV are presented. These searches are focused on inclusive production of squarks and gluinos, on production of third generations squarks, and on electroweak production of charginos and neutralinos. Searches for long-lived particles and R-parity violation are also summarized in the document. 10. Unification of SUSY breaking and GUT breaking Energy Technology Data Exchange (ETDEWEB) Kobayashi, Tatsuo [Department of Physics, Hokkaido University,Sapporo 060-0810 (Japan); Omura, Yuji [Department of Physics, Nagoya University,Nagoya 464-8602 (Japan) 2015-02-18 We build explicit supersymmetric unification models where grand unified gauge symmetry breaking and supersymmetry (SUSY) breaking are caused by the same sector. Besides, the SM-charged particles are also predicted by the symmetry breaking sector, and they give the soft SUSY breaking terms through the so-called gauge mediation. We investigate the mass spectrums in an explicit model with SU(5) and additional gauge groups, and discuss its phenomenological aspects. Especially, nonzero A-term and B-term are generated at one-loop level according to the mediation via the vector superfields, so that the electro-weak symmetry breaking and 125 GeV Higgs mass may be achieved by the large B-term and A-term even if the stop mass is around 1 TeV. 11. R-symmetry violation in N=2 SUSY International Nuclear Information System (INIS) Volkov, G.G.; Maslikov, A.A. 1990-01-01 The present paper discusses the spontaneous R-symmetry violation in the N=2 SUSY SU(4)xU(1) model with soft SUSY breaking terms preserving finiteness. (In this case an invisible axion appears). In particular, the mechanism producting a light photino mass up to some GeV is suggested. In R-odd version of this model the mechanisms of enhancement of the neutrino decay is discussed. 10 refs.; 3 figs 12. Some features of SUSY breaking in N=2 supergravity International Nuclear Information System (INIS) Cecotti, S.; Giradello, L.; Porrati, M. 1984-08-01 We discuss some features of SUSY breaking in N=2 Supergravity. Firstly, we show that in a general N=2 Sugra model (constructed according to the tensor calculus) all stationary points of the potential, at Λ=0, are fully supersymmetric if the compensating multiplet is not gauged. Thus a viable super-Higgs effect in N=2 supergravity can occur only in the presence of a Fayet-Iliopoulos term. Then we present an explicit model with two scales of breaking in anti-de Sitter space. Moreover, the ratio of the two gravitino masses is sliding i.e. not determined by the classical potential. In the extreme situation one of the gravitino mass equals √-Λ/3, and thus we have partial super-Higgs (in AdS space). The cosmological constant may be arranged to an arbitrary small value while keeping the mass of the heavy gravitino constant. (author) 13. Latest news on SUSY from the ATLAS experiment CERN Multimedia CERN. Geneva 2016-01-01 Despite the absence of experimental evidence, weak scale supersymmetry remains one of the best motivated and studied Standard Model extensions. This talk reports the latest ATLAS results for searches for supersymmetric (SUSY) particles, obtained with 13 to 18 fb-1 of 13 TeV data. Weak and strong production in both R-Parity conserving and R-Parity violating SUSY scenarios are considered. The searches involved final states including jets, missing transverse momentum, light leptons, taus or photons. 14. Signatures of non-universal soft breaking sfermion masses at Hadron colliders International Nuclear Information System (INIS) Datta, Amitava; Datta, Aseshkrishna; Parida, M.K. 1997-12-01 We identify several mass patterns, within the framework of N = 1 SUGRA with nonuniversal soft breaking masses for the sfermions, which may significantly alter SUSY signals and the current squark-gluino mass limits from the Tevatron. These effects are illustrated in a SO(10) SUSY GUT with an intermediate mass scale, but the conclusions are also valid in SUSU SO(10) models with grand deserts. (author) 15. Kaehler geometry and SUSY mechanics International Nuclear Information System (INIS) Bellucci, Stefano; Nersessian, Armen 2001-01-01 We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed 16. Extraction of the Susy and Higgs parameters International Nuclear Information System (INIS) Adam-Bourdarios, Claire 2010-01-01 If supersymmetry is discovered by the next generation of collider experiments, it will be crucial to determine its fundamental high-scale parameters. Three scenarios have been recently investigated by the SFitter collaboration : the case where the LHC 'only' measures a light Higgs like signal, the case where SUSY signal are discovered at the LHC, and the dream scenario, where LHC and ILC measurements can be combined. 17. Supersimplicity: a Remarkable High Energy SUSY Property International Nuclear Information System (INIS) Gounaris, G.J.; Renard, F.M. 2011-01-01 It is known that for any 2-to-2 process in MSSM, only the helicity conserving (HC) amplitudes survive asymptotically. Studying many such processes, at the 1-loop Electroweak (EW) order, it is found that their high energy HC amplitudes are determined by just three forms: a log-squared function of the ratio of two of the (s, t, u) variables, to which a π 2 is added; and two Sudakov-like ln- and ln 2 -terms accompanied by respective mass-dependent constants. Apart from a possible additional residual constant (which is also discussed), these HC amplitudes, may be expressed as linear combinations of the above three forms, with coefficients being rational functions of the (s, t, u) variables. This 1-loop property, called supersimplicity, is of course claimed for the 2-to-2 processes considered; but no violating examples are known at present. For ug → dW, supersimplicity is found to be a very good approximation at LHC energies, provided the SUSY scale is not too high. SM processes are also discussed, and their differences are explored. (authors) 18. R-Parity Violating SUSY Results from ATLAS and CMS CERN Document Server AUTHOR\|(INSPIRE)INSPIRE-00360876; The ATLAS collaboration 2016-01-01 Experimental searches for Supersymmetry (SUSY) at the Large Hadronic Collider (LHC) often assume R-Parity Conservation (RPC) to avoid proton decay. A consequence of RPC is that it implies the existence of a stable SUSY-particle that cannot decay. The search strategies are strongly based on the hypothesize of weakly interacting massive particles escaping without detection - yielding missing transverse energy (MET) to the collision events. It is vital to explore all possibilities considering that no observation of SUSY has been made and that strong exclusions already have been placed on RPC-SUSY scenarios. Introducing individually baryon- and lepton-number violating couplings in R-Parity Violating (RPV) models would avoid rapid proton decay. The strong mass and cross-section exclusion set for RPC-SUSY are weaken if RPV couplings are allowed in the SUSY Lagrangian - as these standard searches lose sensitivity due to less expected MET. A summarization a few of the experimental searches for both prompt and long-li... 19. Hilltop supernatural inflation and SUSY unified models Science.gov (United States) Kohri, Kazunori; Lim, C. S.; Lin, Chia-Min; Mimura, Yukihiro 2014-01-01 In this paper, we consider high scale (100TeV) supersymmetry (SUSY) breaking and realize the idea of hilltop supernatural inflation in concrete particle physics models based on flipped-SU(5)and Pati-Salam models in the framework of supersymmetric grand unified theories (SUSY GUTs). The inflaton can be a flat direction including right-handed sneutrino and the waterfall field is a GUT Higgs. The spectral index is ns = 0.96 which fits very well with recent data by PLANCK satellite. There is no both thermal and non-thermal gravitino problems. Non-thermal leptogenesis can be resulted from the decay of right-handed sneutrino which plays (part of) the role of inflaton. 20. Hilltop supernatural inflation and SUSY unified models Energy Technology Data Exchange (ETDEWEB) Kohri, Kazunori [Cosmophysics Group, Theory Center, IPNS KEK, and The Graduate University for Advanced Studies (Sokendai), 1-1 Oho, Tsukuba, 305-0801 (Japan); Lim, C.S. [Department of Mathematics, Tokyo Woman' s Christian University, Tokyo, 167-8585 (Japan); Lin, Chia-Min [Department of Physics, Chuo University, Bunkyo-ku, Tokyo, 112 (Japan); Mimura, Yukihiro, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Department of Physics, National Taiwan University, Taipei, 10617 Taiwan (China) 2014-01-01 In this paper, we consider high scale (100TeV) supersymmetry (SUSY) breaking and realize the idea of hilltop supernatural inflation in concrete particle physics models based on flipped-SU(5)and Pati-Salam models in the framework of supersymmetric grand unified theories (SUSY GUTs). The inflaton can be a flat direction including right-handed sneutrino and the waterfall field is a GUT Higgs. The spectral index is n{sub s} = 0.96 which fits very well with recent data by PLANCK satellite. There is no both thermal and non-thermal gravitino problems. Non-thermal leptogenesis can be resulted from the decay of right-handed sneutrino which plays (part of) the role of inflaton. 1. Hilltop supernatural inflation and SUSY unified models International Nuclear Information System (INIS) Kohri, Kazunori; Lim, C.S.; Lin, Chia-Min; Mimura, Yukihiro 2014-01-01 In this paper, we consider high scale (100TeV) supersymmetry (SUSY) breaking and realize the idea of hilltop supernatural inflation in concrete particle physics models based on flipped-SU(5)and Pati-Salam models in the framework of supersymmetric grand unified theories (SUSY GUTs). The inflaton can be a flat direction including right-handed sneutrino and the waterfall field is a GUT Higgs. The spectral index is n s = 0.96 which fits very well with recent data by PLANCK satellite. There is no both thermal and non-thermal gravitino problems. Non-thermal leptogenesis can be resulted from the decay of right-handed sneutrino which plays (part of) the role of inflaton 2. Higgs mass determination in supersymmetry Energy Technology Data Exchange (ETDEWEB) Vega, Javier Pardo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Villadoro, Giovanni [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy) 2015-07-29 We present the state-of-the-art of the effective field theory computation of the MSSM Higgs mass, improving the existing ones by including extra threshold corrections. We show that, with this approach, the theoretical uncertainty is within 1 GeV in most of the relevant parameter space. We confirm the smaller value of the Higgs mass found in the EFT computations, which implies a slightly heavier SUSY scale. We study the large tan β region, finding that sbottom thresholds might relax the upper bound on the scale of SUSY. We present SUSYHD, a fast computer code that computes the Higgs mass and its uncertainty for any SUSY scale, from the TeV to the Planck scale, even in Split SUSY, both in the (DR)-bar and in the on-shell schemes. Finally, we apply our results to derive bounds on some well motivated SUSY models, in particular we show how the value of the Higgs mass allows to determine the complete spectrum in minimal gauge mediation. 3. Post LHC8 SUSY benchmark points for ILC physics International Nuclear Information System (INIS) Baer, Howard; List, Jenny 2013-07-01 We re-evaluate prospects for supersymmetry at the proposed International Linear e + e - Collider (ILC) in light of the first two years of serious data taking at LHC: LHC7 with ∝5 fb -1 of pp collisions at √(s)=7 TeV and LHC8 with ∝20 fb -1 at √(s)=8 TeV. Strong new limits from LHC8 SUSY searches, along with the discovery of a Higgs boson with m h ≅125 GeV, suggest a paradigm shift from previously popular models to ones with new and compelling signatures. After a review of the current status of supersymmetry, we present a variety of new ILC benchmark models, including: natural SUSY, radiatively-driven natural SUSY (RNS), NUHM2 with low m A , a focus point case from mSUGRA/CMSSM, non-universal gaugino mass (NUGM) model, τ-coannihilation, Kallosh-Linde/spread SUSY model, mixed gauge-gravity mediation, normal scalar mass hierarchy (NMH), and one example with the recently discovered Higgs boson being the heavy CP-even state H. While all these models at present elude the latest LHC8 limits, they do offer intriguing case study possibilities for ILC operating at √(s)≅ 0.25-1 TeV. The benchmark points also present a view of the widely diverse SUSY phenomena which might still be expected in the post LHC8 era at both LHC and ILC. 4. Cornering natural SUSY at LHC Run II and beyond Science.gov (United States) Buckley, Matthew R.; Feld, David; Macaluso, Sebastian; Monteux, Angelo; Shih, David 2017-08-01 We derive the latest constraints on various simplified models of natural SUSY with light higgsinos, stops and gluinos, using a detailed and comprehensive reinterpretation of the most recent 13 TeV ATLAS and CMS searches with ˜ 15 fb-1 of data. We discuss the implications of these constraints for fine-tuning of the electroweak scale. While the most "vanilla" version of SUSY (the MSSM with R-parity and flavor-degenerate sfermions) with 10% fine-tuning is ruled out by the current constraints, models with decoupled valence squarks or reduced missing energy can still be fully natural. However, in all of these models, the mediation scale must be extremely low ( model-building directions for natural SUSY that are motivated by this work. 5. Electric dipole moments from spontaneous CP violation in SU(3)-flavoured SUSY International Nuclear Information System (INIS) Jones Perez, J 2009-01-01 The SUSY flavour problem is deeply related to the origin of flavour and hence to the origin of the SM Yukawa couplings themselves. Since all CP-violation in the SM is restricted to the flavour sector, it is possible that the SUSY CP problem is related to the origin of flavour as well. In this work, we present three variations of an SU(3) flavour model with spontaneous CP violation. Such models explain the hierarchy in the fermion masses and mixings, and predict the structure of the flavoured soft SUSY breaking terms. In such a situation, both SUSY flavour and CP problems do not exist. We use electric dipole moments and lepton flavour violation processes to distinguish between these models, and place constraints on the SUSY parameter space. 6. Leptogenesis scenarios for natural SUSY with mixed axion-higgsino dark matter International Nuclear Information System (INIS) Bae, Kyu Jung; Baer, Howard; Serce, Hasan; Zhang, Yi-Fan 2016-01-01 Supersymmetric models with radiatively-driven electroweak naturalness require light higgsinos of mass ∼ 100–300 GeV . Naturalness in the QCD sector is invoked via the Peccei-Quinn (PQ) axion leading to mixed axion-higgsino dark matter. The SUSY DFSZ axion model provides a solution to the SUSY μ problem and the Little Hierarchy μ\|\| m 3/2 may emerge as a consequence of a mismatch between PQ and hidden sector mass scales. The traditional gravitino problem is now augmented by the axino and saxion problems, since these latter particles can also contribute to overproduction of WIMPs or dark radiation, or violation of BBN constraints. We compute regions of the T R vs. m 3/2 plane allowed by BBN, dark matter and dark radiation constraints for various PQ scale choices f a . These regions are compared to the values needed for thermal leptogenesis, non-thermal leptogenesis, oscillating sneutrino leptogenesis and Affleck-Dine leptogenesis. The latter three are allowed in wide regions of parameter space for PQ scale f a∼ 10 10 –10 12 GeV which is also favored by naturalness: f a ∼ √μM P /λ μ ∼ 10 10 –10 12 GeV . These f a values correspond to axion masses somewhat above the projected ADMX search regions 7. SUSY Without Prejudice at Linear Colliders International Nuclear Information System (INIS) Rizzo, T. 2008-01-01 We explore the physics of the general CP-conserving MSSM with Minimal Flavor Violation, the pMSSM. The 19 soft SUSY breaking parameters are chosen so to satisfy all existing experimental and theoretical constraints assuming that the WIMP is the lightest neutralino. We scan this parameter space twice using both flat and log priors and compare the results which yield similar conclusions. Constraints from both LEP and the Tevatron play an important role in obtaining our final model samples. Implications for future TeV-scale e + e - linear colliders (LC) are discussed 8. Vast antimatter regions and SUSY-condensate baryogenesis International Nuclear Information System (INIS) Kirilova, D.; Panayotova, M.; Valchanov, T. 2002-10-01 Natural and abundant creation of antimatter in the Universe in a SUSY baryogenesis model is described. The scenario predicts vast quantities of antimatter, corresponding to galaxy and galaxy cluster scales, separated from the matter ones by baryonically empty voids. Observational constraints on such antimatter regions are discussed. (author) 9. Scaling properties of the transverse mass spectra International Nuclear Information System (INIS) Schaffner-Bielich, J. 2002-01-01 Motivated from the formation of an initial state of gluon-saturated matter, we discuss scaling relations for the transverse mass spectra at BNL's relativistic heavy-ion collider (RHIC). We show on linear plots, that the transverse mass spectra for various hadrons can be described by an universal function in m t . The transverse mass spectra for different centralities can be rescaled into each other. Finally, we demonstrate that m t -scaling is also present in proton-antiproton collider data and compare it to m t -scaling at RHIC. (orig.) 10. Low-scale gaugino mass unification International Nuclear Information System (INIS) Endo, M.; Yoshioka, K. 2008-04-01 We present a new class of scenarios with the gaugino mass unification at the weak scale. The unification conditions are generally classified and then, the mirage gauge mediation is explored where gaugino masses are naturally unified and scalar partners of quarks and leptons have no mass hierarchy. The low-energy mass spectrum is governed by the mirage of unified gauge coupling which is seen by low-energy observers. We also study several explicit models for dynamically realizing the TeV-scale unification. (orig.) 11. Low-scale gaugino mass unification Energy Technology Data Exchange (ETDEWEB) Endo, M [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Yoshioka, K [Kyoto Univ. (Japan). Dept. of Physics 2008-04-15 We present a new class of scenarios with the gaugino mass unification at the weak scale. The unification conditions are generally classified and then, the mirage gauge mediation is explored where gaugino masses are naturally unified and scalar partners of quarks and leptons have no mass hierarchy. The low-energy mass spectrum is governed by the mirage of unified gauge coupling which is seen by low-energy observers. We also study several explicit models for dynamically realizing the TeV-scale unification. (orig.) 12. Post LHC7 SUSY benchmark points for ILC physics Energy Technology Data Exchange (ETDEWEB) Baer, Howard [Oklahoma Univ., Norman, OK (United States); List, Jenny [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2012-05-15 We re-evaluate prospects for supersymmetry at the proposed International Linear e{sup +}e{sup -} Collider (ILC) in light of the first year of serious data taking at LHC with {radical}(s)=7 TeV and {proportional_to}5 fb{sup -1} of pp collisions (LHC7). Strong new limits from LHC SUSY searches, along with a hint of a Higgs boson signal around m{sub h}{proportional_to}125 GeV, suggest a paradigm shift from previously popular models to ones with new and compelling signatures. We present a variety of new ILC benchmark models, including: natural SUSY, hidden SUSY, NUHM2 with low m{sub A}, non-universal gaugino mass (NUGM) model, pMSSM, Kallosh-Linde model, Bruemmer-Buchmueller model, normal scalar mass hierarchy (NMH) plus one surviving case from mSUGRA/CMSSM in the far focus point region. While all these models at present elude the latest LHC limits, they do offer intriguing case study possibilities for ILC operating at {radical}(s){proportional_to}0.25-1 TeV, and present a view of some of the diverse SUSY phenomena which might be expected at both LHC and ILC in the post LHC7 era. 13. Post LHC7 SUSY benchmark points for ILC physics International Nuclear Information System (INIS) Baer, Howard; List, Jenny 2012-05-01 We re-evaluate prospects for supersymmetry at the proposed International Linear e + e - Collider (ILC) in light of the first year of serious data taking at LHC with √(s)=7 TeV and ∝5 fb -1 of pp collisions (LHC7). Strong new limits from LHC SUSY searches, along with a hint of a Higgs boson signal around m h ∝125 GeV, suggest a paradigm shift from previously popular models to ones with new and compelling signatures. We present a variety of new ILC benchmark models, including: natural SUSY, hidden SUSY, NUHM2 with low m A , non-universal gaugino mass (NUGM) model, pMSSM, Kallosh-Linde model, Bruemmer-Buchmueller model, normal scalar mass hierarchy (NMH) plus one surviving case from mSUGRA/CMSSM in the far focus point region. While all these models at present elude the latest LHC limits, they do offer intriguing case study possibilities for ILC operating at √(s)∝0.25-1 TeV, and present a view of some of the diverse SUSY phenomena which might be expected at both LHC and ILC in the post LHC7 era. 14. METing SUSY on the Z peak Energy Technology Data Exchange (ETDEWEB) Barenboim, G.; Bernabeu, J.; Vives, O. [Universitat de Valencia, Departament de Fisica Teorica, Burjassot (Spain); Universitat de Valencia-CSIC, Parc Cientific U.V., IFIC, Paterna (Spain); Mitsou, V.A.; Romero, E. [Universitat de Valencia-CSIC, Parc Cientific U.V., IFIC, Paterna (Spain) 2016-02-15 Recently the ATLAS experiment announced a 3 σ excess at the Z-peak consisting of 29 pairs of leptons together with two or more jets, E{sub T}{sup miss} > 225 GeV and HT > 600 GeV, to be compared with 10.6 ± 3.2 expected lepton pairs in the Standard Model. No excess outside the Z-peak was observed. By trying to explain this signal with SUSY we find that only relatively light gluinos, m{sub g} or similar 400 GeV decaying predominantly to Z-boson plus a light gravitino, such that nearly every gluino produces at least one Z-boson in its decay chain, could reproduce the excess. We construct an explicit general gauge mediation model able to reproduce the observed signal overcoming all the experimental limits. Needless to say, more sophisticated models could also reproduce the signal, however, any model would have to exhibit the following features: light gluinos, or heavy particles with a strong production cross section, producing at least one Z-boson in its decay chain. The implications of our findings for the Run II at LHC with the scaling on the Z peak, as well as for the direct search of gluinos and other SUSY particles, are pointed out. (orig.) 15. METing SUSY on the Z peak International Nuclear Information System (INIS) Barenboim, G.; Bernabeu, J.; Vives, O.; Mitsou, V.A.; Romero, E. 2016-01-01 Recently the ATLAS experiment announced a 3 σ excess at the Z-peak consisting of 29 pairs of leptons together with two or more jets, E T miss > 225 GeV and HT > 600 GeV, to be compared with 10.6 ± 3.2 expected lepton pairs in the Standard Model. No excess outside the Z-peak was observed. By trying to explain this signal with SUSY we find that only relatively light gluinos, m g or similar 400 GeV decaying predominantly to Z-boson plus a light gravitino, such that nearly every gluino produces at least one Z-boson in its decay chain, could reproduce the excess. We construct an explicit general gauge mediation model able to reproduce the observed signal overcoming all the experimental limits. Needless to say, more sophisticated models could also reproduce the signal, however, any model would have to exhibit the following features: light gluinos, or heavy particles with a strong production cross section, producing at least one Z-boson in its decay chain. The implications of our findings for the Run II at LHC with the scaling on the Z peak, as well as for the direct search of gluinos and other SUSY particles, are pointed out. (orig.) 16. Search for compressed SUSY scenarios with the ATLAS detector CERN Document Server Maurer, Julien; The ATLAS collaboration 2017-01-01 Scenarios where multiple SUSY states are nearly degenerate in mass produce soft decay products, and they represent an experimental challenge for ATLAS. This talk presents recent results of analyses explicitly targeting such “compressed” scenarios with a variety of experimental techniques. All results make use of proton-proton collisions collected at a centre of mass of 13 TeV with the ATLAS detector. 17. Search for compressed SUSY scenarios with the ATLAS detector CERN Document Server Maurer, Julien; The ATLAS collaboration 2017-01-01 Scenarios where multiple SUSY states are nearly degenerate in mass produce soft decay products, and they represent an experimental challenge for ATLAS. This contribution presented recent results of analyses explicitly targeting such compressed'' scenarios with a variety of experimental techniques. All results made use of proton-proton collisions collected at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. 18. Post LHC8 SUSY benchmark points for ILC physics Energy Technology Data Exchange (ETDEWEB) Baer, Howard [Oklahoma Univ., Norman, OK (United States); List, Jenny [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2013-07-15 We re-evaluate prospects for supersymmetry at the proposed International Linear e{sup +}e{sup -} Collider (ILC) in light of the first two years of serious data taking at LHC: LHC7 with {proportional_to}5 fb{sup -1} of pp collisions at {radical}(s)=7 TeV and LHC8 with {proportional_to}20 fb{sup -1} at {radical}(s)=8 TeV. Strong new limits from LHC8 SUSY searches, along with the discovery of a Higgs boson with m{sub h}{approx_equal}125 GeV, suggest a paradigm shift from previously popular models to ones with new and compelling signatures. After a review of the current status of supersymmetry, we present a variety of new ILC benchmark models, including: natural SUSY, radiatively-driven natural SUSY (RNS), NUHM2 with low m{sub A}, a focus point case from mSUGRA/CMSSM, non-universal gaugino mass (NUGM) model, {tau}-coannihilation, Kallosh-Linde/spread SUSY model, mixed gauge-gravity mediation, normal scalar mass hierarchy (NMH), and one example with the recently discovered Higgs boson being the heavy CP-even state H. While all these models at present elude the latest LHC8 limits, they do offer intriguing case study possibilities for ILC operating at {radical}(s){approx_equal} 0.25-1 TeV. The benchmark points also present a view of the widely diverse SUSY phenomena which might still be expected in the post LHC8 era at both LHC and ILC. 19. On dark matter selected high-scale supersymmetry Energy Technology Data Exchange (ETDEWEB) Zheng, Sibo [Department of Physics, Chongqing University,Chongqing 401331 (China) 2015-03-11 The prediction for the Higgs mass in the dark matter selected high-scale SUSY is explored. We show the bounds on SUSY-breaking scale in models of SM +w-tilde and SM +h-tilde/s-tilde due to the observed Higgs mass at the LHC. We propose that effective theory below scale m-tilde described by SM +w-tilde is possibly realized in gauge mediation with multiple spurion fields that exhibit significant mass hierarchy, and that by SM +h-tilde/s-tilde can be realized with direct singlet-messenger-messenger coupling for singlet Yukawa coupling λ∼(v/m-tilde){sup 1/2}g{sub SM}. Finally, the constraint on high-scale SUSY is investigated in the light of inflation physics if these two subjects are directly related. 20. Status of SUSY searches at the LHC (including SUSY Higgs bosons) CERN Document Server Marshall, Zach; The ATLAS collaboration 2017-01-01 We review the status of SUSY searches at the LHC, including searches for SUSY Higgs Bosons. ATLAS and CMS have both prepared a large number of search results on the full 2015+2016 dataset, pushing the bounds on SUSY further than ever before. 1. Neutrino mass as the probe of intermediate mass scales International Nuclear Information System (INIS) Senjanovic, G. 1980-01-01 A discussion of the calculability of neutrino mass is presented. The possibility of neutrinos being either Dirac or Majorana particles is analyzed in detail. Arguments are offered in favor of the Majorana case: the smallness of neutrino mass is linked to the maximality of parity violation in weak interactions. It is shown how the measured value of neutrino mass would probe the existence of an intermediate mass scale, presumably in the TeV region, at which parity is supposed to become a good symmetry. Experimental consequences of the proposed scheme are discussed, in particular the neutrino-less double β decay, where observation would provide a crucial test of the model, and rare muon decays such as μ → eγ and μ → ee anti e. Finally, the embedding of this model in an O(10) grand unified theory is analyzed, with the emphasis on the implications for intermediate mass scales that it offers. It is concluded that the proposed scheme provides a distinct and testable alternative for understanding the smallness of neutrino mass. 4 figures 2. Neutrino mass as the probe of intermediate mass scales Energy Technology Data Exchange (ETDEWEB) Senjanovic, G. 1980-01-01 A discussion of the calculability of neutrino mass is presented. The possibility of neutrinos being either Dirac or Majorana particles is analyzed in detail. Arguments are offered in favor of the Majorana case: the smallness of neutrino mass is linked to the maximality of parity violation in weak interactions. It is shown how the measured value of neutrino mass would probe the existence of an intermediate mass scale, presumably in the TeV region, at which parity is supposed to become a good symmetry. Experimental consequences of the proposed scheme are discussed, in particular the neutrino-less double ..beta.. decay, where observation would provide a crucial test of the model, and rare muon decays such as ..mu.. ..-->.. e..gamma.. and ..mu.. ..-->.. ee anti e. Finally, the embedding of this model in an O(10) grand unified theory is analyzed, with the emphasis on the implications for intermediate mass scales that it offers. It is concluded that the proposed scheme provides a distinct and testable alternative for understanding the smallness of neutrino mass. 4 figures. 3. The Challenge of Determining SUSY Parameters in Focus-Point-Inspired Cases CERN Document Server Rolbiecki, K.; Kalinowski, J.; Moortgat-Pick, G. 2006-01-01 We discuss the potential of combined LHC and ILC experiments for SUSY searches in a difficult region of the parameter space, in which all sfermion masses are above the TeV scale. Precision analyses of cross sections of light chargino production and forward--backward asymmetries of decay leptons and hadrons at the ILC, together with mass information on \\tilde{\\chi}^0_2 and squarks from the LHC, allow us to fit rather precisely the underlying fundamental gaugino/higgsino MSSM parameters and to constrain the masses of the heavy virtual sparticles. For such analyses the complete spin correlations between the production and decay processes have to be taken into account. We also took into account expected experimental uncertainties. 4. Scaling analysis of meteorite shower mass distributions DEFF Research Database (Denmark) Oddershede, Lene; Meibom, A.; Bohr, Jakob 1998-01-01 Meteorite showers are the remains of extraterrestrial objects which are captivated by the gravitational field of the Earth. We have analyzed the mass distribution of fragments from 16 meteorite showers for scaling. The distributions exhibit distinct scaling behavior over several orders of magnetude......; the observed scaling exponents vary from shower to shower. Half of the analyzed showers show a single scaling region while the orther half show multiple scaling regimes. Such an analysis can provide knowledge about the fragmentation process and about the original meteoroid. We also suggest to compare...... the observed scaling exponents to exponents observed in laboratory experiments and discuss the possibility that one can derive insight into the original shapes of the meteoroids.... 5. Where is SUSY? Indian Academy of Sciences (India) Amitava Datta 2017-10-05 Oct 5, 2017 ... out in details how the production of strongly interacting sparticles can ... C2 is large have masses ∼1 TeV (see [1] for a lucid exposition ... the Planck satellites have accurately measured the. DM relic .... plane corresponding to. 6. Supersymmetric grand unified theories from quarks to strings via SUSY GUTs CERN Document Server Raby, Stuart 2017-01-01 These course-tested lectures provide a technical introduction to Supersymmetric Grand Unified Theories (SUSY GUTs), as well as a personal view on the topic by one of the pioneers in the field. While the Standard Model of Particle Physics is incredibly successful in describing the known universe it is, nevertheless, an incomplete theory with many free parameters and open issues. An elegant solution to all of these quandaries is the proposed theory of SUSY GUTs. In a GUT, quarks and leptons are related in a simple way by the unifying symmetry and their electric charges are quantized, further the relative strength of the strong, weak and electromagnetic forces are predicted. SUSY GUTs additionally provide a framework for understanding particle masses and offer candidates for dark matter. Finally, with the extension of SUSY GUTs to string theory, a quantum-mechanically consistent unification of the four known forces (including gravity) is obtained. The book is organized in three sections: the first section contai... 7. Instantons versus SUSY International Nuclear Information System (INIS) Shifman, M.A.; Vainstejn, A.I.; Zakharov, V.I. 1985-01-01 This survey is a written version of lectures given at the Bakuriani Workshop on High Energy Physics, January, 1985. The authors discuss the recent discovery on a new phenomenon - dynamical symmetry breaking in supersymmetric gauge theories with matter - which is generated by instantons. Under a certain choice of the matter multiplets the gauge invariance is inevitably spontaneously broken, gauge bosons acquire masses, the evolution of the running coupling constant is frozen and there is a weak coupling regime. Sometimes the pattern includes also spontaneous supersymmetry breaking. Both basic aspects of the mechanism and particular dynamical scenarios realized in typical models are described 8. SLAM, a Mathematica interface for SUSY spectrum generators International Nuclear Information System (INIS) Marquard, Peter; Zerf, Nikolai 2013-09-01 We present and publish a Mathematica package, which can be used to automatically obtain any numerical MSSM input parameter from SUSY spectrum generators, which follow the SLHA standard, like SPheno, SOFTSUSY or Suspect. The package enables a very comfortable way of numerical evaluations within the MSSM using Mathematica. It implements easy to use predefined high scale and low scale scenarios like mSUGRA or m h max and if needed enables the user to directly specify the input required by the spectrum generators. In addition it supports an automatic saving and loading of SUSY spectra to and from a SQL data base, avoiding the rerun of a spectrum generator for a known spectrum. 9. SLAM, a Mathematica interface for SUSY spectrum generators Energy Technology Data Exchange (ETDEWEB) Marquard, Peter [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Zerf, Nikolai [Alberta Univ., Edmonton, AB (Canada). Dept. of Physics 2013-09-15 We present and publish a Mathematica package, which can be used to automatically obtain any numerical MSSM input parameter from SUSY spectrum generators, which follow the SLHA standard, like SPheno, SOFTSUSY or Suspect. The package enables a very comfortable way of numerical evaluations within the MSSM using Mathematica. It implements easy to use predefined high scale and low scale scenarios like mSUGRA or m{sub h}{sup max} and if needed enables the user to directly specify the input required by the spectrum generators. In addition it supports an automatic saving and loading of SUSY spectra to and from a SQL data base, avoiding the rerun of a spectrum generator for a known spectrum. 10. Fixed mass and scaling sum rules International Nuclear Information System (INIS) Ward, B.F.L. 1975-01-01 Using the correspondence principle (continuity in dynamics), the approach of Keppell-Jones-Ward-Taha to fixed mass and scaling current algebraic sum rules is extended so as to consider explicitly the contributions of all classes of intermediate states. A natural, generalized formulation of the truncation ideas of Cornwall, Corrigan, and Norton is introduced as a by-product of this extension. The formalism is illustrated in the familiar case of the spin independent Schwinger term sum rule. New sum rules are derived which relate the Regge residue functions of the respective structure functions to their fixed hadronic mass limits for q 2 → infinity. (Auth.) 11. Highlights on SUSY phenomenology International Nuclear Information System (INIS) Masiero, Antonio 2004-01-01 In spite of the extraordinary success of the Standard Model (SM) supplemented with massive neutrinos in accounting for the whole huge bulk of phenomenology which has been accumulating in the last three decades, there exist strong theoretical reasons in particle physics and significant 'observational' hints in astroparticle physics for new physics beyond it. My lecture is devoted to a critical assessment of our belief in such new physics at the electroweak scale, in particular identifying it with low-energy supersymmetric extensions of the SM. I'll explain why we have concrete hopes that this decade will shed definite light on what stands behind the phenomenon of electroweak symmetry breaking 12. Where is SUSY? International Nuclear Information System (INIS) Datta, Amitava 2017-01-01 The searches for supersymmetry at the Large Hadron Collider (LHC) have so far yielded only null results and have considerably tightened the bounds on the sparticle masses. This has generated some skepticism in the literature regarding the ‘naturalness of SUSY’ which qualitatively requires some sparticles to be relatively light. Re-examining some of the bounds from LHC searches, it is argued with specific examples that the above skepticism is a red herring because (i) a quantitative and universally accepted definition of ‘naturalness’ is not available and (ii) even if some conventional definitions of naturalness is accepted at their face values, the alleged tension with the apparently stringent LHC bounds wither away once the strong assumptions, by no means compelling, underlying such bounds are relaxed. (author) 13. Rencontres de Moriond QCD 2012: Searches for Dark Matter, SUSY and other exotic particles CERN Multimedia CERN Bulletin 2012-01-01 The fact that SUSY and other new physics signals do not seem to hide in “obvious” places is bringing a healthy excitement to Moriond. Yesterday’s presentations confirmed that, with the 2012 LHC data, experiments will concentrate on searches for exotic particles that might decay into yet unexplored modes. In the meantime, they are setting unprecedented boundaries to regions where new particles (not just SUSY) could exist. The limits of what particle accelerators can bring to enlighten the mystery of Dark Matter were also presented and discussed. Each bar on the picture represents a decay channel that the ATLAS Collaboration (top) and the CMS Collaborations (bottom) have analysed. The value indicated on the scale (or on the relevant bar) defines the maximum mass that the particle in that search cannot have. Not knowing what kind of new physics we should really expect, and given the fact that it does not seem to be hiding in any of the obvious places, e... 14. Fine-tuning implications for complementary dark matter and LHC SUSY searches CERN Document Server Cassel, S; Kraml, S; Lessa, A; Ross, G G 2011-01-01 The requirement that SUSY should solve the hierarchy problem without undue fine-tuning imposes severe constraints on the new supersymmetric states. With the MSSM spectrum and soft SUSY breaking originating from universal scalar and gaugino masses at the Grand Unification scale, we show that the low-fine-tuned regions fall into two classes that will require complementary collider and dark matter searches to explore in the near future. The first class has relatively light gluinos or squarks which should be found by the LHC in its first run. We identify the multijet plus E_T^miss signal as the optimal channel and determine the discovery potential in the first run. The second class has heavier gluinos and squarks but the LSP has a significant Higgsino component and should be seen by the next generation of direct dark matter detection experiments. The combined information from the 7 TeV LHC run and the next generation of direct detection experiments can test almost all of the CMSSM parameter space consistent with ... 15. Natural X-ray lines from the low scale supersymmetry breaking Energy Technology Data Exchange (ETDEWEB) Kang, Zhaofeng, E-mail: [email protected] [Center for High-Energy Physics, Peking University, Beijing 100871 (China); School of Physics, Korea Institute for Advanced Study, Seoul 130-722 (Korea, Republic of); Ko, P., E-mail: [email protected] [School of Physics, Korea Institute for Advanced Study, Seoul 130-722 (Korea, Republic of); Li, Tianjun, E-mail: [email protected] [State Key Laboratory of Theoretical Physics and Kavli Institute for Theoretical Physics China (KITPC), Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China); Liu, Yandong, E-mail: [email protected] [State Key Laboratory of Theoretical Physics and Kavli Institute for Theoretical Physics China (KITPC), Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China) 2015-03-06 In the supersymmetric models with low scale supersymmetry (SUSY) breaking where the gravitino mass is around keV, we show that the 3.5 keV X-ray lines can be explained naturally through several different mechanisms: (I) a keV scale dark gaugino plays the role of sterile neutrino in the presence of bilinear R-parity violation. Because the light dark gaugino obtains Majorana mass only via gravity mediation, it is a decaying warm dark matter (DM) candidate; (II) the compressed cold DM states, whose mass degeneracy is broken by gravity mediated SUSY breaking, emit such a line via the heavier one decay into the lighter one plus photon(s). A highly supersymmetric dark sector may readily provide such kind of system; (III) the light axino, whose mass again is around the gravitino mass, decays to neutrino plus gamma in the R-parity violating SUSY. Moreover, we comment on dark radiation from dark gaugino. 16. Implications of low and high energy measurements on SUSY models Energy Technology Data Exchange (ETDEWEB) Jegerlehner, Fred [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik 2012-04-15 New Physics searches at the LHC have increased significantly lower bounds on unknown particle masses. This increases quite dramatically the tension in the interpretation of the data: low energy precision data which are predicted accurately by the SM (LEP observables like M{sub W} or loop induced rare processes like B {yields}X{sub s}{gamma} or B{sub s}{yields}{mu}{sup +}{mu}{sup -}) and quantities exhibiting an observed discrepancy between SM theory and experiment, most significantly found for the muon g-2 seem to be in conflict now. (g-2){sub {mu}} appears to be the most precisely understood observable which at the same time reveals a 3-4 {sigma} deviation between theory and experiment and thus requires a significant new physics contribution. The hints for a Higgs of mass about 125 GeV, which is precisely what SUSY extensions of the SM predict, seem to provide a strong indication for SUSY. At the same time it brings into serious trouble the interpretation of the (g-2){sub {mu}} deviation as a SUSY contribution. 17. Search for SUSY in the AMSB scenario with the DELPHI detector CERN Document Server Abdallah, J.; Adam, W.; Adzic, P.; Albrecht, T.; Alderweireld, T.; Alemany-Fernandez, R.; Allmendinger, T.; Allport, P.P.; Amaldi, U.; Amapane, N.; Amato, S.; Anashkin, E.; Andreazza, A.; Andringa, S.; Anjos, N.; Antilogus, P.; Apel, W.D.; Arnoud, Y.; Ask, S.; Asman, B.; Augustin, J.E.; Augustinus, A.; Baillon, P.; Ballestrero, A.; Bambade, P.; Barbier, R.; Bardin, D.; Barker, G.; Baroncelli, A.; Battaglia, M.; Baubillier, M.; Becks, K.H.; Begalli, M.; Behrmann, A.; Ben-Haim, E.; Benekos, N.; Benvenuti, A.; Berat, C.; Berggren, M.; Berntzon, L.; Bertrand, D.; Besancon, M.; Besson, N.; Bloch, D.; Blom, M.; Bluj, M.; Bonesini, M.; Boonekamp, M.; Booth, P.S.L.; Borisov, G.; Botner, O.; Bouquet, B.; Bowcock, T.J.V.; Boyko, I.; Bracko, M.; Brenner, R.; Brodet, E.; Bruckman, P.; Brunet, J.M.; Bugge, L.; Buschmann, P.; Calvi, M.; Camporesi, T.; Canale, V.; Carena, F.; Castro, Nuno Filipe; Cavallo, F.; Chapkin, M.; Charpentier, Ph.; Checchia, P.; Chierici, R.; Chliapnikov, P.; Chudoba, J.; Chung, S.U.; Cieslik, K.; Collins, P.; Contri, R.; Cosme, G.; Cossutti, F.; Costa, M.J.; Crennell, D.; Cuevas, J.; D'Hondt, J.; Dalmau, J.; da Silva, T.; Da Silva, W.; Della Ricca, G.; De Angelis, A.; De Boer, W.; De Clercq, C.; De Lotto, B.; De Maria, N.; De Min, A.; de Paula, L.; Di Ciaccio, L.; Di Simone, A.; Doroba, K.; Drees, J.; Dris, M.; Eigen, G.; Ekelof, T.; Ellert, M.; Elsing, M.; Espirito Santo, M.C.; Fanourakis, G.; Fassouliotis, D.; Feindt, M.; Fernandez, J.; Ferrer, A.; Ferro, F.; Flagmeyer, U.; Foeth, H.; Fokitis, E.; Fulda-Quenzer, F.; Fuster, J.; Gandelman, M.; Garcia, C.; Gavillet, Ph.; Gazis, Evangelos; Gokieli, R.; Golob, B.; Gomez-Ceballos, G.; Goncalves, P.; Graziani, E.; Grosdidier, G.; Grzelak, K.; Guy, J.; Haag, C.; Hallgren, A.; Hamacher, K.; Hamilton, K.; Haug, S.; Hauler, F.; Hedberg, V.; Hennecke, M.; Herr, H.; Hoffman, J.; Holmgren, S.O.; Holt, P.J.; Houlden, M.A.; Hultqvist, K.; Jackson, John Neil; Jarlskog, G.; Jarry, P.; Jeans, D.; Johansson, Erik Karl; Johansson, P.D.; Jonsson, P.; Joram, C.; Jungermann, L.; Kapusta, Frederic; Katsanevas, S.; Katsoufis, E.; Kernel, G.; Kersevan, B.P.; Kerzel, U.; Kiiskinen, A.; King, B.T.; Kjaer, N.J.; Kluit, P.; Kokkinias, P.; Kourkoumelis, C.; Kouznetsov, O.; Krumstein, Z.; Kucharczyk, M.; Lamsa, J.; Leder, G.; Ledroit, Fabienne; Leinonen, L.; Leitner, R.; Lemonne, J.; Lepeltier, V.; Lesiak, T.; Liebig, W.; Liko, D.; Lipniacka, A.; Lopes, J.H.; Lopez, J.M.; Loukas, D.; Lutz, P.; Lyons, L.; MacNaughton, J.; Malek, A.; Maltezos, S.; Mandl, F.; Marco, J.; Marco, R.; Marechal, B.; Margoni, M.; Marin, J.C.; Mariotti, C.; Markou, A.; Martinez-Rivero, C.; Masik, J.; Mastroyiannopoulos, N.; Matorras, F.; Matteuzzi, C.; Mazzucato, F.; Mazzucato, M.; McNulty, R.; Meroni, C.; Migliore, E.; Mitaroff, W.; Mjoernmark, U.; Moa, T.; Moch, M.; Monig, Klaus; Monge, R.; Montenegro, J.; Moraes, D.; Moreno, S.; Morettini, P.; Mueller, U.; Muenich, K.; Mulders, M.; Mundim, L.; Murray, W.; Muryn, B.; Myatt, G.; Myklebust, T.; Nassiakou, M.; Navarria, F.; Nawrocki, K.; Nicolaidou, R.; Nikolenko, M.; Oblakowska-Mucha, A.; Obraztsov, V.; Olshevski, A.; Onofre, A.; Orava, R.; Osterberg, K.; Ouraou, A.; Oyanguren, A.; Paganoni, M.; Paiano, S.; Palacios, J.P.; Palka, H.; Papadopoulou, Th.D.; Pape, L.; Parkes, C.; Parodi, F.; Parzefall, U.; Passeri, A.; Passon, O.; Peralta, L.; Perepelitsa, V.; Perrotta, A.; Petrolini, A.; Piedra, J.; Pieri, L.; Pierre, F.; Pimenta, M.; Piotto, E.; Podobnik, T.; Poireau, V.; Pol, M.E.; Polok, G.; Poropat, P.; Pozdniakov, V.; Pukhaeva, N.; Pullia, A.; Rames, J.; Ramler, L.; Read, Alexander L.; Rebecchi, P.; Rehn, J.; Reid, D.; Reinhardt, R.; Renton, P.; Richard, F.; Ridky, J.; Rivero, M.; Rodriguez, D.; Romero, A.; Ronchese, P.; Roudeau, P.; Rovelli, T.; Ruhlmann-Kleider, V.; Ryabtchikov, D.; Sadovsky, A.; Salmi, L.; Salt, J.; Savoy-Navarro, A.; Schwickerath, U.; Segar, A.; Sekulin, R.; Siebel, M.; Sisakian, A.; Smadja, G.; Smirnova, O.; Sokolov, A.; Sopczak, A.; Sosnowski, R.; Spassov, T.; Stanitzki, M.; Stocchi, A.; Strauss, J.; Stugu, B.; Szczekowski, M.; Szeptycka, M.; Szumlak, T.; Tabarelli, T.; Taffard, A.C.; Tegenfeldt, F.; Timmermans, Jan; Tkatchev, L.; Tobin, M.; Todorovova, S.; Tome, B.; Tonazzo, A.; Tortosa, P.; Travnicek, P.; Treille, D.; Tristram, G.; Trochimczuk, M.; Troncon, C.; Turluer, M.L.; Tyapkin, I.A.; Tyapkin, P.; Tzamarias, S.; Uvarov, V.; Valenti, G.; Van Dam, Piet; Van Eldik, J.; Van Lysebetten, A.; van Remortel, N.; Van Vulpen, I.; Vegni, G.; Veloso, F.; Venus, W.; Verdier, P.; Verzi, V.; Vilanova, D.; Vitale, L.; Vrba, V.; Wahlen, H.; Washbrook, A.J.; Weiser, C.; Wicke, D.; Wickens, J.; Wilkinson, G.; Winter, M.; Witek, M.; Yushchenko, O.; Zalewska, A.; Zalewski, P.; Zavrtanik, D.; Zhuravlov, V.; Zimine, N.I.; Zintchenko, A.; Zupan, M. 2004-01-01 The DELPHI experiment at the LEP e+e- collider collected almost 700 pb^-1 at centre-of-mass energies above the Z0 mass pole and up to 208 GeV. Those data were used to search for SUSY in the Anomaly Mediated SUSY Breaking (AMSB) scenario with a flavour independent common sfermion mass parameter. The searches covered several possible signatures experimentally accessible at LEP, with either the neutralino, the sneutrino or the stau being the Lightest Supersymmetric Particle (LSP). They included: the search for nearly mass-degenerate chargino and neutralino, which is a typical feature of AMSB; the search for Standard-Model-like or invisibly decaying Higgs boson; the search for stable staus; the search for cascade decays of SUSY particles resulting in the LSP and a low multiplicity final state containing neutrinos. No evidence of a signal was found, and thus constraints were set in the space of the parameters of the model. 18. Muon g−2 in anomaly mediated SUSY breaking Energy Technology Data Exchange (ETDEWEB) Chowdhury, Debtosh; Yokozaki, Norimi [Istituto Nazionale di Fisica Nucleare, Sezione di Roma,Piazzale Aldo Moro 2, I-00185 Rome (Italy) 2015-08-24 Motivated by two experimental facts, the muon g−2 anomaly and the observed Higgs boson mass around 125 GeV, we propose a simple model of anomaly mediation, which can be seen as a generalization of mixed modulus-anomaly mediation. In our model, the discrepancy of the muon g−2 and the Higgs boson mass around 125 GeV are easily accommodated. The required mass splitting between the strongly and weakly interacting SUSY particles are naturally achieved by the contribution from anomaly mediation. This model is easily consistent with SU(5) or SO(10) grand unified theory. 19. Muon g−2 in anomaly mediated SUSY breaking International Nuclear Information System (INIS) Chowdhury, Debtosh; Yokozaki, Norimi 2015-01-01 Motivated by two experimental facts, the muon g−2 anomaly and the observed Higgs boson mass around 125 GeV, we propose a simple model of anomaly mediation, which can be seen as a generalization of mixed modulus-anomaly mediation. In our model, the discrepancy of the muon g−2 and the Higgs boson mass around 125 GeV are easily accommodated. The required mass splitting between the strongly and weakly interacting SUSY particles are naturally achieved by the contribution from anomaly mediation. This model is easily consistent with SU(5) or SO(10) grand unified theory. 20. SUSY searches at$\\sqrt{s}=13$TeV with two same-sign leptons or three leptons, jets and$E_T^{miss}$at the ATLAS detector - Background estimation and latest analysis results. CERN Document Server Tornambe, Peter; The ATLAS collaboration 2017-01-01 Supersymmetry (SUSY) is one of the most studied theories to extend the Standard Model (SM) beyond the electroweak scale. If R-parity is conserved, SUSY particles are produced in pairs and the lightest supersymmetric particle (LSP), which is typically the lightest neutrino$\\tilde{\\chi}_1^0, is stable. In many models the LSP can be a suitable candidate for dark matter. This poster presents a search for supersymmetric phenomena in final states with two leptons (electrons or muons) of the same electric charge or three leptons, jets and missing transverse energy. While the same-sign or three leptons signature is present in many SUSY scenarios, SM processes leading to such events have very small cross-sections. Therefore, this analysis benefits from a small SM background in the signal regions leading to a good sensitivity especially in SUSY scenarios with compressed mass spectra or in which the R-parity is not conserved. Except from the prompt production of same-sign lepton pairs or three leptons, the main source... 1. Precision natural SUSY at CEPC, FCC-ee, and ILC International Nuclear Information System (INIS) Fan, JiJi; Reece, Matthew; Wang, Lian-Tao 2015-01-01 Testing the idea of naturalness is and will continue to be one of the most important goals of high energy physics experiments. It will play a central role in the physics program of future colliders. In this paper, we present projections of the reach of natural SUSY at future lepton colliders: CEPC, FCC-ee and ILC. We focus on the observables which give the strongest reach, the electroweak precision observables (for left-handed stops), and Higgs to gluon and photon decay rates (for both left- and right-handed stops). There is a “blind spot” when the stop mixing parameter X t is approximately equal to the average stop mass. We argue that in natural scenarios, bounds on the heavy Higgs bosons from tree-level mixing effects that modify the hbb̄ coupling together with bounds from b→sγ play a complementary role in probing the blind spot region. For specific natural SUSY scenarios such as folded SUSY in which the top partners do not carry Standard Model color charges, electroweak precision observables could be the most sensitive probe. In all the scenarios discussed in this paper, the combined set of precision measurements will probe down to a few percent in fine-tuning. 2. Nucleon decay in a realistic SO(10) SUSY GUT International Nuclear Information System (INIS) Lucas, V.; Raby, S. 1997-01-01 In this paper, we calculate neutron and proton decay rates and branching ratios in a predictive SO(10) SUSY GUT which agrees well with low energy data. We show that the nucleon lifetimes are consistent with the experimental bounds. The nucleon decay rates are calculated using all one-loop chargino and gluino-dressed diagrams regardless of their chiral structure. We show that the four-fermion operator C jk (u R d jR )(d kL ν τL ), commonly neglected in previous nucleon decay calculations, not only contributes significantly to nucleon decay, but, for many values of the initial GUT parameters and for large tanβ, actually dominates the decay rate. As a consequence, we find that τ p /τ n is often substantially larger than the prediction obtained in small tanβ models. We also find that gluino-dressed diagrams, often neglected in nucleon decay calculations, contribute significantly to nucleon decay. In addition we find that the branching ratios obtained from this realistic SO(10) SUSY GUT differ significantly from the predictions obtained from open-quotes genericclose quotes SU(5) SUSY GUT close-quote s. Thus, nucleon decay branching ratios, when observed, can be used to test theories of fermion masses. copyright 1997 The American Physical Society 3. SUSY see-saw and NMSO(10)GUT inflation after BICEP2 International Nuclear Information System (INIS) Garg, Ila 2016-01-01 Supersymmetric see-saw slow roll inflection point inflation occurs along a MSSM D-flat direction associated with gauge invariant combination of Higgs, s lepton and right-handed s neutrino at a scale set by the right-handed neutrino mass M vc ∼ 10 6 -10 13 GeV. The tensor to scalar perturbation ratio r ∼ 10 -3 can be achieved in this scenario. However, this scenario faced difficulty in being embedded in the realistic new minimal supersymmetric SO(10) grand unified theory (NMSO(10)GUT). The recent discovery of B-mode polarization by BICEP2, changes the prospects of NMSO(10) GUT inflation. Inflection point models become strongly disfavoured, as the trilinear coupling of SUSY see-saw inflation potential gets suppressed relative to the mass parameter favoured by BICEP2. Large values of r ≈ 0.2 can be achieved with super-Planck scale inflaton values and mass scales of inflaton ≥10 13 GeV. In NMSO(10)GUT, this can be made possible with an admixture of heavy Higgs doublet fields, i.e., other than MSSM Higgs field, which are present and have masses of order GUT scale. (author) 4. Beyond the Standard Model: The Weak Scale, Neutrino Mass, and the Dark Sector International Nuclear Information System (INIS) Weiner, Neal 2010-01-01 The goal of this proposal was to advance theoretical studies into questions of collider physics at the weak scale, models and signals of dark matter, and connections between neutrino mass and dark energy. The project was a significant success, with a number of developments well beyond what could have been anticipated at the outset. A total of 35 published papers and preprints were produced, with new ideas and signals for LHC physics and dark matter experiments, in particular. A number of new ideas have been found on the possible indirect signals of models of dark matter which relate to the INTEGRAL signal of astrophysical positron production, high energy positrons seen at PAMELA and Fermi, studies into anomalous gamma rays at Fermi, collider signatures of sneutrino dark matter, scenarios of Higgs physics arising in SUSY models, the implications of galaxy cluster surveys for photon-axion conversion models, previously unconsidered collider phenomenology in the form of 'lepton jets' and a very significant result for flavor physics in supersymmetric theories. Progress continues on all fronts, including development of models with dramatic implications for direct dark matter searches, dynamics of dark matter with various excited states, flavor physics, and consequences of modified missing energy signals for collider searches at the LHC. 5. The flavour of natural SUSY Energy Technology Data Exchange (ETDEWEB) Bruemmer, Felix [SISSA/ISAS, Trieste (Italy); Kraml, Sabine; Kulkarni, Suchita; Smith, Christopher [Universite Grenoble-Alpes, CNRS/IN2P3, Laboratoire de Physique Subatomique et de Cosmologie, Grenoble Cedex (France) 2014-09-15 An inverted mass hierarchy in the squark sector, as in so-called ''natural supersymmetry'', requires non-universal boundary conditions at the mediation scale of supersymmetry breaking. We propose a formalism to define such boundary conditions in a basis-independent manner and apply it to generic scenarios where the third-generation squarks are light, while the first two-generation squarks are heavy and near-degenerate. We show that not only is our formalism particularly well suited to study such hierarchical squark mass patterns, but in addition the resulting soft terms at the TeV scale are manifestly compatible with the principle of minimal flavour violation, and thus automatically obey constraints from flavour physics. (orig.) 6. Signatures of High-Scale Supersymmetry at the LHC CERN Multimedia CERN. Geneva; Spiropulu, Maria; Treille, D 2004-01-01 I will discuss the experimental signatures at the LHC of a novel paradigm-shift away from naturalness, suggested by the cosmological constant problem and the multitude of vacua in string theory. In the new paradigm supersymmetry can be broken near the unification scale, and the only light superparticles are the gauginos and higgsinos, which account for the successful unification of gauge couplings. This framework removes all the phenomenological difficulties of standard SUSY. The mass of the Higgs is in the range 120-160 GeV. Measuring the couplings of the Higgs to the gauginos and higgsinos precicely tests for high-scale SUSY. The gluino is strikingly long lived, and a measurement of its lifetime can determine the SUSY breaking scale. Signatures at the LHC detectors include out-of-time energy depositions, displaced vertices, and intermittent tracks. 7. Impact of physical properties at very high energy scales on the superparticle mass spectrum International Nuclear Information System (INIS) Baer, H.; Diaz, M.; Quintana, P.; Tata, X. 2000-01-01 We survey a variety of proposals for new physics at high scales that serve to relate the multitude of soft supersymmetry breaking parameters of the MSSM. We focus on models where the new physics results in non-universal soft parameters, in sharp contrast with the usually assumed mSUGRA framework. These include (i) SU(5) and SO(10) grand unified (GUT) models, (ii) the MSSM plus a right-handed neutrino, (iii) models with effective supersymmetry, (iv) models with anomaly-mediated SUSY breaking and gaugino mediated SUSY breaking, (v) models with non-universal soft terms due to string dynamics, and (vi) models based on M-theory. We outline the physics behind these models, point out some distinctive features of the weak scale sparticle spectrum, and allude to implications for collider experiments. To facilitate future studies, for each of these scenarios, we describe how collider events can be generated using the program ISAJET. Our hope is that detailed studies of a variety of alternatives will help point to the physics underlying SUSY breaking and how this is mediated to the observable sector, once sparticles are discovered and their properties measured. (author) 8. On SUSY inspired minimal lepton number violation International Nuclear Information System (INIS) Chkareuli, J.L.; Gogoladze, I.G.; Green, M.G.; Hutchroft, D.E.; Kobakhidze, A.B. 2000-03-01 A minimal lepton number violation (LNV) is proposed which could naturally appear in SUSY theories, if Yukawa and LNV couplings had a common origin. According to this idea properly implemented into MSSM with an additional abelian flavor symmetry the prototype LNV appears due to a mixing of leptons with superheavy Higgs doublet mediating Yukawa couplings. As a result, all significant physical manifestations of LNV reduce to those of the effective trilinear couplings LLE-bar and LQD-bar aligned, by magnitude and orientation in a flavor space, with the down fermion (charged lepton and down quark) effective Yukawa couplings, while the effective bilinear terms appear generically suppressed relative to an ordinary μ-term of MSSM. Detailed phenomenology of the model related to the flavor-changing processes both in quark and lepton sectors, radiatively induced neutrino masses and decays of the LSP is presented. Remarkably, the model can straightforwardly be extended to a Grand Unified framework and an explicit example with SU(7) GUT is thoroughly discussed. (author) 9. Long-lived and compressed SUSY searches at CMS and ATLAS CERN Document Server Barlow, Nick; The ATLAS collaboration 2015-01-01 Two challenging scenarios for SUSY searches at the LHC are when there are small mass differences between particles in the decay chain ("compressed" spectra) and where the SUSY particles have a non-negligible lifetime. The compressed case can be addressed by looking at events containing Initial State Radiation (ISR), while long-lifetimes can give rise to a wide range of possible detector signatures. This talk describes these diverse and interesting searches, performed by the ATLAS and CMS collaborations on the Run 1 LHC data. 10. Beyond the standard seesaw neutrino masses from Kahler operators and broken supersymmetry CERN Document Server Brignole, Andrea; Rossi, Anna 2010-01-01 We investigate supersymmetric scenarios in which neutrino masses are generated by effective d=6 operators in the Kahler potential, rather than by the standard d=5 superpotential operator. First, we discuss some general features of such effective operators, also including SUSY-breaking insertions, and compute the relevant renormalization group equations. Contributions to neutrino masses arise at low energy both at the tree level and through finite threshold corrections. In the second part we present simple explicit realizations in which those Kahler operators arise by integrating out heavy SU(2)_W triplets, as in the type II seesaw. Distinct scenarios emerge, depending on the mechanism and the scale of SUSY-breaking mediation. In particular, we propose an appealing and economical picture in which the heavy seesaw mediators are also messengers of SUSY breaking. In this case, strong correlations exist among neutrino parameters, sparticle and Higgs masses, as well as lepton flavour violating processes. Hence, thi... 11. Improved determination of the Higgs mass in the MSSM with heavy superpartners Energy Technology Data Exchange (ETDEWEB) Bagnaschi, Emanuele [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Pardo Vega, Javier [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); SISSA International School for Advanced Studies, Trieste (Italy); INFN, Trieste (Italy); Slavich, Pietro [UPMC Univ. Paris 06 Sorbonne Univs., Paris (France). LPTHE; CNRS, Paris (France). LPTHE 2017-03-15 We present several advances in the effective field theory calculation of the Higgs mass in MSSM scenarios with heavy superparticles. In particular, we compute the dominant two-loop threshold corrections to the quartic Higgs coupling for generic values of the relevant SUSY-breaking parameters, including all contributions controlled by the strong gauge coupling and by the third-family Yukawa couplings. We also study the effects of a representative subset of dimension-six operators in the effective theory valid below the SUSY scale. Our results will allow for an improved determination of the Higgs mass and of the associated theoretical uncertainty. 12. Improved determination of the Higgs mass in the MSSM with heavy superpartners. Science.gov (United States) Bagnaschi, Emanuele; Vega, Javier Pardo; Slavich, Pietro 2017-01-01 We present several advances in the effective field theory calculation of the Higgs mass in MSSM scenarios with heavy superparticles. In particular, we compute the dominant two-loop threshold corrections to the quartic Higgs coupling for generic values of the relevant SUSY-breaking parameters, including all contributions controlled by the strong gauge coupling and by the third-family Yukawa couplings. We also study the effects of a representative subset of dimension-six operators in the effective theory valid below the SUSY scale. Our results will allow for an improved determination of the Higgs mass and of the associated theoretical uncertainty. 13. Improved determination of the Higgs mass in the MSSM with heavy superpartners Energy Technology Data Exchange (ETDEWEB) Bagnaschi, Emanuele [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Vega, Javier Pardo [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); SISSA International School for Advanced Studies, Trieste (Italy); INFN Trieste, Trieste (Italy); Slavich, Pietro [LPTHE, UPMC Univ. Paris 06, Sorbonne Universites, Paris (France); LPTHE, CNRS, Paris (France) 2017-05-15 We present several advances in the effective field theory calculation of the Higgs mass in MSSM scenarios with heavy superparticles. In particular, we compute the dominant two-loop threshold corrections to the quartic Higgs coupling for generic values of the relevant SUSY-breaking parameters, including all contributions controlled by the strong gauge coupling and by the third-family Yukawa couplings. We also study the effects of a representative subset of dimension-six operators in the effective theory valid below the SUSY scale. Our results will allow for an improved determination of the Higgs mass and of the associated theoretical uncertainty. (orig.) 14. Large tan β in gauge-mediated SUSY-breaking models International Nuclear Information System (INIS) Rattazzi, R. 1997-01-01 We explore some topics in the phenomenology of gauge-mediated SUSY-breaking scenarios having a large hierarchy of Higgs VEVs, v U /v D = tan β>>1. Some motivation for this scenario is first presented. We then use a systematic, analytic expansion (including some threshold corrections) to calculate the μ-parameter needed for proper electroweak breaking and the radiative corrections to the B-parameter, which fortuitously cancel at leading order. If B = 0 at the messenger scale then tan β is naturally large and calculable; we calculate it. We then confront this prediction with classical and quantum vacuum stability constraints arising from the Higgs-slepton potential, and indicate the preferred values of the top quark mass and messenger scale(s). The possibility of vacuum instability in a different direction yields an upper bound on the messenger mass scale complementary to the familiar bound from gravitino relic abundance. Next, we calculate the rate for b→sγ and show the possibility of large deviations (in the direction currently favored by experiment) from standard-model and small tan β predictions. Finally, we discuss the implications of these findings and their applicability to future, broader and more detailed investigations. (orig.) 15. A realistic extension of gauge-mediated SUSY-breaking model with superconformal hidden sector International Nuclear Information System (INIS) Asano, Masaki; Hisano, Junji; Okada, Takashi; Sugiyama, Shohei 2009-01-01 The sequestering of supersymmetry (SUSY) breaking parameters, which is induced by superconformal hidden sector, is one of the solutions for the μ/B μ problem in gauge-mediated SUSY-breaking scenario. However, it is found that the minimal messenger model does not derive the correct electroweak symmetry breaking. In this Letter we present a model which has the coupling of the messengers with the SO(10) GUT-symmetry breaking Higgs fields. The model is one of the realistic extensions of the gauge mediation model with superconformal hidden sector. It is shown that the extension is applicable for a broad range of conformality breaking scale 16. The minimal SUSY B−L model: simultaneous Wilson lines and string thresholds Energy Technology Data Exchange (ETDEWEB) Deen, Rehan; Ovrut, Burt A. [Department of Physics, University of Pennsylvania,209 South 33rd Street, Philadelphia, PA 19104-6396 (United States); Purves, Austin [Department of Physics, University of Pennsylvania,209 South 33rd Street, Philadelphia, PA 19104-6396 (United States); Department of Physics, Manhattanville College,2900 Purchase Street, Purchase, NY 10577 (United States) 2016-07-08 In previous work, we presented a statistical scan over the soft supersymmetry breaking parameters of the minimal SUSY B−L model. For specificity of calculation, unification of the gauge parameters was enforced by allowing the two ℤ{sub 3}×ℤ{sub 3} Wilson lines to have mass scales separated by approximately an order of magnitude. This introduced an additional “left-right” sector below the unification scale. In this paper, for three important reasons, we modify our previous analysis by demanding that the mass scales of the two Wilson lines be simultaneous and equal to an “average unification” mass 〈M{sub U}〉. The present analysis is 1) more “natural” than the previous calculations, which were only valid in a very specific region of the Calabi-Yau moduli space, 2) the theory is conceptually simpler in that the left-right sector has been removed and 3) in the present analysis the lack of gauge unification is due to threshold effects — particularly heavy string thresholds, which we calculate statistically in detail. As in our previous work, the theory is renormalization group evolved from 〈M{sub U}〉 to the electroweak scale — being subjected, sequentially, to the requirement of radiative B−L and electroweak symmetry breaking, the present experimental lower bounds on the B−L vector boson and sparticle masses, as well as the lightest neutral Higgs mass of ∼125 GeV. The subspace of soft supersymmetry breaking masses that satisfies all such constraints is presented and shown to be substantial. 17. Planck-scale physics and neutrino masses International Nuclear Information System (INIS) Akhmedov, E.Kh.; Senjanovic, G.; Berezhiani, Z.G. 1992-05-01 We discuss gravitationally induced masses and mass splittings of Majorana, Zeldovich-Konopinski-Mahmoud and Dirac neutrinos. Among other implications, these effects can provide a solution of the solar neutrino puzzle. In particular, we show how this may work in the 17 keV neutrino picture. (author). 18 refs 18. Recent results on SUSY searches from CMS CERN Multimedia CERN. Geneva 2013-01-01 The latest results on searches for Supersymmetry from CMS are reviewed. We present searches for direct stop production, searches in final states with four W bosons and multiple b-quarks, and searches for R-Parity violating SUSY. The results use up to 20/fb of data from the 8 TeV LHC run of 2012. 19. Kepribadian Dan Komunikasi Susi Pudjiastuti Dalam Membentuk Personal Branding Directory of Open Access Journals (Sweden) Stevani 2017-07-01 Full Text Available The life story of Susi Pudjiastuti is admired by many people for her hard work, until becoming successful by having so much company in the field of aviation and fisheries. Susi Pudjiastuti is also well known to the public for his work in the ministry. Good performance makes Susi Pudjiastuti popular among Jokowi's working cabinet. Currently, the Brand Name in humans is personal branding which is the trend of the formation of self-image and the creation of good perception from others to us. This research will discuss about personality, communication and personal branding Susi Pudjiastuti with qualitative research method. Good personality makes Susi Pudjiastuti has the ability to communicate well and liked by the community. Personality and communication can form a personal branding Susi Pudjiastuti a natural. By exposing the personality and communication of Susi Pudjiastuti in forming personal branding, then people will realize the importance of personality and Communication in forming a natural personal branding. Kisah hidup Susi Pudjiastuti banyak dikagumi oleh banyak orang atas kerja kerasnya hingga menjadi sukses dengan memiliki banyak perusahaan di bidang penerbangan dan perikanan. Susi Pudjiastuti juga dikenal baik oleh masyarakat akan kinerjanya dalam bekerja di kementerian. Kinerja yang baik menjadikan Susi Pudjiastuti popular diantara kabinet kerja Jokowi. Saat ini, Sebutan merek pada manusia adalah personal branding yang merupakan trend dari pembentukan pencitraan diri dan penciptaan persepsi yang baik dari orang lain kepada kita. Penelitian ini akan membahas mengenai kepribadian, komunikasi serta personal branding Susi Pudjiastuti dengan metode penelitian kualitatif. Kepribadian yang baik menjadikan Susi Pudjiastuti memiliki kemampuan berkomunikasi dengan baik dan disenangi oleh masyarakat. Kepribadian dan komunikasi tersebut dapat membentuk personal branding Susi Pudjiastuti yang alami. Dengan memaparkan kepribadian dan komunikasi Susi 20. Probing the Absolute Mass Scale of Neutrinos International Nuclear Information System (INIS) Formaggio, Joseph A. 2011-01-01 The experimental efforts of the Neutrino Physics Group at MIT center primarily around the exploration of neutrino mass and its significance within the context of nuclear physics, particle physics, and cosmology. The group has played a prominent role in the Sudbury Neutrino Observatory, a neutrino experiment dedicated to measure neutrino oscillations from 8B neutrinos created in the sun. The group is now focusing its efforts in the measurement of the neutrino mass directly via the use of tritium beta decay. The MIT group has primary responsibilities in the Karlsruhe Tritium Neutrino mass experiment, expected to begin data taking by 2013. Specifically, the MIT group is responsible for the design and development of the global Monte Carlo framework to be used by the KATRIN collaboration, as well as responsibilities directly associated with the construction of the focal plane detector. In addition, the MIT group is sponsoring a new research endeavor for neutrino mass measurements, known as Project 8, to push beyond the limitations of current neutrino mass experiments. 1. Influence of light-quark masses in dynamical scale breaking International Nuclear Information System (INIS) Barcelos Neto, J.; Chanda, R. 1984-01-01 It is demonstrated that light quark masses may significantly contribute to the logarithmic scale breaking in deep inelastic electromagnetic lepton-nucleon scattering. This is mainly due to the combination of scale variables together with large 'current' masses for u and d quarks, recently reported in the literature. Upper limits for current masses of u and d quarks, using positivity properties of the forward electromagnetic structure function F 2 of the nucleon are also estimated. (Author) [pt 2. Muon g - 2 through a flavor structure on soft SUSY terms International Nuclear Information System (INIS) Flores-Baez, F.V.; Gomez Bock, M.; Mondragon, M. 2016-01-01 In this work we analyze the possibility to explain the muon anomalous magnetic moment discrepancy within theory and experiment through lepton-flavor violation processes. We propose a flavor extended MSSM by considering a hierarchical family structure for the trilinear scalar soft-supersymmetric terms of the Lagrangian, present at the SUSY breaking scale. We obtain analytical results for the rotation mass matrix, with the consequence of having non-universal slepton masses and the possibility of leptonic flavor mixing. The one-loop supersymmetric contributions to the leptonic flavor violating process τ → μγ are calculated in the physical basis, instead of using the well-known mass-insertion method. The flavor violating processes BR(l_i → l_jγ) are also obtained, in particular τ → μγ is well within the experimental bounds. We present the regions in parameter space where the muon g - 2 problem is either entirely solved or partially reduced through the contribution of these flavor violating processes. (orig.) 3. Muon g - 2 through a flavor structure on soft SUSY terms Energy Technology Data Exchange (ETDEWEB) Flores-Baez, F.V. [Universidad Autonoma de Nuevo Leon, UANL Ciudad Universitaria, FCFM, San Nicolas de los Garza, Nuevo Leon (Mexico); Gomez Bock, M. [Universidad de las Americas Puebla, UDLAP, Ex-Hacienda Sta. Catarina Martir, DAFM, Cholula, Puebla (Mexico); Mondragon, M. [Universidad Nacional Autonoma de Mexico, Instituto de Fisica, Apdo. Postal 20-364, Mexico, D.F. (Mexico) 2016-10-15 In this work we analyze the possibility to explain the muon anomalous magnetic moment discrepancy within theory and experiment through lepton-flavor violation processes. We propose a flavor extended MSSM by considering a hierarchical family structure for the trilinear scalar soft-supersymmetric terms of the Lagrangian, present at the SUSY breaking scale. We obtain analytical results for the rotation mass matrix, with the consequence of having non-universal slepton masses and the possibility of leptonic flavor mixing. The one-loop supersymmetric contributions to the leptonic flavor violating process τ → μγ are calculated in the physical basis, instead of using the well-known mass-insertion method. The flavor violating processes BR(l{sub i} → l{sub j}γ) are also obtained, in particular τ → μγ is well within the experimental bounds. We present the regions in parameter space where the muon g - 2 problem is either entirely solved or partially reduced through the contribution of these flavor violating processes. (orig.) 4. SUSY-hierarchy of one-dimensional reflectionless potentials International Nuclear Information System (INIS) Maydanyuk, Sergei P. 2005-01-01 A class of one-dimensional reflectionless potentials is studied. It is found that all possible types of the reflectionless potentials can be combined into one SUSY-hierarchy with a constant potential. An approach for determination of a general form of the reflectionless potential on the basis of construction of such a hierarchy by the recurrent method is proposed. A general integral form of interdependence between superpotentials with neighboring numbers of this hierarchy, opening a possibility to find new reflectionless potentials, is found and has a simple analytical view. It is supposed that any possible type of the reflectionless potential can be expressed through finite number of elementary functions (unlike some presentations of the reflectionless potentials, which are constructed on the basis of soliton solutions or are shape invariant in one or many steps with involving scaling of parameters, and are expressed through series). An analysis of absolute transparency existence for the potential which has the inverse power dependence on space coordinate (and here tunneling is possible), i.e., which has the form V (x) = ± α/ vertical bar x-x 0 vertical bar n (where α and x 0 are constants, n is natural number), is fulfilled. It is shown that such a potential can be reflectionless at n = 2 only. A SUSY-hierarchy of the inverse power reflectionless potentials is constructed. Isospectral expansions of this hierarchy are analyzed 5. Low scale gravity as the source of neutrino masses? Energy Technology Data Exchange (ETDEWEB) Berezinsky, Veniamin [INFN, Laboratori Nazionali del Gran Sasso, I-67010 Assergi, AQ (Italy); Narayan, Mohan [INFN, Laboratori Nazionali del Gran Sasso, I-67010 Assergi, AQ (Italy); Vissani, Francesco [INFN, Laboratori Nazionali del Gran Sasso, I-67010 Assergi, AQ (Italy) 2005-04-01 We address the question whether low-scale gravity alone can generate the neutrino mass matrix needed to accommodate the observed phenomenology. In low-scale gravity the neutrino mass matrix in the flavor basis is characterized by one parameter (the gravity scale M{sub X}) and by an exact or approximate flavor blindness (namely, all elements of the mass matrix are of comparable size). Neutrino masses and mixings are consistent with the observational data for certain values of the matrix elements, but only when the spectrum of mass is inverted or degenerate. For the latter type of spectra the parameter M{sub ee} probed in double beta experiments and the mass parameter probed by cosmology are close to existing upper limits. 6. Low scale gravity as the source of neutrino masses? International Nuclear Information System (INIS) Berezinsky, Veniamin; Narayan, Mohan; Vissani, Francesco 2005-01-01 We address the question whether low-scale gravity alone can generate the neutrino mass matrix needed to accommodate the observed phenomenology. In low-scale gravity the neutrino mass matrix in the flavor basis is characterized by one parameter (the gravity scale M X ) and by an exact or approximate flavor blindness (namely, all elements of the mass matrix are of comparable size). Neutrino masses and mixings are consistent with the observational data for certain values of the matrix elements, but only when the spectrum of mass is inverted or degenerate. For the latter type of spectra the parameter M ee probed in double beta experiments and the mass parameter probed by cosmology are close to existing upper limits 7. On the diversity of gauge mediation: footprints of dynamical SUSY breaking International Nuclear Information System (INIS) Abel, Steven; Jaeckel, Joerg; Khoze, Valentin V.; Matos, Luis 2009-01-01 Recent progress in realising dynamical supersymmetry breaking allows the construction of simple and calculable models of gauge mediation. We discuss the phenomenology of the particularly minimal case in which the mediation is direct, and show that there are generic new and striking predictions. These include new particles with masses comparable to those of the Standard Model superpartners, associated with the pseudo-Goldstone modes of the dynamical SUSY breaking sector. Consequently there is an unavoidable departure from the MSSM. In addition the gaugino masses are typically significantly lighter than the sfermions, and their mass ratios can be different from the pattern dictated by the gauge couplings in standard (i.e. explicit) gauge mediation. We investigate these features in two distinct realisations of the dynamical SUSY breaking sector. 8. Local supersymmetry and the problem of the mass scales International Nuclear Information System (INIS) Nilles, H.P. 1983-02-01 Spontaneously broken supergravity might help us to understand the puzzle of the mass scales in grand unified models. We describe the general mechanism and point out the remaining problems. Some new results on local supercolor are presented 9. Status of the SUSY Les Houches Accord II Project International Nuclear Information System (INIS) Allanch, B.C.; Balazs, C.; Belanger, G.; Boudjema, F.; Choudhury, D.; Desch, K.; Ellwanger, U.; Gambino, P.; Godbole, R.; Guasch, J.; Guchait, M.; Heinemeyer, S.; Hugonie, C.; Hurth, T.; Kraml, S.; Lykken, J.; Mangano, M.; Moortgat, F.; Moretti, S.; Penaranda, S.; Porod, W.; Fermilab 2005-01-01 Supersymmetric (SUSY) spectrum generators, decay packages, Monte-Carlo programs, dark matter evaluators, and SUSY fitting programs often need to communicate in the process of an analysis. The SUSY Les Houches Accord provides a common interface that conveys spectral and decay information between the various packages. Here, we propose extensions of the conventions of the first SUSY Les Houches Accord to include various generalizations: violation of CP, R-parity and flavor as well as the simplest next-to-minimal supersymmetric standard model (NMSSM) 10. Natural inflation in SUSY and gauge-mediated curvature of the flat directions CERN Document Server Dvali, Gia 1996-01-01 Supersymmetric theories often include the non-compact directions in the field space along which the tree level potential grows only up to a certain limited value (determined by the mass scale of the theory) and then stays constant for the arbitrarily large expectation value of the field parametrizing the direction. Above the critical value, the tree-level curvature is large and positive in the other directions. Such plateaux are natural candidates for the hybrid inflaton. The non-zero F-term density along the plateau spontaneously breaks SUSY and induces the one-loop logarithmic slope for the inflaton potential. The coupling of the inflaton to the Higgs fields in the complex representations of the gauge group, may result in a radiatively induced Fayet--Iliopoulos D-term during inflation, which destabilizes some of the squark and slepton flat directions. Corresponding soft masses can be larger than the Hubble parameter and thus, play a crucial role for the Affleck--Dine baryogenesis. 11. Verifiable origin of neutrino mass at TeV scale International Nuclear Information System (INIS) Ma, Ernest 2002-01-01 The physics responsible for neutrino mass may reside at or below the TeV energy scale. The neutrino mass matrix in the (ν e ν μ ν gt ) basis may then be deduced from future high-energy accelerator experiments. The newly observed excess in the muon anomalous magnetic moment may also be related 12. Large neutrino mixings in MSSM and SUSY GUTs: Democratic approach International Nuclear Information System (INIS) Shafi, Qaisar; Tavartkiladze, Zurab 2003-01-01 We show how, with aid from a U (1) flavor symmetry, the hierarchical structure in the charged fermion sector and a democratic approach for neutrinos that yields large solar and atmospheric neutrino mixings can be simultaneously realized in the MSSM framework. In SU(5), due to the unified multiplets, we encounter difficulties. Namely, democracy for the neutrinos leads to a wrong hierarchical pattern for charged fermion masses and mixings. We discuss how this is overcome in flipped SU(5). We then proceed to an example based on 5D SUSY SU(5) GUT in which the neutrino democracy idea can be realized. A crucial role is played by bulk states, the so-called 'copies', which are split by compactifying the fifth dimension on an S(1)/Z2 x Z'2 orbifold 13. SUSY S4×SU(5) revisited International Nuclear Information System (INIS) Hagedorn, Claudia; King, Stephen F.; Luhn, Christoph 2012-01-01 Following the recent results from Daya Bay and RENO, which measure the lepton mixing angle θ 13 l ≈0.15, we revisit a supersymmetric (SUSY) S 4 ×SU(5) model, which predicts tri-bimaximal (TB) mixing in the neutrino sector with θ 13 l being too small in its original version. We show that introducing one additional S 4 singlet flavon into the model gives rise to a sizable θ 13 l via an operator which leads to the breaking of one of the two Z 2 symmetries preserved in the neutrino sector at leading order (LO). The results of the original model for fermion masses, quark mixing and the solar mixing angle are maintained to good precision. The atmospheric and solar mixing angle deviations from TB mixing are subject to simple sum rule bounds. 14. Flavour and collider interplay for SUSY at LHC7 International Nuclear Information System (INIS) Calibbi, L.; Hodgkinson, R.N.; Vives, O.; Jones Perez, J.; Masiero, A. 2012-01-01 The current 7 TeV run of the LHC experiment shall be able to probe gluino and squark masses up to values larger than 1 TeV. Assuming that hints for SUSY are found in the jets plus missing energy channel by the end of a 5 fb -1 run, we explore the flavour constraints on three models with a CMSSM-like spectrum: the CMSSM itself, a seesaw extension of the CMSSM, and Flavoured CMSSM. In particular, we focus on decays that might have been measured by the time the run is concluded, such as B s →μμ and μ→e γ. We also analyse constraints imposed by neutral meson bounds and electric dipole moments. The interplay between collider and flavour experiments is explored through the use of three benchmark scenarios, finding the flavour feedback useful in order to determine the model parameters and to test the consistency of the different models. (orig.) 15. Charm production and mass scales in deep inelastic processes International Nuclear Information System (INIS) Close, F.E.; Scott, D.M.; Sivers, D. 1976-07-01 Because of their large mass, the production of charmed particles offers the possibility of new insight into fundamental dynamics. An approach to deep inelastic processes is discussed in which Generalized Vector Meson Dominance is used to extend parton model results away from the strict Bjorken scaling limit into regions where mass scales play an important role. The processes e + e - annihilation, photoproduction, deep inelastic leptoproduction, photon-photon scattering and the production of lepton pairs in hadronic collisions are discussed. The GCMD approach provides a reasonably unified framework and makes specific predictions concerning the way in which these reactions reflect an underlying flavour symmetry, broken by large mass differences. (author) 16. Mesino oscillation in MFV SUSY Energy Technology Data Exchange (ETDEWEB) Berger, Joshua [Cornell University, Department of Physics, LEPP, Ithaca, NY (United States); SLAC National Accelerator Laboratory, Menlo Park, CA (United States); Csaki, Csaba; Grossman, Yuval; Heidenreich, Ben [Cornell University, Department of Physics, LEPP, Ithaca, NY (United States) 2013-04-15 R-parity violating supersymmetry in a Minimal Flavor Violation paradigm can produce same-sign dilepton signals via direct sbottom-LSP pair production. Such signals arise when the sbottom hadronizes and the resulting mesino oscillates into an antimesino. The first bounds on the sbottom mass are placed in this scenario using current LHC results. (orig.) 17. Radiative natural SUSY spectrum from deflected AMSB scenario with messenger-matter interactions Energy Technology Data Exchange (ETDEWEB) Wang, Fei [School of Physics, Zhengzhou University,Zhengzhou 450000 (China); State Key Laboratory of Theoretical Physics,Institute of Theoretical Physics, Chinese Academy of Sciences,Beijing 100080 (China); Yang, Jin Min [State Key Laboratory of Theoretical Physics,Institute of Theoretical Physics, Chinese Academy of Sciences,Beijing 100080 (China); Department of Physics, Tohoku University,Sendai 980-8578 (Japan); Zhang, Yang [State Key Laboratory of Theoretical Physics,Institute of Theoretical Physics, Chinese Academy of Sciences,Beijing 100080 (China) 2016-04-29 A radiative natural SUSY spectrum are proposed in the deflected anomaly mediation scenario with general messenger-matter interactions. Due to the contributions from the new interactions, positive slepton masses as well as a large \|A{sub t}\| term can naturally be obtained with either sign of deflection parameter and few messenger species (thus avoid the possible Landau pole problem). In this scenario, in contrast to the ordinary (radiative) natural SUSY scenario with under-abundance of dark matter (DM), the DM can be the mixed bino-higgsino and have the right relic density. The 125 GeV Higgs mass can also be easily obtained in our scenario. The majority of low EW fine tuning points can be covered by the XENON-1T direct detection experiments. 18. Calibrating the Planck cluster mass scale with CLASH Science.gov (United States) Penna-Lima, M.; Bartlett, J. G.; Rozo, E.; Melin, J.-B.; Merten, J.; Evrard, A. E.; Postman, M.; Rykoff, E. 2017-08-01 We determine the mass scale of Planck galaxy clusters using gravitational lensing mass measurements from the Cluster Lensing And Supernova survey with Hubble (CLASH). We have compared the lensing masses to the Planck Sunyaev-Zeldovich (SZ) mass proxy for 21 clusters in common, employing a Bayesian analysis to simultaneously fit an idealized CLASH selection function and the distribution between the measured observables and true cluster mass. We used a tiered analysis strategy to explicitly demonstrate the importance of priors on weak lensing mass accuracy. In the case of an assumed constant bias, bSZ, between true cluster mass, M500, and the Planck mass proxy, MPL, our analysis constrains 1-bSZ = 0.73 ± 0.10 when moderate priors on weak lensing accuracy are used, including a zero-mean Gaussian with standard deviation of 8% to account for possible bias in lensing mass estimations. Our analysis explicitly accounts for possible selection bias effects in this calibration sourced by the CLASH selection function. Our constraint on the cluster mass scale is consistent with recent results from the Weighing the Giants program and the Canadian Cluster Comparison Project. It is also consistent, at 1.34σ, with the value needed to reconcile the Planck SZ cluster counts with Planck's base ΛCDM model fit to the primary cosmic microwave background anisotropies. 19. SUSY-hierarchy of one-dimensional reflectionless potentials CERN Document Server Maydanyuk, Sergei P 2004-01-01 A class of one-dimensional reflectionless potentials, an absolute transparency of which is concerned with their belonging to one SUSY-hierarchy with a constant potential, is studied. An approach for determination of a general form of the reflectionless potential on the basis of construction of such a hierarchy by the recurrent method is proposed. A general form of interdependence between superpotentials with neighboring numbers of this hierarchy, opening a possibility to find new reflectionless potentials, have a simple analytical view and are expressed through finite number of elementary functions (unlike some reflectionless potentials, which are constructed on the basis of soliton solutions or are shape invariant in one or many steps with involving scaling of parameters, and are expressed through series), is obtained. An analysis of absolute transparency existence for the potential which has the inverse power dependence on space coordinate (and here tunneling is possible), i.e. which has the formV(x) = \\p... 20. Recent SUSY Results from CMS CERN Multimedia CERN. Geneva 2012-01-01 We present a summary of the recent results of searches for supersymmetry conducted by the CMS experiment. Several searches are reported using complementary final states and methods. The results presented include searches for stops and sbottoms, production of charginos and neutralinos, and R-parity violating signatures. Several of them are the first results of their kind from CMS, while others increased the mass reach significantly over previously published results from the LHC. 1. Results from GRACE/SUSY at one-loop We report the recent development on the SUSY calculations with the help of GRACE system. GRACE/SUSY/1LOOP is the computer code which can generate Feynman diagrams in the MSSM automatically and compute one-loop amplitudes in the numerical way. We present new results of various two-body decay widths ... 2. A low energy dynamical SUSY breaking scenario motivated from superstring derived unification CERN Document Server Faraggi, Alon E. 1996-01-01 Recently there has been a resurgence of interest in gauge mediated dynamical supersymmetry breaking scenarios. I investigate how low energy dynamical SUSY breaking may arise from superstring models. In a three generation string derived model I propose that the unbroken hidden non--Abelian gauge group at the string scale is SU(3)_H with matter multiplets. Due to the small gauge content of the hidden gauge group the supersymmetry breaking scale may be consistent with the dynamical SUSY breaking scenarios. The messenger states are obtained in the superstring model from sectors which arise due to the Wilson--line'' breaking of the unifying non--Abelian gauge symmetry. An important property of the string motivated messenger states is the absence of superpotential terms with the Standard Model states. The stringy symmetries therefore forbid the flavor changing processes which may arise due to couplings between the messenger sector states and the Standard Model states. Motivated from the problem of string gauge co... 3. The fine-tuning cost of the likelihood in SUSY models International Nuclear Information System (INIS) Ghilencea, D.M.; Ross, G.G. 2013-01-01 In SUSY models, the fine-tuning of the electroweak (EW) scale with respect to their parameters γ i ={m 0 ,m 1/2 ,μ 0 ,A 0 ,B 0 ,…} and the maximal likelihood L to fit the experimental data are usually regarded as two different problems. We show that, if one regards the EW minimum conditions as constraints that fix the EW scale, this commonly held view is not correct and that the likelihood contains all the information about fine-tuning. In this case we show that the corrected likelihood is equal to the ratio L/Δ of the usual likelihood L and the traditional fine-tuning measure Δ of the EW scale. A similar result is obtained for the integrated likelihood over the set {γ i }, that can be written as a surface integral of the ratio L/Δ, with the surface in γ i space determined by the EW minimum constraints. As a result, a large likelihood actually demands a large ratio L/Δ or equivalently, a small χ new 2 =χ old 2 +2lnΔ. This shows the fine-tuning cost to the likelihood (χ new 2 ) of the EW scale stability enforced by SUSY, that is ignored in data fits. A good χ new 2 /d.o.f.≈1 thus demands SUSY models have a fine-tuning amount Δ≪exp(d.o.f./2), which provides a model-independent criterion for acceptable fine-tuning. If this criterion is not met, one can thus rule out SUSY models without a further χ 2 /d.o.f. analysis. Numerical methods to fit the data can easily be adapted to account for this effect. 4. Relative scale and the strength and deformability of rock masses Science.gov (United States) Schultz, Richard A. 1996-09-01 The strength and deformation of rocks depend strongly on the degree of fracturing, which can be assessed in the field and related systematically to these properties. Appropriate Mohr envelopes obtained from the Rock Mass Rating (RMR) classification system and the Hoek-Brown criterion for outcrops and other large-scale exposures of fractured rocks show that rock-mass cohesive strength, tensile strength, and unconfined compressive strength can be reduced by as much as a factor often relative to values for the unfractured material. The rock-mass deformation modulus is also reduced relative to Young's modulus. A "cook-book" example illustrates the use of RMR in field applications. The smaller values of rock-mass strength and deformability imply that there is a particular scale of observation whose identification is critical to applying laboratory measurements and associated failure criteria to geologic structures. 5. SUSY searches in early CMS data International Nuclear Information System (INIS) Tricomi, A 2008-01-01 In the first year of data taking at LHC, the CMS experiment expects to collect about 1 fb -1 of data, which make possible the first searches for new phenomena. All such searches require however the measurement of the SM background and a detailed understanding of the detector performance, reconstruction algorithms and triggering. The CMS efforts are hence addressed to designing a realistic analysis plan in preparation to the data taking. In this paper, the CMS perspectives and analysis strategies for Supersymmetry (SUSY) discovery with early data are presented 6. Higgs mass naturalness and scale invariance in the UV CERN Document Server Tavares, Gustavo Marques; Skiba, Witold 2014-01-01 It has been suggested that electroweak symmetry breaking in the Standard Model may be natural if the Standard Model merges into a conformal field theory (CFT) at short distances. In such a scenario the Higgs mass would be protected from quantum corrections by the scale invariance of the CFT. In order for the Standard Model to merge into a CFT at least one new ultraviolet (UV) scale is required at which the couplings turn over from their usual Standard Model running to the fixed point behavior. We argue that the Higgs mass is sensitive to such a turn-over scale even if there are no associated massive particles and the scale arises purely from dimensional transmutation. We demonstrate this sensitivity to the turnover scale explicitly in toy models. Thus if scale invariance is responsible for Higgs mass naturalness, then the transition to CFT dynamics must occur near the TeV scale with observable consequences at colliders. In addition, the UV fixed point theory in such a scenario must be interacting because loga... 7. Viable and testable SUSY GUTs with Yukawa unification the case of split trilinears CERN Document Server 2009-01-01 We explore general SUSY GUT models with exact third-generation Yukawa unification, but where the requirement of universal soft terms at the GUT scale is relaxed. We consider the scenario in which the breaking of universality inherits from the Yukawa couplings, i.e. is of minimal flavor violating (MFV) type. In particular, the MFV principle allows for a splitting between the up-type and the down-type soft trilinear couplings. We explore the viability of this trilinear splitting scenario by means of a fitting procedure to electroweak observables, quark masses as well as flavor-changing neutral current processes. Phenomenological viability singles out one main scenario. This scenario is characterized by a sizable splitting between the trilinear soft terms and a large mu term. Remarkably, this scenario does not invoke a partial decoupling of the sparticle spectrum, as in the case of universal soft terms, but instead it requires part of the spectrum, notably the lightest stop, the gluino and the lightest charginos... 8. Effective Planck Mass and the Scale of Inflation CERN Document Server Kleban, Matthew; Porrati, Massimo 2016-01-11 A recent paper argued that it is not possible to infer the energy scale of inflation from the amplitude of tensor fluctuations in the Cosmic Microwave Background, because the usual connection is substantially altered if there are a large number of universally coupled fields present during inflation, with mass less than the inflationary Hubble scale. We give a simple argument demonstrating that this is incorrect. 9. Leptogenesis in a Δ(27)×SO(10) SUSY GUT Energy Technology Data Exchange (ETDEWEB) Björkeroth, Fredrik [School of Physics and Astronomy, University of Southampton,SO17 1BJ Southampton (United Kingdom); Anda, Francisco J. de [Departamento de Física, CUCEI, Universidad de Guadalajara,Guadalajara (Mexico); Varzielas, Ivo de Medeiros; King, Stephen F. [School of Physics and Astronomy, University of Southampton,SO17 1BJ Southampton (United Kingdom) 2017-01-17 Although SO(10) Supersymmetric (SUSY) Grand Unification Theories (GUTs) are very attractive for neutrino mass and mixing, it is often quite difficult to achieve successful leptogenesis from the lightest right-handed neutrino N{sub 1} due to the strong relations between neutrino and up-type quark Yukawa couplings. We show that in a realistic model these constraints are relaxed, making N{sub 1} leptogenesis viable. To illustrate this, we calculate the baryon asymmetry of the Universe Y{sub B} from flavoured N{sub 1} leptogenesis in a recently proposed Δ(27)×SO(10) SUSY GUT. The flavoured Boltzmann equations are solved numerically, and comparison with the observed Y{sub B} places constraints on the allowed values of right-handed neutrino masses and neutrino Yukawa couplings. The flavoured SO(10) SUSY GUT is not only fairly complete and predictive in the lepton sector, but can also explain the BAU through leptogenesis with natural values in the lepton sector albeit with some tuning in the quark sector. 10. Geoelectrical Measurement of Multi-Scale Mass Transfer Parameters Energy Technology Data Exchange (ETDEWEB) Day-Lewis, Frederick David [US Geological Survey, Storrs, CT (United States); Singha, Kamini [Colorado School of Mines, Golden, CO (United States); Johnson, Timothy C. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Haggerty, Roy [Oregon State Univ., Corvallis, OR (United States); Binley, Andrew [Lancaster Univ. (United Kingdom); Lane, John W. [US Geological Survey, Storrs, CT (United States) 2014-11-25 Mass transfer affects contaminant transport and is thought to control the efficiency of aquifer remediation at a number of sites within the Department of Energy (DOE) complex. An improved understanding of mass transfer is critical to meeting the enormous scientific and engineering challenges currently facing DOE. Informed design of site remedies and long-term stewardship of radionuclide-contaminated sites will require new cost-effective laboratory and field techniques to measure the parameters controlling mass transfer spatially and across a range of scales. In this project, we sought to capitalize on the geophysical signatures of mass transfer. Previous numerical modeling and pilot-scale field experiments suggested that mass transfer produces a geoelectrical signature—a hysteretic relation between sampled (mobile-domain) fluid conductivity and bulk (mobile + immobile) conductivity—over a range of scales relevant to aquifer remediation. In this work, we investigated the geoelectrical signature of mass transfer during tracer transport in a series of controlled experiments to determine the operation of controlling parameters, and also investigated the use of complex-resistivity (CR) as a means of quantifying mass transfer parameters in situ without tracer experiments. In an add-on component to our grant, we additionally considered nuclear magnetic resonance (NMR) to help parse mobile from immobile porosities. Including the NMR component, our revised study objectives were to: 1. Develop and demonstrate geophysical approaches to measure mass-transfer parameters spatially and over a range of scales, including the combination of electrical resistivity monitoring, tracer tests, complex resistivity, nuclear magnetic resonance, and materials characterization; and 2. Provide mass-transfer estimates for improved understanding of contaminant fate and transport at DOE sites, such as uranium transport at the Hanford 300 Area. To achieve our objectives, we implemented a 3 11. Supersymmetry production from a TeV scale black hole at CERN LHC International Nuclear Information System (INIS) Chamblin, Andrew; Cooper, Fred; Nayak, Gouranga C. 2004-01-01 If the fundamental Planck scale is near a TeV, then we should expect to see TeV scale black holes at the CERN LHC. Similarly, if the scale of supersymmetry (SUSY) breaking is sufficiently low, then we might expect to see light supersymmetric particles in the next generation of colliders. If the mass of the supersymmetric particle is of order a TeV and is comparable to the temperature of a typical TeV scale black hole, then such sparticles will be copiously produced via Hawking radiation: The black hole will act as a resonance for sparticles, among other things. In this paper we compare various signatures for SUSY production at LHC, and we contrast the situation where the sparticles are produced directly via parton fusion processes with the situation where they are produced indirectly through black hole resonances. We found that black hole resonances provide a larger source for heavy mass SUSY (squark and gluino) production than the direct perturbative QCD-SUSY production via parton fusion processes depending on the values of the Planck mass and black hole mass. Hence black hole production at LHC may indirectly act as a dominant channel for SUSY production. We also found that the differential cross section dσ/dp t for SUSY production increases as a function of the p t (up to p t equal to about 1 TeV or more) of the SUSY particles (squarks and gluinos), which is in sharp contrast with the pQCD predictions where the differential cross section dσ/dp t decreases as p t increases for high p t about 1 TeV or higher. This is a feature for any particle emission from a TeV scale black hole as long as the temperature of the black hole is very high (∼TeV). Hence the measurement of increase of dσ/dp t with p t for p t up to about 1 TeV or higher for final state particles might be a useful signature for black hole production at LHC 12. Implicit Priors in Galaxy Cluster Mass and Scaling Relation Determinations Science.gov (United States) Mantz, A.; Allen, S. W. 2011-01-01 Deriving the total masses of galaxy clusters from observations of the intracluster medium (ICM) generally requires some prior information, in addition to the assumptions of hydrostatic equilibrium and spherical symmetry. Often, this information takes the form of particular parametrized functions used to describe the cluster gas density and temperature profiles. In this paper, we investigate the implicit priors on hydrostatic masses that result from this fully parametric approach, and the implications of such priors for scaling relations formed from those masses. We show that the application of such fully parametric models of the ICM naturally imposes a prior on the slopes of the derived scaling relations, favoring the self-similar model, and argue that this prior may be influential in practice. In contrast, this bias does not exist for techniques which adopt an explicit prior on the form of the mass profile but describe the ICM non-parametrically. Constraints on the slope of the cluster mass-temperature relation in the literature show a separation based the approach employed, with the results from fully parametric ICM modeling clustering nearer the self-similar value. Given that a primary goal of scaling relation analyses is to test the self-similar model, the application of methods subject to strong, implicit priors should be avoided. Alternative methods and best practices are discussed. 13. HMC algorithm with multiple time scale integration and mass preconditioning Science.gov (United States) Urbach, C.; Jansen, K.; Shindler, A.; Wenger, U. 2006-01-01 We present a variant of the HMC algorithm with mass preconditioning (Hasenbusch acceleration) and multiple time scale integration. We have tested this variant for standard Wilson fermions at β=5.6 and at pion masses ranging from 380 to 680 MeV. We show that in this situation its performance is comparable to the recently proposed HMC variant with domain decomposition as preconditioner. We give an update of the "Berlin Wall" figure, comparing the performance of our variant of the HMC algorithm to other published performance data. Advantages of the HMC algorithm with mass preconditioning and multiple time scale integration are that it is straightforward to implement and can be used in combination with a wide variety of lattice Dirac operators. 14. GUT scale and superpartner masses from anomaly mediated supersymmetry breaking International Nuclear Information System (INIS) Chacko, Z.; Luty, Markus A.; Ponton, Eduardo; Shadmi, Yael; Shirman, Yuri 2001-01-01 We consider models of anomaly-mediated supersymmetry breaking (AMSB) in which the grand unification (GUT) scale is determined by the vacuum expectation value of a chiral superfield. If the anomaly-mediated contributions to the potential are balanced by gravitational-strength interactions, a GUT scale of M Planck /(16π 2 ) can be generated. The GUT threshold also affects superpartner masses, and can easily give rise to realistic predictions if the GUT gauge group is asymptotically free. We give an explicit example of a model with these features, in which the doublet-triplet splitting problem is solved. The resulting superpartner spectrum is very different from that of previously considered AMSB models, with gaugino masses typically unifying at the GUT scale 15. Geoelectrical Measurement of Multi-Scale Mass Transfer Parameters Energy Technology Data Exchange (ETDEWEB) Day-Lewis, Frederick; Singha, Kamini; Haggerty, Roy; Johnson, Tim; Binley, Andrew; Lane, John 2014-01-16 Mass transfer affects contaminant transport and is thought to control the efficiency of aquifer remediation at a number of sites within the Department of Energy (DOE) complex. An improved understanding of mass transfer is critical to meeting the enormous scientific and engineering challenges currently facing DOE. Informed design of site remedies and long-term stewardship of radionuclide-contaminated sites will require new cost-effective laboratory and field techniques to measure the parameters controlling mass transfer spatially and across a range of scales. In this project, we sought to capitalize on the geophysical signatures of mass transfer. Previous numerical modeling and pilot-scale field experiments suggested that mass transfer produces a geoelectrical signature—a hysteretic relation between sampled (mobile-domain) fluid conductivity and bulk (mobile + immobile) conductivity—over a range of scales relevant to aquifer remediation. In this work, we investigated the geoelectrical signature of mass transfer during tracer transport in a series of controlled experiments to determine the operation of controlling parameters, and also investigated the use of complex-resistivity (CR) as a means of quantifying mass transfer parameters in situ without tracer experiments. In an add-on component to our grant, we additionally considered nuclear magnetic resonance (NMR) to help parse mobile from immobile porosities. Including the NMR component, our revised study objectives were to: 1. Develop and demonstrate geophysical approaches to measure mass-transfer parameters spatially and over a range of scales, including the combination of electrical resistivity monitoring, tracer tests, complex resistivity, nuclear magnetic resonance, and materials characterization; and 2. Provide mass-transfer estimates for improved understanding of contaminant fate and transport at DOE sites, such as uranium transport at the Hanford 300 Area. To achieve our objectives, we implemented a 3 16. Finite N=1 SUSY gauge field theories International Nuclear Information System (INIS) Kazakov, D.I. 1986-01-01 The authors give a detailed description of the method to construct finite N=1 SUSY gauge field theories in the framework of N=1 superfields within dimensional regularization. The finiteness of all Green functions is based on supersymmetry and gauge invariance and is achieved by a proper choice of matter content of the theory and Yukawa couplings in the form Y i =f i (ε)g, where g is the gauge coupling, and the function f i (ε) is regular at ε=0 and is calculated in perturbation theory. Necessary and sufficient conditions for finiteness are determined already in the one-loop approximation. The correspondence with an earlier proposed approach to construct finite theories based on aigenvalue solutions of renormalization-group equations is established 17. One-loop stabilization of the fuzzy four-sphere via softly broken SUSY Energy Technology Data Exchange (ETDEWEB) Steinacker, Harold C. [Faculty of Physics, University of Vienna,Boltzmanngasse 5, A-1090 Vienna (Austria) 2015-12-17 We describe a stabilization mechanism for fuzzy S{sub N}{sup 4} in the Euclidean IIB matrix model due to vacuum energy in the presence of a positive mass term. The one-loop effective potential for the radius contains an attractive contribution attributed to supergravity, while the mass term induces a repulsive contribution for small radius due to SUSY breaking. This leads to a stabilization of the radius. The mechanism should be pertinent to recent results on the genesis of 3+1-dimensional space-time in the Minkowskian IIB model. 18. Neutralino Dark Matter in non-universal and non-minimal SUSY International Nuclear Information System (INIS) King, S.F. 2010-01-01 We discuss neutralino dark matter in non-universal SUSY including the NUHM, SU(5) with non-universal gauginos. In the MSSM we argue from naturalness that non-universal soft mass parameters are preferred, with non-universal gaugino masses enabling supernatural dark matter beyond the MSSM, we also discuss neutralino dark matter in the U SSM and E 6 SSM. In the E 6 SSM a light neutralino LSP coming from the inert Higgsino and singlino sector is unavoidable and makes an attractive dark matter candidate. 19. Lightest Higgs boson mass in split supersymmetry with the seesaw mechanism International Nuclear Information System (INIS) Cao Junjie; Yang Jinmin 2005-01-01 In the minimal supersymmetric standard model extended by including right-handed neutrinos with seesaw mechanism, the neutrino Yukaka couplings can be as large as the top-quark Yukawa couplings and thus the neutrino/sneutrino may cause sizable effects in Higgs boson self-energy loops. Our explicit one-loop calculations show that the neutrino/sneutrino effects may have an opposite sign to top/stop effects and thus lighten the lightest Higgs boson. If the soft-breaking mass of the right-handed neutrino is very large (at the order of Majorana mass scale), such as in the split-supersymmetry (SUSY) scenario, the effects can lower the lightest Higgs boson mass by a few tens of GeV. So the Higgs mass bound of about 150 GeV in split-SUSY may be lowered significantly if right-handed neutrinos come into play with seesaw mechanism 20. Search for the decay stau --> tau + gravitino in the framework of the Minimal Gauge Mediated SUSY Breaking models CERN Document Server Cavallo, F R 1997-01-01 A search for these decays was carried out in the context of Gauge Mediated SUSY Breaking models, using the data collected by DELPHI in 1995 and 1996 at the center of mass energies of 133, 161 and 172 GeV. No evidence of these processes was found for a decay length ranging from ~ 1mm to ~ 20cm and limits were derived on the gravitino and scalar tau masses. 1. Concordia elas tuleviku arvelt / Mart Susi ; interv. Krister Kivi Index Scriptorium Estoniae Susi, Mart, 1965- 2003-01-01 Ilmunud ka: Infopress 21. märts nr. 12 lk. 30-31. Concordia Ülikooli rektor Mart Susi räägib kooli senisest juhtimisest ning asjaoludest, mis on põhjustanud pankroti. Tabel: Concordia kronoloogia 2. Search for non-standard SUSY signatures in CMS International Nuclear Information System (INIS) Teyssier, Daniel 2008-01-01 New studies of the CMS collaboration are presented on the sensitivity to searches for non-standard signatures of particular SUSY scenarios. These signatures include non-pointing photons as well as pairs of prompt photons as expected GMSB SUSY models, as well as heavy stable charged particles produced in split supersymmetry models, long lived staus from GMSB SUSY and long lived stops in other SUSY scenarios. Detailed detector simulation is used for the study, and all relevant Standard Model background and detector effects that can mimic these special signatures are included. It is shown that with already with less than 100 pb -1 the CMS sensitivity will probe an interesting as yet by data unexplored parameter range of these models. 3. Scales of guide field reconnection at the hydrogen mass ratio International Nuclear Information System (INIS) Lapenta, G.; Markidis, S.; Divin, A.; Goldman, M.; Newman, D. 2010-01-01 We analyze the signatures of component reconnection for a Harris current sheet with a guide field using the physical mass ratio of hydrogen. The study uses the fully kinetic particle in cell code IPIC3D to investigate the scaling with mass ratio of the following three main component reconnection features: electron density cavities along the separatrices, channels of fast electron flow within the cavities, and electron phase space holes due to the Buneman instability in the electron high speed channels. The width and strength of the electron holes and of the electron cavities are studied up the mass ratio proper of hydrogen, considering the effect of the simulation box size, and of the boundary conditions. The results compare favorably with the existing data from the Cluster and Themis missions and provide quantitative predictions for realistic conditions to be encountered by the planned magnetospheric multiscale mission. 4. Results from GRACE/SUSY at one-loop International Nuclear Information System (INIS) Fujimoto, J.; Ishikawa, T.; Kurihara, Y.; Jimbo, M.; Yasui, Y.; Kaneko, T.; Kon, T.; Kuroda, M.; Shimizu, Y. 2007-01-01 We report the recent development on the SUSY calculations with the help of GRACE system. GRACE/SUSY/1LOOP is the computer code which can generate Feynman diagrams in the MSSM automatically and compute one-loop amplitudes in the numerical way. We present new results of various two-body widths and chargino pair production at ILC (international linear collider) at one-loop level. (author) 5. The effective potential in the presence of several mass scales International Nuclear Information System (INIS) Casas, J.A.; Di Clemente, V.; Quiros, M. 1999-01-01 We consider the problem of improving the effective potential in mass independent schemes, as e.g. the MS-bar or DR-bar renormalization scheme, in the presence of an arbitrary number of fields with PHI-dependent masses M i(PHI c ) . We use the decoupling theorem at the scales μ i M i (PHI c ) such that the matching between the effective (low energy) and complete (high energy) one-loop theories contains no thresholds. We find that for any value of PHI c , there is a convenient scale μ * ≡ min i M i (PHI c ), at which the loop expansion has the best behaviour and the effective potential has the least μ-dependence. Furthermore, at this scale the effective potential coincides with the (improved) tree-level one in the effective field theory. The decoupling method is explicitly illustrated with a simple Higgs-Yukawa model, along with its relationship with other decoupling prescriptions and with proposed multi-scale renormalization approaches. The procedure leads to a nice suppression of potentially large logarithms and can be easily adapted to include higher-loop effects, which is explicitly shown at the two-loop level 6. The evolving Planck mass in classically scale-invariant theories Energy Technology Data Exchange (ETDEWEB) Kannike, K.; Raidal, M.; Spethmann, C.; Veermäe, H. [National Institute of Chemical Physics and Biophysics,Rävala 10, 10143 Tallinn (Estonia) 2017-04-05 We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe. 7. The evolving Planck mass in classically scale-invariant theories Science.gov (United States) Kannike, K.; Raidal, M.; Spethmann, C.; Veermäe, H. 2017-04-01 We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe. 8. Stable SUSY breaking model with O(10) eV gravitino from combined D-term gauge mediation and U(1)' mediation International Nuclear Information System (INIS) Nakayama, Yu 2008-01-01 We show a calculable example of stable supersymmetry (SUSY) breaking models with O(10) eV gravitino mass based on the combination of D-term gauge mediation and U(1)' mediation. A potential problem of the negative mass squared for the SUSY standard model (SSM) sfermions in the D-term gauge mediation is solved by the contribution from the U(1)' mediation. On the other hand, the splitting between the SSM gauginos and sfermions in the U(1)' mediation is circumvented by the contributions from the D-term gauge mediation. Since the U(1)' mediation does not introduce any new SUSY vacua, we achieve a completely stable model under thermal effects. Our model, therefore, has no cosmological difficulty 9. Predictions from a flavour GUT model combined with a SUSY breaking sector Science.gov (United States) Antusch, Stefan; Hohl, Christian 2017-10-01 We discuss how flavour GUT models in the context of supergravity can be completed with a simple SUSY breaking sector, such that the flavour-dependent (non-universal) soft breaking terms can be calculated. As an example, we discuss a model based on an SU(5) GUT symmetry and A 4 family symmetry, plus additional discrete "shaping symmetries" and a ℤ 4 R symmetry. We calculate the soft terms and identify the relevant high scale input parameters, and investigate the resulting predictions for the low scale observables, such as flavour violating processes, the sparticle spectrum and the dark matter relic density. 10. Searching for vortex solutions in graphene within an N=2 SUSY framework International Nuclear Information System (INIS) Abreu, Everton M.C.; Assis, Leonardo P.G. de; Helayel-Neto, Jose Abdalla; Nogueira, Alvaro L.M.A.; Paschoal, Ricardo C. 2011-01-01 Full text: In a recent work, we proposed an N=1-D=3 supersymmetric (SUSY) extension of Jackiw's et al. chiral gauge theory for graphene. As a first approach, we explored the idea that the chiral gauge formulation for Dirac fermions in graphene could be a sector of a wider SUSY theoretical setup, namely, the N=1 π 3 -QED. As a matter of fact, adding a superpotential operator to the N=1 π 3 -QED prescription, properly endowed with the constitutive chiral gauge and discrete symmetries that prevail in Jackiw's proposal, allows for the recognition of the Yukawa-like terms, along with spontaneous symmetry breaking configurations and corresponding non-null mass eigenvalues to the physical degrees of freedom. However, the additional requirement of invariance under a global phase transformation (GPT), meant to be associated to the electric charge, severely constrains the superpotential, leading to the exclusion of the sector that contains Jackiw's operators. As we proceed to investigate how the GP symmetry could be accommodated in a SUSY formulation, in the work of Ref. [E.M.C. Abreu, M.A. De Andrade, L.P.G. de Assis, J.A. Helayel-Neto, A.L.M.A. Nogueira and R.C. Paschoal, N=2-D=3 Supersymmetry and the Electric Charge in Graphene] we assess the straightforward N=1-generalization of Jackiw-Pi's chiral gauge theory, obtained at the cost of adding an extra superfield to the original SUSY-π 3 -QED field content. Moreover, we are able to construct an N=2-D=3 further extension of the chiral gauge theory for electrons in graphene. Such an N=2 SUSY framework provides an algebraic structure rich enough to imply a set of equations that minimizes the energy functional, namely, the well-known Bogomol'nyi equations. In this work, by taking the action of one of the supersymmetry charges to be trivial, we obtain the proper set of Bogomol'nyi equations. We finally impose a vortex-like trial solution, as we wish to discuss the resulting non-perturbative spectrum of the present N=2 setup 11. Searching for vortex solutions in graphene within an N=2 SUSY framework Energy Technology Data Exchange (ETDEWEB) Abreu, Everton M.C. [Universidade Federal Rural do Rio de Janeiro (UFRRJ), Seropedica, RJ (Brazil). Dept. de Fisica; Andrade, Marco A. de [Universidade do Estado do Rio de Janeiro (UERJ), Resende, RJ (Brazil); Grupo de Fisica Teorica Jose Leite Lopes (GFT-JLL), Petropolis, RJ (Brazil); Assis, Leonardo P.G. de [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Helayel-Neto, Jose Abdalla [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Grupo de Fisica Teorica Jose Leite Lopes (GFT-JLL), Petropolis, RJ (Brazil); Nogueira, Alvaro L.M.A.; Paschoal, Ricardo C. [Centro Federal de Educacao Tecnologica Celso Suckow da Fonseca (CEFET/RJ), Rio de Janeiro, RJ (Brazil); Grupo de Fisica Teorica Jose Leite Lopes (GFT-JLL), Petropolis, RJ (Brazil) 2011-07-01 Full text: In a recent work, we proposed an N=1-D=3 supersymmetric (SUSY) extension of Jackiw's et al. chiral gauge theory for graphene. As a first approach, we explored the idea that the chiral gauge formulation for Dirac fermions in graphene could be a sector of a wider SUSY theoretical setup, namely, the N=1 {pi}{sub 3}-QED. As a matter of fact, adding a superpotential operator to the N=1 {pi}{sub 3}-QED prescription, properly endowed with the constitutive chiral gauge and discrete symmetries that prevail in Jackiw's proposal, allows for the recognition of the Yukawa-like terms, along with spontaneous symmetry breaking configurations and corresponding non-null mass eigenvalues to the physical degrees of freedom. However, the additional requirement of invariance under a global phase transformation (GPT), meant to be associated to the electric charge, severely constrains the superpotential, leading to the exclusion of the sector that contains Jackiw's operators. As we proceed to investigate how the GP symmetry could be accommodated in a SUSY formulation, in the work of Ref. [E.M.C. Abreu, M.A. De Andrade, L.P.G. de Assis, J.A. Helayel-Neto, A.L.M.A. Nogueira and R.C. Paschoal, N=2-D=3 Supersymmetry and the Electric Charge in Graphene] we assess the straightforward N=1-generalization of Jackiw-Pi's chiral gauge theory, obtained at the cost of adding an extra superfield to the original SUSY-{pi}{sub 3}-QED field content. Moreover, we are able to construct an N=2-D=3 further extension of the chiral gauge theory for electrons in graphene. Such an N=2 SUSY framework provides an algebraic structure rich enough to imply a set of equations that minimizes the energy functional, namely, the well-known Bogomol'nyi equations. In this work, by taking the action of one of the supersymmetry charges to be trivial, we obtain the proper set of Bogomol'nyi equations. We finally impose a vortex-like trial solution, as we wish to discuss the resulting non 12. Large scale electromechanical transistor with application in mass sensing Energy Technology Data Exchange (ETDEWEB) Jin, Leisheng; Li, Lijie, E-mail: [email protected] [Multidisciplinary Nanotechnology Centre, College of Engineering, Swansea University, Swansea SA2 8PP (United Kingdom) 2014-12-07 Nanomechanical transistor (NMT) has evolved from the single electron transistor, a device that operates by shuttling electrons with a self-excited central conductor. The unfavoured aspects of the NMT are the complexity of the fabrication process and its signal processing unit, which could potentially be overcome by designing much larger devices. This paper reports a new design of large scale electromechanical transistor (LSEMT), still taking advantage of the principle of shuttling electrons. However, because of the large size, nonlinear electrostatic forces induced by the transistor itself are not sufficient to drive the mechanical member into vibration—an external force has to be used. In this paper, a LSEMT device is modelled, and its new application in mass sensing is postulated using two coupled mechanical cantilevers, with one of them being embedded in the transistor. The sensor is capable of detecting added mass using the eigenstate shifts method by reading the change of electrical current from the transistor, which has much higher sensitivity than conventional eigenfrequency shift approach used in classical cantilever based mass sensors. Numerical simulations are conducted to investigate the performance of the mass sensor. 13. Analytical expressions for radiatively corrected Higgs masses and couplings in the MSSM International Nuclear Information System (INIS) Carena, M. 1995-03-01 We propose, for the computation of the Higgs mass spectrum and couplings, a renormalization-group improved leading-log approximation, where the renormalization scale is fixed to the top-quark pole mass. For the case m A ∝M SUSY , our leading-log approximation differs by less than 2 GeV from previous results on the Higgs mass computed using a nearly scale independent renormalization-group improved effective potential up to next-to-leading order. Moreover, for the general case m A SUSY , we provide analytical formulae (including two-loop leading-log corrections) for all the masses and couplings in the Higgs sector. For M SUSY A , tan β and the stop mixing parameters, they reproduce the numerical renormalization-group improved leading-log result for the Higgs masses with an error of less than 3 GeV. For the Higgs couplings, our analytical formulae reproduce the numerical results equally well. Comparison with other methods is also performed. (orig.) 14. Prospects for mass unification at low energy scales International Nuclear Information System (INIS) Volkas, R.R. 1995-01-01 A simple Pati-Salam SU(4) model with a low symmetry breaking scale of about 1000 TeV is presented. The analysis concentrates on calculating radiative corrections to tree level mass relations for third generation fermions. The tree-level relation m b /m τ = 1 predicted by such models can receive large radiative corrections up to about 50% due to threshold effects at the mass unification scale. These corrections are thus of about the same importance as those that give rise to renormalisation group running. The high figure of 50% can be achieved because l-loop graphs involving the physical charged Higgs boson give corrections to m τ -m b that are proportional to the large top quark mass. These corrections can either increase or decrease m b /m τ depending on the value of an unknown parameter. They can also be made to vanish through a fine-tuning. A related model of tree-level t-b-τ unification which uses the identification of SU(2) R with custodial SU(2) is then discussed. A curious relation m b ∼ √2m τ is found to be satisfied at tree-level in this model. The overall conclusion of this work is that the tree-level relation m b =m τ at low scales such as 1000 TeV or somewhat higher can produce a successful value for m b /m τ after corrections, but one must be mindful that radiative corrections beyond those incorporated through the renormalisation group can be very important. 14 refs., 7 figs 15. Prospects for mass unification at low energy scales Energy Technology Data Exchange (ETDEWEB) Volkas, R.R. 1995-12-31 A simple Pati-Salam SU(4) model with a low symmetry breaking scale of about 1000 TeV is presented. The analysis concentrates on calculating radiative corrections to tree level mass relations for third generation fermions. The tree-level relation m{sub b}/m{sub {tau}} = 1 predicted by such models can receive large radiative corrections up to about 50% due to threshold effects at the mass unification scale. These corrections are thus of about the same importance as those that give rise to renormalisation group running. The high figure of 50% can be achieved because l-loop graphs involving the physical charged Higgs boson give corrections to m{sub {tau}} -m{sub b} that are proportional to the large top quark mass. These corrections can either increase or decrease m{sub b}/m{sub {tau}} depending on the value of an unknown parameter. They can also be made to vanish through a fine-tuning. A related model of tree-level t-b-{tau} unification which uses the identification of SU(2){sub R} with custodial SU(2) is then discussed. A curious relation m{sub b}{approx} {radical}2m{sub {tau}} is found to be satisfied at tree-level in this model. The overall conclusion of this work is that the tree-level relation m{sub b}=m{sub {tau}} at low scales such as 1000 TeV or somewhat higher can produce a successful value for m{sub b}/m{sub {tau}} after corrections, but one must be mindful that radiative corrections beyond those incorporated through the renormalisation group can be very important. 14 refs., 7 figs. 16. On Two-Scale Modelling of Heat and Mass Transfer International Nuclear Information System (INIS) Vala, J.; Stastnik, S. 2008-01-01 Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro- and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies. 17. On Two-Scale Modelling of Heat and Mass Transfer Science.gov (United States) Vala, J.; Št'astník, S. 2008-09-01 Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro- and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies. 18. Evidence of ghost suppression in gluon mass scale dynamics Science.gov (United States) Aguilar, A. C.; Binosi, D.; Figueiredo, C. T.; Papavassiliou, J. 2018-03-01 In this work we study the impact that the ghost sector of pure Yang-Mills theories may have on the generation of a dynamical gauge boson mass scale, which hinges on the appearance of massless poles in the fundamental vertices of the theory, and the subsequent realization of the well-known Schwinger mechanism. The process responsible for the formation of such structures is itself dynamical in nature, and is governed by a set of Bethe-Salpeter type of integral equations. While in previous studies the presence of massless poles was assumed to be exclusively associated with the background-gauge three-gluon vertex, in the present analysis we allow them to appear also in the corresponding ghost-gluon vertex. The full analysis of the resulting Bethe-Salpeter system reveals that the contribution of the poles associated with the ghost-gluon vertex are particularly suppressed, their sole discernible effect being a slight modification in the running of the gluon mass scale, for momenta larger than a few GeV. In addition, we examine the behavior of the (background-gauge) ghost-gluon vertex in the limit of vanishing ghost momentum, and derive the corresponding version of Taylor's theorem. These considerations, together with a suitable Ansatz, permit us the full reconstruction of the pole sector of the two vertices involved. 19. Mart ja Mari-Ann Susi taotlevad omanikena Concordia pankrotti / Andri Maimets Index Scriptorium Estoniae Maimets, Andri, 1979- 2003-01-01 Concordia Ülikooli rektor Mart Susi esitas kohtule avalduse, milles taotleb ülikooli pidanud Concordia Varahalduse OÜ pankroti väljakuulutamist. Vt. samas: Mari-Ann Susi õigustas ülikooli raha kasutamist 20. Search for SUSY with two same-sign leptons or three leptons and jets at $\\sqrt{s} = 13 \\text{ TeV}$ with the ATLAS Detector CERN Document Server Liu, Yang; The ATLAS collaboration 2017-01-01 Supersymmetry (SUSY) is a well motivated extension of the Standard Model (SM) that postulates the existence of a superpartner for each SM particle. A search for strongly produced SUSY particles decaying to a pair of two isolated \\textbf{same-sign leptons (SS)} or \\textbf{three leptons (3L)} has been carried out using the complete data set collected by the ATLAS experiment in 2015-16 at 13 TeV ($36.5 fb^{-1}$). The analysis benefits from a low SM background and uses looser kinematic requirements compared to other beyond the SM (BSM) searches which increases its sensitivity to scenarios with small mass differences between the SUSY particles, or in which R-parity is not conserved. The results are interpreted in the context of \\textbf{R-parity conserving (RPC)} or \\textbf{R-parity violating (RPV)} simplified signal models 1. Automated calculation of sinθ{sub W} and M{sub W} from muon decay within FlexibleSUSY Energy Technology Data Exchange (ETDEWEB) Bach, Markus; Stoeckinger, Dominik [IKTP, TU Dresden (Germany); Voigt, Alexander [DESY, Hamburg (Germany) 2016-07-01 The spectrum generator generator FlexibleSUSY can be utilized to investigate a variety of supersymmetric and non-supersymmetric models. We present an implementation which calculates the weak mixing angle from the precisely measured muon decay, especially taking vertex and box diagram corrections of the respective model into account. This framework also offers a prediction of the W boson mass which can be compared to the experimental value and thus used to exclude parameter regions. 2. Susy Les Houches accord: Interfacing SUSY spectrum calculators, decay packages, and event generators International Nuclear Information System (INIS) Skands, P.; Allanach, B.C.; Baer, H. 2003-11-01 An accord specifying generic file structures for 1) supersymmetric model specifications and input parameters, 2) electroweak scale supersymmetric mass and coupling spectra, and 3) decay tables is defined, to provide a universal interface between spectrum calculation programs, decay packages, and high energy physics event generators. (orig.) 3. Global-scale hydrological response to future glacier mass loss Science.gov (United States) Huss, Matthias; Hock, Regine 2018-01-01 Worldwide glacier retreat and associated future runoff changes raise major concerns over the sustainability of global water resources1-4, but global-scale assessments of glacier decline and the resulting hydrological consequences are scarce5,6. Here we compute global glacier runoff changes for 56 large-scale glacierized drainage basins to 2100 and analyse the glacial impact on streamflow. In roughly half of the investigated basins, the modelled annual glacier runoff continues to rise until a maximum (peak water') is reached, beyond which runoff steadily declines. In the remaining basins, this tipping point has already been passed. Peak water occurs later in basins with larger glaciers and higher ice-cover fractions. Typically, future glacier runoff increases in early summer but decreases in late summer. Although most of the 56 basins have less than 2% ice coverage, by 2100 one-third of them might experience runoff decreases greater than 10% due to glacier mass loss in at least one month of the melt season, with the largest reductions in central Asia and the Andes. We conclude that, even in large-scale basins with minimal ice-cover fraction, the downstream hydrological effects of continued glacier wastage can be substantial, but the magnitudes vary greatly among basins and throughout the melt season. 4. Dark matter and Bs→μ+μ- with minimal SO10 soft SUSY breaking International Nuclear Information System (INIS) Dermisek, R.; Roszkowski, L.; Ruiz de Austri, R.; Raby, S. 2003-01-01 CMSSM boundary conditions are usually used when calculating cosmological dark matter densities. In this paper we calculate the cosmological density of dark matter in the MSSM using minimal SO 10 soft SUSY breaking boundary conditions. These boundary conditions incorporate several attractive features: they are consistent with SO 10 Yukawa unification, they result in a 'natural' inverted scalar mass hierarchy and they reduce the dimension 5 operator contribution to the proton decay rate. With regards to dark matter, on the other hand, this is to a large extent an unexplored territory with large squark and slepton masses m 16 , large A 0 and small {μ,M 1/2 }. We find that in most regions of parameter space the cosmological density of dark matter is considerably less than required by the data. However there is a well-defined, narrow region of parameter space which provides the observed relic density of dark matter, as well as a good fit to precision electroweak data, including top, bottom and tau masses, and acceptable bounds on the branching fraction of B s →μ + μ - . We present predictions for Higgs and SUSY spectra, the dark matter detection cross section and the branching ratio BR(B s →μ + μ - ) in this region of parameter space. (author) 5. Validation and operational measurements with SUSIE – A sar ice motion processing chain developed within promice (Programme for monitoring of Greenland ice-sheet) DEFF Research Database (Denmark) Merryman Boncori, John Peter; Dall, Jørgen; Ahlstrøm, A. P. 2010-01-01 This paper describes the validation of an ice-motion processing chain developed for the PROMICE project – a long-term program funded by the Danish ministry of Climate and Energy to monitor the mass budget of the Greenland ice-sheet. The processor, named SUSIE, (Scripts and Utilities for SAR Ice... 6. Coupling between scattering channels with SUSY transformations for equal thresholds International Nuclear Information System (INIS) Pupasov, Andrey M; Samsonov, Boris F; Sparenberg, Jean-Marc; Baye, Daniel 2009-01-01 Supersymmetric (SUSY) transformations of the multichannel Schroedinger equation with equal thresholds and arbitrary partial waves in all channels are studied. The structures of the transformation function and the superpotential are analysed. Relations between Jost and scattering matrices of superpartner potentials are obtained. In particular, we show that a special type of SUSY transformation allows us to introduce a coupling between scattering channels starting from a potential with an uncoupled scattering matrix. The possibility for this coupling to be trivial is discussed. We show that the transformation introduces bound and virtual states with a definite degeneracy at the factorization energy. A detailed study of the potential and scattering matrices is given for the 2 x 2 case. The possibility of inverting coupled-channel scattering data by such a SUSY transformation is demonstrated by several examples (s-s, s-p and s-d partial waves) 7. Low mass-scale parity restoration in expanded gauge theories International Nuclear Information System (INIS) Rajpoot, S. 1982-07-01 It is shown that schemes of grand unification with SU(2n) 4 gauge symmetry permit the embedding of the left-right symmetric SU(2)sub(L)xSU(2)sub(R)xU(1)xSU(3) intermediate symmetry at relatively low energies (between 250 GeV and 1 TeV) as well as allowing light unification mass-scales ( 5 TeV) if n>=3 for values of the weak angle Sin 2 thetasub(W) and the strong coupling αsub(s) in the ranges 0.20 2 thetasub(W)<=0.25, 0.10<=αsub(s)<=0.15. (author) 8. RPC Production at General Tecnica: a mass scale production International Nuclear Information System (INIS) Della Volpe, D.; Morganti, S. 2006-01-01 The construction of LHC has deeply changed the RPC production. The enormous amount of detector needed and the strong requirements on gas volume quality had a deep impact on the production chain and on the QC and QA at the production site. This basically has brought the RPC from an almost hand-crafted detector to a medium scale mass product. The most critical aspects of the production chain have been modified and/or improved introducing new and more rigorous QC and QA procedures to guarantee the detector quality and improve the management of storage and the procurement on materials. Here it will be presented the work carried on in the last four year at the production site to improve and check the quality and the results achieved. Something like 10000 RPC were produced between 2002 and 2005. Also a preliminary and rough analysis on the efficiencies of the various phases in the chain production based on ATLAS production will be presented 9. Membranes for nanometer-scale mass fast transport Science.gov (United States) Bakajin, Olgica [San Leandro, CA; Holt, Jason [Berkeley, CA; Noy, Aleksandr [Belmont, CA; Park, Hyung Gyu [Oakland, CA 2011-10-18 Nanoporous membranes comprising single walled, double walled, and multiwalled carbon nanotubes embedded in a matrix material were fabricated for fluid mechanics and mass transfer studies on the nanometer scale and commercial applications. Average pore size can be 2 nm to 20 nm, or seven nm or less, or two nanometers or less. The membrane can be free of large voids spanning the membrane such that transport of material such as gas or liquid occurs exclusively through the tubes. Fast fluid, vapor, and liquid transport are observed. Versatile micromachining methods can be used for membrane fabrication. A single chip can comprise multiple membranes. These membranes are a robust platform for the study of confined molecular transport, with applications in liquid and gas separations and chemical sensing including desalination, dialysis, and fabric formation. 10. Fixing the EW scale in supersymmetric models after the Higgs discovery CERN Document Server Ghilencea, D M 2013-01-01 TeV-scale supersymmetry was originally introduced to solve the hierarchy problem and therefore fix the electroweak (EW) scale in the presence of quantum corrections. Numerical methods testing the SUSY models often report a good likelihood L (or chi^2=-2ln L) to fit the data {\\it including} the EW scale itself (m_Z^0) with a {\\it simultaneously} large fine-tuning i.e. a large variation of this scale under a small variation of the SUSY parameters. We argue that this is inconsistent and we identify the origin of this problem. Our claim is that the likelihood (or chi^2) to fit the data that is usually reported in such models does not account for the chi^2 cost of fixing the EW scale. When this constraint is implemented, the likelihood (or chi^2) receives a significant correction (delta_chi^2) that worsens the current data fits of SUSY models. We estimate this correction for the models: constrained MSSM (CMSSM), models with non-universal gaugino masses (NUGM) or higgs soft masses (NUHM1, NUHM2), the NMSSM and the ... 11. Peter J Derrick and the Grand Scale 'Magnificent Mass Machine' mass spectrometer at Warwick. Science.gov (United States) Colburn, A W; Derrick, Peter J; Bowen, Richard D 2017-12-01 The value of the Grand Scale 'Magnificent Mass Machine' mass spectrometer in investigating the reactivity of ions in the gas phase is illustrated by a brief analysis of previously unpublished work on metastable ionised n-pentyl methyl ether, which loses predominantly methanol and an ethyl radical, with very minor contributions for elimination of ethane and water. Expulsion of an ethyl radical is interpreted in terms of isomerisation to ionised 3-pentyl methyl ether, via distonic ions and, possibly, an ion-neutral complex comprising ionised ethylcyclopropane and methanol. This explanation is consistent with the closely similar behaviour of the labelled analogues, C 3 H 7 CH 2 CD 2 OCH 3 +. and C 3 H 7 CD 2 CH 2 OCH 3 +. , and is supported by the greater kinetic energy release associated with loss of ethane from ionised n-propyl methyl ether compared to that starting from directly generated ionised 3-pentyl methyl ether. 12. Direct geoelectrical evidence of mass transfer at the laboratory scale Science.gov (United States) Swanson, Ryan D.; Singha, Kamini; Day-Lewis, Frederick D.; Binley, Andrew; Keating, Kristina; Haggerty, Roy 2012-10-01 Previous field-scale experimental data and numerical modeling suggest that the dual-domain mass transfer (DDMT) of electrolytic tracers has an observable geoelectrical signature. Here we present controlled laboratory experiments confirming the electrical signature of DDMT and demonstrate the use of time-lapse electrical measurements in conjunction with concentration measurements to estimate the parameters controlling DDMT, i.e., the mobile and immobile porosity and rate at which solute exchanges between mobile and immobile domains. We conducted column tracer tests on unconsolidated quartz sand and a material with a high secondary porosity: the zeolite clinoptilolite. During NaCl tracer tests we collected nearly colocated bulk direct-current electrical conductivity (σb) and fluid conductivity (σf) measurements. Our results for the zeolite show (1) extensive tailing and (2) a hysteretic relation between σf and σb, thus providing evidence of mass transfer not observed within the quartz sand. To identify best-fit parameters and evaluate parameter sensitivity, we performed over 2700 simulations of σf, varying the immobile and mobile domain and mass transfer rate. We emphasized the fit to late-time tailing by minimizing the Box-Cox power transformed root-mean square error between the observed and simulated σf. Low-field proton nuclear magnetic resonance (NMR) measurements provide an independent quantification of the volumes of the mobile and immobile domains. The best-fit parameters based on σf match the NMR measurements of the immobile and mobile domain porosities and provide the first direct electrical evidence for DDMT. Our results underscore the potential of using electrical measurements for DDMT parameter inference. 13. The SUSY oscillator from local geometry: Dynamics and coherent states International Nuclear Information System (INIS) Thienel, H.P. 1994-01-01 The choice of a coordinate chart on an analytical R n (R a n ) provides a representation of the n-dimensional SUSY oscillator. The corresponding Hilbert space is Cartan's exterior algebra endowed with a suitable scalar product. The exterior derivative gives rise to the algebra of the n-dimensional SUSY oscillator. Its euclidean dynamics is an inherent consequence of the geometry imposed by the Lie derivative generating the dilations, i.e. evolution of the quantum system corresponds to parametrization of a sequence of charts by euclidean time. Coherent states emerge as a natural structure related to the Lie derivative generating the translations. (orig.) 14. A Bottom-Up Approach to SUSY Analyses Energy Technology Data Exchange (ETDEWEB) Horn, Claus; /SLAC 2011-11-11 This paper proposes a new way to do event generation and analysis in searches for new physics at the LHC. An abstract notation is used to describe the new particles on a level which better corresponds to detector resolution of LHC experiments. In this way the SUSY discovery space can be decomposed into a small number of eigenmodes each with only a few parameters, which allows to investigate the SUSY parameter space in a model-independent way. By focusing on the experimental observables for each process investigated the Bottom-Up Approach allows to systematically study the boarders of the experimental efficiencies and thus to extend the sensitivity for new physics. 15. Reconstruction of tau leptons and prospects for SUSY in ATLAS International Nuclear Information System (INIS) Zendler, Carolin 2010-01-01 Final states with tau leptons may play a special role among the broad variety of signatures for the production of supersymmetric particles at the LHC. The algorithms for tau reconstruction and identification are discussed, which are essential ingredients to reject the huge background from QCD processes. The status of analyses of SUSY tau lepton final states within the ATLAS experiment at the LHC are presented, which range from a study of semi-inclusive discovery prospects to more exclusive processes with two tau leptons from χ-tilde 2 0 decays and their implications for the determination of SUSY parameters. Also, the prospects for exploiting tau lepton polarization are discussed. 16. Critical masses of bare metal spheres using SCALE/XSDRN International Nuclear Information System (INIS) Wright, R.Q.; Jordan, W.C.; Westfall, R.M. 2000-01-01 minimum critical masses. The minimum critical masses of metal spheres using the SCALE/XSDRN program have been calculated and are given in Sec. II of this paper. Results for reflected spheres are also available. Results for 28 actinides are included in Table 1; only 1 nuclide, 232 Pa (T 1/2 = 1.31 day), has a half-life <40 days 17. Testing SUSY at the LHC: Electroweak and Dark matter fine tuning at two-loop order CERN Document Server Cassel, S; Ross, G G 2010-01-01 In the framework of the Constrained Minimal Supersymmetric Standard Model (CMSSM) we evaluate the electroweak fine tuning measure that provides a quantitative test of supersymmetry as a solution to the hierarchy problem. Taking account of current experimental constraints we compute the fine tuning at two-loop order and determine the limits on the CMSSM parameter space and the measurements at the LHC most relevant in covering it. Without imposing the LEPII bound on the Higgs mass, it is shown that the fine tuning computed at two-loop has a minimum $\\Delta=8.8$ corresponding to a Higgs mass $m_h=114\\pm 2$ GeV. Adding the constraint that the SUSY dark matter relic density should be within present bounds we find $\\Delta=15$ corresponding to $m_h=114.7\\pm 2$ GeV and this rises to $\\Delta=17.8$ ($m_h=115.9\\pm 2$ GeV) for SUSY dark matter abundance within 3$\\sigma$ of the WMAP constraint. We extend the analysis to include the contribution of dark matter fine tuning. In this case the overall fine tuning and Higgs mas... 18. Bose-fermi symmetries and SUSY in nuclei International Nuclear Information System (INIS) Casten, R.F. 1986-01-01 Most of the comparison with theory has compared energy levels and we have seen many beautiful examples of one-to-one level correspondences, sometimes supported with a few B(E2) values. However, what we really need to check, the author thinks, is the structural correspondence, to make sure these levels really correspond to each other, and that the energy level agreement is not just accidental; for that we need to look at transfer reactions, and more B(E2)'s. This brings up the very important question of the transfer operator. The author hopes that its importance can be seen in recent cases where a few B(E2)'s for a few transfer strengths have substantially changed the correspondence between theoretical and experimental levels even though the overall energy level agreement is neither better or worse. So it's clearly sensitive to that question. Also cases have been seen now where several different supergroups have been applied to the same regions, U(6/4) and U(6/20) for example, to the mass 130 region, and so the question of the single-particle spaces and the single-particle energies is an important one. The question of microscopic understanding of the parameters and the interactions, these bose-fermi symmetries is important since it probes the underlying physical basis. And finally there have be some very interesting, what the author calls ''exotic'' extensions of bose-fermi symmetry ideas presented at this meeting. One is the extension to odd-odd nuclei, another is the generalized SUSY extension that can apply to transition regions, and this is the interesting beta decay calculations of Dobes that were reported yesterday, and probably some others the author has missed 19. From high-scale leptogenesis to low-scale one-loop neutrino mass generation Science.gov (United States) Zhou, Hang; Gu, Pei-Hong 2018-02-01 We show that a high-scale leptogenesis can be consistent with a low-scale one-loop neutrino mass generation. Our models are based on the SU(3)c × SU(2)L × U(1)Y × U(1) B - L gauge groups. Except a complex singlet scalar for the U(1) B - L symmetry breaking, the other new scalars and fermions (one scalar doublet, two or more real scalar singlets/triplets and three right-handed neutrinos) are odd under an unbroken Z2 discrete symmetry. The real scalar decays can produce an asymmetry stored in the new scalar doublet which subsequently decays into the standard model lepton doublets and the right-handed neutrinos. The lepton asymmetry in the standard model leptons then can be partially converted to a baryon asymmetry by the sphaleron processes. By integrating out the heavy scalar singlets/triplets, we can realize an effective theory to radiatively generate the small neutrino masses at the TeV scale. Furthermore, the lightest right-handed neutrino can serve as a dark matter candidate. 20. Micro-scale mass-transfer variations during electrodeposition Energy Technology Data Exchange (ETDEWEB) Sutija, D.P. 1991-08-01 Results of two studies on micro-scale mass-transfer enhancement are reported: (1) Profiled cross-sections of striated zinc surfaces deposited in laminar channel flow were analyzed with fast-fourier transforms (FFT) to determine preferred striation wavelengths. Striation frequency increases with current density until a minimum separation between striae of 150 {mu}m is reached. Beyond this point, independent of substrate used, striae meld together and form a relatively smooth, nodular deposit. Substrates equipped with artificial micron-sized protrusions result in significantly different macro-morphology in zinc deposits. Micro-patterned electrodes (MPE) with hemispherical protrusions 5 {mu}m in diameter yield thin zinc striae at current densities that ordinarily produce random nodular deposits. MPEs with artificial hemi-cylinders, 2.5 {mu}m in height and spaced 250 {mu}m apart, form striae with a period which matches the spacing of micron-sized ridges. (2) A novel, corrosion-resistant micromosaic electrode was fabricated on a silicon wafer. Measurements of mass-transport enhancement to a vertical micromosaic electrode caused by parallel bubble streams rising inside of the diffusion boundary-layer demonstrated the presence of two co-temporal enhancement mechanisms: surface-renewal increases the limiting current within five bubble diameters of the rising column, while bubble-induced laminar flows cause weaker enhancement over a much broader swath. The enhancement caused by bubble curtains is predicted accurately by linear superposition of single-column enhancements. Two columns of smaller H{sub 2} bubbles generated at the same volumetric rate as a single column of larger bubbles cause higher peak and far-field enhancements. 168 refs., 96 figs., 6 tabs. 1. A common source for neutrino and sparticle masses CERN Document Server Brignole, Andrea; Rossi, Anna 2010-01-01 We discuss supersymmetric scenarios in which neutrino masses arise from effective d=6 operators in the Kahler potential (including SUSY-breaking insertions). Simple explicit realizations of those Kahler operators are presented in the context of the type II seesaw. An appealing scenario emerges upon identifying the seesaw mediators with SUSY-breaking messengers. 2. Mass splittings within composite Goldstone supermultiplets from broken supersymmetry International Nuclear Information System (INIS) Clark, T.E.; Love, S.T. 1985-01-01 The supersymmetric (SUSY) Dashen formulas are modified to include effects of softly broken supersymmetry and are used to compute the mass splittings and differences in decay constants among the various components of a Goldstone supermultiplet. The general results are applied to chiral-symmetry breaking in two-flavor SUSY QCD 3. SUSY formalism for the symmetric double well potential symmetric double well potential barrier we have obtained a class of exactly solvable potentials subject to moving boundary condition. The eigenstates are also obtained by the same technique. Keywords. SUSY; moving boundary condition; exactly solvable; symmetric double well; NH3 molecule. PACS Nos 02.30.Ik; 03.50. 4. F-theory, GUTs, and the weak scale International Nuclear Information System (INIS) Heckman, Jonathan J.; Vafa, Cumrun 2009-01-01 In this paper we study a deformation of gauge mediated supersymmetry breaking in a class of local F-theory GUT models where the scale of supersymmetry breaking determines the value of the μ term. Geometrically correlating these two scales constrains the soft SUSY breaking parameters of the MSSM. In this scenario, the hidden SUSY breaking sector involves an anomalous U(1) Peccei-Quinn symmetry which forbids bare μ and Bμ terms. This sector typically breaks supersymmetry at the desired range of energy scales through a simple stringy hybrid of a Fayet and Polonyi model. A variant of the Giudice-Masiero mechanism generates the value μ ∼ 10 2 -10 3 GeV when the hidden sector scale of supersymmetry breaking is F 1/2 ∼ 10 8.5 GeV. Further, the Bμ problem is solved due to the mild hierarchy between the GUT scale and Planck scale. These models relate SUSY breaking with the QCD axion, and solve the strong CP problem through an axion with decay constant f a ∼ M GUT cμ/Λ, where Λ ∼ 10 5 GeV is the characteristic scale of gaugino mass unification in gauge mediated models, and the ratio μ/Λ ∼ M GUT /M pl ∼ 10 -3 . We find f a ∼ 10 12 GeV, which is near the high end of the phenomenologically viable window. Here, the axino is the goldstino mode which is eaten by the gravitino. The gravitino is the LSP with a mass of about 10 1 -10 2 MeV, and a bino-like neutralino is (typically) the NLSP with mass of about 10 2 -10 3 GeV. Compatibility with electroweak symmetry breaking also determines the value of tanβ ∼ 30±7. 5. Non-simplified SUSY. {tau}-coannihilation at LHC and ILC Energy Technology Data Exchange (ETDEWEB) Berggren, M.; Cakir, A.; Krueger, D.; List, J.; Lobanov, A.; Melzer-Pellmann, I.A. 2013-07-15 Simplified models have become a widely used and important tool to cover the more diverse phenomenology beyond constrained SUSY models. However, they come with a substantial number of caveats themselves, and great care needs to be taken when drawing conclusions from limits based on the simplified approach. To illustrate this issue with a concrete example, we examine the applicability of simplified model results to a series of full SUSY model points which all feature a small {tau} -LSP mass difference, and are compatible with electroweak and flavor precision observables as well as current LHC results. Various channels have been studied using the Snowmass Combined LHC detector implementation in the Delphes simulation package, as well as the Letter of Intent or Technical Design Report simulations of the ILD detector concept at the ILC. We investigated both the LHC and ILC capabilities for discovery, separation and identification of all parts of the spectrum. While parts of the spectrum would be discovered at the LHC, there is substantial room for further discoveries and property determination at the ILC. 6. Squark production in R-symmetric SUSY with Dirac gluinos. NLO corrections Energy Technology Data Exchange (ETDEWEB) Diessner, Philip [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Kotlarski, Wojciech [Technische Univ. Dresden (Germany). Inst. fuer Kern- und Teilchenphysik; Warsaw Univ. (Poland). Faculty of Physics; Liebschner, Sebastian; Stoeckinger, Dominik [Technische Univ. Dresden (Germany). Inst. fuer Kern- und Teilchenphysik 2017-11-15 R-symmetry leads to a distinct realisation of SUSY with a significantly modified coloured sector featuring a Dirac gluino and a scalar colour octet (sgluon). We present the impact of R-symmetry on squark production at the 13 TeV LHC. We study the total cross sections and their NLO corrections from all strongly interacting states, their dependence on the Dirac gluino mass and sgluon mass as well as their systematics for selected benchmark points. We find that tree-level cross sections in the R-symmetric model are reduced compared to the MSSM but the NLO K-factors are generally larger in the order of ten to twenty per cent. In the course of this work we derive the required DREG → DRED transition counterterms and necessary on-shell renormalisation constants. The real corrections are treated using FKS subtraction, with results cross checked against an independent calculation employing the two cut phase space slicing method. 7. Squark production in R-symmetric SUSY with Dirac gluinos. NLO corrections International Nuclear Information System (INIS) Diessner, Philip; Kotlarski, Wojciech; Warsaw Univ.; Liebschner, Sebastian; Stoeckinger, Dominik 2017-11-01 R-symmetry leads to a distinct realisation of SUSY with a significantly modified coloured sector featuring a Dirac gluino and a scalar colour octet (sgluon). We present the impact of R-symmetry on squark production at the 13 TeV LHC. We study the total cross sections and their NLO corrections from all strongly interacting states, their dependence on the Dirac gluino mass and sgluon mass as well as their systematics for selected benchmark points. We find that tree-level cross sections in the R-symmetric model are reduced compared to the MSSM but the NLO K-factors are generally larger in the order of ten to twenty per cent. In the course of this work we derive the required DREG → DRED transition counterterms and necessary on-shell renormalisation constants. The real corrections are treated using FKS subtraction, with results cross checked against an independent calculation employing the two cut phase space slicing method. 8. Search for resonant sneutrino production in R-parity violating SUSY scenarios with CMS Energy Technology Data Exchange (ETDEWEB) Keller, Henning; Erdweg, Soeren; Gueth, Andreas; Hebbeker, Thomas; Meyer, Arnd; Mukherjee, Swagata [III. Physikalisches Institut A, RWTH Aachen (Germany) 2016-07-01 Supersymmetric models are among the most promising extensions of the standard model. In many models R-parity is said to be conserved. However, allowing R-parity violation can permit interesting final states and signatures that are not covered by SUSY scenarios with R-parity conservation. The decay of a resonant sneutrino to two standard model leptons of different flavour is analyzed. The focus lies on the electron-muon final state investigating the R-parity violating couplings and the mass of the resonantly produced sneutrino. The analysis is based on the 2015 data of proton-proton collisions corresponding to an integrated luminosity of 2.5 fb{sup -1} at a centre-of-mass energy of 13 TeV recorded with the CMS detector at the LHC. 9. Scaling Factor Estimation Using an Optimized Mass Change Strategy, Part 1: Theory DEFF Research Database (Denmark) Aenlle, Manuel López; Fernández, Pelayo Fernández; Brincker, Rune 2007-01-01 In natural input modal analysis, only un-scaled mode shapes can be obtained. The mass change method is, in many cases, the simplest way to estimate the scaling factors, which involves repeated modal testing after changing the mass in different points of the structure where the mode shapes are known....... The scaling factors are determined using the natural frequencies and mode shapes of both the modified and the unmodified structure. However, the uncertainty on the scaling factor estimation depends on the modal analysis and the mass change strategy (number, magnitude and location of the masses) used to modify... 10. Exercise-induced maximum metabolic rate scaled to body mass by ... African Journals Online (AJOL) Exercise-induced maximum metabolic rate scaled to body mass by the fractal ... rate scaling is that exercise-induced maximum aerobic metabolic rate (MMR) is ... muscle stress limitation, and maximized oxygen delivery and metabolic rates. 11. Calibrating the Planck Cluster Mass Scale with Cluster Velocity Dispersions Science.gov (United States) Amodeo, Stefania; Mei, Simona; Stanford, Spencer A.; Bartlett, James G.; Melin, Jean-Baptiste; Lawrence, Charles R.; Chary, Ranga-Ram; Shim, Hyunjin; Marleau, Francine; Stern, Daniel 2017-08-01 We measure the Planck cluster mass bias using dynamical mass measurements based on velocity dispersions of a subsample of 17 Planck-detected clusters. The velocity dispersions were calculated using redshifts determined from spectra that were obtained at the Gemini observatory with the GMOS multi-object spectrograph. We correct our estimates for effects due to finite aperture, Eddington bias, and correlated scatter between velocity dispersion and the Planck mass proxy. The result for the mass bias parameter, (1-b), depends on the value of the galaxy velocity bias, {b}{{v}}, adopted from simulations: (1-b)=(0.51+/- 0.09){b}{{v}}3. Using a velocity bias of {b}{{v}}=1.08 from Munari et al., we obtain (1-b)=0.64+/- 0.11, I.e., an error of 17% on the mass bias measurement with 17 clusters. This mass bias value is consistent with most previous weak-lensing determinations. It lies within 1σ of the value that is needed to reconcile the Planck cluster counts with the Planck primary cosmic microwave background constraints. We emphasize that uncertainty in the velocity bias severely hampers the precision of the measurements of the mass bias using velocity dispersions. On the other hand, when we fix the Planck mass bias using the constraints from Penna-Lima et al., based on weak-lensing measurements, we obtain a positive velocity bias of {b}{{v}}≳ 0.9 at 3σ . 12. Heavy colored SUSY partners from deflected anomaly mediation Energy Technology Data Exchange (ETDEWEB) Wang, Fei [Department of Physics and Engineering, Zhengzhou University,Zhengzhou 450000 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Academia Sinica,Beijing 100190 (China); Wang, Wenyu [Institute of Theoretical Physics, College of Applied Science, Beijing University of Technology,Beijing 100124 (China); Yang, Jin Min; Zhang, Yang [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Academia Sinica,Beijing 100190 (China) 2015-07-27 We propose a deflected anomaly mediation scenario from SUSY QCD which can lead to both positive and negative deflection parameters (there is a smooth transition between these two deflection parameter regions by adjusting certain couplings). Such a scenario can naturally give a SUSY spectrum in which all the colored sparticles are heavy while the sleptons are light. As a result, the discrepancy between the Brookheaven g{sub μ}−2 experiment and LHC data can be reconciled in this scenario. We also find that the parameter space for explaining the g{sub μ}−2 anomaly at 1σ level can be fully covered by the future LUX-ZEPLIN 7.2 Ton experiment. 13. Finding viable models in SUSY parameter spaces with signal specific discovery potential Science.gov (United States) Burgess, Thomas; Lindroos, Jan Øye; Lipniacka, Anna; Sandaker, Heidi 2013-08-01 Recent results from ATLAS giving a Higgs mass of 125.5 GeV, further constrain already highly constrained supersymmetric models such as pMSSM or CMSSM/mSUGRA. As a consequence, finding potentially discoverable and non-excluded regions of model parameter space is becoming increasingly difficult. Several groups have invested large effort in studying the consequences of Higgs mass bounds, upper limits on rare B-meson decays, and limits on relic dark matter density on constrained models, aiming at predicting superpartner masses, and establishing likelihood of SUSY models compared to that of the Standard Model vis-á-vis experimental data. In this paper a framework for efficient search for discoverable, non-excluded regions of different SUSY spaces giving specific experimental signature of interest is presented. The method employs an improved Markov Chain Monte Carlo (MCMC) scheme exploiting an iteratively updated likelihood function to guide search for viable models. Existing experimental and theoretical bounds as well as the LHC discovery potential are taken into account. This includes recent bounds on relic dark matter density, the Higgs sector and rare B-mesons decays. A clustering algorithm is applied to classify selected models according to expected phenomenology enabling automated choice of experimental benchmarks and regions to be used for optimizing searches. The aim is to provide experimentalist with a viable tool helping to target experimental signatures to search for, once a class of models of interest is established. As an example a search for viable CMSSM models with τ-lepton signatures observable with the 2012 LHC data set is presented. In the search 105209 unique models were probed. From these, ten reference benchmark points covering different ranges of phenomenological observables at the LHC were selected. 14. New two-dimensional integrable quantum models from SUSY intertwining International Nuclear Information System (INIS) Ioffe, M V; Negro, J; Nieto, L M; Nishnianidze, D N 2006-01-01 Supersymmetrical intertwining relations of second order in the derivatives are investigated for the case of supercharges with deformed hyperbolic metric g ik = diag(1, - a 2 ). Several classes of particular solutions of these relations are found. The corresponding Hamiltonians do not allow the conventional separation of variables, but they commute with symmetry operators of fourth order in momenta. For some of these models the specific SUSY procedure of separation of variables is applied 15. SUSY Flat Directions - to get a VEV or not? International Nuclear Information System (INIS) Basboell, Anders 2010-01-01 We investigate the potential of SUSY flat directions (FDs). Large FD vacuum expectation values (VEVs) can delay thermalisation and solve the gravitino problem--if FDs decay perturbatively. This depends on how many and which directions get the VEVs. Recently the decay of the FDs have been studied with the VEVs as input. Here we look at how the VEVs come about--statistically and analytically. 16. Electroweak contributions to SUSY particle production processes at the LHC International Nuclear Information System (INIS) Mirabella, Edoardo 2009-01-01 In this thesis we have computed the electroweak contributions of O(α s α), O(α 2 ) and O(α s 2 ) to three different classes of processes leading to the hadronic production of the SUSY partners of quarks and gluons, i.e. squarks and gluinos. The theoretical framework is the Minimal Supersymmetric extension of the Standard Model, the MSSM. The three processes are gluino pair production, diagonal squark-antisquark and associated squark-gluino production. 17. Flavour symmetries and SUSY soft breaking in the LHC era International Nuclear Information System (INIS) Vives, O 2008-01-01 The so-called supersymmetric flavour problem does not exist in isolation to the Standard Model flavour problem. We show that a realistic flavour symmetry can simultaneously solve both problems without ad hoc modifications of the SUSY model. Furthermore, departures from the SM expectations in these models can be used to discriminate among different possibilities. In particular we present the expected values for the electron EDM in a flavour model solving the supersymmetric flavour and CP problems 18. Hidden SUSY from precision gauge unification Energy Technology Data Exchange (ETDEWEB) Krippendorf, Sven; Nilles, Hans Peter [Bonn Univ. (Germany). Bethe Center for Theoretical Physics; Bonn Univ. (Germany). Physikalisches Inst.; Ratz, Michael [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Winkler, Martin Wolfgang [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2013-06-15 We revisit the implications of naturalness and gauge unification in the MSSM. We find that precision unification of the couplings in connection with a small {mu} parameter requires a highly compressed gaugino pattern as it is realized in mirage mediation. Due to the small mass difference between gluino and LSP, collider limits on the gluino mass are drastically relaxed. Without further assumptions, the relic density of the LSP is very close to the observed dark matter density due to coannihilation effects. 19. Hidden SUSY from precision gauge unification International Nuclear Information System (INIS) Krippendorf, Sven; Nilles, Hans Peter 2013-06-01 We revisit the implications of naturalness and gauge unification in the MSSM. We find that precision unification of the couplings in connection with a small μ parameter requires a highly compressed gaugino pattern as it is realized in mirage mediation. Due to the small mass difference between gluino and LSP, collider limits on the gluino mass are drastically relaxed. Without further assumptions, the relic density of the LSP is very close to the observed dark matter density due to coannihilation effects. 20. A large scale double beta and dark matter experiment: On the physics potential of GENIUS International Nuclear Information System (INIS) Klapdor-Kleingrothaus, H.V.; Hirsch, M. 1997-01-01 The physics potential of GENIUS, a recently proposed double beta decay anddark matter experiment is discussed. The experiment will allow to probe neutrino masses down to 10 -(2-3) eV. GENIUS will test the structure of the neutrino mass matrix, and therefore implicitly neutrino oscillation parameters comparable or superior in sensitivity to the best proposed dedicated terrestrial neutrino oscillation experiments. If the 10 -3 eV level is reached, GENIUS will even allow to test the large angle MSW solution of the solar neutrino problem. Even in its first stage GENIUS will confirm or rule out degenerate or inverted neutrino mass scenarios, which have been widely discussed in the literature as a possible solution to current hints on finite neutrino masses and also test the ν e ν μ hypothesis of the atmospheric neutrino problem.GENIUS would contribute to the search for R-parity violating SUSY and right-handed W-bosons on a scale similar or superior to LHC. In addition, GENIUS would largely improve the current 0νββ decay searches for R-parity conserving SUSY and leptoquarks. Concerning cold dark matter (CDM) search, the low background anticipated for GENIUS would, for thefirst time ever, allow to cover the complete MSSM neutralino parameter space, making GENIUS competitive to LHC in SUSY discovery. If GENIUS could find SUSY CDM as a by-product it would confirm that R-parity must be conserved exactly. GENIUS will thus be a major tool for future non-accelerator particle physics. (orig.) 1. Optimization of Markov chains for a SUSY fitter: Fittino Energy Technology Data Exchange (ETDEWEB) Prudent, Xavier [IKTP, Technische Universitaet, Dresden (Germany); Bechtle, Philip [DESY, Hamburg (Germany); Desch, Klaus; Wienemann, Peter [Universitaet Bonn (Germany) 2010-07-01 A Markov chains is a ''random walk'' algorithm which allows an efficient scan of a given profile and the search of the absolute minimum, even when this profil suffers from the presence of many secondary minima. This property makes them particularly suited to the study of Supersymmetry (SUSY) models, where minima have to be found in up-to 18-dimensional space for the general MSSM. Hence the SUSY fitter ''Fittino'' uses a MetropolisHastings Markov chain in a frequentist interpretation to study the impact of current low -energy measurements, as well as expected measurements from LHC and ILC, on the SUSY parameter space. The expected properties of an optimal Markov chain should be the independence of final results with respect to the starting point and a fast convergence. These two points can be achieved by optimizing the width of the proposal distribution, that is the ''average step length'' between two links in the chain. We developped an algorithm for the optimization of the proposal width, by modifying iteratively the width so that the rejection rate be around fifty percent. This optimization leads to a starting point independent chain as well as a faster convergence. 2. Scale effects and morphological diversification in hindlimb segment mass proportions in neognath birds. Science.gov (United States) Kilbourne, Brandon M 2014-01-01 In spite of considerable work on the linear proportions of limbs in amniotes, it remains unknown whether differences in scale effects between proximal and distal limb segments has the potential to influence locomotor costs in amniote lineages and how changes in the mass proportions of limbs have factored into amniote diversification. To broaden our understanding of how the mass proportions of limbs vary within amniote lineages, I collected data on hindlimb segment masses - thigh, shank, pes, tarsometatarsal segment, and digits - from 38 species of neognath birds, one of the most speciose amniote clades. I scaled each of these traits against measures of body size (body mass) and hindlimb size (hindlimb length) to test for departures from isometry. Additionally, I applied two parameters of trait evolution (Pagel's λ and δ) to understand patterns of diversification in hindlimb segment mass in neognaths. All segment masses are positively allometric with body mass. Segment masses are isometric with hindlimb length. When examining scale effects in the neognath subclade Land Birds, segment masses were again positively allometric with body mass; however, shank, pedal, and tarsometatarsal segment masses were also positively allometric with hindlimb length. Methods of branch length scaling to detect phylogenetic signal (i.e., Pagel's λ) and increasing or decreasing rates of trait change over time (i.e., Pagel's δ) suffer from wide confidence intervals, likely due to small sample size and deep divergence times. The scaling of segment masses appears to be more strongly related to the scaling of limb bone mass as opposed to length, and the scaling of hindlimb mass distribution is more a function of scale effects in limb posture than proximo-distal differences in the scaling of limb segment mass. Though negative allometry of segment masses appears to be precluded by the need for mechanically sound limbs, the positive allometry of segment masses relative to body mass may 3. SUSY/non-SUSY duality in U(N gauge model with partially broken N=2 supersymmetry Directory of Open Access Journals (Sweden) Kazunobu Maruyoshi 2009-03-01 Full Text Available We study the vacuum structure of the U(N gauge model with partially broken N=2 supersymmetry. From the analysis of the classical vacua of this model, we point out that in addition to the ordinary N=1 supersymmetric vacua, there are vacua with negative gauge coupling constants, which preserve another N=1 supersymmetry. These latter vacua can be analyzed by using SUSY/non-SUSY duality which is recently proposed by Aganagic, Beem, Seo and Vafa. A dual description of these in UV is U(N gauge theory where the supersymmetry is broken by spurion superfields. Following them, we see that there are supersymmetry preserving vacua as well as supersymmetry breaking vacua of low energy effective theory. 4. Hadronic EDMs in SUSY SU(5) GUTs with right-handed neutrinos International Nuclear Information System (INIS) Hisano, Junji; Kakizaki, Mitsuru; Nagai, Minoru; Shimizu, Yasuhiro 2004-01-01 We discuss hadronic EDM constraints on the neutrino sector in the SUSY SU(5) GUT with the right-handed neutrinos. The hadronic EDMs are sensitive to the right-handed down-type squark mixings, especially between the second and third generations and between the first and third ones, compared with the other low-energy hadronic observables, and the flavor mixings are induced by the neutrino Yukawa interaction. The current experimental bound of the neutron EDM may imply that the right-handed tau neutrino mass is smaller than about 10 14 GeV in the minimal supergravity scenario, and it may be improved furthermore in future experiments, such as the deuteron EDM measurement 5. PySLHA: a Pythonic interface to SUSY Les Houches accord data International Nuclear Information System (INIS) Buckley, Andy 2015-01-01 This paper describes the PySLHA package, a Python language module and program collection for reading, writing and visualising SUSY model data in the SLHA format. PySLHA can read and write SLHA data in a very general way, including the official SLHA2 extension and user customisations, and with arbitrarily deep indexing of data block entries and a dedicated, intuitive interface for particle data and decay information. The draft SLHA3 XSECTION feature is also fully supported. PySLHA can additionally read and write the legacy ISAWIG model format, and provides format conversion scripts. A publication-quality mass spectrum and decay chain plotting tool, slhaplot, is included in the package. (orig.) 6. A low Fermi scale from a simple gaugino-scalar mass relation Energy Technology Data Exchange (ETDEWEB) Bruemmer, F. [International School for Advanced Studies, Trieste (Italy); Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Buchmueller, W. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2013-11-15 In supersymmetric extensions of the Standard Model, the Fermi scale of electroweak symmetry breaking is determined by the pattern of supersymmetry breaking. We present an example, motivated by a higher-dimensional GUT model, where a particular mass relation between the gauginos, third-generation squarks and Higgs fields of the MSSM leads to a Fermi scale smaller than the soft mass scale. This is in agreement with the measured Higgs boson mass. The {mu} parameter is generated independently of supersymmetry breaking, however the {mu} problem becomes less acute due to the little hierarchy between the soft mass scale and the Fermi scale as we argue. The resulting superparticle mass spectra depend on the localization of quark and lepton fields in higher dimensions. In one case, the squarks of the first two generations as well as the gauginos and higgsinos can be in the range of the LHC. Alternatively, only the higgsinos may be accessible at colliders. The lightest superparticle is the gravitino. 7. The Effective Planck Mass and the Scale of Inflation CERN Document Server 2015-01-01 Observable quantities in cosmology are dimensionless, and therefore independent of the units in which they are measured. This is true of all physical quantities associated with the primordial perturbations that source cosmic microwave background anisotropies such as their amplitude and spectral properties. However, if one were to try and infer an absolute energy scale for inflation-- a priori, one of the more immediate corollaries of detecting primordial tensor modes-- one necessarily makes reference to a particular choice of units, the natural choice for which is Planck units. In this note, we discuss various aspects of how inferring the energy scale of inflation is complicated by the fact that the effective strength of gravity as seen by inflationary quanta necessarily differs from that seen by gravitational experiments at presently accessible scales. The uncertainty in the former relative to the latter has to do with the unknown spectrum of universally coupled particles between laboratory scales and the pu... 8. Complex scaling and residual flavour symmetry in the neutrino mass ... Probir Roy 2017-10-09 Oct 9, 2017 ... Leptonic Dirac CP violation must be maximal while atmospheric neutrino mixing need not be exactly maximal. Each of the two Majorana phases, to be probed by the search for 0νββ decay, has to be zero or π and a normal neutrino mass hierarchy is allowed. Keywords. Neutrinos; residual flavour symmetry; ... 9. Cosmological origin of the grand-unification mass scale International Nuclear Information System (INIS) Brout, R.; Englert, F.; Spindel, P. 1979-01-01 The origin of the universe as a quantum phenomenon leads to a self-consistently generated space-time structure in which the mass of the created particles is O (kappa/sup -1/2/). We interpret the origin of the universe as a phase transition in which the grand unified symmetry is spontaneously broken 10. Experimental results on SUSY searches with top CERN Document Server Eifert, Till 2014-01-01 Searches for supersymmetric partner particles of the top and bottom quarks at the Large Hadron Collider are reviewed. The focus is on the status of searches for a relatively light partner of the top quark performed by the CMS and ATLAS Collaborations. No excess beyond Standard Model expectations is observed and exclusion limits are set on the masses of supersymmetric particles. 11. Higgs mass prediction in the MSSM at three-loop level in a pure DR context Energy Technology Data Exchange (ETDEWEB) Harlander, Robert V.; Klappert, Jonas; Voigt, Alexander [RWTH Aachen University, Institute for Theoretical Particle Physics and Cosmology, Aachen (Germany) 2017-12-15 The impact of the three-loop effects of order α{sub t}α{sub s}{sup 2} on the mass of the light CP-even Higgs boson in the MSSM is studied in a pure DR context. For this purpose, we implement the results of Kant et al. (JHEP 08:104, 2010) into the C++ module Himalaya and link it to FlexibleSUSY, a Mathematica and C++ package to create spectrum generators for BSM models. The three-loop result is compared to the fixed-order two-loop calculations of the original FlexibleSUSY and of FeynHiggs, as well as to the result based on an EFT approach. Aside from the expected reduction of the renormalization scale dependence with respect to the lower-order results, we find that the three-loop contributions significantly reduce the difference from the EFT prediction in the TeV-region of the SUSY scale M{sub S}. Himalaya can be linked also to other two-loop DR codes, thus allowing for the elevation of these codes to the three-loop level. (orig.) 12. Prospects for early SUSY searches at Lhc International Nuclear Information System (INIS) Borjanovic, I. 2009-01-01 Search for the physics beyond the Standard Model is one of the most relevant goals of the CMS and Atlas experiments at the Large Hadron Collider at CERN. Prospects for early R-parity conserving supersymmetry discovery and mass measurements with the CMS and Atlas detector for the first fb -1 of data are presented. All the presented studies are based on realistic Monte Carlo simulations. 13. Neutrino oscillations in a predictive SUSY GUT International Nuclear Information System (INIS) Blazek, T.; Raby, S.; Tobe, K. 1999-01-01 In this paper we present a predictive SO(10) supersymmetric grand unified theory with the family symmetry U(2)xU(1) which has several nice features. We are able to fit fermion masses and mixing angles, including recent neutrino data, with nine parameters in the charged fermion sector and four in the neutrino sector. The family symmetry plays a preeminent role. (i) The model is ''natural''--we include all terms allowed by the symmetry. It restricts the number of arbitrary parameters and enforces many zeros in the effective mass matrices. (ii) Family symmetry breaking from U(2)xU(1)→U(1)→ nothing generates the family hierarchy. It also constrains squark and slepton mass matrices, thus ameliorating flavor violation resulting from squark and slepton loop contributions. (iii) It naturally gives large angle ν μ -ν τ mixing describing atmospheric neutrino oscillation data and small angle ν e -ν s mixing, consistent with the small mixing angle Mikheyev-Smirnov-Wolfenstein (MSW) solution to solar neutrino data. (iv) Finally, in this paper we assume minimal family symmetry-breaking vacuum expectation values (VEV's). As a result we cannot obtain a three neutrino solution to both atmospheric and solar neutrino oscillations. In addition, the solution discussed here cannot fit liquid scintillation neutrino detector (LSND) data even though this solution requires a sterile neutrino ν s . It is important to note, however, that with nonminimal family symmetry-breaking VEV's, a three neutrino solution is possible with the small mixing angle MSW solution to solar neutrino data and large angle ν μ -ν τ mixing describing atmospheric neutrino oscillation data. In the four neutrino case, nonminimal family VEV's may also permit a solution for LSND. The results with nonminimal family breaking are still under investigation and will be reported in a future paper. (c) 1999 The American Physical Society 14. Searches for SUSY signals at ATLAS CERN Document Server Meloni, Federico; The ATLAS collaboration 2017-01-01 The High Luminosity-Large Hadron Collider (HL-LHC) is expected to start in 2026 and to pro- vide an integrated luminosity of 3000 fb−1 in ten years, a factor 10 more than what will be collected by 2023. This high statistics will allow ATLAS to improve searches for new physics at the TeV scale. The search prospects for Supersymmetry are presented, with a programme spanning from strong to electroweak production of sparticles. 15. Mart ja Mari-Ann Susi taotlevad omanikena Concordia pankrotti / Andri Maimets Index Scriptorium Estoniae Maimets, Andri 2003-01-01 Concordia Ülikooli rektori kohast loobunud Mart Susi ning prorektori ametikohalt lahkunud Mari-Ann Susi taotlevad neile kuuluvat ülikooli pidanud miljonivõlgades firma pankrotti. Hiljuti loodi õppejõududest, tudengitest js töötajatest mittetulundusühing Concordia Akadeemiline Ühisus (CAU), selle nõukogu esimees on Hagi Šein 16. Non-linear way to supersymmetry and N-extended SUSY International Nuclear Information System (INIS) Akulov, V. 2001-01-01 In this report I give a short historical review of some of the first steps that were done towards the invention of SUSY by the Kharkov team headed by D. Volkov. This article is dedicated to the memory of Prof. Yuri Golfand, whose ideas of SUSY inspired the most active developments in High Energy Physics over thirty years 17. Predicting {theta}{sub 13} and the neutrino mass scale from quark lepton mass hierarchies Energy Technology Data Exchange (ETDEWEB) Buchmueller, W.; Domcke, V.; Schmitz, K. 2011-11-15 Flavour symmetries of Froggatt-Nielsen type can naturally reconcile the large quark and charged lepton mass hierarchies and the small quark mixing angles with the observed small neutrino mass hierarchies and their large mixing angles. We point out that such a flavour structure, together with the measured neutrino mass squared differences and mixing angles, strongly constrains yet undetermined parameters of the neutrino sector. Treating unknown O(1) parameters as random variables, we obtain surprisingly accurate predictions for the smallest mixing angle, sin{sup 2}2{theta}{sub 13}=0.07{sup +0.11}{sub -0.05}, the smallest neutrino mass, m{sub 1}=2.5{sup +1.7}{sub -1.6} x 10{sup -3} eV, and one Majorana phase, {alpha}{sub 21}/{pi}=1.0{sup +0.2}{sub -0.2}. (orig.) 18. Structure and dating errors in the geologic time scale and periodicity in mass extinctions Science.gov (United States) Stothers, Richard B. 1989-01-01 Structure in the geologic time scale reflects a partly paleontological origin. As a result, ages of Cenozoic and Mesozoic stage boundaries exhibit a weak 28-Myr periodicity that is similar to the strong 26-Myr periodicity detected in mass extinctions of marine life by Raup and Sepkoski. Radiometric dating errors in the geologic time scale, to which the mass extinctions are stratigraphically tied, do not necessarily lessen the likelihood of a significant periodicity in mass extinctions, but do spread the acceptable values of the period over the range 25-27 Myr for the Harland et al. time scale or 25-30 Myr for the DNAG time scale. If the Odin time scale is adopted, acceptable periods fall between 24 and 33 Myr, but are not robust against dating errors. Some indirect evidence from independently-dated flood-basalt volcanic horizons tends to favor the Odin time scale. 19. A universal scaling relationship between body mass and proximal limb bone dimensions in quadrupedal terrestrial tetrapods. Science.gov (United States) Campione, Nicolás E; Evans, David C 2012-07-10 Body size is intimately related to the physiology and ecology of an organism. Therefore, accurate and consistent body mass estimates are essential for inferring numerous aspects of paleobiology in extinct taxa, and investigating large-scale evolutionary and ecological patterns in the history of life. Scaling relationships between skeletal measurements and body mass in birds and mammals are commonly used to predict body mass in extinct members of these crown clades, but the applicability of these models for predicting mass in more distantly related stem taxa, such as non-avian dinosaurs and non-mammalian synapsids, has been criticized on biomechanical grounds. Here we test the major criticisms of scaling methods for estimating body mass using an extensive dataset of mammalian and non-avian reptilian species derived from individual skeletons with live weights. Significant differences in the limb scaling of mammals and reptiles are noted in comparisons of limb proportions and limb length to body mass. Remarkably, however, the relationship between proximal (stylopodial) limb bone circumference and body mass is highly conserved in extant terrestrial mammals and reptiles, in spite of their disparate limb postures, gaits, and phylogenetic histories. As a result, we are able to conclusively reject the main criticisms of scaling methods that question the applicability of a universal scaling equation for estimating body mass in distantly related taxa. The conserved nature of the relationship between stylopodial circumference and body mass suggests that the minimum diaphyseal circumference of the major weight-bearing bones is only weakly influenced by the varied forces exerted on the limbs (that is, compression or torsion) and most strongly related to the mass of the animal. Our results, therefore, provide a much-needed, robust, phylogenetically corrected framework for accurate and consistent estimation of body mass in extinct terrestrial quadrupeds, which is important for a 20. A universal scaling relationship between body mass and proximal limb bone dimensions in quadrupedal terrestrial tetrapods Directory of Open Access Journals (Sweden) Campione Nicolás E 2012-07-01 Full Text Available Abstract Background Body size is intimately related to the physiology and ecology of an organism. Therefore, accurate and consistent body mass estimates are essential for inferring numerous aspects of paleobiology in extinct taxa, and investigating large-scale evolutionary and ecological patterns in the history of life. Scaling relationships between skeletal measurements and body mass in birds and mammals are commonly used to predict body mass in extinct members of these crown clades, but the applicability of these models for predicting mass in more distantly related stem taxa, such as non-avian dinosaurs and non-mammalian synapsids, has been criticized on biomechanical grounds. Here we test the major criticisms of scaling methods for estimating body mass using an extensive dataset of mammalian and non-avian reptilian species derived from individual skeletons with live weights. Results Significant differences in the limb scaling of mammals and reptiles are noted in comparisons of limb proportions and limb length to body mass. Remarkably, however, the relationship between proximal (stylopodial limb bone circumference and body mass is highly conserved in extant terrestrial mammals and reptiles, in spite of their disparate limb postures, gaits, and phylogenetic histories. As a result, we are able to conclusively reject the main criticisms of scaling methods that question the applicability of a universal scaling equation for estimating body mass in distantly related taxa. Conclusions The conserved nature of the relationship between stylopodial circumference and body mass suggests that the minimum diaphyseal circumference of the major weight-bearing bones is only weakly influenced by the varied forces exerted on the limbs (that is, compression or torsion and most strongly related to the mass of the animal. Our results, therefore, provide a much-needed, robust, phylogenetically corrected framework for accurate and consistent estimation of body mass in 1. Magnetic Origin of Black Hole Winds Across the Mass Scale Science.gov (United States) Fukumura, Keigo; Kazanas, Demosthenes; Shrader, Chris; Behar, Ehud; Tombesi, Francesco; Contopoulos, Ioannis 2017-01-01 Black hole accretion disks appear to produce invariably plasma outflows that result in blue-shifted absorption features in their spectra. The X-ray absorption-line properties of these outflows are quite diverse, ranging in velocity from non-relativistic (approx. 300 km/sec) to sub-relativistic (approx. 0.1c where c is the speed of light) and a similarly broad range in the ionization states of the wind plasma. We report here that semi-analytic, self-similar magnetohydrodynamic (MHD) wind models that have successfully accounted for the X-ray absorber properties of supermassive black holes, also fit well the high-resolution X-ray spectrum of the accreting stellar-mass black hole, GRO J1655-40. This provides an explicit theoretical argument of their MHD origin (aligned with earlier observational claims) and supports the notion of a universal magnetic structure of the observed winds across all known black hole sizes. 2. SUSY field theories in higher dimensions and integrable spin chains International Nuclear Information System (INIS) Gorsky, A.; Gukov, S.; Mironov, A. 1998-01-01 Five- and six-dimensional SUSY gauge theories, with one or two compactified directions, are discussed. The 5d theories with the matter hypermultiplets in the fundamental representation are associated with the twisted XXZ spin chain, while the group product case with bi-fundamental matter corresponds to the higher rank spin chains. The Riemann surfaces for 6d theories with fundamental matter and two compact directions are proposed to correspond to the XYZ spin chain based on the Sklyanin algebra. We also discuss the obtained results within the brane and geometrical engineering frameworks and explain the relation to the toric diagrams. (orig.) 3. Electroweak contributions to SUSY particle production processes at the LHC Energy Technology Data Exchange (ETDEWEB) Mirabella, Edoardo 2009-07-22 In this thesis we have computed the electroweak contributions of O({alpha}{sub s}{alpha}), O({alpha}{sup 2}) and O({alpha}{sub s}{sup 2}) to three different classes of processes leading to the hadronic production of the SUSY partners of quarks and gluons, i.e. squarks and gluinos. The theoretical framework is the Minimal Supersymmetric extension of the Standard Model, the MSSM. The three processes are gluino pair production, diagonal squark-antisquark and associated squark-gluino production. 4. Hilkka Punainen & Susi : mediakasvatuksellisen iPad-kirjan suunnittelu OpenAIRE Kontiola, Sanna 2012-01-01 Opinnäytetyön tavoitteena oli tehdä mediakasvatuksellinen iPad-kirja "Hilkka Punainen & Susi", jota voitaisiin käyttää kirjastoissa, kouluissa ja kotona mediakasvatuksen apuvälineenä. Mediakasvatus ei ole ainoastaan medioiden ja välineiden käyttötaidon opettelua, vaan myös sellaisten turvataitojen opettelua, joiden tarkoituksena on parantaa lasten taitoja selviytyä uhkaavissa tilanteissa ja ohjata heitä turvautumaan luotettaviin aikuisiin. Teoksella on useita mediakasvatuksellisia tasoja. Teo... 5. Mass-flux subgrid-scale parameterization in analogy with multi-component flows: a formulation towards scale independence Directory of Open Access Journals (Sweden) J.-I. Yano 2012-11-01 Full Text Available A generalized mass-flux formulation is presented, which no longer takes a limit of vanishing fractional areas for subgrid-scale components. The presented formulation is applicable to a~situation in which the scale separation is still satisfied, but fractional areas occupied by individual subgrid-scale components are no longer small. A self-consistent formulation is presented by generalizing the mass-flux formulation under the segmentally-constant approximation (SCA to the grid–scale variabilities. The present formulation is expected to alleviate problems arising from increasing resolutions of operational forecast models without invoking more extensive overhaul of parameterizations. The present formulation leads to an analogy of the large-scale atmospheric flow with multi-component flows. This analogy allows a generality of including any subgrid-scale variability into the mass-flux parameterization under SCA. Those include stratiform clouds as well as cold pools in the boundary layer. An important finding under the present formulation is that the subgrid-scale quantities are advected by the large-scale velocities characteristic of given subgrid-scale components (large-scale subcomponent flows, rather than by the total large-scale flows as simply defined by grid-box average. In this manner, each subgrid-scale component behaves as if like a component of multi-component flows. This formulation, as a result, ensures the lateral interaction of subgrid-scale variability crossing the grid boxes, which are missing in the current parameterizations based on vertical one-dimensional models, and leading to a reduction of the grid-size dependencies in its performance. It is shown that the large-scale subcomponent flows are driven by large-scale subcomponent pressure gradients. The formulation, as a result, furthermore includes a self-contained description of subgrid-scale momentum transport. The main purpose of the present paper 6. From X-ray binaries to quasars black holes on all mass scales black holes on all mass scales CERN Document Server Ho, L C; Maccarone, T J 2005-01-01 This volume brings together contributions from many of the world's leading authorities on black hole accretion. The papers within represent part of a new movement to make use of the relative advantages of studying stellar mass and supermassive black holes and to bring together the knowledge gained from the two approaches. The topics discussed here run the gamut of the state of the art in black hole observational and theoretical work-variability, spectroscopy, disk-jet connections, and multi-wavelength campaigns on black holes are all covered. Reprinted from ASTROPHYSICS AND SPACE SCIENCE, 300:1-3 (2005) 7. Heat and mass transfer intensification and shape optimization a multi-scale approach CERN Document Server 2013-01-01 Is the heat and mass transfer intensification defined as a new paradigm of process engineering, or is it just a common and old idea, renamed and given the current taste? Where might intensification occur? How to achieve intensification? How the shape optimization of thermal and fluidic devices leads to intensified heat and mass transfers? To answer these questions, Heat & Mass Transfer Intensification and Shape Optimization: A Multi-scale Approach clarifies the definition of the intensification by highlighting the potential role of the multi-scale structures, the specific interfacial area, the distribution of driving force, the modes of energy supply and the temporal aspects of processes. A reflection on the methods of process intensification or heat and mass transfer enhancement in multi-scale structures is provided, including porous media, heat exchangers, fluid distributors, mixers and reactors. A multi-scale approach to achieve intensification and shape optimization is developed and clearly expla... 8. Software in windows for staple compounding system of microcomputer nuclear mass scale International Nuclear Information System (INIS) Wang Yanting; Zhang Yongming; Wang Yu; Jin Dongping 1998-01-01 The software exploited in windows for staple compounding system of microcomputer nuclear mass scale is described. The staple compounding system is briefly narrated. The software structure and its realizing method are given 9. SUSY dark matter: Beyond the standard paradigm International Nuclear Information System (INIS) Sandick, Pearl 2016-01-01 Within the framework of the Minimal Supersymmetric Standard Model (MSSM), we explore a decoupling of the parameters into separate sectors that determine consistency with collider data, the abundance of dark matter, and potential signatures at direct dark matter searches. We consider weak-scale bino-like neutralino dark matter, and find that annihilations via light slepton exchange present a viable mechanism for obtaining the appropriate dark matter abundance assuming a thermal history. Constraints and prospects for discovery of these models are discussed, including the possibility that direct dark matter searches may be sensitive to these models if light squarks exhibit left-right mixing. Differences between the scenarios presented here and the typical expectations for the MSSM are discussed. 10. Reconciling EFT and hybrid calculations of the light MSSM Higgs-boson mass Energy Technology Data Exchange (ETDEWEB) Bahl, Henning; Hollik, Wolfgang [Max-Planck Institut fuer Physik, Munich (Germany); Heinemeyer, Sven [Campus of International Excellence UAM+CSIC, Madrid (Spain); Universidad Autonoma de Madrid, Instituto de Fisica Teorica, (UAM/CSIC), Madrid (Spain); Instituto de Fisica Cantabria (CSIC-UC), Santander (Spain); Weiglein, Georg [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany) 2018-01-15 Various methods are used in the literature for predicting the lightest CP-even Higgs boson mass in the Minimal Supersymmetric Standard Model (MSSM). Fixed-order diagrammatic calculations capture all effects at a given order and yield accurate results for scales of supersymmetric (SUSY) particles that are not separated too much from the weak scale. Effective field theory calculations allow a resummation of large logarithmic contributions up to all orders and therefore yield accurate results for a high SUSY scale. A hybrid approach, where both methods have been combined, is implemented in the computer code FeynHiggs. So far, however, at large scales sizeable differences have been observed between FeynHiggs and other pure EFT codes. In this work, the various approaches are analytically compared with each other in a simple scenario in which all SUSY mass scales are chosen to be equal to each other. Three main sources are identified that account for the major part of the observed differences. Firstly, it is shown that the scheme conversion of the input parameters that is commonly used for the comparison of fixed-order results is not adequate for the comparison of results containing a series of higher-order logarithms. Secondly, the treatment of higher-order terms arising from the determination of the Higgs propagator pole is addressed. Thirdly, the effect of different parametrizations in particular of the top Yukawa coupling in the non-logarithmic terms is investigated. Taking into account all of these effects, in the considered simple scenario very good agreement is found for scales above 1 TeV between the results obtained using the EFT approach and the hybrid approach of FeynHiggs. (orig.) 11. Reconciling EFT and hybrid calculations of the light MSSM Higgs-boson mass International Nuclear Information System (INIS) Bahl, Henning; Hollik, Wolfgang; Heinemeyer, Sven; Weiglein, Georg 2017-06-01 Various methods are used in the literature for predicting the lightest CP-even Higgs boson mass in the Minimal Supersymmetric Standard Model (MSSM). Fixed-order diagrammatic calculations capture all effects at a given order and yield accurate results for scales of supersymmetric (SUSY) particles that are not separated too much from the weak scale. Effective field theory calculations allow a resummation of large logarithmic contributions up to all orders and therefore yield accurate results for a high SUSY scale. A hybrid approach, where both methods have been combined, is implemented in the computer code FeynHiggs. So far, however, at large scales sizeable differences have been observed between FeynHiggs and other pure EFT codes. In this work, the various approaches are analytically compared with each other in a simple scenario in which all SUSY mass scales are chosen to be equal to each other. Three main sources are identified that account for the major part of the observed differences. Firstly, it is shown that the scheme conversion of the input parameters that is commonly used for the comparison of fixed-order results is not adequate for the comparison of results containing a series of higher-order logarithms. Secondly, the treatment of higher-order terms arising from the determination of the Higgs propagator pole is addressed. Thirdly, the effect of different parametrizations in particular of the top Yukawa coupling in the non-logarithmic terms is investigated. Taking into account all of these effects, in the considered simple scenario very good agreement is found for scales above 1 TeV between the results obtained using the EFT approach and the hybrid approach of FeynHiggs. 12. Reconciling EFT and hybrid calculations of the light MSSM Higgs-boson mass Energy Technology Data Exchange (ETDEWEB) Bahl, Henning; Hollik, Wolfgang [Max-Planck-Institut fuer Physik, Muenchen (Germany); Heinemeyer, Sven [Campus of International Excellence UAM+CSIC, Madrid (Spain); Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica; Instituto de Fisica Cantabria (CSIC-UC), Santander (Spain); Weiglein, Georg [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2017-06-15 Various methods are used in the literature for predicting the lightest CP-even Higgs boson mass in the Minimal Supersymmetric Standard Model (MSSM). Fixed-order diagrammatic calculations capture all effects at a given order and yield accurate results for scales of supersymmetric (SUSY) particles that are not separated too much from the weak scale. Effective field theory calculations allow a resummation of large logarithmic contributions up to all orders and therefore yield accurate results for a high SUSY scale. A hybrid approach, where both methods have been combined, is implemented in the computer code FeynHiggs. So far, however, at large scales sizeable differences have been observed between FeynHiggs and other pure EFT codes. In this work, the various approaches are analytically compared with each other in a simple scenario in which all SUSY mass scales are chosen to be equal to each other. Three main sources are identified that account for the major part of the observed differences. Firstly, it is shown that the scheme conversion of the input parameters that is commonly used for the comparison of fixed-order results is not adequate for the comparison of results containing a series of higher-order logarithms. Secondly, the treatment of higher-order terms arising from the determination of the Higgs propagator pole is addressed. Thirdly, the effect of different parametrizations in particular of the top Yukawa coupling in the non-logarithmic terms is investigated. Taking into account all of these effects, in the considered simple scenario very good agreement is found for scales above 1 TeV between the results obtained using the EFT approach and the hybrid approach of FeynHiggs. 13. Top-squark in natural SUSY under current LHC run-2 data Energy Technology Data Exchange (ETDEWEB) Han, Chengcheng [University of Tokyo, Kavli IPMU (WPI), UTIAS, Kashiwa (Japan); Ren, Jie [Chinese Academy of Sciences, Computer Network Information Center, Beijing (China); Wu, Lei [Nanjing Normal University, Department of Physics and Institute of Theoretical Physics, Nanjing, Jiangsu (China); The University of Sydney, ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, Sydney, NSW (Australia); Yang, Jin Min [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); Zhang, Mengchao [Institute for Basic Science (IBS), Center for Theoretical Physics and Universe, Taejon (Korea, Republic of) 2017-02-15 We utilize the recent LHC-13 TeV data to study the lower mass bound on the top-squark (stop) in natural supersymmetry. We recast the LHC sparticle inclusive search of (≥1)jets + E{sub T} with α{sub T} variable, the direct stop pair search (1-lepton channel and all-hadronic channel) and the monojet analyses. We find that these searches are complementary depending on stop and higgsino masses: for a heavy stop the all-hadronic stop pair search provides the strongest bound, for an intermediate stop the inclusive SUSY analysis with α{sub T} variable is most efficient, while for a compressed stop-higgsino scenario the monojet search plays the key role. Finally, the lower mass bound on a stop is: (1) 320 GeV for compressed stop-higgsino scenario (mass splitting less than 20 GeV); (2) 765 (860) GeV for higgsinos lighter than 300 (100) GeV. (orig.) 14. Physics at the 100 GeV mass scale: Proceedings Energy Technology Data Exchange (ETDEWEB) Brennan, E.C. (ed.) 1990-01-01 This report contains the following papers: heavy quarks--experimental; the theory of heavy flavour production; precision experiments in electroweak interactions; theory of precision electroweak measurements; applications of QCD to hadron-hadron collisions; W{sup +}W{sup {minus}} interactions and the search for the Higgs Boson; electroweak symmetry breaking: Higgs/Whatever; electron-positron storage rings as heavy quark factories; prospects for next-generation e{sup +}e{sup {minus}} linear colliders; current prospects for hadron colliders; hadron colliders beyond the SSC; recent results on weak decays of charmed mesons from the Mark 3 experiment; recent CLEO results on bottom and charm; recent results on B-decays from ARGUE; a review of recent results on the hadron and photoproduction of charm; search for the top quark at UA1; recent results from the UA2 experiment at the CERN {bar p}p collider; selected preliminary results from CDF; new measurement of the phase difference {Phi}{sub 00} {minus} {Phi}{sub {plus minus}} in CP--violating K{sup 0} decays; a recent result on CP violation by E731 at Fermilab; rare kaon decay experiments; CP violation; inverse muon decay, neutrino dimuon production, and a search for neutral heavy leptons at the tevatron; first results from MACRO; a superstring theory underview; recent results from TRISTAN ; measurements of the Z boson resonance parameters at SLC; decays of the Z boson; and theory--weak neutral currents and the Z mass after the SLC. 15. Physics at the 100 GeV mass scale: Proceedings International Nuclear Information System (INIS) Brennan, E.C. 1990-01-01 This report contains the following papers: heavy quarks--experimental; the theory of heavy flavour production; precision experiments in electroweak interactions; theory of precision electroweak measurements; applications of QCD to hadron-hadron collisions; W + W - interactions and the search for the Higgs Boson; electroweak symmetry breaking: Higgs/Whatever; electron-positron storage rings as heavy quark factories; prospects for next-generation e + e - linear colliders; current prospects for hadron colliders; hadron colliders beyond the SSC; recent results on weak decays of charmed mesons from the Mark 3 experiment; recent CLEO results on bottom and charm; recent results on B-decays from ARGUE; a review of recent results on the hadron and photoproduction of charm; search for the top quark at UA1; recent results from the UA2 experiment at the CERN bar pp collider; selected preliminary results from CDF; new measurement of the phase difference Φ 00 - Φ ± in CP--violating K 0 decays; a recent result on CP violation by E731 at Fermilab; rare kaon decay experiments; CP violation; inverse muon decay, neutrino dimuon production, and a search for neutral heavy leptons at the tevatron; first results from MACRO; a superstring theory underview; recent results from TRISTAN; measurements of the Z boson resonance parameters at SLC; decays of the Z boson; and theory--weak neutral currents and the Z mass after the SLC 16. SUSY and Dark Matter Results from ATLAS CERN Document Server Sandaker, H 2013-01-01 New results from LHC are increasingly challenging the limits of the Standard Model of particle physics. Some of the most attractive scenarios for new physics are Supersymmet- ric models. In addition to solving some of the shortcomings of the Standard Model (e.g. hierarchy problem, Higgs mass corrections, gauge coupling unification) they also provide a suitable Dark Matter candidate, which could be produced at the LHC. We present the latest searches for Supersymmetry in events with high-energy final states and large missing transverse momentum for 4.7 fb−1 of proton-proton collisions at √s = 7 TeV as recorded by the ATLAS detector at the Large Hadron Collider. The data is interpreted in models where the Dark Matter candidate is dominantly produced in cascade decays of heavier unstable supersymmetric particles together with high-pT Standard Model parti- cles. We also present more model-independent searches for one single highly energetic jet or photon together with large amount of missing energy, showing th... 17. SUSY breaking mediation by throat fields International Nuclear Information System (INIS) Bruemmer, F.; Hebecker, A.; Trapletti, M. 2006-01-01 We investigate, in the general framework of KKLT, the mediation of supersymmetry breaking by fields propagating in the strongly warped region of the compactification manifold ('throat fields'). Such fields can couple both to the supersymmetry breaking sector at the IR end of the throat and to the visible sector at the UV end. We model the supersymmetry breaking sector by a chiral superfield which develops an F term vacuum expectation value (also responsible for the uplift). It turns out that the mediation effect of vector multiplets propagating in the throat can compete with modulus-anomaly mediation. Moreover, such vector fields are naturally present as the gauge fields arising from isometries of the throat (most notably the SO(4) isometry of the Klebanov-Strassler solution). Their mediation effect is important in spite of their large 4d mass. The latter is due to the breaking of the throat isometry by the compact manifold at the UV end of the throat. The contribution from heavy chiral superfields is found to be subdominant 18. Characterization and Upscaling of Pore Scale Hydrodynamic Mass Transfer Science.gov (United States) Gouze, P.; Roubinet, D.; Dentz, M.; Planes, V.; Russian, A. 2017-12-01 Imaging reservoir rocks in 3D using X-ray microtomography with spatial resolution ranging from about 1 to 10 mm provides us a unique opportunity not only to characterize pore space geometry but also for simulating hydrodynamical processes. Yet, pores and throats displaying sizes smaller than the resolution cannot be distinguished on the images and must be assigned to a so called microporous phase during the process of image segmentation. Accordingly one simulated mass transfers caused by advection and diffusion in the connected pores (mobile domain) and diffusion in the microporous clusters (immobile domain) using Time Domain Random Walk (TDRW) and developed a set of metrics that can be used to monitor the different mechanisms of transport in the sample, the final objective being of proposing a simple but accurate upscaled 1D model in which the particle travel times in the mobile and immobile domain and the number of mobile-immobile transfer events (called trapping events) are independently distributed random variables characterized by PDFs. For TDRW the solute concentration is represented by the density distribution of non-interacting point-like solute particles which move due to advection and dispersion. The set of metrics derives from different spatial and temporal statistical analyses of the particle motion, and is used for characterizing the particles transport (i) in the mobile domain in relation with the velocity field properties, (ii) in the immobile domain in relation with the structure and the properties of microporous phase and at the mobile-immobile interface. We specifically focused on how to model the trapping frequency and rate into the immobile domain in relation with the structure and the spatial distribution of the mobile-immobile domain interface. This thorough analysis of the particle motion for both simple artificial structures and real rock images allowed us to derive the parametrization of the upscaled 1D model. 19. Constraints on Dark Energy, Observable-mass Scaling Relations, Neutrino Properties and Gravity from Galaxy Clusters DEFF Research Database (Denmark) Rapetti Serra, David Angelo Using a data set of 238 cluster detections drawn from the ROSAT All-Sky Survey and X-ray follow-up observations from the Chandra X-ray Observatory and/or ROSAT for 94 of those clusters we obtain tight constraints on dark energy, both luminosity-mass and temperature-mass scaling relations, neutrin... 20. Scaling Factor Estimation Using Optimized Mass Change Strategy, Part 2: Experimental Results DEFF Research Database (Denmark) Fernández, Pelayo Fernández; Aenlle, Manuel López; Garcia, Luis M. Villa 2007-01-01 The mass change method is used to estimate the scaling factors, the uncertainty is reduced when, for each mode, the frequency shift is maximized and the changes in the mode shapes are minimized, which in turn, depends on the mass change strategy chosen to modify the dynamic behavior of the struct... 1. Higgs mass prediction in the MSSM at three-loop level in a pure \\overline{{ {DR}}} context Science.gov (United States) Harlander, Robert V.; Klappert, Jonas; Voigt, Alexander 2017-12-01 The impact of the three-loop effects of order α _tα _s^2 on the mass of the light CP-even Higgs boson in the { {MSSM}} is studied in a pure \\overline{{ {DR}}} context. For this purpose, we implement the results of Kant et al. (JHEP 08:104, 2010) into the C++ module Himalaya and link it to FlexibleSUSY, a Mathematica and C++ package to create spectrum generators for BSM models. The three-loop result is compared to the fixed-order two-loop calculations of the original FlexibleSUSY and of FeynHiggs, as well as to the result based on an EFT approach. Aside from the expected reduction of the renormalization scale dependence with respect to the lower-order results, we find that the three-loop contributions significantly reduce the difference from the EFT prediction in the TeV-region of the { {SUSY}} scale {M_S}. Himalaya can be linked also to other two-loop \\overline{{ {DR}}} codes, thus allowing for the elevation of these codes to the three-loop level. 2. Multijet Background Estimation For SUSY Searches And Particle Flow Offline Reconstruction Using The ATLAS Detector At The LHC CERN Document Server AUTHOR\|(SzGeCERN)731691 This thesis describes the jet smearing method, a data-driven technique for estimating the multijet background to Supersymmetry (SUSY) searches using the ATLAS detector at the Large Hadron Collider (LHC). The final 2011 and 2012 “ATLAS jets, missing transverse energy and zero leptons analysis” searches for SUSY are also documented. These analyses used the full ATLAS 2011 4.7 fb^{-1} $\\sqrt{s}$ = 7 TeV and 2012 20.3 fb$^{-1}$ $\\sqrt{s}$ = 8 TeV data sets. No statistically significant excess was found in either of these analyses; therefore, 95% C.L. mass exclusion limits were set on the mSUGRA/CMSSM m$_{0}$-m$_{1/2}$ and $m_{\\tilde{q}}$-$m_{\\tilde{g}}$ mass planes, and the simplified squark-gluino-neutralino pMSSM model. The jet smearing method was used in these analyses to estimate the multijet distributions of the Signal, Validation and Control Regions and also to calculate the multijet background Transfer Factors. This thesis also describes the missing transverse energy (E$_{miss}^{T}$ ) performance studi... 3. Non-SUSY Searches at the Tevatron International Nuclear Information System (INIS) Strologas, John 2011-01-01 We present recent results from searches for new physics beyond supersymmetry performed at the Tevatron accelerator at Fermilab. The CDF and D0 analyses presented here utilized data of integrated luminosity up to 6 fb -1 . We cover leptonic and bosonic resonances interpreted in the Randall-Sundrum graviton and new-boson models, rare final states, and the search for vector-like quarks. The search for new phenomena beyond the weak-scale supersymmetry is a vital part of the Fermilab program. Both CDF and D0 experiments at the Tevatron collider actively look for signals not expected by the standard model (SM) or minimal supersymmetric models. The searches can be sorted in three categories: (a) searches for generic resonances that can be interpreted in several new-physics models; (b) searches for exotic combinations of final-state objects or abnormal kinematics (not necessarily predicted by current theories); and (c) model-dependent searches that test a particular theory. We present here latest results from all these categories: searches for new dilepton and diboson resonances (interpreted as gravitons and new gauge bosons), searches for anomalous γ + E T + X production, and searches for vector-like quarks. 4. Leptogenesis after chaotic sneutrino inflation and the supersymmetry breaking scale Directory of Open Access Journals (Sweden) Fredrik Björkeroth 2017-03-01 Full Text Available We discuss resonant leptogenesis arising from the decays of two nearly-degenerate right-handed neutrinos, identified as the inflaton and stabiliser superfields in a model of chaotic sneutrino inflation. We compare an analytical estimate of the baryon asymmetry ηB in the Boltzmann approximation to a numerical solution of the full density matrix equations, and find that the analytical result fails to capture the correct physics in certain regions of parameter space. The observed baryon asymmetry can be realised for a breaking of the mass degeneracy as small as O(10−8. The origin of such a small mass splitting is explained by considering supersymmetry (SUSY breaking in supergravity, which requires a constant in the superpotential of the order of the gravitino mass m3/2 to cancel the cosmological constant. This yields additional terms in the (sneutrino mass matrices, lifting the degeneracy and linking ηB to the SUSY breaking scale. We find that achieving the correct baryon asymmetry requires a gravitino mass m3/2≥O(100 TeV. 5. Scaling of human body composition to stature: new insights into body mass index. Science.gov (United States) Heymsfield, Steven B; Gallagher, Dympna; Mayer, Laurel; Beetsch, Joel; Pietrobelli, Angelo 2007-07-01 Although Quetelet first reported in 1835 that adult weight scales to the square of stature, limited or no information is available on how anatomical body compartments, including adipose tissue (AT), scale to height. We examined the critical underlying assumptions of adiposity-body mass index (BMI) relations and extended these analyses to major anatomical compartments: skeletal muscle (SM), bone, residual mass, weight (AT+SM+bone), AT-free mass, and organs (liver, brain). This was a cross-sectional analysis of 2 body-composition databases: one including magnetic resonance imaging and dual-energy X-ray absorptiometry (DXA) estimates of evaluated components in adults (total n=411; organs=76) and the other a larger DXA database (n=1346) that included related estimates of fat, fat-free mass, and bone mineral mass. Weight, primary lean components (SM, residual mass, AT-free mass, and fat-free mass), and liver scaled to height with powers of approximately 2 (all P2 (2.31-2.48), and the fraction of weight as bone mineral mass was significantly (Pshort and tall subjects with equivalent BMIs have similar but not identical body composition, provide new insights into earlier BMI-related observations and thus establish a foundation for height-normalized indexes, and create an analytic framework for future studies. 6. Scaling of human body composition to stature: new insights into body mass index 123 Science.gov (United States) Heymsfield, Steven B; Gallagher, Dympna; Mayer, Laurel; Beetsch, Joel; Pietrobelli, Angelo 2009-01-01 Background Although Quetelet first reported in 1835 that adult weight scales to the square of stature, limited or no information is available on how anatomical body compartments, including adipose tissue (AT), scale to height. Objective We examined the critical underlying assumptions of adiposity–body mass index (BMI) relations and extended these analyses to major anatomical compartments: skeletal muscle (SM), bone, residual mass, weight (AT+SM+bone), AT-free mass, and organs (liver, brain). Design This was a cross-sectional analysis of 2 body-composition databases: one including magnetic resonance imaging and dual-energy X-ray absorptiometry (DXA) estimates of evaluated components in adults (total n = 411; organs = 76) and the other a larger DXA database (n = 1346) that included related estimates of fat, fat-free mass, and bone mineral mass. Results Weight, primary lean components (SM, residual mass, AT-free mass, and fat-free mass), and liver scaled to height with powers of ≈2 (all P 2 (2.31–2.48), and the fraction of weight as bone mineral mass was significantly (P short and tall subjects with equivalent BMIs have similar but not identical body composition, provide new insights into earlier BMI-related observations and thus establish a foundation for height-normalized indexes, and create an analytic framework for future studies. PMID:17616766 7. Non-universal gaugino mass GUT models in the light of dark matter and LHC constraints International Nuclear Information System (INIS) Chakrabortty, Joydeep; Mohanty, Subhendra; Rao, Soumya 2014-01-01 We perform a comprehensive study of SU(5), SO(10) and E(6) supersymmetric GUT models where the gaugino masses are generated through the F-term breaking vacuum expectation values of the non-singlet scalar fields. In these models the gauginos are non-universal at the GUT scale unlike in the mSUGRA scenario. We discuss the properties of the LSP which is stable and a viable candidate for cold dark matter. We look for the GUT scale parameter space that leads to the the lightest SM like Higgs mass in the range of 122–127 GeV compatible with the observations at ATLAS and CMS, the relic density in the allowed range of WMAP-PLANCK and compatible with other constraints from colliders and direct detection experiments. We scan universal scalar (m 0 G ), trilinear coupling A 0 and SU(3) C gaugino mass (M 3 G ) as the independent free parameters for these models. Based on the gaugino mass ratios at the GUT scale, we classify 25 SUSY GUT models and find that of these only 13 models satisfy the dark matter and collider constraints. Out of these 13 models there is only one model where there is a sizeable SUSY contribution to muon (g−2) 8. Neutrino masses, scale-dependent growth, and redshift-space distortions Energy Technology Data Exchange (ETDEWEB) Hernández, Oscar F., E-mail: [email protected] [Marianopolis College, 4873 Westmount Ave., Westmount, QC H3Y 1X9 (Canada) 2017-06-01 Massive neutrinos leave a unique signature in the large scale clustering of matter. We investigate the wavenumber dependence of the growth factor arising from neutrino masses and use a Fisher analysis to determine the aspects of a galaxy survey needed to measure this scale dependence. 9. Does the planck mass run on the cosmological-horizon scale? Science.gov (United States) Robbers, Georg; Afshordi, Niayesh; Doran, Michael 2008-03-21 Einstein's theory of general relativity contains a universal value of the Planck mass. However, one may envisage that in alternative theories of gravity the effective value of the Planck mass (or Newton's constant), which quantifies the coupling of matter to metric perturbations, can run on the cosmological-horizon scale. In this Letter, we study the consequences of a glitch in the Planck mass from subhorizon to superhorizon scales. We show that current cosmological observations severely constrain this glitch to less than 1.2%. 10. Scanning of the supersymmetry breaking scale and the gravitino mass in supergravity Energy Technology Data Exchange (ETDEWEB) Farakos, Fotis [Dipartimento di Fisica “Galileo Galilei”, Universita di Padova,Via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova,Via Marzolo 8, 35131 Padova (Italy); Kehagias, Alex [Physics Division, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece); Racco, Davide; Riotto, Antonio [Department of Theoretical Physics and Center for Astroparticle Physics (CAP),24 quai E. Ansermet, CH-1211 Geneva 4 (Switzerland) 2016-06-21 We consider the minimal three-form N=1 supergravity coupled to nilpotent three-form chiral superfields. The supersymmetry breaking is sourced by the three-forms of the chiral multiplets, while the value of the gravitino mass is controlled by the three-form of the supergravity multiplet. The three-forms can nucleate membranes which scan both the supersymmetry breaking scale and the gravitino mass. The peculiar supergravity feature that the cosmological constant is the sum of a positive contribution from the supersymmetry breaking scale and a negative contribution from the gravitino mass makes the cosmological constant jump. This can lead to a phenomenologically allowed small value of the cosmological constant even though the supersymmetry breaking scale and the gravitino mass are dynamically large. 11. Constraining SUSY models with Fittino using measurements before, with and beyond the LHC Energy Technology Data Exchange (ETDEWEB) Bechtle, Philip [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Desch, Klaus; Uhlenbrock, Mathias; Wienemann, Peter [Bonn Univ. (Germany). Physikalisches Inst. 2009-07-15 We investigate the constraints on Supersymmetry (SUSY) arising from available precision measurements using a global fit approach.When interpreted within minimal supergravity (mSUGRA), the data provide significant constraints on the masses of supersymmetric particles (sparticles), which are predicted to be light enough for an early discovery at the Large Hadron Collider (LHC). We provide predicted mass spectra including, for the first time, full uncertainty bands. The most stringent constraint is from the measurement of the anomalous magnetic moment of the muon. Using the results of these fits, we investigate to which precision mSUGRA and more general MSSM parameters can be measured by the LHC experiments with three different integrated luminosities for a parameter point which approximately lies in the region preferred by current data. The impact of the already available measurements on these precisions, when combined with LHC data, is also studied. We develop a method to treat ambiguities arising from different interpretations of the data within one model and provide a way to differentiate between values of different digital parameters of a model (e. g. sign({mu}) within mSUGRA). Finally, we show how measurements at a linear collider with up to 1 TeV centre-of-mass energy will help to improve precision by an order of magnitude. (orig.) 12. The QCD mass gap and quark deconfinement scales as mass bounds in strong gravity Energy Technology Data Exchange (ETDEWEB) Burikham, Piyabut [Chulalongkorn University, High Energy Physics Theory Group, Department of Physics, Faculty of Science, Bangkok (Thailand); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom); Lake, Matthew J. [Sun Yat-Sen University, School of Physics, Guangzhou (China); Nanyang Technological University, School of Physical and Mathematical Sciences, Singapore (Singapore); Naresuan University, The Institute for Fundamental Study, ' ' The Tah Poe Academia Institute' ' , Phitsanulok (Thailand); Thailand Center of Excellence in Physics, Ministry of Education, Bangkok (Thailand) 2017-11-15 Though not a part of mainstream physics, Salam's theory of strong gravity remains a viable effective model for the description of strong interactions in the gauge singlet sector of QCD, capable of producing particle confinement and asymptotic freedom, but not of reproducing interactions involving SU(3) color charge. It may therefore be used to explore the stability and confinement of gauge singlet hadrons, though not to describe scattering processes that require color interactions. It is a two-tensor theory of both strong interactions and gravity, in which the strong tensor field is governed by equations formally identical to the Einstein equations, apart from the coupling parameter, which is of order 1 GeV{sup -1}. We revisit the strong gravity theory and investigate the strong gravity field equations in the presence of a mixing term which induces an effective strong cosmological constant, Λ{sub f}. This introduces a strong de Sitter radius for strongly interacting fermions, producing a confining bubble, which allows us to identify Λ{sub f} with the 'bag constant' of the MIT bag model, B ≅ 2 x 10{sup 14} g cm{sup -3}. Assuming a static, spherically symmetric geometry, we derive the strong gravity TOV equation, which describes the equilibrium properties of compact hadronic objects. From this, we determine the generalized Buchdahl inequalities for a strong gravity 'particle', giving rise to upper and lower bounds on the mass/radius ratio of stable, compact, strongly interacting objects. We show, explicitly, that the existence of the lower mass bound is induced by the presence of Λ{sub f}, producing a mass gap, and that the upper bound corresponds to a deconfinement phase transition. The physical implications of our results for holographic duality in the context of the AdS/QCD and dS/QCD correspondences are also discussed. (orig.) 13. Possible constraints on SUSY-model parameters from direct dark matter search International Nuclear Information System (INIS) Bednyakov, V.A.; Kovalenko, S.G. 1993-01-01 We consider the SUSY-model neutralino as a dominant Dark Matter particle in the galactic halo and investigate some general issues of direct DM searches via elastic neutralino-nucleus scattering. On the basis of conventional assumptions about the nuclear and nucleon structure, without referring to a specific SUSY-model, we prove that it is impossible in principle to extract more than three constrains on fundamental SUSY-model parameters from the direct Dark Matter searches. Three types of Dark Matter detector probing different groups of parameters are recognized. 21 refs., 1 tab 14. The warm dark matter halo mass function below the cut-off scale Science.gov (United States) Angulo, Raul E.; Hahn, Oliver; Abel, Tom 2013-10-01 Warm dark matter (WDM) cosmologies are a viable alternative to the cold dark matter (CDM) scenario. Unfortunately, an accurate scrutiny of the WDM predictions with N-body simulations has proven difficult due to numerical artefacts. Here, we report on cosmological simulations that, for the first time, are devoid of those problems, and thus are able to accurately resolve the WDM halo mass function well below the cut-off. We discover a complex picture, with perturbations at different evolutionary stages populating different ranges in the halo mass function. On the smallest mass scales we can resolve, identified objects are typically centres of filaments that are starting to collapse. On intermediate mass scales, objects typically correspond to fluctuations that have collapsed and are in the process of relaxation, whereas the high-mass end is dominated by objects similar to haloes identified in CDM simulations. We then explicitly show how the formation of low-mass haloes is suppressed, which translates into a strong cut-off in the halo mass function. This disfavours some analytic formulations that predict a halo mass function that would extend well below the free streaming mass. We argue for a more detailed exploration of the formation of the smallest structures expected to form in a given cosmology, which, we foresee, will advance our overall understanding of structure formation. 15. Scaling Mode Shapes in Output-Only Structure by a Mass-Change-Based Method Directory of Open Access Journals (Sweden) Liangliang Yu 2017-01-01 Full Text Available A mass-change-based method based on output-only data for the rescaling of mode shapes in operational modal analysis (OMA is introduced. The mass distribution matrix, which is defined as a diagonal matrix whose diagonal elements represent the ratios among the diagonal elements of the mass matrix, is calculated using the unscaled mode shapes. Based on the theory of null space, the mass distribution vector or mass distribution matrix is obtained. A small mass with calibrated weight is added to a certain location of the structure, and then the mass distribution vector of the modified structure is estimated. The mass matrix is identified according to the difference of the mass distribution vectors between the original and modified structures. Additionally, the universal set of modes is unnecessary when calculating the mass distribution matrix, indicating that modal truncation is allowed in the proposed method. The mass-scaled mode shapes estimated in OMA according to the proposed method are compared with those obtained by experimental modal analysis. A simulation is employed to validate the feasibility of the method. Finally, the method is tested on output-only data from an experiment on a five-storey structure, and the results confirm the effectiveness of the method. 16. Conceptual Design and Demonstration of Space Scale for Measuring Mass in Microgravity Environment Directory of Open Access Journals (Sweden) Youn-Kyu Kim 2015-12-01 Full Text Available In this study, a new idea for developing a space scale for measuring mass in a microgravity environment was proposed by using the inertial force properties of an object to measure its mass. The space scale detected the momentum change of the specimen and reference masses by using a load-cell sensor as the force transducer based on Newton’s laws of motion. In addition, the space scale calculated the specimen mass by comparing the inertial forces of the specimen and reference masses in the same acceleration field. By using this concept, a space scale with a capacity of 3 kg based on the law of momentum conservation was implemented and demonstrated under microgravity conditions onboard International Space Station (ISS with an accuracy of ±1 g. By the performance analysis on the space scale, it was verified that an instrument with a compact size could be implemented and be quickly measured with a reasonable accuracy under microgravity conditions. 17. TESTING THE ASTEROSEISMIC MASS SCALE USING METAL-POOR STARS CHARACTERIZED WITH APOGEE AND KEPLER Energy Technology Data Exchange (ETDEWEB) Epstein, Courtney R.; Johnson, Jennifer A.; Tayar, Jamie; Pinsonneault, Marc [Department of Astronomy, Ohio State University, 140 W. 18th Avenue, Columbus, OH 43210 (United States); Elsworth, Yvonne P.; Chaplin, William J. [School of Physics and Astronomy, University of Birmingham, Edgbaston Park Road, West Midlands, Birmingham B15 2TT (United Kingdom); Shetrone, Matthew [McDonald Observatory, The University of Texas at Austin, 1 University Station, C1400, Austin, TX 78712-0259 (United States); Mosser, Benoît [LESIA, CNRS, Université Pierre et Marie Curie, Université Denis Diderot, Observatoire de Paris, F-92195 Meudon Cedex (France); Hekker, Saskia [Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany); Harding, Paul [Department of Astronomy, Case Western Reserve University, Cleveland, OH 44106-7215 (United States); Silva Aguirre, Víctor [Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C (Denmark); Basu, Sarbani [Department of Astronomy, Yale University, P.O. Box 208101, New Haven, CT 06520-8101 (United States); Beers, Timothy C. [National Optical Astronomy Observatory, Tucson, AZ 85719, USA and JINA: Joint Institute for Nuclear Astrophysics (United States); Bizyaev, Dmitry [Apache Point Observatory, Sunspot, NM 88349 (United States); Bedding, Timothy R. [Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006 (Australia); Frinchaboy, Peter M. [Department of Physics and Astronomy, Texas Christian University, TCU Box 298840, Fort Worth, TX 76129 (United States); García, Rafael A. [Laboratoire AIM, CEA/DSM-CNRS, Universit Paris 7 Diderot, IRFU/SAp, Centre de Saclay, F-91191, Gif-sur-Yvette (France); Pérez, Ana E. García; Hearty, Fred R., E-mail: [email protected] [Department of Astronomy, University of Virginia, Charlottesville, VA 22904 (United States); and others 2014-04-20 Fundamental stellar properties, such as mass, radius, and age, can be inferred using asteroseismology. Cool stars with convective envelopes have turbulent motions that can stochastically drive and damp pulsations. The properties of the oscillation frequency power spectrum can be tied to mass and radius through solar-scaled asteroseismic relations. Stellar properties derived using these scaling relations need verification over a range of metallicities. Because the age and mass of halo stars are well-constrained by astrophysical priors, they provide an independent, empirical check on asteroseismic mass estimates in the low-metallicity regime. We identify nine metal-poor red giants (including six stars that are kinematically associated with the halo) from a sample observed by both the Kepler space telescope and the Sloan Digital Sky Survey-III APOGEE spectroscopic survey. We compare masses inferred using asteroseismology to those expected for halo and thick-disk stars. Although our sample is small, standard scaling relations, combined with asteroseismic parameters from the APOKASC Catalog, produce masses that are systematically higher (<ΔM > =0.17 ± 0.05 M {sub ☉}) than astrophysical expectations. The magnitude of the mass discrepancy is reduced by known theoretical corrections to the measured large frequency separation scaling relationship. Using alternative methods for measuring asteroseismic parameters induces systematic shifts at the 0.04 M {sub ☉} level. We also compare published asteroseismic analyses with scaling relationship masses to examine the impact of using the frequency of maximum power as a constraint. Upcoming APOKASC observations will provide a larger sample of ∼100 metal-poor stars, important for detailed asteroseismic characterization of Galactic stellar populations. 18. Naturalness and superpartner masses or when to give up on weak scale supersymmetry International Nuclear Information System (INIS) Anderson, G.W.; Castano, D.J. 1995-01-01 Superpartner masses cannot be arbitrarily heavy if supersymmetric extensions of the standard model explain the stability of the gauge hierarchy. This ancient and hallowed motivation for weak scale supersymmetry is often quoted, yet no reliable determination of this upper limit on superpartner masses exists. In this paper we compute upper bounds on superpartner masses in the minimal supersymmetric model, and we identify which values of the superpartner masses correspond to the most natural explanation of the hierarchy stability. We compare the most natural value of these masses and their upper limits to the physics reach of current and future colliders. As a result, we find that supersymmetry could explain weak scale stability naturally even if no superpartners are discovered at the CERN LEP II or the Fermilab Tevatron (even with the Main Injector upgrade). However, we find that supersymmetry cannot provide a complete explanation of weak scale stability, if squarks and gluinos have masses beyond the physics reach of the CERN LHC. Moreover, in the most natural scenarios, many sparticles, for example, charginos, squarks, and gluinos, lie within the physics reach of either LEP II or the Tevatron. Our analysis determines the most natural value of the chargino (squark) [(gluino)] mass consistent with current experimental constraints is ∼50 (250) [(250)] GeV and the corresponding theoretical upper bound is ∼250 (700) [(800)] GeV 19. UPDATED MASS SCALING RELATIONS FOR NUCLEAR STAR CLUSTERS AND A COMPARISON TO SUPERMASSIVE BLACK HOLES International Nuclear Information System (INIS) Scott, Nicholas; Graham, Alister W. 2013-01-01 We investigate whether or not nuclear star clusters and supermassive black holes (SMBHs) follow a common set of mass scaling relations with their host galaxy's properties, and hence can be considered to form a single class of central massive object (CMO). We have compiled a large sample of galaxies with measured nuclear star cluster masses and host galaxy properties from the literature and fit log-linear scaling relations. We find that nuclear star cluster mass, M NC , correlates most tightly with the host galaxy's velocity dispersion: log M NC = (2.11 ± 0.31)log (σ/54) + (6.63 ± 0.09), but has a slope dramatically shallower than the relation defined by SMBHs. We find that the nuclear star cluster mass relations involving host galaxy (and spheroid) luminosity and stellar and dynamical mass, intercept with but are in general shallower than the corresponding black hole scaling relations. In particular, M NC ∝M 0.55±0.15 Gal,dyn ; the nuclear cluster mass is not a constant fraction of its host galaxy or spheroid mass. We conclude that nuclear stellar clusters and SMBHs do not form a single family of CMOs. 20. SUSY searches in events with two opposite-sign same-flavor leptons, jets and MET with the CMS detector CERN Document Server Schulte, Jan-Frederik 2017-01-01 Searches for Supersymmetry (SUSY) in events with two opposite-sign same-flavour leptons offer sensitivity to the production of sleptons or Z bosons in the cascade decays of initially produced heavy SUSY particles. In the considered models, this signature is accompanied by the presence of several jets and high missing transverse energy. Analysing their respective datasets recorded at √ s = 8 TeV, the ATLAS and CMS collaborations previously reported deviations from the pre- dicted Standard Model backgrounds in this final state, with significances between 2.6 and 3.0 σ . However, these excesses had been observed in different regions of the dilepton invariant mass. The dataset recorded with the CMS detector at √ s = 13 TeV in 2015, corresponding to 2.3 fb − 1 , offers the opportunity to substantiate or refute these interesting hints for new phenomena. Unfor- tunately, no significant deviation from the background estimates are observed in either of the two selections which had shown excesses in the √ s = ... 1. SUSY breaking mediation mechanisms and (g-2)μ, B→Xsγ, B→Xsl+l- and Bs→μ+μ- International Nuclear Information System (INIS) Baek, Seungwon; Ko, P.; Song, Wan Young 2003-01-01 We show that there are qualitative differences in correlations among (g-2)μ, B→X s γ, B→X l + l - and B s →μ + μ - in various SUSY breaking mediation mechanisms: minimal supergravity (mSUGRA), gauge mediation (GMSB), anomaly mediation (AMSB), guagino mediation (g-tildeMSB), weakly and strongly interacting string theories, and D brane models. After imposing the direct search limits on the Higgs boson and SUSY particle search limits and B→X s γ branching ratio, we find all the scenarios can accommodate the aμ≡(g-2)μ/2 in the range of (a few tens) x 10 -10 , and predict that the branching ratio for B→X s l + l - can differ from the standard model (SM) prediction by ±20% but no more. On the other hand, the B s →μ + μ - is sensitive to the SUSY breaking mediation mechanisms through the pseudoscalar and stop masses (m A and mt-tilde 1 ), and the stop mixing angle. In the GMSB with a small messenger number, the AMSB, the g-tildeMSB and the noscale scenarios, one finds that B(B s →μ + μ - ) -8 , which is below the search limit at the Tevatron Run II. Only the mSUGRA or string inspired models can generate a large branching ratio for this decay. (author) 2. The fine-tuning cost of the likelihood in SUSY models CERN Document Server Ghilencea, D M 2013-01-01 In SUSY models, the fine tuning of the electroweak (EW) scale with respect to their parameters gamma_i={m_0, m_{1/2}, mu_0, A_0, B_0,...} and the maximal likelihood L to fit the experimental data are usually regarded as two different problems. We show that, if one regards the EW minimum conditions as constraints that fix the EW scale, this commonly held view is not correct and that the likelihood contains all the information about fine-tuning. In this case we show that the corrected likelihood is equal to the ratio L/Delta of the usual likelihood L and the traditional fine tuning measure Delta of the EW scale. A similar result is obtained for the integrated likelihood over the set {gamma_i}, that can be written as a surface integral of the ratio L/Delta, with the surface in gamma_i space determined by the EW minimum constraints. As a result, a large likelihood actually demands a large ratio L/Delta or equivalently, a small chi^2_{new}=chi^2_{old}+2ln(Delta). This shows the fine-tuning cost to the likelihood ... 3. Threshold corrections to dimension-six proton decay operators in non-minimal SUSY SU(5 GUTs Directory of Open Access Journals (Sweden) Borut Bajc 2016-09-01 Full Text Available We calculate the high and low scale threshold corrections to the D=6 proton decay mode in supersymmetric SU(5 grand unified theories with higher-dimensional representation Higgs multiplets. In particular, we focus on a missing-partner model in which the grand unified group is spontaneously broken by the 75-dimensional Higgs multiplet and the doublet–triplet splitting problem is solved. We find that in the missing-partner model the D=6 proton decay rate gets suppressed by about 60%, mainly due to the threshold effect at the GUT scale, while the SUSY-scale threshold corrections are found to be less prominent when sfermions are heavy. 4. Nucleon electric dipole moments in high-scale supersymmetric models International Nuclear Information System (INIS) Hisano, Junji; Kobayashi, Daiki; Kuramoto, Wataru; Kuwahara, Takumi 2015-01-01 The electric dipole moments (EDMs) of electron and nucleons are promising probes of the new physics. In generic high-scale supersymmetric (SUSY) scenarios such as models based on mixture of the anomaly and gauge mediations, gluino has an additional contribution to the nucleon EDMs. In this paper, we studied the effect of the CP-violating gluon Weinberg operator induced by the gluino chromoelectric dipole moment in the high-scale SUSY scenarios, and we evaluated the nucleon and electron EDMs in the scenarios. We found that in the generic high-scale SUSY models, the nucleon EDMs may receive the sizable contribution from the Weinberg operator. Thus, it is important to compare the nucleon EDMs with the electron one in order to discriminate among the high-scale SUSY models. 5. Nucleon electric dipole moments in high-scale supersymmetric models Energy Technology Data Exchange (ETDEWEB) Hisano, Junji [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI),Nagoya University,Nagoya 464-8602 (Japan); Department of Physics, Nagoya University,Nagoya 464-8602 (Japan); Kavli IPMU (WPI), UTIAS, University of Tokyo,Kashiwa, Chiba 277-8584 (Japan); Kobayashi, Daiki; Kuramoto, Wataru; Kuwahara, Takumi [Department of Physics, Nagoya University,Nagoya 464-8602 (Japan) 2015-11-12 The electric dipole moments (EDMs) of electron and nucleons are promising probes of the new physics. In generic high-scale supersymmetric (SUSY) scenarios such as models based on mixture of the anomaly and gauge mediations, gluino has an additional contribution to the nucleon EDMs. In this paper, we studied the effect of the CP-violating gluon Weinberg operator induced by the gluino chromoelectric dipole moment in the high-scale SUSY scenarios, and we evaluated the nucleon and electron EDMs in the scenarios. We found that in the generic high-scale SUSY models, the nucleon EDMs may receive the sizable contribution from the Weinberg operator. Thus, it is important to compare the nucleon EDMs with the electron one in order to discriminate among the high-scale SUSY models. 6. SUSY Higgs at the LHC large stop mixing effects and associated production CERN Document Server Bélanger, G; Sridhar, K 2000-01-01 We revisit the effect of the large stop mixing on the decay and production of the lightest SUSY Higgs at the LHC. We stress that whenever the inclusive 2-photon signature is substantially reduced, associated production, $Wh$ and $t\\bar t h$, with the subsequent decay of the Higgs into photons is enhanced and becomes an even more important discovery channel. We also point out that these reductions in the inclusive channel do not occur for the smallest Higgs mass where the significance is known to be lowest. We show that in such scenarios the Higgs can be produced in the decay of the heaviest stop. For not too heavy masses of the pseudo-scalar Higgs where the inclusive channel is even further reduced, we show that large stop mixing also allows the production of the pseudo-scalar Higgs through stop decays. These large mixing scenarios therefore offer much better prospects than previously thought. As a by-product we have recalculated stop1-stop1-h production at the LHC and give a first evaluation of stop1-stop1-Z... 7. Non-simplified SUSY. τ-coannihilation at LHC and ILC Energy Technology Data Exchange (ETDEWEB) Berggren, M.; Kruecker, D.; List, J.; Melzer-Pellmann, I.A.; Seitz, C. [DESY, Hamburg (Germany); Cakir, A. [DESY, Hamburg (Germany); Istanbul Technical University, Department of Physics Engineering, Istanbul (Turkey); Samani, B.S. [DESY, Hamburg (Germany); IPM, P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Wayand, S. [KIT IEKP, Karlsruhe (Germany) 2016-04-15 If new phenomena beyond the Standard Model will be discovered at the LHC, the properties of the new particles could be determined with data from the High-Luminosity LHC and from a future linear collider like the ILC. We discuss the possible interplay between measurements at the two accelerators in a concrete example, namely a full SUSY model which features a small τ-LSP mass difference. Various channels have been studied using the Snowmass 2013 combined LHC detector implementation in the Delphes simulation package, as well as simulations of the ILD detector concept from the Technical Design Report. We investigate both the LHC and the ILC capabilities for discovery, separation and identification of various parts of the spectrum. While some parts would be discovered at the LHC, there is substantial room for further discoveries at the ILC. We finally highlight examples where the precise knowledge about the lower part of the mass spectrum which could be acquired at the ILC would enable a more in-depth analysis of the LHC data with respect to the heavier states. (orig.) 8. Evaluation of mixing and mass transfer in a stirred pilot scale bioreactor utilizing CFD DEFF Research Database (Denmark) Bach, Christian; Yang, Jifeng; Larsson, Hilde Kristina 2017-01-01 Knowledge and prediction of mixing and mass transfer in agitated bioreactors is fundamental for process development and scale up. In particular key process parameters such as mixing time and volumetric mass transfer coefficient are essential for bioprocess development. In this work the mixing...... and mass transfer performance of a high power agitated pilot scale bioreactor has been characterized using a novel combination of computational fluid dynamics (CFD) and experimental investigations. The effect of turbulence inside the vessel was predicted using a standard RANS k-ε model. Mixing time...... transfer coefficients were in accordance with the experimental data. This work illustrates the possibility of predicting the two phase fluid dynamic performance of an agitated pilot scale bioreactor using validated CFD models. These models can be applied to illustrate the effect of changing the physical... 9. Low-energy consequences of superstring-inspired models with intermediate-mass scales International Nuclear Information System (INIS) Gabbiani, F. 1987-01-01 The phenomenological consequences of implementing intermediate-mass scales in E 6 superstring-inspired models are discussed. Starting from a suitable Calabi-Yau compactification with b 1,1 >1, one gets, after Hosotani breaking, the rank r=5 gauge group SU(3) C x SU(2) L x U(1) Y x U(1) E , that is broken at an intermediate-mass scale down to the standard-model group. The analysis of both the intermediate and the electroweak breaking is performed in the two cases Λ c = M x and Λ c x , where Λ c is the scale at which the hidden sector gauginos condensate. It is performed quantitatively the minimization of the low-energy effective potential and the renormalization group analysis, yielding a viable set of mass spectra and confirming the reliability of the intermediate-breaking scheme 10. On the mass-coupling relation of multi-scale quantum integrable models Energy Technology Data Exchange (ETDEWEB) Bajnok, Zoltán; Balog, János [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary); Ito, Katsushi [Department of Physics, Tokyo Institute of Technology,2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan); Satoh, Yuji [Institute of Physics, University of Tsukuba,1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571 (Japan); Tóth, Gábor Zsolt [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary) 2016-06-13 We determine exactly the mass-coupling relation for the simplest multi-scale quantum integrable model, the homogenous sine-Gordon model with two independent mass-scales. We first reformulate its perturbed coset CFT description in terms of the perturbation of a projected product of minimal models. This representation enables us to identify conserved tensor currents on the UV side. These UV operators are then mapped via form factor perturbation theory to operators on the IR side, which are characterized by their form factors. The relation between the UV and IR operators is given in terms of the sought-for mass-coupling relation. By generalizing the Θ sum rule Ward identity we are able to derive differential equations for the mass-coupling relation, which we solve in terms of hypergeometric functions. We check these results against the data obtained by numerically solving the thermodynamic Bethe Ansatz equations, and find a complete agreement. 11. SUSY WT identity in a lattice formulation of 2D N=(2,2) SYM International Nuclear Information System (INIS) 2010-01-01 We address some issues relating to a supersymmetric (SUSY) Ward-Takahashi (WT) identity in Sugino's lattice formulation of two-dimensional (2D) N=(2,2)SU(k) supersymmetric Yang-Mills theory (SYM). A perturbative argument shows that the SUSY WT identity in the continuum theory is reproduced in the continuum limit without any operator renormalization/mixing and tuning of lattice parameters. As application of the lattice SUSY WT identity, we show that a prescription for the Hamiltonian density in this lattice formulation, proposed by Kanamori, Sugino and Suzuki, is justified also from a perspective of an operator algebra among correctly-normalized supercurrents. We explicitly confirm the SUSY WT identity in the continuum limit to the first nontrivial order in a semi-perturbative expansion. 12. Effective Lagrangians for SUSY QCD with properties seen in perturbation theory International Nuclear Information System (INIS) Sharatchandra, H.S. 1984-06-01 We construct effective Lagrangians for supersymmetric QCD which properly incorporate the relevant Ward identities and possess features encountered in perturbation theory. This shows that the unusual scenarios, proposed for SUSY QCD, are not necessary. (author) 13. Interpretation of Higgs and Susy searches in MSUGRA and GMSB Models International Nuclear Information System (INIS) Vivie, J.B. de 1999-10-01 HIGGS and SUSY searches performed by the ALEPH Experiment at LEP are interpreted in the framework of two constrained R-parity conserving models: Minimal Supergravity and minimal Gauge Mediated Supersymmetry Breaking. (author) 14. Improved mass-measurement accuracy using a PNB Load Cell Scale International Nuclear Information System (INIS) Suda, S.; Pontius, P.; Schoonover, R. 1981-08-01 15. Prospects for SUSY discovery based on inclusive searches with the ATLAS detector International Nuclear Information System (INIS) Ventura, Andrea 2009-01-01 The search for Supersymmetry (SUSY) among the possible scenarios of new physics is one of the most relevant goals of the ATLAS experiment running at CERN's Large Hadron Collider. In the present work the expected prospects for discovering SUSY with the ATLAS detector are reviewed, in particular for the first fb -1 of collected integrated luminosity. All studies and results reported here are based on inclusive search analyses realized with Monte Carlo signal and background data simulated through the ATLAS apparatus. 16. Final Report: Geoelectrical Measurement of Multi-Scale Mass Transfer Parameters Energy Technology Data Exchange (ETDEWEB) Haggerty, Roy [Oregon State Univ., Corvallis, OR (United States); Day-Lewis, Fred [U.S. Geological Survey, Storrs, CT (United States); Singha, Kamini [Colorado School of Mines, Golden, CO (United States); Johnson, Timothy [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Binley, Andrew [Lancaster Univ. (United Kingdom); Lane, John [U.S. Geological Survey, Storrs, CT (United States) 2014-03-20 Mass transfer affects contaminant transport and is thought to control the efficiency of aquifer remediation at a number of sites within the Department of Energy (DOE) complex. An improved understanding of mass transfer is critical to meeting the enormous scientific and engineering challenges currently facing DOE. Informed design of site remedies and long-term stewardship of radionuclide-contaminated sites will require new cost-effective laboratory and field techniques to measure the parameters controlling mass transfer spatially and across a range of scales. In this project, we sought to capitalize on the geophysical signatures of mass transfer. Previous numerical modeling and pilot-scale field experiments suggested that mass transfer produces a geoelectrical signature—a hysteretic relation between sampled (mobile-domain) fluid conductivity and bulk (mobile + immobile) conductivity—over a range of scales relevant to aquifer remediation. In this work, we investigated the geoelectrical signature of mass transfer during tracer transport in a series of controlled experiments to determine the operation of controlling parameters, and also investigated the use of complex-resistivity (CR) as a means of quantifying mass transfer parameters in situ without tracer experiments. In an add-on component to our grant, we additionally considered nuclear magnetic resonance (NMR) to help parse mobile from immobile porosities. Including the NMR component, our revised study objectives were to: 1. Develop and demonstrate geophysical approaches to measure mass-transfer parameters spatially and over a range of scales, including the combination of electrical resistivity monitoring, tracer tests, complex resistivity, nuclear magnetic resonance, and materials characterization; and 2. Provide mass-transfer estimates for improved understanding of contaminant fate and transport at DOE sites, such as uranium transport at the Hanford 300 Area. To achieve our objectives, we implemented a 3 17. Effects of reservoir heterogeneity on scaling of effective mass transfer coefficient for solute transport Science.gov (United States) Leung, Juliana Y.; Srinivasan, Sanjay 2016-09-01 Modeling transport process at large scale requires proper scale-up of subsurface heterogeneity and an understanding of its interaction with the underlying transport mechanisms. A technique based on volume averaging is applied to quantitatively assess the scaling characteristics of effective mass transfer coefficient in heterogeneous reservoir models. The effective mass transfer coefficient represents the combined contribution from diffusion and dispersion to the transport of non-reactive solute particles within a fluid phase. Although treatment of transport problems with the volume averaging technique has been published in the past, application to geological systems exhibiting realistic spatial variability remains a challenge. Previously, the authors developed a new procedure where results from a fine-scale numerical flow simulation reflecting the full physics of the transport process albeit over a sub-volume of the reservoir are integrated with the volume averaging technique to provide effective description of transport properties. The procedure is extended such that spatial averaging is performed at the local-heterogeneity scale. In this paper, the transport of a passive (non-reactive) solute is simulated on multiple reservoir models exhibiting different patterns of heterogeneities, and the scaling behavior of effective mass transfer coefficient (Keff) is examined and compared. One such set of models exhibit power-law (fractal) characteristics, and the variability of dispersion and Keff with scale is in good agreement with analytical expressions described in the literature. This work offers an insight into the impacts of heterogeneity on the scaling of effective transport parameters. A key finding is that spatial heterogeneity models with similar univariate and bivariate statistics may exhibit different scaling characteristics because of the influence of higher order statistics. More mixing is observed in the channelized models with higher-order continuity. It 18. Higgsino dark matter in high-scale supersymmetry International Nuclear Information System (INIS) Nagata, Natsumi 2014-11-01 We study a supersymmetric (SUSY) Standard Model in which a Higgsino is light enough to be dark matter, while the other SUSY particles are much heavier than the weak scale. We carefully treat the effects of heavy SUSY particles to the Higgsino nature, especially taking into account the renormalization effects due to the large hierarchy between the Higgsino and the SUSY breaking scales. Inelastic scattering of the Higgsino dark matter with a nucleus is studied, and the constraints on the scattering by the direct detection experiments are discussed. This gives an upper limit on the new physics scale. Bounds on the dark matter-nucleon elastic scattering, the electric dipole moments, and direct production of Higgsinos, on the other hand, give a lower limit. We show the current status on the limits and discuss the future prospects. 19. The Children's Body Image Scale: reliability and use with international standards for body mass index. Science.gov (United States) Truby, Helen; Paxton, Susan J 2008-03-01 To test the reliability of the Children's Body Image Scale (CBIS) and assess its usefulness in the context of new body size charts for children. Participants were 281 primary schoolchildren with 50% being retested after 3 weeks. The CBIS figure scale was compared with a range of international body mass index (BMI) reference standards. Children had a high degree of body image dissatisfaction. The test-retest reliability of the CBIS was supported. The CBIS is a useful tool for assessing body image in children with sound scale properties. It can also be used to identify the body size of children, which lies outside the healthy weight range of BMI. 20. Basal metabolic rate scaled to body mass within species by the ... African Journals Online (AJOL) Basal metabolic rate scaled to body mass within species by the fractal dimension of the vascular system and body composition. ... The postulate bd = c is shown to hold for both these species within the limits of experimental error, with the crucian carp evidence being especially convincing, since b, c and d are estimated from ... 1. Deep inelastic scattering as a probe of new hadronic mass scales International Nuclear Information System (INIS) Burges, C.J.C.; Schnitzer, H.J. 1984-01-01 We present the general form for deep-inelastic cross sections obtained from all SU(3) x SU(2) x U(1) invariant operators of dimension six or less. The operators of dimension six generate corrections to the predictions of the standard model, which serve as a probe of a possible new mass-scale Λ and other new physics. (orig.) 2. Ontogenetic scaling of fish metabolism in the mouse-to-elephant mass magnitude range DEFF Research Database (Denmark) Moran, Damian; Wells, R.M.G. 2007-01-01 , and are therefore not statistically comparable. In this study the metabolic rate of yellowtail kingfish was measured from 0.6 mg-2.2 kg, a mass range comparable to that between a mouse and an elephant. Linear regression of the log transformed data resulted in a scaling exponent of 0.90 and high correlation... 3. Basal metabolic rate scaled to body mass between species by the ... African Journals Online (AJOL) The principal reason that basal metabolic rate (BMR) and MMR scale with different power exponents to whole body mass is that MMR is due mainly to respiration in skeletal muscle during exercise and BMR to respiration in the viscera during rest. It follows, therefore, from the self-similarity of the vascular system that BMR is ... 4. Necessity of intermediate mass scales in grand unified theories with spontaneously broken CP invariance International Nuclear Information System (INIS) Senjanovic, G. 1982-07-01 It is demonstrated that the spontaneous breakdown of CP invariance in grand unified theories requires the presence of intermediate mass scales. The simplest realization is provided by weakly broken left-right symmetry in the context of SU(2)sub(L) x SU(2)sub(R) x U(1)sub(B-L) model embedded in grand unified theories. (author) 5. Exercise-induced maximum metabolic rate scaled to body mass by ... African Journals Online (AJOL) user 2016-10-27 Oct 27, 2016 ... maximum aerobic metabolic rate (MMR) is proportional to the fractal extent ... metabolic rate with body mass can be obtained by taking body .... blood takes place. ..... MMR and BMR is that MMR is owing mainly to respiration in skeletal .... the spectra of surface area scaling strategies of cells and organisms:. 6. A model for a unification of scales. From MPlanck TO mν International Nuclear Information System (INIS) Pati, J.C. 1989-01-01 It is proposed that the hierarchical scales - from M Planck to m ν - have a common origin. Using M Planck and the coupling constant associated with a preonic metacolor gauge force as the only input parameters, it is shown how large ratios such as (M Pl /M I ), (M Pl /δm s ), (M Pl /m W ), (M Pl /m t ) and even (M Pl /m ν )> or approx.10 27 can arise naturally. Here M I denotes an intermediate scale ≅ 10 11 GeV, which is identified with the scale parameter of the metacolor force, while δm s denotes SUSY-breaking mass splittings ≅ 1 TeV. Local supersymmetry together with an inhibition in the breaking of global SUSY (index theorem) as well as compositeness of quarks, leptons and Higgs play crucial roles in this approach. Two key features of the model are the natural origins of composite vector-like families with masses of order of a few hundred GeV to 1 TeV and the consequent see-saw mechanism for the generations of quark-lepton masses and CP violation. (orig.) 7. Plasmon mass scale in two-dimensional classical nonequilibrium gauge theory Science.gov (United States) Lappi, T.; Peuron, J. 2018-02-01 We study the plasmon mass scale in classical gluodynamics in a two-dimensional configuration that mimics the boost-invariant initial color fields in a heavy-ion collision. We numerically measure the plasmon mass scale using three different methods: a hard thermal loop (HTL) expression involving the quasiparticle spectrum constructed from Coulomb gauge field correlators, an effective dispersion relation, and the measurement of oscillations between electric and magnetic energies after introducing a spatially uniform perturbation to the electric field. We find that the HTL expression and the uniform electric field measurement are in rough agreement. The effective dispersion relation agrees with other methods within a factor of 2. We also study the dependence on time and occupation number, observing similar trends as in three spatial dimensions, where a power-law dependence sets in after an occupation-number-dependent transient time. We observe a decrease of the plasmon mass squared as t-1 / 3 at late times. 8. Atomic scale mass delivery driven by bend kink in single walled carbon nanotube International Nuclear Information System (INIS) Kan Biao; Ding Jianning; Ling Zhiyong; Yuan Ningyi; Cheng Guanggui 2010-01-01 The possibility of atomic scale mass delivery by bend kink in single walled carbon nanotube was investigated with the aid of molecular dynamics simulation. By keeping the bending angle while moving the tube end, the encapsulated atomic scale mass such as atom, molecule and atom group were successfully delivered through the nanotube. The van der Waals interaction between the encapsulated mass and the tube wall provided the driving force for the delivery. There were no dramatic changes in the van der Waals interaction, and a smooth and steady delivery was achieved when constant loading rate was applied. The influence of temperature on the atom group delivery was also analyzed. It is found raising temperature is harmful to the smooth movement of the atom group. However, the delivery rate can be promoted under higher temperature when the atom group is situated before the kink during the delivery. 9. SUSY non-Abelian gauge models: exact beta function from one loop of perturbation theory International Nuclear Information System (INIS) Shifman, M.A.; Vajnshtejn, A.I.; Zakharov, V.I. 1985-01-01 The method for calculating the exact β function (to all orders in the coupling constant) proposed earlier in supersymmetric electrodynamics is extended. The starting point is the observation that the low-energy effective action is exhausted by one loop provided that the theory is regularized supersymmetrically both in the ultraviolet and infrared domains in four dimensions. The Pouli-Villars method of the ultraviolet regularization is used. Two methods for the infrared regularization are considered. The first one - quantization in a box with a finite volume L 3 - is universally applicable to anygauge theory. The second method is based on the effective Higgs mechanism for mass generation and requires the presence of certain matter superfields in the lagrangian. Within this method the necessary condition is the existence of flat directions, so called valeys, along which the vacuum energy vanishes. The theory is quantized near epsilon non-vanishing value of the scalar field from the bottom of the valley. After calculating the one-loop effective action one and the same exact expression is obtained for the β function within the both approaches, and it also coincides with our earlier result extracted from instanton calculus. A few remarks on the problem of anomalies in SUSY gauge theories are presented 10. Large-scale correlations in gas traced by Mg II absorbers around low-mass galaxies Science.gov (United States) Kauffmann, Guinevere 2018-03-01 The physical origin of the large-scale conformity in the colours and specific star formation rates of isolated low-mass central galaxies and their neighbours on scales in excess of 1 Mpc is still under debate. One possible scenario is that gas is heated over large scales by feedback from active galactic nuclei (AGNs), leading to coherent modulation of cooling and star formation between well-separated galaxies. In this Letter, the metal line absorption catalogue of Zhu & Ménard is used to probe gas out to large projected radii around a sample of a million galaxies with stellar masses ˜1010M⊙ and photometric redshifts in the range 0.4 Survey imaging data. This galaxy sample covers an effective volume of 2.2 Gpc3. A statistically significant excess of Mg II absorbers is present around the red-low-mass galaxies compared to their blue counterparts out to projected radii of 10 Mpc. In addition, the equivalent width distribution function of Mg II absorbers around low-mass galaxies is shown to be strongly affected by the presence of a nearby (Rp < 2 Mpc) radio-loud AGNs out to projected radii of 5 Mpc. 11. Multiscale N=2 SUSY field theories, integrable systems and their stringy/brane origin International Nuclear Information System (INIS) Gorsky, A.; Gukov, S.; Mironov, A. 1998-01-01 We discuss supersymmetric Yang-Mills theories with multiple scales in the brane language. The issue concerns N=2 SUSY gauge theories with massive fundamental matter including the UV finite case of n f =2n c , theories involving products of SU(n) gauge groups with bifundamental matter, and systems with several parameters similar to Λ QCD . We argue that the proper integrable systems are, accordingly, twisted XXX SL(2) spin chain, SL(p) magnets and degenerations of the spin Calogero system. The issue of symmetries underlying integrable systems is addressed. Relations with the monopole systems are specially discussed. Brane pictures behind all these integrable structures in the IIB and M-theory are suggested. We argue that degrees of freedom in integrable systems are related to KK excitations in M-theory or D-particles in the IIA string theory, which substitute the infinite number of instantons in the field theory. This implies the presence of more BPS states in the low-energy sector. (orig.) 12. Baryon asymmetry via leptogenesis in a neutrino mass model with complex scaling International Nuclear Information System (INIS) Samanta, Rome; Ghosal, Ambar; Chakraborty, Mainak; Roy, Probir 2017-01-01 Baryogenesis via leptogenesis is investigated in a specific model of light neutrino masses and mixing angles. The latter was proposed on the basis of an assumed complex-extended scaling property of the neutrino Majorana mass matrix M ν , derived with a type-1 seesaw from a Dirac mass matrix m D and a heavy singlet neutrino Majorana mass matrix M R . One of its important features, highlighted here, is that there is a common source of the origin of a nonzero θ 13 and the CP violating lepton asymmetry through the imaginary part of m D . The model predicted CP violation to be maximal for the Dirac type and vanishing for the Majorana type. We assume strongly hierarchical mass eigenvalues for M R . The leptonic CP asymmetry parameter ε α 1 mm with lepton flavor α, originating from the decays of the lightest of the heavy neutrinos N 1 (of mass M 1 ) at a temperature T ∼ M 1 , is what matters here with the lepton asymmetries, originating from the decays of N 2,3 , being washed out. The light leptonic and heavy neutrino number densities (normalized to the entropy density) are evolved via Boltzmann equations down to electroweak temperatures to yield a baryon asymmetry through sphaleronic transitions. The effects of flavored vs. unflavored leptogenesis in the three mass regimes (1) M 1 < 10 9 GeV, (2) 10 9 GeV < M 1 < 10 12 GeV and (3) M 1 > 10 12 GeV are numerically worked out for both a normal and an inverted mass ordering of the light neutrinos. Corresponding results on the baryon asymmetry of the universe are obtained, displayed and discussed. For values close to the best-fit points of the input neutrino mass and mixing parameters, obtained from neutrino oscillation experiments, successful baryogenesis is achieved for the mass regime (2) and a normal mass ordering of the light neutrinos with a nonzero θ 13 playing a crucial role. However, the other possibility of an inverted mass ordering for the same mass regime, though disfavored, cannot be excluded. A 13. Baryon asymmetry via leptogenesis in a neutrino mass model with complex scaling Energy Technology Data Exchange (ETDEWEB) Samanta, Rome; Ghosal, Ambar [Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata 700064 (India); Chakraborty, Mainak [Centre of Excellence in Theoretical and Mathematical Sciences, SOA University, Khandagiri Square, Bhubaneswar 751030 (India); Roy, Probir, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Center for Astroparticle Physics and Space Science, Bose Institute, Kolkata 700091 (India) 2017-03-01 Baryogenesis via leptogenesis is investigated in a specific model of light neutrino masses and mixing angles. The latter was proposed on the basis of an assumed complex-extended scaling property of the neutrino Majorana mass matrix M {sub ν}, derived with a type-1 seesaw from a Dirac mass matrix m {sub D} and a heavy singlet neutrino Majorana mass matrix M {sub R} . One of its important features, highlighted here, is that there is a common source of the origin of a nonzero θ{sub 13} and the CP violating lepton asymmetry through the imaginary part of m {sub D} . The model predicted CP violation to be maximal for the Dirac type and vanishing for the Majorana type. We assume strongly hierarchical mass eigenvalues for M {sub R} . The leptonic CP asymmetry parameter ε{sup α}{sub 1} mm with lepton flavor α, originating from the decays of the lightest of the heavy neutrinos N {sub 1} (of mass M {sub 1}) at a temperature T ∼ M {sub 1}, is what matters here with the lepton asymmetries, originating from the decays of N {sub 2,3}, being washed out. The light leptonic and heavy neutrino number densities (normalized to the entropy density) are evolved via Boltzmann equations down to electroweak temperatures to yield a baryon asymmetry through sphaleronic transitions. The effects of flavored vs. unflavored leptogenesis in the three mass regimes (1) M {sub 1} < 10{sup 9} GeV, (2) 10{sup 9} GeV < M {sub 1} < 10{sup 12} GeV and (3) M {sub 1} > 10{sup 12} GeV are numerically worked out for both a normal and an inverted mass ordering of the light neutrinos. Corresponding results on the baryon asymmetry of the universe are obtained, displayed and discussed. For values close to the best-fit points of the input neutrino mass and mixing parameters, obtained from neutrino oscillation experiments, successful baryogenesis is achieved for the mass regime (2) and a normal mass ordering of the light neutrinos with a nonzero θ{sub 13} playing a crucial role. However, the other 14. Basin-scale heterogeneity in Antarctic precipitation and its impact on surface mass variability Directory of Open Access Journals (Sweden) J. Fyke 2017-11-01 Full Text Available Annually averaged precipitation in the form of snow, the dominant term of the Antarctic Ice Sheet surface mass balance, displays large spatial and temporal variability. Here we present an analysis of spatial patterns of regional Antarctic precipitation variability and their impact on integrated Antarctic surface mass balance variability simulated as part of a preindustrial 1800-year global, fully coupled Community Earth System Model simulation. Correlation and composite analyses based on this output allow for a robust exploration of Antarctic precipitation variability. We identify statistically significant relationships between precipitation patterns across Antarctica that are corroborated by climate reanalyses, regional modeling and ice core records. These patterns are driven by variability in large-scale atmospheric moisture transport, which itself is characterized by decadal- to centennial-scale oscillations around the long-term mean. We suggest that this heterogeneity in Antarctic precipitation variability has a dampening effect on overall Antarctic surface mass balance variability, with implications for regulation of Antarctic-sourced sea level variability, detection of an emergent anthropogenic signal in Antarctic mass trends and identification of Antarctic mass loss accelerations. 15. Low-energy parity restoration and unification mass scale within maximal symmetries Directory of Open Access Journals (Sweden) Ajaya K. Mohanty 1984-01-01 Full Text Available We investigate the hierarchy of gauge boson masses in the maximal grand unified theory by studying the renormalization group equations for the running coupling constants associated with the symmetry breaking of SU(16viaSU(12 q×SU(4 l×U(1 \|B\|−\|L\| chain. Particular attention is given to the contribution of Higgs scalars to these equations. It is found that the intermediate mass scale ML, associated with right-handed gauge bosons could be as low as 10 3 GeV only for sin 2θ w(M L as high as 0.265 with α s(M L=0.13. In this chain of symmetry breaking, we have also examined the lowest unification mass that is allowed by the low-energy data for sin 2θ w(M L and the assumed gauge hierarchy. This has been done in two cases; first for the case where SU(3 c is vectorial, second, for the case where SU(3 c is axial. In both cases the lowest unification mass scales were found to be 10 13, 10 11, 10 8 and 10 7 GeV for sin 2θ w(M L = 0.22, 0.24, 0.26,and0.265 respectively with α s(M L = 0.13. The implication of these low unification masses on baryon non-conserving processes is also discussed. 16. Scaling of avian bipedal locomotion reveals independent effects of body mass and leg posture on gait. Science.gov (United States) Daley, Monica A; Birn-Jeffery, Aleksandra 2018-05-22 Birds provide an interesting opportunity to study the relationships between body size, limb morphology and bipedal locomotor function. Birds are ecologically diverse and span a large range of body size and limb proportions, yet all use their hindlimbs for bipedal terrestrial locomotion, for at least some part of their life history. Here, we review the scaling of avian striding bipedal gaits to explore how body mass and leg morphology influence walking and running. We collate literature data from 21 species, spanning a 2500× range in body mass from painted quail to ostriches. Using dynamic similarity theory to interpret scaling trends, we find evidence for independent effects of body mass, leg length and leg posture on gait. We find no evidence for scaling of duty factor with body size, suggesting that vertical forces scale with dynamic similarity. However, at dynamically similar speeds, large birds use relatively shorter stride lengths and higher stride frequencies compared with small birds. We also find that birds with long legs for their mass, such as the white stork and red-legged seriema, use longer strides and lower swing frequencies, consistent with the influence of high limb inertia on gait. We discuss the observed scaling of avian bipedal gait in relation to mechanical demands for force, work and power relative to muscle actuator capacity, muscle activation costs related to leg cycling frequency, and considerations of stability and agility. Many opportunities remain for future work to investigate how morphology influences gait dynamics among birds specialized for different habitats and locomotor behaviors. © 2018. Published by The Company of Biologists Ltd. 17. Effects of Contingency versus Constraints on the Body-Mass Scaling of Metabolic Rate Directory of Open Access Journals (Sweden) Douglas S. Glazier 2018-01-01 Full Text Available I illustrate the effects of both contingency and constraints on the body-mass scaling of metabolic rate by analyzing the significantly different influences of ambient temperature (Ta on metabolic scaling in ectothermic versus endothermic animals. Interspecific comparisons show that increasing Ta results in decreasing metabolic scaling slopes in ectotherms, but increasing slopes in endotherms, a pattern uniquely predicted by the metabolic-level boundaries hypothesis, as amended to include effects of the scaling of thermal conductance in endotherms outside their thermoneutral zone. No other published theoretical model explicitly predicts this striking variation in metabolic scaling, which I explain in terms of contingent effects of Ta and thermoregulatory strategy in the context of physical and geometric constraints related to the scaling of surface area, volume, and heat flow across surfaces. My analysis shows that theoretical models focused on an ideal 3/4-power law, as explained by a single universally applicable mechanism, are clearly inadequate for explaining the diversity and environmental sensitivity of metabolic scaling. An important challenge is to develop a theory of metabolic scaling that recognizes the contingent effects of multiple mechanisms that are modulated by several extrinsic and intrinsic factors within specified constraints. 18. Scaling of Myocardial Mass to Flow and Morphometry of Coronary Arteries OpenAIRE Choy, Jenny Susana; Kassab, Ghassan S. 2008-01-01 There is no doubt that scaling relations exist between myocardial mass and morphometry of coronary vasculature. The purpose of this study is to quantify several morphological (diameter, length, and volume) and functional (flow) parameters of the coronary arterial tree in relation to myocardial mass. Eight normal porcine hearts of 117-244 g (mean of 177.5±32.7) were used in this study. Various coronary sub-trees of the Left Anterior Descending (LAD), Right Coronary (RCA) and Left Circumflex (L... 19. Absolute calibration of the mass scale in the inverse problem of the physical theory of fireballs Science.gov (United States) Kalenichenko, V. V. 1992-08-01 A method of the absolute calibration of the mass scale is proposed for solving the inverse problem of the physical theory of fireballs. The method is based on data on the masses of fallen meteorites whose fireballs have been photographed in flight. The method can be applied to fireballs whose bodies have not experienced significant fragmentation during their flight in the atmosphere and have kept their shape relatively well. Data on the Lost City and Innisfree meteorites are used to calculate the calibration coefficients. 20. Absolute mass scale calibration in the inverse problem of the physical theory of fireballs. Science.gov (United States) Kalenichenko, V. V. A method of the absolute mass scale calibration is suggested for solving the inverse problem of the physical theory of fireballs. The method is based on the data on the masses of the fallen meteorites whose fireballs have been photographed in their flight. The method may be applied to those fireballs whose bodies have not experienced considerable fragmentation during their destruction in the atmosphere and have kept their form well enough. Statistical analysis of the inverse problem solution for a sufficiently representative sample makes it possible to separate a subsample of such fireballs. The data on the Lost City and Innisfree meteorites are used to obtain calibration coefficients. 1. Strange star candidates revised within a quark model with chiral mass scaling Institute of Scientific and Technical Information of China (English) Ang Li; Guang-Xiong Peng; Ju-Fu Lu 2011-01-01 We calculate the properties of static strange stars using a quark model with chiral mass scaling. The results are characterized by a large maximum mass (～ 1.6 M⊙) and radius (～ 10 km). Together with a broad collection of modern neutron star models, we discuss some recent astrophysical observational data that could shed new light on the possible presence of strange quark matter in compact stars. We conclude that none of the present astrophysical observations can prove or confute the existence of strange stars. 2. Dark-Matter Particles without Weak-Scale Masses or Weak Interactions International Nuclear Information System (INIS) Feng, Jonathan L.; Kumar, Jason 2008-01-01 We propose that dark matter is composed of particles that naturally have the correct thermal relic density, but have neither weak-scale masses nor weak interactions. These models emerge naturally from gauge-mediated supersymmetry breaking, where they elegantly solve the dark-matter problem. The framework accommodates single or multiple component dark matter, dark-matter masses from 10 MeV to 10 TeV, and interaction strengths from gravitational to strong. These candidates enhance many direct and indirect signals relative to weakly interacting massive particles and have qualitatively new implications for dark-matter searches and cosmological implications for colliders 3. Predictions of the marviken subcooled critical mass flux using the critical flow scaling parameters Energy Technology Data Exchange (ETDEWEB) Park, Choon Kyung; Chun, Se Young; Cho, Seok; Yang, Sun Ku; Chung, Moon Ki [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of) 1997-12-31 A total of 386 critical flow data points from 19 runs of 27 runs in the Marviken Test were selected and compared with the predictions by the correlations based on the critical flow scaling parameters. The results show that the critical mass flux in the very large diameter pipe can be also characterized by two scaling parameters such as discharge coefficient and dimensionless subcooling (C{sub d,ref} and {Delta}{Tau}{sup } {sub sub}). The agreement between the measured data and the predictions are excellent. 8 refs., 8 figs. 1 tab. (Author) 4. Predictions of the marviken subcooled critical mass flux using the critical flow scaling parameters Energy Technology Data Exchange (ETDEWEB) Park, Choon Kyung; Chun, Se Young; Cho, Seok; Yang, Sun Ku; Chung, Moon Ki [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of) 1998-12-31 A total of 386 critical flow data points from 19 runs of 27 runs in the Marviken Test were selected and compared with the predictions by the correlations based on the critical flow scaling parameters. The results show that the critical mass flux in the very large diameter pipe can be also characterized by two scaling parameters such as discharge coefficient and dimensionless subcooling (C{sub d,ref} and {Delta}{Tau}{sup } {sub sub}). The agreement between the measured data and the predictions are excellent. 8 refs., 8 figs. 1 tab. (Author) 5. ADVANTAGES OF RAPID METHOD FOR DETERMINING SCALE MASS AND DECARBURIZED LAYER OF ROLLED COIL STEEL Directory of Open Access Journals (Sweden) E. V. Parusov 2016-08-01 Full Text Available Purpose. To determine the universal empirical relationships that allow for operational calculation of scale mass and decarbonized layer depth based on the parameters of the technological process for rolled coil steel production. Methodology. The research is carried out on the industrial batches of the rolled steel of SAE 1006 and SAE 1065 grades. Scale removability was determined in accordance with the procedure of «Bekaert» company by the specifi-cations: GA-03-16, GA-03-18, GS-03-02, GS-06-01. The depth of decarbonized layer was identified in accordance with GOST 1763-68 (M method. Findings. Analysis of experimental data allowed us to determine the rational temperature of coil formation of the investigated steel grades, which provide the best possible removal of scale from the metal surface, a minimal amount of scale, as well as compliance of the metal surface color with the require-ments of European consumers. Originality. The work allowed establishing correlation of the basic quality indicators of the rolled coil high carbon steel (scale mass, depth of decarbonized layer and inter-laminar distance in pearlite with one of the main parameters (coil formation temperature of the deformation and heat treatment mode. The re-sulting regression equations, without metallographic analysis, can be used to determine, with a minimum error, the quantitative values of the total scale mass, depth of decarbonized layer and the average inter-lamellar distance in pearlite of the rolled coil high carbon steel. Practical value. Based on the specifications of «Bekaert» company (GA-03-16, GA-03-18, GS-03-02 and GS-06-01 the method of testing descaling by mechanical means from the surface of the rolled coil steel of low- and high-carbon steel grades was developed and approved in the environment of PJSC «ArcelorMittal Kryvyi Rih». The work resulted in development of the rapid method for determination of total and remaining scale mass on the rolled coil steel 6. 2MASS Constraints on the Local Large-Scale Structure: A Challenge to LCDM? OpenAIRE Frith, W. J.; Shanks, T.; Outram, P. J. 2004-01-01 We investigate the large-scale structure of the local galaxy distribution using the recently completed 2 Micron All Sky Survey (2MASS). First, we determine the K-band number counts over the 4000 sq.deg. APM survey area where evidence for a large-scale local hole' has previously been detected and compare them to a homogeneous prediction. Considering a LCDM form for the 2-point angular correlation function, the observed deficiency represents a 5 sigma fluctuation in the galaxy distribution. We... 7. Vacuum stability with tachyonic boundary Higgs masses in no-scale supersymmetry or gaugino mediation International Nuclear Information System (INIS) Evans, Jason L.; Wells, James D.; Morrissey, David E. 2009-01-01 No-scale supersymmetry or gaugino mediation augmented with large negative Higgs soft masses at the input scale provides a simple solution to the supersymmetric flavor problem while giving rise to a neutralino lightest superpartner particle. However, to obtain a neutralino lightest superpartner particle it is often necessary to have tachyonic input Higgs soft masses that can give rise to charge-and-color-breaking minima and unbounded-from-below directions in the low-energy theory. We investigate the vacuum structure in these theories to determine when such problematic features are present. When the standard electroweak vacuum is only metastable, we compute its lifetime under vacuum tunneling. We find that vacuum metastability leads to severe restrictions on the parameter space for larger tanβ∼30, while for smaller tanβ∼10, only minor restrictions are found. Along the way, we derive an exact bounce solution for tunneling through an inverted parabolic potential. 8. Vacuum Stability with Tachyonic Boundary Higgs Masses in No-Scale Supersymmetry or Gaugino Mediation CERN Document Server Evans, Jason L; Wells, James D 2009-01-01 No-scale supersymmetry or gaugino mediation augmented with large negative Higgs soft masses at the input scale provides a simple solution to the supersymmetric flavor problem while giving rise to a neutralino LSP. However, to obtain a neutralino LSP it is often necessary to have tachyonic input Higgs soft masses that can give rise to charge-and-color-breaking (CCB) minima and unbounded-from-below (UFB) directions in the low energy theory. We investigate the vacuum structure in these theories to determine when such problematic features are present. When the standard electroweak vacuum is only metastable, we compute its lifetime under vacuum tunneling. We find that vacuum metastability leads to severe restrictions on the parameter space for larger $\\tan\\beta \\sim 30$, while for smaller $\\tan\\beta\\sim 10$, only minor restrictions are found. Along the way, we derive an exact bounce solution for tunneling through an inverted parabolic potential. 9. Large scale mass redistribution and surface displacement from GRACE and SLR Science.gov (United States) Cheng, M.; Ries, J. C.; Tapley, B. D. 2012-12-01 Mass transport between the atmosphere, ocean and solid earth results in the temporal variations in the Earth gravity field and loading induced deformation of the Earth. Recent space-borne observations, such as GRACE mission, are providing extremely high precision temporal variations of gravity field. The results from 10-yr GRACE data has shown a significant annual variations of large scale vertical and horizontal displacements occurring over the Amazon, Himalayan region and South Asia, African, and Russian with a few mm amplitude. Improving understanding from monitoring and modeling of the large scale mass redistribution and the Earth's response are a critical for all studies in the geosciences, in particular for determination of Terrestrial Reference System (TRS), including geocenter motion. This paper will report results for the observed seasonal variations in the 3-dimentional surface displacements of SLR and GPS tracking stations and compare with the prediction from time series of GRACE monthly gravity solution. 10. On the MSSM Higgsino mass and fine tuning CERN Document Server Ross, Graham G. 2016-08-10 It is often argued that low fine tuning in the MSSM necessarily requires a rather light Higgsino. In this note we show that this need not be the case when a more complete set of soft SUSY breaking mass terms are included. In particular an Higgsino mass term, that correlates the $\\mu-$term contribution with the soft SUSY-breaking Higgsino masses, significantly reduces the fine tuning even for Higgsinos in the TeV mass range where its relic abundance means it can make up all the dark matter. 11. Sgoldstino-less inflation and low energy SUSY breaking Energy Technology Data Exchange (ETDEWEB) Argurio, Riccardo [Physique Théorique et Mathématique and International Solvay Institutes, Université Libre de Bruxelles, CP231, B-1050 Brussels (Belgium); Coone, Dries; Mariotti, Alberto [Theoretische Natuurkunde and IIHE/ELEM, Vrije Universiteit Brussel, and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Heurtier, Lucien, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Service de Physique Théorique, Université Libre de Bruxelles, CP225, B-1050 Brussels (Belgium) 2017-07-01 We assess the range of validity of sgoldstino-less inflation in a scenario of low energy supersymmetry breaking. We first analyze the consistency conditions that an effective theory of the inflaton and goldstino superfields should satisfy in order to be faithfully described by a sgoldstino-less model. Enlarging the scope of previous studies, we investigate the case where the effective field theory cut-off, and hence also the sgoldstino mass, are inflaton-dependent. We then introduce a UV complete model where one can realize successfully sgoldstino-less inflation and gauge mediation of supersymmetry breaking, combining the α-attractor mechanism and a weakly coupled model of spontaneous breaking of supersymmetry. In this class of models we find that, given current limits on superpartner masses, the gravitino mass has a lower bound of the order of the MeV, i.e. we cannot reach very low supersymmetry breaking scales. On the plus side, we recognize that in this framework, one can derive the complete superpartner spectrum as well as compute inflation observables, the reheating temperature, and address the gravitino overabundance problem. We then show that further constraints come from collider results and inflation observables. Their non trivial interplay seems a staple feature of phenomenological studies of supersymmetric inflationary models. 12. Starobinsky-like inflation and neutrino masses in a no-scale SO(10) model Energy Technology Data Exchange (ETDEWEB) Ellis, John [Theoretical Particle Physics and Cosmology Group,Department of Physics, King’s College London, WC2R 2LS London (United Kingdom); Theoretical Physics Department, CERN,CH-1211 Geneva 23 (Switzerland); Garcia, Marcos A.G. [Physics and Astronomy Department, Rice University,6100 Main Street, Houston, TX 77005 (United States); Nagata, Natsumi [Department of Physics, University of Tokyo,Bunkyo-ku, Tokyo 113-0033 (Japan); Nanopoulos, Dimitri V. [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University, College Station, 77843 Texas (United States); Olive, Keith A. [William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of Minnesota,116 Church Street SE, Minneapolis, MN 55455 (United States) 2016-11-08 Using a no-scale supergravity framework, we construct an SO(10) model that makes predictions for cosmic microwave background observables similar to those of the Starobinsky model of inflation, and incorporates a double-seesaw model for neutrino masses consistent with oscillation experiments and late-time cosmology. We pay particular attention to the behaviour of the scalar fields during inflation and the subsequent reheating. 13. Hydrogen-antihydrogen oscillations: Signature of intermediate mass scales in GUTs Directory of Open Access Journals (Sweden) Uptal Sarkar 1983-01-01 Full Text Available Hydrogen-antihydrogen oscillations and the double nucleon decay (pp, np and nn into two antileptons are discussed in the context of SO(10, E(6 and SU(16 GUTs. It is shown that the intermediate mass scales of the GUTs concerned govern the amplitude of these processes which are found to compete with the other baryon nonconserving processes in SU(16 GUT. 14. Starobinsky-Like Inflation and Neutrino Masses in a No-Scale SO(10) Model CERN Document Server Ellis, John 2016-11-08 Using a no-scale supergravity framework, we construct an SO(10) model that makes predictions for cosmic microwave background observables similar to those of the Starobinsky model of inflation, and incorporates a double-seesaw model for neutrino masses consistent with oscillation experiments and late-time cosmology. We pay particular attention to the behaviour of the scalar fields during inflation and the subsequent reheating. 15. Renormalization group and relations between scattering amplitudes in a theory with different mass scales International Nuclear Information System (INIS) Gulov, A.V.; Skalozub, V.V. 2000-01-01 In the Yukawa model with two different mass scales the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. Considering fermion-fermion scattering as an example, a basic one-loop renormalization group relation is derived which gives possibility to reduce the problem to the scattering of light particles on the external field substituting a heavy virtual state. Applications of the results to problem of searching new physics beyond the Standard Model are discussed [ru 16. GUT scale threshold corrections in a complete supersymmetric SO(10) model: αs(MZ) versus proton lifetime International Nuclear Information System (INIS) Lucas, V.; Raby, S. 1996-01-01 We show that one-loop GUT scale threshold corrections to gauge couplings are a significant constraint on the GUT symmetry-breaking sector of the theory. The one-loop threshold corrections relate the prediction for α s (M Z ) to the proton lifetime. We have calculated these corrections in a new complete SO(10) SUSY GUT. The results are consistent with the low-energy measurement of α s (M Z ). We have also calculated the proton lifetime and branching ratios in this model. We show that proton decay rates provide a powerful test for theories of fermion masses. copyright 1996 The American Physical Society 17. The BSM-AI project: SUSY-AI-generalizing LHC limits on supersymmetry with machine learning Energy Technology Data Exchange (ETDEWEB) Caron, Sascha [Radboud Universiteit, Institute for Mathematics, Astro- and Particle Physics IMAPP, Nijmegen (Netherlands); Nikhef, Amsterdam (Netherlands); Kim, Jong Soo [UAM/CSIC, Instituto de Fisica Teorica, Madrid (Spain); Rolbiecki, Krzysztof [UAM/CSIC, Instituto de Fisica Teorica, Madrid (Spain); University of Warsaw, Faculty of Physics, Warsaw (Poland); Ruiz de Austri, Roberto [IFIC-UV/CSIC, Instituto de Fisica Corpuscular, Valencia (Spain); Stienen, Bob [Radboud Universiteit, Institute for Mathematics, Astro- and Particle Physics IMAPP, Nijmegen (Netherlands) 2017-04-15 A key research question at the Large Hadron Collider is the test of models of new physics. Testing if a particular parameter set of such a model is excluded by LHC data is a challenge: it requires time consuming generation of scattering events, simulation of the detector response, event reconstruction, cross section calculations and analysis code to test against several hundred signal regions defined by the ATLAS and CMS experiments. In the BSM-AI project we approach this challenge with a new idea. A machine learning tool is devised to predict within a fraction of a millisecond if a model is excluded or not directly from the model parameters. A first example is SUSY-AI, trained on the phenomenological supersymmetric standard model (pMSSM). About 300, 000 pMSSM model sets - each tested against 200 signal regions by ATLAS - have been used to train and validate SUSY-AI. The code is currently able to reproduce the ATLAS exclusion regions in 19 dimensions with an accuracy of at least 93%. It has been validated further within the constrained MSSM and the minimal natural supersymmetric model, again showing high accuracy. SUSY-AI and its future BSM derivatives will help to solve the problem of recasting LHC results for any model of new physics. SUSY-AI can be downloaded from http://susyai.hepforge.org/. An on-line interface to the program for quick testing purposes can be found at http://www.susy-ai.org/. (orig.) 18. The BSM-AI project: SUSY-AI-generalizing LHC limits on supersymmetry with machine learning International Nuclear Information System (INIS) Caron, Sascha; Kim, Jong Soo; Rolbiecki, Krzysztof; Ruiz de Austri, Roberto; Stienen, Bob 2017-01-01 A key research question at the Large Hadron Collider is the test of models of new physics. Testing if a particular parameter set of such a model is excluded by LHC data is a challenge: it requires time consuming generation of scattering events, simulation of the detector response, event reconstruction, cross section calculations and analysis code to test against several hundred signal regions defined by the ATLAS and CMS experiments. In the BSM-AI project we approach this challenge with a new idea. A machine learning tool is devised to predict within a fraction of a millisecond if a model is excluded or not directly from the model parameters. A first example is SUSY-AI, trained on the phenomenological supersymmetric standard model (pMSSM). About 300, 000 pMSSM model sets - each tested against 200 signal regions by ATLAS - have been used to train and validate SUSY-AI. The code is currently able to reproduce the ATLAS exclusion regions in 19 dimensions with an accuracy of at least 93%. It has been validated further within the constrained MSSM and the minimal natural supersymmetric model, again showing high accuracy. SUSY-AI and its future BSM derivatives will help to solve the problem of recasting LHC results for any model of new physics. SUSY-AI can be downloaded from http://susyai.hepforge.org/. An on-line interface to the program for quick testing purposes can be found at http://www.susy-ai.org/. (orig.) 19. Neutrino masses and a low breaking scale of left-right symmetry International Nuclear Information System (INIS) 2002-01-01 In left-right symmetric models (LRSMs) the light neutrino masses arise from two sources: the seesaw mechanism and a vacuum expectation value of an SU(2) L triplet. If the left-right symmetry breaking v R is low, v R (less-or-similar sign)15 TeV, the contributions to the light neutrino masses from both the seesaw mechanism and the triplet Yukawa couplings are expected to be well above the experimental bounds. We present a minimal LRSM with an additional U(1) symmetry in which the masses induced by the two sources are below the eV scale and the twofold problem is solved. We further show that, if the U(1) symmetry is also responsible for the lepton flavor structure, the model yields a small mixing angle within the first two lepton generations 20. Studies on reducing the scale of a double focusing mass spectrometer International Nuclear Information System (INIS) Chambers, D.M.; Gregg, H.R.; Andresen, B.D. 1993-05-01 Several groups have developed miniaturized sector mass spectrometers with the goal of remote sensing in confined spaces or portability. However, these achievements have been overshadowed by more successful development of man-portable quadrupole and ion trap mass spectrometers. Despite these accomplishments the development of a reduced-scale sector mass spectrometer remains attractive as a potentially low-cost, robust instrument requiring very simple electronics and low power. Previous studies on miniaturizing sector instruments include the use of a Mattauch-Herzog design for a portable mass spectrograph weighing less than 10 kg. Other work has included the use of a Nier-Johnson design in spacecraft-mountable gas chromatography mass spectrometers for the Viking spacecraft as well as miniature sector-based MS/MS instrument. Although theory for designing an optimized system with high resolution and mass accuracy is well understood, such specifications have not yet been achieved in a miniaturized instrument. To proceed further toward the development of a miniaturized sector mass spectrometer, experiments were conducted to understand and optimize a practical, yet nonideal instrument configuration. The sector mass spectrometer studied in this work is similar to the ones developed for the Viking project, but was further modified to be low cost, simple and robust. Characteristics of this instrument that highlight its simplicity include the use of a modified Varian leak detector ion source, source ion optics that use one extraction voltage, and an unshunted fixed nonhomogeneous magnetic sector. The effects of these design simplifications on ion trajectory were studied by manipulating the ion beam along with the magnetic sector position. This latter feature served as an aid to study ion focusing amidst fringing fields as well as nonhomogeneous forces and permitted empirical realignment of the instrument 1. On a generalized Dirac oscillator interaction for the nonrelativistic limit 3 D generalized SUSY model oscillator Hamiltonian of Celka and Hussin International Nuclear Information System (INIS) Jayaraman, Jambunatha; Lima Rodrigues, R. de 1994-01-01 In the context of the 3 D generalized SUSY model oscillator Hamiltonian of Celka and Hussin (CH), a generalized Dirac oscillator interaction is studied, that leads, in the non-relativistic limit considered for both signs of energy, to the CH's generalized 3 D SUSY oscillator. The relevance of this interaction to the CH's SUSY model and the SUSY breaking dependent on the Wigner parameter is brought out. (author). 6 refs 2. Large-scale subduction of continental crust implied by India-Asia mass-balance calculation Science.gov (United States) Ingalls, Miquela; Rowley, David B.; Currie, Brian; Colman, Albert S. 2016-11-01 Continental crust is buoyant compared with its oceanic counterpart and resists subduction into the mantle. When two continents collide, the mass balance for the continental crust is therefore assumed to be maintained. Here we use estimates of pre-collisional crustal thickness and convergence history derived from plate kinematic models to calculate the crustal mass balance in the India-Asia collisional system. Using the current best estimates for the timing of the diachronous onset of collision between India and Eurasia, we find that about 50% of the pre-collisional continental crustal mass cannot be accounted for in the crustal reservoir preserved at Earth's surface today--represented by the mass preserved in the thickened crust that makes up the Himalaya, Tibet and much of adjacent Asia, as well as southeast Asian tectonic escape and exported eroded sediments. This implies large-scale subduction of continental crust during the collision, with a mass equivalent to about 15% of the total oceanic crustal subduction flux since 56 million years ago. We suggest that similar contamination of the mantle by direct input of radiogenic continental crustal materials during past continent-continent collisions is reflected in some ocean crust and ocean island basalt geochemistry. The subduction of continental crust may therefore contribute significantly to the evolution of mantle geochemistry. 3. Split-Family SUSY, U(2)^5 Flavour Symmetry and Neutrino Physics CERN Document Server Jones-Pérez, Joel 2014-01-01 In split-family SUSY, one can use a U(2)^3 symmetry to protect flavour observables in the quark sector from SUSY contributions. However, attempts to extend this procedure to the lepton sector by using an analogous U(2)^5 symmetry fail to reproduce the neutrino data without introducing some form of fine-tuning. In this work, we solve this problem by shifting the U(2)^2 symmetry acting on leptons towards the second and third generations. This allows neutrino data to be reproduced without much difficulties, as well as protecting the leptonic flavour observables from SUSY. Key signatures are a $\\mu\\to e\\gamma$ branching ratio possibly observable in the near future, as well as having selectrons as the lightest sleptons. 4. Deletion analysis of susy-sl promoter for the identification of optimal promoter sequence International Nuclear Information System (INIS) Bacha, S.; Khatoon, A.; Asif, M.; Bshir, A. 2015-01-01 The promoter region of sucrose synthase (susy-Sl) was identified and isolated from tomato. The 5? deletion analysis was carried out for the identification of minimum optimal promoter. Transgenic lines of Arabidopsis thaliana were developed by floral dip method incorporating various promoter deletion cassettes controlling GUS reporter gene. GUS assay of transgenic tissues indicated that full length susy-Sl promoter and its deletion mutants were constitutively expressed in vegetative and floral tissues of A. thaliana. The expression was observed in roots, shoots and flowers of A. thaliana. Analysis of 5? deletion series of susy-Sl promoter showed that a minimum of 679 bp fragment of the promoter was sufficient to drive expression of GUS reporter gene in the major tissues of transgenic A. thaliana. (author) 5. Towards N = 2 SUSY homogeneous quantum cosmology; Einstein-Yang-Mills systems International Nuclear Information System (INIS) Donets, E.E.; Tentyukov, M.N.; Tsulaya, M.M. 1998-01-01 The application of N = 2 supersymmetric Quantum Mechanics for the quantization of homogeneous systems coupled with gravity is discussed. Starting with the superfield formulation of N = 2 SUSY sigma-model, Hermitian self-adjoint expressions for quantum Hamiltonians and Lagrangians for any signature of a sigma-model metric are obtained. This approach is then applied to coupled SU (2) Einstein-Yang-Mills (EYM) systems in axially-symmetric Bianchi - I,II,VIII, IX, Kantowski-Sachs and closed Friedmann-Robertson-Walker cosmological models. It is shown that all these models admit the embedding into N = 2 SUSY sigma-model with the explicit expressions for superpotentials, being direct sums of gravitational and Yang-Mills (YM) parts. In addition, YM parts of superpotentials exactly coincide with the corresponding Chern-Simons terms. The spontaneous SUSY breaking, caused by YM instantons in EYM systems is discussed in a number of examples 6. Large-Scale Ichthyoplankton and Water Mass Distribution along the South Brazil Shelf Science.gov (United States) de Macedo-Soares, Luis Carlos Pinto; Garcia, Carlos Alberto Eiras; Freire, Andrea Santarosa; Muelbert, José Henrique 2014-01-01 Ichthyoplankton is an essential component of pelagic ecosystems, and environmental factors play an important role in determining its distribution. We have investigated simultaneous latitudinal and cross-shelf gradients in ichthyoplankton abundance to test the hypothesis that the large-scale distribution of fish larvae in the South Brazil Shelf is associated with water mass composition. Vertical plankton tows were collected between 21°27′ and 34°51′S at 107 stations, in austral late spring and early summer seasons. Samples were taken with a conical-cylindrical plankton net from the depth of chlorophyll maxima to the surface in deep stations, or from 10 m from the bottom to the surface in shallow waters. Salinity and temperature were obtained with a CTD/rosette system, which provided seawater for chlorophyll-a and nutrient concentrations. The influence of water mass on larval fish species was studied using Indicator Species Analysis, whereas environmental effects on the distribution of larval fish species were analyzed by Distance-based Redundancy Analysis. Larval fish species were associated with specific water masses: in the north, Sardinella brasiliensis was found in Shelf Water; whereas in the south, Engraulis anchoita inhabited the Plata Plume Water. At the slope, Tropical Water was characterized by the bristlemouth Cyclothone acclinidens. The concurrent analysis showed the importance of both cross-shelf and latitudinal gradients on the large-scale distribution of larval fish species. Our findings reveal that ichthyoplankton composition and large-scale spatial distribution are determined by water mass composition in both latitudinal and cross-shelf gradients. PMID:24614798 7. Large-scale ichthyoplankton and water mass distribution along the South Brazil Shelf. Directory of Open Access Journals (Sweden) Luis Carlos Pinto de Macedo-Soares Full Text Available Ichthyoplankton is an essential component of pelagic ecosystems, and environmental factors play an important role in determining its distribution. We have investigated simultaneous latitudinal and cross-shelf gradients in ichthyoplankton abundance to test the hypothesis that the large-scale distribution of fish larvae in the South Brazil Shelf is associated with water mass composition. Vertical plankton tows were collected between 21°27' and 34°51'S at 107 stations, in austral late spring and early summer seasons. Samples were taken with a conical-cylindrical plankton net from the depth of chlorophyll maxima to the surface in deep stations, or from 10 m from the bottom to the surface in shallow waters. Salinity and temperature were obtained with a CTD/rosette system, which provided seawater for chlorophyll-a and nutrient concentrations. The influence of water mass on larval fish species was studied using Indicator Species Analysis, whereas environmental effects on the distribution of larval fish species were analyzed by Distance-based Redundancy Analysis. Larval fish species were associated with specific water masses: in the north, Sardinella brasiliensis was found in Shelf Water; whereas in the south, Engraulis anchoita inhabited the Plata Plume Water. At the slope, Tropical Water was characterized by the bristlemouth Cyclothone acclinidens. The concurrent analysis showed the importance of both cross-shelf and latitudinal gradients on the large-scale distribution of larval fish species. Our findings reveal that ichthyoplankton composition and large-scale spatial distribution are determined by water mass composition in both latitudinal and cross-shelf gradients. 8. Large-scale ichthyoplankton and water mass distribution along the South Brazil Shelf. Science.gov (United States) de Macedo-Soares, Luis Carlos Pinto; Garcia, Carlos Alberto Eiras; Freire, Andrea Santarosa; Muelbert, José Henrique 2014-01-01 Ichthyoplankton is an essential component of pelagic ecosystems, and environmental factors play an important role in determining its distribution. We have investigated simultaneous latitudinal and cross-shelf gradients in ichthyoplankton abundance to test the hypothesis that the large-scale distribution of fish larvae in the South Brazil Shelf is associated with water mass composition. Vertical plankton tows were collected between 21°27' and 34°51'S at 107 stations, in austral late spring and early summer seasons. Samples were taken with a conical-cylindrical plankton net from the depth of chlorophyll maxima to the surface in deep stations, or from 10 m from the bottom to the surface in shallow waters. Salinity and temperature were obtained with a CTD/rosette system, which provided seawater for chlorophyll-a and nutrient concentrations. The influence of water mass on larval fish species was studied using Indicator Species Analysis, whereas environmental effects on the distribution of larval fish species were analyzed by Distance-based Redundancy Analysis. Larval fish species were associated with specific water masses: in the north, Sardinella brasiliensis was found in Shelf Water; whereas in the south, Engraulis anchoita inhabited the Plata Plume Water. At the slope, Tropical Water was characterized by the bristlemouth Cyclothone acclinidens. The concurrent analysis showed the importance of both cross-shelf and latitudinal gradients on the large-scale distribution of larval fish species. Our findings reveal that ichthyoplankton composition and large-scale spatial distribution are determined by water mass composition in both latitudinal and cross-shelf gradients. 9. Kinematic scaling relations of CALIFA galaxies: A dynamical mass proxy for galaxies across the Hubble sequence. Science.gov (United States) Aquino-Ortíz, E.; Valenzuela, O.; Sánchez, S. F.; Hernández-Toledo, H.; Ávila-Reese, V.; van de Ven, G.; Rodríguez-Puebla, A.; Zhu, L.; Mancillas, B.; Cano-Díaz, M.; García-Benito, R. 2018-06-01 We used ionized gas and stellar kinematics for 667 spatially resolved galaxies publicly available from the Calar Alto Legacy Integral Field Area survey (CALIFA) 3rd Data Release with the aim of studying kinematic scaling relations as the Tully & Fisher (TF) relation using rotation velocity, Vrot, the Faber & Jackson (FJ) relation using velocity dispersion, σ, and also a combination of Vrot and σ through the SK parameter defined as SK^2 = KV_{rot}^2 + σ ^2 with constant K. Late-type and early-type galaxies reproduce the TF and FJ relations. Some early-type galaxies also follow the TF relation and some late-type galaxies the FJ relation, but always with larger scatter. On the contrary, when we use the SK parameter, all galaxies, regardless of the morphological type, lie on the same scaling relation, showing a tight correlation with the total stellar mass, M⋆. Indeed, we find that the scatter in this relation is smaller or equal to that of the TF and FJ relations. We explore different values of the K parameter without significant differences (slope and scatter) in our final results with respect the case K = 0.5 besides than a small change in the zero point. We calibrate the kinematic SK^2 dynamical mass proxy in order to make it consistent with sophisticated published dynamical models within 0.15 dex. We show that the SK proxy is able to reproduce the relation between the dynamical mass and the stellar mass in the inner regions of galaxies. Our result may be useful in order to produce fast estimations of the central dynamical mass in galaxies and to study correlations in large galaxy surveys. 10. Strong orientation dependence of surface mass density profiles of dark haloes at large scales Science.gov (United States) Osato, Ken; Nishimichi, Takahiro; Oguri, Masamune; Takada, Masahiro; Okumura, Teppei 2018-06-01 We study the dependence of surface mass density profiles, which can be directly measured by weak gravitational lensing, on the orientation of haloes with respect to the line-of-sight direction, using a suite of N-body simulations. We find that, when major axes of haloes are aligned with the line-of-sight direction, surface mass density profiles have higher amplitudes than those averaged over all halo orientations, over all scales from 0.1 to 100 Mpc h-1 we studied. While the orientation dependence at small scales is ascribed to the halo triaxiality, our results indicate even stronger orientation dependence in the so-called two-halo regime, up to 100 Mpc h-1. The orientation dependence for the two-halo term is well approximated by a multiplicative shift of the amplitude and therefore a shift in the halo bias parameter value. The halo bias from the two-halo term can be overestimated or underestimated by up to {˜ } 30 per cent depending on the viewing angle, which translates into the bias in estimated halo masses by up to a factor of 2 from halo bias measurements. The orientation dependence at large scales originates from the anisotropic halo-matter correlation function, which has an elliptical shape with the axis ratio of ˜0.55 up to 100 Mpc h-1. We discuss potential impacts of halo orientation bias on other observables such as optically selected cluster samples and a clustering analysis of large-scale structure tracers such as quasars. 11. Seesaw induced electroweak scale, the hierarchy problem and sub-eV neutrino masses International Nuclear Information System (INIS) Atwood, D.; Bar-Shalom, S.; Soni, A. 2006-01-01 We describe a model for the scalar sector where all interactions occur either at an ultra-high scale, Λ U ∝10 16 -10 19 GeV, or at an intermediate scale, Λ I =10 9 -10 11 GeV. The interaction of physics on these two scales results in an SU(2) Higgs condensate at the electroweak (EW) scale, Λ EW , through a seesaw-like Higgs mechanism, Λ EW ∝Λ I 2 /Λ U , while the breaking of the SM SU(2) x U(1) gauge symmetry occurs at the intermediate scale Λ I . The EW scale is, therefore, not fundamental but is naturally generated in terms of ultra-high energy phenomena and so the hierarchy problem is alleviated. We show that the class of such ''seesaw Higgs'' models predict the existence of sub-eV neutrino masses which are generated through a ''two-step'' seesaw mechanism in terms of the same two ultra-high scales: m ν ∝Λ I 4 /Λ U 3 ∝Λ EW 2 /Λ U . The neutrinos can be either Dirac or Majorana, depending on the structure of the scalar potential. We also show that our seesaw Higgs model can be naturally embedded in theories with tiny extra dimensions of size R∝Λ U -1 ∝10 -16 fm, where the seesaw induced EW scale arises from a violation of a symmetry at a distant brane; in particular, in the scenario presented there are seven tiny extra dimensions. (orig.) 12. Identification of hadronic τ decays and observation potentional of CP-violating effects in SUSY at ATLAS International Nuclear Information System (INIS) Gosdzik, Bjoern 2011-03-01 In November 2009 the ATLAS experiment started operation at the Large Hadron Collider (LHC) at CERN. The detector is optimized to search for the Higgs Boson and new physics at the TeV scale. Until the end of the data-taking period with proton-proton collisions on November 3rd, 2010, the ATLAS detector recorded an integrated luminosity of 45.0 pb -1 at a center-of-mass energy of √(s) = 7 TeV. In many signals of the Standard Model and new physics (e.g. SUSY and Higgs) τ-leptons play an important role. A cut-based approach for the identification of hadronically decaying τ-leptons is being used, particularly for the first data-taking period. Using Monte Carlo Data, the development of a cut-based identification method for hadronically decaying τ-lepton with the ATLAS detector at the Large Hadron Collider (LHC) with a center-of-mass energy of √(s) = 14 TeV is presented. The separation of signal and the large QCD jet background is a challenge to the identification of hadronically decaying τ-lepton. The identification is separated into two methods: the calorimeter-based method uses exclusive calorimeter information, while the calorimeter+track-based method combines calorimeter and tracking information. The cut optimization is separately accomplished for τ candidates with one charged decay product (1-prong) and τ candidates with three charged decay products (3-prong). Additionally the optimisation is split into bins of the visible transverse energy of the τ candidate (E T vis ). First of all the optimization is presented and afterwards the performance of the cut-based identification method is discussed. The reconstruction efficiency for τ-leptons is determined by comparing first data corresponding to an integrated luminosity of 244 nb -1 and Monte Carlo simulation. The effect of systematic uncertainties is investigated. The CP violation predicted by the Standard Model is not sufficient to explain the matter - anti-matter asymmetry in the universe of the order of 13. Identification of hadronic {tau} decays and observation potentional of CP-violating effects in SUSY at ATLAS Energy Technology Data Exchange (ETDEWEB) Gosdzik, Bjoern 2011-03-15 In November 2009 the ATLAS experiment started operation at the Large Hadron Collider (LHC) at CERN. The detector is optimized to search for the Higgs Boson and new physics at the TeV scale. Until the end of the data-taking period with proton-proton collisions on November 3rd, 2010, the ATLAS detector recorded an integrated luminosity of 45.0 pb{sup -1} at a center-of-mass energy of {radical}(s) = 7 TeV. In many signals of the Standard Model and new physics (e.g. SUSY and Higgs) {tau}-leptons play an important role. A cut-based approach for the identification of hadronically decaying {tau}-leptons is being used, particularly for the first data-taking period. Using Monte Carlo Data, the development of a cut-based identification method for hadronically decaying {tau}-lepton with the ATLAS detector at the Large Hadron Collider (LHC) with a center-of-mass energy of {radical}(s) = 14 TeV is presented. The separation of signal and the large QCD jet background is a challenge to the identification of hadronically decaying {tau}-lepton. The identification is separated into two methods: the calorimeter-based method uses exclusive calorimeter information, while the calorimeter+track-based method combines calorimeter and tracking information. The cut optimization is separately accomplished for {tau} candidates with one charged decay product (1-prong) and {tau} candidates with three charged decay products (3-prong). Additionally the optimisation is split into bins of the visible transverse energy of the {tau} candidate (E{sub T}{sup vis}). First of all the optimization is presented and afterwards the performance of the cut-based identification method is discussed. The reconstruction efficiency for {tau}-leptons is determined by comparing first data corresponding to an integrated luminosity of 244 nb{sup -1} and Monte Carlo simulation. The effect of systematic uncertainties is investigated. The CP violation predicted by the Standard Model is not sufficient to explain the matter 14. Identification of hadronic {tau} decays and observation potentional of CP-violating effects in SUSY at ATLAS Energy Technology Data Exchange (ETDEWEB) Gosdzik, Bjoern 2011-03-15 In November 2009 the ATLAS experiment started operation at the Large Hadron Collider (LHC) at CERN. The detector is optimized to search for the Higgs Boson and new physics at the TeV scale. Until the end of the data-taking period with proton-proton collisions on November 3rd, 2010, the ATLAS detector recorded an integrated luminosity of 45.0 pb{sup -1} at a center-of-mass energy of {radical}(s) = 7 TeV. In many signals of the Standard Model and new physics (e.g. SUSY and Higgs) {tau}-leptons play an important role. A cut-based approach for the identification of hadronically decaying {tau}-leptons is being used, particularly for the first data-taking period. Using Monte Carlo Data, the development of a cut-based identification method for hadronically decaying {tau}-lepton with the ATLAS detector at the Large Hadron Collider (LHC) with a center-of-mass energy of {radical}(s) = 14 TeV is presented. The separation of signal and the large QCD jet background is a challenge to the identification of hadronically decaying {tau}-lepton. The identification is separated into two methods: the calorimeter-based method uses exclusive calorimeter information, while the calorimeter+track-based method combines calorimeter and tracking information. The cut optimization is separately accomplished for {tau} candidates with one charged decay product (1-prong) and {tau} candidates with three charged decay products (3-prong). Additionally the optimisation is split into bins of the visible transverse energy of the {tau} candidate (E{sub T}{sup vis}). First of all the optimization is presented and afterwards the performance of the cut-based identification method is discussed. The reconstruction efficiency for {tau}-leptons is determined by comparing first data corresponding to an integrated luminosity of 244 nb{sup -1} and Monte Carlo simulation. The effect of systematic uncertainties is investigated. The CP violation predicted by the Standard Model is not sufficient to explain the matter 15. Testing feasibility of scalar-tensor gravity by scale dependent mass and coupling to matter International Nuclear Information System (INIS) Mota, D. F.; Salzano, V.; Capozziello, S. 2011-01-01 We investigate whether there is any cosmological evidence for a scalar field with a mass and coupling to matter which change accordingly to the properties of the astrophysical system it ''lives in,'' without directly focusing on the underlying mechanism that drives the scalar field scale-dependent-properties. We assume a Yukawa type of coupling between the field and matter and also that the scalar-field mass grows with density, in order to overcome all gravity constraints within the Solar System. We analyze three different gravitational systems assumed as ''cosmological indicators'': supernovae type Ia, low surface brightness spiral galaxies and clusters of galaxies. Results show (i) a quite good fit to the rotation curves of low surface brightness galaxies only using visible stellar and gas-mass components is obtained; (ii) a scalar field can fairly well reproduce the matter profile in clusters of galaxies, estimated by x-ray observations and without the need of any additional dark matter; and (iii) there is an intrinsic difficulty in extracting information about the possibility of a scale-dependent massive scalar field (or more generally about a varying gravitational constant) from supernovae type Ia. 16. Mass transfer processes and field-scale transport of organic solutes International Nuclear Information System (INIS) Brusseau, M.L. 1990-01-01 The influence of mass transfer processes, such as sorption/desorption and mass transfer between immiscible liquids and water, on the transport of organic solutes is discussed. Rate-limited sorption of organic solutes caused by a diffusion-constrained mechanism is shown to be significant under laboratory conditions. The significance of the impact of nonequilibrium sorption on field-scale transport is scale dependent. The impact of organic liquids on mass transfer and transport of organic solutes depends upon the nature of the solute and the nature and form of the organic liquid. For example, while retardation of nonionic solutes is decreased in mixed-solvent systems, (i.e. systems comprised of water and a miscible organic liquid or an immiscible liquid present in concentrations below phase separation), the retardation of organic acids may, in some cases, increase with addition of a cosolvent. While the presence of an immiscible liquid existing as a mobile phase will reduce retention of organic solutes, the presence of residual saturation of an immiscible liquid can significantly increase retention. A model is presented that incorporates the effects of retention resulting from residual saturation, as well as nonequilibrium sorption, on the transport of organic solutes. (Author) (70 refs., 3 figs.) 17. Hierarchy of symmetry-breaking scales in SO(10) grand unification and particle masses International Nuclear Information System (INIS) Asatryan, G.M.; Ioannisyan, A.N. 1987-01-01 An SO(10) grand unification model is proposed in which the introduction of an additional discrete symmetry solves the problem of the quark mass spectrum arising in SO(10) breaking schemes with intermediate SU(4) x SU(2)/sub L/ x SU(2)/sub R/ or SU(3)/sub C/ x U(1)/sub B//sub -//sub L/ x SU(2)/sub L/ x SU(2)/sub R/ symmetry. When the breaking of this discrete symmetry is taken into account the condition that there exist only a single light Higgs boson leads to a relation between the b- and t-quark masses which makes it possible to fix the ratio of the grand unification scale M/sub X/ and the quark--lepton symmetry-breaking scale M/sub C/. The specific values of M/sub X/ and M/sub C/ and also the scale of the SU(2)/sub R/ symmetry breaking M/sub R/ depend on the experimental value of the Weinberg angle and are in agreement with the experimental data on proton decay 18. Neutrino Mass and Flavour Models International Nuclear Information System (INIS) King, Stephen F. 2010-01-01 We survey some of the recent promising developments in the search for the theory behind neutrino mass and tri-bimaximal mixing, and indeed all fermion masses and mixing. We focus in particular on models with discrete family symmetry and unification, and show how such models can also solve the SUSY flavour and CP problems. We also discuss the theoretical implications of the measurement of a non-zero reactor angle, as hinted at by recent experimental measurements. 19. ON THE ASSEMBLY OF THE MILKY WAY DWARF SATELLITES AND THEIR COMMON MASS SCALE International Nuclear Information System (INIS) Rashkov, Valery; Madau, Piero; Kuhlen, Michael; Diemand, Jürg 2012-01-01 We use a particle tagging technique to dynamically populate the N-body Via Lactea II high-resolution simulation with stars. The method is calibrated using the observed luminosity function of Milky Way (MW) satellites and the concentration of their stellar populations, and self-consistently follows the accretion and disruption of progenitor dwarfs and the buildup of the stellar halo in a cosmological 'live host'. Simple prescriptions for assigning stellar populations to collisionless particles are able to reproduce many properties of the observed MW halo and its surviving dwarf satellites, like velocity dispersions, sizes, brightness profiles, metallicities, and spatial distribution. Our model predicts the existence of approximately 1850 subhalos harboring 'extremely faint' satellites (with mass-to-light ratios >5 × 10 3 ) lying beyond the Sloan Digital Sky Survey detection threshold. Of these, about 20 are 'first galaxies', i.e., satellites that formed a stellar mass above 10 M ☉ before redshift 9. The 10 most luminous satellites (L > 10 6 L ☉ ) in the simulation are hosted by subhalos with peak circular velocities today in the range V max = 10-40 km s –1 that have shed between 80% and 99% of their dark mass after being accreted at redshifts 1.7 max and stellar line-of-sight velocity dispersion σ los today follow the relation V max = 2.2σ los . We apply a standard mass estimation algorithm based on Jeans modeling of the line-of-sight velocity dispersion profiles to the simulated dwarf spheroidals and test the accuracy of this technique. The inner (within 300 pc) mass-luminosity relation for currently detectable satellites is nearly flat in our model, in qualitative agreement with the 'common mass scale' found in MW dwarfs. We do, however, predict a weak, but significant positive correlation for these objects: M 300 ∝L 0.088±0.024 . 20. Genetic algorithms and experimental discrimination of SUSY models International Nuclear Information System (INIS) Allanach, B.C.; Quevedo, F.; Grellscheid, D. 2004-01-01 We introduce genetic algorithms as a means to estimate the accuracy required to discriminate among different models using experimental observables. We exemplify the technique in the context of the minimal supersymmetric standard model. If supersymmetric particles are discovered, models of supersymmetry breaking will be fit to the observed spectrum and it is beneficial to ask beforehand: what accuracy is required to always allow the discrimination of two particular models and which are the most important masses to observe? Each model predicts a bounded patch in the space of observables once unknown parameters are scanned over. The questions can be answered by minimising a 'distance' measure between the two hypersurfaces. We construct a distance measure that scales like a constant fraction of an observable, since that is how the experimental errors are expected to scale. Genetic algorithms, including concepts such as natural selection, fitness and mutations, provide a solution to the minimisation problem. We illustrate the efficiency of the method by comparing three different classes of string models for which the above questions could not be answered with previous techniques. The required accuracy is in the range accessible to the Large Hadron Collider (LHC) when combined with a future linear collider (LC) facility. The technique presented here can be applied to more general classes of models or observables. (author) 1. Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants Science.gov (United States) Bitsch, Bertram; Morbidelli, Alessandro; Johansen, Anders; Lega, Elena; Lambrechts, Michiel; Crida, Aurélien 2018-04-01 The growth of a planetary core by pebble accretion stops at the so-called pebble isolation mass, when the core generates a pressure bump that traps drifting pebbles outside its orbit. The value of the pebble isolation mass is crucial in determining the final planet mass. If the isolation mass is very low, gas accretion is protracted and the planet remains at a few Earth masses with a mainly solid composition. For higher values of the pebble isolation mass, the planet might be able to accrete gas from the protoplanetary disc and grow into a gas giant. Previous works have determined a scaling of the pebble isolation mass with cube of the disc aspect ratio. Here, we expand on previous measurements and explore the dependency of the pebble isolation mass on all relevant parameters of the protoplanetary disc. We use 3D hydrodynamical simulations to measure the pebble isolation mass and derive a simple scaling law that captures the dependence on the local disc structure and the turbulent viscosity parameter α. We find that small pebbles, coupled to the gas, with Stokes number τf gap at pebble isolation mass. However, as the planetary mass increases, particles must be decreasingly smaller to penetrate the pressure bump. Turbulent diffusion of particles, however, can lead to an increase of the pebble isolation mass by a factor of two, depending on the strength of the background viscosity and on the pebble size. We finally explore the implications of the new scaling law of the pebble isolation mass on the formation of planetary systems by numerically integrating the growth and migration pathways of planets in evolving protoplanetary discs. Compared to models neglecting the dependence of the pebble isolation mass on the α-viscosity, our models including this effect result in higher core masses for giant planets. These higher core masses are more similar to the core masses of the giant planets in the solar system. 2. Ultra high energy cosmic rays: clustering, GUT scale and neutrino masses International Nuclear Information System (INIS) Fodor, Z. 2002-01-01 The clustering of ultra high energy (above 5 · 10 19 eV) cosmic rays (UHECR) suggests that they might be emitted by compact sources. We present a statistical analysis on the source density based on the multiplicities. The propagation of UHECR protons is studied in detail. The UHECR spectrum is consistent with the decay of GUT scale particles and/or with the Z-burst. The predicted GUT mass is m x = 10 b GeV, where b 14.6 -1.7 +1.6 . Our neutrino mass prediction depends on the origin of the power part of the spectrum: m ν = 2.75 -0.97 +1.28 eV for halo and 0.26 -0.14 +0.20 eV for extragalactic (EG) origin 3. Comparison of relativity theories with observer-independent scales of both velocity and length/mass International Nuclear Information System (INIS) Amelino-Camelia, Giovanni; Benedetti, Dario; D'Andrea, Francesco; Procaccini, Andrea 2003-01-01 We consider the two most studied proposals of relativity theories with observer-independent scales of both velocity and length/mass: the one discussed by Amelino-Camelia as an illustrative example for the original proposal (Preprint gr-qc/0012051) of theories with two relativistic invariants, and an alternative more recently proposed by Magueijo and Smolin (Preprint hep-th/0112090). We show that these two relativistic theories are much more closely connected than it would appear on the basis of a naive analysis of their original formulations. In particular, in spite of adopting a rather different formal description of the deformed boost generators, they end up assigning the same dependence of momentum on rapidity, which can be described as the core feature of these relativistic theories. We show that this observation can be used to clarify the concepts of particle mass, particle velocity and energy-momentum conservation rules in these theories with two relativistic invariants 4. Higgs mass scales and matter-antimatter oscillations in grand unified theories International Nuclear Information System (INIS) Senjanovic, G. 1982-01-01 A general discussion of mass scales in grand unified theories is presented, with special emphasis on Higgs scalars which mediate neutron-antineutron (n-anti n) and hydrogen-antihydrogen (H-anti H) oscillations. It is shown that the analogue of survival hypothesis for fermions naturally makes such particles superheavy, thus leading to unobservable lifetimes. If this hypothesis is relaxed, an interesting possibility of potentially observable n-anti n and H-anti H transitions, mutually related arises in the context of SU(5) theory with spontaneously broken B-L symmetry 5. Theoretical Re-evaluations of Scaling Relations between SMBHs and Their Host Galaxies—1. Effect of Seed BH Mass Energy Technology Data Exchange (ETDEWEB) Shirakata, Hikari [Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo (Japan); Kawaguchi, Toshihiro [Department of Economics, Management and Information Science, Onomichi City University, Onomichi (Japan); Okamoto, Takashi [Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo (Japan); Makiya, Ryu [Kavli Institute for the Physics and Mathematics of the Universe, Todai Institutes for Advanced Study, University of Tokyo, Kashiwa (Japan); Max-Planck-Institut fur Astrophysik, Garching (Germany); Ishiyama, Tomoaki [Institute of Management and Information Technologies, Chiba University, Chiba (Japan); Matsuoka, Yoshiki [Research Center for Space and Cosmic Evolution, Ehime University, Matsuyama (Japan); Nagashima, Masahiro [Faculty of Education, Bunkyo University, Koshigaya (Japan); Enoki, Motohiro [Faculty of Business Administration, Tokyo Keizai University, Kokubunji (Japan); Oogi, Taira [Kavli Institute for the Physics and Mathematics of the Universe, Todai Institutes for Advanced Study, University of Tokyo, Kashiwa (Japan); Kobayashi, Masakazu A. R., E-mail: [email protected] [Faculty of Natural Sciences, National Institute of Technology, Kure College, Kure (Japan) 2017-09-21 We use a semi-analytic model of galaxy formation and investigate how the mass of a seed black hole affect the scaling relation between black hole mass and bulge mass at z ~ 0. When the mass of the seed is set at 10{sup 5}M{sub ⊙}, we find that the model results become inconsistent with recent observational results of the scaling relation for dwarf galaxies. On the other hand, when we set seed black hole mass as 10{sup 3}M{sub ⊙} or as randomly chosen value within a 10{sup 3-5}M{sub ⊙} range, we find the results are consistent with observational results including the dispersion. We also find that black hole mass—bulge mass relations for less massive bulges at z ~ 0 put stronger constraints on the seed BH mass than the relations at higher redshifts. 6. A Three Dimensional Picture of Galactic Center Mass Flows From Kiloparsec to Subparsec Scales Science.gov (United States) Mills, Elisabeth A. 2018-06-01 The centers of galaxies host extreme and energetic phenomena, from the amassing of incredibly dense reservoirs of gas to nuclear starbursts producing tens to hundreds of solar masses per year to accreting supermassive black holes launching jets. All of these are found on compact scales from hundreds of parsecs to less than a microparsec. The nearest laboratory for examining these processes is the center of our own Milky Way Galaxy. Although the black hole is not currently active and the star formation rate is relatively low, it is still our best opportunity for detailed insight into the processes that regulate the growth of the central supermassive black hole. By providing access to mid and far infrared wavelengths, SOFIA plays a unique role in connecting large and small scales in the Galactic center and studying the cycling of gas through this region. In this talk I will highlight several key open questions and outline the role that SOFIA continues to play in answering them. 7. Effects of the application of different particle sizes of mill scale (residue) in mass red ceramic International Nuclear Information System (INIS) Arnt, A.B.C.; Rocha, M.R.; Meller, J.G. 2012-01-01 This study aims to evaluate the influence of particle size of mill scale, residue, when added to a mass ceramic. This residue rich in iron oxide may be used as pigment in the ceramics industry. The use of pigments in ceramic products is related to the characteristics of non-toxicity, chemical stability and determination of tone. The tendency to solubilize the pigment depends on the specific surface area. The residue study was initially subjected to physical and chemical characterization and added in a proportion of 5% at a commercial ceramic white burning, with different particle sizes. Both formulations were sintered at a temperature of 950 ° C and evaluated for: loss on ignition, firing linear shrinkage, water absorption, flexural strength and difference of tone. Samples with finer particles of mill scale 0.038 μ showed higher mechanical strength values in the order of 18 MPa. (author) 8. Mass International Nuclear Information System (INIS) Quigg, Chris 2007-01-01 In the classical physics we inherited from Isaac Newton, mass does not arise, it simply is. The mass of a classical object is the sum of the masses of its parts. Albert Einstein showed that the mass of a body is a measure of its energy content, inviting us to consider the origins of mass. The protons we accelerate at Fermilab are prime examples of Einsteinian matter: nearly all of their mass arises from stored energy. Missing mass led to the discovery of the noble gases, and a new form of missing mass leads us to the notion of dark matter. Starting with a brief guided tour of the meanings of mass, the colloquium will explore the multiple origins of mass. We will see how far we have come toward understanding mass, and survey the issues that guide our research today. 9. Measurement of Galaxy Cluster Integrated Comptonization and Mass Scaling Relations with the South Pole Telescope Energy Technology Data Exchange (ETDEWEB) Saliwanchik, B. R.; et al. 2015-01-22 We describe a method for measuring the integrated Comptonization (Y (SZ)) of clusters of galaxies from measurements of the Sunyaev-Zel'dovich (SZ) effect in multiple frequency bands and use this method to characterize a sample of galaxy clusters detected in the South Pole Telescope (SPT) data. We use a Markov Chain Monte Carlo method to fit a β-model source profile and integrate Y (SZ) within an angular aperture on the sky. In simulated observations of an SPT-like survey that include cosmic microwave background anisotropy, point sources, and atmospheric and instrumental noise at typical SPT-SZ survey levels, we show that we can accurately recover β-model parameters for inputted clusters. We measure Y (SZ) for simulated semi-analytic clusters and find that Y (SZ) is most accurately determined in an angular aperture comparable to the SPT beam size. We demonstrate the utility of this method to measure Y (SZ) and to constrain mass scaling relations using X-ray mass estimates for a sample of 18 galaxy clusters from the SPT-SZ survey. Measuring Y (SZ) within a 0.'75 radius aperture, we find an intrinsic log-normal scatter of 21% ± 11% in Y (SZ) at a fixed mass. Measuring Y (SZ) within a 0.3 Mpc projected radius (equivalent to 0.'75 at the survey median redshift z = 0.6), we find a scatter of 26% ± 9%. Prior to this study, the SPT observable found to have the lowest scatter with mass was cluster detection significance. We demonstrate, from both simulations and SPT observed clusters that Y (SZ) measured within an aperture comparable to the SPT beam size is equivalent, in terms of scatter with cluster mass, to SPT cluster detection significance. 10. Lepton Dipole Moments in Supersymmetric Low-Scale Seesaw Models CERN Document Server Ilakovac, Amon; Popov, Luka 2014-01-01 We study the anomalous magnetic and electric dipole moments of charged leptons in supersymmetric low-scale seesaw models with right-handed neutrino superfields. We consider a minimally extended framework of minimal supergravity, by assuming that CP violation originates from complex soft SUSY-breaking bilinear and trilinear couplings associated with the right-handed sneutrino sector. We present numerical estimates of the muon anomalous magnetic moment and the electron electric dipole moment (EDM), as functions of key model parameters, such as the Majorana mass scale mN and tan(\\beta). In particular, we find that the contributions of the singlet heavy neutrinos and sneutrinos to the electron EDM are naturally small in this model, of order 10^{-27} - 10^{-28} e cm, and can be probed in the present and future experiments. 11. Generalized Jaynes-Cummings Hamiltonians by shape-invariant hierarchies and their SUSY partners International Nuclear Information System (INIS) Hussin, V; Kuru, S; Negro, J 2006-01-01 A generalization of the matrix Jaynes-Cummings model in the rotating wave approximation is proposed by means of the shape-invariant hierarchies of scalar factorized Hamiltonians. A class of Darboux transformations (sometimes called SUSY transformations in this context) suitable for these generalized Jaynes-Cummings models is constructed. Finally one example is worked out using the methods developed 12. Holographic entanglement entropy and entanglement thermodynamics of 'black' non-susy D3 brane Science.gov (United States) Bhattacharya, Aranya; Roy, Shibaji 2018-06-01 Like BPS D3 brane, the non-supersymmetric (non-susy) D3 brane of type IIB string theory is also known to have a decoupling limit and leads to a non-supersymmetric AdS/CFT correspondence. The throat geometry in this case represents a QFT which is neither conformal nor supersymmetric. The 'black' version of the non-susy D3 brane in the decoupling limit describes a QFT at finite temperature. Here we first compute the entanglement entropy for small subsystem of such QFT from the decoupled geometry of 'black' non-susy D3 brane using holographic technique. Then we study the entanglement thermodynamics for the weakly excited states of this QFT from the asymptotically AdS geometry of the decoupled 'black' non-susy D3 brane. We observe that for small subsystem this background indeed satisfies a first law like relation with a universal (entanglement) temperature inversely proportional to the size of the subsystem and an (entanglement) pressure normal to the entangling surface. Finally we show how the entanglement entropy makes a cross-over to the thermal entropy at high temperature. 13. Bremsstrahlung and Ion Beam Current Measurements with SuSI ECR Ion Source International Nuclear Information System (INIS) Ropponen, T. 2012-01-01 This series of slides presents: the Superconducting Source for Ions (SuSI), the X-ray measurement setup, the different collimation schemes, the flat B operation versus B(min) operation, and the impact of tuning ∇B while keeping fixed field profile 14. Primordial cosmological inflation versus local supersymmetry breaking in SUSY GUTs coupled to N = 1 supergravity International Nuclear Information System (INIS) Gato, B.; Leon, J.; Ramon-Medrano, M. 1984-01-01 We present a model for a SUSY GUT coupled to N=1 supergravity in which local supersymmetry breaks down in the gauge singlet sector. The constraints for the model to be physically acceptable are incompatible with inflation. The simultaneous breaking of local supersymmetry and gauge symmetry is proposed as a good prospect for inflation. (orig.) 15. Decoupling limit and throat geometry of non-susy D3 brane Energy Technology Data Exchange (ETDEWEB) Nayek, Kuntal, E-mail: [email protected]; Roy, Shibaji, E-mail: [email protected] 2017-03-10 Recently it has been shown by us that, like BPS Dp branes, bulk gravity gets decoupled from the brane even for the non-susy Dp branes of type II string theories indicating a possible extension of AdS/CFT correspondence for the non-supersymmetric case. In that work, the decoupling of gravity on the non-susy Dp branes has been shown numerically for the general case as well as analytically for some special case. Here we discuss the decoupling limit and the throat geometry of the non-susy D3 brane when the charge associated with the brane is very large. We show that in the decoupling limit the throat geometry of the non-susy D3 brane, under appropriate coordinate change, reduces to the Constable–Myers solution and thus confirming that this solution is indeed the holographic dual of a (non-gravitational) gauge theory discussed there. We also show that when one of the parameters of the solution takes a specific value, it reduces, under another coordinate change, to the five-dimensional solution obtained by Csaki and Reece, again confirming its gauge theory interpretation. 16. Effect of enhanced manganese oxidation in the hyporheic zone on basin-scale geochemical mass balance Science.gov (United States) Harvey, Judson W.; Fuller, Christopher C. 1998-01-01 cumulative effect of hyporheic exchange in Pinal Creek basin was to remove approximately 20% of the dissolved manganese flowing out of the drainage basin. Our results illustrate that the cumulative significance of reactive uptake in the hyporheic zone depends on the balance between chemical reaction rates, hyporheic porewater residence time, and turnover of streamflow through hyporheic flow paths. The similarity between the hyporheic reaction timescale (1/λs ≈ 1.3 hours), and the hyporheic porewater residence timescale (ts ≈ 8 min) ensured that there was adequate time for the reaction to progress. Furthermore, it was the similarity between the turnover length for stream water flow through hyporheic flow paths (Ls = stream velocity/storage-zone exchange coefficient ≈ 1.3 km) and the length of Pinal Creek (L ≈ 7 km), which ensured that all stream water passed through hyporheic flow paths several times. As a means to generalize our findings to other sites where similar types of hydrologic and chemical information are available, we suggest a cumulative significance index for hyporheic reactions, Rs = λstsL/Ls (dimensionless); higher values indicate a greater potential for hyporheic reactions to influence geochemical mass balance. Our experience in Pinal Creek basin suggests that values of Rs > 0.2 characterize systems where hyporheic reactions are likely to influence geochemical mass balance at the drainage-basin scale. 17. Determining Central Black Hole Masses in Distant Active Galaxies and Quasars. II. Improved Optical and UV Scaling Relationships DEFF Research Database (Denmark) Vestergaard, Marianne; Peterson, B. M. 2006-01-01 We present four improved empirical relationships useful for estimating the central black hole mass in nearby AGNs and distant luminous quasars alike using either optical or UV single-epoch spectroscopy. These mass-scaling relationships between line widths and luminosity are based on recently... 18. Search for SUperSYmmetry (SUSY) in Opposite Sign (OS) di-lepton final states with Parked Data collected at $\\sqrt{s}$ = 8 TeV using the CMS detector CERN Document Server Bhattacharya, Saptaparna 2015-01-01 The Large Hadron Collider (LHC) has had a very successful data-taking phase with Run 1. After the discovery of the Higgs, confirming the predictions of the Standard Model (SM), the focus is on finding new physics, especially in the context of supersymmetry (SUSY). One of the potential hiding places of natural SUSY is in models with compressed spectra, that is, models where the mass difference between the parent SUSY particle and the Lightest Supersymmetric Particle (LSP) is small. Such signals are characterized by low transverse momentum (p${_T}$) objects, low hadronic activity and missing transverse energy (MET). In this analysis, we focus on di-lepton final states, specifically in the low p${_T}$ regime. We use 7.4 fb$^{-1}$ of parked data collected at $\\sqrt{s}$ = 8 TeV. The analysis is enabled by the use of triggers that place no restrictions on the di-lepton p${_T}$, instead relying on methods like Initial State Radiation (ISR) tagging by triggering on a high p${_T}$ photon, to reduce the trigger rate.... 19. Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice Directory of Open Access Journals (Sweden) Kurkela Aleksi 2018-01-01 Full Text Available Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations, which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuation showing that the linearization indeed works and that the Gauss’s law is conserved. 20. Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice Science.gov (United States) Kurkela, Aleksi; Lappi, Tuomas; Peuron, Jarkko 2018-03-01 Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations, which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuation showing that the linearization indeed works and that the Gauss's law is conserved. 1. Starobinsky-like inflation, supercosmology and neutrino masses in no-scale flipped SU(5) Energy Technology Data Exchange (ETDEWEB) Ellis, John [Theoretical Particle Physics and Cosmology Group, Department of Physics, King' s College London, WC2R 2LS London (United Kingdom); Garcia, Marcos A.G. [Physics and Astronomy Department, Rice University, 6100 Main Street, Houston, TX 77005 (United States); Nagata, Natsumi [Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan); Nanopoulos, Dimitri V. [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A and M University, College Station, 77843 Texas (United States); Olive, Keith A., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of Minnesota, 116 Church Street SE, Minneapolis, MN 55455 (United States) 2017-07-01 We embed a flipped SU(5) × U(1) GUT model in a no-scale supergravity framework, and discuss its predictions for cosmic microwave background observables, which are similar to those of the Starobinsky model of inflation. Measurements of the tilt in the spectrum of scalar perturbations in the cosmic microwave background, n {sub s} , constrain significantly the model parameters. We also discuss the model's predictions for neutrino masses, and pay particular attention to the behaviours of scalar fields during and after inflation, reheating and the GUT phase transition. We argue in favor of strong reheating in order to avoid excessive entropy production which could dilute the generated baryon asymmetry. 2. Performance ceramic red mass containing mill scale of rolling in different firing temperatures International Nuclear Information System (INIS) Meller, J.G.; Arnt, A.B.C; Rocha, M.R. 2014-01-01 This study aimed to evaluate the performance of the properties of samples of red clay with addition of mill scale steel. This residue consists of oxides of iron has the function replace pigments used in ceramic materials. The mechanical strength of the sintered material can be associated with reactions that occur during sintering, leading to the formation of compounds provided with good mechanical characteristics, particle size of the components and the structure of the dough piece after the compactation. After chemical and microstructural characterization diffraction and fluorescence X-rays, this residue was added in the proportion of 1.45% of a commercial ceramic mass. The formulations were subjected to different temperatures and performance of the formulations was evaluated for physical characteristics: loss on ignition, linear firing shrinkage, water absorption, flexural strength by 3 and intensity of tone. The loss on ignition and linear firing shrinkage tests relate to the sintering temperature with the performance of the tested formulations. (author) 3. A Fault-Tolerant Radiation-Robust Mass Storage Concept for Highly Scaled Flash Memory Science.gov (United States) Fuchs, Cristian M.; Trinitis, Carsten; Appel, Nicolas; Langer, Martin 2015-09-01 Future spacemissions will require vast amounts of data to be stored and processed aboard spacecraft. While satisfying operational mission requirements, storage systems must guarantee data integrity and recover damaged data throughout the mission. NAND-flash memories have become popular for space-borne high performance mass memory scenarios, though future storage concepts will rely upon highly scaled flash or other memory technologies. With modern flash memory, single bit erasure coding and RAID based concepts are insufficient. Thus, a fully run-time configurable, high performance, dependable storage concept, requiring a minimal set of logic or software. The solution is based on composite erasure coding and can be adjusted for altered mission duration or changing environmental conditions. 4. Modeling Coronal Mass Ejections with the Multi-Scale Fluid-Kinetic Simulation Suite International Nuclear Information System (INIS) Pogorelov, N. V.; Borovikov, S. N.; Wu, S. T.; Yalim, M. S.; Kryukov, I. A.; Colella, P. C.; Van Straalen, B. 2017-01-01 The solar eruptions and interacting solar wind streams are key drivers of geomagnetic storms and various related space weather disturbances that may have hazardous effects on the space-borne and ground-based technological systems as well as on human health. Coronal mass ejections (CMEs) and their interplanetary counterparts, interplanetary CMEs (ICMEs), belong to the strongest disturbances and therefore are of great importance for the space weather predictions. In this paper we show a few examples of how adaptive mesh refinement makes it possible to resolve the complex CME structure and its evolution in time while a CME propagates from the inner boundary to Earth. Simulations are performed with the Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS). (paper) 5. Higgs and superparticle mass predictions from the landscape Science.gov (United States) Baer, Howard; Barger, Vernon; Serce, Hasan; Sinha, Kuver 2018-03-01 Predictions for the scale of SUSY breaking from the string landscape go back at least a decade to the work of Denef and Douglas on the statistics of flux vacua. The assumption that an assortment of SUSY breaking F and D terms are present in the hidden sector, and their values are uniformly distributed in the landscape of D = 4, N = 1 effective supergravity models, leads to the expectation that the landscape pulls towards large values of soft terms favored by a power law behavior P( m soft) ˜ m soft n . On the other hand, similar to Weinberg's prediction of the cosmological constant, one can assume an anthropic selection of weak scales not too far from the measured value characterized by m W,Z,h ˜ 100 GeV. Working within a fertile patch of gravity-mediated low energy effective theories where the superpotential μ term is ≪ m 3/2, as occurs in models such as radiative breaking of Peccei-Quinn symmetry, this biases statistical distributions on the landscape by a cutoff on the parameter ΔEW, which measures fine-tuning in the m Z - μ mass relation. The combined effect of statistical and anthropic pulls turns out to favor low energy phenomenology that is more or less agnostic to UV physics. While a uniform selection n = 0 of soft terms produces too low a value for m h , taking n = 1 and 2 produce most probabilistically m h ˜ 125 GeV for negative trilinear terms. For n ≥ 1, there is a pull towards split generations with {m}_{\\tilde{q},\\tilde{ℓ}}(1,2)˜ 10-30 TeV whilst {m}_{{\\tilde{t}}_1}˜ 1-2 TeV . The most probable gluino mass comes in at ˜ 3 - 4 TeV — apparently beyond the reach of HL-LHC (although the required quasi-degenerate higgsinos should still be within reach). We comment on consequences for SUSY collider and dark matter searches. 6. Mass and charge transfer on various relevant scales in polymer electrolyte fuel cells[Dissertation 16991 Energy Technology Data Exchange (ETDEWEB) Freunberger, S. A. 2007-07-01 This dissertation is concerned with the development, experimental diagnostics and mathematical modelling and simulation of polymer electrolyte fuel cells (PEFC). The central themes throughout this thesis are the closely interlinked phenomena of mass and charge transfer. In the face of developing a PEFC system for vehicle propulsion these phenomena are scrutinized on a broad range of relevant scales. Starting from the material related level of the membrane and the gas diffusion layer (GDL) we turn to length scales, where structural features of the cell additionally come into play. These are the scale of flow channels and ribs, the single cell and the cell stack followed by the cell, stack, and system development for an automotive power train. In Chapter 3 selected fundamental material models and properties, respectively, are explored that are crucial for the mathematical modelling and simulation of PEFC, as needed in some succeeding parts of this work. First, established mathematical models for mass and charge transfer in the membrane are compared within the framework of the membrane electrode assembly (MEA), which represents the electrochemical unit. Second, reliable values for effective diffusivities in the GDLs which are vital for the simulation of gaseous mass transport are measured. Therefore, a method is developed that allows measuring this quantity both as a function of compression and direction as this is a prerequisite of sophisticated more-dimensional numerical PEFC-models. Besides the cross section of the catalyst layer (CL) mass transfer under channels and ribs is considered as a major source of losses in particular under high load operation. As up to now there have been solely non-validated theoretical investigations, in Chapter 4 an experimental method is developed that is for the first time capable of resolving the current density distribution on the this scale. For this, the electron conductors in the cell are considered as 2-dimensional shunt 7. Pore-scale investigation of mass transport and electrochemistry in a solid oxide fuel cell anode Energy Technology Data Exchange (ETDEWEB) Grew, Kyle N.; Joshi, Abhijit S.; Peracchio, Aldo A.; Chiu, Wilson K.S. [Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, Storrs, CT 06269-3139 (United States) 2010-04-15 The development and validation of a model for the study of pore-scale transport phenomena and electrochemistry in a Solid Oxide Fuel Cell (SOFC) anode are presented in this work. This model couples mass transport processes with a detailed reaction mechanism, which is used to model the electrochemical oxidation kinetics. Detailed electrochemical oxidation reaction kinetics, which is known to occur in the vicinity of the three-phase boundary (TPB) interfaces, is discretely considered in this work. The TPB regions connect percolating regions of electronic and ionic conducting phases of the anode, nickel (Ni) and yttria-stabilized zirconia (YSZ), respectively; with porous regions supporting mass transport of the fuel and product. A two-dimensional (2D), multi-species lattice Boltzmann method (LBM) is used to describe the diffusion process in complex pore structures that are representative of the SOFC anode. This diffusion model is discretely coupled to a kinetic electrochemical oxidation mechanism using localized flux boundary conditions. The details of the oxidation kinetics are prescribed as a function of applied activation overpotential and the localized hydrogen and water mole fractions. This development effort is aimed at understanding the effects of the anode microstructure within TPB regions. This work describes the methods used so that future studies can consider the details of SOFC anode microstructure. (author) 8. Strain in shock-loaded skeletal muscle and the time scale of muscular wobbling mass dynamics. Science.gov (United States) Christensen, Kasper B; Günther, Michael; Schmitt, Syn; Siebert, Tobias 2017-10-16 In terrestrial locomotion, muscles undergo damped oscillations in response to limb impacts with the ground. Muscles are also actuators that generate mechanical power to allow locomotion. The corresponding elementary contractile process is the work stroke of an actin-myosin cross-bridge, which may be forcibly detached by superposed oscillations. By experimentally emulating rat leg impacts, we found that full activity and non-fatigue must meet to possibly prevent forcible cross-bridge detachment. Because submaximal muscle force represents the ordinary locomotor condition, our results show that forcible, eccentric cross-bridge detachment is a common, physiological process even during isometric muscle contractions. We also calculated the stiffnesses of the whole muscle-tendon complex and the fibre material separately, as well as Young's modulus of the latter: 1.8 MPa and 0.75 MPa for fresh, fully active and passive fibres, respectively. Our inferred Young's modulus of the tendon-aponeurosis complex suggests that stiffness in series to the fibre material is determined by the elastic properties of the aponeurosis region, rather than the tendon material. Knowing these stiffnesses and the muscle mass, the complex' eigenfrequency for responses to impacts can be quantified, as well as the size-dependency of this time scale of muscular wobbling mass dynamics. 9. RECONNECTION PROPERTIES OF LARGE-SCALE CURRENT SHEETS DURING CORONAL MASS EJECTION ERUPTIONS Energy Technology Data Exchange (ETDEWEB) Lynch, B. J.; Kazachenko, M. D. [Space Sciences Laboratory, University of California, Berkeley, CA 94720 (United States); Edmondson, J. K. [Climate and Space Sciences and Engineering Department, University of Michigan, Ann Arbor, MI 48109 (United States); Guidoni, S. E. [Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States) 2016-07-20 We present a detailed analysis of the properties of magnetic reconnection at large-scale current sheets (CSs) in a high cadence version of the Lynch and Edmondson 2.5D MHD simulation of sympathetic magnetic breakout eruptions from a pseudostreamer source region. We examine the resistive tearing and break-up of the three main CSs into chains of X- and O-type null points and follow the dynamics of magnetic island growth, their merging, transit, and ejection with the reconnection exhaust. For each CS, we quantify the evolution of the length-to-width aspect ratio (up to ∼100:1), Lundquist number (∼10{sup 3}), and reconnection rate (inflow-to-outflow ratios reaching ∼0.40). We examine the statistical and spectral properties of the fluctuations in the CSs resulting from the plasmoid instability, including the distribution of magnetic island area, mass, and flux content. We show that the temporal evolution of the spectral index of the reconnection-generated magnetic energy density fluctuations appear to reflect global properties of the CS evolution. Our results are in excellent agreement with recent, high-resolution reconnection-in-a-box simulations even though our CSs’ formation, growth, and dynamics are intrinsically coupled to the global evolution of sequential sympathetic coronal mass ejection eruptions. 10. Measuring the black hole mass in ultraluminous X-ray sources with the X-ray scaling method Science.gov (United States) Jang, I.; Gliozzi, M.; Satyapal, S.; Titarchuk, L. 2018-01-01 In our recent work, we demonstrated that a novel X-ray scaling method, originally introduced for Galactic black holes (BH), could be reliably extended to estimate the mass of supermassive black holes accreting at moderate to high level. Here, we apply this X-ray scaling method to ultraluminous X-ray sources (ULXs) to constrain their MBH. Using 49 ULXs with multiple XMM-Newton observations, we infer that ULXs host both stellar mass BHs and intermediate mass BHs. The majority of the sources of our sample seem to be consistent with the hypothesis of highly accreting massive stellar BHs with MBH ∼ 100 M⊙. Our results are in general agreement with the MBH values obtained with alternative methods, including model-independent variability methods. This suggests that the X-ray scaling method is an actual scale-independent method that can be applied to all BH systems accreting at moderate-high rate. 11. Identifying fake leptons in ATLAS while hunting SUSY in 8 TeV proton-proton collisions CERN Document Server Gillam, Thomas P S For several theoretically and experimentally motivated reasons, super- symmetry (SUSY) has for some time been identified as an interesting candidate for a theory of fundamental particle physics beyond the Stan- dard Model. The ATLAS collaboration, of which I am a member, possess a detector emplaced in the Large Hadron Collider experiment at CERN. If SUSY does in fact describe our universe, then it is hoped that evidence of it will be visible in data collected in the ATLAS detector. I present an analysis looking for a particular signature that could indicate the presence of SUSY; events containing two like-charge leptons (e or μ). This signature benefits from having both low Standard Model backgrounds as well as potential to observe several SUSY scenarios, par- ticularly those involving strong production processes. These include pair production of squarks and gluinos. The latter of these are particularly relevant for the analysis presented herein since gluinos are Majorana fermions; hence they can decay to... 12. Lifting scalar-quark and -lepton masses with sideways U(1)-II International Nuclear Information System (INIS) 1984-01-01 We investigate the phenomenological consequences of an SUSY model with a gauged O'Raifeartaigh sector on scalar partner masses. The model has the gauge symmetry SU(5) x U(1). We find that this form of spontaneous SUSY breaking leads to large scalar partner masses through one loop graphs without changing quark and lepton masses from tree values, and without breaking SU(5) symmetries by the scalar partner sector. To calculate the scalar partner masses we extend previous work on supergraph techniques to include cases when SUSY is broken at tree level. We are able to sum exactly the corrections to unbroken propagators with the aid of a supersymmetric version of tree-level Dyson equations. We show how the same ideas can be implemented in an SU(5) gauge model where the normal Higgs give large masses radiatively to the scalar-quarks and -leptons. 7 references 13. Feasibility study of a large-scale tuned mass damper with eddy current damping mechanism Science.gov (United States) Wang, Zhihao; Chen, Zhengqing; Wang, Jianhui 2012-09-01 Tuned mass dampers (TMDs) have been widely used in recent years to mitigate structural vibration. However, the damping mechanisms employed in the TMDs are mostly based on viscous dampers, which have several well-known disadvantages, such as oil leakage and difficult adjustment of damping ratio for an operating TMD. Alternatively, eddy current damping (ECD) that does not require any contact with the main structure is a potential solution. This paper discusses the design, analysis, manufacture and testing of a large-scale horizontal TMD based on ECD. First, the theoretical model of ECD is formulated, then one large-scale horizontal TMD using ECD is constructed, and finally performance tests of the TMD are conducted. The test results show that the proposed TMD has a very low intrinsic damping ratio, while the damping ratio due to ECD is the dominant damping source, which can be as large as 15% in a proper configuration. In addition, the damping ratios estimated with the theoretical model are roughly consistent with those identified from the test results, and the source of this error is investigated. Moreover, it is demonstrated that the damping ratio in the proposed TMD can be easily adjusted by varying the air gap between permanent magnets and conductive plates. In view of practical applications, possible improvements and feasibility considerations for the proposed TMD are then discussed. It is confirmed that the proposed TMD with ECD is reliable and feasible for use in structural vibration control. 14. Multi-scale mass movements: example of the Nile deep-sea fan (NDSF) Science.gov (United States) Loncke, L.; Droz, L.; Bellaiche, G.; Gaullier, V.; Mascle, J.; Migeon, S. 2003-04-01 The almost 90 000 km2 NDSF, fed by one of the major river in the world, has been nearly entirely surveyed by swath bathymetry and back-scatter imagery during the last four years. Seismic-reflection and 3-5 kHz profiles, and in some places, high resolution data were collected. Some profiles have been provided by BP-Egypt. Using this set of data, we have conducted a multi-scale regional synthesis which stresses the importance of gravity processes in the edification and evolution of this major deep turbidite system. Gravity processes range from regional gravity-driven spreading and gliding of the Plio-Pleistocene sediments above the Messinian mobile evaporites, to huge collapses of large areas of the upper continental slope as well as very localized levee destabilizations and related avulsion mechanisms. The Eastern - tectonized - area of the NDSF is characterized by lens-shaped transparent bodies, likely indicating debris-flow deposits, settled at crestal graben flanks, themselves generated by reactive diapir rise. Debris flows are probably triggered by local readjustments of salt-related tectonic features destabilizing their sedimentary cover. In contrast, within the poorly deformed Western part of the NDSF, we mainly observe recent slumping and gliding phenomenons, incising the upper slope where salt layers are absent. These slumps and glidings evolved downslope to large debris flows. Some of them exhibit volumes up to 1900 km3 and are covered by recent stacked channel-levees units. Smaller scale debris-flows are inter-fingered within these constructional units and led to numerous channel migrations and avulsions, characterized by typical HARP's seismic facies. Recent sedimentary destabilizations seem to be associated with gas seeping or under-compacted mud ascents: in the Central NDSF, the association between pock-marks (or mounds) and destabilizated masses suggest the existence of gas hydrates. Given the variety of processes (either triggered by tectonics 15. Higgs mass prediction with non-universal soft supersymmetry breaking in MSSM International Nuclear Information System (INIS) Codoban, S.; Jurcisin, M.; Kazakov, D. 2001-01-01 In the framework of the MSSM (Minimal supersymmetric extension of the standard model) the non-universal boundary conditions of soft SUSY breaking parameters are considered. Taking as input the top, bottom and Z-boson masses, the values of the gauge couplings at the EW scale and the infrared quasi-fixed points for Yukawa couplings and the soft parameters the mass of the lightest CP-even Higgs boson is found to be m h = 92.7 -4.9 +10 ± 5 ± 0.4 GeV/c 2 for the low tan(β) case and m h 125.7 -9.0 +6.4 ± 5 ± 0.4 GeV/c 2 (μ > 0) or m h 125.4 -9.0 +6.6 ± 5 ± 0.4 Ge V/c 2 (μ < 0) in the case of large tan(β). (authors) 16. Post-sphaleron baryogenesis and n- anti n oscillation in non-SUSY SO(10) GUT with gauge coupling unification International Nuclear Information System (INIS) Patra, Sudhanwa; Pritimita, Prativa 2014-01-01 ''Post-sphaleron baryogenesis'', a fresh and profound mechanism of baryogenesis accounts for the matter-antimatter asymmetry of our present universe in a framework of Pati-Salam symmetry. We attempt here to embed this mechanism in a non-SUSY SO(10) grand unified theory by reviving a novel symmetry breaking chain with Pati-Salam symmetry as an intermediate symmetry breaking step and as well to address post-sphaleron baryogenesis and neutron-antineutron oscillation in a rational manner. The Pati-Salam symmetry based on the gauge group SU(2) L x SU(2) R x SU(4) C is realized in our model at 10 5 -10 6 GeV and the mixing time for the neutron-antineutron oscillation process having ΔB = 2 is found to be τ n- anti n ≅ 10 8 -10 10 s with the model parameters, which is within the reach of forthcoming experiments. Other novel features of the model include low scale right-handed W R ± , Z R gauge bosons, explanation for neutrino oscillation data via the gauged inverse (or extended) seesaw mechanism and most importantly TeV scale color sextet scalar particles responsible for an observable n- anti n oscillation which may be accessible to LHC. We also look after gauge coupling unification and an estimation of the proton lifetime with and without the addition of color sextet scalars. (orig.) 17. A low-energy β-function in a finite super-Yang-Mills model with multiple mass scales International Nuclear Information System (INIS) Foda, O.; Helayel-Neto, J.A. 1985-01-01 We compute the one-loop contribution to the low-energy light-fermion gauge coupling in a finite supersymmetric gauge theory with two mass scales: a heavy mass that breaks an initial N=4 supersymmetry down to N=2, but respects the finiteness, and a light mass that, for simplicity, is set to zero. We find that coupling grows with the mass of the heavy intermediate states. Hence the latter do not decouple at low energies, leading to large logarithms that invalidate low-energy perturbation theory. Consequently, further manipulations are required to obtain a meaningful perturbative expansion. Enforcing decoupling through finite renormalizations, that absorb the heavy mass effects into a redefinition of the parameters of the lagrangian, introduces an arbitrary subtraction mass μ. The requirement that the S-matrix elements be independent of μ leads to a non-trivial renormalization-group equation for the low-energy theory, with a non-vanishing β-function. (orig.) 18. Low-energy. beta. -function in a finite super-Yang-Mills model with multiple mass scales Energy Technology Data Exchange (ETDEWEB) Foda, O.; Helayel-Neto, J.A. (International Centre for Theoretical Physics, Trieste (Italy)) 1985-02-14 We compute the one-loop contribution to the low-energy light-fermion gauge coupling in a finite supersymmetric gauge theory with two mass scales: a heavy mass that breaks an initial N=4 supersymmetry down to N=2, but respects the finiteness, and a light mass that, for simplicity, is set to zero. We find that coupling grows with the mass of the heavy intermediate states. Hence the latter do not decouple at low energies, leading to large logarithms that invalidate low-energy perturbation theory. Consequently, further manipulations are required to obtain a meaningful perturbative expansion. Enforcing decoupling through finite renormalizations, that absorb the heavy mass effects into a redefinition of the parameters of the lagrangian, introduces an arbitrary subtraction mass ..mu... The requirement that the S-matrix elements be independent of ..mu.. leads to a non-trivial renormalization-group equation for the low-energy theory, with a non-vanishing ..beta..-function. 19. AS ABOVE, SO BELOW: EXPLOITING MASS SCALING IN BLACK HOLE ACCRETION TO BREAK DEGENERACIES IN SPECTRAL INTERPRETATION International Nuclear Information System (INIS) Markoff, Sera; Silva, Catia V.; Nowak, Michael A.; Gallo, Elena; Plotkin, Richard M.; Hynes, Robert; Wilms, Jörn; Maitra, Dipankar; Drappeau, Samia 2015-01-01 Over the past decade, evidence has mounted that several aspects of black hole (BH) accretion physics proceed in a mass-invariant way. One of the best examples of this scaling is the empirical “fundamental plane of BH accretion” relation linking mass, radio, and X-ray luminosity over eight orders of magnitude in BH mass. The currently favored theoretical interpretation of this relation is that the physics governing power output in weakly accreting BHs depends more on relative accretion rate than on mass. In order to test this theory, we explore whether a mass-invariant approach can simultaneously explain the broadband spectral energy distributions from two BHs at opposite ends of the mass scale but that are at similar Eddington accretion fractions. We find that the same model, with the same value of several fitted physical parameters expressed in mass-scaling units to enforce self-similarity, can provide a good description of two data sets from V404 Cyg and M81*, a stellar and supermassive BH, respectively. Furthermore, only one of several potential emission scenarios for the X-ray band is successful, suggesting it is the dominant process driving the fundamental plane relation at this accretion rate. This approach thus holds promise for breaking current degeneracies in the interpretation of BH high-energy spectra and for constructing better prescriptions of BH accretion for use in various local and cosmological feedback applications 20. Benchmark models, planes lines and points for future SUSY searches at the LHC International Nuclear Information System (INIS) AbdusSalam, S.S.; Allanach, B.C.; Dreiner, H.K. 2012-03-01 We define benchmark models for SUSY searches at the LHC, including the CMSSM, NUHM, mGMSB, mAMSB, MM-AMSB and p19MSSM, as well as models with R-parity violation and the NMSSM. Within the parameter spaces of these models, we propose benchmark subspaces, including planes, lines and points along them. The planes may be useful for presenting results of the experimental searches in different SUSY scenarios, while the specific benchmark points may serve for more detailed detector performance tests and comparisons. We also describe algorithms for defining suitable benchmark points along the proposed lines in the parameter spaces, and we define a few benchmark points motivated by recent fits to existing experimental data. 1. Mandelstam cuts and light-like Wilson loops in N=4 SUSY Energy Technology Data Exchange (ETDEWEB) Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; St. Petersburg Inst. of Nuclear Physics, Gatchina (Russian Federation); Prygarin, A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik 2010-08-15 We perform an analytic continuation of the two-loop remainder function for the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin, Vergu and Volovich from the light-like Wilson loop representation. The remainder function is continued into a physical region, where all but two energy invariants are negative. It turns out to be pure imaginary in the multi-Regge kinematics, which is in an agreement with the predictions based on the Steinmann relations for the Regge poles and Mandelstam cut contributions. The leading term reproduces correctly the expression calculated by one of the authors in the BFKL approach, while the subleading term presents a result, that was not yet found with the use of the unitarity techniques. This supports the applicability of the Wilson loop approach to the planar MHV amplitudes in N=4 SUSY. (orig.) 2. Mandelstam cuts and light-like Wilson loops in N=4 SUSY International Nuclear Information System (INIS) Lipatov, L.N.; Prygarin, A. 2010-08-01 We perform an analytic continuation of the two-loop remainder function for the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin, Vergu and Volovich from the light-like Wilson loop representation. The remainder function is continued into a physical region, where all but two energy invariants are negative. It turns out to be pure imaginary in the multi-Regge kinematics, which is in an agreement with the predictions based on the Steinmann relations for the Regge poles and Mandelstam cut contributions. The leading term reproduces correctly the expression calculated by one of the authors in the BFKL approach, while the subleading term presents a result, that was not yet found with the use of the unitarity techniques. This supports the applicability of the Wilson loop approach to the planar MHV amplitudes in N=4 SUSY. (orig.) 3. Benchmark models, planes lines and points for future SUSY searches at the LHC Energy Technology Data Exchange (ETDEWEB) AbdusSalam, S.S. [The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Allanach, B.C. [Cambridge Univ. (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics; Dreiner, H.K. [Bonn Univ. (DE). Bethe Center for Theoretical Physics and Physikalisches Inst.] (and others) 2012-03-15 We define benchmark models for SUSY searches at the LHC, including the CMSSM, NUHM, mGMSB, mAMSB, MM-AMSB and p19MSSM, as well as models with R-parity violation and the NMSSM. Within the parameter spaces of these models, we propose benchmark subspaces, including planes, lines and points along them. The planes may be useful for presenting results of the experimental searches in different SUSY scenarios, while the specific benchmark points may serve for more detailed detector performance tests and comparisons. We also describe algorithms for defining suitable benchmark points along the proposed lines in the parameter spaces, and we define a few benchmark points motivated by recent fits to existing experimental data. 4. Analytic properties of high energy production amplitudes in N=4 SUSY International Nuclear Information System (INIS) Lipatov, L.N.; Hamburg Univ. 2010-08-01 We investigate analytic properties of the six point planar amplitude in N=4 SUSY at the multi-Regge kinematics for final state particles. For inelastic processes the Steinmann relations play an important role because they give a possibility to fix the phase structure of the Regge pole and Mandelstam cut contributions. The analyticity and factorization constraints allow us to reproduce the two-loop correction to the 6- point BDS amplitude in N=4 SUSY obtained earlier in the leading logarithmic approximation with the use of the s-channel unitarity. The cut contribution has the Moebius invariant form in the transverse momentum subspace. The exponentiation hypothesis for the amplitude in the multi-Regge kinematics is also investigated in LLA. (orig.) 5. Prospects for R-Parity Conserving SUSY searches at the LHC CERN Document Server The ATLAS collaboration 2009-01-01 The talk reviews the current strategies to search for generic SUSY models with R-parity conservation in the ATLAS and CMS detectors at the LHC. The discovery reach in early data is presented for different search channels based on missing transverse momentum from undetected neutralinos and multiple jets. The talk will also describe the search for models of gauge-mediated supersymmetry breaking for which the NLSP is a neutralino decaying to a photon and a gravitino. In this scenario, the search strategy exploits the distinct signature of a non-pointing photon. Finally, we present recent work on techniques used to reconstruct the decays of SUSY particles at the LHC in early data, based on the selection of final-state exclusive decay chains. 6. Prospects for R-Parity Conserving SUSY searches at the LHC CERN Document Server Genest, Marie-Helene 2009-01-01 We review the current strategies to search for generic SUSY models with R-parity conservation in the ATLAS and CMS detectors at the LHC. The discovery reach in early data will be presented for the diﬀerent search channels based on missing transverse momentum from undetected neutralinos and multiple jets. We will also describe the search for models of gauge-mediated supersymmetry breaking for which the NLSP is a neutralino decaying to a photon and a gravitino. Finally, we will present recent work on techniques used to reconstruct the decays of SUSY particles at the LHC in early data, based on the selection of ﬁnal-state exclusive decay chains. 7. Benchmark Models, Planes, Lines and Points for Future SUSY Searches at the LHC CERN Document Server AbdusSalam, S S; Dreiner, H K; Ellis, J; Ellwanger, U; Gunion, J; Heinemeyer, S; Krämer, M; Mangano, M L; Olive, K A; Rogerson, S; Roszkowski, L; Schlaffer, M; Weiglein, G 2011-01-01 We define benchmark models for SUSY searches at the LHC, including the CMSSM, NUHM, mGMSB, mAMSB, MM-AMSB and p19MSSM, as well as models with R-parity violation and the NMSSM. Within the parameter spaces of these models, we propose benchmark subspaces, including planes, lines and points along them. The planes may be useful for presenting results of the experimental searches in different SUSY scenarios, while the specific benchmark points may serve for more detailed detector performance tests and comparisons. We also describe algorithms for defining suitable benchmark points along the proposed lines in the parameter spaces, and we define a few benchmark points motivated by recent fits to existing experimental data. 8. Analytic properties of high energy production amplitudes in N=4 SUSY Energy Technology Data Exchange (ETDEWEB) Lipatov, L.N. [St. Petersburg Inst. of Nuclear Physics, Gatchina (Russian Federation); Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik 2010-08-15 We investigate analytic properties of the six point planar amplitude in N=4 SUSY at the multi-Regge kinematics for final state particles. For inelastic processes the Steinmann relations play an important role because they give a possibility to fix the phase structure of the Regge pole and Mandelstam cut contributions. The analyticity and factorization constraints allow us to reproduce the two-loop correction to the 6- point BDS amplitude in N=4 SUSY obtained earlier in the leading logarithmic approximation with the use of the s-channel unitarity. The cut contribution has the Moebius invariant form in the transverse momentum subspace. The exponentiation hypothesis for the amplitude in the multi-Regge kinematics is also investigated in LLA. (orig.) 9. Multiple linear regression to develop strength scaled equations for knee and elbow joints based on age, gender and segment mass DEFF Research Database (Denmark) D'Souza, Sonia; Rasmussen, John; Schwirtz, Ansgar 2012-01-01 and valuable ergonomic tool. Objective: To investigate age and gender effects on the torque-producing ability in the knee and elbow in older adults. To create strength scaled equations based on age, gender, upper/lower limb lengths and masses using multiple linear regression. To reduce the number of dependent...... flexors. Results: Males were signifantly stronger than females across all age groups. Elbow peak torque (EPT) was better preserved from 60s to 70s whereas knee peak torque (KPT) reduced significantly (PGender, thigh mass and age best...... predicted KPT (R2=0.60). Gender, forearm mass and age best predicted EPT (R2=0.75). Good crossvalidation was established for both elbow and knee models. Conclusion: This cross-sectional study of muscle strength created and validated strength scaled equations of EPT and KPT using only gender, segment mass... 10. Extension of the SUSY Les Houches Accord 2 for see-saw mechanisms International Nuclear Information System (INIS) Basso, L.; Belyaev, A.; Chowdhury, D.; Ghosh, D.K.; Hirsch, M.; Khalil, S.; Moretti, S.; O'Leary, B.; Porod, W.; Staub, F. 2012-01-01 The SUSY Les Houches Accord (SLHA) 2 extended the first SLHA to include various generalisations of the Minimal Supersymmetric Standard Model (MSSM) as well as its simplest next-to-minimal version. Here, we propose further extensions to it, to include the most general and well-established see-saw descriptions (types I/II/III, inverse, and linear) in both an effective and a simple gauged extension of the MSSM framework. (authors) 11. Convergence of macroscopic tongue anatomy in ruminants and scaling relationships with body mass or tongue length. Science.gov (United States) Meier, Andrea R; Schmuck, Ute; Meloro, Carlo; Clauss, Marcus; Hofmann, Reinhold R 2016-03-01 Various morphological measures demonstrate convergent evolution in ruminants with their natural diet, in particular with respect to the browser/grazer dichotomy. Here, we report quantitative macroanatomical measures of the tongue (length and width of specific parts) of 65 ruminant species and relate them to either body mass (BM) or total tongue length, and to the percentage of grass in the natural diet (%grass). Models without and with accounting for the phylogenetic structures of the dataset were used, and models were ranked using Akaike's Information Criterion. Scaling relationships followed geometric principles, that is, length measures scaled with BM to the power of 0.33. Models that used tongue length rather than BM as a body size proxy were consistently ranked better, indicating that using size proxies that are less susceptible to a wider variety of factors (such as BM that fluctuates with body condition) should be attempted whenever possible. The proportion of the freely mobile tongue tip of the total tongue (and hence also the corpus length) was negatively correlated to %grass, in accordance with concepts that the feeding mechanism of browsers requires more mobile tongues. It should be noted that some nonbrowsers, such as cattle, use a peculiar mechanism for grazing that also requires long, mobile tongues, but they appear to be exceptions. A larger corpus width with increasing %grass corresponds to differences in snout shape with broader snouts in grazers. The Torus linguae is longer with increasing %grass, a finding that still warrants functional interpretation. This study shows that tongue measures covary with diet in ruminants. In contrast, the shape of the tongue (straight or "hourglass-shaped" as measured by the ratio of the widest and smallest corpus width) is unrelated to diet and is influenced strongly by phylogeny. © 2015 Wiley Periodicals, Inc. 12. Scale effect experiment in a fractured rock mass. Pilot study in the certified Fanay-Augeres mine (F) International Nuclear Information System (INIS) Durand, E.; Peaudecerf, P.; Ledoux, E.; De Marsily, G. 1985-01-01 This report (in two volumes) presents the results of a first phase of research about ''scale effect'' on permeability and solute transport in a fractured rock mass, to assess its suitability for future disposal of radioactive wastes. The gallery which was ''certified'' is located in the Fanay-Augeres mine(F), at a depth of about 175 m, in a granite mass. The portion selected for the subsequent experimental work is about 100 m long 13. Neutrino Majorana masses from string theory instanton effects International Nuclear Information System (INIS) Ibanez, Luis E.; Uranga, Angel M. 2007-01-01 Finding a plausible origin for right-handed neutrino Majorana masses in semirealistic compactifications of string theory remains one of the most difficult problems in string phenomenology. We argue that right-handed neutrino Majorana masses are induced by non-perturbative instanton effects in certain classes of string compactifications in which the U(1) B-L gauge boson has a Stueckelberg mass. The induced operators are of the form e -U ν R ν R where U is a closed string modulus whose imaginary part transforms appropriately under B-L. This mass term may be quite large since this is not a gauge instanton and Re U is not directly related to SM gauge couplings. Thus the size of the induced right-handed neutrino masses could be a few orders of magnitude below the string scale, as phenomenologically required. It is also argued that this origin for neutrino masses would predict the existence of R-parity in SUSY versions of the SM. Finally we comment on other phenomenological applications of similar instanton effects, like the generation of a μ-term, or of Yukawa couplings forbidden in perturbation theory 14. The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays Energy Technology Data Exchange (ETDEWEB) Gadella, M. [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, E-47011 Valladolid (Spain); Kuru, Ş. [Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J., E-mail: [email protected] [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, E-47011 Valladolid (Spain) 2017-04-15 We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum representation has a branch cut and an infinite number of simple poles on the negative imaginary axis which are related with the so called anti-bound states. This model does not show resonances. Using the wave functions of the anti-bound states, we obtain supersymmetric (SUSY) partners which are the series of Rosen–Morse II potentials. We have computed the Wigner reflection and transmission time delays for the hyperbolic step and such SUSY partners. Our results show that the more bound states a partner Hamiltonian has the smaller is the time delay. We also have evaluated time delays for the hyperbolic step potential in the classical case and have obtained striking similitudes with the quantum case. - Highlights: • The scattering matrix of hyperbolic step potential is studied. • The scattering matrix has a branch cut and an infinite number of poles. • The poles are associated to anti-bound states. • Susy partners using antibound states are computed. • Wigner time delays for the hyperbolic step and partner potentials are compared. 15. An industry-scale mass marking technique for tracing farmed fish escapees. Directory of Open Access Journals (Sweden) Fletcher Warren-Myers Full Text Available Farmed fish escape and enter the environment with subsequent effects on wild populations. Reducing escapes requires the ability to trace individuals back to the point of escape, so that escape causes can be identified and technical standards improved. Here, we tested if stable isotope otolith fingerprint marks delivered during routine vaccination could be an accurate, feasible and cost effective marking method, suitable for industrial-scale application. We tested seven stable isotopes, (134Ba, (135Ba, (136Ba, (137Ba, (86Sr, (87Sr and (26Mg, on farmed Atlantic salmon reared in freshwater, in experimental conditions designed to reflect commercial practice. Marking was 100% successful with individual Ba isotopes at concentrations as low as 0.001 µg. g-1 fish and for Sr isotopes at 1 µg. g-1 fish. Our results suggest that 63 unique fingerprint marks can be made at low cost using Ba (0.0002 - 0.02 $US per mark and Sr (0.46 - 0.82$US per mark isotopes. Stable isotope fingerprinting during vaccination is feasible for commercial application if applied at a company level within the world's largest salmon producing nations. Introducing a mass marking scheme would enable tracing of escapees back to point of origin, which could drive greater compliance, better farm design and improved management practices to reduce escapes. 16. Quantifying in-stream retention of nitrate at catchment scales using a practical mass balance approach. Science.gov (United States) Schwientek, Marc; Selle, Benny 2016-02-01 As field data on in-stream nitrate retention is scarce at catchment scales, this study aimed at quantifying net retention of nitrate within the entire river network of a fourth-order stream. For this purpose, a practical mass balance approach combined with a Lagrangian sampling scheme was applied and seasonally repeated to estimate daily in-stream net retention of nitrate for a 17.4 km long, agriculturally influenced, segment of the Steinlach River in southwestern Germany. This river segment represents approximately 70% of the length of the main stem and about 32% of the streambed area of the entire river network. Sampling days in spring and summer were biogeochemically more active than in autumn and winter. Results obtained for the main stem of Steinlach River were subsequently extrapolated to the stream network in the catchment. It was demonstrated that, for baseflow conditions in spring and summer, in-stream nitrate retention could sum up to a relevant term of the catchment's nitrogen balance if the entire stream network was considered. 17. Thermospheric mass density model error variance as a function of time scale Science.gov (United States) Emmert, J. T.; Sutton, E. K. 2017-12-01 In the increasingly crowded low-Earth orbit environment, accurate estimation of orbit prediction uncertainties is essential for collision avoidance. Poor characterization of such uncertainty can result in unnecessary and costly avoidance maneuvers (false positives) or disregard of a collision risk (false negatives). Atmospheric drag is a major source of orbit prediction uncertainty, and is particularly challenging to account for because it exerts a cumulative influence on orbital trajectories and is therefore not amenable to representation by a single uncertainty parameter. To address this challenge, we examine the variance of measured accelerometer-derived and orbit-derived mass densities with respect to predictions by thermospheric empirical models, using the data-minus-model variance as a proxy for model uncertainty. Our analysis focuses mainly on the power spectrum of the residuals, and we construct an empirical model of the variance as a function of time scale (from 1 hour to 10 years), altitude, and solar activity. We find that the power spectral density approximately follows a power-law process but with an enhancement near the 27-day solar rotation period. The residual variance increases monotonically with altitude between 250 and 550 km. There are two components to the variance dependence on solar activity: one component is 180 degrees out of phase (largest variance at solar minimum), and the other component lags 2 years behind solar maximum (largest variance in the descending phase of the solar cycle). 18. A scale space approach for unsupervised feature selection in mass spectra classification for ovarian cancer detection. Science.gov (United States) Ceccarelli, Michele; d'Acierno, Antonio; Facchiano, Angelo 2009-10-15 Mass spectrometry spectra, widely used in proteomics studies as a screening tool for protein profiling and to detect discriminatory signals, are high dimensional data. A large number of local maxima (a.k.a. peaks) have to be analyzed as part of computational pipelines aimed at the realization of efficient predictive and screening protocols. With this kind of data dimensions and samples size the risk of over-fitting and selection bias is pervasive. Therefore the development of bio-informatics methods based on unsupervised feature extraction can lead to general tools which can be applied to several fields of predictive proteomics. We propose a method for feature selection and extraction grounded on the theory of multi-scale spaces for high resolution spectra derived from analysis of serum. Then we use support vector machines for classification. In particular we use a database containing 216 samples spectra divided in 115 cancer and 91 control samples. The overall accuracy averaged over a large cross validation study is 98.18. The area under the ROC curve of the best selected model is 0.9962. We improved previous known results on the problem on the same data, with the advantage that the proposed method has an unsupervised feature selection phase. All the developed code, as MATLAB scripts, can be downloaded from http://medeaserver.isa.cnr.it/dacierno/spectracode.htm. 19. Considerations of anthropometric, tissue volume, and tissue mass scaling for improved patient specificity of skeletal S values International Nuclear Information System (INIS) Bolch, W.E.; Patton, P.W.; Shah, A.P.; Rajon, D.A.; Jokisch, D.W. 2002-01-01 It is generally acknowledged that reference man (70 kg in mass and 170 cm in height) does not adequately represent the stature and physical dimensions of many patients undergoing radionuclide therapy, and thus scaling of radionuclide S values is required for patient specificity. For electron and beta sources uniformly distributed within internal organs, the mean dose from self-irradiation is noted to scale inversely with organ mass, provided no escape of electron energy occurs at the organ boundaries. In the skeleton, this same scaling approach is further assumed to be correct for marrow dosimetry; nevertheless, difficulties in quantitative assessments of marrow mass in specific skeletal regions of the patient make this approach difficult to implement clinically. Instead, scaling of marrow dose is achieved using various anthropometric parameters that presumably scale in the same proportion. In this study, recently developed three-dimensional macrostructural transport models of the femoral head and humeral epiphysis in three individuals (51-year male, 82-year female, and 86-year female) are used to test the abilities of different anthropometric parameters (total body mass, body surface area, etc.) to properly scale radionuclide S values from reference man models. The radionuclides considered are 33 P, 177 Lu, 153 Sm, 186 Re, 89 Sr, 166 Ho, 32 P, 188 Re, and 90 Y localized in either the active marrow or endosteal tissues of the bone trabeculae. S value scaling is additionally conducted in which the 51-year male subject is assigned as the reference individual; scaling parameters are then expanded to include tissue volumes and masses for both active marrow and skeletal spongiosa. The study concludes that, while no single anthropometric parameter emerges as a consistent scaler of reference man S values, lean body mass is indicated as an optimal scaler when the reference S values are based on 3D transport techniques. Furthermore, very exact patient-specific scaling of 20. Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses Directory of Open Access Journals (Sweden) Marte Gutierrez 2015-12-01 Full Text Available Fracture systems have strong influence on the overall mechanical behavior of fractured rock masses due to their relatively lower stiffness and shear strength than those of the rock matrix. Understanding the effects of fracture geometrical distribution, such as length, spacing, persistence and orientation, is important for quantifying the mechanical behavior of fractured rock masses. The relation between fracture geometry and the mechanical characteristics of the fractured rock mass is complicated due to the fact that the fracture geometry and mechanical behaviors of fractured rock mass are strongly dependent on the length scale. In this paper, a comprehensive study was conducted to determine the effects of fracture distribution on the equivalent continuum elastic compliance of fractured rock masses over a wide range of fracture lengths. To account for the stochastic nature of fracture distributions, three different simulation techniques involving Oda's elastic compliance tensor, Monte Carlo simulation (MCS, and suitable probability density functions (PDFs were employed to represent the elastic compliance of fractured rock masses. To yield geologically realistic results, parameters for defining fracture distributions were obtained from different geological fields. The influence of the key fracture parameters and their relations to the overall elastic behavior of the fractured rock mass were studied and discussed. A detailed study was also carried out to investigate the validity of the use of a representative element volume (REV in the equivalent continuum representation of fractured rock masses. A criterion was also proposed to determine the appropriate REV given the fracture distribution of the rock mass. 1. Geoelectrical Measurement of Multi-Scale Mass Transfer Parameters Final Report to the Subsurface Biogeochemical Research Program Energy Technology Data Exchange (ETDEWEB) Day-Lewis, Frederick; Singha, Kamini; Haggerty, Roy; Johnson, Timothy; Binley, Andrew; Lane, John 2014-03-10 . In this project, we sought to capitalize on the geophysical signatures of mass transfer. Previous numerical modeling and pilot-scale field experiments suggested that mass transfer produces a geoelectrical signature—a hysteretic relation between sampled (mobile-domain) fluid conductivity and bulk (mobile + immobile) conductivity—over a range of scales relevant to aquifer remediation. In this work, we investigated the geoelectrical signature of mass transfer during tracer transport in a series of controlled experiments to determine the operation of controlling parameters, and also investigated the use of complex-resistivity (CR) as a means of quantifying mass transfer parameters in situ without tracer experiments. In an add-on component to our grant, we additionally considered nuclear magnetic resonance (NMR) to help parse mobile from immobile porosities. Our study objectives were to: 1. Develop and demonstrate geophysical approaches to measure mass-transfer parameters spatially and over a range of scales, including the combination of electrical resistivity monitoring, tracer tests, complex resistivity, nuclear magnetic resonance, and materials characterization; and 2. Provide mass-transfer estimates for improved understanding of contaminant fate and transport at DOE sites, such as uranium transport at the Hanford 300 Area. To achieve our objectives, we implemented a 3-part research plan involving (1) development of computer codes and techniques to estimate mass-transfer parameters from time-lapse electrical data; (2) bench-scale experiments on synthetic materials and materials from cores from the Hanford 300 Area; and (3) field demonstration experiments at the DOE’s Hanford 300 Area. 2. SUSI 62 A ROBUST AND SAFE PARACHUTE UAV WITH LONG FLIGHT TIME AND GOOD PAYLOAD Directory of Open Access Journals (Sweden) H. P. Thamm 2012-09-01 Full Text Available In many research areas in the geo-sciences (erosion, land use, land cover change, etc. or applications (e.g. forest management, mining, land management etc. there is a demand for remote sensing images of a very high spatial and temporal resolution. Due to the high costs of classic aerial photo campaigns, the use of a UAV is a promising option for obtaining the desired remote sensed information at the time it is needed. However, the UAV must be easy to operate, safe, robust and should have a high payload and long flight time. For that purpose, the parachute UAV SUSI 62 was developed. It consists of a steel frame with a powerful 62 cm3 2- stroke engine and a parachute wing. The frame can be easily disassembled for transportation or to replace parts. On the frame there is a gimbal mounted sensor carrier where different sensors, standard SLR cameras and/or multi-spectral and thermal sensors can be mounted. Due to the design of the parachute, the SUSI 62 is very easy to control. Two different parachute sizes are available for different wind speed conditions. The SUSI 62 has a payload of up to 8 kg providing options to use different sensors at the same time or to extend flight duration. The SUSI 62 needs a runway of between 10 m and 50 m, depending on the wind conditions. The maximum flight speed is approximately 50 km/h. It can be operated in a wind speed of up to 6 m/s. The design of the system utilising a parachute UAV makes it comparatively safe as a failure of the electronics or the remote control only results in the UAV coming to the ground at a slow speed. The video signal from the camera, the GPS coordinates and other flight parameters are transmitted to the ground station in real time. An autopilot is available, which guarantees that the area of investigation is covered at the desired resolution and overlap. The robustly designed SUSI 62 has been used successfully in Europe, Africa and Australia for scientific projects and also for 3. High-frequency spectral ultrasound imaging (SUSI) visualizes early post-traumatic heterotopic ossification (HO) in a mouse model. Science.gov (United States) Ranganathan, Kavitha; Hong, Xiaowei; Cholok, David; Habbouche, Joe; Priest, Caitlin; Breuler, Christopher; Chung, Michael; Li, John; Kaura, Arminder; Hsieh, Hsiao Hsin Sung; Butts, Jonathan; Ucer, Serra; Schwartz, Ean; Buchman, Steven R; Stegemann, Jan P; Deng, Cheri X; Levi, Benjamin 2018-04-01 Early treatment of heterotopic ossification (HO) is currently limited by delayed diagnosis due to limited visualization at early time points. In this study, we validate the use of spectral ultrasound imaging (SUSI) in an animal model to detect HO as early as one week after burn tenotomy. Concurrent SUSI, micro CT, and histology at 1, 2, 4, and 9weeks post-injury were used to follow the progression of HO after an Achilles tenotomy and 30% total body surface area burn (n=3-5 limbs per time point). To compare the use of SUSI in different types of injury models, mice (n=5 per group) underwent either burn/tenotomy or skin incision injury and were imaged using a 55MHz probe on VisualSonics VEVO 770 system at one week post injury to evaluate the ability of SUSI to distinguish between edema and HO. Average acoustic concentration (AAC) and average scatterer diameter (ASD) were calculated for each ultrasound image frame. Micro CT was used to calculate the total volume of HO. Histology was used to confirm bone formation. Using SUSI, HO was visualized as early as 1week after injury. HO was visualized earliest by 4weeks after injury by micro CT. The average acoustic concentration of HO was 33% more than that of the control limb (n=5). Spectroscopic foci of HO present at 1week that persisted throughout all time points correlated with the HO present at 9weeks on micro CT imaging. SUSI visualizes HO as early as one week after injury in an animal model. SUSI represents a new imaging modality with promise for early diagnosis of HO. Copyright © 2018 Elsevier Inc. All rights reserved. 4. Calibration of a surface mass balance model for global-scale applications NARCIS (Netherlands) Giesen, R. H.; Oerlemans, J. 2012-01-01 Global applications of surface mass balance models have large uncertainties, as a result of poor climate input data and limited availability of mass balance measurements. This study addresses several possible consequences of these limitations for the modelled mass balance. This is done by applying a 5. The potential for optical beam shaping of UV laser sources for mass scale quarantine disinfection applications Science.gov (United States) Lizotte, Todd 2010-08-01 Recent events concerning H1N1 "swine flu", have demonstrated to the world the significant potential of rapid increases in death and illness among all age groups and even among the healthy population [1] when a highly infectious influenza virus is introduced. In terms of mass casualties due to a pandemic, preparedness and response planning must be done. One course of action to prevent a pandemic outbreak or reduce the impact of a bioterrorist event is the use of isolation or quarantine facilities. The first level of isolation or quarantine is within the personal residence of the person exposed or infected. In the case where, the specific virus is extremely contagious and its onset of symptoms is rapid and severe, there will be a need for the deployment and setup of larger self contained quarantine facilities. Such facilities are used to house infectious individuals to minimize the exposure of susceptible individuals to contagious individuals, especially when specialized care or treatment is required and during the viral shedding period (5 to 7 days). These types of facilities require non-shared air conditioning, heating and ventilating systems where 100% of air is vented to the outside through a series of disinfection systems and staged filters. Although chemical disinfection is possible, there is a desire to incorporate intense UV radiation as a means to deactivate and disinfect airborne virus within hospital settings and isolated mass scale quarantine facilities. UV radiation is also being considered for disinfection of contaminated surfaces, such as table tops, walls and floors in hospitals and temporary quarantine facilities. In such applications the use of UV bulb technology can create many problems, for instance bulb technology requires numerous bulbs to treat a large volume of air, generates significant heat, uses significant power and does not produce large fluxes of UV light efficiently. This paper provides several methods of creating quarantine level 6. MSSM with mh = 125 GeV in high-scale gauge mediation International Nuclear Information System (INIS) Zheng, Sibo 2014-01-01 After the discovery of an SM-like Higgs with m h = 125 GeV, it is increasingly urgent to explore a solution to the hierarchy problem. In the context of MSSM from gauge-mediated SUSY breaking, the lower bound on the gluino mass suggests that the messenger scale M is probably large if the magnitude of Λ ∝ 100 TeV. In this paper, we study the 5 + 5 model with M ∝ 10 8 -10 12 GeV and Λ ≅ 100 TeV. For moderate Higgs C messenger coupling, a viable model will be shown with moderate fine tuning. In this model, μ ∝ 800 GeV, and B μ nearly vanishes at the input scale, which can be constructed in a microscopic model. (orig.) 7. Strong Sector in non-minimal SUSY model Directory of Open Access Journals (Sweden) Costantini Antonio 2016-01-01 Full Text Available We investigate the squark sector of a supersymmetric theory with an extended Higgs sector. We give the mass matrices of stop and sbottom, comparing the Minimal Supersymmetric Standard Model (MSSM case and the non-minimal case. We discuss the impact of the extra superfields on the decay channels of the stop searched at the LHC. 8. The sea-level budget along the Northwest Atlantic coast : GIA, mass changes, and large-scale ocean dynamics NARCIS (Netherlands) Frederikse, T.; Simon, K.M.; Katsman, C.A.; Riva, R.E.M. 2017-01-01 Sea-level rise and decadal variability along the northwestern coast of the North Atlantic Ocean are studied in a self-consistent framework that takes into account the effects of solid-earth deformation and geoid changes due to large-scale mass redistribution processes. Observations of sea and 9. Ontogenetic body-mass scaling of nitrogen excretion relates to body surface area in diverse pelagic invertebrates DEFF Research Database (Denmark) Hirst, Andrew G.; Lilley, M.K.S.; Glazier, D.S. 2017-01-01 . Among diverse pelagic invertebrates that change shape during ontogeny, recent analysis has demonstrated a significant positive correlation between the body-mass allometry of respiration rates (measured as the ontogenetic body mass-scaling exponent bR) and the allometry of body surface area (b......A, as predicted from body-shape changes using a Euclidean model). As many pelagic invertebrates use a large portion of their external body surface for both resource uptake and waste excretion, we predicted that body-mass scaling exponents for rates of excretion of soluble N (bN) should also then relate...... to the degree of body-shape change during growth. We tested this hypothesis using literature data on bN for 39 species of pelagic invertebrates across five different phyla, and find strong support: bN is significantly positively correlated with predicted bA, whilst also co-varying with bR. Intraspecific... 10. A new approach to Naturalness in SUSY models CERN Document Server Ghilencea, D M 2013-01-01 We review recent results that provide a new approach to the old problem of naturalness in supersymmetric models, without relying on subjective definitions for the fine-tuning associated with {\\it fixing} the EW scale (to its measured value) in the presence of quantum corrections. The approach can address in a model-independent way many questions related to this problem. The results show that naturalness and its measure (fine-tuning) are an intrinsic part of the likelihood to fit the data that {\\it includes} the EW scale. One important consequence is that the additional {\\it constraint} of fixing the EW scale, usually not imposed in the data fits of the models, impacts on their overall likelihood to fit the data (or chi^2/ndf, ndf: number of degrees of freedom). This has negative implications for the viability of currently popular supersymmetric extensions of the Standard Model. 11. HICOSMO - cosmology with a complete sample of galaxy clusters - I. Data analysis, sample selection and luminosity-mass scaling relation Science.gov (United States) Schellenberger, G.; Reiprich, T. H. 2017-08-01 The X-ray regime, where the most massive visible component of galaxy clusters, the intracluster medium, is visible, offers directly measured quantities, like the luminosity, and derived quantities, like the total mass, to characterize these objects. The aim of this project is to analyse a complete sample of galaxy clusters in detail and constrain cosmological parameters, like the matter density, Ωm, or the amplitude of initial density fluctuations, σ8. The purely X-ray flux-limited sample (HIFLUGCS) consists of the 64 X-ray brightest galaxy clusters, which are excellent targets to study the systematic effects, that can bias results. We analysed in total 196 Chandra observations of the 64 HIFLUGCS clusters, with a total exposure time of 7.7 Ms. Here, we present our data analysis procedure (including an automated substructure detection and an energy band optimization for surface brightness profile analysis) that gives individually determined, robust total mass estimates. These masses are tested against dynamical and Planck Sunyaev-Zeldovich (SZ) derived masses of the same clusters, where good overall agreement is found with the dynamical masses. The Planck SZ masses seem to show a mass-dependent bias to our hydrostatic masses; possible biases in this mass-mass comparison are discussed including the Planck selection function. Furthermore, we show the results for the (0.1-2.4) keV luminosity versus mass scaling relation. The overall slope of the sample (1.34) is in agreement with expectations and values from literature. Splitting the sample into galaxy groups and clusters reveals, even after a selection bias correction, that galaxy groups exhibit a significantly steeper slope (1.88) compared to clusters (1.06). 12. LoCuSS: THE SUNYAEV–ZEL'DOVICH EFFECT AND WEAK-LENSING MASS SCALING RELATION International Nuclear Information System (INIS) Marrone, Daniel P.; Carlstrom, John E.; Gralla, Megan; Greer, Christopher H.; Hennessy, Ryan; Leitch, Erik M.; Plagge, Thomas; Smith, Graham P.; Okabe, Nobuhiro; Bonamente, Massimiliano; Hasler, Nicole; Culverhouse, Thomas L.; Hawkins, David; Lamb, James W.; Muchovej, Stephen; Joy, Marshall; Martino, Rossella; Mazzotta, Pasquale; Miller, Amber; Mroczkowski, Tony 2012-01-01 We present the first weak-lensing-based scaling relation between galaxy cluster mass, M WL , and integrated Compton parameter Y sph . Observations of 18 galaxy clusters at z ≅ 0.2 were obtained with the Subaru 8.2 m telescope and the Sunyaev-Zel'dovich Array. The M WL -Y sph scaling relations, measured at Δ = 500, 1000, and 2500 ρ c , are consistent in slope and normalization with previous results derived under the assumption of hydrostatic equilibrium (HSE). We find an intrinsic scatter in M WL at fixed Y sph of 20%, larger than both previous measurements of M HSE -Y sph scatter as well as the scatter in true mass at fixed Y sph found in simulations. Moreover, the scatter in our lensing-based scaling relations is morphology dependent, with 30%-40% larger M WL for undisturbed compared to disturbed clusters at the same Y sph at r 500 . Further examination suggests that the segregation may be explained by the inability of our spherical lens models to faithfully describe the three-dimensional structure of the clusters, in particular, the structure along the line of sight. We find that the ellipticity of the brightest cluster galaxy, a proxy for halo orientation, correlates well with the offset in mass from the mean scaling relation, which supports this picture. This provides empirical evidence that line-of-sight projection effects are an important systematic uncertainty in lensing-based scaling relations. 13. Scaling and χPT description of pions from Nf=2 twisted mass QCD International Nuclear Information System (INIS) Dimopoulos, Petros; Frezzotti, Roberto; Herdoiza, Gregorio; Jansen, Karl; Michael, Chris; Urbach, Carsten; Bonn Univ. 2009-12-01 We study light-quark observables by means of dynamical lattice QCD simulations using two flavours of twisted mass fermions at maximal twist. We employ chiral perturbation theory to describe our data for the pion mass and decay constant. In this way, we extract precise determinations for the low-energy constants of the effective theory as well as for the light-quark mass and the chiral condensate. (orig.) 14. Radiative corrections to light neutrino masses in low scale type I seesaw scenarios and neutrinoless double beta decay Energy Technology Data Exchange (ETDEWEB) Lopez-Pavon, J. [SISSA and INFN - sezione di Trieste, via Bonomea 265, 34136 Trieste (Italy); Molinaro, E. [CP-Origins and Danish Institute for Advanced Study, University of Southern Denmark,Campusvej 55, DK-5230 Odense M (Denmark); Petcov, S.T. [SISSA and INFN - sezione di Trieste, via Bonomea 265, 34136 Trieste (Italy); Kavli IPMU (WPI), University of Tokyo, 5-1-5 Kashiwanoha, 277-8583 Kashiwa (Japan) 2015-11-05 We perform a detailed analysis of the one-loop corrections to the light neutrino mass matrix within low scale type I seesaw extensions of the Standard Model and their implications in experimental searches for neutrinoless double beta decay. We show that a sizable contribution to the effective Majorana neutrino mass from the exchange of heavy Majorana neutrinos is always possible, provided one requires a fine-tuned cancellation between the tree-level and one-loop contribution to the light neutrino masses. We quantify the level of fine-tuning as a function of the seesaw parameters and introduce a generalisation of the Casas-Ibarra parametrization of the neutrino Yukawa matrix, which easily allows to include the one-loop corrections to the light neutrino masses. 15. Confronting SUSY models with LHC data via electroweakino production International Nuclear Information System (INIS) Arina, Chiara; Chala, Mikael; Martin-Lozano, Victor; Bonn Univ.; Nardini, Germano 2016-12-01 We investigate multi-lepton signals produced by ElectroWeakino (EWino) decays in the MSSM and the TMSSM scenarios with sfermions, gluinos and non Standard Model Higgses at the TeV scale, being the Bino electroweak-scale dark matter. We recast the present LHC constraints on EWinos for these models and we find that wide MSSM and TMSSM parameter regions prove to be allowed. We forecast the number of events expected in the signal regions of the experimental multi-lepton analyses in the next LHC runs. The correlations among these numbers will help to determine whether future deviations in multi-lepton data are ascribable to the EWinos, as well as the supersymmetric model they originate from. 16. Confronting SUSY models with LHC data via electroweakino production Energy Technology Data Exchange (ETDEWEB) Arina, Chiara [Centre for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,B-1348 Louvain-la-Neuve (Belgium); Chala, Mikael [Deutsches Elektronen Synchrotron,Notkestrasse 85, D-22603, Hamburg (Germany); Martín-Lozano, Víctor [Departamento de Física Teórica & Instituto de Física Teórica UAM/CSIC,Universidad Autónoma de Madrid,E-28049, Madrid (Spain); Bethe Center for Theoretical Physics & Physikalisches Institut der Universität Bonn,Nußallee 12, 53115, Bonn (Germany); Nardini, Germano [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics,University of Bern,Sidlerstrasse 5, CH-3012 Bern (Switzerland) 2016-12-29 We investigate multi-lepton signals produced by ElectroWeakino (EWino) decays in the MSSM and the TMSSM scenarios with sfermions, gluinos and non Standard Model Higgses at the TeV scale, with dark matter due to electroweak-scale Binos. We recast the present LHC constraints on EWinos for these models and we find that wide MSSM and TMSSM parameter regions prove to be allowed. We forecast the number of events expected in the signal regions of the experimental multi-lepton analyses in the next LHC runs. The correlations among these numbers will help to determine whether future deviations in multi-lepton data are ascribable to the EWinos, as well as the supersymmetric model they originate from. 17. Results on SUSY and Higgs searches at CMS CERN Multimedia CERN. Geneva 2011-01-01 We present the results of searches for Supersymmetry and the Higgs boson performed using data collected in 2010 by the CMS experiment at the LHC in pp-collisions at a centre-of-mass energy of 7 TeV. Searches for Supersymmetry are performed in all-hadronic final states with jets and missing transverse energy and in final states including one or more isolated leptons or photons. No evidence for new physics is observed and limits are set on the predictions of a range of Supersymmetric scenarios. The results of searches for the Higgs boson are presented and limits set. 18. Extracting SUSY parameters from selectron and chargino production International Nuclear Information System (INIS) Diaz, M.A. 1997-08-01 We review the extraction of fundamental supersymmetric parameters from experimental observables related to the detection of charginos and selectrons at e + e - colliders. We consider supergravity models with universal scalar and gaugino masses and radiatively broken electroweak symmetry. Two scenarios are considered: (a) the lightest chargino is light enough to be produced at LEP2, and (b) the right handed selectron is light enough to be produced at LEP2. We show how the validity of supergravity models can be tested even if experimental errors are large. Interesting differences between the spectrum in the two scenarios are pointed out. (author). 16 refs, 9 figs 19. Searches for electroweak SUSY with ATLAS at HL-LHC CERN Document Server Amoroso, Simone; The ATLAS collaboration 2018-01-01 The High Luminosity-Large Hadron Collider (HL-LHC) is expected to start in 2026 and to pro- vide an integrated luminosity of 3000 fb$^{−1}$ in ten years, a factor 10 more than what will be collected by 2023. This high statistics will allow ATLAS to improve searches for new physics at the TeV scale. In this talk search prospects for the electroweak production of supersymmetric particles are presented. 20. Mixing and mass transfer in a pilot scale U-loop bioreactor DEFF Research Database (Denmark) 2017-01-01 A system capable of handling a large volumetric gas fraction while providing a high gas to liquid mass transfer is a necessity if the metanotrophic bacterium Methylococcus capsulatus is to be used in single cell protein (SCP) production. In this study mixing time and mass transfer coefficients we... 1. Nine cases of nonpalpable testicular mass. An incidental finding in a large scale ultrasonography survey International Nuclear Information System (INIS) Avci, A.; Eken, C.; Ozgok, Y.; Erol, B. 2008-01-01 Nonpalpable testicular masses are usually diagnosed during routine ultrasonography (US) examinations for other conditions. There are conflicting results on the final diagnosis and management of these lesions. In the present study we report the results of a large US series of 5104 patients on nonpalpable testicular masses and discuss the management of these patients. This retrospective observational study was performed in a secondary care military hospital. A total of 5104 patients underwent a US and 11 of them were diagnosed as having a nonpalpable testicular mass. These 11 patients also underwent magnetic resonance imaging (MRI). Two of them refused surgery and were excluded from the study. The remaining nine patients underwent intraoperative US-guided localization and excisional biopsy of the non-palpable testicular parenchymal mass. A radical orchiectomy was required in all of them. US and MRI findings, frozen and final pathology results were recorded. The median age of study subjects was 24 years. The final pathology revealed a malign tumor in eight patients and an inflammatory mass in one patient. There were inconsistent results in four patients between frozen section analysis and final pathology. MRI improved the definition of the solid masses in all patients. MRI enhances the certainty of the diagnosis of malignity in nonpalpable testicular masses, particularly in conditions that generally can not be diagnosed with ultrasonography alone. Frozen section analysis is not an accredited method in diagnosing malign lesions in non-palpable testicular masses. (author) 2. SARAH 4: A tool for (not only SUSY) model builders Science.gov (United States) Staub, Florian 2014-06-01 We present the new version of the Mathematica package SARAH which provides the same features for a non-supersymmetric model as previous versions for supersymmetric models. This includes an easy and straightforward definition of the model, the calculation of all vertices, mass matrices, tadpole equations, and self-energies. Also the two-loop renormalization group equations for a general gauge theory are now included and have been validated with the independent Python code PyR@TE. Model files for FeynArts, CalcHep/CompHep, WHIZARD and in the UFO format can be written, and source code for SPheno for the calculation of the mass spectrum, a set of precision observables, and the decay widths and branching ratios of all states can be generated. Furthermore, the new version includes routines to output model files for Vevacious for both, supersymmetric and non-supersymmetric, models. Global symmetries are also supported with this version and by linking Susyno the handling of Lie groups has been improved and extended. 3. Soil organic matter dynamics and CO2 fluxes in relation to landscape scale processes: linking process understanding to regional scale carbon mass-balances Science.gov (United States) Van Oost, Kristof; Nadeu, Elisabet; Wiaux, François; Wang, Zhengang; Stevens, François; Vanclooster, Marnik; Tran, Anh; Bogaert, Patrick; Doetterl, Sebastian; Lambot, Sébastien; Van wesemael, Bas 2014-05-01 In this paper, we synthesize the main outcomes of a collaborative project (2009-2014) initiated at the UCL (Belgium). The main objective of the project was to increase our understanding of soil organic matter dynamics in complex landscapes and use this to improve predictions of regional scale soil carbon balances. In a first phase, the project characterized the emergent spatial variability in soil organic matter storage and key soil properties at the regional scale. Based on the integration of remote sensing, geomorphological and soil analysis techniques, we quantified the temporal and spatial variability of soil carbon stock and pool distribution at the local and regional scales. This work showed a linkage between lateral fluxes of C in relation with sediment transport and the spatial variation in carbon storage at multiple spatial scales. In a second phase, the project focused on characterizing key controlling factors and process interactions at the catena scale. In-situ experiments of soil CO2 respiration showed that the soil carbon response at the catena scale was spatially heterogeneous and was mainly controlled by the catenary variation of soil physical attributes (soil moisture, temperature, C quality). The hillslope scale characterization relied on advanced hydrogeophysical techniques such as GPR (Ground Penetrating Radar), EMI (Electromagnetic induction), ERT (Electrical Resistivity Tomography), and geophysical inversion and data mining tools. Finally, we report on the integration of these insights into a coupled and spatially explicit model and its application. Simulations showed that C stocks and redistribution of mass and energy fluxes are closely coupled, they induce structured spatial and temporal patterns with non negligible attached uncertainties. We discuss the main outcomes of these activities in relation to sink-source behavior and relevance of erosion processes for larger-scale C budgets. 4. Dark matter and the Higgs in natural SUSY Energy Technology Data Exchange (ETDEWEB) Basirnia, Aria; Macaluso, Sebastian; Shih, David [NHETC, Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854 (United States) 2017-03-14 Null results from dark matter (DM) direct detection experiments and the 125 GeV Higgs both pose serious challenges to minimal supersymmetry. In this paper, we propose a simple extension of the MSSM that economically solves both problems: a “dark sector” consisting of a singlet and a pair of SU(2) doublets. Loops of the dark sector fields help lift the Higgs mass to 125 GeV consistent with naturalness, while the lightest fermion in the dark sector can be viable thermal relic DM, provided that it is mostly singlet. The DM relic abundance is controlled by s-wave annihilation to tops and Higgsinos, leading to a tight relation between the relic abundance and the spin-dependent direct detection cross section. As a result, the model will be fully probed by the next generation of direct detection experiments. Finally we discuss the discovery potential at LHC Run II. 5. Search for SUSY in final states with photons at CMS Directory of Open Access Journals (Sweden) Ntomari Eleni 2013-05-01 Full Text Available Résumé The Compact Muon Solenoid (CMS collaboration has developed a complete program of searches beyond the Standard Model (SM covering a wide range of final states. This document focuses on searches in final states with photons and missing transverse energy ETmiss organised in three analyses. The first two include comparison of the ETmiss distribution (isolation sideband method in events with either at least two photons plus at least one hadronic jet, or at least one photon plus at least two hadronic jets. The third analysis corresponds to a new approach, the Jet-Gamma Balance (JGB method, for events with at least one photon plus at least three hadronic jets.We observe no significant deviations from the SM expectation and thus derive upper limits on the signal cross section at the 95% confidence level (CL for a range of squark, gluino and neutralino mass points in the Gauge Mediated Supersymmetry Breaking scenario. 6. Agent-Based Simulation of Mass Shootings: Determining How to Limit the Scale of a Tragedy OpenAIRE Roy Hayes; Reginald Hayes 2014-01-01 An agent-based simulation was created to examine key parameters in mass shootings. The goal of the simulation was to examine the potential effectiveness of Senator Dianne Feinsteinâ€™s (D-Calif.) assault weapons and high-capacity magazines bill. Based on the analysis, the proposed law would have a negligible effect on the number of people shot during mass shootings. The assault weapons portion of the proposed bill will have no effect on the number of people killed or wounded in a mass shootin... 7. Susy-QCD corrections to neutrlino pair production in association with a jet Energy Technology Data Exchange (ETDEWEB) Cullen, Gavin [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Greiner, Nicolas; Heinrich, Gudrun [Max-Planck-Institut fuer Physik, Muenchen (Germany) 2012-12-15 We present the NLO Susy-QCD corrections to the production of a pair of the lightest neutralinos plus one jet at the LHC, appearing as a monojet signature in combination with missing energy. We fully include all non-resonant diagrams, i.e. we do not assume that production and decay factorise. We derive a parameter point based on the p19MSSM which is compatible with current experimental bounds and show distributions based on missing transverse energy and jet observables. Our results are produced with the program GoSam for automated one-loop calculations in combination with MadDipole/- MadGraph for the real radiation part. 8. SUSY-QCD corrections to Higgs boson production at hadron colliders International Nuclear Information System (INIS) 1999-12-01 We analyze the next-to-leading order SUSY-QCD corrections to the production of Higgs particles at hadron colliders in supersymmetric extensions of the standard model. Besides the standard QCD corrections due to gluon exchange and emission, genuine supersymmetric corrections due to the virtual exchange of squarks and gluinos are present. At both the Tevatron and the LHC, these corrections are found to be small in the Higgs-strahlung, Drell-Yan-like Higgs pair production and vector boson fusion processes. (orig.) 9. Prospects for (non-SUSY) new physics with first LHC data International Nuclear Information System (INIS) Butterworth, Jonathan 2007-01-01 The ATLAS and CMS experiments will take first data soon. I consider here the prospects for new physics (excluding SUSY) with a few fb -1 of data. This means processes with signal cross sections of a few 100 fb or less, with clear and fairly simple signatures--precision comparison of data to Standard Model tails will take longer, needing more luminosity and very good understanding of detector calibrations, resolutions and trigger efficiencies. The approach I take here is signature rather than model based, but examples of models will be given 10. On new scaling group of transformation for Prandtl-Eyring fluid model with both heat and mass transfer Science.gov (United States) Rehman, Khalil Ur; Malik, Aneeqa Ashfaq; Malik, M. Y.; Tahir, M.; Zehra, Iffat 2018-03-01 A short communication is structured to offer a set of scaling group of transformation for Prandtl-Eyring fluid flow yields by stretching flat porous surface. The fluid flow regime is carried with both heat and mass transfer characteristics. To seek solution of flow problem a set of scaling group of transformation is proposed by adopting Lie approach. These transformations are used to step down the partial differential equations into ordinary differential equations. The reduced system is solved by numerical method termed as shooting method. A self-coded algorithm is executed in this regard. The obtain results are elaborated by means of figures and tables. 11. Measurement of the High-Mass Drell-Yan Cross Section and Limits on Quark-Electron Compositeness Scales International Nuclear Information System (INIS) Grinstein, S.; Mostafa, M.; Piegaia, R.; Alves, G.A.; Carvalho, W.; Maciel, A.K.; Motta, H. da; Oliveira, E.; Santoro, A.; Lima, J.G.; Oguri, V.; Gomez, B.; Hoeneisen, B.; Mooney, P.; Negret, J.P.; Ducros, Y.; Beri, S.B.; Bhatnagar, V.; Kohli, J.M.; Singh, J.B.; Shivpuri, R.K.; Acharya, B.S.; Banerjee, S.; Dugad, S.R.; Gupta, A.; Krishnaswamy, M.R.; Mondal, N.K.; Narasimham, V.S.; Parua, N.; Shankar, H.C.; Park, Y.M.; Choi, S.; Kim, S.K.; Castilla-Valdez, H.; Gonzalez Solis, J.L.; Hernandez-Montoya, R.; Magana-Mendoza, L.; Sanchez-Hernandez, A.; Pawlik, B.; Gavrilov, V.; Gershtein, Y.; Kuleshov, S.; Belyaev, A.; Dudko, L.V.; Ermolov, P.; Karmanov, D.; Leflat, A.; Manankov, V.; Merkin, M.; Shabalina, E.; Abramov, V.; Babintsev, V.V.; Bezzubov, V.A.; Bojko, N.I.; Burtovoi, V.S.; Chekulaev, S.V.; Denisov, S.P.; Dyshkant, A.; Eroshin, O.V.; Evdokimov, V.N.; Galyaev, A.N.; Goncharov, P.I.; Gurzhiev, S.N.; Kostritskiy, A.V.; Kozelov, A.V.; Kozlovsky, E.A.; Mayorov, A.A.; Babukhadia, L.; Davis, K.; Fein, D.; Forden, G.E.; Guida, J.A.; Johns, K.; Nang, F.; Narayanan, A.; Rutherfoord, J.; Shupe, M.; Aihara, H.; Barberis, E.; Clark, A.R. 1999-01-01 We present a measurement of the Drell-Yan cross section at high dielectron invariant mass using 120 pb -1 of data collected in p bar p collisions at √ (s) =1.8 TeV by the D0 Collaboration during 1992 - 1996. No deviation from standard model expectations is observed. We use the data to set limits on the quark-electron compositeness scale. The 95% confidence level lower limits on the compositeness scale vary between 3.3 and 6.1thinspthinspTeV depending on the assumed form of the effective contact interaction. copyright 1999 The American Physical Society 12. On the relation between E.M. mass differences and scaling in deep inelastic scattering, ch. 1 International Nuclear Information System (INIS) Holwerda, M.J. 1977-01-01 The author concentrates on the problem of electromagnetic mass differences. The possible connection with the experimental phenomenon of Bjorken-scaling in deep inelastic electron-nucleon scattering is investigated. He starts from the formalism, implied by the ansatz by H. Fritsch and M. Gell-Mann for a light cone algebra of (bilocal) current operators, that is abstracted from free field theory. Later on the problem is reconsidered with the help of field theoretic techniques in the framework of a color gauge theory model for the strong interactions; this theory exhibits the property of 'asymptotic freedom' and thus offers the famous explanation for (approximate) Bjorken scaling 13. A low-energy β-function in a finite super-Yang-Mills model with multiple mass scales International Nuclear Information System (INIS) Foda, O.; Helayel-Neto, J.A. 1984-08-01 We compute the one-loop contribution to the low-energy light-fermion gauge coupling in a finite supersymmetric gauge theory with two mass scales: a heavy mass that breaks an initial N=4 supersymmetry down to N=2, but respects the finiteness, and a light mass that, for simplicity, is set to zero. We find that the coupling grows with the mass of the heavy intermediate states. Hence the latter do not decouple at low energies, leading to large logarithms that invalidate low-energy perturbation theory. Consequently, further manipulations are required to obtain a meaningful perturbative expansion. Enforcing decoupling through finite renormalizations, that absorb the heavy mass effects into a redefinition of the parameters of the Lagrangian, introduces an arbitrary subtraction mass μ. The requirement that the S-matrix elements be independent of μ leads to a non-trivial renormalization-group equation for the low-energy theory, with a non-vanishing β-function. (author) 14. Breeding and mass-scale rearing of three spotted seahorse, Hippocampus trimaculatus Leach under captive conditions Digital Repository Service at National Institute of Oceanography (India) Murugan, A.; Dhanya, S.; Sreepada, R.A.; Rajagopal, S.; Balasubramanian, T. ornamental fish markets (Project Seahorse, 2006). 3 Compared to the proposition of mass culture of other seahorse species, H. trimaculatus, inhabiting different geographical regions, has not been thought of seriously from a commercial standpoint... 15. Comparison of direct and geodetic mass balances on a multi-annual time scale Directory of Open Access Journals (Sweden) A. Fischer 2011-02-01 Full Text Available The geodetic mass balances of six Austrian glaciers over 19 periods between 1953 and 2006 are compared to the direct mass balances over the same periods. For two glaciers, Hintereisferner and Kesselwandferner, case studies showing possible reasons for discrepancies between the geodetic and the direct mass balance are presented. The mean annual geodetic mass balance for all periods is −0.5 m w.e. a−1, the mean annual direct mass balance −0.4 m w.e. a−1. The mean cumulative difference is −0.6 m w.e., the minimum −7.3 m w.e., and the maximum 5.6 m w.e. The accuracy of geodetic mass balance may depend on the accuracy of the DEMs, which ranges from 2 m w.e. for photogrammetric data to 0.02 m w.e. for airborne laser scanning (LiDAR data. Basal melt, seasonal snow cover, and density changes of the surface layer also contribute up to 0.7 m w.e. to the difference between the two methods over the investigated period of 10 yr. On Hintereisferner, the fraction of area covered by snow or firn has been changing within 1953–2006. The accumulation area is not identical with the firn area, and both are not coincident with areas of volume gain. Longer periods between the acquisition of the DEMs do not necessarily result in a higher accuracy of the geodetic mass balance. Trends in the difference between the direct and the geodetic data vary from glacier to glacier and can differ systematically for specific glaciers under specific types of climate forcing. Ultimately, geodetic and direct mass balance data are complementary, and great care must be taken when attempting to combine them. 16. Rate of mass deposition of scaling compounds from seawater on the outer surface of heat exchangers in MED evaporators Energy Technology Data Exchange (ETDEWEB) Omar, W. [Department of Natural Resources and Chemical Engineering, Tafila Technical University, Tafila (Jordan); Ulrich, J. [FB Ingenieurwissenschaften, Institut fuer Verfahrenstechnik/TVT, Martin-Luther-Universitaet Halle-Wittenberg, Halle (Germany) 2006-08-15 The scaling problem in Multi Effect Distillation (MED) evaporators is investigated by the experimental measurement of the deposition rate under different operating conditions. The measurements are conducted in a batch vessel containing artificial seawater, which is allowed to contact the outer surface of a hot pipe under controlled temperature, salinity and pH. The rate of mass deposition is higher at elevated temperature. The salinity of the seawater also influences the scaling process - an increase in salinity from 47-59 g/L leads to an increase of 75.6 % in the deposition rate. Decreasing the pH value of seawater to 2.01 results in a complete inhibition of scaling, whereas the severity of the scaling increases in neutral and basic mediums. Polyacrylic acid is tested as an antifoulant and it was found that its presence in seawater reduces the scaling process. The nature of the heat transfer surface material also plays an important role in the scaling process. It is found experimentally that the rate of scaling is higher in the case of a Cu-Ni alloy as the surface material of the tube rather than stainless steel. (Abstract Copyright [2006], Wiley Periodicals, Inc.) 17. The di-photon excess in a perturbative SUSY model Energy Technology Data Exchange (ETDEWEB) Benakli, Karim, E-mail: [email protected] [Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005, Paris (France); CNRS, UMR 7589, LPTHE, F-75005, Paris (France); Darmé, Luc, E-mail: [email protected] [Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005, Paris (France); CNRS, UMR 7589, LPTHE, F-75005, Paris (France); Sorbonne Universités, Institut Lagrange de Paris (ILP), 98 bis Boulevard Arago, 75014 Paris (France); Goodsell, Mark D., E-mail: [email protected] [Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005, Paris (France); CNRS, UMR 7589, LPTHE, F-75005, Paris (France); Harz, Julia, E-mail: [email protected] [Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005, Paris (France); CNRS, UMR 7589, LPTHE, F-75005, Paris (France); Sorbonne Universités, Institut Lagrange de Paris (ILP), 98 bis Boulevard Arago, 75014 Paris (France) 2016-10-15 We show that a 750 GeV di-photon excess as reported by the ATLAS and CMS experiments can be reproduced by the Minimal Dirac Gaugino Supersymmetric Standard Model (MDGSSM) without the need of any ad-hoc addition of new states. The scalar resonance is identified with the spin-0 partner of the Dirac bino. We perform a thorough analysis of constraints coming from the mixing of the scalar with the Higgs boson, the stability of the vacuum and the requirement of perturbativity of the couplings up to very high energy scales. We exhibit examples of regions of the parameter space that respect all the constraints while reproducing the excess. We point out how trilinear couplings that are expected to arise in supersymmetry-breaking mediation scenarios, but were ignored in the previous literature on the subject, play an important role. 18. Shifts in mass-scaling of respiration, feeding, and growth rates across life-form transitions in marine pelagic organisms DEFF Research Database (Denmark) Kiørboe, Thomas; Hirst, Andrew G. 2014-01-01 The metabolic rate of organisms may be viewed as a basic property from which other vital rates and many ecological patterns emerge and that follows a universal allometric mass scaling law, or it may be considered a property of the organism that emerges as a result of the adaptation to the environ...... and be the result of the optimization of trade-offs that allow sufficient feeding and growth rates to balance mortality... 19. Anomalous leptonic U(1) symmetry: Syndetic origin of the QCD axion, weak-scale dark matter, and radiative neutrino mass Science.gov (United States) Ma, Ernest; Restrepo, Diego; Zapata, Óscar 2018-01-01 The well-known leptonic U(1) symmetry of the Standard Model (SM) of quarks and leptons is extended to include a number of new fermions and scalars. The resulting theory has an invisible QCD axion (thereby solving the strong CP problem), a candidate for weak-scale dark matter (DM), as well as radiative neutrino masses. A possible key connection is a color-triplet scalar, which may be produced and detected at the Large Hadron Collider. 20. Higgs mass in the gauge-Higgs unification International Nuclear Information System (INIS) Haba, Naoyuki; Takenaga, Kazunori; Yamashita, Toshifumi 2005-01-01 The gauge-Higgs unification theory identifies the zero mode of the extra-dimensional component of the gauge field as the usual Higgs doublet. Since this degree of freedom is the Wilson line phase, the Higgs does not have the mass term nor quartic coupling at the tree level. Through quantum corrections, the Higgs can take a vacuum expectation value, and its mass is induced. The radiatively induced mass tends to be small, although it can be lifted to O(100) GeV by introducing the O(10) numbers of bulk fields. Perturbation theory becomes unreliable when a large number of bulk fields are introduced. We reanalyze the Higgs mass based on useful expansion formulae for the effective potential and find that even a small number of bulk field can have the suitable heavy Higgs mass. We show that a small (large) number of bulk fields are enough (needed) when the SUSY breaking mass is large (small). We also study the case of introducing the soft SUSY breaking scalar masses in addition to the Scherk-Schwarz SUSY breaking and obtain the heavy Higgs mass due to the effect of the scalar mass	{"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": 0.9180156588554382, "perplexity": 3025.763640859863}, "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/1537267155676.21/warc/CC-MAIN-20180918185612-20180918205612-00032.warc.gz"}
http://usersguidetotheuniverse.com/index.php/2011/11/02/what-is-the-biggest-problem-in-physics/	# What is the biggest problem in physics? I like to be reasonably forthcoming both here and in my “Ask a Physicist” columns at io9 about what we do and don’t know about the world. As successful as physics (and in particular, the idea of symmetry) has been in unifying various phenomena, there are at least two classes of questions that we don’t seem to be particularly close to answering at all: 1. Why these symmetries and not others? It seems very strange that the laws of the universe are symmetric under CPT transformations (simultaneously flipping the arrow of time, looking at the universe in a mirror, and trading every particle for its antiparticle) or the continuous “U(1) symmetry,” while other symmetries, like “SU(5),” (which was thought to be a prime candidate for a Grand Unified Theory), turn out to be wrong, experimentally. All we can do is check with the universe and see whether certain symmetries hold, and if they don’t, check other symmetries instead. 2. What about all of the free parameters? Some of my colleagues are experimental neutrino physicists. They spend their efforts trying to figure out the masses and mixing angles between the various neutrino species — numbers that tell us, essentially how likely it is that one type of neutrino turns into another. But these angles and the masses, and the mixing angles in quarks and the strength of the various forces and so forth… all of these numbers have to be put into our theories more or less by hand. Even “obvious” numbers like the number of spatial dimensions in the universe or the fact that there are three generations of quarks and leptons ($e^-, mu^-,tau^-$, for instance) are put in in a completely ad hoc way. Many, perhaps all of these numbers may not ultimately have a deeper explanation. They may, in fact, vary significantly over the multiverse. This is the origin, as you may know, the so-called “weak anthropic principle.” It’s only in our region of space that the parameters and symmetries are just right to produce complicated life. But to my mind, these aren’t anywhere near the worst problems in physics. The biggest problem in physics comes from the vacuum all around us. I don’t want to make this an overly mathematical discussion, but I do want to give you a feel of why the vacuum poses such a big problem in physics. But first, let me give you a simple result that comes from the Uncertainty Principle of quantum mechanics. Suppose you had a little mass on a spring. This is a good model for lots of physical systems. The most obvious is molecules, which are in a continuous state of oscillation, but as we’ll see, if we take a lot of these, it turns out to be a great model for the universe as a whole. No matter how much you cool down your oscillator, it turns out that you can’t extract all of the energy. There’s a lowest possible energy, which is: $displaystyle E_0=frac{1}{2}hbar omega$ where $hbar$ is the reduced Planck constant (which basically says that we’re doing quantum mechanics) and $omega$ is the angular frequency of the oscillator. One way of thinking of this is that if it were possible to stop the oscillations exactly, you’d be able to know the exact position of the mass (the equilibrium position) and the exact momentum (zero) simultaneously. That is expressly forbidden by the Uncertainty Principle. Now here’s the big twist: There are fields surrounding us, even in empty space, and the way a physicist might imagine it, the field behaves a lot like a rubber sheet or a mattress: What you see here is a cartoon version of a field (like the electromagnetic field) in a two dimensional universe. The height of each of the points is something like the amplitude of the field. In this picture, we basically have two particles flying around, hence two peaks. (Notes to experts: a) I realize that this really only describes a spin-zero field, and even so, we could have troughs or imaginary numbers as well as positive amplitudes. b) Nobody likes a showoff.) But then quantum mechanics intervenes. I described our field as behaving exactly like little masses on springs. As a result of that, every single spring contributes some minimum amount of energy to the universe. Given that there are an infinite number of them, this is an infinite contribution — an infinite vacuum energy density. In practice, we expect that you wouldn’t get any oscillations smaller than the Planck Length, about $10^{-35} m$. This is the scale where quantum mechanics and gravity combine to make all of our knowledge of physics completely useless. Saying anything smaller than the Planck scale just makes us look silly. So the good news is that the vacuum energy isn’t infinite. The bad news comes in two parts: 1. Even if the vacuum energy density isn’t infinite, it still ends up being about $10^{96} kg/m^3$, or about 120 orders of magnitude denser than the universe itself. 2. Experimentally, there really is a non-zero vacuum density out there. I’m not going to get into the Casimir effect, but the basic idea is that you can use metal plates to measure a force from the vacuum directly. The diagram up top or the wikipedia link may be of some help, but in either case, it’s a discussion for another day. If the vacuum energy is so huge (and real), why don’t we see it gravitationally? Ah, but we do see a gravitational source in the universe that has the exact properties of the vacuum energy (including a bizarre “negative pressure.”) It’s called “Dark Energy” or “Cosmological Constant,” and as you may recall, it’s the mysterious substance that drives the acceleration of the universe. Unfortunately, the cosmological constant is about $10^{120}$ times smaller than reasonable estimates of the vacuum energy. This, in my opinion, is the worst problem in physics. Without getting into even further anthropic arguments, the question remains as to why we should have any cosmological constant at all? And yet, as the Nobel committee recently confirmed, we do seem to have just that. Curious universe. -Dave This entry was posted in Uncategorized and tagged , . Bookmark the permalink.	{"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": 7, "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": 0.8055911064147949, "perplexity": 323.2846302180654}, "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/1495463607593.1/warc/CC-MAIN-20170523083809-20170523103809-00464.warc.gz"}
http://math.stackexchange.com/questions/214634/prove-that-sum-k-1n-frac2k1a-1a-2-a-k4-sum-k-1n-frac1a-k	# Prove that $\sum_{k=1}^n \frac{2k+1}{a_1+a_2+…+a_k}<4\sum_{k=1}^n\frac1{a_k}.$ Prove that for $a_k>0,k=1,2,\dots,n$, $$\sum_{k=1}^n \frac{2k+1}{a_1+a_2+\ldots+a_k}<4\sum_{k=1}^n\frac1{a_k}\;.$$ - I must confess this problem took me a very long time! Step1. If $a_1,a_2,\alpha,\beta,\gamma$ are positive real numbers and $\gamma=\alpha+\beta$ holds, $$\frac{\gamma^2}{a_1+a_2}\leq \frac{\alpha^2}{a_1}+\frac{\beta^2}{a_2}$$ holds too, since it is equivalent to $(\alpha a_2-\beta a_1)^2\geq 0$. Step2. If $a_1,a_2,\alpha,\beta,\gamma,\delta$ are positive real numbers and $\delta=\alpha+\beta+\gamma$ holds, $$\frac{\delta^2}{a_1+(a_2+a_3)}\leq \frac{\alpha^2}{a_1}+\frac{(\beta+\gamma)^2}{a_2+a_3}\leq\frac{\alpha^2}{a_1}+\frac{\beta^2}{a_2}+\frac{\gamma^2}{a_3}$$ holds too, in virtue of Step2. By induction, it is easy to prove the analogous statement for $k$ variables $a_1,\ldots,a_k$. In fact, this is useless to the proof, but quite interesting in itself :) Step3. By Step1, $$\sum_{k=1}^{n}\frac{2k+1}{a_1+\ldots+a_k}-\frac{4}{a_n}\leq \sum_{k=1}^{n-1}\frac{2k+1}{a_1+\ldots+a_k}+\frac{(\sqrt{2n+1}-2)^2}{a_1+\ldots+a_{n-1}}\leq \sum_{k=1}^{n-2}\frac{2k+1}{a_1+\ldots+a_k}+\frac{n^2}{a_1+\ldots+a_{n-1}}$$ Step4. By Step3, $$\sum_{k=1}^{n}\frac{2k+1}{a_1+\ldots+a_k}-\left(\frac{4}{a_n}+\frac{4}{a_{n-1}}\right)\leq \sum_{k=1}^{n-2}\frac{2k+1}{a_1+\ldots+a_k}+\frac{(n-2)^2}{a_1+\ldots+a_{n-2}}\leq \sum_{k=1}^{n-3}\frac{2k+1}{a_1+\ldots+a_k}+\frac{(n-1)^2}{a_1+\ldots+a_{n-2}}.$$ Step5. By Step3, Step4, induction and Step1 again: $$\sum_{k=1}^{n}\frac{2k+1}{a_1+\ldots+a_k}\leq \frac{3}{a_1}+\frac{9}{a_2}+\sum_{j=3}^{n}\frac{4}{a_j}\leq \sum_{j=1}^{n}\frac{4}{a_j}.$$ - In fact, it is much easier to prove the stronger inequality: $$\sum_{k=1}^{n}\frac{2k+1}{a_1+\ldots+a_k}\leq -\frac{n^2}{a_1+\ldots+a_n}+\sum_{k=1}^{n}\frac{4}{a_k}.$$ – Jack D'Aurizio Oct 30 '12 at 9:17	{"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": 0.9717926979064941, "perplexity": 281.1069690610121}, "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-2014-23/segments/1405997865523.12/warc/CC-MAIN-20140722025745-00106-ip-10-33-131-23.ec2.internal.warc.gz"}
https://inlieuofabettertitle.wordpress.com/2012/06/02/721/	It is well known that it is impossible to trisect an arbitrary angle using only a compass and straightedge. However, as we will see in this post, it is possible to trisect an angle using origami. The technique shown here dates back to the 1970s and is due to Hisashi Abe. Assume, as in the figure below, that we begin with an acute angle $latex {\theta}&fg=000000$ formed by the bottom edge of the square of origami paper and a line (a fold, presumably), $latex {l_{1}}&fg=000000$, meeting at the lower left corner of the square. Create an arbitrary horizontal fold to form the line $latex {l_{2}}&fg=000000$, then fold the bottom edge up to $latex {l_{2}}&fg=000000$ to form the line $latex {l_{3}}&fg=000000$. Let $latex {B}&fg=000000$ be the lower left corner of the square and $latex {A}&fg=000000$ be the left endpoint of $latex {l_{2}}&fg=000000$. Fold the square so that $latex {A}&fg=000000$ and \$latex… View original post 413 more words	{"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": 0.9477601051330566, "perplexity": 115.7945397533691}, "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-2016-22/segments/1464049278244.51/warc/CC-MAIN-20160524002118-00071-ip-10-185-217-139.ec2.internal.warc.gz"}
http://cms.math.ca/10.4153/CJM-2011-087-3	Abstract view # Finitely Related Algebras in Congruence Distributive Varieties Have Near Unanimity Terms Published:2011-12-24 Printed: Feb 2013 • Libor Barto, Department of Mathematics and Statistics, McMaster University, Hamilton, ON Features coming soon: Citations (via CrossRef) Tools: Search Google Scholar: Format: LaTeX MathJax PDF ## Abstract We show that every finite, finitely related algebra in a congruence distributive variety has a near unanimity term operation. As a consequence we solve the near unanimity problem for relational structures: it is decidable whether a given finite set of relations on a finite set admits a compatible near unanimity operation. This consequence also implies that it is decidable whether a given finite constraint language defines a constraint satisfaction problem of bounded strict width. Keywords: congruence distributive variety, Jónsson operations, near unanimity operation, finitely related algebra, constraint satisfaction problem MSC Classifications: 08B05 - Equational logic, Mal'cev (Mal'tsev) conditions 08B10 - Congruence modularity, congruence distributivity	{"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": 0.9118609428405762, "perplexity": 3895.251305276101}, "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-2013-48/segments/1386164033438/warc/CC-MAIN-20131204133353-00051-ip-10-33-133-15.ec2.internal.warc.gz"}
http://mathoverflow.net/questions/28480/finite-tor-dimension?sort=newest	# finite tor dimension Hi. Can, every one, give me an example of finite surjective morphism of finite tor dimension (but not flat!) between reduced schemes or complex analytic spaces... Thank you. - Consider a smooth surface $Y$ with a point $p\in Y$. Let $X$ be obtained by gluing two copies of $Y$ at $p$, with the obvious morphism $X \to Y$. This is surjective and finite, and has finite Tor-dimension (because $Y$ is regular, hence every morphism to $Y$ has finite Tor dimension). However, it is not flat (for example, because $X$ is not Cohen-Macaulay).	{"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": 0.9993929862976074, "perplexity": 311.31606423024226}, "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/1454701152130.53/warc/CC-MAIN-20160205193912-00234-ip-10-236-182-209.ec2.internal.warc.gz"}
http://dimacs.rutgers.edu/Events/2008/abstracts/chen.html	DIMACS Theoretical Computer Science Seminar Title: Graph Homomorphisms with Complex Values: A Dichotomy Theorem Speaker: Xi Chen, Rutgers University Date: Wednesday, November 26, 2008 11:00-12:00pm Location: CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ Abstract: The graph homomorphism problem has been studied intensively. Given an m by m symmetric matrix A, the graph homomorphism function is defined as Z_A(G) = \sum_{f:V \rightarrow [m]} \prod_{(u,v) \in E} A_{f(u),f(v)}, where G = (V,E) is any undirected graph. The function Z_A(G) can encode many interesting graph properties, including counting vertex covers and k-colorings. We study the computational complexity of Z_A(G) for arbitrary complex valued matrices A. Building on work by Dyer and Greenhill, Bulatov and Grohe, and especially the recent beautiful work by Goldberg, Grohe, Jerrum and Thurley, we prove a complete dichotomy theorem for this problem. Joint work with Jin-Yi Cai and Pinyan Lu.	{"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": 0.9703375697135925, "perplexity": 3822.7476574227667}, "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-2017-13/segments/1490218189032.76/warc/CC-MAIN-20170322212949-00283-ip-10-233-31-227.ec2.internal.warc.gz"}
http://umj-old.imath.kiev.ua/article/?lang=en&article=4449	2019 Том 71 № 11 # On a property of the entire dirichlet series with decreasing coefficients Sheremeta M. M. Abstract The class $S_{Ψ}^{ *} (A)$ of the entire Dirichlet series $F(s) = \sum\nolimits_{n = 0}^\infty {a_n exp(s\lambda _n )}$ is studied, which is defined for a fixed sequence $A = (a_n ),\; 0 < a_n \downarrow 0,\sum\nolimits_{n = 0}^\infty {a_n< + \infty } ,$ by the conditions $0 ≤ λ_n ↗ +∞$ and $λ_n ≤ (1n^+(1/a_n ))$ imposed on the parameters $λ_n$, where $ψ$ is a positive continuous function on $(0, +∞)$ such that $ψ(x) ↑ +∞$ and $x/ψ(x) ↑ +∞$ as $x →+ ∞$. In this class, the necessary and sufficient conditions are given for the relation $ϕ(\ln M(σ, F)) ∼ ϕ(\ln μ(σ, F))$ to hold as $σ → +∞$, where $M(\sigma ,F) = sup\{ \|F(\sigma + it)\|:t \in \mathbb{R}\} ,\mu (\sigma ,F) = max\{ a_n exp(\sigma \lambda _n ):n \in \mathbb{Z}_ + \}$, and $ϕ$ is a positive continuous function increasing to $+∞$ on $(0, +∞)$, forwhich $\ln ϕ(x)$ is a concave function and $ϕ(\ln x)$ is a slowly increasing function. English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 6, pp 929-942. Citation Example: Sheremeta M. M. On a property of the entire dirichlet series with decreasing coefficients // Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 843–853. Full text	{"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": 0.9798334240913391, "perplexity": 169.36934399922703}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2020-40/segments/1600400203096.42/warc/CC-MAIN-20200922031902-20200922061902-00524.warc.gz"}
http://math.stackexchange.com/questions/284611/find-the-values-of-the-positive-constants-k-and-c-such-that-37-le-k3-sin	# Find the values of the positive constants $k$ and $c$ such that $-37\le k(3\sin\theta + 4\cos\theta) +c\le 43$ for all values of $\theta$ Hi how do i go about solving this? Find the values of the positive constants $k$ and $c$ such that $$-37\le k(3\sin\theta + 4\cos\theta) +c\le 43$$for all values of $\theta$ $$\rightarrow-37\le k(5(\sin\theta + 53.1)) +c\le 43$$ Then what? Cheers - Write $-37-c \le5k\sin(\phi)\le 43-c$. The range of the middle expression is $[-5k,5k]$. So if the inequality is "tight", you have $c=3$. Then solving for $k$ gives $k=8$. – David Mitra Jan 22 '13 at 23:55 Hint: $\|\sin \alpha\| \leq 1$. Hence, this implies that $c = \frac {43+(-37)} {2}$. - Hi cheers for the help! Where did the hint come from? Can you show me a step after? – maxmitch Jan 22 '13 at 23:37 The hint is just stating the behavior of the $\sin$ function. The next step will be $-5k \leq k 5 \sin(\theta + 53.1) \leq 5k$. – Calvin Lin Jan 23 '13 at 0:34 By Cauchy Schwartz $$(3\sin(x)+4\cos(x))^2 \leq 25 (\sin^2(x)+\cos^2(x))=25$$ and equality is possible. Then $$-5 \leq 3\sin(x)+4\cos(x) \leq 5$$ this shows that $$-5k+c \leq - k(3\sin\theta + 4\cos\theta) +c\le 5k+c \,.$$ and the lower/upper bounds can be atatined. You can finish it easely. -	{"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": 0.9642244577407837, "perplexity": 373.2645466312606}, "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/1414119649133.8/warc/CC-MAIN-20141024030049-00140-ip-10-16-133-185.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/74501-area-enclosed-print.html	# Area Enclosed Printable View • Feb 19th 2009, 10:57 AM qzno Area Enclosed Find the area of the enclosed region given by the functions: $y = \frac{1}{x^2+1}$ and $y = \frac{x^2}{2}$ I Got It Down To: $A = \int_{-1}^{\frac{1}{2}} \left( (\sqrt{\frac{1-y}{y}}) - (\sqrt{2y}) \right) dy$ I Just Dont Know How To Integrate This Equation Thanks • Feb 19th 2009, 11:17 AM running-gag Hi I am a little bit surprised by your answer http://nsa05.casimages.com/img/2009/...2055408371.jpg $A = \int_{-1}^{1} \left(\frac{1}{x^2+1} - \frac{x^2}{2}\right)\:dx$ • Feb 19th 2009, 11:22 AM qzno haha i was integrating in terms of y thank you : )	{"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": 4, "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": 0.9600619077682495, "perplexity": 2361.3685621934346}, "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-2018-09/segments/1518891816912.94/warc/CC-MAIN-20180225190023-20180225210023-00680.warc.gz"}
http://www.transtutors.com/questions/tts-limiting-distribution-178905.htm	# Limiting Distribution Suppose P(Xn = i) = n + i / (3n+6) , for i = 1,2,3 Find the limiting distribution of Xn Related Questions in Theory of probability • Finding the limiting distribution of given i.i.d. standardised variates. (Solved) August 03, 2016 Finding the limiting distribution of given i.i .d. standardised variates. • Limiting distribution (Solved) May 06, 2012 Let Zn BE X2( n ) (Chi-square) and let Wn = Zn/ n 2. Find the limiting distribution of Wn Solution Preview : When Zn ~ ? 2 (n), we want to obtain the limiting distribution of Wn = Zn/n2 . The mgf of Wn is- M(t; n) = E(e^tWn ) = E[e^(t/n^2)* Zn ] = [1 - 2 t/n^2 ]^-n/2 , for t To find the limit of... • In Exercise 1, find the limiting distribution of n ln X 1.n ,,.... August 19, 2016 In Exercise 1, find the limiting distribution of n ln X1. n ,,. Exercise 1 Consider a random sample of size n from a distribution with CDF F(x) =... • Limiting Distribution May 09, 2012 Let Xn have PDF fn(x) = (1 + x/n ) / (1 + 1/2 n ), for 0 Find the limiting distribution of Xn . • MGF and limiting distribution (Solved) May 06, 2012 Let Xn denote the mean of a random sample of size n from a distribution that has pdf f(x) = e^-x, 0 zero elsewhere a) Show that the mgf Myn(t) of Yn = vn( Xn -1)...	{"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": 0.9849799871444702, "perplexity": 3221.6092618477114}, "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-2017-13/segments/1490218189198.71/warc/CC-MAIN-20170322212949-00425-ip-10-233-31-227.ec2.internal.warc.gz"}
https://mathoverflow.net/questions/291828/if-a-is-normal-and-omega1-b-a-0-then-b-is-normal	# If $A$ is normal and $\Omega^1_{B/A}=0$ then $B$ is normal Let $A\subseteq B$ be two noetherian domains with fraction fields $k$ and $L$, respectively. Assume that $A$ is normal and $B$ is finite as $A$-module. I'm asking myself if $B$ is also normal if $\Omega^1_{B/A}=0$? Any suggestion or reference in the literature is welcome. EDIT: I'm trying to show the claim above, the idea is the following. IDEA: Let $\mathfrak{q}\subset B$ be a maximal ideal of $B$ and set $\mathfrak{p}=\mathfrak{q}\cap A$, where $\mathfrak{p}$ is maximal since $B$ is integral over $A$. Consider the map $k:=A/\mathfrak p\longrightarrow B/\mathfrak p B:=B'$ induced by the inclusion $A\subseteq B$. We get a finite $k$-algebra $B'$, with module of differentials $\Omega^1_{B'/k}\simeq B'\otimes_{B}\Omega^1_{B/A}=0$. Now, since $\Omega^1_{B'/k}=0$, then $B'\simeq K_1\times\cdots\times K_n$, where any $K_i$ is a finite (and separable) field extension of $k$, hence we get $$B'_{\mathfrak q}\simeq B_\mathfrak q/\mathfrak pB_\mathfrak q,$$ but the localization at a prime of a finite product of fields (which is $B'$) is a field, hence $\mathfrak p B_\mathfrak q$ is maximal, i.e. $\mathfrak p B_\mathfrak q=\mathfrak q B_\mathfrak q$. Now let $\mathfrak q'$ a prime strictly contained in $\mathfrak q$. We have $\mathfrak q'B_\mathfrak q\subset \mathfrak pB_\mathfrak q$, then $(\mathfrak q'B_\mathfrak q )\cap A=\mathfrak p'\subset \mathfrak p$. This shows (localizing at $\mathfrak q'$) that $\mathfrak q'B_{\mathfrak q'}= \mathfrak p'B_{\mathfrak q'}$, where $\mathfrak q'\cap A=\mathfrak p'$. We showed that for any prime $\mathfrak q\subset B$ there is a prime $\mathfrak p\subset A$ (with $\mathfrak q\cap A=\mathfrak p$), such that $$\mathfrak p B_\mathfrak q=\mathfrak q B_\mathfrak q \, \, \, (*).$$ By Serre's Normality Criterion (SNC) the ring $B$ is normal if and only if for every prime $\mathfrak q$ associated to a principal ideal the ring $B_\mathfrak q$ is a DVR, i.e. $\mathfrak q B_\mathfrak q$ is principal. If we are able to show (I don't know if it is true) that for every prime $\mathfrak q$ associated to a principal ideal we have $\mathrm{ht}(\mathfrak q)=1$, since $\mathrm{ht}(\mathfrak q)=\mathrm{ht}(\mathfrak q\cap A)$ ($B$ is integral over $A$) and $(\mathfrak pA_\mathfrak p)(B_\mathfrak q)=\mathfrak q B_\mathfrak q$, being $\mathfrak p A_\mathfrak p$ principal, we obtain that $\mathfrak qB_\mathfrak q$ is principal, hence by SNC the ring $B$ is normal. • SGA 1, Corollaire I.9.11: "Let $f \colon X \to Y$ be a dominant morphism [of schemes], $Y$ being normal and $X$ connected. If $f$ is unramified, then $f$ is étale, and therefore $X$ is normal." – Martin Bright Jan 31 '18 at 15:32 • This result is also proved as Lemma 1.5 in Chapter I of the book "Etale Cohomology and the Weil Conjectures" by Freitag & Kiehl in much more robust generality: you can relax "finite as $A$-module" to "finitely generated as $A$-algebra" (they state it for localization of such). It ultimately rests on the etale-local structure of unramified maps. – nfdc23 Jan 31 '18 at 15:46 • Just for completeness, here's a counterexample if $B/A$ is not flat; take $A=R[x,y]$ and $B=R[x,y]/(y^2-x^3)$, for $R$ any field. – Daniel Litt Jan 31 '18 at 16:31 • @DanielLitt The map $A\longrightarrow B$ is not injective. – Vincenzo Zaccaro Jan 31 '18 at 16:37 • The whole point of the result in SGA1 and the Freitag-Kiehl book is that flatness does not need to be assumed (only injectivity/dominance), and the conclusion gives that flatness is therefore a consequence of the assumptions. Please remove the "EDIT" about the flat case; there is nothing interesting being asserted if one allows to assume flatness. – nfdc23 Jan 31 '18 at 17:10	{"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": 0.9841035604476929, "perplexity": 185.56769431278823}, "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/1623488519735.70/warc/CC-MAIN-20210622190124-20210622220124-00190.warc.gz"}
https://engineering.stackexchange.com/questions/41099/what-do-the-rectangular-components-of-the-complex-frequency-s-in-laplace-trans	# What do the rectangular components of the complex frequency (s) in Laplace transform stand for? I tried doing a quick search on this question and was very surprised that this information feels very obscure as if it is almost never discussed. Complex frequencies appear in many mathematical concepts such as Laplace Transforms and sources mention the rectangular form as $$s = σ + jω$$, but fail to actually explain what the rectangular components stand for. I saw one source mention this. https://www.quora.com/What-does-the-real-part-of-s-in-laplace-transform-represents the real part(sigma) is called nepper frequency it control amplitude of function and its unit is nepper/second . and imaginary part(omega) is called oscillation (radian) frequency it control oscillation and its unit is radian/second. I just decided to ask here to know what those actually mean. Also, if some people might respond with the rectangular components being irrelevant or having little significant application I just really want to ask this for the sake of knowing. EDIT: I am asking what σ and ω in $$s = σ + jω$$ stand for and why those quantities represent the real and imaginary components of the complex frequency. The source which I cited said that σ is nepper frequency and ω is oscillation frequency. • s = jω , that's essentially it. There are some details of range of integration and convergence conditions for LT vs FT but in engineering practice just make that substitution. Thus, complex s corresponds to real ω (sinusoids), real s corresponds to complex ω (exponential growth/decay). Note that complex s (just like real ω) always comes in +/- pairs, as it is a consequence of a solution to 2nd order (or more) differential eqn. Units are 1/time, with a factor of 2pi. The angle in complex plane corresponds to phase. [Not totally sure if this all is what you're asking] Mar 21 at 14:09 • also note that "multiplication by j" is a 90 degree rotation in the complex plane. So IMO the "s" plane is just ω turned on its side ... so the question of "what is real s" is equivalent to "what is complex ω" Mar 21 at 14:17 • finally, the usage is often different. s plane tends to be used for representation of systems, i.e. poles/zeros, while ω tends to be used for signals going into and out of those systems ... but the way i see it, they're both complex quantity representing units of 1/time and a phase shift Mar 21 at 14:24 • With rectangular component do you mean the same as the real component of $s$? Mar 21 at 15:09 • Just to be clear, I am talking about what sigma (σ) and omega (ω) are in s = σ + jω. Mar 21 at 22:04	{"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": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8865505456924438, "perplexity": 879.4240351688194}, "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-2021-49/segments/1637964358153.33/warc/CC-MAIN-20211127073536-20211127103536-00134.warc.gz"}
https://www.physicsforums.com/threads/limit-of-a-sequence.190601/	# Limit of a Sequence 1. Oct 11, 2007 ### TWM Find the limit of the sequence whose terms are given by an = ( [1/(e^(4n)+n^2)] )^1/n I am not really sure how to approach this problem. thanks! 2. Oct 11, 2007 ### Amauta2K Try the binomial expansion of denominator and apply the limits to each term (don't forget that you always can use the L'Hopital rule for those limits). I guess the that the limit is 1/e^4. Similar Discussions: Limit of a Sequence	{"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": 0.9902435541152954, "perplexity": 949.4214884243544}, "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-2017-17/segments/1492917120349.46/warc/CC-MAIN-20170423031200-00371-ip-10-145-167-34.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/485822/why-is-compactness-so-important	# Why is compactness so important? I've read many times that 'compactness' is such an extremely important and useful concept, though it's still not very apparent why. The only theorems I've seen concerning it are the Heine-Borel theorem, and a proof continuous functions on R from closed subintervals of R are bounded. It seems like such a strange thing to define; why would the fact every open cover admits a finite refinement be so useful? Especially as stating "for every" open cover makes compactness a concept that must be very difficult thing to prove in general - what makes it worth the effort? If it helps answering, I am about to enter my third year of my undergraduate degree, and came to wonder this upon preliminary reading of introductory topology, where I first found the definition of compactness. - Finite subcover. A refinement is something different, used to define weaker related ideas. – dfeuer Sep 6 '13 at 15:32 Essentially, compactness is "almost as good as" finiteness. I can't think of a good example to make this more precise now, though. – Johannes Kloos Sep 6 '13 at 15:36 FireGarden, perhaps you are reading about paracompactness? – Asaf Karagila Sep 6 '13 at 16:39 M. R. Sundström's paper A pedagogical history of compactness may be useful here. It discusses the original motivations for the notion of compactness, and its historical development. If you want to understand the reasons for studying compactness, then looking at the reasons that it was invented, and the problems it was invented to solve, is one of the things you should do. – MJD Sep 6 '13 at 16:47 @dfeuer: The condition of having finite subcover and finite refinement are equivalent. – user87690 Sep 6 '13 at 17:33 As many have said, compactness is sort of a topological generalization of finiteness. And this is true in a deep sense, because topology deals with open sets, and this means that we often "care about how something behaves on an open set", and for compact spaces this means that there are only finitely many possible behaviors. But why finiteness is important? Well, finiteness allows us to construct things "by hand" and constructive results are a lot deeper, and to some extent useful to us. Moreover finite objects are well-behaved ones, so while compactness is not exactly finiteness, it does preserve a lot of this behavior (because it behaves "like a finite set" for important topological properties) and this means that we can actually work with compact spaces. The point we often miss is that given an arbitrary topological space on an infinite set $X$, the well-behaved structures which we can actually work with are the pathologies and the rare instances. This is throughout most of mathematics. It's far less likely that a function from $\Bbb R$ to $\Bbb R$ is continuous, differentiable, continuously differentiable, and so on and so forth. And yet, we work so much with these properties. Why? Because those are well-behaved properties, and we can control these constructions and prove interesting things about them. Compact spaces, being "pseudo-finite" in their nature are also well-behaved and we can prove interesting things about them. So they end up being useful for that reason. - +1. I particularly like the phrase "finitely many possible behaviors". In every other respect, one could have used "discrete" in place of "compact". Honestly, discrete spaces come closer to my intuition for finite spaces than do compact spaces. However, as you pointed out, compactness is deep; in contrast, discreteness is the ultimate separation axiom while most spaces we're interested in are comparatively low on the separation hierarchy. – Karl Kronenfeld Sep 6 '13 at 21:37 And when one learns about first order logic, gets the feeling that compactness is, somehow, deduce information about an "infinite" object by deducing it from its "finite" (or from a finite number of) parts. By the way, as always, very nice to read your answers. – leo Sep 11 '13 at 3:12 @leo: Thank you for the compliment. – Asaf Karagila Sep 11 '13 at 5:37 Compactness does for continuous functions what finiteness does for functions in general. If a set $A$ is finite then every function $f:A\to \mathbb R$ has a max and a min, and every function $f:A\to\mathbb R^n$ is bounded. If $A$ is compact, the every continuous function from $A$ to $\mathbb R$ has a max and a min and every continuous function from $A$ to $\mathbb R^n$ is bounded. If $A$ is finite then every sequence of members of $A$ has a subsequence that is eventually constant, and "eventually constant" is the only kind of convergence you can talk about without talking about a topology on the set. If $A$ is compact, then every sequence of members of $A$ has a convergent subsequence. - – sdcvvc Sep 6 '13 at 22:21 Compactness is the next best thing to finiteness. Let $A$ be a finite set, let $f: A \to \mathbb{R}$ be a function. Then $f$ is trivially bounded. Now let $X$ be a compact set, set $f: X \to \mathbb{R}$ be a continuous function. Then $f$ is also bounded... - Compactness is important because: 1)It behaves greatly when using topological operations a)It's a condition that is carried on by continuous functions on any topological space, that is, if $C$ is compact and $f:C \rightarrow Y$ where $Y$ is a topological space, then $f(C)$ is compact in Y. b)An arbitrary product of compact sets is compact in the product topology. 2) Compact sets behave almost as finite sets, which are way easier to understand and work with than uncountable pathologies which are common in topology. Compactness is useful even when it emerges as a property of subspaces: 3) Most of topological groups we face in math every day are locally compact, e.g $\mathbb{R}$, $\mathbb{C}$, even $\mathbb{Q_P}$ and $\mathbb{R_P}$ the p-adic numbers. 4) It is often easier to solve a differential equation in a compact domain than in a non-compact. 5) There are many types of convergence of functions, one of which is convergence in compact set. 6) Regular borel measure, one of the most important class of measures is defined by limits of measures in compact sets. This list is far from over... Anyone care to join in? - Historically, it led to the compactness theorem for first-order logic, but that's over my head. – dfeuer Sep 6 '13 at 15:44 One reason is that boundedness doesn't make sense in a general topological space. For example $(-1, 1) \subset \mathbb{R}$ is bounded when viewing $\mathbb{R}$ as a metric space with the usual Euclidean metric, but as topological spaces, $(-1, 1)$ and $\mathbb{R}$ really are the same, that is, homeomorphic. So why then compactness? Well, I suppose part of the motivation is the Heine-Borel Theorem, which says a subset of $\mathbb{R}^n$ is compact if and only if it is closed and bounded; or said another way, a closed set is compact if and only if it is bounded. So, at least for closed sets, compactness and boundedness are the same. This relationship is a useful one because we now have a notion which is strongly related to boundedness which does generalise to topological spaces, unlike boundedness itself. In addition, at least for Hausdorff topological spaces, compact sets are closed. So one way to think about compact sets in topological spaces is that they are analogous to the bounded sets in metric spaces. The analogy here is not exact because the Heine-Borel Theorem only applies to $\mathbb{R}^n$, not every metric space, but hopefully this gives you some intuition. - It's already been said that compact spaces act like finite sets. A variation on that theme is to contrast compact spaces with discrete spaces. A compact space looks finite on large scales. A discrete space looks finite on small scales. A $T_1$ space is finite if and only if it is both compact and discrete. So we have the slogan "compactness = finiteness modulo discreteness". A locally compact abelian group is compact if and only if its Pontyagin dual is discrete. So we have another slogan, "compactness = Fourier transform of discreteness". - Is there a redefinition of discrete so this principle works for all topological spaces (e.g., discrete modulo indistinguishability)? Or of compactness. – zyx Sep 6 '13 at 19:08 @zyx I guess we could loosen the discreteness condition (every point has a singleton neighborhood) by requiring instead that every point has a finite neighborhood. Not sure what this property P should be called... Anyway, a topological space is finite iff it is both compact and P. – Chris Culter Sep 6 '13 at 22:20 I would like to give here a example showing why compactness is important. Consider the following Theorem: Theorem: Let $f:\mathbb{R}\to \mathbb{R}$ be a continuous coercive function. Then, there exist $x_0\in \mathbb{R}$ such that $$\tag{1} f(x_0)=\inf_{x\in\mathbb{R}}f(x)$$ Proof: Let $I=\inf_{x\in\mathbb{R}}f(x)$ and choose $x_n\in \mathbb{R}$ with $f(x_n)\to I$. We claim that $x_n$ is bounded. Indeed, if $x_n$ was not bounded, then we could extract a subsequence of $x_n$ not relabeld such that $f(x_n)\to \infty$ (by coercivity) which is an absurd. Now, $x_n$ being bounded implies without loss of generality that (compactness) $x_n\to x$. Because $f$ is continuous, we conclude that $f(x_n)\to f(x)=I$. The main argument of the proof was the fact that the closure of any bounded set in $\mathbb{R}$ is compact. Now consider the problem ($\Omega\subset\mathbb{R}^N$ bounded domain) $$\tag{P} \left\{ \begin{array}{ccc} -\Delta u =f&\mbox{ in \Omega} \\ u\in H_0^1(\Omega) &\mbox{ } \end{array} \right.$$ We say that $u\in H_0^1(\Omega)$ is a solution of (P) if $$\int_\Omega\nabla u\nabla v=\int_\Omega fv,\ \forall\ v\in H_0^1(\Omega)\tag{3}$$ Let $F:H_0^1(\Omega)\to \mathbb{R}$ be defined by $$F(u)=\frac{1}{2}\int_\Omega \|\nabla u\|^2-\int_\Omega fu$$ $(3)$ is equivalently to $\langle F'(u),v\rangle =0$ for all $v\in H_0^1(\Omega)$ and this equality is equivalently to find a local minimum of $F$ in $H_0^1(\Omega)$. One can check that $F$ is continuous and coercive, so we could try to use the same argument as above to find a minimum to $F$, but the problem here is lack of compactness, i.e. if $K\subset H_0^1(\Omega)$ is bounded we can't conclude that the closure of $K$ is compact. Therefore to see how important compactness is, the above problem can be solved by considering a new topology in $H_0^1(\Omega)$, to wit, the weak topology. In this topology we have less open sets which implies more compact sets and in particular, bounded sets are pre-compact sets. It can be show that $F$ is weakly sequentially lower semi continuous, i.e. $F$ is lower sequentially continuous in the weak topoogy, which together with coercivity implis the existence of a minimum. To conclude,take a look on these examples (they show how worse can be lack of compactnes): here and here. - The concept of a "coercive" function was unfamiliar to me until I read your answer; I suspect the same will be true for many readers. If by "coercive" you mean that $\lim_{x \rightarrow \pm \infty} = \infty$, then the fact that a continuous coercive function must attain its minimum value is an exercise that I assign to my honors calculus students: it requires only the extreme value theorem (which of course can be thought of in terms of compactness but need not be, and probably most of us learn it without compactness first). So I'm not sure this is a good example... – Pete L. Clark Sep 18 '13 at 18:39 (The rest of your example is very interesting and strong...if not necessarily accessible to the broadest possible audience who could be interested in the question.) – Pete L. Clark Sep 18 '13 at 18:42 Thank you for your comment @PeteL.Clark. Let me ask you one thing: in my point of view the extreme value theorem (EVT) relies strongly on the fact that the domain is compact, hence this would implie that compactness is important in proving the statement, howerver, even if we do not use this argument, I think that a proof using (EVT) would use compactness. For example, a proof which comes from my head is: write $(-\infty,\infty)=\cup_{i=1}^\infty [-i,i]$. Take the infimum of $f$ in each $[-i,i]$ (which exist because of EVT) and show that this sequence WLOG converge (using compactness) – Tomás Sep 18 '13 at 19:03 Please, could you detail more your point of view to me? – Tomás Sep 18 '13 at 19:03 To prove your theorem without it: since $\lim_{x \rightarrow \pm \infty} f(x) = \infty$, there is some $M > 0$ such that $f(x) > f(0)$ for all $x$ with $\|x\| > M$. Thus the minimum value of $f$ on $[-M,M]$ is its minimum value on all of $\mathbb{R}$. – Pete L. Clark Sep 18 '13 at 19:37 Well, here are some facts that give equivalent definitions: 1. Every net on a compact set has a convergent subnet. 2. Every ultrafilter on a compact set converges. 3. Every filter on a compact set has a limit point. 4. Every net in a compact set has a limit point. 5. Every universal net in a compact set converges. Here are some more useful things: 1. Every continuous bijection from a compact space to a Hausdorff space is a homeomorphism. 2. Every compact Hausdorff space is normal. 3. The image of a compact space under a continuous function is compact. 4. Every infinite subset of a compact space has a limit point. - Simply put, compactness gives you something to work with, this "something" depending on the particular context. But for example, it gives you extremums when working with continuous functions on compact sets. It gives you convergent subsequences when working with arbitrary sequences that aren't known to converge; the Arzela-Ascoli theorem is an important instance of this for the space of continuous functions (this point of view is the basis for various "compactness" methods in the theory of non-linear PDE). It gives you the representation of regular Borel measures as continuous linear functionals (Riesz Representation theorem). Etc. - If you have some object, then compactness allows you to extend results that you know are true for all finite sub-objects to the object itself. The main result used to prove this kind of thing is the fact that if $X$ is a compact space, and $(K_\alpha)_{\alpha\in A}$ is a family of closed sets with the finite intersection property (no finite collection has empty intersection) then $(K_\alpha)$ has non-empty intersection. For if $(K_\alpha)$ has empty intersection then the complements of the $K_\alpha$ form an open cover of $X$, which then has to have a finite subcover $(X\setminus K_{\alpha(i)})_{i=1}^n$, and so the $(K_{\alpha(i)})_{i=1}^n$ is a finite collection of the $K_\alpha$ with empty intersection. For example, the De Bruijn-Erdős Theorem in graph theory states that an infinite graph $G$ is $n$-colourable if all its finite subgraphs are $n$-colourable (i.e., you can colour the vertices with $n$ colours in such a way that no two vertices connected by an edge are the same colour). You can prove this by noting that the space $X$ of all colourings of the vertices of $G$ with $n$ colours (for which vertices of the same colour may share an edge) is a compact topological space (since it is the product of discrete spaces). Then, for each finite subgraph $F$, let $X_F$ be the set of all colourings of $G$ that give an $n$-colouring of $F$. It can be checked that the $X_F$ are closed and have the finite intersection property, so they have non-empty intersection, and any member of their intersection must $n$-colour the whole of $G$. In general, if you have some property that you know is true for finite sub-objects, then you can often encode that in a collection of closed sets in a topological space $X$ that have the finite intersection property. Then, if $X$ is compact, you can show that the closed sets have non-empty intersection, which normally tells you that the result is true for the object itself (sorry that this is all so imprecise!) A very closely-related example is the compactness theorem in propositional logic: an infinite collection of sentences is consistent if every finite sub-collection is consistent. This can be proved using topological compactness, or it can be proved using the completeness theorem: if the collection is inconsistent, then it must be possible to derive a contradiction using finitely many finite statements, so some finite collection of sentences must be inconsistent. Either way you look at it, though, the compactness theorem is a statement about the topological compactness of a particular space (products of compact Stone spaces). - I want to elaborate Sargera's and Tomás' theme. Topological considerations are great, but to me the examples are not as concrete as for when we speak of "sequential compactness" (which unfortunately in general topologies does not equate to compactness, but includes for example weak/weak* compactness). In this situation, for practical purposes, all I want to know about topologically for a given setting is, given a sequence of points in my space, define a notion of convergence. Give me the definition of convergence to play with, and we can talk about sequential compactness. For sequential compactness of a set, we ask: "Given an arbitrary sequence in the set, does there exist a convergent subsequence?" In general, the usefulness of this is that often we want to find a function with some property $P$, but we can only find functions with property $P_n$, which is close to $P$ as $n$ gets larger, and taking a limit as $n \to \infty$ would get property $P$. (In Tomás' example, $P_n$: "functions that achieve objective value within $1/n$ of the infimum", and $P$: "function that achieves infimum"). However, the functions satisfying property $P_n$ may not converge as we take $n$ to $\infty$, so we would not be able to take a limit of the function sequence. If the set of functions is sequentially compact (with respect to whatever notion of convergence we are working with), we can take a subsequence that converges and obtain the desired function satisfying property $P$! (Replace function in previous part by point in set, and we can talk about other things like measures, $\mathbb{R}^N$, etc... it's just so often I am applying this to functions or measures. In probability they use the term "tightness" for measures) Hmm.. one caveat for the above: for the notion of convergence being used, one would have to prove that the convergence preserves the property, or the property is continuous with respect to the notion of convergence. So in Tomás' example again, weak convergence is still good enough to obtain the minimizer. I think it's a great example because it motivates the study of weaker notions of convergence. Note that we need weak convergence in that example (the PDE example with $H^1$) because it is infinite dimensional, and it is not true that the feasible set of the optimization problem is compact under the usual norm-convergence. - Every continuous function is Riemann integrable-uses Heine-Borel theorem. Since there are a lot of theorems in real and complex analysis that uses Heine-Borel theorem, so the idea of compactness is too important. - Perhaps you could improve this Answer by adding further specific examples of "theorems in real and complex analysis that [use] Heine-Borel theorem", or by explaining how proving continuous $\implies$ Riemann integrable makes use of it. – hardmath Mar 16 '14 at 14:45	{"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": 0.9168884754180908, "perplexity": 224.13163763450413}, "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-2015-40/segments/1443737898933.47/warc/CC-MAIN-20151001221818-00038-ip-10-137-6-227.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/216021/prove-that-a-and-b-are-invertible-and-b-a-1	# Prove that $A$ and $B$ are invertible and $B=A^{-1}$ Suppose $A$ and $B$ are $n \times n$ matrices. Assume $AB=I$. Prove that $A$ and $B$ are invertible and that $B=A^{-1}$. Please let me know whether my proof is correct and if there are any improvements to be made. Assume $AB=I$. Then $(AB)A=IA=A$. So, $A(BA)=AI=A$. Then $BA=I$. Therefore $AB=BA=I$. Thus $A$ and $B$ are invertible. And by definition $B=A^{-1}$, so $AB=AA^{-1}=I$. - (1) How did you get "Then $BA=I$"? (2) Do you know the rank-nullity theorem? – wj32 Oct 18 '12 at 2:17 Your proof is correct if you assume that $CD = C$ implies that $D = I$. – Thomas Oct 18 '12 at 2:18 Unfortunately, the argument is invalid: $A(BA)=A$ does not imply that $BA=I$ unless you already know that $A$ is invertible, and of course you don’t, since that’s (part of) what you’re trying to prove. There are lots of ways to prove this result, but which ones you can use depends on what you know at this point. What do you know about invertible matrices? Do you know any theorems of the form ‘$A$ is invertible if and only if something’? – Brian M. Scott Oct 18 '12 at 2:19 @Thomas: But tkrm can’t legitimately assume that. – Brian M. Scott Oct 18 '12 at 2:19 Hint: If $AB = I$ then $A$ represents an injective linear transformation on a finite dimensional vector space, hence surjective, hence bijective. – Jason Polak Oct 18 '12 at 2:23 Proof #1: (along the lines mentioned in the comments) As $AB=I$, you know that $A$ is onto as a linear transformation, because $x=Ix=ABx=A(Bx)$ for any $x\in\mathbb{R}^n$. This implies that $A$ is bijective, being a surjective linear transformation in a finite-dimensional space. So there exists $A^{-1}$. Now $$A^{-1}=A^{-1}I=A^{-1}AB=B.$$ Proof #2 (using determinants) Since $AB=I$, we have $$1=\det I=\det AB=\det A\,\det B.$$ So $\det A\ne0$ and $A$ is invertible, and again we can do $$B=IB=A^{-1}AB=A^{-1}I=A^{-1}.$$ - A good first step would be to look at some of the answers to this question. The accepted one, by Davidac897, is pretty elementary and is probably the place to start. You’re almost certainly not yet ready for Martin Brandenberg’s answer, and I’d also skip Bill Dubuque’s answers for now: they’re also aimed at someone with more background. The proof given by falagar, on the other hand, is well worth a look, and you should certainly look at Blue’s answer, which is deliberately very elementary. - Suppose $AB = I$. ($A$ and $B$ are $n \times n$ matrices.) First note that $R(A) = \mathbb{R}^n$. (If $y \in \mathbb{R}^n$, then $y = Ax$, where $x = By$.) It follows that $N(A) = \{0\}$. We wish to show that $BAx = x$ for all $x \in \mathbb{R}^n$. So let $x \in \mathbb{R}^n$, and let $z = BAx$. Then $Az = A(BAx) = (AB)Ax = Ax$, which implies that $z = x$ because $N(A) = \{ 0 \}$. So $BAx = x$. -	{"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": 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": 0.9830973744392395, "perplexity": 177.7726024377745}, "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-2015-35/segments/1440646313806.98/warc/CC-MAIN-20150827033153-00349-ip-10-171-96-226.ec2.internal.warc.gz"}
https://sgmathsacad.com/resources/9758-2019-p1-q03/	9758/2019/P1/Q03 A function is defined as $f(x)=2 x^{3}-6 x^{2}+6 x-12$. (i) Show that $\mathrm{f}(x)$ can be written in the form $p\{(x+q)^{3}+r\}$, where $p, q$ and $r$ are constants to be found. (ii) Hence, or otherwise, describe a sequence of transformations that transform the graph of $y=x^{3}$ onto the graph of $y=f(x)$.	{"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": 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": 0.9947715401649475, "perplexity": 76.16555362354778}, "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/1679296948756.99/warc/CC-MAIN-20230328011555-20230328041555-00434.warc.gz"}
http://tex.stackexchange.com/questions/2397/lists-in-tabular-environment?answertab=active	# Lists in Tabular Environment So I'm writing up a CV and I would like to use the nifty itemize environment to list some things within a tabular environment. Unfortunately, things end up looking a bit this, which isn't at all what I want. Specifically, I want to the itemize environment to hug closely to "BIG COMPANY NAME" so that it appears as "Software Development Intern" does, and likewise at the bottom. My current code looks a bit like so: \textsc{May 2010 to Aug 2010} & Software Development Intern \\ & \textsc{BIG COMPANY NAME} \\ & \begin{itemize} \setlength{\itemsep}{0pt} \setlength{\parskip}{0pt} \setlength{\parsep}{0pt} \setlength{\partopsep}{0pt} \setlength{\topsep}{0pt} \item item1 \item item2 \end{itemize} \\ & \small{Cool Details}\\ Buuut it's not doing the job at all. Any suggestions, Latex gurus? - I was also looking how to get rid mostly of the extra space before and after (!) a list of \begin{list} ... \end{list} in a tabular environment. I now found a somewhat very easy way to solve the latter problem: \begin{tabular} \multicolumn{2}{l} & \vspace{-0.3cm}\begin{list}{-} % \vspace to align the '-' with the title line {\setlength{\topsep}{1pt}\setlength{\partopsep}{0pt}\setlength{\itemsep}{1pt}\setlength{\parsep}{0pt}\leftmargin=10pt} % I wanted small extra-spaces inbetween the items (\itemsep) and just on top (\topsep)for better readibility \item item1 \item item2 \end{list} \\[-0.4cm] % This is what really helps me to have a coherent table without extra-spacings! & \small{Cool Details}\\ \end{tabular} So, [-0.xcm] (adjust x to what suits you best) squeezes the extra-space after the list generated by the list environment. I hope this also helps other people. - Welcome to TeX.SX. If you highlight text and click the button marked {} it will be marked as code, as you see from my edit. – Torbjørn T. Dec 17 '13 at 21:34 Including an itemized list within a tabular column using the paralist package is a good solution to the vertical space issue at the top. However, the space at the bottom is not solved by this, which, I guess, is why the @Ulricke Fischer uses the parbox also. Note the paralist doesn't solve the problem, in that the space is added to the top and bottom when in a tabular environment. So this is the solution I eventually went with. \usepackage{array} \makeatletter \newcolumntype{P}[1]{>{\@minipagetrue}p{#1}} \makeatother Gets rid of the initial vertical space (of course you have to change the tabular argument from p to P. Then include a negative vspace after the final item: \begin{tabular}{r\|P{13cm} & \begin{compactitem} \item blah \item final item\vspace*{-\baselineskip} \end{compactitem} It's a bit manual, but it does at least work relatively easily. - You can use the package paralist which defines among others the compactitem environment (which is a compact itemize). It also redefines itemize that way, but there are options to leave it, like olditem. \usepackage[olditem,oldenum]{paralist} and use \begin{compactitem} ... \end{compactitem} inside tables. - You can use \novspace to get rid of the space at the top, nolistsep from enumitem for the spaces in the list, the internal \parbox for the space at the bottom and the \strut to give the \parbox the correct depth. \documentclass[]{book} \usepackage{enumitem} \makeatletter \newcommand\novspace{\@minipagetrue} \makeatother \begin{document} \begin{tabular}{lp{5cm}} \textsc{May 2010 to Aug 2010} & Software Development Intern \\ & \textsc{BIG COMPANY NAME} \\ &\parbox[t]{5cm}{\novspace \begin{itemize}[nolistsep] \item item1 \item item2\strut \end{itemize}}\\ & \small Cool Details \end{tabular} \end{document} - I have several suggestions. I would suggest using one of the numerous cv/resumé packages. My own cv uses currvita. The next suggestion would be to use the enumitem package for changing the spacing of your lists. Finally, you don't have a table of data so tabular is probably the wrong thing to use. - What would you recommend in its place? I suppose what I'm really looking for is a list of items with a left and right side -- perhaps a list of 2-column 1-row tables? – duckworthd Aug 27 '10 at 11:34 I would recommend the currvita package. Or you can take a look at this question which is about writing a CV in LaTeX. – TH. 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http://mathhelpforum.com/algebra/93410-demonstration-deduction.html	# Math Help - Demonstration and deduction 1. ## Demonstration and deduction a,b,c is the reals numbers , Prove this equality : Deduct all resolutions of this equation in R : 2. Originally Posted by dhiab a,b,c is the reals numbers , Prove this equality : This is wrong. If you take a=b=c you get 3a^3 on the left side and 0 on the right side. I think the correct equality is $a^3 + b^3 + c^3 - 3abc = \frac12 \: (a+b+c) \: \left[(b-c)^2+(c-a)^2+(a-b)^2\right]$ 3. [QUOTE=dhiab;332083]a,b,c is the reals numbers , Prove this equality : Looks to me like the best thing to do is just go ahead and multiply out the right side: $(b-c)^2= b^2- 2bc+ c^2$ $(c-a)^2= c^2- 2ac+ a^2$ $(a-b)^2= a^2- 2ab+ b^2$ so $(b-c)^2+ (c-a)^2+ (a-b)^2= 2a^2+ 2b^2+ 2c^2- 2(ab+ac+ bc)$ Now multiply that by a+ b+ c: $a(2a^2+ 2b^2+ 2c^2- 2(ab+ac+ bc))= 2a^3+ 2ab^2+ 2ac^2- 2(a^2b+ a^2c+ abc)$ $b(2a^2+ 2b^2+ 2c^2- 2(ab+ac+ bc))= 2a^2b+ 2b^3+ 2bc^2- 2(ab^2+ abc+ 2bc^2)$ [tex]c(2a^2+ 2b^2+ 2c^2- 2(ab+ac+ bc))= 2a^2c+ 2b^2c+ 2c^3- 2(abc+ ac^2+ bc^2) Now note that the " $2ab^2$" term in the first equation is canceled by the " $-2ab^2$" term in the second equation, etc. Deduct all resolutions of this equation in R : 4. Originally Posted by running-gag This is wrong. If you take a=b=c you get 3a^3 on the left side and 0 on the right side. I think the correct equality is $a^3 + b^3 + c^3 - 3abc = \frac12 \: (a+b+c) \: \left[(b-c)^2+(c-a)^2+(a-b)^2\right]$ HELLO : equality is correct : LOOCK THIS RESOLUTION Deduct : Conclusion : 5. Originally Posted by dhiab HELLO : equality is correct : LOOCK THIS RESOLUTION Deduct : Conclusion : What have become the 3 factors equal to -2abc ?	{"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": 0.973659098148346, "perplexity": 2371.355467094903}, "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-2014-35/segments/1408500833525.81/warc/CC-MAIN-20140820021353-00348-ip-10-180-136-8.ec2.internal.warc.gz"}
https://suncat.stanford.edu/publications/bayesian-framework-adsorption-energy-prediction-bimetallic-alloy-catalysts	A Bayesian framework for adsorption energy prediction on bimetallic alloy catalysts Authors: Osman Mamun, Kirsten T. Winther, Jacob R. Boes, Thomas Bligaard Year of publication: 2020 Journal: npj Computational Materials For high-throughput screening of materials for heterogeneous catalysis, scaling relations provides an efficient scheme to estimate the chemisorption energies of hydrogenated species. However, conditioning on a single descriptor ignores the model uncertainty and leads to suboptimal prediction of the chemisorption energy. In this article, we extend the single descriptor linear scaling relation to a multi-descriptor linear regression models to leverage the correlation between adsorption energy of any two pair of adsorbates. With a large dataset, we use Bayesian Information Criteria (BIC) as the model evidence to select the best linear regression model. Furthermore, Gaussian Process Regression (GPR) based on the meaningful convolution of physical properties of the metal-adsorbate complex can be used to predict the baseline residual of the selected model. This integrated Bayesian model selection and Gaussian process regression, dubbed as residual learning, can achieve performance comparable to standard DFT error (0.1 eV) for most adsorbate system. For sparse and small datasets, we propose an ad hoc Bayesian Model Averaging (BMA) approach to make a robust prediction. With this Bayesian framework, we significantly reduce the model uncertainty and improve the prediction accuracy. The possibilities of the framework for high-throughput catalytic materials exploration in a realistic setting is illustrated using large and small sets of both dense and sparse simulated dataset generated from a public database of bimetallic alloys available in Catalysis-Hub.org. Funding sources:	{"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": 0.8427896499633789, "perplexity": 1577.6897985418443}, "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-2021-49/segments/1637964362619.23/warc/CC-MAIN-20211203091120-20211203121120-00630.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/algebra-2-common-core/skills-handbook-operations-with-exponents-exercises-page-978/11	Algebra 2 Common Core $$c^{6}$$ To divide powers of the same base, subtract the exponents: $$\frac{c^{7}}{c}=c^{7-1}=c^{6}.$$	{"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": 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": 0.8177480101585388, "perplexity": 3401.1134244157456}, "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-2018-26/segments/1529267860684.14/warc/CC-MAIN-20180618164208-20180618184208-00181.warc.gz"}
http://farside.ph.utexas.edu/teaching/336k/lectures/node115.html	Next: Perihelion Precession of Mercury Up: Gravitational Potential Theory Previous: Potential Due to a # Perihelion Precession of the Planets The Solar System consists of eight major planets (Mercury to Neptune) moving around the Sun in slightly elliptical orbits which are approximately co-planar with one another. According to Chapter 5, if we neglect the relatively weak interplanetary gravitational interactions then the perihelia of the various planets (i.e., the points on their orbits at which they are closest to the Sun) remain fixed in space. However, once these interactions are taken into account, it turns out that the planetary perihelia all slowly precess around the Sun. We can calculate the approximate rate of perihelion precession of a given planet by treating the other planets as uniform concentric rings, centered on the Sun, of mass equal to the planetary mass, and radius equal to the mean orbital radius. This is equivalent to averaging the interplanetary gravitational interactions over the orbits of the other planets. It is reasonable to do this, since the precession period in question is very much longer than the orbital period of any planet in the Solar System. Thus, by treating the other planets as rings, we can calculate the mean gravitational perturbation due to these planets, and, thereby, determine the desired precession rate. We can conveniently index the planets in the Solar System such that Mercury is planet 1, and Neptune planet 8. Let the and the , for , be the planetary masses and orbital radii, respectively. Furthermore, let be the mass of the Sun. It follows, from the previous section, that the gravitational potential generated at the th planet by the Sun and the other planets is (1018) Now, the radial force per unit mass acting on the th planet is written , giving (1019) Hence, we obtain (1020) where . It follows that (1021) Thus, according to Equation (317), the apsidal angle for the th planet is (1022) Hence, the perihelion of the th planet advances by (1023) radians per revolution around the Sun. Now, the time for one revolution is , where . Thus, the rate of perihelion precession, in arc seconds per year, is given by (1024) Table 1: Data for the major planets in the Solar System, giving the planetary mass relative to that of the Sun, the orbital period in years, and the mean orbital radius relative to that of the Earth. Planet R( au) Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Table 2: The observed perihelion precession rates of the planets compared with the theoretical precession rates calculated from Equation (1024) and Table 1. The precession rates are in arc seconds per year. Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Table 2 and Figure 46 compare the observed perihelion precession rates with the theoretical rates calculated from Equation (1024) and the planetary data given in Table 1. It can be seen that there is excellent agreement between the two, except for the planet Venus. The main reason for this is that Venus has an unusually low eccentricity (), which renders its perihelion point extremely sensitive to small perturbations. Next: Perihelion Precession of Mercury Up: Gravitational Potential Theory Previous: Potential Due to a Richard Fitzpatrick 2011-03-31	{"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": 0.9795991778373718, "perplexity": 771.6521776521253}, "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-2015-40/segments/1443736676622.16/warc/CC-MAIN-20151001215756-00064-ip-10-137-6-227.ec2.internal.warc.gz"}
http://mathhelpforum.com/number-theory/198676-multiplicative-inverse-print.html	# Multiplicative Inverse • May 11th 2012, 09:34 AM alyosha2 Multiplicative Inverse This is in regard to proving that the statements (a) $a$ and $n$ are coprime and (c) row $a$ of the multiplication table for $Z_{n}$ includes all of $Z_{n}$ $ab = kn + 1$ "this equation implies that $a$ and $n$ are coprime because any common factor of $a$ and $n$ must also be a factor of 1 I don't see why this is so. • May 11th 2012, 09:44 AM Sylvia104 Re: Multiplicative inverse Let $d$ be a common factor of $a$ and $n,$ so $a=a_0d,$ $n=n_0d$ for some integers $a_0,n_0.$ Then $\begin{array}{rcl} ab &=& kn+1 \\ a_0db &=& kn_0d+1 \\ \left(a_0b-kn_0\right)d &=& 1 \end{array}$ Thus $d\mid1.$ • May 13th 2012, 01:07 AM alyosha2 Re: Multiplicative Inverse So because the difference is 1 we know the only factor we can pull out is 1. Good stuff. Thanks for the help. • May 13th 2012, 11:02 PM kalwin Re: Multiplicative Inverse Thank you Sylvia for solving this problem, even i had the same problem and i was also thinking of posting this but i saw Alyosha2 had already posted it and from here i got the solution of the problem and this is the best forum where we get maximum math problem solved.	{"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": 18, "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": 0.9219178557395935, "perplexity": 402.2335577220689}, "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-2016-30/segments/1469257824109.37/warc/CC-MAIN-20160723071024-00196-ip-10-185-27-174.ec2.internal.warc.gz"}
https://socratic.org/questions/find-all-zeros-f-x-3x-7-32x-6-28x-5-591x-4-1181x-3-2810x-2-5550x-1125	Precalculus Topics # Find all zeros: f(x)=3x^7-32x^6+28x^5+591x^4-1181x^3-2810x^2+5550x-1125? Dec 29, 2017 I don't have time to give a detailed explanation, but the zeroes are $x = 5$ (multiplicity 3), $x = - 3$ (multiplicity 2), and $x = \frac{5 \pm \sqrt{13}}{6}$ (each of multiplicity 1).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "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": 0.8479404449462891, "perplexity": 478.6667754093752}, "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-2021-43/segments/1634323583087.95/warc/CC-MAIN-20211015222918-20211016012918-00074.warc.gz"}
https://www.solumaths.com/en/website/learn/numerical-sequences	A numerical sequence is any application of ℕ or a part of ℕ to ℝ. The calculators provided here allow you to practice calculations on numerical sequences. ## Numerical sequences : games, quizzes and exercises Quiz on numerical sequences (Numeric ... ## Numerical sequences : Reminder A numerical sequence or a numerical progression is any application of ℕ or a part of ℕ to ℝ ### Direction of variation of a sequence: strictly increasing sequence, strictly decreasing sequence. • To say that the sequence (u_(n)) is strictly increasing means that: For any natural number n, u_(n+1)>u_(n) • To say that the sequence (u_(n)) is strictly decreasing means that: For any natural number n, u_(n)>u_(n+1). To show that a sequence is increasing or decreasing: • We can calculate the difference u_(n+1)-u_(n), if this difference is positive then the sequence is increasing, otherwise it is decreasing. • We can also, if the sequence is positive and u_n!=0, calculate the ratio u_(n+1)/u_(n), if this ratio is greater than 1 the sequence is increasing, otherwise it is decreasing. ### Arithmetic sequences, geometric sequences #### Arithmetic sequences (arithmetic progression) To say that a sequence (u_(n)) is arithmetic means that there is a real r such that for any natural number n, u_(n+1)=u_(n)+r. The real r is called the common difference of the sequence (u_(n)). If (u_(n)) is an arithmetic sequence of first term u_(0), and common difference r. Then for any natural number n, u_(n)=u_(0)+nr ##### Sum of consecutive terms of an arithmetic sequence If S=a+...+k is the sum of p consecutive terms of an arithmetic sequence then S = p(a+k)/2. We deduce that 1+2+3+...+n=n(n+1)/2 #### Geometric sequences (geometric progression) To say that a sequence (u_(n)) is geometric means that there is a real q such that for any natural n, u_(n+1)=qu_(n). The real q is called the common ratio for the sequence (u_(n)). If (u_(n)) is a geometric sequence of first term u_(0), and common ratio q. Then for any natural number n, u_(n)=u_(0)q^n ##### Sum of consecutive terms of a geometric sequence If S=a+...+k is the sum of p consecutive terms of a geometric sequence of common ratio q (q != 1) then S = (a-kq)/(1-q). We deduce that 1+q+q^2+...+q^n=(1-q^(n+1))/(1-q)	{"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": 0.9691879153251648, "perplexity": 933.9001288566695}, "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/1652662556725.76/warc/CC-MAIN-20220523071517-20220523101517-00149.warc.gz"}
https://arxiv.org/abs/1806.00726?context=math	math # Title:Group schemes and local densities of ramified hermitian lattices in residue characteristic 2 Part II, Expanded version Authors:Sungmun Cho Abstract: This paper is the complementary work of [Cho16]. Ramified quadratic extensions $E/F$, where $F$ is a finite unramified field extension of $\mathbb{Q}_2$, fall into two cases that we call $\textit{Case 1}$ and $\textit{Case 2}$. In the previous work [Cho16], we obtained the local density formula for a ramified hermitian lattice in $\textit{Case 1}$. In this paper, we obtain the local density formula for the remaining $\textit{Case 2}$, by constructing a smooth integral group scheme model for an appropriate unitary group. Consequently, this paper, combined with the paper [GY00] of W. T. Gan and J.-K. Yu and [Cho16], allows the computation of the mass formula for any hermitian lattice $(L, H)$, when a base field is unramified over $\mathbb{Q}$ at a prime $(2)$. Comments: 89 pages. This is the expanded version of the published one. One error in the last line of Appendix B of 'Group schemes and local densities of ramified hermitian lattices in residue characteristic 2 Part I, Algebra & Number Theory, 10-3, 451-532, 2016' is explained in Remark B.1 of this version Subjects: Number Theory (math.NT) MSC classes: 11E41, 11E95, 14L15, 20G25 Journal reference: Forum Mathematicum Volume 30 Issue 6, pages 1487-1520, 2018 DOI: 10.1515/forum-2017-0080 Cite as: arXiv:1806.00726 [math.NT] (or arXiv:1806.00726v1 [math.NT] for this version) ## Submission history From: Sungmun Cho [view email] [v1] Sun, 3 Jun 2018 02:01:23 UTC (65 KB)	{"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": 0.9148028492927551, "perplexity": 1287.7362456959524}, "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/1568514572896.15/warc/CC-MAIN-20190924083200-20190924105200-00089.warc.gz"}
http://human-web.org/Utah/error-gauss-function.html	Address 53 S Main St, Ephraim, UT 84627 (435) 462-9814 # error gauss function Moroni, Utah Web browsers do not support MATLAB commands. The inverse imaginary error function is defined as erfi − 1 ⁡ ( x ) {\displaystyle \operatorname {erfi} ^{-1}(x)} .[10] For any real x, Newton's method can be used to compute Despite the name "imaginary error function", erfi ⁡ ( x ) {\displaystyle \operatorname π 8 (x)} is real when x is real. History and Terminology>Wolfram Language Commands> MathWorld Contributors>D'Orsogna> Less... Another approximation is given by erf ⁡ ( x ) ≈ sgn ⁡ ( x ) 1 − exp ⁡ ( − x 2 4 π + a x 2 1 is the double factorial: the product of all odd numbers up to (2n–1). http://mathworld.wolfram.com/Erf.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Erf is implemented in the Wolfram Language as Erf[z]. Whittaker, E.T. Acton, F.S. Princeton, NJ: Princeton University Press, p.105, 2003. Wolfram Problem Generator» Unlimited random practice problems and answers with built-in Step-by-step solutions. The system returned: (22) Invalid argument The remote host or network may be down. New York: Dover, pp.179-182, 1967. Cambridge, England: Cambridge University Press, 1990. See Alsoerfc \| erfcinv \| erfcx \| erfinv Introduced before R2006a × MATLAB Command You clicked a link that corresponds to this MATLAB command: Run the command by entering it in comm., May 9, 2004). For details, see Tips.Plot the CDF of the normal distribution with and .x = -3:0.1:3; y = (1/2)*(1+erf(x/sqrt(2))); plot(x,y) grid on title('CDF of normal distribution with \mu = 0 and \sigma Your cache administrator is webmaster. Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. A Course in Modern Analysis, 4th ed. A complex generalization of is defined as (39) (40) Integral representations valid only in the upper half-plane are given by (41) (42) SEE ALSO: Dawson's Integral, Erfc, Erfi, Fresnel Integrals, Gaussian Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. This substitution maintains accuracy. Data Types: single \| doubleMore Aboutcollapse allError FunctionThe error function erf of x iserf(x)=2π∫0xe−t2dt.Tall Array SupportThis function fully supports tall arrays. The relationship between the error function erf and normcdf is normcdf(x)=12(1−erf(−x2)).For expressions of the form 1 - erf(x), use the complementary error function erfc instead. For any complex number z: erf ⁡ ( z ¯ ) = erf ⁡ ( z ) ¯ {\displaystyle \operatorname β 0 ({\overline − 9})={\overline {\operatorname − 8 (z)}}} where z When erf(x) is close to 1, then 1 - erf(x) is a small number and might be rounded down to 0. The system returned: (22) Invalid argument The remote host or network may be down. Mathematical Methods for Physicists, 3rd ed. Translate erfError functioncollapse all in page Syntaxerf(x) exampleDescriptionexampleerf(x) returns the Error Function evaluated for each element of x.Examplescollapse allFind Error FunctionOpen ScriptFind the error function of a value.erf(0.76) ans The inverse error function is usually defined with domain (−1,1), and it is restricted to this domain in many computer algebra systems. and Stegun, I.A. (Eds.). "Error Function and Fresnel Integrals." Ch.7 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. Negative integer values of Im(ƒ) are shown with thick red lines. At the imaginary axis, it tends to ±i∞. and Watson, G.N. Definite integrals involving include Definite integrals involving include (34) (35) (36) (37) (38) The first two of these appear in Prudnikov et al. (1990, p.123, eqns. 2.8.19.8 and 2.8.19.11), with , Erf is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is defined as:[1][2] erf ⁡ ( x ) = 1 π ∫ − x x e − t 2 d t = 2 π ∫ 0 x e − t Continued fraction expansion A continued fraction expansion of the complementary error function is:[11] erfc ⁡ ( z ) = z π e − z 2 1 z 2 + a 1 Sequences A000079/M1129, A001147/M3002, A007680/M2861, A103979, A103980 in "The On-Line Encyclopedia of Integer Sequences." Spanier, J. Erf can also be defined as a Maclaurin series (6) (7) (OEIS A007680). The denominator terms are sequence A007680 in the OEIS. Prudnikov, A.P.; Brychkov, Yu.A.; and Marichev, O.I. Erf has the continued fraction (32) (33) (Wall 1948, p.357), first stated by Laplace in 1805 and Legendre in 1826 (Olds 1963, p.139), proved by Jacobi, and rediscovered by Ramanujan (Watson Numerical Methods That Work, 2nd printing. New York: Dover, pp.297-309, 1972. The error function at +∞ is exactly 1 (see Gaussian integral). Back to English × Translate This Page Select Language Bulgarian Catalan Chinese Simplified Chinese Traditional Czech Danish Dutch English Estonian Finnish French German Greek Haitian Creole Hindi Hmong Daw Hungarian Indonesian	{"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": 0.8933738470077515, "perplexity": 4191.1509660963}, "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-2018-51/segments/1544376823320.11/warc/CC-MAIN-20181210080704-20181210102204-00055.warc.gz"}
https://www.esaral.com/q/the-difference-between-87178	Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too! # The difference between Question: The difference between $\Delta \mathrm{H}$ and $\Delta \mathrm{U}(\Delta \mathrm{H}-\Delta \mathrm{U})$, when the combustion of one mole of heptane (1) is carried out at a temperature $T$, is equal to: 1. 3RT 2. $-3 \mathrm{RT}$ 3. $-4 R T$ 4. 4RT Correct Option: , 3 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": 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": 0.8703432679176331, "perplexity": 4583.059951724699}, "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/1674764499524.28/warc/CC-MAIN-20230128054815-20230128084815-00787.warc.gz"}
https://www.educator.com/mathematics/ap-calculus-ab/hovasapian/optimization-problems-i.php	INSTRUCTORS Raffi Hovasapian John Zhu Raffi Hovasapian Optimization Problems I Slide Duration: Table of Contents Section 1: Limits and Derivatives Overview & Slopes of Curves 42m 8s Intro 0:00 Overview & Slopes of Curves 0:21 Differential and Integral 0:22 Fundamental Theorem of Calculus 6:36 Differentiation or Taking the Derivative 14:24 What Does the Derivative Mean and How do We Find it? 15:18 Example: f'(x) 19:24 Example: f(x) = sin (x) 29:16 General Procedure for Finding the Derivative of f(x) 37:33 More on Slopes of Curves 50m 53s Intro 0:00 Slope of the Secant Line along a Curve 0:12 Slope of the Tangent Line to f(x) at a Particlar Point 0:13 Slope of the Secant Line along a Curve 2:59 Instantaneous Slope 6:51 Instantaneous Slope 6:52 Example: Distance, Time, Velocity 13:32 Instantaneous Slope and Average Slope 25:42 Slope & Rate of Change 29:55 Slope & Rate of Change 29:56 Example: Slope = 2 33:16 Example: Slope = 4/3 34:32 Example: Slope = 4 (m/s) 39:12 Example: Density = Mass / Volume 40:33 Average Slope, Average Rate of Change, Instantaneous Slope, and Instantaneous Rate of Change 47:46 Example Problems for Slopes of Curves 59m 12s Intro 0:00 Example I: Water Tank 0:13 Part A: Which is the Independent Variable and Which is the Dependent? 2:00 Part B: Average Slope 3:18 Part C: Express These Slopes as Rates-of-Change 9:28 Part D: Instantaneous Slope 14:54 Example II: y = √(x-3) 28:26 Part A: Calculate the Slope of the Secant Line 30:39 Part B: Instantaneous Slope 41:26 Part C: Equation for the Tangent Line 43:59 Example III: Object in the Air 49:37 Part A: Average Velocity 50:37 Part B: Instantaneous Velocity 55:30 Desmos Tutorial 18m 43s Intro 0:00 Desmos Tutorial 1:42 Desmos Tutorial 1:43 Things You Must Learn To Do on Your Particular Calculator 2:39 Things You Must Learn To Do on Your Particular Calculator 2:40 Example I: y=sin x 4:54 Example II: y=x³ and y = d/(dx) (x³) 9:22 Example III: y = x² {-5 <= x <= 0} and y = cos x {0 < x < 6} 13:15 The Limit of a Function 51m 53s Intro 0:00 The Limit of a Function 0:14 The Limit of a Function 0:15 Graph: Limit of a Function 12:24 Table of Values 16:02 lim x→a f(x) Does not Say What Happens When x = a 20:05 Example I: f(x) = x² 24:34 Example II: f(x) = 7 27:05 Example III: f(x) = 4.5 30:33 Example IV: f(x) = 1/x 34:03 Example V: f(x) = 1/x² 36:43 The Limit of a Function, Cont. 38:16 Infinity and Negative Infinity 38:17 Does Not Exist 42:45 Summary 46:48 Example Problems for the Limit of a Function 24m 43s Intro 0:00 Example I: Explain in Words What the Following Symbols Mean 0:10 Example II: Find the Following Limit 5:21 Example III: Use the Graph to Find the Following Limits 7:35 Example IV: Use the Graph to Find the Following Limits 11:48 Example V: Sketch the Graph of a Function that Satisfies the Following Properties 15:25 Example VI: Find the Following Limit 18:44 Example VII: Find the Following Limit 20:06 Calculating Limits Mathematically 53m 48s Intro 0:00 Plug-in Procedure 0:09 Plug-in Procedure 0:10 Limit Laws 9:14 Limit Law 1 10:05 Limit Law 2 10:54 Limit Law 3 11:28 Limit Law 4 11:54 Limit Law 5 12:24 Limit Law 6 13:14 Limit Law 7 14:38 Plug-in Procedure, Cont. 16:35 Plug-in Procedure, Cont. 16:36 Example I: Calculating Limits Mathematically 20:50 Example II: Calculating Limits Mathematically 27:37 Example III: Calculating Limits Mathematically 31:42 Example IV: Calculating Limits Mathematically 35:36 Example V: Calculating Limits Mathematically 40:58 Limits Theorem 44:45 Limits Theorem 1 44:46 Limits Theorem 2: Squeeze Theorem 46:34 Example VI: Calculating Limits Mathematically 49:26 Example Problems for Calculating Limits Mathematically 21m 22s Intro 0:00 Example I: Evaluate the Following Limit by Showing Each Application of a Limit Law 0:16 Example II: Evaluate the Following Limit 1:51 Example III: Evaluate the Following Limit 3:36 Example IV: Evaluate the Following Limit 8:56 Example V: Evaluate the Following Limit 11:19 Example VI: Calculating Limits Mathematically 13:19 Example VII: Calculating Limits Mathematically 14:59 Calculating Limits as x Goes to Infinity 50m 1s Intro 0:00 Limit as x Goes to Infinity 0:14 Limit as x Goes to Infinity 0:15 Let's Look at f(x) = 1 / (x-3) 1:04 Summary 9:34 Example I: Calculating Limits as x Goes to Infinity 12:16 Example II: Calculating Limits as x Goes to Infinity 21:22 Example III: Calculating Limits as x Goes to Infinity 24:10 Example IV: Calculating Limits as x Goes to Infinity 36:00 Example Problems for Limits at Infinity 36m 31s Intro 0:00 Example I: Calculating Limits as x Goes to Infinity 0:14 Example II: Calculating Limits as x Goes to Infinity 3:27 Example III: Calculating Limits as x Goes to Infinity 8:11 Example IV: Calculating Limits as x Goes to Infinity 14:20 Example V: Calculating Limits as x Goes to Infinity 20:07 Example VI: Calculating Limits as x Goes to Infinity 23:36 Continuity 53m Intro 0:00 Definition of Continuity 0:08 Definition of Continuity 0:09 Example: Not Continuous 3:52 Example: Continuous 4:58 Example: Not Continuous 5:52 Procedure for Finding Continuity 9:45 Law of Continuity 13:44 Law of Continuity 13:45 Example I: Determining Continuity on a Graph 15:55 Example II: Show Continuity & Determine the Interval Over Which the Function is Continuous 17:57 Example III: Is the Following Function Continuous at the Given Point? 22:42 Theorem for Composite Functions 25:28 Theorem for Composite Functions 25:29 Example IV: Is cos(x³ + ln x) Continuous at x=π/2? 27:00 Example V: What Value of A Will make the Following Function Continuous at Every Point of Its Domain? 34:04 Types of Discontinuity 39:18 Removable Discontinuity 39:33 Jump Discontinuity 40:06 Infinite Discontinuity 40:32 Intermediate Value Theorem 40:58 Intermediate Value Theorem: Hypothesis & Conclusion 40:59 Intermediate Value Theorem: Graphically 43:40 Example VI: Prove That the Following Function Has at Least One Real Root in the Interval [4,6] 47:46 Derivative I 40m 2s Intro 0:00 Derivative 0:09 Derivative 0:10 Example I: Find the Derivative of f(x)=x³ 2:20 Notations for the Derivative 7:32 Notations for the Derivative 7:33 Derivative & Rate of Change 11:14 Recall the Rate of Change 11:15 Instantaneous Rate of Change 17:04 Graphing f(x) and f'(x) 19:10 Example II: Find the Derivative of x⁴ - x² 24:00 Example III: Find the Derivative of f(x)=√x 30:51 Derivatives II 53m 45s Intro 0:00 Example I: Find the Derivative of (2+x)/(3-x) 0:18 Derivatives II 9:02 f(x) is Differentiable if f'(x) Exists 9:03 Recall: For a Limit to Exist, Both Left Hand and Right Hand Limits Must Equal to Each Other 17:19 Geometrically: Differentiability Means the Graph is Smooth 18:44 Example II: Show Analytically that f(x) = \|x\| is Nor Differentiable at x=0 20:53 Example II: For x > 0 23:53 Example II: For x < 0 25:36 Example II: What is f(0) and What is the lim \|x\| as x→0? 30:46 Differentiability & Continuity 34:22 Differentiability & Continuity 34:23 How Can a Function Not be Differentiable at a Point? 39:38 How Can a Function Not be Differentiable at a Point? 39:39 Higher Derivatives 41:58 Higher Derivatives 41:59 Derivative Operator 45:12 Example III: Find (dy)/(dx) & (d²y)/(dx²) for y = x³ 49:29 More Example Problems for The Derivative 31m 38s Intro 0:00 Example I: Sketch f'(x) 0:10 Example II: Sketch f'(x) 2:14 Example III: Find the Derivative of the Following Function sing the Definition 3:49 Example IV: Determine f, f', and f'' on a Graph 12:43 Example V: Find an Equation for the Tangent Line to the Graph of the Following Function at the Given x-value 13:40 Example VI: Distance vs. Time 20:15 Example VII: Displacement, Velocity, and Acceleration 23:56 Example VIII: Graph the Displacement Function 28:20 Section 2: Differentiation Differentiation of Polynomials & Exponential Functions 47m 35s Intro 0:00 Differentiation of Polynomials & Exponential Functions 0:15 Derivative of a Function 0:16 Derivative of a Constant 2:35 Power Rule 3:08 If C is a Constant 4:19 Sum Rule 5:22 Exponential Functions 6:26 Example I: Differentiate 7:45 Example II: Differentiate 12:38 Example III: Differentiate 15:13 Example IV: Differentiate 16:20 Example V: Differentiate 19:19 Example VI: Find the Equation of the Tangent Line to a Function at a Given Point 12:18 Example VII: Find the First & Second Derivatives 25:59 Example VIII 27:47 Part A: Find the Velocity & Acceleration Functions as Functions of t 27:48 Part B: Find the Acceleration after 3 Seconds 30:12 Part C: Find the Acceleration when the Velocity is 0 30:53 Part D: Graph the Position, Velocity, & Acceleration Graphs 32:50 Example IX: Find a Cubic Function Whose Graph has Horizontal Tangents 34:53 Example X: Find a Point on a Graph 42:31 The Product, Power & Quotient Rules 47m 25s Intro 0:00 The Product, Power and Quotient Rules 0:19 Differentiate Functions 0:20 Product Rule 5:30 Quotient Rule 9:15 Power Rule 10:00 Example I: Product Rule 13:48 Example II: Quotient Rule 16:13 Example III: Power Rule 18:28 Example IV: Find dy/dx 19:57 Example V: Find dy/dx 24:53 Example VI: Find dy/dx 28:38 Example VII: Find an Equation for the Tangent to the Curve 34:54 Example VIII: Find d²y/dx² 38:08 Derivatives of the Trigonometric Functions 41m 8s Intro 0:00 Derivatives of the Trigonometric Functions 0:09 Let's Find the Derivative of f(x) = sin x 0:10 Important Limits to Know 4:59 d/dx (sin x) 6:06 d/dx (cos x) 6:38 d/dx (tan x) 6:50 d/dx (csc x) 7:02 d/dx (sec x) 7:15 d/dx (cot x) 7:27 Example I: Differentiate f(x) = x² - 4 cos x 7:56 Example II: Differentiate f(x) = x⁵ tan x 9:04 Example III: Differentiate f(x) = (cos x) / (3 + sin x) 10:56 Example IV: Differentiate f(x) = e^x / (tan x - sec x) 14:06 Example V: Differentiate f(x) = (csc x - 4) / (cot x) 15:37 Example VI: Find an Equation of the Tangent Line 21:48 Example VII: For What Values of x Does the Graph of the Function x + 3 cos x Have a Horizontal Tangent? 25:17 Example VIII: Ladder Problem 28:23 Example IX: Evaluate 33:22 Example X: Evaluate 36:38 The Chain Rule 24m 56s Intro 0:00 The Chain Rule 0:13 Recall the Composite Functions 0:14 Derivatives of Composite Functions 1:34 Example I: Identify f(x) and g(x) and Differentiate 6:41 Example II: Identify f(x) and g(x) and Differentiate 9:47 Example III: Differentiate 11:03 Example IV: Differentiate f(x) = -5 / (x² + 3)³ 12:15 Example V: Differentiate f(x) = cos(x² + c²) 14:35 Example VI: Differentiate f(x) = cos⁴x +c² 15:41 Example VII: Differentiate 17:03 Example VIII: Differentiate f(x) = sin(tan x²) 19:01 Example IX: Differentiate f(x) = sin(tan² x) 21:02 More Chain Rule Example Problems 25m 32s Intro 0:00 Example I: Differentiate f(x) = sin(cos(tanx)) 0:38 Example II: Find an Equation for the Line Tangent to the Given Curve at the Given Point 2:25 Example III: F(x) = f(g(x)), Find F' (6) 4:22 Example IV: Differentiate & Graph both the Function & the Derivative in the Same Window 5:35 Example V: Differentiate f(x) = ( (x-8)/(x+3) )⁴ 10:18 Example VI: Differentiate f(x) = sec²(12x) 12:28 Example VII: Differentiate 14:41 Example VIII: Differentiate 19:25 Example IX: Find an Expression for the Rate of Change of the Volume of the Balloon with Respect to Time 21:13 Implicit Differentiation 52m 31s Intro 0:00 Implicit Differentiation 0:09 Implicit Differentiation 0:10 Example I: Find (dy)/(dx) by both Implicit Differentiation and Solving Explicitly for y 12:15 Example II: Find (dy)/(dx) of x³ + x²y + 7y² = 14 19:18 Example III: Find (dy)/(dx) of x³y² + y³x² = 4x 21:43 Example IV: Find (dy)/(dx) of the Following Equation 24:13 Example V: Find (dy)/(dx) of 6sin x cos y = 1 29:00 Example VI: Find (dy)/(dx) of x² cos² y + y sin x = 2sin x cos y 31:02 Example VII: Find (dy)/(dx) of √(xy) = 7 + y²e^x 37:36 Example VIII: Find (dy)/(dx) of 4(x²+y²)² = 35(x²-y²) 41:03 Example IX: Find (d²y)/(dx²) of x² + y² = 25 44:05 Example X: Find (d²y)/(dx²) of sin x + cos y = sin(2x) 47:48 Section 3: Applications of the Derivative Linear Approximations & Differentials 47m 34s Intro 0:00 Linear Approximations & Differentials 0:09 Linear Approximations & Differentials 0:10 Example I: Linear Approximations & Differentials 11:27 Example II: Linear Approximations & Differentials 20:19 Differentials 30:32 Differentials 30:33 Example III: Linear Approximations & Differentials 34:09 Example IV: Linear Approximations & Differentials 35:57 Example V: Relative Error 38:46 Related Rates 45m 33s Intro 0:00 Related Rates 0:08 Strategy for Solving Related Rates Problems #1 0:09 Strategy for Solving Related Rates Problems #2 1:46 Strategy for Solving Related Rates Problems #3 2:06 Strategy for Solving Related Rates Problems #4 2:50 Strategy for Solving Related Rates Problems #5 3:38 Example I: Radius of a Balloon 5:15 Example II: Ladder 12:52 Example III: Water Tank 19:08 Example IV: Distance between Two Cars 29:27 Example V: Line-of-Sight 36:20 More Related Rates Examples 37m 17s Intro 0:00 Example I: Shadow 0:14 Example II: Particle 4:45 Example III: Water Level 10:28 Example IV: Clock 20:47 Example V: Distance between a House and a Plane 29:11 Maximum & Minimum Values of a Function 40m 44s Intro 0:00 Maximum & Minimum Values of a Function, Part 1 0:23 Absolute Maximum 2:20 Absolute Minimum 2:52 Local Maximum 3:38 Local Minimum 4:26 Maximum & Minimum Values of a Function, Part 2 6:11 Function with Absolute Minimum but No Absolute Max, Local Max, and Local Min 7:18 Function with Local Max & Min but No Absolute Max & Min 8:48 Formal Definitions 10:43 Absolute Maximum 11:18 Absolute Minimum 12:57 Local Maximum 14:37 Local Minimum 16:25 Extreme Value Theorem 18:08 Theorem: f'(c) = 0 24:40 Critical Number (Critical Value) 26:14 Procedure for Finding the Critical Values of f(x) 28:32 Example I: Find the Critical Values of f(x) x + sinx 29:51 Example II: What are the Absolute Max & Absolute Minimum of f(x) = x + 4 sinx on [0,2π] 35:31 Example Problems for Max & Min 40m 44s Intro 0:00 Example I: Identify Absolute and Local Max & Min on the Following Graph 0:11 Example II: Sketch the Graph of a Continuous Function 3:11 Example III: Sketch the Following Graphs 4:40 Example IV: Find the Critical Values of f (x) = 3x⁴ - 7x³ + 4x² 6:13 Example V: Find the Critical Values of f(x) = \|2x - 5\| 8:42 Example VI: Find the Critical Values 11:42 Example VII: Find the Critical Values f(x) = cos²(2x) on [0,2π] 16:57 Example VIII: Find the Absolute Max & Min f(x) = 2sinx + 2cos x on [0,(π/3)] 20:08 Example IX: Find the Absolute Max & Min f(x) = (ln(2x)) / x on [1,3] 24:39 The Mean Value Theorem 25m 54s Intro 0:00 Rolle's Theorem 0:08 Rolle's Theorem: If & Then 0:09 Rolle's Theorem: Geometrically 2:06 There May Be More than 1 c Such That f'( c ) = 0 3:30 Example I: Rolle's Theorem 4:58 The Mean Value Theorem 9:12 The Mean Value Theorem: If & Then 9:13 The Mean Value Theorem: Geometrically 11:07 Example II: Mean Value Theorem 13:43 Example III: Mean Value Theorem 21:19 Using Derivatives to Graph Functions, Part I 25m 54s Intro 0:00 Using Derivatives to Graph Functions, Part I 0:12 Increasing/ Decreasing Test 0:13 Example I: Find the Intervals Over Which the Function is Increasing & Decreasing 3:26 Example II: Find the Local Maxima & Minima of the Function 19:18 Example III: Find the Local Maxima & Minima of the Function 31:39 Using Derivatives to Graph Functions, Part II 44m 58s Intro 0:00 Using Derivatives to Graph Functions, Part II 0:13 Concave Up & Concave Down 0:14 What Does This Mean in Terms of the Derivative? 6:14 Point of Inflection 8:52 Example I: Graph the Function 13:18 Example II: Function x⁴ - 5x² 19:03 Intervals of Increase & Decrease 19:04 Local Maxes and Mins 25:01 Intervals of Concavity & X-Values for the Points of Inflection 29:18 Intervals of Concavity & Y-Values for the Points of Inflection 34:18 Graphing the Function 40:52 Example Problems I 49m 19s Intro 0:00 Example I: Intervals, Local Maxes & Mins 0:26 Example II: Intervals, Local Maxes & Mins 5:05 Example III: Intervals, Local Maxes & Mins, and Inflection Points 13:40 Example IV: Intervals, Local Maxes & Mins, Inflection Points, and Intervals of Concavity 23:02 Example V: Intervals, Local Maxes & Mins, Inflection Points, and Intervals of Concavity 34:36 Example Problems III 59m 1s Intro 0:00 Example I: Intervals, Local Maxes & Mins, Inflection Points, Intervals of Concavity, and Asymptotes 0:11 Example II: Intervals, Local Maxes & Mins, Inflection Points, Intervals of Concavity, and Asymptotes 21:24 Example III: Cubic Equation f(x) = Ax³ + Bx² + Cx + D 37:56 Example IV: Intervals, Local Maxes & Mins, Inflection Points, Intervals of Concavity, and Asymptotes 46:19 L'Hospital's Rule 30m 9s Intro 0:00 L'Hospital's Rule 0:19 Indeterminate Forms 0:20 L'Hospital's Rule 3:38 Example I: Evaluate the Following Limit Using L'Hospital's Rule 8:50 Example II: Evaluate the Following Limit Using L'Hospital's Rule 10:30 Indeterminate Products 11:54 Indeterminate Products 11:55 Example III: L'Hospital's Rule & Indeterminate Products 13:57 Indeterminate Differences 17:00 Indeterminate Differences 17:01 Example IV: L'Hospital's Rule & Indeterminate Differences 18:57 Indeterminate Powers 22:20 Indeterminate Powers 22:21 Example V: L'Hospital's Rule & Indeterminate Powers 25:13 Example Problems for L'Hospital's Rule 38m 14s Intro 0:00 Example I: Evaluate the Following Limit 0:17 Example II: Evaluate the Following Limit 2:45 Example III: Evaluate the Following Limit 6:54 Example IV: Evaluate the Following Limit 8:43 Example V: Evaluate the Following Limit 11:01 Example VI: Evaluate the Following Limit 14:48 Example VII: Evaluate the Following Limit 17:49 Example VIII: Evaluate the Following Limit 20:37 Example IX: Evaluate the Following Limit 25:16 Example X: Evaluate the Following Limit 32:44 Optimization Problems I 49m 59s Intro 0:00 Example I: Find the Dimensions of the Box that Gives the Greatest Volume 1:23 Fundamentals of Optimization Problems 18:08 Fundamental #1 18:33 Fundamental #2 19:09 Fundamental #3 19:19 Fundamental #4 20:59 Fundamental #5 21:55 Fundamental #6 23:44 Example II: Demonstrate that of All Rectangles with a Given Perimeter, the One with the Largest Area is a Square 24:36 Example III: Find the Points on the Ellipse 9x² + y² = 9 Farthest Away from the Point (1,0) 35:13 Example IV: Find the Dimensions of the Rectangle of Largest Area that can be Inscribed in a Circle of Given Radius R 43:10 Optimization Problems II 55m 10s Intro 0:00 Example I: Optimization Problem 0:13 Example II: Optimization Problem 17:34 Example III: Optimization Problem 35:06 Example IV: Revenue, Cost, and Profit 43:22 Newton's Method 30m 22s Intro 0:00 Newton's Method 0:45 Newton's Method 0:46 Example I: Find x2 and x3 13:18 Example II: Use Newton's Method to Approximate 15:48 Example III: Find the Root of the Following Equation to 6 Decimal Places 19:57 Example IV: Use Newton's Method to Find the Coordinates of the Inflection Point 23:11 Section 4: Integrals Antiderivatives 55m 26s Intro 0:00 Antiderivatives 0:23 Definition of an Antiderivative 0:24 Antiderivative Theorem 7:58 Function & Antiderivative 12:10 x^n 12:30 1/x 13:00 e^x 13:08 cos x 13:18 sin x 14:01 sec² x 14:11 secxtanx 14:18 1/√(1-x²) 14:26 1/(1+x²) 14:36 -1/√(1-x²) 14:45 Example I: Find the Most General Antiderivative for the Following Functions 15:07 Function 1: f(x) = x³ -6x² + 11x - 9 15:42 Function 2: f(x) = 14√(x) - 27 4√x 19:12 Function 3: (fx) = cos x - 14 sinx 20:53 Function 4: f(x) = (x⁵+2√x )/( x^(4/3) ) 22:10 Function 5: f(x) = (3e^x) - 2/(1+x²) 25:42 Example II: Given the Following, Find the Original Function f(x) 26:37 Function 1: f'(x) = 5x³ - 14x + 24, f(2) = 40 27:55 Function 2: f'(x) 3 sinx + sec²x, f(π/6) = 5 30:34 Function 3: f''(x) = 8x - cos x, f(1.5) = 12.7, f'(1.5) = 4.2 32:54 Function 4: f''(x) = 5/(√x), f(2) 15, f'(2) = 7 37:54 Example III: Falling Object 41:58 Problem 1: Find an Equation for the Height of the Ball after t Seconds 42:48 Problem 2: How Long Will It Take for the Ball to Strike the Ground? 48:30 Problem 3: What is the Velocity of the Ball as it Hits the Ground? 49:52 Problem 4: Initial Velocity of 6 m/s, How Long Does It Take to Reach the Ground? 50:46 The Area Under a Curve 51m 3s Intro 0:00 The Area Under a Curve 0:13 Approximate Using Rectangles 0:14 Let's Do This Again, Using 4 Different Rectangles 9:40 Approximate with Rectangles 16:10 Left Endpoint 18:08 Right Endpoint 25:34 Left Endpoint vs. Right Endpoint 30:58 Number of Rectangles 34:08 True Area 37:36 True Area 37:37 Sigma Notation & Limits 43:32 When You Have to Explicitly Solve Something 47:56 Example Problems for Area Under a Curve 33m 7s Intro 0:00 Example I: Using Left Endpoint & Right Endpoint to Approximate Area Under a Curve 0:10 Example II: Using 5 Rectangles, Approximate the Area Under the Curve 11:32 Example III: Find the True Area by Evaluating the Limit Expression 16:07 Example IV: Find the True Area by Evaluating the Limit Expression 24:52 The Definite Integral 43m 19s Intro 0:00 The Definite Integral 0:08 Definition to Find the Area of a Curve 0:09 Definition of the Definite Integral 4:08 Symbol for Definite Integral 8:45 Regions Below the x-axis 15:18 Associating Definite Integral to a Function 19:38 Integrable Function 27:20 Evaluating the Definite Integral 29:26 Evaluating the Definite Integral 29:27 Properties of the Definite Integral 35:24 Properties of the Definite Integral 35:25 Example Problems for The Definite Integral 32m 14s Intro 0:00 Example I: Approximate the Following Definite Integral Using Midpoints & Sub-intervals 0:11 Example II: Express the Following Limit as a Definite Integral 5:28 Example III: Evaluate the Following Definite Integral Using the Definition 6:28 Example IV: Evaluate the Following Integral Using the Definition 17:06 Example V: Evaluate the Following Definite Integral by Using Areas 25:41 Example VI: Definite Integral 30:36 The Fundamental Theorem of Calculus 24m 17s Intro 0:00 The Fundamental Theorem of Calculus 0:17 Evaluating an Integral 0:18 Lim as x → ∞ 12:19 Taking the Derivative 14:06 Differentiation & Integration are Inverse Processes 15:04 1st Fundamental Theorem of Calculus 20:08 1st Fundamental Theorem of Calculus 20:09 2nd Fundamental Theorem of Calculus 22:30 2nd Fundamental Theorem of Calculus 22:31 Example Problems for the Fundamental Theorem 25m 21s Intro 0:00 Example I: Find the Derivative of the Following Function 0:17 Example II: Find the Derivative of the Following Function 1:40 Example III: Find the Derivative of the Following Function 2:32 Example IV: Find the Derivative of the Following Function 5:55 Example V: Evaluate the Following Integral 7:13 Example VI: Evaluate the Following Integral 9:46 Example VII: Evaluate the Following Integral 12:49 Example VIII: Evaluate the Following Integral 13:53 Example IX: Evaluate the Following Graph 15:24 Local Maxs and Mins for g(x) 15:25 Where Does g(x) Achieve Its Absolute Max on [0,8] 20:54 On What Intervals is g(x) Concave Up/Down? 22:20 Sketch a Graph of g(x) 24:34 More Example Problems, Including Net Change Applications 34m 22s Intro 0:00 Example I: Evaluate the Following Indefinite Integral 0:10 Example II: Evaluate the Following Definite Integral 0:59 Example III: Evaluate the Following Integral 2:59 Example IV: Velocity Function 7:46 Part A: Net Displacement 7:47 Part B: Total Distance Travelled 13:15 Example V: Linear Density Function 20:56 Example VI: Acceleration Function 25:10 Part A: Velocity Function at Time t 25:11 Part B: Total Distance Travelled During the Time Interval 28:38 Solving Integrals by Substitution 27m 20s Intro 0:00 Table of Integrals 0:35 Example I: Evaluate the Following Indefinite Integral 2:02 Example II: Evaluate the Following Indefinite Integral 7:27 Example IIII: Evaluate the Following Indefinite Integral 10:57 Example IV: Evaluate the Following Indefinite Integral 12:33 Example V: Evaluate the Following 14:28 Example VI: Evaluate the Following 16:00 Example VII: Evaluate the Following 19:01 Example VIII: Evaluate the Following 21:49 Example IX: Evaluate the Following 24:34 Section 5: Applications of Integration Areas Between Curves 34m 56s Intro 0:00 Areas Between Two Curves: Function of x 0:08 Graph 1: Area Between f(x) & g(x) 0:09 Graph 2: Area Between f(x) & g(x) 4:07 Is It Possible to Write as a Single Integral? 8:20 Area Between the Curves on [a,b] 9:24 Absolute Value 10:32 Formula for Areas Between Two Curves: Top Function - Bottom Function 17:03 Areas Between Curves: Function of y 17:49 What if We are Given Functions of y? 17:50 Formula for Areas Between Two Curves: Right Function - Left Function 21:48 Finding a & b 22:32 Example Problems for Areas Between Curves 42m 55s Intro 0:00 Instructions for the Example Problems 0:10 Example I: y = 7x - x² and y=x 0:37 Example II: x=y²-3, x=e^((1/2)y), y=-1, and y=2 6:25 Example III: y=(1/x), y=(1/x³), and x=4 12:25 Example IV: 15-2x² and y=x²-5 15:52 Example V: x=(1/8)y³ and x=6-y² 20:20 Example VI: y=cos x, y=sin(2x), [0,π/2] 24:34 Example VII: y=2x², y=10x², 7x+2y=10 29:51 Example VIII: Velocity vs. Time 33:23 Part A: At 2.187 Minutes, Which care is Further Ahead? 33:24 Part B: If We Shaded the Region between the Graphs from t=0 to t=2.187, What Would This Shaded Area Represent? 36:32 Part C: At 4 Minutes Which Car is Ahead? 37:11 Part D: At What Time Will the Cars be Side by Side? 37:50 Volumes I: Slices 34m 15s Intro 0:00 Volumes I: Slices 0:18 Rotate the Graph of y=√x about the x-axis 0:19 How can I use Integration to Find the Volume? 3:16 Slice the Solid Like a Loaf of Bread 5:06 Volumes Definition 8:56 Example I: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Given Functions about the Given Line of Rotation 12:18 Example II: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Given Functions about the Given Line of Rotation 19:05 Example III: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Given Functions about the Given Line of Rotation 25:28 Volumes II: Volumes by Washers 51m 43s Intro 0:00 Volumes II: Volumes by Washers 0:11 Rotating Region Bounded by y=x³ & y=x around the x-axis 0:12 Equation for Volumes by Washer 11:14 Process for Solving Volumes by Washer 13:40 Example I: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Following Functions around the Given Axis 15:58 Example II: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Following Functions around the Given Axis 25:07 Example III: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Following Functions around the Given Axis 34:20 Example IV: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Following Functions around the Given Axis 44:05 Volumes III: Solids That Are Not Solids-of-Revolution 49m 36s Intro 0:00 Solids That Are Not Solids-of-Revolution 0:11 Cross-Section Area Review 0:12 Cross-Sections That Are Not Solids-of-Revolution 7:36 Example I: Find the Volume of a Pyramid Whose Base is a Square of Side-length S, and Whose Height is H 10:54 Example II: Find the Volume of a Solid Whose Cross-sectional Areas Perpendicular to the Base are Equilateral Triangles 20:39 Example III: Find the Volume of a Pyramid Whose Base is an Equilateral Triangle of Side-Length A, and Whose Height is H 29:27 Example IV: Find the Volume of a Solid Whose Base is Given by the Equation 16x² + 4y² = 64 36:47 Example V: Find the Volume of a Solid Whose Base is the Region Bounded by the Functions y=3-x² and the x-axis 46:13 Volumes IV: Volumes By Cylindrical Shells 50m 2s Intro 0:00 Volumes by Cylindrical Shells 0:11 Find the Volume of the Following Region 0:12 Volumes by Cylindrical Shells: Integrating Along x 14:12 Volumes by Cylindrical Shells: Integrating Along y 14:40 Volumes by Cylindrical Shells Formulas 16:22 Example I: Using the Method of Cylindrical Shells, Find the Volume of the Solid 18:33 Example II: Using the Method of Cylindrical Shells, Find the Volume of the Solid 25:57 Example III: Using the Method of Cylindrical Shells, Find the Volume of the Solid 31:38 Example IV: Using the Method of Cylindrical Shells, Find the Volume of the Solid 38:44 Example V: Using the Method of Cylindrical Shells, Find the Volume of the Solid 44:03 The Average Value of a Function 32m 13s Intro 0:00 The Average Value of a Function 0:07 Average Value of f(x) 0:08 What if The Domain of f(x) is Not Finite? 2:23 Let's Calculate Average Value for f(x) = x² [2,5] 4:46 Mean Value Theorem for Integrate 9:25 Example I: Find the Average Value of the Given Function Over the Given Interval 14:06 Example II: Find the Average Value of the Given Function Over the Given Interval 18:25 Example III: Find the Number A Such that the Average Value of the Function f(x) = -4x² + 8x + 4 Equals 2 Over the Interval [-1,A] 24:04 Example IV: Find the Average Density of a Rod 27:47 Section 6: Techniques of Integration Integration by Parts 50m 32s Intro 0:00 Integration by Parts 0:08 The Product Rule for Differentiation 0:09 Integrating Both Sides Retains the Equality 0:52 Differential Notation 2:24 Example I: ∫ x cos x dx 5:41 Example II: ∫ x² sin(2x)dx 12:01 Example III: ∫ (e^x) cos x dx 18:19 Example IV: ∫ (sin^-1) (x) dx 23:42 Example V: ∫₁⁵ (lnx)² dx 28:25 Summary 32:31 Tabular Integration 35:08 Case 1 35:52 Example: ∫x³sinx dx 36:39 Case 2 40:28 Example: ∫e^(2x) sin 3x 41:14 Trigonometric Integrals I 24m 50s Intro 0:00 Example I: ∫ sin³ (x) dx 1:36 Example II: ∫ cos⁵(x)sin²(x)dx 4:36 Example III: ∫ sin⁴(x)dx 9:23 Summary for Evaluating Trigonometric Integrals of the Following Type: ∫ (sin^m) (x) (cos^p) (x) dx 15:59 #1: Power of sin is Odd 16:00 #2: Power of cos is Odd 16:41 #3: Powers of Both sin and cos are Odd 16:55 #4: Powers of Both sin and cos are Even 17:10 Example IV: ∫ tan⁴ (x) sec⁴ (x) dx 17:34 Example V: ∫ sec⁹(x) tan³(x) dx 20:55 Summary for Evaluating Trigonometric Integrals of the Following Type: ∫ (sec^m) (x) (tan^p) (x) dx 23:31 #1: Power of sec is Odd 23:32 #2: Power of tan is Odd 24:04 #3: Powers of sec is Odd and/or Power of tan is Even 24:18 Trigonometric Integrals II 22m 12s Intro 0:00 Trigonometric Integrals II 0:09 Recall: ∫tanx dx 0:10 Let's Find ∫secx dx 3:23 Example I: ∫ tan⁵ (x) dx 6:23 Example II: ∫ sec⁵ (x) dx 11:41 Summary: How to Deal with Integrals of Different Types 19:04 Identities to Deal with Integrals of Different Types 19:05 Example III: ∫cos(5x)sin(9x)dx 19:57 More Example Problems for Trigonometric Integrals 17m 22s Intro 0:00 Example I: ∫sin²(x)cos⁷(x)dx 0:14 Example II: ∫x sin²(x) dx 3:56 Example III: ∫csc⁴ (x/5)dx 8:39 Example IV: ∫( (1-tan²x)/(sec²x) ) dx 11:17 Example V: ∫ 1 / (sinx-1) dx 13:19 Integration by Partial Fractions I 55m 12s Intro 0:00 Integration by Partial Fractions I 0:11 Recall the Idea of Finding a Common Denominator 0:12 Decomposing a Rational Function to Its Partial Fractions 4:10 2 Types of Rational Function: Improper & Proper 5:16 Improper Rational Function 7:26 Improper Rational Function 7:27 Proper Rational Function 11:16 Proper Rational Function & Partial Fractions 11:17 Linear Factors 14:04 Irreducible Quadratic Factors 15:02 Case 1: G(x) is a Product of Distinct Linear Factors 17:10 Example I: Integration by Partial Fractions 20:33 Case 2: D(x) is a Product of Linear Factors 40:58 Example II: Integration by Partial Fractions 44:41 Integration by Partial Fractions II 42m 57s Intro 0:00 Case 3: D(x) Contains Irreducible Factors 0:09 Example I: Integration by Partial Fractions 5:19 Example II: Integration by Partial Fractions 16:22 Case 4: D(x) has Repeated Irreducible Quadratic Factors 27:30 Example III: Integration by Partial Fractions 30:19 Section 7: Differential Equations Introduction to Differential Equations 46m 37s Intro 0:00 Introduction to Differential Equations 0:09 Overview 0:10 Differential Equations Involving Derivatives of y(x) 2:08 Differential Equations Involving Derivatives of y(x) and Function of y(x) 3:23 Equations for an Unknown Number 6:28 What are These Differential Equations Saying? 10:30 Verifying that a Function is a Solution of the Differential Equation 13:00 Verifying that a Function is a Solution of the Differential Equation 13:01 Verify that y(x) = 4e^x + 3x² + 6x + e^π is a Solution of this Differential Equation 17:20 General Solution 22:00 Particular Solution 24:36 Initial Value Problem 27:42 Example I: Verify that a Family of Functions is a Solution of the Differential Equation 32:24 Example II: For What Values of K Does the Function Satisfy the Differential Equation 36:07 Example III: Verify the Solution and Solve the Initial Value Problem 39:47 Separation of Variables 28m 8s Intro 0:00 Separation of Variables 0:28 Separation of Variables 0:29 Example I: Solve the Following g Initial Value Problem 8:29 Example II: Solve the Following g Initial Value Problem 13:46 Example III: Find an Equation of the Curve 18:48 Population Growth: The Standard & Logistic Equations 51m 7s Intro 0:00 Standard Growth Model 0:30 Definition of the Standard/Natural Growth Model 0:31 Initial Conditions 8:00 The General Solution 9:16 Example I: Standard Growth Model 10:45 Logistic Growth Model 18:33 Logistic Growth Model 18:34 Solving the Initial Value Problem 25:21 What Happens When t → ∞ 36:42 Example II: Solve the Following g Initial Value Problem 41:50 Relative Growth Rate 46:56 Relative Growth Rate 46:57 Relative Growth Rate Version for the Standard model 49:04 Slope Fields 24m 37s Intro 0:00 Slope Fields 0:35 Slope Fields 0:36 Graphing the Slope Fields, Part 1 11:12 Graphing the Slope Fields, Part 2 15:37 Graphing the Slope Fields, Part 3 17:25 Steps to Solving Slope Field Problems 20:24 Example I: Draw or Generate the Slope Field of the Differential Equation y'=x cos y 22:38 Section 8: AP Practic Exam AP Practice Exam: Section 1, Part A No Calculator 45m 29s Intro 0:00 Exam Link 0:10 Problem #1 1:26 Problem #2 2:52 Problem #3 4:42 Problem #4 7:03 Problem #5 10:01 Problem #6 13:49 Problem #7 15:16 Problem #8 19:06 Problem #9 23:10 Problem #10 28:10 Problem #11 31:30 Problem #12 33:53 Problem #13 37:45 Problem #14 41:17 AP Practice Exam: Section 1, Part A No Calculator, cont. 41m 55s Intro 0:00 Problem #15 0:22 Problem #16 3:10 Problem #17 5:30 Problem #18 8:03 Problem #19 9:53 Problem #20 14:51 Problem #21 17:30 Problem #22 22:12 Problem #23 25:48 Problem #24 29:57 Problem #25 33:35 Problem #26 35:57 Problem #27 37:57 Problem #28 40:04 AP Practice Exam: Section I, Part B Calculator Allowed 58m 47s Intro 0:00 Problem #1 1:22 Problem #2 4:55 Problem #3 10:49 Problem #4 13:05 Problem #5 14:54 Problem #6 17:25 Problem #7 18:39 Problem #8 20:27 Problem #9 26:48 Problem #10 28:23 Problem #11 34:03 Problem #12 36:25 Problem #13 39:52 Problem #14 43:12 Problem #15 47:18 Problem #16 50:41 Problem #17 56:38 AP Practice Exam: Section II, Part A Calculator Allowed 25m 40s Intro 0:00 Problem #1: Part A 1:14 Problem #1: Part B 4:46 Problem #1: Part C 8:00 Problem #2: Part A 12:24 Problem #2: Part B 16:51 Problem #2: Part C 17:17 Problem #3: Part A 18:16 Problem #3: Part B 19:54 Problem #3: Part C 21:44 Problem #3: Part D 22:57 AP Practice Exam: Section II, Part B No Calculator 31m 20s Intro 0:00 Problem #4: Part A 1:35 Problem #4: Part B 5:54 Problem #4: Part C 8:50 Problem #4: Part D 9:40 Problem #5: Part A 11:26 Problem #5: Part B 13:11 Problem #5: Part C 15:07 Problem #5: Part D 19:57 Problem #6: Part A 22:01 Problem #6: Part B 25:34 Problem #6: Part C 28:54 Loading... This is a quick preview of the lesson. For full access, please Log In or Sign up. For more information, please see full course syllabus of AP Calculus AB Bookmark & Share Embed ## Copy & Paste this embed code into your website’s HTML Please ensure that your website editor is in text mode when you paste the code. (In Wordpress, the mode button is on the top right corner.) × • - Allow users to view the embedded video in full-size. Since this lesson is not free, only the preview will appear on your website. • ## Transcription Lecture Comments (3) 0 answersPost by Michael Yang on January 7 at 04:08:15 PMCan I use langrange multipliers to solve the first example too? 1 answerLast reply by: Professor HovasapianFri Dec 8, 2017 11:38 PMPost by Maya Balaji on November 11, 2017Hello Professor. For question 1- I'm not sure why you would check the endpoints of the domain (variable at 0, volume at 0) to see if they are plausible absolute maximums, because technically this domain is not a closed interval. The volume can never be 0, and the length can never be 0- so these would not be included in the domain- so it would not be a closed interval, correct?- and you must only check endpoints if it is a part of a closed interval (please correct me if this isn't true!). Thank you. ### Optimization Problems I Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. • Intro 0:00 • Example I: Find the Dimensions of the Box that Gives the Greatest Volume 1:23 • Fundamentals of Optimization Problems 18:08 • Fundamental #1 • Fundamental #2 • Fundamental #3 • Fundamental #4 • Fundamental #5 • Fundamental #6 • Example II: Demonstrate that of All Rectangles with a Given Perimeter, the One with the Largest Area is a Square 24:36 • Example III: Find the Points on the Ellipse 9x² + y² = 9 Farthest Away from the Point (1,0) 35:13 • Example IV: Find the Dimensions of the Rectangle of Largest Area that can be Inscribed in a Circle of Given Radius R 43:10 ### Transcription: Optimization Problems I Hello, welcome back to www.educator.com, and welcome back to AP Calculus.0000 Today, we are going to start talking about optimization and optimization problems,0004 otherwise referred to as maxima and minima with practical application.0010 We have talked about maxima and minima in terms of just functions themselves.0015 Now we are going to apply them to real life situations.0019 There is going to be some quantity that we are going to want to maximize or minimize.0023 In other words, optimize, how to make it the best for our particular situation.0029 The calculus of these problems is actually very simple.0037 Essentially, what you are doing is just taking the first derivative.0040 You are setting it equal to 0 and you are solving.0042 The difficulty with these problems is putting all of this information into an equation.0045 It is the normal problems that people had with word problems, ever since we are introduced to word problems.0054 In any case, let us just jump right on in.0063 What I’m going to do is the first problem, I’m just going to launch right into it so that you get a sense of what it is.0066 I’m going to quickly discuss what is necessary for these problems, and then we are just going to do more.0071 The only way to make sense of them is to do as many problems as possible.0076 This is going to be the first of those lessons.0080 This problem says, if 1400 m² is available to make a box with a square base and no top,0086 find the dimensions of the box that gives the greatest volume.0094 I think I’m going to do this in blue again.0102 Probably, the most important thing to do with all of these optimization problems is draw a picture.0106 Always draw a picture.0112 99% of the time you really need to just draw a picture.0117 Let us see what this is asking.0120 I have got myself a box, let me go ahead and draw a little box here.0122 It is telling me that this box has no top.0133 I want to find the dimensions of the box that gives the greatest volume and also tells me that it has a square base.0137 Therefore, I’m going to call this x, I’m going to call this x.0143 It says nothing about the height, I’m just going to call this h.0146 Find the dimensions of the box that gives the greatest volume.0153 The thing that we are trying to maximize is the volume.0156 All of these problems will always be the same.0159 They are going to ask for some quantity that is maximized or minimized.0161 They are going to give you other information that relates to the problem.0166 The first thing you want to do is find just the general equation for what is being maximized.0170 In this case, it is the volume, greatest volume.0175 What we want to do is, volume, I know here is going to be x² × h.0180 We want to maximize that.0185 When you maximize or minimize something, you are finding the places where the derivative is equal to 0.0189 Once you have an equation, you are going to take the derivative of that equation, set it equal to 0, and solve for x.0195 The problem arises, notice that this is a function of two variables.0200 We cannot do that, this is a single variable calculus.0204 We need to find a way to convert this equation into an equation and just one variable, either h or x.0208 That is going to be our task.0215 This is where the problems tend to get more complicated.0217 Let us see what we can, let us write all of this out.0221 We want to maximize v but it is a function of two variables, mainly x and h.0224 Now we use the other information in the problem to establish a relation between these two variables,0254 so that I can solve for one of those variables.0260 Plug into this one and turn it into a function of one variable, that is essentially all of these problems are like that.0263 There is other information in the problem0272 that allows us to establish a relation between x and h, and that is this.0286 They are telling me that I have a total of 1400 m² total, that means the base, the area of the base, and the 4 sides.0311 The base, this side, this side, that side, and that side, let us write that out0323 The area of the base is going to be x².0329 The area of one of these side panels is going to be xh.0334 There are 4 of them, + 4 xh.0337 The sum of those has to be 1400.0342 That is it, we have a second equation, it relates x and h.0346 Let us solve for either x or h and put it in, not a problem at all.0349 What I'm going to do is I'm going to go ahead and solve for h.0355 4 xh = 1400 - x².0358 Therefore, h = 1400 - x²/ 4x.0364 We put this, we put this h into there, and we turn it into a function of one variable x which we can solve.0381 We put this h into v = x² h to get an equation in one variable.0399 In this case, I chose x.0418 Let us go ahead and do that.0425 We have v is equal to x² × h which is 1400 - x²/ 4x.0428 Cancel that, cancel that, multiply through.0444 We end up with 1400 x – x³/ 4.0448 If you want, you can rewrite it as –x³/ 4 + 350x.0458 It is totally up to you how you want to do it.0467 But now I have my equation, I have my v.0469 Now the volume of this box is expressed as a function of a single variable.0479 We know that a function achieves its absolute max or min, in this case, we are talking about a max,0489 I’m just going to leave it as maximum.0515 It achieves its absolute max either at an endpoint of the domain or somewhere in between where the derivative is 0.0518 In other words, a local max/local min.0527 We know that a function achieves its absolute max either at the endpoints of its domain or where f’ is equal to 0.0529 We differentiate this function now.0556 This is the equation of volume, we want to maximize this equation.0562 In order to maximize it, we are going to take the derivative of it, set it equal to 0,0566 and find the places where it either hits a maximum or a minimum.0570 Vx is a function of x is equal to 350x – x³/ 4.0577 V’(x) = 350 - ¾ x².0591 I’m going to set that equal to 0.0598 I have got ¾ x² is equal to 350.0601 When I solve this, I get x² = 1400/3 which gives me x is equal to + or -21.6.0608 We are talking about a distance.0627 Clearly, the negative is not going to be one of the solutions.0628 It is the +21.6 that is going to be the solutions.0632 Let us go over to the next page.0642 First of all, x is a physical length.0644 The -21.6 is not an option.0657 Second, if you rather not think about it physically and have to decide which value that you are going to take, there is another way of doing it.0668 If you prefer a more systematic or analytical approach0680 to excluding a given root or a given possibility, you can do it this way.0702 We said that v(x) is equal to -3/ 4 x³ + 350x.0716 That was the function that we want.0732 That was our original function, -x³.0740 Let me write this again.0747 We said that we had –x³/ 4 + 350x.0752 I will write it this way.0763 I know that when I graph this, I'm looking at this, and this is a cubic function.0765 This is a cubic function and the coefficient of -1/4, the leading coefficient is negative.0772 A normal cubic function begins up here, has two turns and ends down here.0779 This is negative, negative begins up here and ends down here.0790 I already took the derivative and I found that -21.6 and +21.6 are places0804 where it hits a local max or local min because I set the derivative equal to 0.0808 Therefore, I know that -21.6, there is all local min.0814 +21.6, there is a local max.0820 In this particular case, I also know that when x is equal to 0, the function is equal to 0.0823 I know it crosses here.0829 Therefore, I know for a fact that the thing goes like this.0830 Therefore, the maximum is achieved at +21.6.0836 The minimum of the function is achieved at -21.6.0841 We can also use our physical intuition to say that you cannot have, like we did for the first part,0845 like we did for our first consideration, right here.0850 It is a physical length.0853 This is the part of the graph that I'm concerned with.0856 As x gets bigger, there is a certain value of x which happens to be 21.6 where the function –x³/ 4 + 350x is maximized.0859 They gave us the greatest volume.0871 You want to use all the resources at your disposal, if you are dealing with a function.0873 You know what a cubic function looks like, where the negative over the leading coefficient is negative, it looks like this.0877 This tells you systematically, analytically, that -21.6 is not your solution.0885 Not to mention the fact that it physically makes no sense.0891 There are many things that you want to consider.0894 You do not just want to do the calculus.0896 Whatever you get, you want to stop and think about if the calculus makes sense.0899 Does your -21.6, does your +21.6 actually makes sense?0904 It does, based on other things that you need to consider.0909 Let us see, where are we, we are not done yet.0916 Let us go ahead.0922 We know that x = 21.6, that is the dimension of our base.0928 For h, h is equal to 1400 - x²/ 4x which is equal to 1400 - 21.6²/ 4 × 21.6.0934 When we do the calculation, we get xh = 10.8.0957 There you go, our box is 21.6 by 21.6 by 10.8.0963 Our unit happens to be in centimeters.0975 There you go, that is it, nice and simple.0978 Let us go ahead and actually show you the particular graph.0983 This is the graph of the function, volume function.0987 This is volume = 1400x – x³/ 4.0992 21.6 is right about there, that is our maximum point.1006 This was the function that we wanted to maximize.1011 In this particular case , we have a certain restriction on the domain.1014 This right here, that is the particular domain of this function.1019 The smallest that x can be is 0, no length.1026 The biggest that x can be is whatever that happens to be, when you set this equal to 0.1030 It turns out that x is equal to about 37.4, that is the other root of this equation.1037 That is the other 0 of that equation so that give us a natural domain.1044 In other words, if x = 0, there is no box.1048 If x = 37.4, there is no box.1052 Between 0 and 37.4, for a value of x, which is the base of the box, x by x, the volume goes up and comes down.1055 There is some x value that maximizes the volume.1067 That x is the 21.6 that we found, local maximum of this function.1070 Again, you can use the graph to help you out to find your domain, to restrict your domain, whatever it is that you need.1077 Let us talk about this a little bit.1087 All optimization problems are fundamentally the same.1089 There is a quantity that is asked to be maximized or minimized.1116 It might be an area, might be a volume.1143 It might be a distance, it might be an angle, whatever it is.1145 There are some quantity that is maximized or minimized.1150 Two, your task is to find a general equation for that quantity, for this quantity.1153 Number 3, if the equation that you get in part 2, if the equation is a function of more than one variable,1172 you use other information in the problem + any other mathematical manipulation you need1197 to find a relation between or among the variables.1236 I say among because you might end up with a general equation that has 3 or 4 variables.1250 And you have to find the relationship among all 3 or 4, not just between the two.1255 Part 4, you use the relations above among the variables1263 to express the desired quantity as a function of one variable, if possible.1285 Again, there might be situations where, we will do when we come up with them, not a problem.1308 I know the thing that you might want to do, this is a little looser but it is always a good idea to do this, if you need to.1317 A lot of this will come up with more experiences in solving these kind of problems.1323 You want to find the domain of the equation.1328 The reason you want to find the domain is,1335 Remember, what we are find here is absolute maximum of a function.1339 The absolute maximum of a function can happen within the domain, at places where it is a local max or min.1344 That is where you set the function, the derivative of a function equal to 0.1349 But you also have to consider the endpoints.1352 If you know the domain, if a domain is a closed interval, like it was in the first problem, 0 and 37.4,1355 you are still going to check those points to see if the value of the function that you get is going to be greater.1363 Because we want to find the absolute maximum.1370 Let us say there were two points in an interval, in the domain.1374 Let us go back to the first problem.1380 You had, 0 you have a 21.6, and you have a 37.4.1381 The 21.6 is the answer but you still have to technically check the 0 and the 37.4.1386 Put those values of x into the original equation.1392 You are going to get 0 for the value of the function.1395 When you put 21.6 in, you are actually going to get a number that is the biggest one among the three.1399 You remember when we were doing absolute maxes and absolute mins,1406 we have to check the values at the endpoints to see if maybe f of those values was actually bigger than what it is at a local max or min.1409 Again, the problems will help make more sense of this.1420 And then, once you have all of this information, you find the absolute max or min.1426 You find the absolute max or min.1434 If your domain is not a closed interval, that does not matter.1439 All you need to do is look for the local maxes and mins.1443 That is where you are going to pick one of those to maximize or minimize, whichever is it that you are trying to do.1446 Again, if you have a closed interval, you have to check the end points of the domain.1452 Most important, draw a picture always.1458 Always draw a picture.1471 Let us do some more examples here.1475 Demonstrate that of all rectangles with a given perimeter, the one with the largest area is a square.1477 Pick a random rectangle.1487 I’m going to call this x, I’m going to call this y.1491 In short, demonstrate that the one with the largest area is a square.1496 In short, we must show that y is equal to x, that it is a square.1502 Of all rectangles with a given perimeter.1520 The perimeter, that equals 2x + 2y, and they say of a given perimeter, some constant 5, 10, 20, 30, 86.6, whatever.1523 I'm just going to say c, c stands for a constant.1536 One of the largest area is a square.1540 The general equation for area is xy.1544 The largest area, that is the one they want us to maximize right here.1548 Largest area means maximize this, maximize this.1554 It is a function of two variables.1570 It is a function of two variables, I need a relationship between those two variables x and y,1573 in order for me to turn this into a function of one variable.1577 I have a relationship, that is my relationship right there.1582 I’m going to solve for y and plug it into this equation right over here.1585 I’m going to write 2y = c - 2x.1589 I have y = c - 2x/ 2.1595 I’m going to put this into here.1603 I get the area = c/2 – x.1608 I get the area = cx/2 – x².1622 This is my function, that is the function.1628 Now it is a function, I’m trying to maximize it.1634 I now have the area expressed as a function of one variable, x and x².1636 It is taken into account the perimeter.1641 The c, that is where that comes in.1643 Now I have to differentiate.1646 A’ is equal to c/2 - 2x, I set that equal to 0.1648 When I solve for this, I get 2x = c/2 which implies that x = c/4.1656 I found what x has to be.1673 Let us find y.1678 We said that y is equal to c/2 – x, that is equal to c/2 – c/4.1686 C/2 – c/4, it is equal to c/4.1697 Y does equal x which equals c/4.1705 I have demonstrated that, in order to maximize an area of a given rectangle.1710 I have maximized it by finding the derivative of the function of the area.1716 Found the value of x, it turns out that it has to be a square.1721 For a fixed perimeter, the sides have to be the perimeter divided by 4.1725 That is it, square.1730 I have demonstrated what is it that I set out to demonstrate.1733 Let us see here.1740 Notice that I did not explicitly specify a domain.1745 Let us tighten this up a little bit and talk about the domain.1773 Let us tight this up and discuss domain.1781 For a rectangle with a given perimeter c, the domain 0 to c/2.1790 The domain is what the x value can be.1824 If x = 0, if I take the endpoint x = 0.1826 Then, 2 × 0 + 2y is equal to c.1834 2y is equal to c, y = c/2.1847 The area is equal to x × y, that is equal to 0 × c/2, the area is 0.1856 That is this endpoint.1872 If x = c/2, then the perimeter 2 × c/2 + 2y which is equal to c, we get c + 2y = c.1879 We get 2y = 0, we get y = 0.1900 The area equals xy which equals c/2 × 0.1904 Again, the area = 0, our domain is this.1909 X cannot go past c/2 because we already set that the perimeter has to be c.1917 If you have a rectangle where this is c/2 and this is c/2, basically what you have is just a line because there is no y.1926 X, our domain, has to be between 0 and c/2.1943 When we check the endpoints, we got a value of 0.1947 C/4 is in the domain and it happens to be the local max.1952 When you put c/4 into this, you are actually going to get an area that is a number.1957 We know that that number is the maximum, precisely because of how we did it.1973 We took the derivative, we set it equal to 0, and that is what happened.1978 Let us go ahead and actually take a look at this.1984 In both cases, let me actually draw it out.1987 In both cases that we just did for the endpoints, the area was equal to 0.1993 Between 0 and c/2, there is a number such that a is maximized.2005 That number was c/4.2024 What did we say our function was, our a’, our a?2029 We said that our area function of x was equal to -x² + cx/2.2034 This is a quadratic function where the leading coefficient is negative.2041 I know that the graph goes like this.2047 I know that there are some point where I’m going to hit a maximum, that is what is going on here.2049 This is my 0, this is my c/2.2055 Let us see what this actually looks like.2058 I have entered the function cx/2 - x².2061 I have taken a particular value of c = 15.2064 I end up with this graph.2068 Notice 0, c/2, 15/2 is 7.5, that 7.5.2069 This right here, this is c/2, this is c/4.2077 That is why I hit my max.2080 This is the function that I’m maximizing.2082 It happens to be the quadratic function where the leading coefficient is negative.2086 Therefore, I know that this is the shape.2090 If I do not know it, let me use a graphical utility to help me out.2092 If I need a graphical utility to help me get the domain, that is fine.2095 I do not necessarily need this, I already know that if my perimeter is c, the most that any one side can be is c/2.2099 Therefore, my domain is 0 to c/2, hope that makes sense.2107 Let us see what we have got here.2115 What is our next one?2119 Find the points on the ellipse 9x² + y² = 9, farthest away from the point 1,0.2120 Let us go ahead and draw this out.2130 I got myself an ellipse.2134 I have got 9x² + y² = 9 x²/ 1² + y²/ 3² is equal to 1.2141 I have got, this is 1, this is 1, this is 1, 2, 3, 1, 2, 3.2158 I have an ellipse that looks like this.2166 Find the points on the ellipse farthest away from the point 1,0.2172 Here is my point 1,0, I need to find the points on the ellipse that are the farthest away from this.2176 Just eyeballing it, I’m guessing it is somewhere around here.2181 We will try to maximize this distance right here.2187 We want to maximize the distance from the point 1,0 to some random point xy on the ellipse, that satisfies this equation.2194 We know we are going to have two answers.2220 We already know that.2222 This is going to be xy1, xy2.2225 Probably you are going to have the same value of x, different values of y.2228 We want to maximize the distance, the distance formula.2233 The distance formula = x2 - x1² + y2 - y1², all under the radical sign.2239 Let me put it in.2252 I have x - 1² - y - 0².2253 This is going to give me x - 1² + y², all under the radical.2270 Let us move on to the next one.2282 I have got d is equal to, I expand the x - 1².2285 I get x² - 2x + 1 + y², all under the radical.2290 I know that 9x² + y² = 9.2300 Therefore, y² = 9 - x².2305 I put that into here, I find my d is equal to x² - 2x + 1 + 9 - 9x².2310 Therefore, I get d = -8x² - 2x + 10.2326 This is my distance function expressed as a single variable x.2337 This is what I want to maximize.2341 Maximize this, we maximize it, we take the derivative and set it equal to 0.2346 D’(x) that is going to equal ½ of -8x² - 2x + 10⁻¹/2 × the derivative of what is inside which is -16x -2.2354 D’(x), when I rearrange this, I get -8x – 1/ √-8x² – 2x + 10.2376 I set that equal to 0.2393 What I get is -8x - 1 = 0.2396 When I solve this, I get 8x = -1, x = -1/8.2400 I have found my x, my x value is -1/8.2410 Now I need to find my y so that I can find what the two points are.2414 I know that the function was 9x² + y² = 9.2424 I’m going to go 9 × -1/8² + y² = 9.2431 I get 9/64 + y² = 9, that gives me y² = 9 - 9/64.2441 I get y² = 567/64.2457 Then, I get y = + or -567/64 that equals + or -2.97.2465 Therefore, I have -1/8 - 2.97, that is one point, I have -1/8 and 0.97.2486 These two points are the points that are on the ellipse, farthest away from the point 1,0.2501 Once again, I have an ellipse, this is 1,0.2510 The points are here and they are here.2516 Those are the points that are farthest away from that.2518 This is the function that we have to maximize.2526 This graph, this is not the ellipse.2528 This is the function we have to maximize.2531 This is the -8x² - 2x + 10, under the radical.2535 This is the function that we maximized.2542 It happens to hit a maximum at -1/8.2545 Be careful, this is not the ellipse, this is the function that you end up deriving, that you needed to maximize.2554 We needed to maximize the distance.2563 It actually gives me the x value.2567 Once I have the x value, I put it back into the original equation for the ellipse to find out where the y values are for the ellipse.2570 There are a lot to keep track of.2579 My best advice with all of math and science is go slowly, that is all.2582 Let us do one last example here.2590 Find the dimensions of the rectangle of the largest area.2592 We are going to be maximizing area, know that already.2595 That can be inscribed in a circle of a given radius r.2598 Let us draw it out.2602 We have a circle and we are going to try to inscribe some random rectangle in it.2604 Probably, not going be the best drawing in the world, sorry about that.2612 It tells me that the radius is r.2614 We are going to maximize area.2620 I’m going to call this x, and I’m going to call this side y, of the rectangle.2622 Area is equal to x × y.2627 We have our general equation, we want to maximize this.2631 I have two variables, I need to find the function of one variable.2639 I have to find the relationship between x and y.2642 I have a relationship between x and y.2645 If I draw this little triangle here, this side is y divided by 2 and this side is x/2.2648 Therefore, I have by the Pythagorean theorem, x/ 2² + y/ 2² = r².2663 I have got x²/ 4 + y²/ 4 = r² which gives me x² + y² = 4r²,2674 which gives me y² = 4r² - x², which gives me a y equal to √4r² - x².2688 This is what I plug into here, to this.2701 Therefore, I get an area which is equal to x × 4r² - x².2706 Now I have a function of one variable.2716 Take the derivative and set it equal to 0.2719 A’(x) is equal to this × the derivative of that, x × ½ of 4r² – x²⁻¹/2 × the derivative of what is inside.2722 4r² is just a constant at 0.2737 It is only -2x + that × the derivative of that.2740 We get just 4r² - x² × 1.2745 I rearranged this to get, 2 and 2 cancel, -x².2752 I get -x²/ 4r² - x², under the radical, +√4r² - x².2762 Then, I find myself a nice common denominator.2777 I end up with a’(x) is equal to -x² + 4r².2779 I hope the algebra is not giving you guys any grief.2788 I just found the common denominator, over √4r² - x².2792 This is the derivative we said is equal to 0.2797 When we set it equal to 0, I have the top -x² - x².2801 I end up with a’(x) =, this is 0 so the denominator goes away.2806 I’m left with -2x² + 4r² = 0.2812 2x² = 4r², x² = 2r².2820 Therefore, x is equal to r√2.2829 Again, I take the positive because I’m talking about a distance here.2836 X = r√2.2842 We know what y is, we said that y is equal to √4r² - x² which is equal to 4r² - r√2²,2844 all under the radical, which is equal to 4r² - 2r², all under the radical.2858 That equals √2r² which is equal to r√2.2869 Y is also equal to r√2.2878 Again, I will just say y is equal to x.2891 In other words, the rectangle of largest area that you can describe in a circle is a square,2899 where the sides of the square are equal to the radius of the circle × √2.2908 That is what we have found.2914 Let us go ahead and show you what it looks like.2919 I have the function, the area function that I try to maximize.2922 √4r² - x².2926 I picked a particular value of r radius of the circle happens to equal 2.2931 This is the function.2935 Again, x is the physical distance, really, our domain is here and here.2938 I set the function equal to 0 to find the end points.2946 When I check the endpoints, when I put the endpoints into the area function, I'm going to get an area of 0.2949 0 does not work, 0 does not work.2955 However, there is a point someplace here.2957 What we found is r√2.2960 When I put r√2 into the function for area, I end up getting the largest area.2964 This graph confirms it.2974 The maximum of this graph, the maximum of the area function happens at √2.2975 It happens where the derivative of this function = 0.2981 I hope that helped.2987 Do not worry about it, in the next lesson we are going to be continuing to do more optimization problems,2988 more complicated optimization problems.2993 Thank you so much for joining us here at www.educator.com.2995 We will see you next time, bye.2998 Please sign in to participate in this lecture discussion. 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http://stats.stackexchange.com/questions/15745/metric-for-probability-based-classification	Metric for probability based classification I am doing a system for classifiying documents. The project demands the use of probability based output. So a sample will have a probability for belonging to each class. For now I use logistic regression, but this could be subject to change. So I don't want to do an R^2 approximation. I also don't want to use standard metrics for classification like F-measure because it doesn't work with probabiliies. I have no idea what is the custom metric in this situation. Any ideas? - There are actually two things to evaluate on probability:probability-based ranking performance and probability estimation performance. Common evaluation methods for probability-based ranking is the Area Under ROC curve (AUROC). This measure has been developed to 2-class problems but can also be extended to multi-class problems, for examle have a look to [1] in order to understand ROC analysis; but there are easier methods to calculate ROC curve, see [2] related to Probability Estimation Trees (PETs). Similarly, Brier Score, also known as Mean Square Error, is suited to evaluate the probability estimation accuracy performance. It has been shown that the Brier Score can be decomposed in Calibration and Refinement [3]. These measures are suited for PETs, but you can reproduce them discretizing your probability into buckets. The Calibration component captures how well the PET represents the true distribution of the data; while Refinement component captures how much the model discriminate between classes. In particular, the Calibration measure has an intuitive graphical interpretation as the Reliability Plot, which shows record subset probabilities on the training data and the corresponding probabilities on the test data. Refinement measure has its graphical transposition too, called Sharpness Histogram. See [4] for 2-class problems, in the firsts paragraphs Brier Score, Calibration and Refinement are introduced. They also use Negative Cross Entropy, that is similar to Brier Score. I think it should be easy to find estension for multi-class problems. [1] T. Fawcett, \An introduction to roc analysis," Pattern Recogn. Lett., vol. 27, no. 8, pp. 861{874, 2006. [2] N. Chu, L. Ma, P. Liu, Y. Hu, and M. Zhou, \A comparative analysis of methods for probability estimation tree," W. Trans. on Comp., vol. 10, pp. 71{80, March 2011. [3] G. Blattenberger and F. Lad, \Separating the Brier score into calibration and refinement components: A graphical exposition," vol. 39, pp. 26{32, 1985. [4] K. Zhang, W. Fan, B. Buckles, X. Yuan, and Z. Xu, \Discovering unrevealed properties of probability estimation trees: On algorithm selection and performance explanation," Data Mining, IEEE International Conference on, vol. 0, pp. 741{752, 2006. - The classic error metric for probabilistic classifiers is the cross-entropy, for a two class classifier it is $L = -\sum_{i=1}^n t_i\log(y_i) + (1-t_i)\log(1-y_i)$ where there are n test patterns, $t_i \in [0,1]$ is the target for the $i^{th}$ test pattern and $y_i$ is the outoput of the model for the $i^{th}$ test pattern. The cross-entropy is the negative log-likelihood used in fitting a logistic regression model (or kernel logistic regression or neural networks etc.) so it is fairly natural to use it as the test metric as well. Unlike the AUROC it takes the calibration of the probabilities into account rather than just the ranking (which may or may not be important depending on the application), but it goes off to infinity if the classifier gets the answer wrong with very high confidence. A closely related metric is the mean predictive information, which for a two class problem is $I = \frac{1}{n}\sum_{i=1}^n\left[t_i.log_2(y_i) + (1-t_i).log_2(1-y_i)\right]+1$ which is very similar, but conveniently gives result that normally lies between 0 and 1 bits, which is more easily interpretable than the cross-entropy -	{"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": 0.8640225529670715, "perplexity": 1424.164022548226}, "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-2013-48/segments/1386163036037/warc/CC-MAIN-20131204131716-00087-ip-10-33-133-15.ec2.internal.warc.gz"}
https://physexams.com/blog/Superposition-principle_5	Blog & News Electrostatic # Superposition principle The net electric field or force of a group of point charges at each point in space is the vector sum of the electric fields due to the individual charges at that point. in the mathematical form is written as ${\vec{E}}_{net}={\vec{E}}_1+{\vec{E}}_2+\dots +{\vec{E}}_n$	{"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": 0.8846173286437988, "perplexity": 146.5119653183623}, "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-2020-40/segments/1600400205950.35/warc/CC-MAIN-20200922094539-20200922124539-00230.warc.gz"}
https://www.linstitute.net/archives/700789	# AQA A Level Maths: Statistics复习笔记4.3.3 Standard Normal Distribution ### Standard Normal Distribution #### What is the standard normal distribution? • The standard normal distribution is a normal distribution where the mean is 0 and the standard deviation is 1 • It is denoted by Z #### Why is the standard normal distribution important? • Any normal distribution curve can be transformed to the standard normal distribution curve by a horizontal translation and a horizontal stretch • Therefore we have the relationship: ### Finding Sigma and Mu #### How do I find the mean (μ) or the standard deviation (σ) if one of them is unknown? You will be given x and one of the parameters (μ or σ) in the question • You will have calculated z in STEP 2 • STEP 4: Solve the equation #### How do I find the mean (μ) and the standard deviation (σ) if both of them are unknown? • If both of them are unknown then you will be given two probabilities for two specific values of x • The process is the same as above • You will now be able to calculate two z-values #### Worked Example It is known that the times, in minutes, taken by students at a school to eat their lunch can be modelled using a normal distribution with standard deviation 4 minutes. Given that 10% of students at the school take less than 12 minutes to eat their lunch, find the mean time taken by the students at the school. #### Exam Tip • These questions are normally given in context so make sure you identify the key words in the question. Check whether your z-values are positive or negative and be careful with signs when rearranging.	{"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": 0.945034921169281, "perplexity": 910.8715045358265}, "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/1664030337432.78/warc/CC-MAIN-20221003200326-20221003230326-00271.warc.gz"}
https://mathoverflow.net/questions/203979/could-we-extend-the-exact-sequence-k0x-to-k-0x-to-k-0d-sgx-to-0-to	# Could we extend the exact sequence $K^0(X)\to K_0(X)\to K_0(D_{sg}(X))\to 0$ to the left? Let $X$ be a variety over a field $k$. We have the bounded derived category of coherent sheaves $D^b_{coh}(X)$ and the derived category of perfect complex $Perf(X)$. It is clear that $Perf(X)$ is a strictly full triangulated subcategory of $D^b_{coh}(X)$. Then following Orlov 2003 we define the triangulated category of singularities of $X$ as the quotient of $D^b_{coh}(X)$ and $Perf(X)$, i.e. $$D_{sg}(X)=D^b_{coh}(X)/Perf(X).$$ Recall that we call $\mathcal{A}\to \mathcal{B}\to\mathcal{C}$ an exact sequence of triangulated categories if the composition sends $\mathcal{A}$ to zero, $\mathcal{A}\to \mathcal{B}$ is fully faithful and coincides (up to equivalence) with the subcategory of those objects in $\mathcal{B}$ which are zero in $\mathcal{C}$, and the induced functor $\mathcal{B}/\mathcal{A}\to \mathcal{C}$ is an equivalence. It is easy to verify that $$Perf(X)\to D^b_{coh}(X)\to D_{sg}(X)$$ is an exact sequence of triangulated categories. On the other hand we have the Grothendieck groups of the above triangulated categories. In more details we define $K^0(X)$ the Grothendieck groups of $Perf(X)$, $K_0(X)$ the Grothendieck groups of $D^b_{coh}(X)$, and $K_0( D_{sg}(X))$ the Grothendieck groups of $D_{sg}(X)$. Then from the exact sequence $Perf(X)\to D^b_{coh}(X)\to D_{sg}(X)$ we get an exact sequence of abelian groups $$K^0(X)\to K_0(X)\to K_0(D_{sg}(X))\to 0.$$ See Schlichting 2008 Exercise 3.1.6. We would like to extend the above exact sequence to the left, via higher algebraic K-theory. However, there is not higher K-theory on merely triangulated categories. Nevertheless we have $K^i(X)$ and $K_i(X)$ for $i\geq 1$ in the framework of complicial exact categories. $\textbf{My question}$ is: could we define the higher K-theory of $D_{sg}(X)$ and get a long exact sequence $$\ldots \to K^i(X)\to K_i(X)\to K_i(D_{sg}(X))\to K^{i-1}(X)\to \ldots ?$$ The exact sequence of triangulated categories $$Perf(X)\to D^b_{coh}(X)\to D_{sg}(X)$$ may be lifted to an exact sequence of stable $\infty$-categories or dg-categories in the sense of BGT: choose an enhancement of $D^b_{coh}(X)$, take the induced enhancement on the subcategory $Perf(X)$, and define $D_{sg}(X)$ to be the cofibre of the inclusion in the $\infty$-category of small stable $\infty$-categories. Algebraic K-theory can be defined at the level of stable $\infty$-categories, and it is an additive invariant in the sense of BGT (see Prop. 7.10 of loc. cit.); this means that it sends split exact sequences to (co)fibre sequences of spectra. Its nonconnective version $\mathbb{K}$ has the stronger property of being a localizing invariant, which means that it sends arbitrary exact sequences to cofibre sequences of spectra. Hence applying nonconnective K-theory to the exact sequence above, one gets a (co)fibre sequence of nonconnective K-theory spectra $$\mathbb{K}(Perf(X))\to \mathbb{K}(D^b_{coh}(X))\to \mathbb{K}(D_{sg}(X)).$$ The first term is identified with the Bass-Thomason-Trobaugh K-theory of $X$, and the second is nonconnective G-theory (nonconnective K-theory of the abelian category of coherent sheaves). These agree with their connective versions on nonnegative homotopy groups, so the induced long exact sequence on homotopy groups gives what you are looking for.	{"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": 0.9903173446655273, "perplexity": 150.23790218233606}, "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/1579251705142.94/warc/CC-MAIN-20200127174507-20200127204507-00368.warc.gz"}
http://www.jiskha.com/display.cgi?id=1275020881	Friday December 19, 2014 # Homework Help: Chemistry Posted by Jaden on Friday, May 28, 2010 at 12:28am. Assuming complete dissociation of the solute, how many grams of KNO3 must be added to 275 mL of water to produce a solution that freezes at -14.5 C? The freezing point for pure water is 0.0 C and Kf is equal to 1.86 C/m. * Use Tf = Kfim • Chemistry - bobpursley, Friday, May 28, 2010 at 8:27am i=2 m=gramsKNO3/(molmassKNO3*.275) find grams KNO3 from your fourmula. First Name: School Subject: Answer: Related Questions Chemistry - assuming complete dissociation of the solute, how many grams of KNO3... Chemistry - Assuming complete dissociation of the solute, how many grams of ... chemistry - assuming complete dissociation of the solute, how many grams of \rm ... Chemistry - Assuming complete dissociation of the solute, how many grams of KNO3... CHemistry....Please help - What mass of ethylene glycol C2H6O2, the main ... Chemistry - The vapor pressure of pure water at 90celsius is normally 525.8 but ... Chemistry - The vapor pressure of water at 95C is normally 6.33.9 but decreased ... chemistry - this is a really long question. i don't understand how to answer it... Chemistry - The vapor pressure of pure water at 85 celsius is normally 433.6 ... Chemistry: molality and freezing point? - What mass of ethylene glycol C2H6O2, ... Search Members	{"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": 0.8961848616600037, "perplexity": 3914.343407806341}, "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-2014-52/segments/1418802768741.99/warc/CC-MAIN-20141217075248-00090-ip-10-231-17-201.ec2.internal.warc.gz"}
https://hilbertthm90.wordpress.com/2009/09/09/what-i-talk-about-when-i-talk-about-orientation/	Old Standby 2: $\mathbb{R}P^n$ is orientable iff $n$ is odd. First note that the antipodal map $a:\mathbb{R}^{n+1}\to\mathbb{R}^{n+1}$ by $x\mapsto -x$ is orientation preserving if n is odd and orientation reversing if n is even just because in coordinates it is the matrix with $-1$‘s on the diagonal. Now if we make our natural identifications between $\mathbb{R}^{n+1}$ as a manifold and as the vector space that is tangent space at a given point, then we see that if we restrict $a$ to $S^n$ embedded in $\mathbb{R}^{n+1}$ the orientation preserving/reversing still holds. This is just because if $(v_1, \ldots, v_n)$ is an oriented basis at $p\in S^n$, then $(p, v_1, \ldots, v_n)$ is an oriented basis at that same point in $\mathbb{R}^{n+1}$. Thus the orientation at $-p$ of $a(p, v_1, \ldots , v_n)=(-p, -v_1, \ldots, -v_n)$ is $(-v_1, \ldots, -v_n)$. Now suppose that n is even and that $\mathbb{R}P^n$ has an orientation. Let $\pi: S^n\to\mathbb{R}P^n$ be the standard quotient map. But now the orientation of $\mathbb{R}P^n$ induces an orientation on $S^n$ by letting an ordered basis $(v_1, \ldots , v_n)\subset T_pS^n$ be positively oriented if $(d\pi_p(v_1), \ldots, d\pi_p(v_n))$ is positively oriented. But the induced map of $a$ on $\mathbb{R}P^n$ is just the identity. Thus $a$ is orientation preserving on $S^n$, a contradiction. The other direction we need to put an orientation on $\mathbb{R}P^n$ by $S^n$. Suppose n is odd now. Define a basis $(w_1, \ldots , w_n)\subset T_{\pi(p)}\mathbb{R}P^n$ to be positively if there exists a positively oriented basis $(v_1, \ldots , v_n)\subset T_pS^n$ such that $(d\pi_p(v_1), \ldots , d\pi_p(v_n))=(w_1, \ldots , w_n)$. We just need to make sure this is a well-defined choice. But it is since the fibers of $\pi(p)$ are $p$ and $-p$, and we get from one to the other through the antipodal map which is orientation preserving. So we’re done. Let’s do some analysis of this. First off, there was nothing special about this particular $\pi$. So we actually proved that if $\pi: N\to M$ is a smooth covering and $M$ is orientable, then $N$ is also orientable. I know of two other ways to prove this. Both require that antipodal map observation first. One way is to prove the more general fact that if $M$ is a connected, oriented, smooth manifold and $G$ is a discrete group acting smoothly, freely, and properly on M, then $M/G$ is orientable iff $x\mapsto g\cdot x$ is an orientation preserving diffeo for all $g\in G$. In this case, $G\{\pm 1\}$ and the 1 action is the identity and the $-1$ action is the antipodal map. The other way is far more elegant. It is the algebraic topology method (actually I believe you can prove the stronger statement of the second method using this way). I haven’t quite reworked this way out, yet, but it just involves pulling back nowhere vanishing n-forms or something.	{"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": 45, "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": 0.9736495018005371, "perplexity": 82.2787523191397}, "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-2018-30/segments/1531676590069.15/warc/CC-MAIN-20180718060927-20180718080927-00612.warc.gz"}
https://www.hydrol-earth-syst-sci.net/22/5741/2018/	Journal cover Journal topic Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union Journal topic Hydrol. Earth Syst. Sci., 22, 5741-5758, 2018 https://doi.org/10.5194/hess-22-5741-2018 Hydrol. Earth Syst. Sci., 22, 5741-5758, 2018 https://doi.org/10.5194/hess-22-5741-2018 Research article 08 Nov 2018 Research article \| 08 Nov 2018 Bias correction of simulated historical daily streamflow at ungauged locations by using independently estimated flow duration curves Bias correction of simulated streamflow William H. Farmer1, Thomas M. Over2, and Julie E. Kiang3 William H. Farmer et al. • 1US Geological Survey, Denver, Colorado, USA • 2US Geological Survey, Urbana, Illinois, USA • 3US Geological Survey, Reston, Virginia, USA Abstract In many simulations of historical daily streamflow distributional bias arising from the distributional properties of residuals has been noted. This bias often presents itself as an underestimation of high streamflow and an overestimation of low streamflow. Here, 1168 streamgages across the conterminous USA, having at least 14 complete water years of daily data between 1 October 1980 and 30 September 2013, are used to explore a method for rescaling simulated streamflow to correct the distributional bias. Based on an existing approach that separates the simulated streamflow into components of temporal structure and magnitude, the temporal structure is converted to simulated nonexceedance probabilities and the magnitudes are rescaled using an independently estimated flow duration curve (FDC) derived from regional regression. In this study, this method is applied to a pooled ordinary kriging simulation of daily streamflow coupled with FDCs estimated by regional regression on basin characteristics. The improvement in the representation of high and low streamflows is correlated with the accuracy and unbiasedness of the estimated FDC. The method is verified by using an idealized case; however, with the introduction of regionally regressed FDCs developed for this study, the method is only useful overall for the upper tails, which are more accurately and unbiasedly estimated than the lower tails. It remains for future work to determine how accurate the estimated FDCs need to be to be useful for bias correction without unduly reducing accuracy. In addition to its potential efficacy for distributional bias correction, this particular instance of the methodology also represents a generalization of nonlinear spatial interpolation of daily streamflow using FDCs. Rather than relying on single index stations, as is commonly done to reflect streamflow timing, this approach to simulation leverages geostatistical tools to allow a region of neighbors to reflect streamflow timing. 1 Introduction Simulation of historical daily streamflow at ungauged locations is one of the grand challenges of the hydrological sciences . Over the past 20 years, at least, research into simulation of historical streamflow has increased. In addition to ongoing international efforts, the US Geological Survey has embarked upon a National Water Census of the USA , which seeks to quantify hydrology across the country to provide information to help improve water use and security. However, regardless of the method used for the simulation, uncertainty will always remain and may result in some distributional bias . The objective of this work is to present a technique to correct for bias in the magnitudes of a streamflow simulation. While the mechanics of this technique are not novel, the novelty of this work lies in the generalization of this technique for use in bias correction. The method is intended for use at ungauged sites and an idealized experiment is constructed to demonstrate both the potential utility and one example of realized utility. As defined here, distributional bias in simulated streamflow is an error in reproducing the tails of streamflow distribution. As attested to by many researchers focused on the reproduction of historical streamflow, this bias commonly appears as a general overestimation of low streamflow and underestimation of high streamflow . The result is an effective squeezing of the streamflow distribution, bringing the tails of the distribution closer to the central values. This distributional squeezing is often most notable in the downward bias of extreme high-flow events (Lichty and Liscum1978; Sherwood1994; Thomas1982). Bias of high streamflows is particularly concerning, as examinations of extreme high-flow events are a common and influential use of historical simulation and long-term (decadal) forecast. Consider, for example, the motivation for work by : as simulated streamflows were being routed through a reservoir operations model for flood mitigation, large bias in high streamflows would have severely affected resulting decisions. Of course, this tendency towards distributional compaction is not a universal truth that occurs without variation; the resulting bias will vary widely depending on the structure of the residuals . Because of the importance of accurately representing extreme events, it is necessary to consider how the distributional bias of streamflow simulations can be reduced. The approach presented here assumes that, while the streamflow magnitudes of a historical simulation are biased, the temporal structure or rank order of simulated streamflows is relatively accurate. The nature of this approach is predicated on an assumption that although a historical simulation may produce a distribution of streamflow with biased tails, the temporal sequence of relative rankings or nonexceedance probabilities of the simulated streamflow retains valuable information. With this assumption, it can be hypothesized that distributional bias can be reduced, while not negatively impacting the overall performance, by applying a sufficiently accurate independently estimated representation of the period-of-record flow duration curve (FDC) to rescale each streamflow value based on the streamflow value of the regional FDC for the corresponding nonexceedance probabilities (see Sect. 2 below). The approach presented here can be perceived as a generalization of the nonlinear spatial interpolation of daily streamflow using FDCs as conceived by and and widely used thereafter . As traditionally applied, nonlinear spatial interpolation proceeds by simulating nonexceedance probabilities at a target location using a single neighboring streamgage (though , recommend and , test the use of multiple streamgages) and then interpolating those nonexceedance probabilities along a FDC. The approach tested here seeks to bias-correct a simulated time series of daily discharge using an independently estimated FDC, and, when viewed in another way, presents a novel form of nonlinear spatial interpolation. Furthermore, though necessarily explored in this study through the use of a single technique for hydrograph simulation, this approach may be a means to effectively bias-correct any simulation of streamflow, including those from rainfall–runoff models, as presented by . used a geostatistical tool to produce site-specific FDCs and then used this information to post-process simulated hydrographs from a deterministic model. Though the underlying methods of producing the FDC and simulated hydrograph are different, the approach proposed by is the same as that explored here. Further discussion of the relationship of the approach presented here to others in the field is provided below. The remainder of this work is organized in the following manner. Section 2 provides a description of the retrieval of observed streamflow, the estimation of simulated streamflows, the calculations of observed FDCs, the estimation of simulated FDCs, and the application and evaluation of the bias correction. Section 3 follows and it documents the bias in the original simulated streamflows and analyzes the potential bias correction that could be achieved if it were possible to know the observed FDC at an ungauged location and the bias correction that would be realized through an application of regional regression. Section 4 considers the implications of these results and hypothesizes how the methodology might be applied and improved. The major findings of this work are then summarized in Sect. 5. 2 Material and methods This section, which is divided into four subsections, provides a description of the methods applied here. The first subsection describes the collection of observed streamflow as well as the initial simulation of streamflow. As the approach used here is applicable to any simulated hydrograph, the details of hydrograph simulation are not exhaustively documented. Instead, beyond a brief introduction, the reader is directed to relevant citations, as no modifications to previous methods are introduced here. The second subsection discusses the use of regional regression to define independently estimated FDCs. Again, as any method for the estimation of FDCs could be used and this application is identical to previously reported applications, following a brief introduction, the reader is directed to the relevant citations. The third subsection provides a description of how bias correction was executed, and the fourth subsection describes how the performance of this approach to bias correction was assessed. Figure 1Map of the locations of 1168 reference quality streamgages from the GAGES-II database (Falcone2011) used for analysis. All streamgages used have more than 14 complete water years between 1 October 1980 and 30 September 2013. The outlines of two-digit hydrologic units, which define the regions used here, are provided for further context. 2.1 Observed and simulated streamflow The proposed approach was explored using daily mean streamflow data from the reference quality streamgages included in the GAGES-II database (Falcone2011) within the conterminous USA for the period from 1 October 1980 through 30 September 2013. To allow for the interpolation, rather than extrapolation, of all quantiles considered later, streamgages were screened to ensure that at least 14 complete water years (1 October through 30 September) were available for each record considered; 1168 such streamgages were available. The selected reference streamgages are indicated in Fig. 1. The streamflow data were obtained directly from the website of the National Water Information System (NWISWeb, http://waterdata.usgs.gov; last access: 20 September 2017). For each streamgage, associated basin characteristics were obtained from the GAGES-II database (Falcone2011). To control for streamflow distributions that vary over orders of magnitude, the simulation and analysis of streamflow at these streamgages is best explored through the applications of logarithms. To avoid the complication of taking the logarithm of a zero, a small value was added to each streamflow observation. The US Geological Survey rounds all mean daily streamflow to two decimal places in units of cubic feet per second (cfs, which can be converted to cubic meters per second using a factor of 0.0283). As a result, any value below 0.005 cfs is rounded to and reported as 0.00 cfs. Because of this rounding procedure, the small additive value applied here was 0.0049 cfs. While there may be some confounding effect produced by the use of an additive adjustment, as long as this value is not subtracted on back transformation, the following assessment of bias and bias correction will remain robust. That is, rather than evaluating bias in streamflow, technically this analysis is evaluating the bias in streamflow plus a correction factor. The conclusions remain valid as the assessment still evaluates the ability of a particular method to remove the bias in the simulation of a particular quantity. Though the potential for distributional bias applies to any hydrologic simulation , for this study, initial predictions of daily streamflow values for each streamgage were obtained by applying the pooled ordinary kriging approach (Farmer2016) to each two-digit hydrologic unit (Fig. 1) through a leave-one-out cross-validation procedure on the streamgages within the two-digit hydrologic unit. The hydrologic unit system is a common method for delineating watersheds in the USA. As described by , the two-digit hydrologic units, or regions (as seen in Fig. 1), roughly align with the major river basins of the USA. This approach considers all pairs of common logarithmically transformed unit streamflow (discharge per unit area) for each day and builds a single, time-invariant semivariogram model of cross-correlation that is then used to estimate ungauged streamflow as a weighted summation of all contemporary observations. A spherical semivariogram was used as the underlying model form. Additional information on the time series simulation procedure is provided by . Note that the choice of pooled ordinary kriging is only made as an example of a streamflow simulation method; it is not implied that the bias observed or methods applied are relevant only to this approach to simulation. Because the novelty of this work is in the application of bias correction, further details on the particular simulation method employed are left for the reader to investigate in the cited works (Farmer2016). 2.2 Estimation of flow duration curves Daily period-of-record FDCs were developed independently of the streamflow simulation procedure by following a regionalization procedure similar to that of and . Observed FDCs were obtained by determining the percentiles of the streamflow distribution across complete water years between 1981 and 2013 using the Weibull plotting position (Weibull1939). A total of 27 percentiles with exceedance probabilities of 0.02 %, 0.05 %, 0.1 %, 0.2 %, 0.5 %, 1 %, 2 %, 5 %, 10 %, 20 %, 25 %, 30 %, 40 %, 50 %, 60 %, 70 %, 75 %, 80 %, 90 %, 95 %, 98 %, 99 %, 99.5 %, 99.8 %, 99.9 %, 99.95 %, and 99.98 % were considered. The selection of streamgages with at least 14 complete water years ensures that all percentiles can be calculated from the observed data. These percentiles derived from the observed hydrograph represent the “unknowable observation” in an application for prediction in ungauged basins. Therefore, to simulate the truly ungauged case, these same percentiles were estimated using a leave-one-out cross-validation of regional regression. A regional regression across the streamgages in each two-digit hydrologic unit of each of the 27 FDC percentiles was developed using best subsets regression. Best subsets regression is a common tool for exhaustive exploration of the space of potential explanatory variables. All models with a given number of explanatory variables are computed, exploring all combinations of variables. The top models for a given number of explanatory variables are then identified by a performance metric like the Akaike information criterion. This is repeated for several model sizes to fully explore the possibilities for variables and regression size. For each regression, the drainage area was required as an explanatory variable. At a minimum, one additional explanatory variable was used. The maximum number of explanatory variables was limited to the smaller of either six explanatory variables or 5 % of the number of streamgages in the region, rounded up to the next larger whole number. The maximum of six arises from what is computationally feasible for the best subsets regression function used, whereas the maximum of 5 % of streamgages was determined from a limited exploration of the optimal number of explanatory variables as a function of the number of streamgages in a region. Explanatory variables were drawn from the GAGES-II database (Falcone2011). As documented by and , a subset of the full GAGES-II dataset was chosen to avoid strong correlations. As the focus of this work is not on the estimation of the FDCs, the reader is referred to the works of and to explore the exact procedures. In order to allow different explanatory variables to be used to explain percentiles at different streamflow regimes, the percentiles were grouped into a maximum of three contiguous streamflow regimes based on the behavior of the unit FDCs (i.e., the FDCs divided by drainage area) in the two-digit hydrologic units. The regimes are contiguous in that only consecutive percentiles from the list above can be included in the same regime; the result is a maximum of three regimes that can be considered “high”, “medium”, and “low” streamflows, though the number of regimes may vary across two-digit hydrologic units. The percentiles in each regime were estimated by the same explanatory variables, allowing only the fitted coefficients to change. The final regression form for each regime was selected by optimizing the average adjusted coefficient of determination, based on censored Gaussian (Tobit) (Tobin1958) regression to allow for values censored below 0.005 cfs, across all percentiles in the regime. The addition of a small value was used to avoid the presence of zeros and enable a logarithmic transformation, but this does not avoid the problem of censoring. Censoring below the small value added must still be accounted for so that smaller numbers do not unduly affect the regression. This approach to percentile grouping was found to provide reasonable estimates while minimizing the risk of non-monotonic or otherwise concerning behavior. Further details on this methodology can be found in the associated data and model archive and in . When estimating a complete FDC as realized through a set of discrete points, non-monotonic behavior is likely . If the regression for each percentile were estimated independently, non-monotonicity would be almost unavoidable. By using three regimes and keeping the explanatory variables the same within each, the potential for non-monotonicity is reduced. The greatest risk of non-monotonic behavior occurs at the regime boundaries. If the FDC used to bias-correct is not perfectly monotonic, the effect will be to alter the relative timing of streamflows. While it would be ideal to avoid any risk of non-monotonic behavior, it is a rather difficult task. An alternative might be to consider the FDC as a parametric function, but demonstrate how difficult this can be for daily streamflows. Of course, the use of regional regression is not the only tool for estimating an FDC (Castellatin et al.2013; Pugliese et al.2014, 2016). Figure 2Diagram showing the bias correction methodology applied here. The simulated daily hydrograph at the ungauged site is presented in (a). For any particular point on the hydrograph (point A) the daily volume of streamflow can be mapped to a nonexceedance probability using the rank order of simulated streamflows (points B and C). With an independently estimated flow duration curve (FDC) from some procedure such as regional regression, the nonexceedance probability can be rescaled to a new volume (point D) and placed back in same sequence as the simulated streamflows (point E) to produce a bias-corrected hydrograph. This example is shown for 1 month, though the FDC applies across the entire period of record. As these data are based on an example site, the observed streamflows and FDC are shown in grey on each figure. 2.3 Bias correction To implement bias correction, the initial predictions of the daily streamflow values using the ordinary kriging approach were converted to streamflow nonexceedance probabilities using the Weibull plotting position (Weibull1939). The nonexceedance probabilities were then converted to standard normal quantiles and linearly interpolated along an independently estimated FDC. For the linear interpolation, the independently estimated FDC was represented as the standard normal quantiles of the associated nonexceedance probabilities versus the common logarithmic transformation of the streamflow percentiles. In the case for which the standard normal quantile being estimated from the simulated hydrograph was beyond the extremes of the FDC, the two nearest percentiles were used for linear extrapolation. In this way, the ordinary kriging simulations were bias-corrected, based on the assumption that the simulated volumes are less accurate than the relative ranks of the simulated values, by rescaling the simulated volumes to an independently estimated FDC. By changing the magnitudes of the simulated streamflow distribution, this approach rescales the distribution of the simulated streamflow. Figure 2 provides a simplified representation of this bias correction methodology. Starting in panel a and proceeding clockwise, after simulating the hydrograph with a given methodology (pooled ordinary kriging was used here), the resulting streamflow value on a given day can be converted to appropriate nonexceedance probabilities by proceeding from point A, through point B, and down to point C. Moving then from point C to point D maps the estimated nonexceedance probability onto an independently estimated FDC. Finally, the streamflow value produced at point D is mapped to the original date (point E) to reconstruct a bias-corrected hydrograph. Note that this is a simplified description: as described above a slightly more complex interpolation procedure is used for the FDCs represented by a set of discrete points. As can be seen in Fig. 2, this methodology is quite similar to that conceived by and . The novelty of this work lies in its application. That is, both and imagine a case in which the original hydrograph from which nonexceedance values will be drawn (Fig. 2a) is drawn from an index station of some sort; here the temporal structure could be drawn from any technique for at-site hydrograph simulation. This generalization allows bias correction of any hydrograph simulation. 2.4 Evaluation The hypothesis of this work, that distributional bias in the simulated streamflow can be corrected by applying independently estimated FDCs, was evaluated by considering the performance of these bias-corrected simulations at both tails of the distribution. The differences in the common logarithms of both high and low streamflow were used to understand and quantify the bias (simulation minus observed) and the correction thereof. That is, $\begin{array}{}\text{(1)}& {\mathrm{bias}}_{\mathrm{s}}=\frac{\sum _{i=\mathrm{1}}^{n}\left({\mathrm{log}}_{\mathrm{10}}\left({\stackrel{\mathrm{^}}{Q}}_{\mathrm{s},i}\right)-{\mathrm{log}}_{\mathrm{10}}\left({Q}_{\mathrm{s},i}\right)\right)}{n},\end{array}$ where s indicates the site of interest, $\stackrel{\mathrm{^}}{Q}$ indicates the predicted streamflow, whether the original simulation or the bias-corrected simulation, Q indicates the observed streamflow, and n indicates the number of values being assessed. This difference can be approximated as a percent by computing 10 to the power of the difference and subtracting 1 from this quantity : $\begin{array}{}\text{(2)}& {\mathrm{bias}}_{\mathrm{s},\mathit{%}}=\mathrm{100}\cdot \left({\mathrm{10}}^{{\mathrm{bias}}_{\mathrm{s}}}-\mathrm{1}\right).\end{array}$ The differences in the root mean squared error of the common logarithms of the predicted streamflow were used to quantify improvements in accuracy. The root mean squared error of the common logarithms of streamflow is calculated as $\begin{array}{}\text{(3)}& {\mathrm{rmsel}}_{\mathrm{s}}=\sqrt{\frac{\sum _{i=\mathrm{1}}^{n}{\left({\mathrm{log}}_{\mathrm{10}}\left({\stackrel{\mathrm{^}}{Q}}_{\mathrm{s},i}\right)-{\mathrm{log}}_{\mathrm{10}}\left({Q}_{\mathrm{s},i}\right)\right)}^{\mathrm{2}}}{n}}.\end{array}$ Improvements in accuracy may or may not occur when bias is reduced. The significance of both these quantities, and the effects of bias correction on these quantities, was assessed using a Wilcoxon signed rank test (Wilcoxon1945). For assessments of bias, the null hypothesis was that the bias was equivalent to zero. For assessments of the difference in bias or accuracy with respect to the baseline result, the null hypothesis was that this difference was zero. Distributional bias and improvement of that bias were considered in both the high and low tails of the streamflow distribution. Two methods were used to capture the bias in each tail. One method, referred to herein as an assessment of the observation-dependent tails, considers the observed nonexceedance probabilities to identify the days on which the highest and lowest 5 % of streamflow occurred. For each respective tail, the errors were assessed based on the observations and simulations of those fixed days. The other method, referred to herein as an assessment of the observation-independent tails, compares the ranked top and bottom 5 % of observations with the independently ranked top and bottom 5 % of simulated streamflow. Errors in the observation-dependent tails are an amalgamation of errors in the sequence of nonexceedance probabilities (the temporal structure) and in the magnitude of streamflow, whereas errors in the observation-independent tails only reflect bias in the ranked magnitudes of streamflow. In the same fashion, evaluation of the complete hydrograph can be assessed sequentially (sequential evaluation), retaining the contemporary sequencing of observations and simulations, or distributionally (distributional evaluation), considering the observations and simulations ranked independently. Though the overall accuracy will vary between the sequential and distributional case, overall bias will be identical in both cases. With an analysis of both observation-dependent and observation-independent tails, it is possible to begin to tease out the effect of temporal structure on distributional bias. The bias in observation-independent tails is not directly tied to the temporal structure, or relative ranking, of simulated streamflow. That is, if the independently estimated FDC is accurate, then even if relative sequencing of streamflow is badly flawed, the bias correction of observation-independent tails will be successful. However, even if the distribution is accurately reproduced after bias correction, the day-to-day performance may still be poor. For observation-dependent tails, the temporal structure plays a vital role on the effect of bias correction. If the temporal structure is inaccurate in the underlying hydrologic simulation, then the bias correction of observation-dependent tails will be less successful. The bias correction approach was first tested with the observed FDCs. These observed FDCs would be unknowable in the truly ungauged case, but this test allows for an assessment of the potential utility of this approach. This examination is followed by an application with the regionally regressed FDCs described above, demonstrating one realization of this generalizable method. This general approach to bias correction could be used with other methods for estimating the FDC and could also be used with an observed FDC for record extension, though neither of these possibilities are explored here. Figure 3Distribution of logarithmic bias, measured as the mean difference between the common logarithms of simulated and observed streamflow (simulated minus observed) at 1168 streamgages across the conterminous USA. Orig. refers to the original simulation with pooled ordinary kriging, BC-RR refers to the Orig. hydrograph bias-corrected with regionally regressed flow duration curves, and BC-Obs. refers to the Orig. hydrograph bias-corrected with observed flow- duration curves. The tails of the box plots extend to the 5th and 95th percentiles of the distribution; the ends of the boxes represent the 25th and 75th percentiles of the distribution; the heavier line in the box represents the median of the distribution; the open circle represents the mean of the distribution; outliers beyond the 5th and 95th percentile are shown as horizontal dashes. 3 Results Figures 3 and 4 show the overall bias and accuracy of the reproduced hydrographs; these figures are quantified in Tables 1 and 2. Figure 5 and Table 1 summarize the tail bias in all approaches to streamflow simulation considered here. Similarly, Fig. 6 and Table 2 summarize the tail accuracy of all approaches. These results are discussed in detail below, beginning with a discussion of the bias and accuracy in the original kriged simulations. This is followed by a consideration of the effectiveness of bias correction with observed FDCs as emblematic of the theoretical potential of this approach. The realization of this theoretical potential through the regionally regressed FDCs is subsequently presented. Complete results can be explored and reproduced using the associated model and data archive . Figure 4Distribution of logarithmic accuracy, measured as the root mean squared error between the common logarithms of observed and simulated streamflow at 1168 streamgages across the conterminous USA. Orig. refers to the original simulation with pooled ordinary kriging, BC-RR refers to the Orig. hydrograph bias-corrected with regionally regressed flow duration curves, and BC-Obs. refers to the Orig. hydrograph bias-corrected with observed flow duration curves. Sequential indicates that contemporary days were compared, while distributional indicates that days of equal rank were compared. The tails of the box plots extend to the 5th and 95th percentiles of the distribution; the ends of the boxes represent the 25th and 75th percentiles of the distribution; the heavier line in the box represents the median of the distribution; the open circle represents the mean of the distribution; outliers beyond the 5th and 95th percentile are shown as horizontal dashes. 3.1 Simulated hydrographs without correction There is statistically significant overall bias at the median (−7.1 %; ${\mathrm{10}}^{-\mathrm{0.0318}}-\mathrm{1}$) in the streamflow distribution simulated by the kriging approach applied here (Fig. 3, box plot A), but more significant bias is apparent in the upper and lower tails of the distribution (Fig. 5, box plots A, D, G, and J). Both the observation-dependent and observation-independent upper tails of the streamflow distribution demonstrate significant downward bias (Fig. 5, box plots D and J). At the median, the observation-dependent upper tail is underestimated by approximately 38 % (Table 1, row 1; Fig. 5, box plot D), while the observation-independent upper tail is underestimated by approximately 23 % (Table 1, row 2; Fig. 5, box plot J). For the lower tail, the observation-dependent tail shows a median overestimation of 36 % (Table 1, row 1; Fig. 5, box plot A), while the observation-independent tail is underestimated by less than 1 % (Table 1, row 2; Fig. 5, box plot G). The bias is much more variable, producing greater magnitudes of bias more often, in the lower tails than in the upper tails. Generally, biases in the observation-independent tails are less severe, both in the median and in range, than those in the observation-dependent tails. To provide some information on regional performance and incidence of bias, Fig. 7 shows the spatial distribution of bias in each tail (discussion of this distribution is provided below). Figure 5Distribution of logarithmic bias, measured as the mean difference between the common logarithms of simulated and observed streamflow at 1168 streamgages across the conterminous USA for observation-dependent and observation-independent upper and lower tails. Observation-dependent tails retain the ranks of observed streamflow, while matching simulations by day. Observation-independent tails rank observations and simulation independently. The upper tail considers the highest 5 % of streamflow, while the lower tail considers the lowest 5 % of streamflow. Orig. refers to the original simulation with pooled ordinary kriging, BC-RR refers to the Orig. hydrograph bias-corrected with regionally regressed flow duration curves, and BC-Obs. refers to the Orig. hydrograph bias-corrected with observed flow duration curves. The tails of the box plots extend to the 5th and 95th percentiles of the distribution; the ends of the boxes represent the 25th and 75th percentiles of the distribution; the heavier line in the box represents the median of the distribution; the open circle represents the mean of the distribution; outliers beyond the 5th and 95th percentile are shown as horizontal dashes. In both observation-dependent and observation-independent cases, downward bias in the upper tail is more probable than upward biases in the lower tail. For the observation-dependent tails, approximately 89% of streamgages show downward bias for the upper tail (Fig. 5, box plot D), and approximately 61 % of the streamgages upward bias in the lower tail (Fig. 5, box plot A). For the observation-independent tails, approximately 80 % of streamgages show downward bias in the upper tail (Fig. 5, box plot J) and approximately 50 % of the streamgages exhibit upward bias in the lower tail (Fig. 5, box plot G), indicating, as does the small median bias value, that the lower tail biases are relatively well balanced around zero for the observation-independent case for these simulations. With respect to their central tendencies, these results show upward bias in lower tails and downward bias in upper tails of the distribution of streamflows from the original simulations for both observation-dependent and observation-independent cases. There is, of course, a great degree of variability around this central tendency. With these baseline results, the bias correction method presented here seeks to mitigate these biases. Figure 6Distribution of logarithmic accuracy, measured as the root mean squared error between the common logarithms of simulated and observed streamflow (simulated minus observed) at 1168 streamgages across the conterminous USA for observation-dependent and observation-independent upper and lower tails. Observation-dependent tails retain the ranks of observed streamflow, while matching simulations by day. Observation-independent tails rank observations and simulation independently. The upper tail considers the highest 5 % of streamflow, while the lower tail considers the lowest 5 % of streamflow. Orig. refers to the original simulation with pooled ordinary kriging, BC-RR refers to the Orig. hydrograph bias-corrected with regionally regressed flow duration curves, and BC-Obs. refers to the Orig. hydrograph bias-corrected with observed flow duration curves. The tails of the box plots extend to the 5th and 95th percentiles of the distribution; the ends of the boxes represent the 25th and 75th percentiles of the distribution; the heavier line in the box represents the median of the distribution; the open circle represents the mean of the distribution; outliers beyond the 5th and 95th percentile are shown as horizontal dashes. 3.2 Bias correction with observed FDCs The results for this idealized case that could not be applied in practice provide clear evidence that distributional bias in simulated streamflow can be reduced by rescaling using independently estimated FDCs. This evidence is apparent in the reduction of the magnitude and variability of overall bias (Fig. 3, box plot C; Table 1, rows 5 and 6) and of the bias in the observation-independent tails of the streamflow distribution (Fig. 5, box plots I and L) when observed FDCs are used for rescaling. Similarly, the overall distributional accuracy is much improved (Fig. 4, box plot F; Table 2, rows 5 and 6), as is the accuracy of observation-independent tails (Fig. 6, box plot I and L). The effect on observation-dependent tails (Fig. 5, box plots C and F) and overall sequential accuracy (Fig. 4, box plot C) is less compelling but still substantial. Figure 7Maps showing the distribution of logarithmic bias, measured as the mean difference between the common logarithms of simulated and observed streamflow (simulated minus observed) at 1168 streamgages across the conterminous USA for observation-dependent and observation-independent upper and lower tails. Observation-dependent tails retain the ranks of observed streamflow, while matching simulations by day. Observation-independent tails rank observations and simulation independently. The upper tail considers the highest 5 % of streamflow, while the lower tail considers the lowest 5 % of streamflow. The bias is derived from the original simulation of daily streamflow using pooled ordinary kriging at 1168 sites regionalized by the two-digit hydrologic units (polygons). Whereas the measures of bias and accuracy are summarized in Tables 1 and 2, Tables 3 and 4 summarize the change in absolute bias and in accuracy, respectively. With the use of observed FDCs, the overall bias is reduced to a tenth of a percent at the median (Table 1, rows 5 and 6). This represents a significant median reduction of 0.14 common logarithm units in the overall absolute bias (Table 3, rows 3 and 4). Overall, the distributional accuracy is improved by a median of 0.21 common logarithm units (Table 4, row 4). Of all streamgages considered, 99 % saw a reduction in the overall absolute bias, and all saw improvements in overall distributional accuracy. These improvements extend to both observation-independent tails of the distributions. The lower observation-independent tails have a median 0.35 common logarithm unit reduction in absolute bias (Table 3, row 4). For the upper tail, the median reduction in absolute bias is 0.14 common logarithm units (Table 3, row 4). Nearly all streamgages (99 %) saw reduction in absolute bias of the observation-independent tails. Table 4 (row 4) shows similar improvements in tail accuracy: −0.37 and −0.15 units in the lower and upper tails, respectively, with nearly all streamgages (excepting the lower tail of a single streamgage, likely the result of the interpolation procedure) showing improved tail accuracy. Table 1Measures of the distribution of logarithmic bias, computed as the mean difference between the common logarithms of simulated and observed streamflow (simulated minus observed) at 1168 streamgages across the conterminous USA for observation-dependent and observation-independent upper and lower tails. Orig. refers to the original simulation with pooled ordinary kriging, BC-RR refers to the Orig. hydrograph bias-corrected with regionally regressed flow duration curves, and BC-Obs. refers to the Orig. hydrograph bias-corrected with observed flow duration curves. Observation-dependent (OD) tails retain the ranks of observed streamflow, while matching simulations by day. Observation-independent (OI) tails rank observations and simulation independently. The upper tail observes the highest 5 % of streamflow, while the lower tail considers the lowest 5 % of streamflow. Significance is the p value resulting from a Wilcoxon signed rank test with continuity correction, with the null hypothesis that the median of distribution is equal to zero and the alternative hypothesis that the median is not equal to zero. Table 2Measures of the distribution of logarithmic accuracy, computed as the root mean squared error between the common logarithms of observed and simulated streamflow at 1168 streamgages across the conterminous USA for observation-dependent and observation-independent upper and lower tails. Orig. refers to the original simulation with pooled ordinary kriging, BC-RR refers to the Orig. hydrograph bias-corrected with regionally regressed flow duration curves, and BC-Obs. refers to the Orig. hydrograph bias-corrected with observed flow duration curves. Observation-dependent (OD) tails retain the ranks of observed streamflow, while matching simulations by day. Observation-independent (OI) tails rank observations and simulation independently. The upper tail observes the highest 5 % of streamflow, while the lower tail considers the lowest 5 % of streamflow. Table 3Measures of the distribution of changes in absolute logarithmic bias with bias correction, for which absolute logarithimic bias is computed as the absolute value of the mean difference between the common logarithms of bias-corrected and simulated streamflow at 1168 streamgages across the conterminous USA for observation-dependent and observation-independent upper and lower tails, for which the simulated streamflow was obtained with pooled ordinary kriging. BC-RR refers to the Orig. hydrograph bias-corrected with regionally regressed flow duration curves, and BC-Obs. refers to the Orig. hydrograph bias-corrected with observed flow duration curves. Observation-dependent (OD) tails retain the ranks of observed streamflow, while matching simulations by day. Observation-independent (OI) tails rank observations and simulation independently. The upper tail observes the highest 5 % of streamflow, while the lower tail considers the lowest 5 % of streamflow. Significance is the p value resulting from a paired Wilcoxon signed rank test with continuity correction, with the null hypothesis that the median difference with respect to the original simulation is equal to zero and the alternative hypothesis that the median difference is not equal to zero. Table 4Measures of the distribution of changes in logarithmic accuracy between original and bias-corrected simulations, for which the logarithmic accuracy is computed as the root mean squared error between the common logarithms of bias-corrected and simulated streamflow at 1168 streamgages across the conterminous USA for observation-dependent and observation-independent upper and lower tails, for which the simulated streamflow was obtained using pooled ordinary kriging. BC-RR refers to the Orig. hydrograph bias-corrected with regionally regressed flow duration curves, and BC-Obs. refers to the Orig. hydrograph bias-corrected with observed flow duration curves. Observation-dependent (OD) tails retain the ranks of observed streamflow, while matching simulations by day. Observation-independent (OI) tails rank observations and simulation independently. The upper tail observes the highest 5 % of streamflow, while the lower tail considers the lowest 5 % of streamflow. Significance is the p value resulting from a paired Wilcoxon signed rank test with continuity correction, with the null hypothesis that the median difference with respect to the original simulation is equal to zero and the alternative hypothesis that the median difference is not equal to zero. With the use of a perfect, observed FDC for bias correction, one would expect that nearly all bias would disappear, but the results do not show this. The temporal structure of the simulated hydrograph continues to play a role in the bias of observation-dependent tails. The observation-independent tail continues to exhibit a small degree of residual bias, though it is still slightly nonintuitive. This residual bias arises from the effect of representing the FDC as a set of discrete points and interpolating between them. There may be some additional effect from the small value added to avoid zero-valued streamflows or the censoring procedure, but initial exploration found little impact. The overall sequential performance (Fig. 4, box plot C) and the performance of observation-dependent tails (Figs. 5 and 6, box plots C and F) demonstrate the degree to which errors in the temporal structure result in bias in the observation-dependent case even when observed FDCs are used for bias correction. Both the observation-dependent lower and upper tails exhibit bias: 30 % and −20 %, respectively, at the median (Table 1, row 5, with transformation using Eq. 2). Absolute bias in both tails shows median reductions; sequential accuracy and observation-dependent tail accuracy are also improved at the median (Tables 3 and 4, row 3). Proportionally, 82 % of the observation-dependent lower tails and 86 % of the observation-dependent upper tails showed reduction in absolute bias (Fig. 5, box plots C and F); 85 % of observation-dependent lower tails and 79 % of observation-dependent upper tails showed improvements in accuracy (Fig. 6, box plots C and F). Despite improvements in overall bias and accuracy from rescaling with observed FDCs, the residual bias in the observation-dependent lower tail (Fig. 5, box plot C) is almost always positive (upward bias) and upper tails (Fig. 5, box plot F) are almost negative (downward bias), a result which arises primarily from errors in the simulated temporal structure. To understand the effect of errors in the temporal structure further, consider Fig. 8, which shows the mean error in the nonexceedance probabilities, i.e., the difference in the ranks of the observed and simulated streamflows, of the observation-dependent upper and lower tails. The nonexceedance percentages in the lower tail are overestimated by a median of 3.8 points, with 5th and 95th percentiles of 0.9 and 20.5, while the percentages in the upper tail are underestimated by 2.4 points, with 5th and 95th percentiles of −0.5 and −12.6 points. The distributions of errors in the nonexceedance probabilities closely reflect the distribution of bias in the observation-dependent tails (Fig. 5, box plots C and F). These results show that the inaccuracy in the nonexceedance probabilities (i.e., errors in temporal structure) will obscure, at least partially, the improvement offered by bias correction when considering the observation-dependent errors, even when an observed FDC is used for bias correction. These errors in temporal structure also almost always result in errors in a particular direction – low for high flow and high for low flows. Figure 8Distribution of mean error in the simulated nonexceedance probabilities of the lowest and highest 5 % of observed daily streamflow (simulated minus observed) at 1168 streamgages across the conterminous USA. The upper tail considers the highest 5 % of streamflow, while the lower tail considers the lowest 5 % of streamflow. The tails of the box plots extend to the 5th and 95th percentiles of the distribution; the ends of the boxes represent the 25th and 75th percentiles of the distribution; the heavier line in the box represents the median of the distribution; the open circle represents the mean of the distribution; outliers beyond the 5th and 95th percentile are shown as horizontal dashes. 3.3 Bias correction with regionally regressed FDCs When the uncertainty of regionally regressed FDCs is introduced into the bias correction procedure, the potential value of the bias correction procedure is not as convincing. There is a slight, but significant, increase in the overall bias (Table 3, rows 1 and 2). Whereas the original estimated streamflow displays a median bias of approximately 7.1 %, the median overall bias is approximately 7.6 % after bias correction with estimated FDCs (Table 1, rows 3 and 4). Though statistically significant, the distribution of bias does not appear to have changed in a meaningful way (Fig. 3, box plots A and B). The overall accuracy, sequential and distributional, is also degraded (Fig. 4, box plots B and E; Table 4, rows 3 and 4), with more than 60 % of streamgages showing degradation in sequential and distributional accuracy. The observation-independent tails, which are not affected by errors in temporal structure, show a divergence in performance between the results obtained using observed FDCs and those obtained using regionally regressed FDCs. With observed FDCs, both tails demonstrated substantial reductions in absolute bias and improvements in accuracy. With regionally regressed FDCs, the upper observation-independent tails continue to show reductions in absolute bias (Table 3, row 2; Fig. 5, box plots J and K) and improvements in accuracy (Table 4, row 2; Fig. 6, box plots J and K), while the lower observation-independent tails show a significant increase in absolute bias (Table 3, row 2; Fig. 5, box plots G and H) and a degradation of accuracy (Table 4, row 2; Fig. 6, box plots G and H). After bias correction with regionally regressed FDCs, only 44 % of observation-dependent lower tails showed reductions in absolute bias; 58 % of upper tails showed reductions in absolute bias. The effects of the rescaling with FDCs estimated with regional regression on overall and observation-independent tail bias and accuracy can be better understood if the properties of the estimated FDCs are considered. Figure 9 shows the bias (panel a) and accuracy (panel b) of the lower and upper tails of the regionally regressed FDCs. Recall that the estimated FDCs are composed of 27 quantiles, of which the upper and lower tails contain only the eight values with nonexceedance probabilities 95 % and larger and 5 % and smaller, respectively. The upper tails are reproduced through regional regression with an insignificant 2.5 % median downward bias, but the lower tails exhibit a significant negative median bias of 38.35 % (Table 1, row 7). Because of this bias in the lower tail of the regionally regressed FDCs, the regionally regressed FDCs are unable to correct the bias in the simulated hydrograph, instead turning a small median bias into large one. As there is no temporal uncertainty in the observation-independent tails, the resulting bias arises from the bias of the regionally regressed FDC. Illustrating this fact, the −38 % bias in the lower tail of the regionally regressed FDC approximates the −33 % in the observation-independent lower tail, while the −2.5 % bias in the upper tail of the regionally regressed FDC approximates the −3.7 % bias in the observation-independent upper tail. The introduction of this additional bias, beyond failing to correct any underlying bias in the simulated hydrograph, also markedly increased the variability of both bias and accuracy. The results are similar for the observation-dependent tails produced after bias correction with regionally regressed FDCs, even when complicated by the addition of temporal uncertainty as discussed in Sect. 3.2 with reference to Fig. 8. In some cases, the errors in the temporal structure (nonexceedance probability) counteract the additional bias from regionally regressed FDCs. For example, the observation-dependent lower tails have a median bias of 13 %, which possesses a smaller magnitude and different sign than the median −33 % bias seen in the observation-independent lower tail (Table 1, rows 3 and 4). The addition of temporal uncertainty actually reduced the increase in absolute bias (Table 3, rows 1 and 2) and reduced the degradation of accuracy in the lower tail (Table 4, rows 1 and 2). These slight improvements result from an offsetting of the underestimated regionally regressed FDCs by the overestimated nonexceedance probabilities. While interesting, it seems unlikely that this result can be generalized in a simple way: that is, the errors in estimated FDCs cannot be expected to balance out the errors in nonexceedance probabilities without deleterious effects on other properties. To this point, as noted, rescaling by these regionally regressed FDCs with underestimated lower tails results in similarly underestimated observation-independent lower tails. Figure 9Distribution of logarithmic bias (a), measured as the mean difference between the common logarithms of quantiles of observed and simulated streamflow (simulated minus observed) at 1168 streamgages across the conterminous USA, and logarithmic accuracy (b), measured as the root mean squared error between the common logarithms of quantiles of observed and simulated streamflow at the same streamgage, in the upper and lower quantiles of regionally regressed flow duration curves. The upper tail considers the eight quantiles in the highest 5 % of streamflow, while the lower tail considers the eight quantiles in the lowest 5% of streamflow. The tails of the box plots extend to the 5th and 95th percentiles of the distribution; the ends of the boxes represent the 25th and 75th percentiles of the distribution; the heavier line in the box represents the median of the distribution; the open circle represents the mean of the distribution; outliers beyond the 5th and 95th percentile are shown as horizontal dashes. The introduction of uncertainty from regionally regressed FDCs diminishes the advantages gained by biased correction with observed FDCs. Considering the observation-independent lower tails, 55 % of streamgages show reductions in absolute bias with observed FDCs that were reversed into increases of absolute bias by the introduction of regionally regressed FDCs. Another 43 % of streamgages show smaller reductions in absolute bias when observed FDCs were replaced with regionally regressed FDCs. For the observation-dependent lower tails, 37 % of streamgages have reversals and 31 % show smaller reductions in absolute bias. For the observation-independent upper tails, 41 % show reversals and 56 % yield smaller reductions in absolute bias. For the observation-dependent upper tails, 24 % produce reversals and 40 % provide smaller reductions in absolute bias. Results are similar with respect to accuracy: while many streamgages saw reversals, a large proportion of streamgages continue to demonstrate improvements. 4 Discussion Though the first analysis presented, which utilized observed FDCs for bias correction, represents only an assessment of hypothetical potential of this general approach, the approach to bias correction presented here produced near universal and substantial reduction in bias and improvements in accuracy, overall and in each tail, for both observation-dependent and observation-independent evaluation cases when the uncertainty in independently estimated FDCs was minimized. For the observation-independent evaluation case, the errors are removed almost completely, and the remaining errors in the observation-dependent case mimic the temporal structure (nonexceedance probability) errors. These results, which are not applicable under the conditions of the true ungauged problem, demonstrate that the bias correction approach introduced here is theoretically valid. However, this improvement becomes inconsistent with respect to bias and generally reduces the accuracy when the biased and uncertain regionally regressed FDCs are used. Furthermore, in both the observation-dependent and observation-independent tails in the case of rescaling by regionally regressed FDCs, the improvements in the lower tails are much more variable than the improvements in the upper tail (Figs. 5 and 6; Tables 3 and 4). This result is not surprising, given the more variable nature of lower tail bias and accuracy (Figs. 5 and 6). The regional regressions developed here were much better at estimating the upper tail of the streamflow distribution than estimating the lower tail. This provides a convenient comparison: the bias correction of lower tails with regionally regressed FDCs only improved the bias in the observation-dependent case when the low bias of the regionally regressed FDC offset the high bias of the observation-dependent tails, and did not improve accuracy in either case. However, the bias correction of upper tails with regionally regressed FDCs, which produced the upper tails with much less bias, continued to show, like in the case of observed FDCs, improvements in bias and accuracy, though to a much smaller degree than the improvements produced by observed FDCs. Particularly in the lower tail of the distribution, the effectiveness of this bias correction method is strongly influenced by the accuracy of the independently estimated FDC. The change in the absolute bias of the observation-independent lower tail has a 0.72 Pearson correlation with the absolute bias of the lowest eight percentiles of the FDC estimated with regional regression, showing that the residual bias in the FDC of the bias-corrected streamflow simulations is strongly correlated with the bias in the independently estimated FDC. The analogous correlation for the upper tail is 0.31. For the observation-dependent these correlations are only 0.33 for each tail, the reduced correlation for the lower tail being a result of the combination of the uncertainty in the temporal structure and in the regionally regressed FDC. Therefore, as regional regression is not the only tool for estimating FDCs (Castellatin et al.2013; Pugliese et al.2014, 2016), improved methods for FDC estimation would further increase the impact of this bias correction procedure. There are also hints that the representation of the FDC as a set of discrete points degraded performance. Further work might address the question of improving FDC simulation. Still further, seasonal FDCs or some other methods of increasing the temporal variability of FDCs could improve performance of this general bias correction approach. While this method of bias correction, as implemented here using regionally regressed FDCs, improves the bias in the upper tails, it had a negative impact on lower tails. This makes the question of application or recommendation more poignant. Under what conditions might this approach be worthwhile? Initial exploration did not find a strong regional component to performance of the bias correction method. Figure 7 shows the original tail bias from pooled ordinary kriging; at each point the accuracy of the bias correction method is dependent on the original bias present as well as the error in the independently estimated FDC. For some regions, like New England, USA, where FDCs are well estimated by regional regression, there is a general improvement in accuracy under bias correction with regionally regressed FDCs, but the improvement is highly variable. Instead, the strongest link is with the reproduction of the FDC. When the magnitude of tail biases of the regionally regressed FDC was under 20 %, more than 50 % of streamgages showed improvements in bias, both overall and in the tails of the distribution. At a particular ungauged site, it may not always be possible to determine the accuracy with which a given FDC estimation technique might perform beyond a regional cross-validated assessment of general uncertainty, making it difficult to determine if these results can be generalized. If accuracy of the estimated FDCs can be estimated, it may also be useful to consider rescaling one tail and not the other, depending on the estimated accuracy. Further work might explore the effects of hydroclimates on the ability to reproduce reliable FDCs with which to implement this bias correction procedure. The results of this work were also discussed in reference to earlier work that suggested a prevalence, though not a universality, of underestimation of high streamflows and overestimation of low streamflows. Similarly, the bias correction approach produced a wide variability of results; where the high tails might have been improved, the lower tails might have been degraded. Figure 10 shows the correspondence of tails across all sites. While there is a move towards unbiasedness at some sites (along the vertical axis), there is a great degree of variability that makes it difficult to draw general conclusions. In some situations, as in panel d, the variability may actually be increasing with bias correction. Though all methods will produce variability, it remains for future research to determine if a more consistent representation of the FDC might reduce the variability of this performance. Figure 10Scatter plots showing the correspondence of logarithmic bias, measured as the mean difference between the common logarithms of simulated and observed streamflow (simulated minus observed) at 1168 streamgages across the conterminous USA for observation-dependent and observation-independent upper and lower tails. Observation-dependent tails retain the ranks of observed streamflow, while matching simulations by day. Observation-independent tails rank observations and simulation independently. The upper tail considers the highest 5 % of streamflow, while the lower tail considers the lowest 5 % of streamflow. Orig. refers to the original simulation with pooled ordinary kriging, and BC-RR refers to the Orig. hydrograph bias-corrected with regionally regressed flow duration curves. When looked at from the point of view of the estimated FDCs that need temporal information in order to simulate streamflow, this approach to bias correction is as akin to an extension of the nonlinear spatial interpolation using FDCs developed by and as it is bias correction. Here it is approached as a method for bias correction, but it can also be thought of as a novel approach to simulate the nonexceedance probabilities at an ungauged location to be used with estimated distributional information (FDCs) to simulate streamflow. In the early uses of nonlinear spatial interpolation using FDCs, the simulated nonexceedance probabilities were obtained from a hydrologically appropriate neighboring or group of neighboring streamgages , though the approach to identifying a hydrologically appropriate neighbor has varied. Here, the entire network is used to approximate the ungauged nonexceedance probabilities, much like the indexing problem being overcome with ordinary kriging of streamflow directly (Farmer2016). Two major sources of uncertainty are inherent in nonlinear spatial interpolation using FDCs: uncertainty in the nonexceedance probabilities and uncertainty in the FDC. This work addresses the general approach by attacking the former and observing that performance may be further limited by the latter. The potential success of this approach to bias correction is likely not specific to simulation with ordinary kriging. That this approach to bias correction does improve the observation-dependent tails and the overall performance when observed FDCs are used shows that the temporal structure of the underlying simulation retains useful information, even if the tails of the original simulation are biased. However, some error remains in the simulated nonexceedance probabilities. A natural extension would be to investigate if it might be more reasonable to estimate nonexceedance probabilities directly rather than extracting their implicit values from the estimated streamflow time series as was done here. Here, the nonexceedance probabilities were derived from a simulation of the complete hydrograph. In this alternative approach, the discharge volumes would not be estimated but rather only the daily nonexceedance probabilities. executed a kriging approach to estimate daily nonexceedance probabilities in a smaller data set in Ohio. They found that modeling probabilities directly resulted in similar tail biases of nonexceedance probability to that observed when, as in , simulating streamflow directly. In earlier work, showed that kriging nonexceedance probabilities directly and then redistributing them via an estimated FDC, as compared with kriging streamflow directly, had only a marginal effect on bias in the tails. Further exploration of this question, whether to estimate nonexceedance probabilities directly or derive them from streamflow simulations, is left for future research. This current study focuses on the more general question of whether the distributional bias in a set of simulated streamflow, the provenance thereof being more or less inconsequential, could be reduced using a regionally regressed FDC. As mentioned earlier, recent work by explores how this generalization of nonlinear spatial interpolation using FDCs can be used to improve simulated hydrographs produced by a continental scale deterministic model. They consider it as an approach to inform a large-scale model with local information, thereby improving local application without further calibration. In 46 basins in Tyrol, saw universal improvement in the simulated hydrographs, though they did not explore tails biases. The results presented here provide an analysis across a wider range of basin characteristics and climates, demonstrating a link between how well the FDC can be reproduced and ultimate improvements in performance or reductions in bias. Although the results presented here are promising, they demonstrate that the performance of two-stage modeling, where temporal structure and magnitude are largely decoupled, is limited by the less well performing stage of modeling. In this case, alternative methods for estimating the FDC might prove worthwhile (Castellatin et al.2013; Pugliese et al.2014, 2016). 5 Summary and conclusions Regardless of the underlying methodology, simulations of historical streamflow often exhibit distributional bias in the tails of the distribution of streamflow, usually an overestimate of the lower tail values and an underestimate of the upper tail values. Such bias can be extremely problematic, as it is often these very tails that affect human populations and other water management objectives the most and, thus, these tails that receive the most attention from water resources planners and managers. Therefore, a bias correction procedure was conceived to rescale simulated time series of daily streamflow to improve simulations of the highest and lowest streamflow values. Being akin to a novel implementation of nonlinear spatial interpolation using flow duration curves, this approach could be extended to other methods of streamflow simulation. In a leave-one-out fashion, daily streamflow was simulated in each two-digit hydrologic unit code using pooled ordinary kriging. Regional regressions of 27 percentiles of the flow duration curve in each two-digit hydrologic unit code were independently developed. Using the Weibull plotting position, the simulated streamflow was converted into nonexceedance probabilities. The nonexceedance probabilities of the simulated streamflow were used to interpolate newly simulated streamflow volumes from the regionally regressed flow duration curves. Assuming that the sequence of relative magnitudes of streamflow retains useful information despite possible biases in the magnitudes themselves, it was hypothesized that simulated magnitudes can be corrected using an independently estimated flow duration curve. This hypothesis was evaluated by considering the performance of simulated streamflow observations and the performance of the relative timing of simulated streamflow. This evaluation was primarily focused on the examination of errors in both the high and low tails of the streamflow distribution, defined as the lowest and highest 5 % of streamflow, and considering changes in both bias and accuracy. When observed flow duration curves were used for bias correction, representing a case with minimal uncertainty in the independently estimated flow duration curve, bias and accuracy of both tails were substantially improved and overall accuracy was noticeably improved. The use of regionally regressed flow duration curves, which were observed to be approximately unbiased in the upper tails but were biased low in the lower tails, corrected the upper tail bias but failed to consistently correct the lower tail bias. Furthermore, the use of the regionally regressed flow duration curves degraded the accuracy of the lower tails but had relatively little effect on the accuracy of the upper tails. Combining the bias correction and accuracy results, the test with regionally regressed flow duration curves can be said to have been successful with the upper tails (for which the regionally regressed flow duration curves were unbiased) but unsuccessful with the lower tails. The effect on accuracy of the bias correction approach using estimated flow duration curves was correlated with the accuracy with which each tail of the flow duration curve was estimated by regional regression. In conclusion, this approach to bias correction has significant potential to improve the accuracy of streamflow simulations, though the potential is limited by how well the flow duration curve can be reproduced. While conceived as a method of bias correction, this approach is an analog of a previously applied nonlinear spatial interpolation method using flow duration curves to reproduce streamflow at ungauged basins. While using the nonexceedance probabilities of kriged streamflow simulations may improve on the use of single index streamgages to obtain nonexceedance probabilities, further improvements are limited by the ability to estimate the flow duration curve more accurately. Code and data availability Code and data availability. The data and scripts used to produce the results discussed herein can be found in . Author contributions Author contributions. WHF, TMO, and JEK jointly conceived of the idea. WHF designed the experiments and carried them out through the development of model code. WHF prepared the manuscript with contributions from all co-authors. Competing interests Competing interests. The authors declare that they have no conflict of interest. Acknowledgements Acknowledgements. This research was supported by the US Geological Survey's National Water Census. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the US Government. We are very grateful for the comments of several reviewers, among whom was Benoit Hingray. The combined reviewer comments helped to greatly improve early versions of this manuscript. Edited by: Monica Riva Reviewed by: Benoit Hingray and three anonymous referees References Alley, W. M., Evenson, E. J., Barber, N. 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http://www.nag.com/numeric/FL/nagdoc_fl24/html/S/s19apf.html	S Chapter Contents S Chapter Introduction NAG Library Manual NAG Library Routine DocumentS19APF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose S19APF returns an array of values for the Kelvin function $\mathrm{bei}x$. 2 Specification SUBROUTINE S19APF ( N, X, F, IVALID, IFAIL) INTEGER N, IVALID(N), IFAIL REAL (KIND=nag_wp) X(N), F(N) 3 Description S19APF evaluates an approximation to the Kelvin function $\mathrm{bei}{x}_{i}$ for an array of arguments ${x}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$. Note: $\mathrm{bei}\left(-x\right)=\mathrm{bei}x$, so the approximation need only consider $x\ge 0.0$. The routine is based on several Chebyshev expansions: For $0\le x\le 5$, $bei⁡x = x24 ∑′r=0 ar Tr t , with t=2 x5 4 - 1 ;$ For $x>5$, $bei⁡x = e x/2 2πx 1 + 1x a t sin⁡α - 1x b t cos⁡α$ $+ e x/2 2π x 1 + 1x c t cos⁡β - 1x d t sin⁡β$ where $\alpha =\frac{x}{\sqrt{2}}-\frac{\pi }{8}$, $\beta =\frac{x}{\sqrt{2}}+\frac{\pi }{8}$, and $a\left(t\right)$, $b\left(t\right)$, $c\left(t\right)$, and $d\left(t\right)$ are expansions in the variable $t=\frac{10}{x}-1$. When $x$ is sufficiently close to zero, the result is computed as $\mathrm{bei}x=\frac{{x}^{2}}{4}$. If this result would underflow, the result returned is $\mathrm{bei}x=0.0$. For large $x$, there is a danger of the result being totally inaccurate, as the error amplification factor grows in an essentially exponential manner; therefore the routine must fail. 4 References Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications 5 Parameters 1: N – INTEGERInput On entry: $n$, the number of points. Constraint: ${\mathbf{N}}\ge 0$. 2: X(N) – REAL (KIND=nag_wp) arrayInput On entry: the argument ${x}_{\mathit{i}}$ of the function, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$. 3: F(N) – REAL (KIND=nag_wp) arrayOutput On exit: $\mathrm{bei}{x}_{i}$, the function values. 4: IVALID(N) – INTEGER arrayOutput On exit: ${\mathbf{IVALID}}\left(\mathit{i}\right)$ contains the error code for ${x}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$. ${\mathbf{IVALID}}\left(i\right)=0$ No error. ${\mathbf{IVALID}}\left(i\right)=1$ $\mathrm{abs}\left({x}_{i}\right)$ is too large for an accurate result to be returned. ${\mathbf{F}}\left(\mathit{i}\right)$ contains zero. The threshold value is the same as for ${\mathbf{IFAIL}}={\mathbf{1}}$ in S19ABF, as defined in the Users' Note for your implementation. 5: IFAIL – INTEGERInput/Output On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details. For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit. On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6). 6 Error Indicators and Warnings If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF). Errors or warnings detected by the routine: ${\mathbf{IFAIL}}=1$ On entry, at least one value of X was invalid. ${\mathbf{IFAIL}}=2$ On entry, ${\mathbf{N}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{N}}\ge 0$. 7 Accuracy Since the function is oscillatory, the absolute error rather than the relative error is important. Let $E$ be the absolute error in the function, and $\delta$ be the relative error in the argument. If $\delta$ is somewhat larger than the machine precision, then we have: $E≃ x2 - ber1⁡x+ bei1⁡x δ$ (provided $E$ is within machine bounds). For small $x$ the error amplification is insignificant and thus the absolute error is effectively bounded by the machine precision. For medium and large $x$, the error behaviour is oscillatory and its amplitude grows like $\sqrt{\frac{x}{2\pi }}{e}^{x/\sqrt{2}}$. Therefore it is impossible to calculate the functions with any accuracy when $\sqrt{x}{e}^{x/\sqrt{2}}>\frac{\sqrt{2\pi }}{\delta }$. Note that this value of $x$ is much smaller than the minimum value of $x$ for which the function overflows. None. 9 Example This example reads values of X from a file, evaluates the function at each value of ${x}_{i}$ and prints the results. 9.1 Program Text Program Text (s19apfe.f90) 9.2 Program Data Program Data (s19apfe.d) 9.3 Program Results Program Results (s19apfe.r)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 60, "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": 0.9970373511314392, "perplexity": 1424.521548389783}, "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-2014-41/segments/1412037663218.28/warc/CC-MAIN-20140930004103-00413-ip-10-234-18-248.ec2.internal.warc.gz"}
https://www.cheenta.com/integer-solutions-of-a-three-variable-equation/	Select Page Problem: Consider the following equation: $$(x-y)^2 + (y-z)^2 + (z – x)^2 = 2018$$. Find the integer solutions to this equation. Discussion: Set x – y = a, y – z = b. Then z – x = – (a+b). Clearly, we have, $$a^2 + b^2 + (-(a+b))^2 = 2018$$. Simplifying we have $$a^2 + b^2 + ab = 1009$$. Now, treating this as a quadratic in a, we have: $$a^2 + ba + b^2 – 1009 = 0$$ Hence $$a = \frac{-b \pm \sqrt{b^2 – 4(b^2 – 1009)}}{2} = \frac{-b \pm \sqrt{4 \times 1009 – 3b^2}}{2}$$ Since a is an integer, we must have $$4 \times 1009 – 3b^2$$ (the discriminant) to be a positive perfect square integer. This severely limits the number of possibilities for b. For example, we need $$b^2 \le \frac{4 \times 1009}{3}$$ or $$b \le 36$$. So one may ‘check’ for these 36 values. Only b = 35 works. Then $$a = \frac{-35 \pm \sqrt{4 \times 1009 – 3\times 35^2}}{2}$$. But this makes $$a$$ negative. Reducing the number of cases: • Suppose b is the smaller of a and b (WLOG) then $$1009 = a^2 + ab + b^2 \ge b^2 + bb + b^2 = 3b^2$$ or $$1009/3 \ge b^2$$ or 19 > b. • Also, b is 0, 1 or -1 mod 7 (if $$4 \times 1009 – 3b^2$$ needs to be a perfect square). Hence we bring it down to 6 cases: b = 6,7,8,13,14,15	{"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": 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": 0.9521740674972534, "perplexity": 330.6627279513172}, "config": {"markdown_headings": true, "markdown_code": false, "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-2019-30/segments/1563195526714.15/warc/CC-MAIN-20190720214645-20190721000645-00292.warc.gz"}
https://www.physicsforums.com/threads/analysis-2-riemann-integrable-functions.427152/	# Analysis 2- Riemann integrable functions 1. Sep 7, 2010 ### perlawin 1. If abs(f) is Riemann integrable on [a,b], then f is Riemann integrable on [a,b]. True or false (show work) 2. A function f is Riem Int iff f is bounded on [a,b], and for every epsilon>0 there is a partition P of [a,b] s.t. U(f,P)-L(f,P)<epsilon 3. I believe that this is true. So, what I want to do is show that f is bounded don [a,b], and I also want to show the second part of the definition. To show it was bounded, I used the fact that abs(f) was bounded and eventually got sup(abs(f))<=sup(f) and inf(f)>=-sup(abs(f)), which I think proved that f is bounded. My question is how do I show that it fits the second part of the definition? 2. Sep 7, 2010 ### Dick You can't show the second part. Because it isn't true. Try to find a counterexample. 3. Sep 7, 2010 ### deluks917 I'm not sure what the question is and whats your answer. However the statement "if abs(f) is Riemann integrable on [a,b] then f is Riemann integrable on [a,b] isn't true." Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook	{"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": 0.9085069298744202, "perplexity": 755.8902860713409}, "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-2018-13/segments/1521257645775.16/warc/CC-MAIN-20180318130245-20180318150245-00796.warc.gz"}
https://slideplayer.com/slide/7288531/	# Significant Figures in Mathematical Operations The result of the mathematical operation cannot be expressed to any greater degree of certainty than the. ## Presentation on theme: "Significant Figures in Mathematical Operations The result of the mathematical operation cannot be expressed to any greater degree of certainty than the."— Presentation transcript: Significant Figures in Mathematical Operations The result of the mathematical operation cannot be expressed to any greater degree of certainty than the measured values used in the operation. In a series of calculations ~ Carry the extra digits through the final results, then round 5.55.6g ÷ (35.60 mL – 22.40mL) = First:Then: 35.60 mL55.6 ÷ 13.20 = 4.21212 g/mL 22.40 mL = 4.21 g/mL 13.20 mL answer should have 3 sig figs as 55.6 had 3 sig figs Adding and subtracting sig figs – the result should have the same number of decimal places as the least precise measurement used in the calculation! Line up decimals and add 150.0 g H2O (using significant figures) 0.507 g salt 150.5 g solution 150.5 g solution 150.0 is the least precise so the answer will have no more than one place to the right of the decimal. Example Answer will have the same number of decimal places as the least precise measurement used. 12.11 cm 18.0 cm 1.013 cm 31.132 cm 9.62 cm 71.875 cm Correct answer would be 71.9 cm – the last sig fig is “8”, so you will round using only the first number to the right of the last significant digit which is “7”. Multiplication and division of sig figs – - your answer must be limited to the measurement with the least number of sig figs. 5.15 X 2.3 11.845 3 sig figs 2 sig figs only allowed 2 sig figs so 11.845 is rounded to 12 5 sig fig 2 sig figs Significant Figures Multiplication and Division Answer will be rounded to the same number of significant figures as the measurement with the fewest number of significant figures. 4.56 cm x 1.4 cm = 6.38 cm 2 = 6.4 cm 2 28.0 inches 1 inch X 2.54 cm Computed measurement is 71.12 cm Answer is 71.1 cm because the measurement of 28.0” had 3 sig figs - you DID NOT measure 1 inch or 2.54 cm – conversion already determined = =71.12 cm More than one operation (1.245g + 6.34 g+ 8.179g)/7.5 Add 1.245 + 6.34 + 8.179 = Then divide by 7.5 = Download ppt "Significant Figures in Mathematical Operations The result of the mathematical operation cannot be expressed to any greater degree of certainty than the." Similar presentations	{"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": 0.8611881732940674, "perplexity": 1087.9666870226167}, "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-2021-21/segments/1620243989637.86/warc/CC-MAIN-20210518125638-20210518155638-00175.warc.gz"}
https://math.stackexchange.com/questions/3050491/stuck-in-calculus-and-derivative-question	# Stuck in calculus and derivative question Let $$f:[a,b] \to \mathbb{R}$$ continues function such that $$f(b)>f(a)$$ and $$f$$ is not linear (meaning $$f \not= c x +d$$) And $$f$$ is differential in $$(a,b)$$ , prove that there is $$c \in (a,b)$$ such that : $$f'(c) > \frac{f(b)-f(a)}{b-a}$$ By Lagrange theorem i know that there is $$t \in (a,b)$$ such that $$f'(t) = \frac{f(b)-f(a)}{b-a}$$ but how to get strictly bigger and not just equal? • Could it happen that $f'(t)\le\frac{f(b)-f(a)}{b-a}$ for all $t\in (a,b)$? – Ted Shifrin Dec 23 '18 at 17:02 Let$$\begin{array}{rccc}g\colon&[a,b]&\longrightarrow&\mathbb R\\&x&\mapsto&f(x)-f(a)-\frac{f(b)-f(a)}{b-a}(x-a).\end{array}$$Then $$g(a)=g(b)=0$$. On the other hand, $$g'(x)=f'(x)-\frac{f(b)-f(a)}{b-a}$$ and so asserting that there is no such $$c$$ is equivalent to asserting that $$g'(x)\leqslant0$$ for each $$x\in[a,b]$$. But then $$g$$ is decreasing. The only way that a decreasing function from $$[a,b]$$ to $$\mathbb R$$ has zeros at $$a$$ and $$b$$ is that $$g$$ is the null function. But then$$(\forall x\in[a,b]):f(x)=f(a)+\frac{f(b)-f(a)}{b-a}(x-a).$$So, $$f$$ would be linear.	{"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": 24, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9117802381515503, "perplexity": 68.83882728566006}, "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-2019-22/segments/1558232257244.16/warc/CC-MAIN-20190523123835-20190523145835-00422.warc.gz"}
http://tex.stackexchange.com/questions/192393/how-to-reduce-the-space-between-the-hat-of-overset-and-the-symbol	# How to reduce the space between the hat of overset and the symbol? I would like to place the \rightharpoonup on r and get them closer. I had tried the \overset and \Rvector package. But the spacing of the former is too much. And the latter performs bad when placing in smaller font size. I provide the code as follow: \documentclass[titlepage]{article} \usepackage[cm]{fullpage} \usepackage{amsmath,amssymb} \begin{document} $\mathbf{e}_{\overset{\rightharpoonup}{r}}$ \end{document} - Welcome to TeX.SX! Please help us to help you and add a minimal working example (MWE) that illustrates your problem. It will be much easier for us to reproduce your situation and find out what the issue is when we see compilable code, starting with \documentclass{...} and ending with \end{document}. – Christian Hupfer Jul 20 at 15:58 A tip: If you indent lines by 4 spaces or enclose words in backticks , they'll be marked as code, as can be seen in my edit. You can also highlight the code and click the "code" button (with "{}" on it). – Christian Hupfer Jul 20 at 16:21 – Werner Jul 20 at 16:32 Here's a quick-and-not-too-dirty offering: a macro called \harp. It assumes it'll be used in subscript and superscript positions only. For now, it only works with letters that do not have an ascender part. I.e., don't use if with letters such as b, d, f, h, etc. (If you do need to use the macro with such letters, you'll need to tweak the argument of the \raise macro.) \documentclass[titlepage]{article} \usepackage[cm]{fullpage} \usepackage{amsmath,amssymb} \newcommand\harp[1]{\mathstrut\mkern2.5mu#1\mkern-11mu\raise0.6ex% \hbox{$\scriptscriptstyle\rightharpoonup$}} \begin{document} $\mathbf{e}_{\overset{\rightharpoonup}{r}} \text{ vs.\ } \mathbf{e}_{\harp{r}}$ \end{document} - Thanks,it works really good. – 陳智圓 Jul 20 at 23:59 There are two orders of problems: 1. the distance from the arrow to the symbol is too big; 2. in subscripts or superscripts, the arrow is too wide. Here's a solution for both. \documentclass[titlepage]{article} \usepackage{amsmath,graphicx} \newcommand{\harp}[1]{\mathpalette\harpoonvec{#1}} \newcommand{\harpvecsign}{\scriptscriptstyle\rightharpoonup} \newcommand{\harpoonvec}[2]{% \ifx\displaystyle#1\doalign{$\harpvecsign$}{#1#2}\fi \ifx\textstyle#1\doalign{$\harpvecsign$}{#1#2}\fi \ifx\scriptstyle#1\doalign{\scalebox{.6}[.9]{$\harpvecsign$}}{#1#2}\fi \ifx\scriptscriptstyle#1\doalign{\scalebox{.5}[.8]{$\harpvecsign$}}{#1#2}\fi } \newcommand{\doalign}[2]{% {\vbox{\offinterlineskip\ialign{\hfil##\hfil\cr#1\cr$#2$\cr}}}% } \begin{document} \begin{equation} \mathbf{e}_{\harp{r}_{\harp{r}}} \harp{\mathbf{g}} \harp{A} \end{equation} \end{document} - A solution using the accents package. The difference of vertical spacing with respect to the O.P. method with \overset is null in scriptscriptstyle, slight in \scriptstyle and more important in \textstyle. Otherwise the placement is different : \documentclass[titlepage]{article} \usepackage{amsmath,amssymb} \usepackage{accents} \newcommand*\harp[1]{\mkern2mu\accentset{\rightharpoonup}{#1}\mkern2mu}% \begin{document} $\begin{array}{cc} \texttt{\small\textbackslash mathaccent: } & \texttt{\small\textbackslash overset: }\\ \mathbf{e}_{\scriptscriptstyle\harp r} & \mathbf{e}_{\scriptscriptstyle\overset{\rightharpoonup}{r}} \\[2pt] \mathbf{e}_{\harp r} & \mathbf{e}_{\overset{\rightharpoonup}{r}} \\[4pt] \harp{\mathbf g } & \overset{\rightharpoonup}{\mathbf g} \end{array}$% \end{document} - The vertical space between the harpoon and the letter seems no smaller (and possibly even a bit larger) in your code as is already the case with the OP's code. – Mico Jul 20 at 21:40 It is slightly smaller in scriptstyle(by 0.4pt), equal in scriptscriptstyle and noticeably smaller in textstyle (by 1.4pt). See my updated answer. – Bernard Jul 20 at 23:04 Macros from the stackengine package allow one to set the vertical stacking gap. Compare items 1 vs. 2 and/or items 3 vs. 4, and/or 5 vs. 6 for a demonstration of changing the stacking gap. In addition, the appearance will also be affected by what is considered the baseline of the subscipt. In 1, 2, the baseline is between the "r" and the harpoon; in 3, 4, the "r" is the baseline, whereas in 5, 6, the "harpoon" is the baseline. \documentclass[titlepage]{article} \usepackage[cm]{fullpage} \usepackage{amsmath,amssymb} \usepackage{stackengine} \stackMath \begin{document} $\mathbf{e}_{\stackanchor[-.5pt]{\scriptscriptstyle \rightharpoonup}{\scriptstyle r}} \mathbf{e}_{\stackanchor[0pt]{\scriptscriptstyle \rightharpoonup}{\scriptstyle r}} ~ \mathbf{e}_{\stackon[-.5pt]{\scriptstyle r}{\scriptscriptstyle \rightharpoonup}} \mathbf{e}_{\stackon[0pt]{\scriptstyle r}{\scriptscriptstyle \rightharpoonup}} ~ \mathbf{e}_{\stackunder[-.5pt]{\scriptscriptstyle \rightharpoonup}{\scriptstyle r}} \mathbf{e}_{\stackunder[0pt]{\scriptscriptstyle \rightharpoonup}{\scriptstyle r}}$ \end{document} ` -	{"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": 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": 0.9086608290672302, "perplexity": 2221.774090163058}, "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-2014-52/segments/1419447555354.63/warc/CC-MAIN-20141224185915-00046-ip-10-231-17-201.ec2.internal.warc.gz"}
https://gateoverflow.in/381374/isi-2020-pcb-mathematics-question-5-2	25 views Deduce that if $N, H, K$ are normal subgroups of a group $G$ such that $$N \bigcap H=N \bigcap K=H \bigcap K=\left\{e_{G}\right\}$$ and $G=H K$, then $N$ is an Abelian group. 1 31 views	{"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": 0.856916606426239, "perplexity": 99.39634206899753}, "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/1669446710473.38/warc/CC-MAIN-20221128034307-20221128064307-00777.warc.gz"}
http://www.physicsforums.com/showthread.php?t=528585	# Associative property of convolution by sainistar Tags: associative, convolution, property P: 4 Hi There The associative property of convolution is proved in literature for infinite interval. I want to prove the associative property of convolution for finite interval. I have explained the problem in the attached pdf file. Any help is appreciated. Regards Aman Attached Files convproblem.pdf (90.5 KB, 15 views) Mentor P: 15,962 Integral (10) is obviously wrong. Your two integrals have $\theta$ in their bounds. But $\theta$ is an integration variable!! This can't be correct. Why do you obtain something wrong here. Because after equation (3) they applied Fubini and switched the both integrals, and THEN they did the substitution. You must do something similar. Apply Fubini after (9). But Fubini will in this case not be simply switching the integral signs... P: 4 Thanks micromass I was looking for the Fubini theorem when the bound are the integration variable. I did not find any. Can you please let me know any source i can read. It will also be helpful if you can suggest how can i apply Fubini after (9). Regards Related Discussions Calculus 0 Linear & Abstract Algebra 1 Calculus & Beyond Homework 4 Precalculus Mathematics Homework 3 General Discussion 13	{"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": 0.971211850643158, "perplexity": 945.5474922435328}, "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-2014-10/segments/1394021767149/warc/CC-MAIN-20140305121607-00055-ip-10-183-142-35.ec2.internal.warc.gz"}
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Anything with a board or chance I can get in the water I love! I am such a big fan I decided to start this website to review all my favorite products and some others. Hope you enjoy!	{"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": 0.9773644804954529, "perplexity": 4824.760702494513}, "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/1618038059348.9/warc/CC-MAIN-20210410210053-20210411000053-00098.warc.gz"}
http://mathhelpforum.com/calculus/133012-integration-problem.html	# Math Help - Integration problem 1. ## Integration problem Evaluate the integral integral (0, pi/2) 60cos^5 xdx... I have no idea how to solve.. 2. Integration by parts will produce a reduction formula. 3. Originally Posted by Jgirl689 Evaluate the integral integral (0, pi/2) 60cos^5 xdx... I have no idea how to solve.. $\int{\cos^5{x}\,dx} = \int{\cos^4{x}\cos{x}\,dx}$ $= \int{(\cos^2{x})^2\cos{x}\,dx}$ $= \int{(1 - \sin^2{x})^2\cos{x}\,dx}$ $= \int{(1 - 2\sin^2{x} + \sin^4{x})\cos{x}\,dx}$. Now make the substitution $u = \sin{x}$ so that $\frac{du}{dx} = \cos{x}$. 4. ## many ways to solve this Originally Posted by Jgirl689 Evaluate the integral integral (0, pi/2) 60cos^5 xdx... I have no idea how to solve.. i find several ways to solve this: 1)you can expand cos^5x in terms of multiples of x using euler's formula considering y=cosx+isinx and 1/y=cosx-isinx. 2)you can use a reduction formula as TKHunny said and 3)the way 'prove it' did it 4)and lastly u can perhaps use some property of definite integrals: integration(0,pi/2)f(x)=integration(0,pi/2)f(pi/2-x). i have not tested any of these methods though but i think they are all very feasible. 5. Originally Posted by Pulock2009 i find several ways to solve this: 1)you can expand cos^5x in terms of multiples of x using euler's formula considering y=cosx+isinx and 1/y=cosx-isinx. 2)you can use a reduction formula as TKHunny said and 3)the way 'prove it' did it 4)and lastly u can perhaps use some property of definite integrals: integration(0,pi/2)f(x)=integration(0,pi/2)f(pi/2-x). i have not tested any of these methods though but i think they are all very feasible. Another alternative is to use trigonometric identities to convert it into functions such as $\sin{nx}$ or $\cos{nx}$.	{"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": 8, "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": 0.9789780974388123, "perplexity": 2668.8513096552215}, "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-2016-30/segments/1469257824757.62/warc/CC-MAIN-20160723071024-00282-ip-10-185-27-174.ec2.internal.warc.gz"}
https://infoscience.epfl.ch/record/234234?ln=en	## Predicting non-linear dynamics by stable local learning in a recurrent spiking neural network The brain needs to predict how the body reacts to motor commands, but how a network of spiking neurons can learn non-linear body dynamics using local, online and stable learning rules is unclear. Here, we present a supervised learning scheme for the feedforward and recurrent connections in a network of heterogeneous spiking neurons. The error in the output is fed back through fixed random connections with a negative gain, causing the network to follow the desired dynamics. The rule for Feedback-based Online Local Learning Of Weights (FOLLOW) is local in the sense that weight changes depend on the presynaptic activity and the error signal projected onto the postsynaptic neuron. We provide examples of learning linear, non-linear and chaotic dynamics, as well as the dynamics of a two-link arm. Under reasonable approximations, we show, using the Lyapunov method, that FOLLOW learning is uniformly stable, with the error going to zero asymptotically. Published in: Elife, 6, e28295 Year: 2017 Publisher: Cambridge, Elife Sciences Publications Ltd ISSN: 2050-084X 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": 0.8233417272567749, "perplexity": 1499.4700207212497}, "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-2019-22/segments/1558232256381.7/warc/CC-MAIN-20190521122503-20190521144503-00110.warc.gz"}
http://math2ever.blogspot.com/2013/05/what-is-exponential-function.html	Exponential function IS JUST another function in mathematics study. To date, most of the time we are dealing with so called power function e.g f(x) = x2 where x is the base the number 2 is the power (index) However, in exponential function we are dealing f(x) = 2x where 2 is the base the number x is the power (index) source: Wikipedia The big difference is in that the variable is now the power, rather than the base. source: Wikipedia The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828. Thus, the above expression becomes:(see also natural logarithm) f (x) = e x Value of e	{"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": 0.9374247789382935, "perplexity": 1149.1587455476379}, "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-2017-47/segments/1510934809419.96/warc/CC-MAIN-20171125051513-20171125071513-00323.warc.gz"}
https://r-forge.r-project.org/forum/forum.php?thread_id=31878&forum_id=4377&group_id=1337	# Forum: support Monitor Forum \| Start New Thread Nested Flat Threaded Ultimate Show 25 Show 50 Show 75 Show 100 RE: size of math font in compiled html [ reply ]By: Markus Loecher on 2016-06-22 15:56 [forum:43309] Thanks, this is very helpful!! Markus RE: size of math font in compiled html [ reply ]By: Achim Zeileis on 2016-06-20 14:30 [forum:43295] (i) The default TeX-to-HTML converter "ttm" does not support \boxed{} but "pandoc" does. So using exams2html("tmp.Rnw", converter = "pandoc") gives what you want. But, of course, "pandoc" may or may not display other things in a slightly different way that you may or may not like. Hence, personally I prefer solutions that are robust across converters but might require a little bit more coding. In this case, you could set up the box manually for example. (ii) For me, the solution with or without \boxed{} uses the same font size. And as the display is browser-specific anyways, I wouldn't worry about this too much. It's simple enough to press Ctrl-+ when viewing the HTML file... However, if you want a somewhat more principled solution you can also do exams2html("tmp.Rnw", converter = "pandoc", mathjax = TRUE). Then MathJax allows to zoom formulas (upon hovering or clicking etc.) or you can set a general zoom factor for all math content. My personal aesthetic preference, however, is that MathJax generally displays formulas too large whereas MathML in Firefox just looks fine. But to a certain degree this is a matter of personal taste... size of math font in compiled html [ reply ]By: Markus Loecher on 2016-06-20 12:27 [forum:43294] tmp.Rnw (5) downloads Dear authors, When I use exams2pdf to compile an Rnw file (attached) that contains the following Latex expression $\displaystyle \boxed{P(x=a;N,A,n,a) = \frac{{A \choose a} \cdot {N-A \choose n-a} }{{N \choose n}}}$ the output looks perfect. But with exams2thml I run into the following difficulties: (i) The Latex \boxed directive seems unrecognized. (ii) When I remove the \boxed command, the displayed fraction seems too small, and I have been unsuccessfully trying to enlarge the math fonts. Is there a way in html output to (i) frame eqns with a box and/or (ii) manipulate the size of math font ? Thanks!! Markus Thanks to:	{"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": 0.8769413232803345, "perplexity": 3788.6729670013247}, "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/1524125949489.63/warc/CC-MAIN-20180427060505-20180427080505-00478.warc.gz"}
http://mathhelpforum.com/differential-geometry/147262-banach-space-print.html	# Banach space • Jun 1st 2010, 06:42 AM cizzzi Banach space prove that, in a Banach space if $Sum\|\|Xn\|\|$ converges then $SumXn$ converges • Jun 1st 2010, 06:43 AM cizzzi Banach space • Jun 1st 2010, 07:02 AM cizzzi prove that , in a Banach space if $\sum^{\infty}_{n=1}\|\|Xn\|\|$ converges then $\sum^{\infty}_{n=1}Xn$ converges. • Jun 1st 2010, 07:11 AM Focus Quote: Originally Posted by cizzzi prove that , in a Banach space if $\sum^{\infty}_{n=1}\|\|Xn\|\|$ converges then $\sum^{\infty}_{n=1}Xn$ converges. Show that the sum is Cauchy, i.e. consider $S_k:=\sum_{n=1}^k X_n$, now consider $\|\|S_k-S_l\|\|$. Hint: If $\sum_{n=1}^\infty x_n < \infty$ then $\sum_{n=k}^\infty x_n \rightarrow 0$ as k goes to infinity. (A fact that you can prove using the fact that $x_n \rightarrow 0$). • Jun 1st 2010, 11:00 AM cizzzi thank you I try to solve but I do not know very well functional analysis :( • Jun 1st 2010, 12:55 PM Focus Quote: Originally Posted by cizzzi thank you I try to solve but I do not know very well functional analysis :( Why don't you post what you have done so far (even if it is wrong)? • Jun 4th 2010, 06:44 AM cizzzi if X is complete and $\sum^{\infty}_{n=1}\|\|X_n\|\|<{\infty}$ then sequence $S_{k}=\sum^{k}_{n=1}X_{n}$ for $k\epsilon\aleph$ is Cauchy because for k>m $\|\|S_{k}-S_{m}\|\|\leq\sum^{k}_{n=m+1}\|\|X_{n}\|\|\rightarrow0$ as $m,k\rightarrow0$ therefore , $S=\sum^{\infty}_{n=1}X_{n}= lim_{k\rightarrow\infty}\sum^{k}_{n=1}X_{n}$ exists in X. is it true? • Jun 6th 2010, 12:22 PM Focus Quote: Originally Posted by cizzzi if X is complete and $\sum^{\infty}_{n=1}\|\|X_n\|\|<{\infty}$ then sequence $S_{k}=\sum^{k}_{n=1}X_{n}$ for $k\epsilon\aleph$ is Cauchy because for k>m $\|\|S_{k}-S_{m}\|\|\leq\sum^{k}_{n=m+1}\|\|X_{n}\|\|\rightarrow0$ as $m,k\rightarrow0$ therefore , $S=\sum^{\infty}_{n=1}X_{n}= lim_{k\rightarrow\infty}\sum^{k}_{n=1}X_{n}$ exists in X. is it true? The sum converges to zero as k and m tend to infinity (not zero).	{"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": 23, "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": 0.9945599436759949, "perplexity": 1309.999260054841}, "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-2016-44/segments/1476988719754.86/warc/CC-MAIN-20161020183839-00162-ip-10-171-6-4.ec2.internal.warc.gz"}
https://tutorme.com/tutors/20340/interview/	Subjects PRICING COURSES Start Free Trial Kelly B. Proud Math Geek Tutor Satisfaction Guarantee Geometry TutorMe Question: Find the area of the equilateral triangle inscribed in a circle with a radius of 4 units. Kelly B. Side note: This problem will be easier to solve if you draw a picture of the information as we go through the problem. Prerequisite knowledge: For any equilateral triangle: 1. The radius of the incircle$$=\frac{side}{2\sqrt{3}}$$ 2. The radius of the circumcircle$$=\frac{side}{\sqrt{3}}$$ Since we are given the radius of the circumcircle (the triangle is inscribed in the circle), we will use #2 to find the area of the equilateral triangle. $$4=\frac{s}{\sqrt{3}}$$ $$4\sqrt{3}=s$$ $$area=\frac{1}{2}bh$$ We now know the base, but we still have to solve for the height. The height of the triangle will divide the base in half and will, by definition, be perpendicular to the base. Therefore, we can solve for the height using the Pythagorean Theorem. $$a^{2}+b^{2}=c^{2}$$ We know the measures of the $$a^{2}$$ and $$c^{2}$$, so we can solve for the height, $$b^{2}$$. $$(2\sqrt{3})^{2}+b^{2}=(4\sqrt{3})^{2}$$ $$(43)+b^{2}=163$$ $$12+b^{2}=48$$ $$b^{2}=36$$ $$b=6$$ Now find the area. $$A=\frac{1}{2}bh$$ $$A=\frac{1}{2}(4\sqrt{3})(6)$$ $$A=12\sqrt{3}$$ Calculus TutorMe Question: Find the derivative: $$f(x)=x^{4}+3x^{3}-16x^{2}+225x-15$$ Kelly B. $$f'(x)=4x^{3}-9x^{2}-32x+225$$ Algebra TutorMe Question: Kelly is older than Parker. Next year Parker will be exactly half Kelly's age. Six years ago Kelly was three times as old as Parker. How old are Parker and Kelly? Kelly B. Step one: Write the equations given in the problem. $$P+1=\frac{1}{2}(K+1)$$ $$K-6=3(P-6)$$ Step two: Solve one of the equations for one variable in order to substitute. $$K-6=3(P-6)$$ $$K-6=3P-18$$ $$K=3P-12$$ Step three: Substitute the final equation from step two into the original equation not solved in step two. Then solve. $$P+1=\frac{1}{2}(K+1)$$ $$P+1=\frac{1}{2}((3P-12)+1)$$ $$P+1=\frac{1}{2}(3P-11)$$ $$P+1=\frac{3}{2}P-\frac{11}{2}$$ $$\frac{13}{2}=\frac{1}{2}P$$ $$13=P$$ Step four: Substitute the answer from step three into the final equation from step two to solve for the final variable. $$K=3P-12$$ $$K=3(13)-12$$ $$K=39-12$$ $$K=27$$ Final Answer: Parker is 13 and Kelly is 27. Send a message explaining your needs and Kelly will reply soon. Contact Kelly	{"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": 0.931362509727478, "perplexity": 383.7311714494266}, "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-2018-09/segments/1518891815500.61/warc/CC-MAIN-20180224073111-20180224093111-00224.warc.gz"}
https://www.zora.uzh.ch/id/eprint/22713/	# On the binary expansion of a random integer Barbour, A D (1992). On the binary expansion of a random integer. Statistics and Probability Letters, 14(3):235-241. ## Abstract It is shown that the distribution of the number of ones in the binary expansion of an integer chosen uniformly at random from the set 0, 1,…, n − 1 can be approximated in total variation by a mixture of two neighbouring binomial distributions, with error of order (log n)−1. The proof uses Stein's method. ## Abstract It is shown that the distribution of the number of ones in the binary expansion of an integer chosen uniformly at random from the set 0, 1,…, n − 1 can be approximated in total variation by a mixture of two neighbouring binomial distributions, with error of order (log n)−1. The proof uses Stein's method. ## Statistics ### Citations Dimensions.ai Metrics 4 citations in Web of Science® 3 citations in Scopus®	{"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": 0.9507614374160767, "perplexity": 322.40218587676947}, "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-2020-50/segments/1606141733120.84/warc/CC-MAIN-20201204010410-20201204040410-00245.warc.gz"}
http://clay6.com/qa/51563/which-of-the-following-is-the-only-noble-gas-not-to-occur-in-the-free-state	Browse Questions # Which of the following is the only noble gas not to occur in the free state in the atomosphere, air, in oute space or in natural gases etc. $\begin{array}{1 1} Radon \\ Argon\\ Xenon \\ Krypton \end{array}$ Can you answer this question? Radon is usually isolated from the radioactive decay of dissolved radium compounds. answered Jul 28, 2014	{"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": 0.8585070371627808, "perplexity": 2315.904584430179}, "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-2017-17/segments/1492917124297.82/warc/CC-MAIN-20170423031204-00146-ip-10-145-167-34.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/145860-approximate-5th-root-20-a.html	# Math Help - Approximate 5th root of 20 1. ## Approximate 5th root of 20 f(x) = x^5 - 20 f'(x) = 5x^4 x2 = x1 - ( x1^5 - 20 ) / ( 5x1^4 ) x2 = 1 - ( (1)^5 - 20 ) / ( 5(1)^4 ) x2 = 1 - ( -19 / 5 ) x2 = 24 / 5 x2 = 4.08 My answer is wrong and the correct answer is 1.82056420. I used an initial approximation of x1 = 1, as no approximation was given. 2. Originally Posted by TsAmE f(x) = x^5 - 20 f'(x) = 5x^4 x2 = x1 - ( x1^5 - 20 ) / ( 5x1^4 ) x2 = 1 - ( (1)^5 - 20 ) / ( 5(1)^4 ) x2 = 1 - ( -19 / 5 ) x2 = 24 / 5 x2 = 4.08 My answer is wrong and the correct answer is 1.82056420. I used an initial approximation of x1 = 1, as no approximation was given. You can use Taylor... x^1/5 ~ 1+(1/5)(x-1) - (2/25)(x-1)^2)+(6/125)*(x-1)^3+O((x-1)^4) You put x=20 and get the needed. 3. I havent learned taylor, I want to do it using newtons method 4. Your method is correct. You made a little slip. 24/5=4.8 rather than 4.08. Just keep going. On a decent calculator you can do this: 1.5 = ANS - (ANS^5-20)/(5ANS^4) = = = = = It gives 1.9901.. 1.8470.. 1.8213.. and pretty soon you will have 1.820564203 5. Originally Posted by TsAmE f(x) = x^5 - 20 f'(x) = 5x^4 x2 = x1 - ( x1^5 - 20 ) / ( 5x1^4 ) x2 = 1 - ( (1)^5 - 20 ) / ( 5(1)^4 ) x2 = 1 - ( -19 / 5 ) x2 = 24 / 5 x2 = 4.08 My answer is wrong and the correct answer is 1.82056420. I used an initial approximation of x1 = 1, as no approximation was given. Well, 24/5= 4.8, not 4.08 but what exactly was the problem? Surely not to do just one iteration? If you keep going, you get successive approximations that converge to 1.82...	{"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": 0.8221979141235352, "perplexity": 1518.179917191566}, "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-2015-18/segments/1429246649738.26/warc/CC-MAIN-20150417045729-00126-ip-10-235-10-82.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/find-the-normal-force-on-an-inclined-plane.561325/	# Find the normal force on an inclined plane. • #1 2 0 ## Homework Statement Find the normal force acting on a mass of 5kg on an incline plane of 30 degrees. ## Homework Equations Fn = mgsin30 or mgcos30 ? ## The Attempt at a Solution I'm not sure if I use sin or cos when finding the normal force on an incline. I have trouble visualizing the angle perpendicular to the plane and moving the angles around. Related Introductory Physics Homework Help News on Phys.org • #2 Redbelly98 Staff Emeritus Homework Helper 12,100 129 Welcome to Physics Forums. If the surface makes an angle θ to the horizontal, then the normal makes the same angle θ from the vertical. Does that help your visualizing? If it's still unclear, think about a horizontal surface, so that θ is zero, and answer these questions: 1. What is the normal force when the surface is horizontal? Draw a force diagram for yourself, if you need to, to figure this out. Hope that helps! • #3 2 0 It works with mgsin theta, but when i try to draw it out it doesn't make sense to me. • #4 Doc Al Mentor 44,940 1,201 • Last Post Replies 3 Views 6K • Last Post Replies 2 Views 25K • Last Post Replies 6 Views 4K • Last Post Replies 2 Views 4K • Last Post Replies 12 Views 9K • Last Post Replies 1 Views 1K • Last Post Replies 3 Views 15K • Last Post Replies 4 Views 5K • Last Post Replies 1 Views 5K • Last Post Replies 2 Views 1K	{"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": 0.8684108853340149, "perplexity": 1913.0929335351439}, "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/1593655881984.34/warc/CC-MAIN-20200703091148-20200703121148-00150.warc.gz"}
http://math.stackexchange.com/questions/223775/exterior-derivative-of-a-complicated-differential-form	# Exterior derivative of a complicated differential form Let $\omega$ be a $2$-form on $\mathbb{R}^3\setminus\{0\}$ defined by $$\omega = \frac{x\,dy\wedge dz+y\,dz\wedge dx +z\,dx\wedge dy}{(x^2+y^2+z^2)^{\frac{3}{2}}}$$ Show that $\omega$ is closed but not exact. In order to show that $\omega$ is closed, I need to show that $d\omega=0$. I'm having some problems getting all of the calculus right and somewhere along the way I'm messing up. I started by rewriting $\omega$ as $$\omega = (x\,dy\wedge dz+y\,dz\wedge dx +z\,dx\wedge dy)(x^2+y^2+z^2)^{-\frac{3}{2}}$$ Now I should be able to use the product rule to evaluate (I think). Then $$d\omega = (dx\wedge dy\wedge dz+dy\wedge dz\wedge dx +dz\wedge dx\wedge dy)(x^2+y^2+z^2)^{-\frac{3}{2}} + (\ast)$$ where $$(\ast) = (x\,dy\wedge dz+y\,dz\wedge dx +z\,dx\wedge dy)\left(-\frac{3}{2}(2x\,dx+2y\,dy+2z\,dz)\right)(x^2+y^2+z^2)^{-\frac{5}{2}}$$ Even after trying to simplify everything, I can't get it to cancel. This makes me think that perhaps I can't apply the product rule like this. What should I do to calculate $d\omega$? If $\omega$ is a globally defined smooth form and if $d\omega=0$, then $\omega$ is exact because there is some other form $\alpha$ with $d\alpha=\omega$ and $d^2\alpha=d\omega=0$. Because $\omega$ is not defined at $(0,0,0)$, it makes sense that it isn't exact. Is there a way to show that there can't be an $\alpha$ such that $d\alpha=\omega$? - Maybe cylindrical or spherical coordinates will help. – Pragabhava Oct 29 '12 at 20:22 To show something that a 2-form is not exact, it is sufficient to integrate it over a closed, bounndaryless region and get something non-zero. In this case, I would recommend integrating over the sphere (since you have an $x^2 + y^2 + z^2$ term). – Eric O. Korman Oct 29 '12 at 20:41 My method for integrating 2-forms has previously involved parameterizing the surface that I'm integrating over. Do I need to do the same thing and parameterize the sphere $S=\{(x,y,z)\|\;x^2+y^2+z^2=1\}$ or is there a way to integrate $\omega$ just using $x^2+y^2+z^2=1$? – chris Oct 29 '12 at 22:41 By the way, this is the Solid Angle form. – diff_math Jul 24 '13 at 21:53 Your idea is good. Define $r = (x^2 + y^2 + z^2)^\frac{1}{2}$, $f(x,y,z) = \frac{1}{r^3}$ and $\mu = x dy \wedge dz + y dz \wedge dz + z dx \wedge dy$. Then by the product rule: $d(\omega) = d(f\mu) = df \wedge \mu + f d\mu$. Let us hold hands and calculate: $$d\mu = dx \wedge dy \wedge dz + dy \wedge dz \wedge dx + dz \wedge dx \wedge dy = 3 dx \wedge dy \wedge dz.$$ $$df = \frac{-3}{r^5} (x dx + y dy + z dz)$$ $$df \wedge \mu = \frac{-3}{r^5} (x dx + y dy + z dz) (x dy \wedge dz + y dz \wedge dz + z dx \wedge dy) = \frac{-3}{r^5} (x^2 dx \wedge dy \wedge dz + y^2 dy \wedge dz \wedge dz + z^2 dz \wedge dz \wedge dy) = \frac{-3}{r^5} (r^2 dx \wedge dy \wedge dz) = \frac{-3}{r^3} dx \wedge dy \wedge dz$$ $$df \wedge \mu + f d\mu = \frac{-3}{r^3} dx \wedge dy \wedge dz + \frac{3}{r^3} dx \wedge dy \wedge dz= 0.$$ Phew. As you see, in the calculations, you use a lot the antisymmetrization properties of the wedge product. You just need to do everything carefully, and it will come out. For the second question, if it would be an exact form, the result of integration of $\omega$ on every two-dimensional closed submanifold (compact, without boundary) of $\mathbb{R}^3$ would be zero by Stokes's theorem. Try to find a closed submanifold on which you can calculate the integral directly relatively easily and for which the result is non-zero. If you are familiar with conservative vector fields, this is just like showing that the field is not conservative by showing that the work done by it along some closed loop is non-zero. - When you're calculating $df\wedge \mu$, you start by saying $df\wedge\mu=df$. Did you mean to write that $df\wedge\mu=df\mu$? – chris Oct 29 '12 at 22:24 No, it's just a typo. $df$ is a one-form, $\mu$ is a two-form, so the wedge is a three-form. $df \mu$ doesn't make sense. I've corrected it. Thanks! – levap Oct 30 '12 at 8:46 Geometric calculus is slightly different in notation from differential forms, but the math is very similar, and I hope I can provide a useful insight into this problem, even with a slightly different background. Geometric calculus replaces differentials like $dx$ by vectors $e_x$, but it still uses wedges, which are still asymmetric. So your $\omega$, in GC language, would be $$\omega = \frac{x e_y \wedge e_z + y e_z \wedge e_x + z e_x \wedge e_y}{(x^2 + y^2 + z^2)^{3/2}}$$ Not a whole lot of difference, I'll grant. Still, GC interprets this as a bivector (field), an oriented planar subspace in 3D space. Instead of Hodge duality, GC uses the geometric product, denoted wholly by juxtaposition: $e_i e_j = -e_j e_i$ if $i \neq j$. Otherwise, $e_i e_i = 1$ (no summation implied). Hodge duality is replaced by multiplication with the pseudoscalar, $e_x \wedge e_y \wedge e_z \equiv i$. For instance, $i(e_y \wedge e_z) = -e_x$. Let's use this to simplify your expression for $\omega$ to: $$\omega = \frac{i r}{\|r\|^3}$$ where $r = xe_x + ye_y + z e_z$. This field, $r/\|r\|^3 \equiv G$, is in fact the free space Green's function for the vector derivative. $\nabla r/\|r\|^3 = 4\pi\delta(r)$. (You might understand this more intuitively if I say $\nabla$ is the rough equivalent of $d + \delta$, the exterior derivative plus the coderivative. We say $\nabla \wedge A$ is the exterior derivative of $A$, and $\nabla \cdot A$ is the interior derivative, or coderivative.) Finally, it suffices in 3D to say that $i$ commutes with everything, at the cost of turning wedges into dots and dots into wedges. You have $\omega = iG$, and you want to prove that $\nabla \wedge \omega = \nabla \wedge (iG) = 0$. Pulling the $i$ out gives $i\nabla \cdot G = 0$, which is true in some places. (Question for you: where is it not true?) As has been said, you can prove that $\omega$ is not exact (that is, there is no $\alpha$ such that $\nabla \wedge \alpha = \omega$) by seeing if $\omega$ is integrable. This is tightly coupled to the question earlier: where, if anywhere, is $\nabla \wedge \omega \neq 0$? When you integrate the exterior derivative of this field over a volume, will you get zero? If you take nothing else from this answer (I know geometric calculus can still look and feel quite different from differential forms), I think you should see that this is problem probes at the nature of the derivative in 3d space. The 2-form you have here is just a disguise for the 3D free space Green's function. - Use spherical coordinates. In spherical coordinates $r,\theta,\phi$, the form reads: $$\omega = \sin\theta\,d\theta\wedge d\phi.$$ This is closed, because the coefficient only depends on a coordinate that is already used: $$d\omega = d(\sin\theta)\wedge d\theta\wedge d\phi = \cos\theta\,d\theta\wedge d\theta\wedge d\phi = 0,$$ since $d\theta\wedge d\theta=0$. This is anyway not exact, because you can integrate it on the sphere! Integrating it on the closed area $0\le\theta\le \pi, 0\le\phi\le2\pi$, that is a sphere (of radius one), you find (it's a simple calculation): $$\oint\omega = 4\pi.$$ Therefore, the form is not exact. -	{"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": 0.947425901889801, "perplexity": 192.09362071239258}, "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/1454701159654.65/warc/CC-MAIN-20160205193919-00159-ip-10-236-182-209.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/lin-alg-is-the-set-a-linearly-independent-subset-of-r-3.183050/	# Lin. Alg. - Is the set a linearly independent subset of R^3 1. Sep 4, 2007 ### b0it0i 1. The problem statement, all variables and given/known data Is {(1,4,-6), (1,5,8), (2,1,1), (0,1,0)} a linearly independent subset of R^3. Justify your answer 2. Relevant equations 3. The attempt at a solution I asssumed a(1,4,-6) + b(1,5,8) + c(2,1,1) + d(0,1,0) = 0 then i set up the system a + b + 2c = 0 4a + 5b + c + d = 0 -6a + 8b + c = 0 My first step was to switch the 2nd row with the 3rd row: a + b + 2c = 0 -6a + 8b + c = 0 4a + 5b + c + d = 0 then i replaced the second row with ( 6R1 + R2) and replaced the third row with (-4R1 + R3) my result is a+ b + 2c = 0 14b + 13c = 0 b - 7c + d = 0 then i replaced thethird row with ( - 1/14 R2 + R3) a + b + 2c = 0 14b + 13c = 0 -111/14 c + d = 0 on this step, it's looking closer to what Dick got, and is there supposed to be another manipulation with the rows? I just solved for d = 111/14 c then i just let c = 1, thus c = 1 d = 111/14 b = -13/14 a = (13/14) - 2 but if i let c = 14 c = 14 d = 111 b = -13 a = -15 are both results correct?? and if not, (meaning Dick's is the only correct solution), what is the next step in the algorithm to find c = 14? thanks for the help nevermind, upon further reading i found that "In this case, the system does not have a unique solution, as it contains at least one free variable. The solution set can then be expressed parametrically (that is, in terms of the free variables, so that if values for the free variables are chosen, a solution will be generated)." so there's no unique solution, since you can choose whatever you want your variable "c" to be. Last edited: Sep 5, 2007 2. Sep 4, 2007 ### proton are you sure you row-reduced the system? even if you didn't, you should have encountered in your class that for R^n, the maximum number of vectors that can be linearly independent is n, which is in this case 3 3. Sep 4, 2007 ### Dick a=-15, b=-13, c=14, d=111. Yes, you've missed some solutions, as proton predicted. 4. Sep 5, 2007 ### b0it0i thanks alot, i'm actually taking the linear algebra course, with an intro to linear algebra course at the same time, so i'm not really familiar with this topic yet but when you mentioned row reduced system, i looked it up, and worked out the problem before, i just tried random substitutions My first step was to switch the 2nd row with the 3rd row: a + b + 2c = 0 -6a + 8b + c = 0 4a + 5b + c + d = 0 then i replaced the second row with ( 6R1 + R2) and replaced the third row with (-4R1 + R3) my result is a+ b + 2c = 0 14b + 13c = 0 b - 7c + d = 0 then i replaced thethird row with ( - 1/14 R2 + R3) a + b + 2c = 0 14b + 13c = 0 -111/14 c + d = 0 on this step, it's looking closer to what Dick got, and is there supposed to be another manipulation with the rows? I just solved for d = 111/14 c then i just let c = 1, thus c = 1 d = 111/14 b = -13/14 a = (13/14) - 2 but if i let c = 14 c = 14 d = 111 b = -13 a = -15 are both results correct?? and if not, (meaning Dick's is the only correct solution), what is the next step in the algorithm to find c = 14? thanks for the help 5. Sep 5, 2007 ### b0it0i nevermind, upon further reading i found that "In this case, the system does not have a unique solution, as it contains at least one free variable. The solution set can then be expressed parametrically (that is, in terms of the free variables, so that if values for the free variables are chosen, a solution will be generated)." so there's no unique solution, since you can choose whatever you want your variable "c" to be. 6. Sep 5, 2007 ### Dick You've got it. My solution was just a 'for instance'. Similar Discussions: Lin. Alg. - Is the set a linearly independent subset of R^3	{"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": 0.8263468742370605, "perplexity": 689.1793279772744}, "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-2017-13/segments/1490218199514.53/warc/CC-MAIN-20170322212959-00388-ip-10-233-31-227.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/integration-of-a-polynomial-problem.780585/	# Integration of a polynomial problem 1. Nov 7, 2014 ### MartinJH Hi, I'm using KA Stroud 6th edition (for anyone with the same book, P407) and there is a example question where I just can't seem to get the answer they have suggested: 1. The problem statement, all variables and given/known data Question: Determine the value of I = ∫(4x3-6x2-16x+4) dx when x = -2, given that at x = 3, I = -13 Their answer is when x = -2, I = 12. 3. The attempt at a solution I found the integral: I = ∫(4x3-6x2-16x+4) dx = x4-2x3-8x2+4x + C and then substituted x for 3 and getting: -13 = -33 + C thus: C = 20 Now when I replace x with -2, plus the constant, I get: -24-2(-2)3-8(-2)2+4(-2) + 20 = -20 I'm a few days into Integrals so I feel I may be doing something daft? Many thanks. 2. Nov 7, 2014 ### Staff: Mentor Your work is fine except for one minor thing. At the end you wrote -24 instead of (-2)4. In the first, 2 is raised to the 4th power, and then you take the negative, resulting in -16. In the latter, -2 is raised to the 4th power, resulting in +16. 3. Nov 7, 2014 ### MartinJH That was an honest slip. I appreciate there is a difference between them both. I finally got the answer, it was a case of not respecting the brackets and powers... I need a break. Thanks for pointing that out and explaining! :) 4. Nov 7, 2014 ### LCKurtz HEY!! I thought micromass's avatar was retired. 5. Nov 8, 2014 ### MartinJH I assume that is for me? :). I use this logo for most online things. EEVBlog, my Steam account etc etc. I was thinking about using Floyds new album cover. 6. Nov 8, 2014 ### LCKurtz Yes, but it was really directed at the old timers, sort of tongue-in-cheek. Turns out one of our previous highly regarded members used to use that logo. Nothing to worry about though. 7. Nov 9, 2014 ### MartinJH Yeah, that's cool. I Understand :). Draft saved Draft deleted Similar Discussions: Integration of a polynomial problem	{"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": 0.817621648311615, "perplexity": 1957.5945155539594}, "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/1502886104634.14/warc/CC-MAIN-20170818102246-20170818122246-00589.warc.gz"}
https://www.edaboard.com/threads/how-to-assign-a-short-point-ideal-ground-in-cst-transient.338155/	# How to assign a short point (ideal ground) in CST transient Status Not open for further replies. #### junsik ##### Junior Member level 2 Joined Feb 17, 2015 Messages 23 Helped 0 Reputation 0 Reaction score 0 Trophy points 1 Activity points 207 Hi everyone! In CST transient simulation, I have some question. When I want to do transient simulation using CST, I want to assign one side of structure as a short point to the ideal ground. It would make the low impedance current path to the ideal ground. But, I don't know how to realize it. there is some boundary condition. open, E=0, H=0, and so on... When I simulate in frequency domain, i usually assign the open space as a boundary condition. But, i understand it is not ground just adding vacuum in transient simulation. am i right? #### volker@muehlhaus Joined Apr 11, 2014 Messages 2,511 Helped 983 Reputation 1,968 Reaction score 963 Trophy points 113 Activity points 14,884 Physically, there is no global ground. Ground is what you call ground, where you place your port's reference pin. However, even if you use PEC (perfect electric conductor) two points at some distance will have (and must have) delay and inductance between them. Status Not open for further replies. Replies 1 Views 2K • Locked Replies 3 Views 2K Replies 2 Views 14K Replies 0 Views 669 Replies 6 Views 2K	{"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": 0.8385151028633118, "perplexity": 4501.33795671417}, "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-2020-45/segments/1603107917390.91/warc/CC-MAIN-20201031092246-20201031122246-00661.warc.gz"}
http://pari.math.u-bordeaux1.fr/archives/pari-users-1310/msg00007.html	Bill Allombert on Thu, 10 Oct 2013 20:45:23 +0200 Re: Degree extension On Thu, Oct 10, 2013 at 05:57:06PM +0200, [email protected] wrote: > Dear All, > > I am Laura, a new member of the list of the > users of PARI. Welcome! > I have a question. I have the roots of > some polynomials of the form y^2=x^3+Ax+B. > For example p:=y^2=x^3+2*x+5. > I call a, b and c the roots of p. > I would like to calculate the degree > of the number field > > Q(sqrt(a-b),sqrt(a-c),sqrt(b-c),sqrt(-1)). > > Is it possible with PARI? Yes, this is possible and K=Q(sqrt(a-b),sqrt(a-c),sqrt(b-c),sqrt(-1)) 1) Build the Galois closure of P as follow: S=polcompositum(P,P)[2]; (This depends on the Galois group of P, but this will work in both case) 2) Compute the roots of P in the field Q[X]/P: N=nfroots(subst(S,x,'alpha),P); Now the roots are given by a=N[1], b=N[2], c=N[3] in term of a root alpha of S. 3) Compute the minimal polynomial of a-b as follow Mab=minpoly(N[1]-N[2]); By Galois theory, it has the same degree as S. 4) The minimal polynomial of sqrt(a-b) is a factor of Mab(x^2) Msab=factor(subst(Mab,x,x^2))[1,1] 5) Build the tensor product Q[x]/Msab \otimes Q(sqrt(-1)) MsabI = polcompositum(Msab,x^2+1)[1] 6) Factor Msab over L=Q[X]/MsabI: R=nffactor(subst(MsabI,x,'beta),Msab); This will be given in term of a root beta of MsabI. 7.1) If Msab split in linear factor, then K=L and the degree is poldegree(MsabI). This can be checked with poldegree(Msab)==#R[,1] 7.2) otherwise, we have to go one step higher. Set MsabcI=rnfequation(subst(MsabI,x,'beta),R[3,1]); In that case K=Q[X]/MsabcI and the degree is poldegree(MsabcI) Cheers, Bill.	{"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": 0.960507333278656, "perplexity": 3426.5403930667003}, "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-2017-47/segments/1510934806842.71/warc/CC-MAIN-20171123142513-20171123162513-00096.warc.gz"}
https://zbmath.org/?q=an:1027.46013	# zbMATH — the first resource for mathematics ##### Examples Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev \| Tschebyscheff The or-operator \| allows to search for Chebyshev or Tschebyscheff. "Quasi* map" py: 1989 The resulting documents have publication year 1989. so: Eur J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A \| 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used. ##### Operators a & b logic and a \| b logic or !ab logic not abc right wildcard "ab c" phrase (ab c) parentheses ##### Fields any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article) Generalized orthogonal decomposition theorem in Banach space and generalized orthogonal complemented subspace. (Chinese. English summary) Zbl 1027.46013 In a Hilbert space $H$, the Riesz orthogonal decomposition theorem says that any closed linear subspace $L\subset H$ has a unique orthogonal complement, i.e., a subspace $M$ of $H$ such that $H=L\oplus M$ and $M\perp L$. In this paper, the authors study the generalization of the Riesz theorem to Banach spaces. We call vectors $x,y$ in a normed space $X$ orthogonal and denote this by $x\perp y$, if $d_{\langle y\rangle }( x) =\\|x\\|$, where $\langle y\rangle$ is the linear span of $y$ and $d_{S}( x) =\inf_{s\in S}\\|x-s\\|$ is the shortest distance from $x$ to a set $S\subset X$, and we also call two subsets $A,B\subset X$ orthogonal and denote this by $A\perp B$, if $d_{B}( x) =\\|x\\|$ for all $x\in A$. Note that in a general Banach space $X$, the orthogonal condition $A\perp B$ is not symmetric in $A,B$, but in a Hilbert space it does coincide with the traditional orthogonal condition. A (closed) linear subspace $L\subset X$ is called orthogonally complementable if there is a (closed) linear subspace $M$ with $X=L\oplus M$ and $M\perp L$. The authors obtain results on the orthogonal decomposition in Banach algebras under suitable conditions. In particular, it is shown that a closed subspace $L$ of a strictly convex space $X$ is orthogonally complementable if and only if $L$ is a Chebyshev subspace of $X$ and $F_{X}^{-1}( L^{\perp }) =\{ x\in X\mid F_{X}( x) \cap L^{\perp }\neq \emptyset \}$ is an additive set, where $F_{X}( x) =\{ x^{\ast }\in X^{\ast }\mid \langle x^{\ast },x\rangle =\\|x\\|^{2}\}$ and $L^{\perp }=\{ x^{\ast }\in X^{\ast }\mid \langle x^{\ast },x\rangle =0 \text{for all }x\in L\}$. ##### MSC: 46B20 Geometry and structure of normed linear spaces 46B15 Summability and bases in normed spaces	{"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": 0.9067765474319458, "perplexity": 1553.620132548929}, "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-2016-18/segments/1461860125897.19/warc/CC-MAIN-20160428161525-00199-ip-10-239-7-51.ec2.internal.warc.gz"}
http://tex.stackexchange.com/questions/26807/problems-with-column-alignment-in-the-lstlisting-environment?answertab=oldest	# Problems with column alignment in the lstlisting environment I'm having some problems with the column alignment in the lstlisting environment provided by listings.sty. In fixed-width column alignment mode, whatever the typeface being used, listings are supposed to be presented with one character per column, where the columns have uniform widths (which may be set by the author). However, I find this not actually to be the case with certain input. Minimal example: \documentclass{article} \usepackage{listings} \begin{document} \begin{lstlisting}[columns=fixed] columnar alignment maligned multiple narrow characters? 1234 6789 1234 6789 1234 6789 1234 6789 1234 6789 1234 \end{lstlisting} \end{document} Result: Note that the second line is exactly one character shorter than the first, which is observed at the far right-hand side. However, the alignment in the middle is somewhat ruined at the occurance of every l character (ambiguous alignment of u in columnar with 3 or 4; ambiguous alignment of i, g, and n in alignment with 1, 2, 3, and 4; etc.). This problem is not helped by tweaking the alignment, by e.g. replacing fixed with {[l]fixed} for the column alignment. Is this a known problem? Is there any fix for it? - This is the expected/default output for columns=fixed in an lstlisting environment. From the listings package documentation: Now, the fixed format puts n characters into a box of width n x base width, where the base width is 0.6em in the example. The format shrinks and stretches the space between the characters to make them fit the box. That is, the alignment is not meant to consistent across lines within the listing. Rather, the chunks of code is placed in boxes and the spacing is modified with no regard for anything else except the box width. Even the example presented in the documentation (page 19) exhibits this behaviour: Notice the misaligned i in write (line 1) and print (line 2) due to the wider w. Even if you modified your minimal example to the following: \documentclass{article} \usepackage{listings} \begin{document} \begin{lstlisting}[columns=fixed] colu mnar alig nmen tmal igne dmul tipl enar rowc hara cters? 1234 6789 1234 6789 1234 6789 1234 6789 1234 6789 1234 \end{lstlisting} \end{document} attempting to align the listing column-wise, the output looks better, but still has the same issues you mention: Notice the misalignment between mnar and 6789 (due to m); tmal and 1234 (again due to m); rowc and 6789 (due to w), etc. The only way around this is to use a mono-spaced font for your entire listing, using (say) basicstyle=\ttfamily: - Hmm. What you're describing sounds an awful lot like the flexible spacing option. "Common to all is that the input characters are translated into a sequence of basic output units"; but surely what counts as a unit differs between the four alignment options, as otherwise the horrible spacing in the example text for the documentation (e.g. the words MEN and WOMEN) would not occur; even in my question, there's an odd space just before the n in columnar which should not occur if it's of one block. Are you quite sure that the blocks are meant to be computed on the syntactic level? – Niel de Beaudrap Aug 29 '11 at 9:41 Basically, what I am asking is this –– this behaviour is obviously known, because you (at least) are taking it for granted that this is normal, and are able to use the documentation itself as evidence. Does anyone view this behaviour as desirable, that the lstlisting ruins the spacing between characters if you use fixed spacing, but doesn't do it well enough to successfully achieve columnar alignment? Or is this an issue which is somehow famously difficult to solve? Basically, I'm asking: is it worth addressing it as a bug to the package maintainer? – Niel de Beaudrap Aug 29 '11 at 9:48 I'm accepting this answer because it seems to explain what my problem is; although I'm unhappy with the fact that the problem exists, because it essentially defeats the purpose of the various spacing options in listings.sty. – Niel de Beaudrap Sep 25 '11 at 1:08 Regardless of the outcome here, it is definitely advisable to follow up with the package maintainer(s). They would have the best idea whether it could be included in future releases, whether a temporary fix exists, or even whether there are others that have expressed similar interests. – Werner Sep 25 '11 at 5:58	{"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": 0.8187068104743958, "perplexity": 1274.7126664842622}, "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/1432207928562.33/warc/CC-MAIN-20150521113208-00269-ip-10-180-206-219.ec2.internal.warc.gz"}

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