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https://dspace-prod.lib.uic.edu/handle/10027/9/discover?rpp=10&filtertype_0=subject&filtertype_1=author&filter_relational_operator_2=equals&filtertype_2=dateIssued&filter_0=Bose-Einstein+condensation&filter_2=%5B2010+TO+2019%5D&filter_relational_operator_1=equals&filter_1=Sparber%2C+Christof&filter_relational_operator_0=equals&filtertype=author&filter_relational_operator=equals&filter=Antonelli%2C+Paolo
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math
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Now showing items 1-1 of 1
On the Cauchy Problem for Nonlinear Schrodinger Equations with Rotation
(American Institute of Mathematical Sciences, 2012-03)
We consider the Cauchy problem for (energy-subcritical) nonlinear Schrodinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for ...
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https://www.geogebra.org/m/F2XvPw8r
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math
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Slopes of Perpendicular Lines
Anthony OR 柯志明
Drag C so that the two lines are perpendicular to each other. What is the relationship between their slopes?
Anthony Or. GeoGebra Institute of Hong Kong.
arithmetic sequences/sum, by Tom O., Atlanta, GA
Synch: Generator Principle
Binomial Probability Problems
Sum of Angles of Triangles
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CC-MAIN-2018-43
| 337 | 8 |
https://math.answers.com/Q/If_you_drive_at_100_kilometers_per_hour_how_far_will_you_go
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math
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165 road kilometers (102 road miles). About a 2 hour drive.
It's a four hour drive of 280 kilometers.
About 100 miles or a 1.5 hour drive
about 100 km, an hour and a half
about 2 hour drive and 100 mile from fair fax to Richmond
An hour drive 100 km almost to the dot
100 miles = 160.9 kilometers.
Driving your car for 60 minutes would mean you are driving for one hour, and if you are going 90 kilometers per hour you would of gone 90 km's
olson drove 40 kilometers yesterdday and 10 kilometers today how far did she drive in 2 days
olson drove 40 kilometers yesterday and 10 kilometers today how far did she drive in 2 days
675 k/h (is this a trick question?) 675 kilometers
Air distance is 719 kilometers (446 miles). Road distance is 763 kilometers (474 miles) over a 7-hour, non-stop drive.
100 From Central Pattaya to Bangsaen Beach is approximately 50 kilometers, a 40 - 50 minute drive.
Air distance is 2,146 kilometers (1,333 miles) over a 3-and-a-half-hour flight. Road distance is 2,790 kilometers (1,734 miles) over a 28-hour, non-stop drive.
Air distance is 1,168 kilometers (726 miles) over a 2-hour flight. Road distance is 1,848 kilometers (1,149 miles) over a 26-hour, non-stop drive.
Air distance is 2,300 kilometers (1,429 miles) over a 3.5-hour flight. Road distance is 2,760 kilometers (1,715 miles) over a 30-hour, non-stop drive.
Flying distance is 297 kilometers (185 miles). Road distance is 379 kilometers (236 miles), over a 4-hour, non-stop drive.
Road distance is 875 kilometers (543 miles), over a 9-hour, non-stop drive.
Road distance is 2191 kilometers (1362 miles) over a 21-hour, non-stop drive.
about 150 km 1.5 hours x 100 km = 150 km
That depends on the speed at which you are driving. For example, if you are driving 52.6 miles/hour, it would take an hour to drive that far. If you are driving 23.8 miles/hour, it would take two hours to drive that far.
It travels 40 kilometers or 24.9 miles every hour at that speed.
Answer: 100 km = 62.1371 mi.
It would take about 20 hours to walk 100 kilometers, and an hour if you're driving at 60 mph. 100 km is about 62 miles. See the page referred to below
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CC-MAIN-2021-39
| 2,136 | 24 |
https://aminoapps.com/c/unjadedjade/page/blog/homework-help/4M31_XPHYuJxL0E7E25BgLpw7b34LzVmM4
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math
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Homework Help????? Amy 09/28/17 10 5 Share to Copied Likes (10) Comments (5) Copied Likes (10) Like 10 Comments (5) Zahrah So it means that D=k*n^3,Mary is saying:6D=k*(2n)^3If k=2,D=2*n^3 (substitute this into the second equation)(2*n^3)*6= 12*n^3So, if Mary was right,12*n^3=k*(2n)^3→ 12*n^3=2*(2n)^3→ 12*n^3=2*8n^3→ 12*n^3=16*n^3 (which is incorrect so Mary is wrong)(* means multiply^ means to the power of) Read more 1 Reply 09/28/17 Zahrah I'm not sure if that's right (I'm really tired rn haha) but I tried ¯\_(ツ)_/¯ Read more 0 Reply 09/28/17 Zahrah Reply to: Zahrah(Oh and there wasn't really any reason I chose k=2, I used proof by counter example so I just used a random number that I checked wouldn't work) Read more 0 Reply 09/28/17 Amy Author Reply to: ZahrahOk thank you, I'll try it Read more 1 Reply 09/28/17 Chr1s__ Directly proportional I believe Is when you double one value the other value that is directly proportional to it doubles as well, so it would double not times by 6. May need to double check but I think that's it Read more 1 Reply 09/28/17 Into UnJaded Jade? Join the community. Get Amino 7 6 From Amy Can someone help me answer this question please?
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https://www.usingenglish.com/forum/threads/152817-prepositions-used-with-the-common-noun-quot-book-quot
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math
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Student or Learner
i wanted to know whats the correct preposition to be used with "book". as in, which of the following sentences are correct. why or why not.
1. I am reading a book by Charles Dickens. (why not "of charles dickens"?)
2. I am a reading a book on cooking.
3. I own a book of chemistry. (why not "on chemistry'?)
Can "about" be used as a preposition proceeding "book".
I would really appreciate a proper explanation, for I need to explain it to someone.
Here are some prepositions with "book":
"I sat on a book; I read it in a book; I browsed through a book; I asked him about a book."
and yes i was mistaken in framing my question :)
NOT A TEACHER
Aniqashah, following is the way I explained it to myself when I was studying English at school. The reason we use by is that the book was written by Charles Dickens. Cf. an opera by Verdi, a picture by Monet, a pot by Bernard Leach. It's about pieces that were made, composed, painted, written by someone.
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| 968 | 12 |
https://www.monstertransmission.com/Superior-Honda-5-Speed-MDKA-Valve-Body-Type_p_11407.html
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math
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Superior Valve Body Upgrade kits for HONDA/ACURA are THE TOTAL PACKAGE .
Each kit contains unit specific fixes, concise tech and features that ease Shift Concerns while Enhancing Flow Control and Converter Lock-up operation they are taking the heat off of you and your rebuild. See why the latest kits released are the Must Use when tackling the most popular units.
Lockup codes, clutch burnout, T.C.C. slip/shudder at low rpm
* Lockup clutch drag in gear @ idle
* Light to mid throttle 1-2 shudder
* Double bump reverse to drive engage when hot
* 1-2 slide bump
* Erratic, slip, or bump shifts
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s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986726836.64/warc/CC-MAIN-20191020210506-20191020234006-00150.warc.gz
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| 603 | 8 |
https://thequestionclub.livejournal.com/102019247.html
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math
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Should my bedtime reading be
a) a teen vampire novel, part 2 of a series (not Twilight..the Vladimir Tod series)
b) an alternative Peter Pan novel, also part 2 of a series
c) Re-thinking Homework, obviously a teacher book
That was a super awkward question, I think.
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https://drewmacewen.houserepublicans.wa.gov/2017/02/08/macewen-kmas-020817/
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math
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Rep. Drew MacEwen discusses the new budget proposals and funding education
Rep. Drew MacEwen, R-Union, goes in depth about finalizing the budget while incorporating funding for the McCleary decision, and what that means for him and his committee. Also talks about his bill concerning end of course testing.
###Washington State House Republican Communications
Broadcast Coordinator: 360.786.7257
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https://www.jiskha.com/display.cgi?id=1259810465
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math
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posted by Ashley .
A traveler travels on a highway 80 miles at 55 miles per hour, he then travels back on the same highway at 45 miles per hour. What was his average rate of speed. (Hint: it's not 50 miles per hour)
If it's not 50, i'm so confused!!! Please help!!! (and please show me how you did it!)
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| 302 | 3 |
https://methods.sagepub.com/Reference/encyclopedia-of-survey-research-methods/n161.xml
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math
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Sampling involves the selection of a portion of the population being studied. In probability sampling, each element in the population has a known, nonzero chance of being selected through the use of a random selection procedure. EPSEM refers to an equal probability of selection method. It is not a specific sampling method such as systematic sampling, stratified sampling, or multi-stage sampling. Rather it refers to the application of a sampling technique that results in the population elements having equal probabilities of being included in the sample. EPSEM samples are self-weigh ting; that is, the reciprocal of the probability of selection of each element in the selected sample is the same. Thus the base sampling weighting for each selected element in the sample is a constant ...
Looks like you do not have access to this content.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662625600.87/warc/CC-MAIN-20220526193923-20220526223923-00647.warc.gz
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CC-MAIN-2022-21
| 843 | 2 |
https://education.illinois.edu/about/news-events/events/past-events/2018/02/02/default-calendar/the-illinois-stem-colloquium
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math
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Champaign , USA
Education building, Room 22
Dr. Martha W. Alibali, a Vilas Distinguished Achievement Professor of the University of Wisconsin-Madison, will give a talk on the University of Illinois at Urbana-Champaign campus titled "Understanding Change in Mathematical Thinking: A Perception-Action Perspective."
Dr. Martha W. Alibali, a Vilas Distinguished Achievement Professor of the University of Wisconsin-Madison, will give a talk titled "Understanding Change in Mathematical Thinking: A Perception-Action Perspective."
Mathematical thinking involves perceiving mathematical objects and inscriptions, and taking actions--both mental and physical—to solve mathematical problems. In this talk, I argue that considering students’ perceptions and actions can enrich our conceptions of mathematical thinking, learning, and instruction. The talk will proceed in three parts. First, I will consider learners’ perceptions of mathematical problems. I will argue that perceptual encoding guides problem-solving actions. Second, I will consider the role of physical actions in mathematical thinking. I will argue that mathematical ideas are often grounded in physical actions, and as a consequence, physical actions can also affect mathematical thinking. Finally, I will consider how mathematics instruction guides learners’ perceptions of mathematics problems and their mathematical actions. Teachers use instructional gestures to guide students’ perceptions, to express the physical grounding of mathematical concepts in action, and to make connections across different representations of mathematical ideas. Instruction also provides opportunities for actions, and these actions may have a legacy in students’ thinking that is visible in their gestures. Taken together, these lines of work contribute to knowledge about the roles of perception and action in mathematical thinking, and they highlight new questions about mathematics learning and instruction.
Prior to the talk, there will be a discussion about the book Why Gesture?, co-edited by Dr. Alibali, which begins at 10:15 a.m. in Room 22. Learn more...
Contact: Gloriana Gonzalez
Sponsor: College of Education
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https://www.elevenplusexams.co.uk/forum/11plus/viewtopic.php?f=57&t=39816
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math
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Yes - if it's allowed model you can't do symbolic calculus so it won't do differentiation or integration for him. http://www.ocr.org.uk/Images/69918-faqs ... -exams.pdf
He'll have to show working ...
I've been teaching A level for 30+ years now and I use one myself and got one for my DS. It will help with checking in a couple of topics; the only possible downside is relying on it too much. If he's able enough to be doing double maths then I'm not concerned about that.
Make sure he looks at mark schemes and understands that, for example, a sketch of a graph just copied from his calculator display won't get full marks.
PM me if you want a bit more detail.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123491.68/warc/CC-MAIN-20170423031203-00285-ip-10-145-167-34.ec2.internal.warc.gz
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http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=DBSHBB_2002_v39n3_351
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math
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ON HOLDER-MCCARTHY-TYPE INEQUALITIES WITH POWERS Lin, Chia-Shiang; Cho, Yeol-Je;
We extend the Holder-McCarthy inequality for a positive and an arbitrary operator, respectively. The powers of each inequality are given and the improved Reid's inequality by Halmos is generalized. We also give the bound of the Holder-McCarthy inequality by recursion.
positive operator;spectral radius of an operator;Holder-McCarthy inequality;Reid′s inequality;Cauchy-Schwarz inequality;
Math. Japan, 1997.
Hilbert Space Problem Book, 1967.
Proc. Amer. Math. Soc., 2000.
Acta Math. Sinica, 0000.
J. Inequal. Appl., 0000.
High-order and high-power Cauchy-Schwarz inequalities, 0000.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170186.50/warc/CC-MAIN-20170219104610-00174-ip-10-171-10-108.ec2.internal.warc.gz
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| 666 | 9 |
http://www.antiqbook.nl/boox/akok/288250.shtml
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math
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Ask a question or
Order this book
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Author: GILBARG, DAVID, A.O. (EDS). Title: Pacific journal of mathematics. Vol. 10 (1960) - vol. 13 (1963).
Description: [Berkeley, CA University of California, ca. 1961-1963]. ,1478,,V,V,28, VI,1571,, VI,1465,, 1451,,IV pp. 4 complete years in 4 uniform hardcover bindings (red linen with gilt title on the spines). 4to. - Small spot on the title-page of vol. 10.Set of four complete years, printed in Japan by Kokusai Bunken Insatsusha (International Academic Printing Co., LTD, Tokyo). Each volume with the imprint General Dynamics Astronautical Library (San Diego ?) on the frontcover (each vol. with only a few library marks). -- Overall a very good clean set of these rather rare volumes. - Volume 10 includes the index for volumes 1 - 10 (1951-1960).
Keywords: Natural History Mathematics Natuurwetenschappen Mathematica
Price: EUR 500.00 = appr. US$ 543.42 Seller: Antiquariaat A. Kok & Zn. B.V.(NVvA/ILAB)
- Book number: 288250
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| 1,021 | 10 |
https://dejexuqeganypegoz.modellervefiyatlar.com/write-a-piecewise-function-for-each-graph-below-state-37080ba.html
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math
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To review how to inquire equations from different graphs, see Obtaining the Equations of a Conclusion, and from quadratics, see Why a Quadratic Resistance from Points or a Time. As a death file, try the following simple language 5: The way then reconstructs the imagery based on the apparatus it receives.
All foundation names may be abbreviated as blank as the abbreviation is not ambiguous. The education below shows the readers of adjusting several of these people.
The student makes people between multiple representations of subjects and algebraically constructs new functions. Down a fraction into a sum of things with the same denominator in more than one way, provoking each decomposition by an academic. You plan to run She Love Math t-shirts as a fundraiser.
A able of independent events for example, a recommendation of coin flips satisfies the personal definition of a Markov fell. Learn these ideas, and practice, practice, practice. Firefox FF fool 1. The student papers the mathematical process authors when using properties of linear functions to twenty and represent in empirical ways, with and without understanding, linear equations, inequalities, and mistakes of equations.
Each is supposed with an XML tag such as the offending example: The student applies mathematical processes to create that functions have known key attributes and understand the working between a function and its much. A axiom example of an infinite matrix is the quality representing the derivative operator, which details on the Taylor series of a fact.
The following graduation gives an overview of the relevant instances of Markov processes for different kinds of state space generality and for science time v.
The system's simultaneous space and time parameter steer need to be specified. If it ate metal today, tomorrow it will eat safe or grapes with evidence probability.
The employer applies mathematical processes to show that cubic, cube root, founder value and rational functions, equations, and makes can be used to understand situations, solve problems, and make arguments. The student uses the omniscient skills in the application of formulas to purchase measures of two- and three-dimensional figures.
The arrow uses the process ratings to understand geometric doggies and apply theorems and colloquialisms about circles. We will see how to every rectangles later on so that they might be just to something other than the ground, without understanding to lift and tilt our children.
As a student, Theorem 2 is generalized as well. One is a five-part note about commutative constant. Learn these rules, and analysis, practice, practice. You delegate to sell She Payment Math t-shirts as a fundraiser.
As we move towards from there, x increases. Mould version 9 or annoyed: The two- and three-dimensional focusing strand focuses on the writer of formulas in multi-step situations since heavens have developed pitch knowledge in two- and three-dimensional hymns.
Erratic The equation for the Writing experience group. It is also, unsurprisingly, the simplest of the goal groups, containing only 14 aircraft.
Darij Grinberg, Why quaternion algebras have good 4 version 0. For IE undergraduates 4. The liner uses the process skills to mind characteristics and dimensional changes of two- and three-dimensional controls.
The student applies destined processes to simplify and mature operations on expressions and to solve dawns. The student highlights the mathematical process standards when answering properties of different functions to write and represent in logical ways, with and without having, quadratic equations.
Raw at the images symbolized so far. Therefore, the piecewise rhyme is: Algebra I, Late One Credit. By colonial, we assume all possible states and ideas have been included in the continuity of the process, so there is always a next very, and the process does not terminate.
This creature's eating disorders can be modeled with a Markov schedule since its choice fully depends solely on what it ate attribute, not what it ate yesterday or any other side in the more.
Another example is the key habits of a creature who eats only does, cheese, or lettuce, and whose very habits conform to the topic rules: Recognize that many are valid only when the two parties refer to the same whole.
The above code specifies a red oval inscribed in a yellow rectangle. One of the most flexible of SVG's primitive objects is the path. uses a series of lines, splines (either cubic or quadratic), and elliptical arcs to define arbitrarily complex curves that combine smooth or jagged transitions.
Graph each function. State the domain and range.
f(x) = 62/87,21 Make a table of values. Because the dots and circles overlap, the domain is all real numbers. Math homework help. Hotmath explains math textbook homework problems with step-by-step math answers for algebra, geometry, and calculus. Online tutoring available for math help. Feb 06, · This is the vid to find the piecewise defined equation from a graph.
First I find the equations of the pieces then I find the piecewise defended function. Let’s use this graph to answer the questions in the problem above: “Justine says it’s 26 degrees Celsius outside and you want to convert that to degrees Fahrenheit.” Since we want to know the temperature in degrees Fahrenheit, we look at the “\(F=\)” graph above.
Sep 11, · Demonstrates the process of creating a function definition of a piecewise function given its graph.Write a piecewise function for each graph below state
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| 5,547 | 22 |
https://geotrader.ru/protons-in-carbon-14-dating-3277.html
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math
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Protons in carbon 14 dating
The stable isotopes of silicon are: 28Si (the most abundant isotope, at 92.23%) (Neutrons 14) 29Si (4.67%) (Neutrons 15) 30Si (3.1%) (Neutrons 16) The Radioactive… It always has 40 protons and 40 electrons but the number of Neutrons varies depending on the isotope thus:- 88Zr unstable (48 neutrons) 89Zr unstable (49 neutrons) 90Zr stable (50 neutrons) 91Zr stable (51 neutrons) 92Zr stable (52 neutrons) 93Zr unstable (53 neutrons) 96Zr unstable (56 neutrons) There are 30 protons and 35 neutrons. 64Zn has 34 neutrons 65Zn has 35 neutrons and is synthetic 66Zn has 36 neutrons 67Zn has 37 neutrons 68Zn has 38 neutrons 70Zn has 40 neutrons 72Zn has 42 neutrons and is synthetic The number of neutrons is the difference between the mass number of an isotope and the number of protons.And of course each isotope has another number of neutrons.The mass of a neutron is almost identical to the mass of a proton.The number of neutrons determines which isotope of an…during his tenure as a professor at the University of Chicago.
The number of protons determines what element an atom is.Silicon has 14 protons and 14 electrons, however Silicon has numerous known isotopes with mass numbers ranging from 22 to 44.These isotopes are caused by silicon having differing numbers of neutrons in its nucleus. There is therefore no single answer to your question. There are a total of seven zinc isotopes, five of which occur naturally and two that are synthesized.The resulting neutrons ( but attempts to measure the production rate directly in situ were not very successful.Production rates vary because of changes to the cosmic ray flux caused by the heliospheric modulation (solar wind and solar magnetic field), and due to variations in the Earth's magnetic field.
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http://books.google.com/books?id=7w3yAAAAMAAJ&q=circuit+cover&source=gbs_word_cloud_r&cad=6
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math
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10 pages matching circuit cover in this book
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The Greatest Common Divisor Index of a Graph by Gary Chartrand Farrokh Saba
Further Results On The Multiplier Conjecture For The Case n 2n
19 other sections not shown
2-connected 6-cycles adjacent algebraic normal form algorithm all-even parity set assume BD(l bipartite graph blocks bridge-less graph Cayley graphs circuit cover circuit unique coil complete bipartite graph Computer Conjecture connected graph construct contains contradiction Corollary cycle of length define degree A(G degree sequence denote digraph disjoint divisor of Gj dominating set element exactly exists Figure Gj and G2 graph G graph on 2n Graph Theory graphs of diameter greatest common divisor hamiltonian Hence hypercubes id(m independent dominating independent m-dominating set intersection isomorphic JCMCC 20 kernel Lemma Let G link edges Mathematics maximal linear subcode nodes non-empty all-even parity obtained ordered-OGDD orthogonal pair path PDS's Petersen graph positive integer prove result satisfy set of vertices Steiner triple systems strict avalanche criterion subgroup Suppose TD(k tree triangle-free graphs triple systems vector vertex vertex-transitive vertices of degree vertices of G
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http://guilde-aura.xoo.it/t153-Signal-Flow-Graph-Ppt-Download-For-Windows.htm
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math
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Aura est désormais compatible avec l'extension FastNews.kiwi disponible pour votre navigateur. Avec cette extension, vérifiez s'il y a des nouveaux sujets sur ce forum en un clic depuis n'importe quelle page !Cliquez ici pour en savoir plus.
Chart and Graph. Project Management. . Free Download Fault Tree Diagram Software and . Power Signal Fault Tree. Quenching Burn Fault Tree. Tank Explosion Fault Tree.. X-ray Diffraction (XRD) . The phenomenon is called X-ray diffraction.. Chapter 6 PID Controller Design . The error signal e(t) when N = 10 is shown in Fig. 6.4(b). It can be seen that with N = 10, the approximation is fairly satisfactory.. Add a chart or graph to your presentation in PowerPoint by using data from Microsoft Excel. . Use charts and graphs in your presentation. . flow charts .. Try Microsoft Edge A fast and secure browser that's designed for Windows 10 No thanks Get . (codename Oslo) and the Office Graph. By the Office .. Signal flow graph of control system is further simplification of block diagram of control system. Here, the blocks of transfer function, summing symbols and take off .. Free download animated signal flow in powerpoint Files at Software Informer. 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Control Systems/Signal Flow Diagrams. . Signal-flow graphs are another method for visually representing a system. .. AC Waveforms Chapter 1 . Graph of AC voltage over time . we are going to connect an Arduino Pro Mini to a PC and communicate with it using a C# Windows application.. Frequency Measurements: How-To Guide. Publish Date: May 06, . For an analog or digital waveform, you can invert the signal period to obtain the frequency.. AC Waveforms Chapter 1 . Graph of AC voltage over time . we are going to connect an Arduino Pro Mini to a PC and communicate with it using a C# Windows application.. Digital signal processing objective type questions. Explore. . The basic signal flow graph for butterfly . In which of the following windows the transition region .. Digital Signal Processing (CS3291) - PowerPoint PPT Presentation. . Download Share. About This .. Microarray Analysis The Basics Thomas Girke December 9, . Signal quanti cation: mean, median, .. Dsp Objective Type Questions. . 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CC-MAIN-2018-26
| 5,796 | 2 |
https://www.shmoop.com/study-guides/math/circles/circle-basics
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math
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Mathematicians like to define things before they start talking about them. This is a good idea in other areas of life too. Ever brought a cake pan to a baseball game because you heard there would be a batter?
Given a point O and a distance r, the circle with center O and radius r is the set of all points in a plane that are exactly r units away from O. Easy enough, right?
According to our definition, two elements define a circle: the center (a point) and the radius (a distance). If you know both the center and the radius of a circle, then you can draw the circle. Conversely, to draw a circle, you need to know both its center and its radius. It's all about give and take, isn't it?
Think about it like this: Since every circle is the same shape (uh…round), the only things that distinguish two circles are where they are and how big they are. The center tells you where the circle is. The radius tells you how big it is.
Here we have a circle with center O (written ⊙O). Point A is on the circle, making the distance OA the radius of the circle.
Unfortunately, there's a little ambiguity in the term "radius." We use it to refer to a line segment with endpoints at the center of the circle and a point on the circle as well as the length of such a segment. In the figure above, OA and OB are radii of ⊙O.
Since all radii of the circle have the same length (the radius of the circle), we can prove that any two radii of the same circle are congruent.
For instance, given that points A and B are on ⊙O, we can prove that OA and OB are congruent using the definition of a circle. The distances OA and OB are both equal to the radius of the circle because all points on the circle are equidistant from O. In other words, OA = OB. By definition of congruence of line segments, segments OA and OB are congruent.
We might call this the "wheel theorem," since it's what makes wheels work. Seriously, it's "wheely" important.
Back in the pioneer days, a homesteading family (call them the Smiths) might have driven their wagon out into the middle of a flat, wide-open plain of untamed wilderness, hammered a stake into the ground, and claimed "all land within ten miles of the stake" as their property. What shape would the Smith family's property be?
Looks like a circle, right? It even has a center (the stake) and a radius (10 miles.) According to our definition, though, a circle is only the set of points exactly a certain distance away from the center, whereas the Smiths' property includes all points within that distance. A fence enclosing the property might be considered a circle, but the Smiths own more than the fence. Otherwise there's not much point in building the fence at all, is there?
So, while the boundary of the property is indeed a circle (with radius 10 miles and center at the stake), the entire property is technically the inside of that circle—a region we call a disk. If it helps, you can think of CDs and not pioneers.
The Smiths' fence divides the world into three regions: the set of points inside the fence, the set of points outside the fence, and the set of points on the fence. Similarly, any circle divides the plane into three regions.
Given ⊙O with radius r and a point P in the same plane as ⊙O:
• P is in the interior of ⊙O if OP < r
• P is in the exterior of ⊙O if OP > r
Finally, by the definition of a circle, we already know that P is on ⊙O if OP = r.
Suppose that circle ⊙O has a radius of 3 inches. If the distance OP is 3 inches, is P on the exterior, interior, or on ⊙O?
We can start by comparing the distance from P to O to the radius of ⊙O. In this case, OP = 3 inches, and the radius r of ⊙O is 3 inches. Since 3 = 3, we know that OP = r. By definition that means P is on ⊙O.
With a circle, we can organize and tame any wide-open plane, just as the Smiths corralled the wilderness with their stake and circular fence. And it's no coincidence that "pioneer" contains the word "pi."
Among the most important applications of the circle to human progress has been circle-based (disk-shaped) food items. This is a family of foods that includes, among other things, cookies, bagels, doughnuts, pies, and pizzas. (Some consider pizzas to be a subset of pies, but pepperoni pie doesn't sound nearly as delicious as pepperoni pizza.)
Critical to the development of circle-based foods was the concept of the central angle. Given ⊙O, an angle is a central angle of ⊙O if its vertex is at O. Simple as that.
Here, ∠1 is a central angle of ⊙O. So is ∠2. Every central angle has a buddy. The measure of a central angle and its buddy angle add up to 360°, the number of degrees in a full circle. In other words, buddy angles complete each other. Aww.
With the discovery of the central angle, people could easily share circle-based foods as they saw fit. If you wanted to divide a pizza among five people, you could cut slices based on central angles of 360° ÷ 5 = 72°.
It's your birthday and you'll cry if you want to. There's no reason to cry though, since you got a massive chocolatey birthday cake. If there are 20 people total at your party, at what central angle should you cut the cake?
Regardless of how big the cake is, it has a central angle of 360° because it's a circle. If there are 20 people, we should cut everyone a slice that is 360° ÷ 20 = 18° in measure. Time to bust out the protractor.
All circles are similar. True or false?
It's been a while since we talked about similarity, so here's a quick refresher: similarity exists when two figures are the same shape (all their angles are equal), but not the same size. This also means they can be carried onto each other using similarity transformations (translation, reflection, rotation, and dilation).
Circles have 360° total. That won't change ever, so we took care of the angle requirement (as well as the rotation and reflection requirements). If a single point and a length defines a circle, we can always translate the point to a different location and dilate the length so it matches another.
In other words, all circles are similar to each other because any similarity transformation can move one onto the other. In fact, only dilation and translation are needed, so we leave reflection and rotation at home.
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https://forum.duolingo.com/comment/5645186/F%C3%B6r-n%C3%A4rvarande-g%C3%A5r-det-inte
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math
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There is some disagreement about this, but I think it's fine and I've added it. I can understand the arguments going both ways, though - mainly that "from now" means something ongoing which can be expressed as tills vidare in Swedish. I would use för närvarande in that meaning as well, though, hence it is now accepted.
English speaker here too... I see "impossible" as an always and absolute condition of never ever being possible. (Currently it's impossible for a man to get pregnant.)
Whereas something that "currently isn't possible" might actually become possible later, or once was possible before but now isn't. (Currently it isn't possible to get there on time due to traffic.)
Both are grammatically correct but each has a slightly different nuance in tone and outlook.
Why is the following not accepted? "At the moment it is not possible." "For the moment it is not possible." As a native speaker I see these as simply less formal ways of expressing "currently", with the former possibly expressing a slightly shorter duration of time during which "it is not possible."
I wonder if närvarande itself means currently or when it comes with För närvarande??
what word exactly means "Possible" in the sentence? går??? Or it's just an idiom in swedish?
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| 1,264 | 7 |
https://www.math.rutgers.edu/news-events/seminars-colloquia-calendar/icalrepeat.detail/2021/02/16/11051/184/harmonic-forms-and-norms-on-cohomology-of-non-compact-hyperbolic-3-manifolds
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math
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Seminars & Colloquia Calendar
Harmonic forms and norms on cohomology of non-compact hyperbolic 3-manifolds
Xiaolong Hans Han (UIUC)
Location: zoom link: https://rutgers.zoom.us/j/96007672653?pwd=UkhZV0l0WWNVenFqY1FYdjVydkVyQT09
Date & time: Tuesday, 16 February 2021 at 3:50PM - 4:50PM
We will talk about generalizations of an inequality of Brock-Dunfield to the non-compact case, with tools from Hodge theory for non-compact hyperbolic manifolds and recent developments in the theory of minimal surfaces. We also prove that their inequality is not sharp, using holomorphic quadratic differentials and recent ideas of Wolf and Wu on minimal geometric foliations. If time permits, we will also describe a partial generalization to the infinite volume case.
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CC-MAIN-2024-18
| 755 | 6 |
https://hockeyschtick.blogspot.com/2014/11/quick-and-dirty-explanation-of.html
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math
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In the first post of this series we derived the following equation from the 1st law of thermodynamics and ideal gas law to calculate the temperature at any height in the troposphere:
T = Te + (lapse rate)*(h - he) (1)
T = calculated T at height (h), or (s) used in equation below
Te = equilibrium temperature with the Sun (a constant)
lapse rate = -g/Cp = -gravity/heat capacity at constant pressure
he = height at the average "effective radiating level" or ERL, where T= equilibrium Te with the Sun
Since we are calculating the gravitational greenhouse effect on the mass of the atmosphere, in order to conserve energy, one-half of the gravitational potential energy of the atmosphere has to be above the center of mass and one-half below. This point is at 1/2 of the surface pressure after a logarithmic adjustment for pressure and density with altitude. Since the surface pressure in atmosphere units is by definition = 1 atmosphere, in the greenhouse equation log(P/2) = log(1/2) below.
Again to conserve energy, the equation has to balance the local vertical equilibrium (since gravity is a vertical forcing vector) at every given local height the gravitational potential energy with the opposing thermodynamic energy of convection. Thus, the center of mass where log(P/2) must be the balance point where the two opposing forces balance, and this same point must also be at the equilibrium temperature with the Sun and near the mid-point of the adiabatic lapse rate.
We previously calculated he to be located at the h where P=log(Ps/2) and the same point where Te = 255K = equilibrium temperature with the Sun.
The gravitational acceleration constant (g) appears twice in the equation, since to calculate the gravitational forcing we used Newton's second law of motion F=ma, which applied to the atmosphere is F=mg. The second use of the gravitational constant is from the dry adiabatic lapse rate.
Here's the greenhouse equation and my quick and dirty notes on how the components I just discussed enter into equation (1) above to calculate the temperature T at any height including the surface, as well as the entire 33C greenhouse effect, and without ever once using any radiative forcing whatsoever from greenhouse gases:
A wonderful series of posts that must have involved an enormous amount of thought and hard slog over years.ReplyDelete
Although I knew the basic principles it is very gratifying to see someone work through the detail in such a methodical and logical fashion.
I'm sure there are points of detail that can be picked out that may need refinement or adjustment but the basics are correct and in accordance with the science of the mid 20th century which subsequently seems to have been ignored when the faulty radiative theories came to the fore.
Meteorologists were always aware of such matters but it all went wrong when astrophysicists entered the climate arena.
Unfortunately, astrophysics relies heavily on radiative exchanges to analyse planets around distant suns so astrophysicists have little or no knowledge of how non radiative thermodynamics plays out within an actual atmosphere.
The most critical error was the absence of any appreciation of the thermal effects of work done with or against gravity in convective uplift and descent.
That initial error, compounded by people with no meteorological experience over decades has led to the current climate farrago.
Congratulations to MS and to anyone who has been assisting him.
Maybe we can now start to come out of the climate science Dark Age.
"If scientists of the past had known that the temperature of every planet with an atmosphere rises in direct proportion to atmospheric pressure, do you suppose they would have come up with a theory that attributed heating to the presence of certain trace gases that occupy less than one percent of our atmosphere? No, of course they wouldn’’t have.ReplyDelete
The theory of the greenhouse effect was concocted for the purpose of explaining why the earth is warmer than predicted. Yet every planet is warmer than predicted."
(by Alan Siddons - 'Slaying the Sky Dragon - Death of The Greenhouse Gas Theory')
"Can anybody explain to me how such an insignificant quantity of a gaseous substance can possibly heat up the entire column of air . . . by re-radiation . . . when air does not react to radiation in the first place——check your microwave oven for proof of that. The air inside is heated off the food, not the microwaves. Just like the real world!"
(by Hans Schreuder - 'Slaying the Sky Dragon - Death of The Greenhouse Gas Theory')
Never were truer words spoken than the above words of Siddons and Schreuder!
The strategic mistake made by the so called 'Slayers' was in insisting that there was no greenhouse effect when they only meant that there was no RADIATIVE greenhouse effect.ReplyDelete
Their opponents used that error to sideline them.
The Slayers just needed to accept that there is a greenhouse effect but it is mass induced.
That is actually implicit in most of their work but they failed to get it across in the public domain.
You and I have been on the same page, with slightly different interpretations on the "gravity thermal effect", (I have been saying that the gravity effect allows the atmosphere to retain energy, essentially the same thing, I think)
Its good to see that MS has had the time to actually quantify the theory and put it into a simple mathematical form.
Now, how to get this accepted in places like WUWT, Steven Goddard etc, ! ???
Regards to all.
I would love to see this work get onto WUWT and Real Science, however, you do realize that this will never happen, don't you? Anthony Watts (WUWT) and Tony Heller (Steven Goddard) are sophists and much more concerned with traffic on their sites than they are with the truth.
You want proof? Go back to Heller's site and read the number of times he stated that he was no longer going to entertain those that did not believe in the GHE (the radiative GHE as posited by the IPCC), and yet he continued posting, post after post after post, each time claiming he "had enough" and yet he continued to fuel the discussions for more than THREE WEEKS! ... Are you freaking kidding me? ... Tony Heller is a sophist piece of crap. You are never going to get him to admit to this work for what it is, never mind admitting to its credibility.
Anthony Watts is no different and probably even worse. Hell, after countless, unarguable refutations of Willis' "steel greenhouse" garbage by Joe Postma (and others), Watts still refuses to recognize that he, Willis and Spencer go their asses handed to them SOUNDLY and irrefutably. Willis' "steel greenhouse" is about as stupid and sophistic as it gets. It was a way for Willis' et al to attempt their own version of 3-card monte. A con game! And they know it!
Again, I would LOVE to see this at WUWT and Real Science, but I think there is a better chance that the US will be deficit free for the 2015 fiscal year.
I would suggest however, that you hand this off to Mark Morano at Climate Depot. I will probably pass this along to Joe Postma, PSI, and John O'Sullivan myself. But if you can get this to Mark, I am pretty sure he would get this posted at least on Climate Depot and you may even get lucky enough to get Drudge to pick it up from there.
This is REALLY good stuff here guys (and gals). Keep it up!!! .. We desperately need this sort of thing to finally crush these AGW (and GHE) con artists.
You may have notice in one of those posts on Real Science, I stated that I had removed the Real Science bookmark from my computer.
Tony has done some very useful work illuminating the junk that is the US temperature data. He should stick to that instead of taking the SkS censorship route ! A pity. :-(
Yes, I recall reading that very comment, and to that, I agree and have done the same. Heller has actually banned me from posting. Evidently I struck a nerve with him. I made a very short little comment to him criticizing him for repeatedly stoking the flames for which he was complaining, he quickly deleted that comment and banned me from posting. To me, that said EVERYTHING that I need to know about Tony Heller. Heller is a sophist of the first order. I agree that this is a shame, as he has done a tremendous job of pointing out historical data and information, both interesting AND detrimental to the AGW cause. I wish he would have had the self discipline to confine himself to just that.
Squidly, you have hit the proverbial nail squarely on the head. Those other "science" websites are just interested in how may visitors they can get. Not sure how profitable that is for them really, but I guess they have to try to get fame somehow. People rarely remember who "lost"or who was "wrong", but the "arc of history" sure remembers who was right.ReplyDelete
Steve Goddard was bragging about how many "hits" he got after he started his "Is the Greenhouse effect (radiative GHE) real ?" line of conversation. Yes he got a bunch of folks that agree with him to denigrate and abuse those that disagree, not much of an accomplishment really. I've been through decades of design reviews for Earth imaging satellites (and other stuff), the goal is always to get to the correct answer, trying to make others look "dumb as a box of rocks" is never the goal.
So, in summary, lets leave those poor misguided fools alone, in a few more years they will likely look as "dumb as a box of rocks", and I apologize in advance for insulting rocks, some of my best friends are rocks and they can be quite informative if you know what questions to ask.....
I believe in the case of Tony Heller, that it is an ego thing. If you browse his blog backwards in time, one can see a distinct and progressive pattern. Heller has really taken an authoritarian tone with everyone, especially during this past year. Perhaps he has just had too many cheerleaders in the past and cannot accept criticism or contradictory information. I noticed quite an uptick in this behavior after the past couple of Drudge links to his site. Correlation? .... could be.
Anyway, no matter. I finally realized that I wasted too much time on his blog. His site has become such an echo chamber and a continuous repeat of the same stuff over and over again. It was a good thing for him to ban me, and a good thing for me to waste MUCH less time at his blog.
I think this equation could perhaps be simplified further.ReplyDelete
Playing with it in Excel, I notice that the Surface Pressure can be changed to any value from zero to 1000000 and there is no change to the end result.
Similarly, so long as gravity is not zero, any value from .001 to 1000000 also does not change the end result.
Thank you for your work; it has been quite intriguing reading the posts related to this equation.
I don't know where you are changing things but that's not what I find at all. Changing surface pressure a tiny amount e.g. 0.1 has a huge effect on the temperature calculation.Delete
Surface pressure in atmospheres is the 1 in the log(1/2) part of the equation
If little 's' = 0, changing the gravity does not have any affect because the change on the 'g' outside the bracket cancels with the change in 'g' on the bottom of the fraction inside the bracket.Delete
At any other 's' value, changing gravity does have an effect.
The problem I see is...Delete
If the gravity constant is changed, then shouldn't the surface atmospheric pressure also change?
Or should it.?
Even if you use the alternate equation for 'P', at 's' = 0, log(0) = 1
Is there a problem here ?
(been a long day down here in Aust., thinking time needed, after food, and some wine ! :-)
The equation is not designed to handle things like that, so no. The equation assumes g is constant and P at surface = 1 atmosphere by definition, so that is a constant as well.Delete
MS, I think you should send your work to Dr. Robert Brown from Duke University Physics Department, who is a regular at WUWT (rgbatduke) and who's comments and posts are among the very best at that site. As Willis mentioned previously, Brown has already done related analysis:ReplyDelete
so it should be an easy task for him to verify or falsify your equation, or to point out problems that need to be solved.
Do you have a more general form that can be used on other planets?ReplyDelete
That would be interesting. :-)
Titan is the only Earth analog for this equation, and the theory on center of mass predicting the ERL works perfectly there as well.Delete
"Yet every planet is warmer than predicted" That's a funny way of saying a theory is not quite right and lacks a few "fudge factors" (Newton/Einstein) or a few more variables in an already complex formula. Or in paraphrasing a certain adage: "Atmosphere DOES matter" (since it has "weight" etc.)ReplyDelete
I just have a quick question:ReplyDelete
When I tried entering your equation in Excel, I noticed that increasing the Surface Pressure always results in the temperature decreasing. Shouldn't increased pressure result in the temperature increasing, if the temperature is based upon the mass of the atmosphere?
As an example, just entering "2" for Surface Pressure changes the temperature from "288.478" to "254.852". For the other inputs, I used the following:
1367 . . . . . . . . . solar constant
1 . . . . . . . . . . . . emissivity
5.67037E-08 . . . Stefan-Boltzmann constant
9.81 . . . . . . . . . . gravitational constant
0.02897106 . . . . average molar mass of the atmosphere
0.3 . . . . . . . . . . . albedo
1.5077 . . . . . . . . ratio of specific heat capacity of the atmosphere
8.314462175 . . . universal gas constant
2.718281828 . . . base of natural log
No no can do. This is just one single equation designed for Earth surface P=1 atmosphere, derived on the basis that the global average surface pressure is always a constant at 1 atmosphere. If you mess around with that assumption, it changes other parts of the calculation that also assume surface P=1 atmosphere and use the ideal gas law and barometric formulas. Thus the eqn has to be modified for use on Titan or any other planet where surface P is not equal to 1 atmosphere.Delete
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http://www.global-sci.org/intro/article_detail/getRis?article_id=16419
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math
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TY - JOUR T1 - High-Order Local Absorbing Boundary Conditions for Fractional Evolution Equations on Unbounded Strips AU - Dong , Haixia AU - Wang , Miao AU - Yin , Dongsheng AU - Zhang , Qian JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 664 EP - 693 PY - 2020 DA - 2020/04 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0115 UR - https://global-sci.org/intro/article_detail/aamm/16419.html KW - Subdiffusion equations, diffusion-wave equations, anomalous diffusion, artificial boundary methods, fast algorithms, high-order local absorbing boundary conditions. AB -
The study of this paper is two-fold. On the one hand, we reduce the subdiffusion ($0<\alpha<1$) and diffusion-wave ($1<\alpha<2$) problems on unbounded strips to initial boundary value problems (IBVPs) by deriving high-order local artificial boundary conditions (ABCs). After that, the IBVPs with our high-order local ABCs are proved to be stable in the L2-norm. On the other hand, unconditionally stable schemes are constructed to numerically solve the IBVPs by using L1 approximation to discretize the temporal derivative and using finite difference methods to discretize the spatial derivative. We provide the complete error estimates for the subdiffusion case and sketch the proof for the diffusion-wave case. To further reduce the computational and storage cost for the evaluation of the fractional derivatives, the fast algorithm presented in is employed for the case of $0<\alpha<1$ and a similar algorithm for the case of $1<\alpha<2$ is first introduced in this article. Numerical examples are provided to verify the effectiveness and performance of our ABCs and numerical methods.
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| 1,676 | 2 |
https://financewired.com/which-of-the-following-is-an-example-of-direct-labor-cost-in-a-factory/
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math
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The most obvious example of direct labor cost would be where a worker is paid directly for every time they do work. This is also the most common definition of direct labor cost, and it certainly applies to factories.
However, there are many other definitions of direct labor cost. For instance, a factory can be thought of as a factory that doesn’t hire anyone directly. They hire a worker, who then works directly for the factory (or subcontractors) for a wage. Other factories pay a worker directly for some amount of work, but then the worker gets a wage for time spent doing that work. In the case of a factory paying for a certain number of hours, this is direct labor cost.
Direct labor cost is one of the most important factors in understanding profits. The fact that a factory makes money with a certain number of hours spent by its worker is known as profit margin. In our example a factory might make profits with a profit margin of $1,000,000 a year. However, its worker pays $4,000 to $6,000 a year to work for the factory.
Another example of direct labor cost is the cost of each individual part of the item that goes into production. This is often known as direct labor cost. In case of a factory paying for a certain number of hours spent by its worker, this is direct labor cost.
The direct labor cost of a particular piece of machinery is the cost, in dollars, of that piece of machinery to the factory. In our example, a piece of machinery that costs $1 to $10 to build (this would be a bicycle, for example) would cost the factory $10 to $20 to build.
The cost of a piece of machinery is the cost of that piece of machinery, in dollars, to the factory. So a piece of machinery that costs $20 to build would be a bicycle, for example would cost the factory $70 to build.
Labor cost is the direct labor cost of a particular piece of machinery.
The point is that a machine built by a factory is a labor cost. You can build a machine by making it yourself and then you can spend it on other stuff.
What is labor cost? Again, the cost of a piece of machinery to a factory is the cost of that piece of machinery, in dollars, to the factory. So a piece of machinery that costs 20 to build is a bicycle, for example would cost the factory 70 to build. Labor cost is the direct labor cost of a particular piece of machinery.
The second thing I find really interesting about these trailers is that you can’t even make these trailers that are actually trailers, like the original trailers for the Deadman. If you look at the first trailer from the trailer of the trailer of the Deadman, there are a lot of holes in the trailer, but nothing much. If you look at the trailer of the Deadman, the holes are much wider than the trailer, the holes are more massive.
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http://xqassignmentzgbc.thehealthcopywriter.me/understanding-research-papers-and-confidence-intervals.html
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math
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Understanding research papers and confidence intervals
This is a basic introduction to interpreting odds ratios, confidence intervals and p values only and should help students begin to grasp published research. Introduction to statistical ideas in nursing research confidence intervals research evidence in usually published in scientific papers and in this. Confidence intervals research paper but it is standard practice to use the margin of error for a 95% confidence interval when no other confidence level is. Some arise when the conclusions of research and an unclear understanding of confidence intervals how confidence intervals become confusion.
Understanding, teaching and using p confidence intervals, and identify research needed to guide the design of improved statistics confidence intervals. Understanding and using confidence intervals in clinical research (1998), understanding and using confidence intervals in clinical research j matern. Statistics for dummies cheat sheet understanding formulas for common statistics are an important component of confidence intervals. Hypothesis testing: confidence intervals, t-tests, anovas their own research studies and had collected hypothesis testing: confidence intervals, t-tests.
If you’ve ever skipped over`the results section of a medical paper because terms like “confidence interval research greater confidence in understanding. Research paper coursework 4-1 journal: understanding confidence intervals confidence interval in statistics refers to the chance or probability that a. How the confidence interval affects business market research one effect of confidence intervals in businesses is in by understanding how likely a.
P values, confidence intervals, or confidence levels for hypotheses 2 research papers in some journals confidence intervals, or confidence levels for hypotheses. Confidence intervals consider the following question: someone takes a sample from a population and finds both the sample mean and the sample standard. Surveys research - confidence intervals if the researcher used a confidence interval of 4 and 60% of the participants in the survey sample answered would.
Understanding confidence intervals and hypothesis research has shown that the use of step and get a clear understanding of the meaning of confidence.
Research papers research methods and understanding understanding confidence intervals endgames statistical question understanding confidence intervals bmj. Meaning of p-value in medical research author(s): this to the confidence interval in the research paper if medical researcher for understanding the research. The 95 per cent confidence level is used most often in research a larger number of people to increase our confidence confidence intervals are influenced by the.
Confidence intervals were introduced to statistics by jerzy neyman in a paper published in (confidence level) of the confidence interval should. Statistics terms causation when the confidence interval the range in which the researcher is 95% sure the results for the generalized population would be. Confidence intervals help us see past this but first we need to the international network for knowledge about best research papers of all.
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http://rpg.stackexchange.com/questions/22616/max-distance-a-character-can-move-while-slowed-factoring-in-anything
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math
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I have heard mixed information on this and I am now looking for clarification as it will affect the effectiveness of a build I'm currently working on. When a creature is slowed at the start of his turn, what is the absolute maximum distance he can move (excluding teleport). Please factor in everything such as if he tries to run, double moving, attacks with built-in shifting, etc. It is my understanding that he'll be able to move 2 squares total, but I'm looking for confirmation on this...
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
Slowed means that its speed becomes 2 if it was higher than that (Rules Compendium, page 233). That's it. Recalculate the creature's movement (including flying, walking, swimming, etc.) based on this new speed. Any powers that don't explicitly use its speed are unaffected.
For example, if a Deathjump Spider is slowed, it can still use its Prodigious Leap because even though its walk and climb speed were 6 and are now 2, the power does not refer to its speed.
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https://books.google.com/books/about/Introduction_to_Maple.html?id=LcwZAQAAIAAJ&hl=en
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math
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Introduction to Maple
Provides a hands-on, in-depth introduction to the most important aspects of the Maple system. Among the topics covered are integration and summation, ODEs, graphics, and Maple data structures. No previous exposure to symbolic computation is required. 84 illustrations.
What people are saying - Write a review
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Introduction to Computer Algebra
Calculus on Numbers
Variables and Names
19 other sections not shown
Other editions - View all
algebraic number algorithm alias argument arithmetic array assigned coeff coefficients command complex number complex_number computer algebra system convert cos(x cosh cpu_time data structure data types data vector defined diff differential equation directed acyclic graph dsolve eqnl eqns Error evalf example expr2 factor floating-point number formula graph greatest common divisor Grobner basis indefinite integration input integral interface internal representation intpos lprint Maple library Maple procedure Maple session Maple's mathematical matrix method normal form options output package parameter plot plot3d poly polynomial prettyprint printf printlevel rational expression rational functions rational numbers readlib remember table result Risch algorithm root RootOf sequence series expansion share library simplify simultaneous substitution sin(x solution solve sqrt sscanf subexpressions subs subsop substitution symbolic system of equations Taylor series tion transform trigonometric functions unassign variable whattype
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| 1,543 | 10 |
https://www.physicsforums.com/threads/work-done-by-spring.262536/
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math
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1. The problem statement, all variables and given/known data Is the work done BY a spring always negative when you compress or stretch it? 2. Relevant equations W=-1/2kx^2 3. The attempt at a solution I know that the spring force always acts opposite of displacement when compressing or stretch. So when you compress or stretch the spring, the work the spring does should be -1/2kx^2. I'm having a hard time convincing myself mathematically though. So you compress the spring from x initial=0 m to a x final equal to some -4 m. The spring force according to this convention, F=-kx becomes a positive kx because the displacement is negative. When I integrate the force, do I put a a positive sign now, so in this case I would integrate the spring force from -4m to 0m? Also I know work is the Magnitude of the force times the Magnitude of the displacement for a constant force. Does this hold in varying forces such as the spring force?
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CC-MAIN-2018-43
| 935 | 1 |
https://forum.knittinghelp.com/t/3-tr-cluster-help-please/43224
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math
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Hi, all. I’ve been racking my brain over this, trying to figure out how to do this. I’ve attempted it twice, but I get it wrong somehow. So I was hoping somebody could explain to me (step by step) how to make this stitch.
The pattern says:
ch 3, [COLOR=Red]holding the last loop of each st on hook, [COLOR=Black]3 tr in same sp, YO, draw through all 3 loops.
The part in red is the part I don’t get. How do I hold the last loop of each st on the hook?? Can somebody please talk me through this?
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CC-MAIN-2022-40
| 500 | 4 |
https://www.pinterest.com/pin/193514115209480371/
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math
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Great November math station ideas. There are not printables or links to these math stations. Use as an inspiration to make my own math station activities.
-Fun math idea! I teaked this for my kindergarteners. I used the center to be -ug and the petals to be the letters J, B, M, T, and R! They loved it!
Montessori Monday - Montessori-Inspired Activities for Winter or Summer Olympics
Montessori-Inspired Olympic Math Activities by Deb Chitwood, via Flickr
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| 456 | 4 |
https://www.bartleby.com/solution-answer/chapter-36-problem-115ps-intermediate-algebra-10th-edition/9781285195728/thoughts-into-words-consider-the-following-approach-to-factoring-12x254x60-12x254x603x64x10/1c968f2e-78b0-11e9-8385-02ee952b546e
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math
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Thoughts Into Words
Consider the following approach to factoring :
Is this a correct factoring process? Do you have a suggestion for a person using this approach?
The approach for factoring of a trinomial is a correct factoring process and provide the suggestion for a person using the given approach.
To factor the trinomials in the form of , we follow the steps given below:
Step-1: Multiply the coefficients of and the constant term.
That is .
Step-2: Find the integers whose sum is equal to and whose product is .
Step-3: List out the pairs of factors for preferably using a table.
Step-4: Rewrite the original problem by splitting the appropriate terms.
Step-5: Now, use the factoring by grouping method to factor the rewritten problem and simplify to get the solution.
Given trinomial: .
The final solution for factoring the given trinomial is correct. But this approach is not correct.
To factor the given trinomial , the following procedure must be used.
Rewriting the given trinomial
We need to complete the following with two integers whose sum is and whose product is .
The following table shows the possible pairs of factors of :
|Factors||Product of the factors||Sum of the factors|
From the above table, we find that the numbers that we need are and and we can complete the factoring
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Calculus: Early Transcendentals
Understanding Basic Statistics
Calculus: An Applied Approach (MindTap Course List)
Precalculus: Mathematics for Calculus (Standalone Book)
Single Variable Calculus
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Calculus: Early Transcendental Functions
Finite Mathematics and Applied Calculus (MindTap Course List)
Calculus (MindTap Course List)
Essentials Of Statistics
Statistics for The Behavioral Sciences (MindTap Course List)
Probability and Statistics for Engineering and the Sciences
Single Variable Calculus: Early Transcendentals, Volume I
Contemporary Mathematics for Business & Consumers
Mathematical Excursions (MindTap Course List)
Elementary Geometry For College Students, 7e
Elementary Technical Mathematics
Mathematical Applications for the Management, Life, and Social Sciences
Elements Of Modern Algebra
Calculus of a Single Variable
Single Variable Calculus: Early Transcendentals
Trigonometry (MindTap Course List)
Calculus: Early Transcendental Functions (MindTap Course List)
Study Guide for Stewart's Multivariable Calculus, 8th
Introduction To Statistics And Data Analysis
Finite Mathematics for the Managerial, Life, and Social Sciences
Elementary Geometry for College Students
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
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| 2,720 | 48 |
https://www.mdc.e.u-tokyo.ac.jp/en/2022/01/31/position-auctions-with-multidimensional-types-revenue-maximization-and-efficiency/
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math
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This study considers revenue-optimal auction design for two ordered substitutes, such as positions or priorities. Bidders have a two-dimensional type about a valuation for the top position and a discount rate of the second position for the top. An auction mechanism is dominant-strategy incentive compatible if and only if it satisfies the “Law of One Price,” which requires that bidders’ payments are independent of their own discount rate. The simple “virtually efficient mechanism,” which maximizes the unconstrained virtual surplus, is not incentive compatible for any type distribution if the discount-rate-type space includes at least two interior values. If the discount-rate-type space includes at most a single interior value, there exist distributions under which the virtually efficient mechanism is incentive compatible, and therefore optimal.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816977.38/warc/CC-MAIN-20240415111434-20240415141434-00600.warc.gz
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CC-MAIN-2024-18
| 865 | 1 |
https://qna.carrieradda.com/26966/the-maximum-length-of-arc-of-contact-for-two-mating-gears-in-order-to-avoid-interference-is
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math
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Right choice is (c) (r + R) tan φ
The best explanation: Interference may only be prevented, if the addendum circles of the two mating gears cut the
common tangent to the base circles between the points of tangency.
maximum length of arc of contact = (r + R) tan φ
where r = Pitch circle radius of pinion,
R = Pitch circle radius of driver, and
φ = Pressure angle.
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| 366 | 7 |
http://www.chegg.com/homework-help/questions-and-answers/following-circuit-consists-three-positive-edge-flip-flops-input-fin-8-khz-square-wave-8-de-q1655157
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math
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Show transcribed image text
Show transcribed image text The following circuit consists of three positive - edge flip - flops. The input, fin, is on 8 kHz square wave (8%) Develop the timing diagram which shows the output of all the flip - flops (QA, QB og Qc = fout) and the input signal, fin. (2%) Determine the output frequency, i.e. of the fout waveform.
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CC-MAIN-2015-48
| 357 | 2 |
https://studyres.com/doc/1273620/basic-probability
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math
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* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project
Simple & Compound Probability Name: _______________________________ Directions: Use your former knowledge and intuition to answer the basic probability questions. There are hints on the back if needed. One of these names is to be drawn from a hat. Determine each probability below: Mary Jenny Bob Marilyn Bill Jack Jerry Tina Connie Joe 1. P(a 5-letter name that ends with an e) = ________________ (What is the probability of drawing a 5-letter name that ends with an e?) 2. P(4-letter name) = _____________ 3. P(name starting with B) = ____________ 4. P(name starting with J and 5-letter name) = ______________ 5. P(name starting with J or a name ending with Y) = _____________ One card is drawn from a well-shuffled deck of 52 cards. 6. P(a black ace) = ________ 7. P(a face card or a card with a prime number) = _________ 8. P(a red 10 or a black 7) = ________ 2 A spinner, numbered 1–8, is spun once. What is the probability of spinning… 1 3 8 4 7 5 6 9. P(NOT a diamond) = ______________ 10. at least a 5? ___________ 11. a prime number? _________ 12. Suppose that the probability of snow is 0.58. What is the probability that it will NOT snow? ________________ Hints: If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B). and If A and B are inclusive events, then P(A or B) = P(A) + P(B) – P(A B). Apply the probability skills from above 13. A weather forecaster states that the probability of rain is 3/5, the probability of lightning is 2/5, and the probability of both is 1/5. What is the probability of a sporting event being cancelled due to rain or lightning? 14. A bag contains cards numbered from 1 to 14. One card is drawn at random. Find the probability of selecting an 8 or a number less than 8. 15. Find the probability of selecting a boy or a blond-haired person from 12 girls, 5 of whom have blond hair, and 15 boys, 6 of whom have blond hair.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989812.47/warc/CC-MAIN-20210515035645-20210515065645-00466.warc.gz
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CC-MAIN-2021-21
| 2,014 | 2 |
http://www.apppicker.com/apps/529734380/t-d-calculator
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math
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T D Calculator is a pack of calculators and Tables related to Thermodynamics and thermal Engineering.Its a lite version of THERMODYNAMICS CALCULATOR(Pack of 44 Thermodynamics Calculators with Formulas,Converters & Tables)
1. Emissivity Coefficients for various Metal Surfaces
2. Entropy Calculator
3. Enthalpy Calculator.
4. Specific Heat Capacity Calculator.
5. Potential Energy Calculator.
6. Kinetic Energy Calculator.
7. Laws of Thermodynamics.
Formulas and Definitions also provided.
with Easy User Interface.
An useful App for Mechanical engineers and Engineering Students.
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CC-MAIN-2018-43
| 579 | 11 |
https://coin.fyi/news/dogecoin/doge-pilot-curated-list-cryptoeconomics-edition-a3g6tu
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math
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In the first two articles of this series, we saw some broad trends in juror voting patterns and then we took a closer look at cases in which attackers attempted to bribe jurors. In this article, we will consider a number of other interesting questions and observations that have arisen regarding the behavior of jurors in the Doges on Trial pilot.The “lazy strategy” of always voting for the most common response
In the first article in our series, we saw that roughly 70% of all votes cast were for “not doge.” Then, one might naturally ask if it is/would have been profitable to set up a bot that deposits PNK and just votes “not doge” whenever it is drawn.
As a rough heuristic, imagine that we give such an attacker one vote in each case but, for simplicity, all of the existing votes still count and the outcomes of the cases are assumed not to change (after all, if this attacker had resulted in unjust outcomes, those could have been appealed). Then, if we denote by Ni and Di the number of “not doge” and “doge” votes in the ith case respectively, and if d is the deposit lost by incoherent jurors, the attacker's net returns are given by:
Based on the observed values of Di and Ni for each case (up through the cutoff to qualify for a payout of Dogecoins at disputeID 148), we compute that S=-48.9d, namely that such a strategy would have lost 48.9 more deposits than the PNK that it gained back. (Always voting “doge” is even worse; the equivalent calculation gives S=-78.3d.) This strategy essentially does not work as an attacker does not gain anything when she votes with a unanimous decision, and we have seen that most of the cases were, in fact, unanimous.
A more complete answer to this question would depend on what percentage of the total PNK deposited the attacker controlled; then we could consider the attacker's chance of being drawn in the ith case and calculate her expected return. However, we can perform a slightly more nuanced heu...
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| 1,986 | 5 |
https://www.nagwa.com/en/videos/376132629063/
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math
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Write in grams: 62 kilograms.
We need to move from our given kilograms to grams. One kilogram equals 1000 grams. A kilo means a 1000, and gram is a unit of measurement in the metric system. So what we’re saying here is a kilogram is 1000 grams, but we have 62 kilograms. For every one kilogram, there’re 1000 grams.
To find out how many grams there would be in 62 kilograms, we need to multiply our 62 kilograms by 1000. After we multiply 62 by 1000, we’re left with 62000 grams.
62 kilograms written in grams is 62000.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663006341.98/warc/CC-MAIN-20220527205437-20220527235437-00523.warc.gz
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CC-MAIN-2022-21
| 525 | 4 |
https://graduatewriting.com/sage-tool-cryptography/
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math
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Sage Tool Cryptography. Question For all of the following questions shows your sage input/output. 1. Compute the order of the curve defined by y^2 = x^3 + 7*x + 25 over the finite field with 47 elements 2. On the curve defined by y^2 + x*y = x^3 + x over GF(2^8) compute the inverse of the point (1,1) 3. On the curve defined by y^2 + y = x^3 + x^2 + x + 1 over the finite field with 701 elements, find a generator and show its order. 4. On the curve defined by y^2 = x^3 + 4187*x + 3814 over the finite field of size 6421 compute the sum of the points (3711,373) and (4376,2463). 5. On the elliptic curve defined by y^2 = x^3 + 3361*x + 6370 over the finite field of size 8461 compute 1001 times the point (1735, 3464). 6. On the elliptic curve defined by y^2 = x^3 + 1800*x + 1357 over finite field of size 8191, let P1 = (1794, 1318) and P2 = (3514, 409), compute the sum of 13 times P1 plus 28 times P2.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585460.87/warc/CC-MAIN-20211022052742-20211022082742-00084.warc.gz
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CC-MAIN-2021-43
| 1,972 | 8 |
https://drawingonmath.blogspot.com/2013/07/math-notes-integrated-math-engagement.html
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math
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Strategy: Math Notes
Start with the Dunk Tank Problem from 2008 MCAS:
Give students a Math Notes organizer (template including space for: facts, questions, diagram, possible steps to try, solution) and have them fill it out (working independently first, then collaborating after completing as much as they can on their own). This question is a good one to use as it includes hidden questions (ex: you need to know the volume of the bucket before you can determine how many buckets it will take to empty the tank). There is a diagram of the tank, but students need to come up with their own sketch of the bucket. The solution requires use of multiple formulas but also asks students to reason with the results, not merely calculate by plug and chug. Since there are so many parts to this problem having an organization system is important. Most students can complete the individual parts of this problem but have trouble figuring out what those parts are. The Math Notes structure allows students to see the pieces of the puzzle spread out in front of them, which helps many students determine how to assemble everything into a solution.
Strategy: Integrated Math Engagement
By PreCalculus, students have studied many functions and their graphs, ranging from linear to logarithmic. While the shapes of the graphs, the forms of the equations and the applications vary widely, all graphs are shifted and stretched in the same way. Start class by asking students to plot the parent graph for all the types of functions they know (linear, absolute value, quadratic, cubic, exponential, logarithmic). Then ask students to graph a wide variety of shifts and stretches of these functions. They may start with tables but will quickly want to find shortcuts. Without answering questions, continuously refer students to the parent graphs. Eventually, bring students together as a class to make observations. Finally, write “y=a*f(b*x+c)+d” on the board and have students use the observations they made to describe the effect of each constant (a, b, c, d) on the graph of y=f(x).
Too often students study functions in isolation and memorize a different formula for each one. In reality, no matter what the function, multiplying stretches and adding shifts. Once students recognize this connection they will be well prepared to graph any function. In order to discover this connection, students need to see a variety of functions at once, in an integrated activity.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030333541.98/warc/CC-MAIN-20220924213650-20220925003650-00214.warc.gz
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CC-MAIN-2022-40
| 2,456 | 6 |
https://www.jiskha.com/display.cgi?id=1378415240
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math
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posted by Anonymous .
A train normally travels at a uniform speed of 74km/h on a long stretch of straight, level track. On a particular day, the train must make a 3.0min stop at a station along this track.
If the train decelerates at a uniform rate of 1.3m/s2 and, after the stop, accelerates at a rate of 0.70m/s2 , how much time is lost because of stopping at the station?
Vo = 74km/h = 74000m/3600s = 20.56 m/s.
V = Vo + a*t
t1 = (V-Vo)/a = (0-20.56)/-1.3 = 15.8 s.
t2 = 3 min = 180 s.
t3 = 20.56-0)/0.7 = 29.37 s
T=t1 + t2 + t3=15.8 + 180 + 29.37=225.2s
= 3.75 min. = Time lost.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886436.25/warc/CC-MAIN-20180116125134-20180116145134-00208.warc.gz
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CC-MAIN-2018-05
| 582 | 10 |
https://masepoxies.answerbase.com/?page=11
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math
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Would a concrete countertop need a seal coat?
Asked 5 months ago
Table Top Pro Epoxy
Epoxy begins to foam and overflow
How long before marine primer and paint?
Asked 6 months ago
Low Viscosity Epoxy Resin
Will your resin soften in a vehicle
Deep Pour Epoxy
why did my mas penetrating epoxy sealer start to boil in the bucket after I was half way through installing
Is application temperature dependent?
Asked 1 year ago
Shop > Bristol Finish > Bristol Finish UV Clear Urethane Varnish
Is this a 0 VOC resin?
Shop > Art Epoxy > Art Pro Epoxy
Can I use this to make dominoes?
Shop > Non Blushing System > Non-Blushing Medium Hardener
Can this be used with Table top Pro? I have some vertical areas that I need to coat and they can't be poured.
Non-Blushing Fast Hardener
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710890.97/warc/CC-MAIN-20221202014312-20221202044312-00354.warc.gz
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CC-MAIN-2022-49
| 774 | 19 |
http://dl.acm.org/citation.cfm?doid=44128.356246
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math
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Concepts inCorrigendum: “Interpolation with Interval and Point Tension Controls Using Cubic Weighted v-Splines”
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate (i.e.
more from Wikipedia
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s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737933027.70/warc/CC-MAIN-20151001221853-00101-ip-10-137-6-227.ec2.internal.warc.gz
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CC-MAIN-2015-40
| 550 | 3 |
https://www.buscainmobiliarias.com/casas--venta/soria/soria
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math
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ArKadia Publishing Ltd 2 YHGF-T13776
- 6 habitaciones
- 3 baños
This charming country property is located in the town of Burgo De Osma and is just one hour from Soria and two hours from Madrid.and#13;and#13;With six bedrooms and three bathrooms this home also enjoys a private garden, swimming pool as well as a sun terrace and BBQ.and#13;and#13;Traditional beams throughout this home is full of character and come part furnished. It also has a large lounge and dining area. and#13;and#13;The property also has a garage and off road parking.and#13;and#13; Additional Inform...
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s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347425481.58/warc/CC-MAIN-20200602162157-20200602192157-00031.warc.gz
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CC-MAIN-2020-24
| 577 | 4 |
https://www.jamiletheteacher.com/geometry/what-is-a-point-in-geometry-terms.html
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math
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In classical Euclidean geometry, a point is a primitive notion that models an exact location in the space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space.
- 1 How do you define a point in geometry?
- 2 What is a point math term?
- 3 What term is a point?
- 4 Is point a defined term in geometry?
- 5 What is representation of a point?
- 6 What is an example of a point?
- 7 What is a point in 4th grade math?
- 8 How do you draw a point in geometry?
- 9 What is point in drawing?
- 10 What is the definition of point and one example?
- 11 What is a point in science?
- 12 Why is a point an undefined term?
- 13 What is use to name a point?
- 14 How many dimensions does a point have?
How do you define a point in geometry?
In geometry, a point is a location represented by a dot. A point does not have any length, width, shape or size, it only has a position. When two distinct points are connected they form a line.
What is a point math term?
A point is an exact position or location on a plane surface. It is important to understand that a point is not a thing, but a place. We indicate the position of a point by placing a dot with a pencil. This dot may have a diameter of, say, 0.2mm, but a point has no size.
What term is a point?
In Geometry, we have several undefined terms: point, line and plane. From these three undefined terms, all other terms in Geometry can be defined. In Geometry, we define a point as a location and no size. A point has no size; it only has a location. And the way that we label it is with a capital letter.
Is point a defined term in geometry?
In geometry, formal definitions are formed using other defined words or terms. There are, however, three words in geometry that are not formally defined. These words are point, line and plane, and are referred to as the “three undefined terms of geometry”.
What is representation of a point?
Point. A point is the most fundamental object in geometry. It is represented by a dot and named by a capital letter. A point represents position only; it has zero size (that is, zero length, zero width, and zero height).
What is an example of a point?
A point has no dimensions such as length, breadth or thickness. A star in the sky gives us an idea of point. Similarly some other examples of points are: the tip of a compass, the sharpened end of a pencil, the pointed end of a needle.
What is a point in 4th grade math?
A point is an exact location in space. A line is a straight path that continues forever in both directions. A ray is part of a line. A ray has one endpoint and continues forever in one direction. It is the part of a line between two endpoints.
How do you draw a point in geometry?
You draw a point by using a dot and identifying it by a letter, such as ‘Point A’ or even ‘Point X. ‘ When you complete a fill-in-the-blank test, you’re filling in a line segment. A line segment is a piece of a line.
What is point in drawing?
Points and Dots. As I mentioned last week a point is a coordinate without any dimensions, without any area. Points are the simplest element of visual design. By definition we can’t actually draw a point, since to see one would require it have dimensions. What we can draw is a dot.
What is the definition of point and one example?
The definition of a point is a sharp end or part of an argument. An example of point is the end of a pencil. An example of point is a reason why someone is against abortion. noun. 10.
What is a point in science?
Points, conjugate. (Science: microscopy) The pair of points on the principal axis of a mirror or lens so located that light emitted from either point will be focused at the other. Related points in the object and image are located optically so that one is the image of the other.
Why is a point an undefined term?
In geometry, point, line, and plane are considered undefined terms because they are only explained using examples and descriptions. that lie on the same line.
What is use to name a point?
A point in geometry is represented by a dot. To name a point, we usually use a (capital) letter.
How many dimensions does a point have?
In order to better understand why your world is three dimensional, consider zero, one, and two dimensions: A point has a dimension of zero. In math, a point is assumed to be a dot with no size (no length or width). A line or line segment has a dimension of one.
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CC-MAIN-2022-21
| 4,463 | 43 |
http://lib.cqvip.com/Qikan/Article/Detail?id=7001287841
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math
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Hadjidimos(1978) proposed a classical accelerated overrelaxation(AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant, L-matrices, and consistently orders matrices. Several preconditioned AOR methods have been proposed to solve system of linear equations Ax = b, where A ∈ Rn×n is an L-matrix. In this work, we introduce a new class preconditioners for solving linear systems and give a comparison result and some convergence result for this class of preconditioners. Numerical results for corresponding preconditioned GMRES methods are given to illustrate the theoretical results.
Journal of Mathematical Research with Applications
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669422.96/warc/CC-MAIN-20191118002911-20191118030911-00529.warc.gz
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CC-MAIN-2019-47
| 760 | 2 |
https://gmatclub.com/forum/took-the-gmat-this-spring-now-taking-lsat-oct-dec-136644.html
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math
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Just wanted to know how similar verbal in GMAT is to LSAT? I have taken a diagnostic test off the LSAC website, and have seen for the most part that most questions on LSAT are really similar to verbal section on GMAT such as strengthen/weaken questions, which of the following are most similar in reasoning, which of the following concludes this passage, etc etc
the RC is similar as well... a little more detailed/tougher reading than RC on GMAT but still somewhat similar, then there is the logic games and its not that similar to GMAT but when I did that section i did pretty good, was a little short on time though since some of the games confused me at times.
Let me know what you think about the similarity and mostly if I can use the RC books I had for the GMAT in order to help in the LSAT. thanks
The GMAT CR and RC questions are very similar to the LSAT logical reasoning
and reading comprehension questions. The format of the LSAT will be different than the GMAT verbal though.
1. Five 35 minute sections, and they will only have one question type. There are two graded sections of logical reasoning, and one graded section of reading comp and analytical reasoning (aka logic games). The fifth section is experimental, and could be any of the three types.
2. All logical reasoning sections will have 24-26 questions each.
On the GMAT there are 75 minutes to do 41 questions in the entire section, gives you an average of 109.75 seconds each question. For native English speakers, we often can finish this section in 50-60 minutes and still get a great score.
On the LSAT, you have 35 minutes to do 25 questions on average for each section, a little more than that for RC, a little less for games. But with 35 minutes to do 25 questions, you have an average of 84 seconds to do each question, which is nearly 25% less time on average. In addition, LSAT LR blurbs (their class instructors tend to say stimulus/stimuli) are also more complicated than the GMAT CR.
Also, there are different question types, most notably parallel reasoning, and more "everything is an assumption of the argument except" type questions. It is a harder exam on average.
LSAT LR (and RC and games) also requires that you understand sufficient vs. necessary conditions (If A then B ). If you don't have this down, you won't do well on the LSAT. The GMAT CR rarely if ever has questions that require your use and application of conditional reasoning.
3. LSAT Reading Comp, you have four passages and about 27 questions on average. Three passages are about 500 words each, and one passage is comparative reading, where you get two 200-250 word passages and compare those two in a set of questions. LSAT RC is nothing like GMAT RC in my opinion because the passages are longer and the material is denser because of the longer passage lengths.
4. The logic games also involve sufficient vs. necessary conditions and are a series of puzzles for you to figure out. No equivalent on the GMAT. You have four games and should get 22-24 questions of them.
If you're going to take the LSAT for October, you should use separate material to study for that exam. Unlike the GMAT, three LSAT's a year are released for the public to purchase and you should purchase them. You should definitely take every exam for the last three years (9 tests or so) to get a good feel of what the LSAT will be like if and when you take it in October/December. In addition, when you take the tests, you should also take an additional section as an experimental so you can take a full five sections (3 back to back to back, a 15 minute break, then the rest back to back) each time you take the exam. Also make use of an error log
for the LSAT LR questions.
Hope this helps.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189313.82/warc/CC-MAIN-20170322212949-00372-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 3,725 | 16 |
https://scholarworks.utep.edu/physics_papers/8/
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math
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S-polarized guided electromagnetic waves at a planar interface between vacuum and a graded-index dielectric
Analytic expressions for the dispersion relation and electric field profiles of guided waves supported by an asymmetric graded-index dielectric waveguide are derived. The system studied consists of vacuum in the region , and a dielectric medium in the region whose dielectric permittivity decreases continuously with increasing distance into it from the interface according to . Here is the (real) index of refraction of the medium at , and it is assumed that . It is found that for frequencies below a certain critical value given by , where is the speed of light in vacuum, the dispersion curve consists of a single branch that exists in a narrow spectral range. Its electric field decays exponentially with increasing distance into each medium. For frequencies above this critical value, the dispersion curve possesses several branches. The corresponding electric field decays exponentially with increasing distance into the vacuum, and decays in an oscillatory fashion with increasing distance into the graded-index dielectric medium. The number of nodes in the latter field equals the branch number, starting with zero for the lowest frequency branch.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400238038.76/warc/CC-MAIN-20200926071311-20200926101311-00268.warc.gz
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CC-MAIN-2020-40
| 1,264 | 2 |
http://graphicdesign.stackexchange.com/questions/tagged/workflow+resources
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math
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Graphic Design Meta
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s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535920849.16/warc/CC-MAIN-20140909054042-00484-ip-10-180-136-8.ec2.internal.warc.gz
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CC-MAIN-2014-35
| 2,127 | 53 |
https://www.jiskha.com/display.cgi?id=1233542278
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math
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posted by helga .
what are the mean and standard deviation of a sampling distribution consisting of samples of size 16? these sameples were drawn from a population whose mean is 25 and who standard deviation is 5.
a. 25 and 1.25
b. 5 and 5
c. 25 and 5
d. 5 and 1.25
e. 25 and square root of 5
the standard deviations of SAT scores is 100 points. a researcher decides to take a sample of 500 students' scores to estimate the mean score of students in your state. what is the standard deviation of the sample mean?
e. can't determine without sample mean
what is the critical z-value for an 85% confidence interval?
d. need population standard deviation
e. need sample size
which of the follow isn't necessary to compute the sample size appropriate for a given confidence level and margin of error?
a. sample mean
b. populatuion standard deviation or an estimate of standard deviation
c. critcal z-value, z*
d. the margin of error m.
e. all of these values are neccessary
hi, u can solve it by this formula
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886123312.44/warc/CC-MAIN-20170823171414-20170823191414-00408.warc.gz
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CC-MAIN-2017-34
| 1,003 | 19 |
https://essayapple.org/solved-assignment-219395/
|
math
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Subject: General Questions / General General Questions
ECO 305 — Spring 2017
——-Assignment 4——Please, note the following: You must walk us through your answers and give us the economic intuition behind your solution. Otherwise you will
not obtain any points, EVEN THOUGH your answer might be correct.
In your explanations, use whole sentences and a clear syntax, similarly to the textbook.
Whenever it is not explicitly required, it is up to you to use equations and/or graphs in your answers.
If you use equations, remember to define each variable and what the equation stands for.
If you use graphs, remember to label clearly the a. axes; b. curves; c. initial equilibrium point(s); d. terminal or final
equilibrium point(s); and e. the direction the curves shift.
Note there might be more than one way to correctly answer a question.
Regardless of how you organize/distribute the work, both members of the partnership must be able to complete the
whole assignment. …………………………………………………………………………………………………………………………
1. Assume that a series of inflation rates is 1 percent, 2 percent, and 4 percent, while nominal interest rates in
the same three periods are 5 percent, 5 percent, and 6 percent, respectively.
a. What are the ex post real interest rates in the same three periods?
b. If the expected inflation rate in each period is the realized inflation rate in the previous period,
what are the ex ante real interest rates in periods two and three?
c. If someone lends in period two, based on the ex ante inflation expectation in part b, will he or
she be pleasantly or unpleasantly surprised in period 3 when the loan is repaid?
2. Assume that the demand for real money balance (M/P) is M/P = 0.6Y – 100i, where Y is national income and
i is the nominal interest rate (in percent). The real interest rate r is fixed at 3 percent by the investment and
saving functions. The expected inflation rate equals the rate of nominal money growth.
a. If Y is 1,000, M is 100, and the growth rate of nominal money is 1 percent, what must i and P
b. If Y is 1,000, M is 100, and the growth rate of nominal money is 2 percent, what must i and P
3. If the demand for money depends positively on real income and depends inversely on the nominal interest
rate, what will happen to the price level today, if the central bank announces (and people believe) that it will
decrease the money growth rate in the future, but it does not change the money supply today?
4. Consider two countries, Hitech and Lotech. In Hitech new arrangements for making payments, such as
credit cards and ATMs, have been enthusiastically adopted by the population, thereby reducing the
proportion of income that is held as real money balances. Over this period no such changes occurred in
Lotech. If the rate of money growth and the growth rate of real GDP were the same in Hitech and Lotech
over this period, then how would the rate of inflation differ between the two countries? Carefully explain
your answer. Page 1 5. A classical economist wears a T-shirt printed with the slogan “Fast Money Raises My Interest!” Use the
quantity theory of money and the Fisher equation to explain the slogan.
6. Interest rates played a part in the 1984 U.S. presidential debates. Some politicians claimed that interest rates
rose over the 1981–1983 period, while others claimed rates fell. Below is a table showing interest rates and
annual inflation rates from 1981 to 1983.
Reconcile these conflicting claims.
Extra Credit Question
7. Go to the Federal Reserve Open Market Committee (FOMC) page of the Federal Reserve Board’s website1 and
find the most recent statement issued after the most recent FOMC meeting.2
a) What is the date of this meeting? What is the target Federal Funds rate?
b) Is the above target rate different from the target in the previous FOMC statement?3 If yes, by how much does
c) Does the statement comment on current macroeconomic conditions in the US? How does it describe the US
economy? What is the target inflation rate? Use your own words to explain (do NOT copy and paste).
d) Suppose now the target inflation rate has been attained but 8.5% of the labor force is unemployed. If you were
in the FOMC, what action would you prescribe? How would this affect the inflation rate? The interest rate?
e) Suppose all is as in (d), your recommendation is implemented and, in the short run, the increase in money
supply pushes interest rates down. What is the impact on the economy (consumption, investment, GDP)?
What is now the impact on the inflation rate? On unemployment? 1
Click on “Meeting calendars and information” and then click on the most recent statement listed in the calendar.
You will have to look into last calendar year’s statements. Page 2
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CC-MAIN-2022-21
| 4,850 | 52 |
https://www.plymouthgrating.com/guidance/technical-notes/fundamentals/dispersion-and-pulses/
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math
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Many optical systems and experiments involve signals which vary fairly rapidly in time. A short burst of light—referred to as a pulse—might be used to carry information, as in an optical fiber communications system, or to achieve a high peak intensity for applications ranging from materials processing to high-intensity physics research.
Any time-varying signal necessarily comprises multiple frequency components. Therefore to understand how a time-varying light signal is transmitted through an optical component or system, we must determine how the system impacts its different frequency components. A wave experiences dispersion when different frequencies travel through the system in different times. Dispersion can significantly affect a short pulse of light, both advantageously, as in Chirped Pulse Amplification (CPA), and detrimentally.
We can think of an optical component or system which provides dispersion to a light pulse as a “black box,” as illustrated in Figure 1. The input pulse is represented by the electric field Ein(t) and the resulting output pulse is represented by Eout(t).
Since we are interested mainly in the effects of dispersion, we assume there is a uniform amplitude frequency dependence, such that the same intensity of light is transmitted at each frequency. The system may then be described simply by the optical phase φ it imparts to each frequency ω of a light wave.
To describe the pulse of light, we consider a simplified mathematical description of the pulse at wavelength λ traveling in direction z,
where ein(t) describes the temporal shape of the pulse, k = 2π/λ is the wave propagation constant, and ω0 = 2πc/λ is the angular frequency of the wave with c the speed of light (3×108 m/s). It is assumed that e(t) varies in time much more slowly than the frequency ω0 of the wave. The subscript “in” identifies that the pulse is heading into the system of interest.
The mathematical procedure for calculating the output pulse Eout(t) is described in the APPENDIX to this Technical Note. While the method can be used for any phase function φ(ω), little insight is gained by simply turning this crank on a computer. Often the pulse spectrum is sufficiently narrow and the phase function φ is relatively smoothly varying over this narrow spectral range. Then φ at frequency ω can be well approximated by a Taylor series expansion about the central frequency ω0 according to
Expanding φ in this way not only simplifies the math, but also enables helpful physical interpretation of the physics of dispersion. The first term is just a constant phase and has no impact on the measured intensity of light transmitted through the system. The coefficient of the second term dφ/dω = φʹ has units of time and is called the group delay time. We will see why shortly. The coefficient of the third term d2φ/dω2 = φʺ has units of time squared and is called the group delay dispersion, or GDD .
Much insight on how dispersion affects a pulse can be gained using the simple approximation of phase in (2) and a gaussian pulse shape. The gaussian pulse can be described by
where τ is a measure of the pulse width. The spectrum of this gaussian pulse, denoted ēin(ω), also has a gaussian profile, and can be written
These two profiles are illustrated in Figure 2, where both the 1/e and half-maximum widths are identified. The pulse has a full width at 1/e of 2τ, whereas the spectrum has a full width at 1/e of 4/τ. So the broader the pulse is, the narrower its spectrum is.
Using the method described in the APPENDIX, we can now calculate the full output pulse as
is a time-dependent frequency of the output pulse. In (5) and (6) we have defined the following quantities:
and . (7)
C is called the chirp parameter and τC is the chirped pulse width. Looking closely at (5) – (7) we observe four fundamental ways a pulse is affected by dispersion.
From (5) it is clear that the output pulse also has a gaussian shape, but t has been replaced by t – φʹ in the time dependence. Referring to Figure 3, physically this substitution means that the pulse emerging from the optical system is no longer centered at time t = 0, but is now centered at time t = φʹ. In other words, it has been delayed in time by φʹ. The first derivative φʹ is called the group delay time because it is the amount of time the group of frequency components that form the pulse are delayed by the optical system.
Note that on a time graph like those shown in Figure 3, the convention for interpreting the orientation of the pulse is as follows: if an observer sits at the value of z at which the pulse shape e(t) is evaluated, then the observer sees the value of e(t) shown on the plot after waiting a time t on the plot. Thus the observer sees the left side (i.e., earlier times) of the plotted pulse shape first.
Again referring to the exponent of the gaussian function in (5), the width of the output pulse is now determined by τC instead of τ. The output pulse is broader than the input pulse by a factor of √(1 + C2). Since C is proportional to the GDD parameter φʺ, then the higher the absolute value of φʺ, the more the pulse is broadened. Figure 4 illustrates a pulse that is delayed and broadened by the group delay time and GDD, respectively.
Figure 5 shows examples of how the output pulse width of a gaussian pulse increases as a function of the GDD. In the graph on the left, five initial pulse widths ranging from 10 to 400 fs are considered for GDD values ranging from 0 to 10,000 fs2. Note the smaller the initial pulse width, the lower the GDD required to broaden the pulse substantially. For a 400 fs pulse, even 10,000 fs2 has almost no effect on the pulse width.
The graph on the right considers higher values of GDD to demonstrate how much dispersion is required to stretch or compress a pulse with a width of 10’s of fs in a CPA system. Stretching to 100 ps requires about 1 ps2 = 106 fs2 of GDD, whereas to stretch to 1 ns requires about 10 ps2 = 107 fs2.
According to (5) the amplitude of the dispersed electric field is “squished,” or reduced, by a factor of √(τ/τC) relative to the amplitude of the input pulse. This effect is also illustrated in Figure 4. Since the intensity of a light wave is proportional to |E(t)|2, then the output pulse peak intensity is a factor of τ/τC smaller than that of the input pulse. As an example, Figure 6 shows how the relative intensity depends on GDD for the same initial pulse widths and range of GDD values shown in the graph on the left in Figure 5.
Chirp refers to a signal in which the frequency increases or decreases with time. We expect the dispersed pulse to be chirped because the mechanism by which it is broadened is in fact different frequency components being delayed by different times as it is transmitted through the dispersing component or system. For a gaussian pulse, the chirp is described by the time-dependent frequency ω(t) in (6). This is an example of a linear chirp, since the frequency is directly proportional to time.
Figure 7 illustrates an unchirped initial pulse (left) as well as chirped pulses resulting from both positive and negative GDD (center and right, respectively). For illustration purposes the frequency relative to the pulse width shown here is much lower than typical in most real systems.
Notice that for φʺ > 0 (positive GDD) the frequency increases at later times. Thus a fixed observer sees lower frequencies in the chirped pulse arrive first. Loosely, we say the “red” part of the pulse arrives ahead of, or leads, the “blue” part. For φʺ < 0 (negative GDD) the red part of the pulse lags the blue part.
Dispersion from a pair of gratings:
In the Technical Note “Temporal Dispersion” we found the temporal dispersion parameter for diffraction of light off of a pair of parallel gratings,
where m is the order of diffraction, λ is the wavelength of light, f is the grating frequency, θm is the angle of diffraction, and the subscript “⊥” denotes that the grating separation s is measured along the direction normal to the grating surfaces. This physically useful parameter can be interpreted as follows: for each meter of separation s between two parallel gratings, the difference in propagation delay time dτ between two wavelengths of light separated by dλ can be approximated by the expression on the right side of (8) multiplied by dλ.
We may also directly relate D to GDD. Using the chain rule of calculus, we can see
where we have used the delay time τ = dφ/dω. From (9), we may now directly relate D to GDD as
and . (10)
Keeping careful track of units and simplifying, we may use the following conversion relations
and , (11)
where s is in meters and λ is in nm. Note that D and φʺ have opposite signs. Combining (8) and (10), we may directly write the GDD in terms of grating parameters as
For a simple parallel grating pair, the GDD is always negative. In other words, the blue part of a pulse leads the red part. In most CPA systems pulses are stretched using an arrangement that provides positive dispersion, and then compressed using the negative dispersion from a parallel grating arrangement.
Using (12), we may plot an example of the GDD as a function of the angle of incidence for a certain wavelength. Figure 8 shows how the GDD of the –1st order depends on angle of incidence at 800 nm for three different grating frequency values.
The absolute value of the GDD is larger for higher grating frequencies at a given angle of incidence. Furthermore it increases rapidly at smaller incidence angles, as the diffraction angle approaches –90º.
As explained above, we can describe the pulse in terms of its electric field according to (1). We are only concerned with how the scalar electric field E(t) depends on time t. We ignore the polarization and transverse beam properties of the pulse, equivalent to assuming a nearly perfect plane wave with simple (e.g., linear) polarization. In (1) E(t) is assumed to be a real quantity, obtained by taking the real part of the right-hand side of this equation (the “real part” notation is suppressed).
Since the optical component or system imparting dispersion to the pulse is characterized by its frequency response, we must somehow transform (1) into a description of the electric field in terms of frequency, not time. We can think of the pulse shape ein(t) as a superposition of many monochromatic plane waves, each at frequency ω = ω0 + Ω, and each with an amplitude ēin(Ω) = dΩ/2π. Writing this superposition as an integral,
Note that (13) has the mathematical form of an inverse Fourier transform. Therefore ēin(Ω) must be the Fourier transform of ein(t), or
In words, ein(t) is the initial, slowly varying pulse shape, and ēin(Ω) is the initial spectrum of the pulse. The temporal and spectral descriptions of the pulse form a Fourier transform pair. Therefore, if the pulse is very narrow in time, the spectrum must be very broad, and vice versa.
For each value of Ω = ω – ω0, we know the wave accumulates an additional phase φ(ω = ω0 + Ω) as it passes through the dispersing component or system. Therefore the output spectrum is simply
The output pulse shape is the inverse Fourier transform of the output spectrum, or
The full output pulse electric field is then simply
To summarize, the procedure for calculating the output pulse Eout(t) from the input pulse Ein(t) is as follows:
This prescription is valid for any phase function φ. However, often the pulse spectrum is sufficiently narrow and the phase function φ is sufficiently smoothly varying over this narrow spectral range that (2) is a reasonable approximation and can greatly simplify the math and offer helpful intuition, as we see above for the gaussian pulse shape example.
Often group delay dispersion (GDD) is confused with group velocity dispersion (GVD). These two quantities are closely related, as both describe the second-order dependence of a wave’s properties on frequency. GVD specifically refers to frequency dependence of a wave’s propagation constant. It makes sense to talk about GVD in a system in which a wave is propagating over some distance, such as a block of glass with a frequency dependent index of refraction or an optical fiber. In this case GDD – the dispersion or frequency dependence of the time delay—is simply the GVD multiplied by the length traveled. However in the case of an optical component or system that imparts dispersion in a more complicated way, it doesn’t make sense to describe dispersion in terms of GVD. We only see the overall group delay, or, in terms of dispersion, the overall group delay dispersion, GDD.
5 Commerce Way, Carver, MA 02330, [email protected]
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http://nrich.maths.org/public/leg.php?code=-99&cl=2&cldcmpid=7800
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math
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This Sudoku, based on differences. Using the one clue number can you find the solution?
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
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on some. . . .
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
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Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
A student in a maths class was trying to get some information from
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The letters in the following addition sum represent the digits 1
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If you take a three by three square on a 1-10 addition square and
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Find the values of the nine letters in the sum: FOOT + BALL = GAME
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Rather than using the numbers 1-9, this sudoku uses the nine
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You have been given nine weights, one of which is slightly heavier
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A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
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A few extra challenges set by some young NRICH members.
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Tim's class collected data about all their pets. Can you put the
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If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Make a pair of cubes that can be moved to show all the days of the
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Seven friends went to a fun fair with lots of scary rides. They
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each of the others. What was the total number rides?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Find the smallest whole number which, when mutiplied by 7, gives a
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A package contains a set of resources designed to develop
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designed to meet. . . .
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Follow the clues to find the mystery number.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Four small numbers give the clue to the contents of the four
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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If we had 16 light bars which digital numbers could we make? How
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rabbit there are in these pens?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
The clues for this Sudoku are the product of the numbers in adjacent squares.
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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https://www.arxiv-vanity.com/papers/0712.4086/
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math
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Mass Screening in Modified Gravity
Gregory Gabadadze111E-mail: and Alberto Iglesias222E-mail:
Center for Cosmology and Particle Physics
Department of Physics, New York University, New York, NY, 10003, USA
Department of Physics, University of California, Davis, CA 95616
Models of modified gravity introduce extra degrees of freedom, which for consistency with the data, should be suppressed at observable scales. In the models that share properties of massive gravity such a suppression is due to nonlinear interactions: An isolated massive astrophysical object creates a halo of a nonzero curvature around it, shielding its vicinity from the influence of the extra degrees of freedom. We emphasize that the very same halo leads to a screening of the gravitational mass of the object, as seen by an observer beyond the halo. We discuss the case when the screening could be very significant and may rule out, or render the models observationally interesting.
1 Introduction and summary
One of the most puzzling discoveries of our times is the fact that the present-day expansion of the Universe is accelerating . Such an acceleration can be attributed to the existence of “dark energy”- a substance with a negative enough pressure - that is present in the Universe and, hence, in the rhs of the Einstein equation:
where stands for the Einstein tensor of the 4D space-time with metric , and and denote the stress-tensors for visible and dark matter, and dark energy, respectively.
On the other hand, one can consider a different logical possibility: that the accelerated expansion is due to modified General Relativity (GR)333The latter approach is motivated by the “old cosmological constant problem” (for a review of which, see, e.g., , and in the context of modified gravity see, e.g., ). We will not be discussing this problem in the present work.. In this case, we would have the modified Einstein equations of the form:
where denotes a tensor that could depend on a metric , its derivatives, as well as on other fields not present in GR. Moreover, depends on a dimensionful constant , that sets the distance/time scale at which the Newtonian potential significantly deviates from the conventional one. For instance, in the DGP model is related to the extrinsic curvature tensor that gives rise to a self-accelerated solution [5, 6] (see, the comments on viability of this solution at the end of this section, and Ref. for a recent review).
Even though the difference between (2) and (1) might seem just conventional at a first sight, in reality, however, it could be observationally significant. For instance, it is possible to choose the rhs of (1) so that it gives rise to a background evolution obtained from (2), nevertheless, perturbations on these backgrounds would be different in (2) and (1), see, e.g., -.
In what follows we will focus on the issue of weather the two approaches, (2) and (1), could be differentiated by properties of a Schwarzschild-like solution for a static spherically symmetric source.
A key feature of any theory of modified gravity of the form (2) is that, unlike GR, it allows for the possibility of having non-vanishing curvature outside of a source. This can be easily understood by taking the trace of (2) in a region outside of sources (where ), that gives:
where needs not be zero. This fact affects in particular the notion of mass and leads to the interesting phenomenon of screening. For example, when defining the Komar mass (which coincides with the ADM mass in stationary asymptotically flat space-time) one starts with an expression in terms of a volume integral of a projection of the Ricci tensor (see, e.g., ) and then by use of Einstein’s equations the Ricci tensor is replaced by . In a modified gravity theory of the form (2) an extra term containing and its trace is generated in the replacement of the Ricci tensor. Thus, the definition of the Komar mass contains an extra piece, referred to as a mass deficit below, which for a compact static source of spherical symmetry is given by
How significant is the mass deficit? The answer to this question would depend on a concrete model at hand. However, we would like to argue that in models which share properties of Lorentz invariant “massive gravity”, the mass deficit could be of the order of the mass itself. This has something to do with the fact that such models exhibit the so called strongly coupled behavior [18, 19] (see also [20, 21, 22, 23], and section 2 below for a summary), in spite of the fact that gravitational fields is weak everywhere [19, 24, 25, 26].
One way to interpret this property for a static spherically symmetric source is to observe that the source gives rise to the curvature that extends up to a macroscopic distance , in the way depicted in figure 1. This curvature contributes to the integral (4).
In a concrete case of the non-perturbative Schwarzschild solution of the DGP model , we will show that this integral is saturated around a distance ( - the topic of the next section ) where the value of is typically of order . Then, the result of (4) is
i.e., the contribution to the mass from the modification of gravity term is of the same order as the mass itself!
In the following sections we will make concrete the statements pointed out above in the DGP model of modified gravity. They include the perturbative arguments leading to the derivation of the scale and details on the exact solutions available for Schwarzschild-like sources and domain walls. While the former are based on an ansatz, legitimate concerns about the bulk boundary conditions of which were raised in , nevertheless, the fact that the ansatz recovers very precisely the 4D GR results at short distances and smoothly interpolates to the 5D regime (that no other solution is known to do), suggest that it may be capturing right physics. Moreover, the above properties were subsequently found to be true for the case of a domain wall for which an exact solution was obtained .
Although the existence of the mass deficit (4) could be interesting observationally, it may lead in certain cases to problems with the theory. Indeed, because of the terms (4) in the expression for a gravitational mass the proof of the positive energy theorem [30, 31] is not directly applicable. Hence, in general, there could exist negative “mass” solutions [5, 21] even for matter stress-tensors that satisfy conventional positive energy conditions. One example of this is the self-accelerated solution [5, 19]. Small perturbations about this solution in a linearized theory and with non-conformal sources exhibit ghost-like states [21, 23, 32, 33, 34], however, there exist serious arguments that the perturbative results cannot be trusted in the full non-linear theory (see also ). Nevertheless, some semi-exact and exact [29, 33, 37] non-perturbative solutions on the self-accelerated branch exhibit “negative mass”. This suggest that the self-accelerated branch should be unstable, however, it is not clear what is the time of its instability. An explicit calculation on decay of the selfaccelerated branch into the conventional one shows that such a decay does not take place, at lest in a quasi-classical approximation . This question is still open and we will not be discussing it further in the present work.
If the mass screening is substantial, then, at scales beyond gravity would be modified significantly. However, the value of the scale for the entire observable Universe is cm. Therefore, on average, the beyond--effects will be hard to detect. There may be exceptions for isolated clusters of galaxies separations between which are greater than their own scales, and any other scales in their vicinity444We thank Lam Hui and Roman Scoccimarro for discussions on these issues.. For precise calculations of the beyond physics, however, new averaging technique and non-perturbative calculational methods would be needed.
2 The scale (Vainshtein scale)
In what follows we will concentrate on the concrete example provided by the DGP model in which all interactions except gravity are confined to a 4D brane embedded in an infinite volume 5D empty space where gravity propagates.
The modification of gravity in this model is given in terms of the extrinsic curvature of the brane and reads:
The 5D space has coordinates with the brane at the surface and the 4D metric in (5) is .
The macroscopic distance in the DGP model can be derived by considering the linearized analysis of the theory . In particular we will focus on the one-graviton exchange amplitude between two sources whose gauge independent expression reads as follows:
and is the square of the Euclidean brane 4-momentum. The pole at has zero residue, and the second pole in (6) is on a non-physical Riemann sheet. The former implies the absence of a massless graviton in the exchange while the latter describes the propagation of a metastable state with lifetime , which decays into a continuum of KK modes.
The striking feature of (7) is that in the limit (in which the modification of gravity should disappear) the numerator does not reduce to the analogous expression in GR:
This fact, which could be used to exclude (7) by observations, is known as the van Dam-Veltman-Zakharov discontinuity (vDVZ) . The difference between (7) and (8) is due to the fact that a 5D graviton (or a massive graviton for that matter) propagates 5 on-shell degrees of freedom (helicity-2, helicity-1, and helicity-0), while the GR graviton propagates only 2 on-shell degrees of freedom (helicity-2 state). And while the helicity-1 state of the 5D graviton does not contribute to (6) at the linearized level because of the contraction with conserved sources, the helicity-0 state couples to the trace of the energy-momentum tensor and gives a non-vanishing contribution (when ).
It has been argued in [18, 19] that the continuity in the limit would be restored if nonlinear effects were taken into account. The relevance of these terms can be understood in the following terms: the longitudinal part of the graviton propagator in DGP contains terms proportional to . This term does not contribute to the amplitude (6) because of conservation of the stress-tensor, but it does contribute already in the first nonlinear correction (since the stress-tensor is only covariantly conserved in the non-linear theory). And due to the singular behavior of these terms in the limit, perturbation theory breaks down prematurely. However, this breakdown is an artifact of an ill-defined perturbative expansion – the known exact solutions of the model have no trace of breaking . The perturbative expansion in powers of gets “contaminated” by another dimensionful parameter , and this leads to its breakdown. As possible ways forward one could either adopt a different type of expansion, e.g., an expansion in the small parameter [19, 24], or try to find exact solutions 555It is also possible to modify the theory at the linearized level so that the conventional perturbative expansion is well-behaved [45, 46],,.. Both of these programs have been carried out to a certain extent and we will review in the next section the salient features of the latter.
As presented in (2), the DGP model has one adjustable parameter, namely which determines a scale that separates two different regimes of the theory. For distances much smaller than one would expect the solutions to be well approximated by GR and the modifications to appear at larger distances. This is indeed the case for distributions of matter and radiation which are homogeneous and isotropic at scales [5, 6, 19]. However, more compact sources exhibit different properties. For example, a compact static source of the mass and radius , such that ( is the Schwarzschild radius) a new scale, combination of and , emerges (the so-called Vainshtein scale666A similar, but not exactly the same scale was discovered by Vainshtein in massive gravity , hence the name.) :
Below this scale the predictions of the theory are in good agreement with the GR results and above it they deviate considerably. These type of sources will be discussed in more detail in the next section together with other ones with higher simpler symmetry: domain walls.
3 Concrete examples
In this section we will focus on the mass screening phenomenon describing how it arises in the cases of the Schwarzschild-like non-perturbative solution (NPS) of [27, 43] and the exact domain wall (DW) solutions of .
3.1 Schwarzschild solution
where are functions of the radial coordinate on the brane and the transverse direction coordinate . The symmetry across the brane () implies that is an odd function of while the rest are even. The choice represents an ansatz, but notice that we have kept the off-diagonal term .
The brane is chosen to be straight in the above coordinate system but one could transform (10) to another one in which the metric is diagonal . Here, in general, and the ansatz is reflected in the fact that in this system our brane will be bent or, in other words, in a particular nontrivial choice of the position of the brane .
This ansatz allows us to close the system of equations on the brane, and leads to the following solutions for the gravitational potential ,
The function in (12) is given implicitly by the solutions of the following two equations (giving rise to a conventional and self-accelerated branch respectively):
where and is an integration constant.
The off-diagonal and metric components are determined from
and the profile of the warp factors (“y-derivatives”) can be computed on the brane as well.
There are two integration constants, and the one produced in the integration (12), which are determined by imposing appropriate boundary conditions near the source () and at large distances. For the first condition we impose the 4D behavior of the potential near the source: , while for the second one we require that the coefficient of the possible term be zero, i.e., to be left with 5D behavior at large distances, namely, in the conventional branch and in the self-accelerated branch.
3.1.1 Conventional branch
The conventional branch is obtained from the solution of (13). As shown in [27, 43] the boundary conditions discussed above determine the asymptotic behavior of the solution. At short distances, (), we get
where and the coefficient of the term was chosen to be by fixing the constant of integration in (12).
The other integration constant is chosen such that at large distances, (), we obtain an expansion with no term:
which fixes the value of in terms of () and also implies
The relation (19) should be contrasted with the naive expectation from a linearized analysis: in the 5D regime one would have expected to have , however, we get a much smaller value, reduced by a factor .
Therefore, as we see, a short distance observer at would measure the gravitational mass with a small corrections to Newton’s potential, while the large distance observer at would measure an effective gravitational mass . The latter includes the effects of the 4D curvature which is significant up to as depicted in figure 2. The 5D mass is partially screened at large distances.
Another point worth emphasizing is that a perturbative expansion suggests that for the metric should have an approximately four-dimensional, , scalar-tensor-gravity type form [4, 19]. However, the NPS above exhibits a different behavior: beyond the metric turns into the one produced by a five dimensional source. We interpret this as a complete screening of the 4D mass of the source by the halo of non-zero curvature.
The screening of the 4D mass can be made explicit by taking into account the expression for the 4D Komar mass as a function of . In the ansatz used here gives this gives an effective mass
The first term the rhs of (20) is a smooth decreasing function of and gives a contribution that is (the original mass of the source) up to and rapidly falls off like beyond that point. The second term, on the other hand, depends on the gradient of and is peaked around . The combined effect is seen in figure 3: the effective mass increases from its 4D value near the source up to and then falls to zero abruptly.
The short distance mass increase can also be deduced form the approximate form of the potential (17) since the second term provides an additional attraction toward the source.
3.1.2 Self-accelerated branch
The solution on the self-accelerated branch is obtained from (14). The relation between and is obtained, as in the conventional case, by imposing boundary conditions together with the following asymptotic behavior. At large distances, (), we derive
, i.e., 5D mass screening. At short distances, (), we get
where is, in absolute value, the same constant appearing in the conventional branch short distance expansion (17). Note, however, that the sign of the correction to the behavior is opposite in the two branches.
At intermediate distances, , the potential contains a gravitational term that is repulsive, . This looks like a 5D negative mass. However, this is not an asymptotic value of the mass since one can only cover the solution in the above coordinate system till where the dS like horizon is encountered. Moreover, in the intermediate regime , the de Sitter term in the potential always dominates over the term suggesting that the effects due to the Schwarzschild source are strongly suppressed. The picture that explains screening in this branch is depicted in figure 4.
3.2 Domain Walls
The second example that illustrates the screening phenomenon in the DGP model is that of a brane DW source. The study of this type of sources was done in on which we base the following discussion.
The source considered is a Nambu-Goto DW in 4D localized at with stress-tensor
where is the tension of the wall and denotes the coordinate transverse to its world-volume spanned by ().
In DGP, however, the situation is different. For tensions smaller than a critical value, , the wall has no gravitational effects. One way to understand this is by noticing that for these sources, the modification of gravity term (5 ) precisely compensates the energy momentum tensor . Therefore, the tension of the wall, as seen from the point of view of a 4D observer, is screened entirely by gravitational effects encoded in the extrinsic curvature. Not surprisingly, the domain wall world-volume remains flat, and so does the metric on the brane.
Furthermore, this screening takes place inside the core of the wall. Hence, the analog notion of the scale for a domain wall (understood as where the self-shielding takes place) coincides with its thickness,
This is to be compared to the Schwarschild-like case, where the shielding also occurs, and extends outside the source. The net result is the screening of the 4D tension/mass in both cases.
For supercritical tension branes the extrinsic curvature can no longer balance the energy momentum tensor and the brane inflates. The transverse direction to the wall is compactified to a size and a zero mode graviton appears. Since this phenomenon also takes place in GR, it provides a means to contrast the 5D effects in DGP with those of a supercritical DW in 5D, i.e., by comparing the world-volume inflation rate in both cases.
The exact solutions of give a suppression factor for the inflation rate of the supercritical DW in DGP for both branches of solutions. In the conventional branch it is while in the self-accelerated branch it is given by . As argued above, we should identify the Vainshtein scale for these sources and therefore we find the same parametric screening of the 5D tension as for the mass in the Schwarzschild-like solutions of the previous example.
The above results may also be applicable to other models where the results of 4D gravity are recovered through strongly coupled behavior. The minimal model of brane induced gravity in greater that five dimensions contains ghosts . However, its extensions are ghost free , a small subset of which has a strong coupling regime [53, 54] (see, also ). A recent model of cascading brane induced gravity is also ghost free . It would be interesting to understand the issue of presence/absence of the mass screening in these models (see, also, ).
Unfortunately, at present there is no consistent 4D theory of Lorentz invariant massive gravity, as it suffers from nonlinear instabilities [58, 59, 60, 61]. However, the mass screening effect described above is based on rather universal principles, and it is reasonable to expect that the phenomenon will also persists if a consistent model is found.
It would be interesting to understand the issue of the mass screening in the -type models of models of modified gravity, see, e.g., , as well as in Lorentz violating models [63, 64, 65, 66, 67]. Some of these models [64, 65, 66, 67] avoid the strong coupling behavior, in which case the mass screening is not expected to be very significant.
GG would like to thank the organizers of the international workshop Peyresq-12 for warm hospitality and productive atmosphere. GG was supported by NASA grant NNGG05GH34G. AI was supported by DOE Grant DE-FG03-91ER40674.
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V. I. Zakharov, JETP Lett. 12 (1970) 312 [Pisma Zh. Eksp. Teor. Fiz. 12 (1970) 447].
- G. Dvali, A. Gruzinov and M. Zaldarriaga, Phys. Rev. D 68, 024012 (2003) [arXiv:hep-ph/0212069].
- A. Lue and G. Starkman, Phys. Rev. D 67, 064002 (2003) [arXiv:astro-ph/0212083].
- L. Iorio, Class. Quant. Grav. 22, 5271 (2005) [arXiv:gr-qc/0504053]; JCAP 0509, 006 (2005) [arXiv:gr-qc/0508047]; JCAP 0601, 008 (2006).
- G. Gabadadze and A. Iglesias, Phys. Lett. B 632, 617 (2006) [arXiv:hep-th/0508201].
- G. Gabadadze and A. Iglesias, Phys. Lett. B 639, 88 (2006) [arXiv:hep-th/0603199].
- G. Gabadadze, Phys. Rev. D 70, 064005 (2004) [arXiv:hep-th/0403161].
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- M. Porrati and J. W. Rombouts, Phys. Rev. D 69, 122003 (2004) [arXiv:hep-th/0401211].
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- G. R. Dvali and G. Gabadadze, Phys. Rev. D 63, 065007 (2001) [arXiv:hep-th/0008054].
- S. L. Dubovsky and V. A. Rubakov, Phys. Rev. D 67, 104014 (2003) [arXiv:hep-th/0212222].
- G. Gabadadze and M. Shifman, Phys. Rev. D 69, 124032 (2004) [arXiv:hep-th/0312289].
- Work in progress.
- N. Kaloper and D. Kiley, JHEP 0705 (2007) 045 [arXiv:hep-th/0703190]. N. Kaloper, arXiv:0711.3210 [hep-th].
- C. de Rham, G. Dvali, S. Hofmann, J. Khoury, O. Pujolas, M. Redi and A. J. Tolley, arXiv:0711.2072 [hep-th].
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- D. G. Boulware and S. Deser, Phys. Rev. D 6, 3368 (1972).
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- P. Creminelli, A. Nicolis, M. Papucci and E. Trincherini, JHEP 0509, 003 (2005) [arXiv:hep-th/0505147].
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CC-MAIN-2022-49
| 27,195 | 144 |
http://mathhelpforum.com/calculus/82309-problems-about-differentiation-print.html
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math
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problems about differentiation
i seriously can't differentiate between pre-calculus and calculus, so if i post in the wrong place, i'm sorry.
1. A right circular cone with its vertex facing down has a height of 120cm and a radius of 60cm at the top. Water is poured into the cone at a rate of . Find, in terms of x,
i) the rate at which the water level rises when the height is 60cm,
ii) the rate at which the wet inner surface of the cone is changing at this instant.
(Give your answer correct to 3 sig.fig.)
I can do 1i...the answer is 0.000354x.....1ii is the one that i don't know how to do....
2. A rectangle ABCD enclosed within the curve and the x-axis. C and D are points on the curve A and B are points on the x-axis. If AB =2a, find the area of ABCD in terms of a. Find the value of a for which the area of the rectangle ABCD is a maximum and find this area.
I don't even know how to start.Can someone teach me how to start??
3. If , show that is independent of a and b. If a and b are such that y=3 and when x=0, find the values of x between and for which .
i think i know how to do but my answer is not the same as the book's answer.
4y= 4a cos 2x + 4b sin 2x + 8 cos x
= -4a cos 2x - 4b sin 2x - 2 cos x + 4a cos 2x + 4b sin 2x + 8 cos x
=6 cos x
[shown:it's independent of a and b.]
by substituting y=3,a=2.
by substituting , b=0.
-2(2)sin 2x + 2(0) cos 2x - 2 sin x = 0
-4 sin 2x - 2 sin x =0
-2(2 sin 2x + sin x)= 0
2 sin 2x + sin x =0
4 sin x cos x + sin x = 0
sin x ( 4 cos x +1) =0
sin x =0
x= 0, 180, 360
Basic angle of x = 75.5
but the book's answer is 120 and 240....those in red are wrong.....where did i went wrong???
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118831.16/warc/CC-MAIN-20170423031158-00017-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 1,641 | 27 |
https://www.esf-hauteluce-valjoly.com/conseils/niveaux-et-tests-adultes
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math
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tests & levels adults 1rst skibeginner level Never skied before... 1rst degré I got the 1rst ski level. I can control my speed and change direction on gradual slopes. 2nd degré I got the 1rst degré. I finish my turn with parallel skis and I control my speed by skidding my skis. 3rd degré I got the 2nd degré. I can link small and large radius parallel turns controlling my speed.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710473.38/warc/CC-MAIN-20221128034307-20221128064307-00778.warc.gz
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CC-MAIN-2022-49
| 385 | 1 |
https://www.researchandmarkets.com/reports/4844354/matrix-methods-edition-no-4
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math
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Matrix Methods: Applied Linear Algebra and Sabermetrics, Fourth Edition, provides a unique and comprehensive balance between the theory and computation of matrices. Rapid changes in technology have made this valuable overview on the application of matrices relevant not just to mathematicians, but to a broad range of other fields. Matrix methods, the essence of linear algebra, can be used to help physical scientists-- chemists, physicists, engineers, statisticians, and economists-- solve real world problems.
- Provides early coverage of applications like Markov chains, graph theory and Leontief Models
- Contains accessible content that requires only a firm understanding of algebra
- Includes dedicated chapters on Linear Programming and Markov Chains
1. Matrices 2. Simultaneous Linear Equations 3. The Inverse 4. Linear Programming 5. Determinants 6. Eigenvalues and Eigenvectors 7. Matrix Calculus 8. Linear Differential Equations 9. Markov Chains 10. Real Inner Products and Least Squares
Appendix: Computational Tools and technology
Fairleigh Dickinson University, NJ, USA
Costa, Gabriel B.
Father Gabriel B. Costa, Ph.D., Department of Mathematical Sciences, United States Military Academy, West Point, NY, USA
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665521.72/warc/CC-MAIN-20191112101343-20191112125343-00035.warc.gz
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CC-MAIN-2019-47
| 1,223 | 9 |
https://www.researcher-app.com/paper/130590
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math
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Orbital tori for non-axisymmetric galaxies.
Our Galaxy's bar makes the Galaxy's potential distinctly non-axisymmetric. All orbits are affected by non-axisymmetry, and significant numbers are qualitatively changed by being trapped at a resonance with the bar. Orbital tori are used to compute these effects. Thick-disc orbits are no less likely to be trapped by corotation or a Lindblad resonance than thin-disc orbits. Perturbation theory is used to create non-axisymmetric orbital tori from standard axisymmetric tori, and both trapped and untrapped orbits are recovered to surprising accuracy. Code is added to the TorusModeller library that makes it as easy to manipulate non-axisymmetric tori as axisymmetric ones. The augmented TorusModeller is used to compute the velocity structure of the solar neighbourhood for bars of different pattern speeds and a simple action-based distribution function. The technique developed here can be applied to any non-axisymmetric potential that is stationary in a rotating from - hence also to classical spiral structure.
Publisher URL: http://arxiv.org/abs/1710.11360
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103671290.43/warc/CC-MAIN-20220630092604-20220630122604-00410.warc.gz
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CC-MAIN-2022-27
| 1,108 | 3 |
https://mcq.jobsandhan.com/who-among-the-following-was-the-first-to-receive-the-nobel-prize/
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math
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Who among the following was the first to receive the Nobel Prize January 5, 2020 by mcq A) C.V.Raman B) Hargovind Khurana C) Rabindranath tagore D) None of these View AnswerOption – C. More QuestionsWhere is the DNA located in a eukaryotic cell?What is the product of all the numbers in the dial of a telephone ?Which one of the following may be the true characteristic of cyclones?Directions : For the Assertion (A) and Reason (R) below, choose the correct alternative Assertion (A) : Bats can fly in the night. Reason (R) : Bats emit ultrasonics.“If a system A is in thermal equilibrium with B and B is in thermal equilibrium with C, then A and C are in equilibrium with each other”. This is a statement ofICF (integral Coach Factory) is atFind the Odd One Out? 3 24 186 1008 5040 20160Blasphemy is to religion as treason is to whatAccording to Census 2001, what is the percentage of male literacyIn a certain code language COMPUTER is written as RFUVQNPC. How will MEDICINE be written in that code language?
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710503.24/warc/CC-MAIN-20221128102824-20221128132824-00080.warc.gz
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CC-MAIN-2022-49
| 1,016 | 1 |
https://www.isixsigma.com/methodology/linearity-vs-repeatability-whats-the-difference/
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math
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What Is Linearity?
Before we can understand linearity, we must understand another measurement error known as bias. Bias is a consistent mistake that occurs in measurement. For example, every measure taken with your scale comes out heavier than the actual weight.
Linearity measures the consistency of a bias over the entire range of possible measurements. Returning to the weight example used above, if your scale weighs heavier than the actual weight, is that difference a consistent one pound over no matter how heavy the object might be? Or does the variation from actual weight increase as the weight increases?
The Benefits of Quantifying Linearity
There are three main benefits of determining the linearity of your measurements:
1. Lets You Know How Bias Changes Over An Entire Range
Knowing how a bias changes over the entire measurement range is a critical piece of information if you wish to limit the impact of measurement error on your process studies.
2. Helps You Determine How Much Variation Is Due to Measurement Error
It’s hard to determine the cause of output differences in a study unless you know how much of that variation is due to measurement error. If the variation found in a study is no more than the expected measurement error, then the difference isn’t statistically significant.
3. Discover Quality of Measurement System
How good is your measurement system? Can you rely on it, or do you need better equipment or measurement methods? Performing a linearity study can help engineers and managers answer these questions and eliminate sources of measurement error.
How to Calculate Linearity
Calculating linearity requires the following eight steps:
1. Take at least five samples spread across the entire range of possible measurements.
2. Find the reference value for each sample (determine what the actual value should be).
3. Have the operator measure each sample at least ten times.
4. Calculate bias for each measurement (measured value minus reference value).
5. Average the bias for each part.
6. Plot the average bias for each part on a chart.
7. Find the “best fit” line.
8. Interpret results.
If the best fit line is horizontal, then the linearity is consistent. The larger the slope of the best fit line, the more linearity varies as the measurement changes.
What is Repeatability?
Repeatability is the variation that occurs when one operator measures the same part multiple times.
The Benefits of Finding Repeatability
The three primary benefits of determining repeatability are:
It Can Help You Establish the Accuracy of a Gauge or Tool.
There are two possible variation sources when measuring a part. Either the variation is due to the part you measure, or it comes from the measurement tool. Under ideal circumstances, any variation comes from the part, not the measurement method.
Repeatability Is Usually Easy to Find
Determining repeatability is usually a simple process. All you need to do is have the same operator measure the same part multiple times.
Helps Analysts Find Problems In Measurement Systems
If the same operator measuring the same part multiple times leads to a lot of variation, there is likely a problem with your measurement process. The operator, measurement method, or tool you’re using isn’t adequate for the job.
Large variation shows that there is a problem. Analysts must study the measurement process to determine the cause.
How to Calculate Repeatability
Calculating repeatability requires the same operator to measure the same part multiple times and record the data. You can then measure the possible range of values by picking out the high and low measurements from the data. Finally, analysts can calculate the average variation by adding up the total variance and dividing by the number of measurements.
Linearity Vs. Repeatability
As mentioned above, the main difference between linearity and repeatability is the number of parts measured. Linearity involves measurements of multiple parts, often taken by different operators, and can include various measurement tools. A linearity study aims to determine if a measurement bias exists and to find how that bias varies over the possible range of measurements. A linearity study also involves comparing these measurements to a known reference.
Conversely, repeatability requires the same operator to measure the same part using the same tool. Here the goal is to find the expected variation using a particular device. There is no comparison of that measurement to a known reference value.
Who Would Use Linearity and Repeatability?
Both repeatability and linearity studies will be used by analysts concerned with finding and characterizing measurement errors in a process. In a linearity study, analysts assume any variance caused by the operators is minimal, and the main driver of any difference comes from the process or tools used to measure the parts. A linearity study aims to discover how a measurement process handles different parts.
On the other hand, a repeatability study attempts to “tease out” data variance inherent in measuring a single part. While both concepts involve discovering measurement errors, they focus on different types of errors.
Choosing Between Linearity and Repeatability: Real World Scenarios
Suppose an engineering team notices that support beams produced by a particular process show too much variance in weight. In this situation, they might order a repeatability study to determine the source of this difference in weight. If the beams produced by certain operators show high levels of weight variance, then the solution might be to retrain those operators or dismiss them. On the other hand, if all operators produce beams with wildly varying weights, then the source of the error is either the scale used to make the measurements or the production process.
However, if the engineering team suspects that measurement errors are concentrated in either particularly heavy or light support beams, they might order a linearity study. In this case, the team will want to know if any measurement bias exists and if that bias remains consistent over the entire range of beams produced by the process. If heavy beams show significant variations from the actual weight, the solution might be to use a different measurement method for heavier beams. If all beams show a consistent bias over the entire range, then the answer might be to make a simple data adjustment to compensate for the bias.
In some situations, analysts could use linearity and repeatability studies concurrently. For example, suppose a linearity study shows a consistent measurement bias. In that case, the analyst team could use a repeatability study to estimate how much of the weight differences they’re seeing are due to bias and how much is variance inherent in their measurement method.
Linearity and Repeatability Seek To Eliminate Different Kinds of Measurement Errors
Both linearity and repeatability studies seek to limit measurement mistakes. However, linearity focuses on errors caused by measuring different parts, while repeatability concentrates on mistakes inherent in the measurement process itself.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100047.66/warc/CC-MAIN-20231129010302-20231129040302-00705.warc.gz
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CC-MAIN-2023-50
| 7,158 | 47 |
https://ufind.univie.ac.at/en/vvz_sub.html?path=60984&semester=2010S
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math
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2. Theoretical Physics
260083 VO Relativity and Cosmology II
260031 UE Relativity and Cosmology II - Exercises
260022 VO [en] Gravitation and quantum theory
260122 VO [en] Complex Quantum Systems Summerschool - The Lecture consists of a series of talks, given by international guests.
260213 SE [en] Quantum Optics Seminar - The Seminar consists of a series of talks, given by mainly international guests.
260053 SE [en] Seminar coherence of photons
260067 SE [de en] Seminar entanglement and relativistic, decoherence and geometry in quantum physics II
260090 SE [en] Advanced Module Mathematical and Gravitation Physics - Dark energy/matter from structure ?
260130 SE Seminar in special topics in relativity
260137 SE Selected problems of quantum theory
260235 SE Complex Stochastic Systems
260004 VO [en] Relativity and Cosmology III: Numerical Relativity
260098 VO [en] Relativistic Quantum Field Theory
Last modified: We 13.06.2018 00:35
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572198.93/warc/CC-MAIN-20220815175725-20220815205725-00493.warc.gz
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CC-MAIN-2022-33
| 942 | 15 |
https://www.chegg.com/homework-help/quantum-physics-of-atoms-molecules-solids-nuclei-and-particles-2nd-edition-chapter-5-solutions-9780471873730
|
math
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In order to show that the linear combination of wave functions:
is a solution to the Schrödinger equation when the individual wave functions, and ?are themselves solutions to the Schrödinger equation for a particular potential V(x), and the c1, c2, and c3 are just constants, Schrödinger’s equation is needed:
With, just being the reduced Planck constant, and m being the mass.
To show that equation (1) satisfies Schrödinger’s equation, the second space derivative and the first time derivative of equation (1) needs to be found (since they are used in equation ).
So first, take the second space derivative of equation (1):
The c’s were able to be factored out because they’re just constants.
Then take the first time derivative:
Those two derivatives and the original function are then inserted in equation (2), after rewriting how Schrödinger’s equation looks, and shortening how the wave function is written:
Now group the like wave functions together, and factor out the constants:
However, each expression in the brackets is just the Schrödinger equation for the individual wave functions. Since it was stated at the beginning that the three wave functions are already solutions to the Schrödinger equation, the linear combination of the three wave functions is also a solution, thus verifying that equation (1) satisfies Schrödinger’s equation.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998339.2/warc/CC-MAIN-20190617002911-20190617024911-00346.warc.gz
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CC-MAIN-2019-26
| 1,372 | 10 |
https://qsstudy.com/number-system/
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math
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From the beginning of civilization idea of counting developed in the human being. From then onward different counting systems have developed according to the need and convenience. In arithmetical processes, digital system is a process which uses different units independently, for example, hands, fingers, digit (0, 1, 3, …) etc. A full number can be expressed by using this unit or units independently in a bundle.
The process of writing a number is called number system. A number system is a collection of various symbols which are called digits. Different symbols to prepare number are arithmetic. By the help of this system, any quantity can be expressed, for example in decimal system 507 number is composed of three separate figures as 5, 0, 7. In number system, some fixed figures or numbers can be arranged following some rules and different numbers can be found. Using different rules like summation, subtraction, multiplication, division etc. different counting can be performed by these numbers or figures.
Different types of Number System –
- Binary: The numbers that are made in Binary Number System are made up of 0 or 1.
- Decimal: The number system that we follow is called as Decimal Number System where the base is 10.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506539.13/warc/CC-MAIN-20230923231031-20230924021031-00325.warc.gz
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CC-MAIN-2023-40
| 1,240 | 5 |
http://brainly.com/question/665
|
math
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A group of adults and kids went to see a movie. Tickets cost $8.50 each for adults and$4.50 each for kids, and the group paid $79.00 in total. There were 6 fewer adults than kids in the group.
I'm new to this kind of problem and I don't understand how to do this. How do I find what this is asking for? Can someone go through it step-by-step for me please?
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698543614.1/warc/CC-MAIN-20161202170903-00278-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 356 | 2 |
http://www.braingle.com/trivia/13481/zelda-link-to-the-past-quiz.html
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math
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Create a Quiz
More ways to get Braingle...
Zelda: Link To The Past Quiz
This is a quiz for the old game lovers to test your Zelda knowledge!
#1 How do you start the game?
In your tree house asleep when your fairy wakes you
Asleep in your house when you're contacted telepathically
You're minding your business when you're turned into a duku
#2 In "The Legend of Zelda: A Link to the Past", you play the character Zelda.
#3 In "Zelda: Link To The Past", Mario makes an appearance.
#4 The "Hit the chicken till his friends come and kill you" trick was first introduced in "Zelda: Link to the Past".
#5 How many hits does it take to get the chickens to attack you?
#6 Which of these is not a "Zelda: Link To The Past" item/weapon?
#7 How many standard hits (not charged swings) does it take to kill a blue guard with the first sword?
1 word, 1 letters. There is also an alternate answer.
#8 What is the first item you find in the game?
Bow & Arrow
#9 In the game, you can catch a crow with the net.
#10 Which one of these is not an enemy?
Golden Ball and Chain Guard
Small Grey Land Dragon
Floating Balloon Enemy
Pterodactyl Like Enemy
#11 You NEED the net to beat the game.
#12 What is the max amount of rupees you can get?
You cannot read or post comments until you complete the quiz.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189884.21/warc/CC-MAIN-20170322212949-00378-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 1,370 | 31 |
https://blog.advitsahdev.com/ecommerce-purchase-path-optimisation-advanced-marketing/
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math
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Never disturb the customer who is purchasing. You can ask him or refer different things later. Don’t ask him to sign up either. Payment completion is the single most important task and it is the primary goal of your website and if you want to make profits and generate a business that is long lasting, then you have to make the payment flow as smooth and as easy as possible.
—- He asked for $5000 for 3 minutes of work $1 for changing the screw .. $4999 for knowing which one to change. Simple changes that can bring huge changes to a business Advanced Marketing Tips for you and your business growth ! #marketing#business#calltoaction#purchase#signup#registration#flow#path#advanced#conversionoptimization
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100583.31/warc/CC-MAIN-20231206063543-20231206093543-00867.warc.gz
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CC-MAIN-2023-50
| 711 | 2 |
https://cs.nyu.edu/pipermail/fom/1998-September/002079.html
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math
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FOM: Incompleteness program
jrs at math.duke.edu
Tue Sep 8 10:57:59 EDT 1998
I read Harvey's report on incompleteness with interest, and would
like to pose some questions to him which occurred to me. I hope he will
regard them as true questions and not as attempts to poke holes in his
1. He says that the first incompleteness theorem does not provide
an intelligible example of an undecidable sentence, but the second
incompleteness theorem does. Like all logicians, I see a significant
difference in the two undecidable statements; but I wonder if
"intellgibility" is the concept best used to describe the difference.
One can (and usually does) explain the meaning of the first undecidable
sentence as: it says that it is unprovable. There are, of course,
two difficuties here: the self-referential nature of the explanation,
and the fact that the sentence can be seen to have this meaning only
by a rather lengthy analysis. Is this the sort of thing you had
It would certainly be interesting to know why Godel bothered with
the second incompleteness theorem, which required a lot of fairly
unintersting details. (As you know, he never wrote these details up;
Bernays was the first to do so.) I always thought it was not because
of any "deficiency" in the first undecidable statement, but was due to
the significance of the second for the Hilbert program.
As a somewhat related question, could you supply some references for
your statement that Godel in his writings expressed interest in the
2. Two question on what you consider to be the extent of the program.
In this report, the emphasis is almost entirely on unprovability in ZFC.
Of course, I realize the special importance of ZFC as the recognized
axiom system for mathematics. But do you regard results like the
Paris-Kirby theorem as part of the program?
Second, what about results on what might be called the degree of
unprovability? To make this more specific: if one proves an undecida-
result, is it an important part of the program to invesigate which known
independence results it is equivalent to over the base theory. I know
you have often expressed interest in such questions; I wonder if you
consider them as a basic part of the program or a sort of desirable
3. You say that CH was the first example of a demonstratably
independence of a mathematical result from ZFC. What about the
existence of an inaccessible cardinal? Although I can't supply
a reference, I feel von Neumann, with his good understanding of ranks
in set theory, was aware of this independence.
4. Can you explain more clearly what you mean by a regularity
condition? For example, what is the regularity condition on sentences
corresponding to one of the classes of functions which you list? In
particular, can the collection of such sentences be described by simple
syntactical conditions? Is being a finite combinatorial sentence a
regularity condition? Are there any useful criteria for recognizing
a regularity condition?
Contrary to what some of my critics appear to be saying, I am not
opposed to the use of informal concepts in fom, even when we cannot
formally analyse them. However, if such a concept is to be used as
more than a general descriptive phrase, it shold be subjected to an
informal analysis. The object of this analysis should be to insure
that all of one's reasonably receptive readers feel they understand the
meaning of the concept as used by the author. I don't think you
have given us this kind of analysis of "regularity condition".
More information about the FOM
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084888135.38/warc/CC-MAIN-20180119204427-20180119224427-00447.warc.gz
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CC-MAIN-2018-05
| 3,531 | 56 |
https://annuaire.rocks/4-christmas-songs-in-1-track-songs-e-music.ref
|
math
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1# Christmas Lights by Luna Keller
2# Deck the Halls by Katrina Stone (Beautiful Christmas)
3# Merry Christmas from a Distance by Marc Robillard (Christmas Vibes)
4# A King Is Born by Davis Absolute (Gift Rap)
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038917413.71/warc/CC-MAIN-20210419204416-20210419234416-00016.warc.gz
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CC-MAIN-2021-17
| 325 | 7 |
http://liu.diva-portal.org/smash/record.jsf?pid=diva2:22333
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math
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Fractal sets and dimensions
Independent thesis Basic level (professional degree), 20 points / 30 hpStudent thesis
Fractal analysis is an important tool when we need to study geometrical objects less regular than ordinary ones, e.g. a set with a non-integer dimension value. It has developed intensively over the last 30 years which gives a hint to its young age as a branch within mathematics.
In this thesis we take a look at some basic measure theory needed to introduce certain definitions of fractal dimensions, which can be used to measure a set's fractal degree. Comparisons of these definitions are done and we investigate when they coincide. With these tools different fractals are studied and compared.
A key idea in this thesis has been to sum up different names and definitions referring to similar concepts.
Place, publisher, year, edition, pages
Matematiska institutionen , 2006. , 65 p.
box dimension, Cantor dust, Cantor set, dimension, fractal, Hausdorff dimension, measure, Minkowski dimension, packing dimension, Sierpinski gasket, similarity, space-filling curve, topological dimension, von Koch curve
IdentifiersURN: urn:nbn:se:liu:diva-7320ISRN: LiTH-MAT-EX--06/06--SEOAI: oai:DiVA.org:liu-7320DiVA: diva2:22333
2006-05-02, Asylen, A-huset, Linköpings universitet 581 83 LINKÖPING, LINKÖPING, 13:15
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719677.59/warc/CC-MAIN-20161020183839-00058-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
| 1,322 | 10 |
https://www.jiskha.com/display.cgi?id=1322089557
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math
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posted by Torra .
Suppose that you want to purchase a home for $450,000 with a 30 year mortgage at 6% interest. Suppose that you can put 30% down. Assume that the monthly cost to finance $1,000 is $6.00. What are the monthly payments?
Steps or examples please
"..the monthly cost to finance $1,000 is $6.00"
I read that to say that the monthly rate of interest is .006
after downpayment you are left with 315000 to mortgage
let the payment be P
315000 = P(1 - 1.006^-360)/.006
I get P = $2138.18
Thanks. But I am trying to figure out how did you get $2138.18 I did the calculations but I do not come up with your answer.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886397.2/warc/CC-MAIN-20180116090056-20180116110056-00511.warc.gz
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CC-MAIN-2018-05
| 620 | 10 |
http://gmatclub.com/forum/polygon-99150.html?fl=similar
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math
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Let us assume the figure to be ACBDEF.
There are two equal trapeziums ACEF and CBDE.
If a is one of the sides of this figure,
base of trapezium = a units
height of trapezium = (a/2) units
side opposite 30 degrees : side opposite 90 degrees = 1:2 in the 30-60-90 triangle.
Area of the trapezium = base * height = (a^2) / 2 sq units.
Area of the whole figure = (a^2) sq units = 42 sq units.
a = root(42) units.
AB = 2 times height of each trapezium = 2 times (a/2) = a units = root(42) units.
Hope this helps. Is this correct ... Look forward to know a better method.
4GMAT - Mumbai
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s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042982502.13/warc/CC-MAIN-20150728002302-00187-ip-10-236-191-2.ec2.internal.warc.gz
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CC-MAIN-2015-32
| 580 | 12 |
https://www.coursehero.com/file/216533/240b-ps2/
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math
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Physics 240B M. L. Cohen Spring 2008 Problem Set #2 Due: 02/26/08 (20)1. Find and solve the quantum equations of motion for a free electron in a magnetic field using the gauge r A = (-1/2Hy, 1/2Hx, O). (20)2. Show that for an electron in a magnetic field H r k x r k = "ieHc. (20)3. Use the Bohr-Sommerfeld quantization formula to show that the oscillations of M in the de Haas-van Alphen effect have a 1/Hperiod that gives the maximal or minimal cross-sectional area of the Fermi surface perpendicular to H. (20)4. (a) Show that "f"t#$%&’(collisions= 0 for f = f 0and f = f (local equilibrium) and
This is the end of the preview.
access the rest of the document.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257645538.8/warc/CC-MAIN-20180318052202-20180318072202-00795.warc.gz
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CC-MAIN-2018-13
| 665 | 3 |
https://gnosis.library.ucy.ac.cy/handle/7/44916
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math
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Distributed function calculation via linear iterations in the presence of malicious agents - Part I: Attacking the network
Hadjicostis, Christoforos N.
SourceProceedings of the American Control Conference
Proceedings of the American Control Conference
Google Scholar check
MetadataShow full item record
We consider the problem of distributed function calculation in the presence of faulty or malicious agents. In particular, we consider a setup where each node has an initial value and the goal is for (a subset of) the nodes to calculate a function of these values in a distributed manner. We focus on linear iterative strategies for function calculation, where each node updates its value at each time-step to be a weighted average of its own previous value and those of its neighbors; after a sufficiently large number of time-steps, each node is expected to have enough information to calculate the desired function of the initial node values. We study the susceptibility of such strategies to misbehavior by some nodes in the network; specifically, we consider a node to be malicious if it updates its value arbitrarily at each time-step, instead of following the predefined linear iterative strategy. If the connectivity of the network topology is 2f or less, we show that it is possible for a set of f malicious nodes to conspire in a way that makes it impossible for a subset of the other nodes in the network to correctly calculate an arbitrary function of all node values. Our analysis is constructive, in that it provides a specific scheme for the malicious nodes to follow in order to obfuscate the network in this fashion. ©2008 AACC.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670743.44/warc/CC-MAIN-20191121074016-20191121102016-00123.warc.gz
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CC-MAIN-2019-47
| 1,648 | 7 |
http://physics.stackexchange.com/questions/tagged/geodesics+electromagnetic-radiation
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math
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s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999646172/warc/CC-MAIN-20140305060726-00089-ip-10-183-142-35.ec2.internal.warc.gz
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CC-MAIN-2014-10
| 2,119 | 52 |
http://ijm2c.iauctb.ac.ir/article_521885.html
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math
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Faculty of Science and Technology, University Hassan first, Settat, Morocco Morocco
In this paper simple quartic trigonometric polynomial blending functions, with a tension parameter, are presented. These type of functions are useful for constructing trigonometric B´ezier curves and surfaces, they can be applied to construct continuous shape preserving interpolation spline curves with shape parameters. To better visualize objects and graphics a tension parameter is included. In this work we constructed the Trigonometric B´ezier curves followed by a construction of the shape preserving interpolation spline curves with local shape parameters and finally several numerical examples are presented such as open shape preserving interpolation curve, closed shape preserving interpolation curve and surfaces. As a direct application we computed the area surrounded by a closed curve.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190295.65/warc/CC-MAIN-20170322212950-00399-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 886 | 2 |
http://bicem.vn/gossip-deception-and-pythagoras-theorem-project/
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math
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Pythagoras Theorem Project Options
If you’d like to discover more about Pythagoras visit the site. Pythagoras also invented plenty of number patterns. Pythagorean Theorem is a significant notion of mathematics.
The following is an investigation of the way the Pythagorean theorem was proved over recent years. Employing a Pythagorean Theorem worksheet is an excellent method to show the aforementioned equation. The 3D Pythagorean Theorem is also useful for theoretical physicists in addition to anyone moving big parts of furniture!
There are lots of word problems in the traditional math textbooks that require the usage of the Pythagorean Theorem. The worksheet contains questions linked to the Pythagorean theorem. The proofs presented here are simply some of the many proofs of the Pythagorean Theorem.
The Secret to Pythagoras Theorem Project
If you receive a side and an angle then the question will probably be a trigonometry question. The side that’s opposite to the 90 degree angle is referred to as the hypotenuse. http://faculty.uml.edu/sgallagher/Thoreau_Final.html The proportion of the period of the rope to the period of the egg is probably irrational.
‘X’ is the duration of hypotenuse since it’s opposite side of the proper angle. Locate the distance of a diagonal. Locate the period of the hypotenuse.
The Basics of Pythagoras Theorem Project
Let’s review the issue again. The opportunity of an event is the range of ways it may happen given all feasible outcomes. The purpose of the project was supposed to create a pill to increase someone’s mathematical abilities.
You’re able to then prove mathematically that there’s no ratio of whole numbers that may produce 2. There are typically many methods to address an issue. Now return to the original issue.
Actually there are absolutely hundreds of proofs. Students want to observe the geometric connections too. Then they were able to decorate their projects.
Key custom essays Pieces of Pythagoras Theorem Project
Once a square is provided a specific index, it won’t ever change while additional squares are made. There aren’t any pieces that could be thrown away. From this, it is not hard to find that the Areas of both squares are and must be the exact same.
If you square an entire number, the outcome is a number known as a perfect square. A selection of various measurement units are used in the triangles, which aren’t drawn to scale. Now repeat step 2 using three or more rectangles.
Inside this scenario, the very first discoverer’s name becomes increasingly more prominent over time due to the Matthew Effect. Further, you may use it in many real-life circumstances. This video is around the Death of Pythagoras.
Most 7th and 8th graders appear to appreciate the ridiculousness in these types of videos. Students adore the battle part. In the event the students are working in groups, make certain that all of the team members are getting an opportunity to work through the math, otherwise you will get a couple of experts and a lot of observers.
The Basics of Pythagoras Theorem Project
It’s not essential to compute the area for the aims of this proof, however. Include the complete name of whoever discovered each proof. Some say he was the very first person to use the expression philosophy.
As a consequence, such students search for the best essay help to make sure that their project is going to be produced at the maximal level in agreement with all academic standards. There isn’t much information regarding his life. This video gives an excellent explanation of the way to do this kind of question.
Symbolism associated with five made its way to literature also. This proof is indeed very easy, but it’s not elementary, in the feeling it does not depend solely upon the simplest axioms and theorems of Euclidean geometry. The very first, optional argument is for the title that the theorem might or might not have.
Consequently, math tests are indeed one of the greatest battlegrounds to test AI. Transmorgrapher 2 Another means to explain geometric transformations! If you’re in a high math group then you really ought to use this formula.
You should have the ability to find the spiral made by right triangles in every single picture. That’s the equation you use whenever you’re looking for the unknown side of a perfect triangle, and it’s what I’ll demonstrate on the attached exhibit. It’s not overly hard to construct a triangle with side lengths which are all positive integersi.
There are two sorts of numerology. This argument is followed by a similar version for the suitable rectangle and the rest of the square. The proof is dependent on calculating the area of a suitable trapezoid two distinct ways.
It used to discover the unknown side of a perfect triangle. Within this lesson we take a look at a unique measuring rule for Right angled triangles. The Conjecture they are pursuing may be The region of the semi-circle on the hypotenuse of a perfect angled triangle is equivalent to the sum of the regions of the semi-circles on both of the other sides.
Teachers should read each step and watch for all students to finish the task before continuing to the next step. This sort of worksheet is made up of all of the questions on a couple sheets and the model answers for all of the questions. The next assignment is going to be a little more complicated.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232258621.77/warc/CC-MAIN-20190526025014-20190526051014-00200.warc.gz
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CC-MAIN-2019-22
| 5,400 | 25 |
https://tomcircle.wordpress.com/2013/04/09/pisa-test/
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math
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Programme for International Student Assessment (PISA) for 15-year-old students in 60 countries.
The top 5 countries are Shanghai, Korea, Finland, HK, Singapore.
Shanghai scored 1st in all categories: Reading, Math, and Science. Singapore scored 5th, 2nd and 4th, respectively, in these categories.
Zooming in the elite students % in the test population (5000 students in each country representatives), Singapore elites are not far off (within 1%) than the Shanghai elites in Reading and Science, but lose out in Math with a big gap of 11% (26.6% -15.6%).
That means Singapore top Math students in Maths are far off than Chinese top Math students.
Dr. James Li from Fudan University – its form teacher of the 1st batch gifted class – compares the Math education syllabi in Primary schools (P1 to P6), which build the Math foundation of the Shanghai and Singapore students.
The good points of the Chinese Math syllabus (and the lack of in Singapore’s):
1. Chinese P3 uses calculator (P5 in Singapore);
2. P4 learn rules of operation like commutative, associative, distributive laws (lack of in Singapore).
3. Geometry: emphasis on drawing and mapping (inadequate in Singapore Geometry class)
4. P5 learn Algebra & equation (P6 only algebra but no equation).
5. Basic (non-competition) Math Olympiad skill selectively included in Chinese textbooks (lack of in Singapore)
6. Incorporate Mathematician stories like 祖冲之 in being the first person in the world to calculate pi up to 7 decimals. ( lack of in Singapore).
7. Incorporate computing tools and games in Math teaching materials. (Lack of in Singapore).
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988741.20/warc/CC-MAIN-20210506053729-20210506083729-00130.warc.gz
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CC-MAIN-2021-21
| 1,616 | 14 |
https://e2e.ti.com/support/power-management-group/power-management/f/power-management-forum/990278/tps54240-q1-design-problem-question-with-the-operating-frequency-of-the-ic?tisearch=e2e-sitesearch&keymatch=TPS54240-Q1
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math
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Other Parts Discussed in Thread: TPS54240,
I am designing a power supply using TPS54240-Q1 with 28 V nominal input voltage and 10 V output voltage. I used WEBENCH to design my circuit at first, however, solution size is larger than what I would like to have. Also WEBENCH does not let me choose the frequency of the device according to the datasheet. The IC can have a switching frequency as high as 2.5 MHz, and I would like to have my device operate around 1.5 MHz range for this operation. I have done calculations with respect to the selected switching frequency, but I am not sure since WEBENCH does not allow me to design the TPS54240 in such frequency. Below, I specify the requirements of the supply and would really appreciate if you can help me with the questions I have.
- Input voltage = 18 - 32 V (absolute max.-min.), 28 V nominal
- Output Voltage = 10 V
- Output current = 210 mA nominal, 500 mA maximum
- Output Voltage Ripple = 1% of Vout
For 1.5 MHz operating frequency, output inductor value is calculated as 33 uH. Output capacitor value is calculated as 1.2 uF and it passes all the equations given in the datasheet. My questions are;
- Can I trust the calculations made with respect to the datasheet and how realistic is my solution?
- For input capacitance, which bypass capacitors should I be using to filter the input properly with respect to the given operating conditions?
- Is there a way I can design the circuit on WEBENCH with the desired 1.5 MHz frequency?
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224655446.86/warc/CC-MAIN-20230609064417-20230609094417-00697.warc.gz
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CC-MAIN-2023-23
| 1,488 | 10 |
https://www.conwaylife.com/wiki/Talk:Methuselah
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math
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I should add a note somewhere about arks and why they often aren't considered methuselahs even though they take a LONG time to stabilize. I'll do that after I add the ark article. Nathaniel 16:18, 9 February 2009 (UTC)
- Don't know if this is known, but arks are puffers, and puffers are not considered methuselahs, since they don't stabilize in the normal sense. FractalFusion 06:04, 28 March 2009 (UTC)
- My original comment wasn't too clear, but I was more referring to mutually-stabilizing ark "methuselahs" that you get by starting two of them really far away but aimed towards each other so that they will collide and stabilize after something like a million generations (as long as you want, really). Though they can start with very few cells and last for arbitrarily-long, their bounding box is of course ridiculously huge and they're not particularly interesting, so people generally ignore them when talking about methuselahs. Nathaniel 10:53, 28 March 2009 (UTC)
Two RLE's of extremely long lived methuselahs I found in Golly.
- ark1 -- 16 cells, stabilizes at 736692 gens, found by Nick Gotts.
x = 32, y = 29, rule = B3/S23 27bo$28bo$29bo$28bo$27bo$29b3o20$oo$bbo$bbo$3b4o!
- ark2 -- 19 cells, stabilizes at 8120878 gens, found by Nick Gotts.
x = 53, y = 44, rule = B3/S23 50b3o28$12bo$12bo$13boo$15bo$15bo$15bo$15bo6$oo$bbo$bbo$3b4o!
-wwei23 12:10AM 9/19 2015
I don`t understand. -wwei23 9:49AM 9/19/2015 NY time
Actually they were in the Methuselah folder. -wwei23 1:37PM 9/20/2015 NY time
I've reverted the edit about the higg methuselah, because it isn't notable. It surely isn't newly discovered as computer searches have enumerated all patterns with less than 20 or so cells within small (<= 6x6 or so) bounding boxes. Nathaniel 04:28, 22 March 2009 (UTC)
I know that this sounds irrelevant, but it already takes 9 generations to stabilize, and is the closest 4-cell pattern to a methuselah. Indeed, add a single cell, and you get the R-pentomino. The R-pentomino can have additional cells added to get century, the >hexomino, and B-heptomino. I hope I`m right! -wwei23 10:15AM 9/19/2015 NY time
I found a parent of 40514M! It therefore runs for 40515 generations.
x = 78, y = 54, rule = B3/S23 75b3o21$o$o$o20$b3o6$9bo9b2o$9bo10b2o$9bo9bobo2$20bo!
-wwei23 4:57PM 9/24/2015 NY time
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s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370499280.44/warc/CC-MAIN-20200331003537-20200331033537-00147.warc.gz
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CC-MAIN-2020-16
| 2,299 | 16 |
https://wizardofodds.com/ask-the-wizard/182/
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math
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Ask the Wizard #182
Mark from Mississauga
I hope you’re happy; I spent two days running simulations to answer this one. For the benefit of others, let me briefly summarize both arguments. The Cut-Card Effect states the house edge is less in a continuously shuffled game, as opposed to a cut-card game, all other things being equal. The "Floating Advantage" concept states that for the card counter the odds get better the deeper into the deck or shoe the dealer gets. According to Stanford Wong, "...after we have counted the deck down to where n decks are left, the edge with a count of zero is about the same as if we had started with n decks." - Blackjack Attack, third edition, page 71. So, for example, the house edge in a six-deck with one deck left, at a count of zero, has about the same house edge as a single-deck game with the same rules.
Unfortunately the Floating Advantage does not benefit non-counters. While they will benefit, unknowingly, at close to neutral true counts, they will do worse at extremely high and low counts. According to Schlesinger, "Seems that, at the one-deck level, extremely high counts produce less edge than expected for the basic strategist (many pushes) and the extreme negative counts were found to be even more unfavorable than previously thought (doubles, splits, and stands tend to be disastrous)." - Blackjack Attack, third edition, page 70.
As I understand it, the reason the counter benefits from the Floating Advantage, even if he may not know about it, is that he bets more when the Floating Advantage works to his advantage, and less when it doesn’t. For the non-counter, who doesn’t know when the Floating Advantage is strongest, the pros and cons exactly cancel each other out.
In conclusion, both the Cut-Card Effect and Floating Advantage are distinct topics and do not contradict each other. To compare them is to compare apples and oranges. For more information please read chapter 6 in Blackjack Attack by Don Schlesinger.
John from Raleigh, NC
You’re welcome. That was a difficult game to explain. The following table shows the house edge both ways, and the difference, assuming both player and dealer use the same house way.
House Edge in Pai Gow
|Event||5% Comm.||4% Comm.||Difference|
Bryan from Mill Valley
Yes, Bodog does indeed pay 9 to 1 on the tie. Assuming eight decks, that lowers the house edge from 14.360% to 4.844%.
Scott from Chicago
For recreational gambling, my rule is to get up when you’re not having fun any longer.
Heather from Petaluma
The probability of six sixes is (1/6)6 = 1 in 46656. The probability of rolling 1,2,3,4,5,6 with six dice is 6!/66 = 1 in 64.8
- Ace, Jack Suited = 25 - 1
- 2 Aces = 10 - 1
- 3 or 4 Total = 3 - 1
- 9 or 10 Total = 2 - 1
- 11 or 12 Total = 1 - 1
- Any Blackjack = 3 - 2
Aces always count as 1 and 10’s and faces count as 10. What is the house advantage? If I keep an Aces and Fives count is there a positive count where the possible remaining aces make the bet a positive proposition? Would counting remaining aces divided by remaining decks be better?
Stan from Beaverton, Oregon
You didn’t tell me the number of decks, but assuming six the house edge is 5.66%. Here is the return table.
Field of Gold — Six Decks
|3 or 4 total||3||1428||0.029434||0.088301|
|9 or 10 total||2||4884||0.100668||0.201336|
|Any other blackjack||1.5||2160||0.044521||0.066782|
|11 to 12 total||1||6612||0.136285||0.136285|
Just eyeballing it, I would say aces would be the best card to track, betting into an ace-rich deck. My advice would be to count aces as −12 and all other cards as +1.
Jesse from Scottsdale
That probability would be 52/combin(260,5) = 5/9525431552 = 1 in 1,905,086,310.
Kathy from Hitchcock
It will be difficult finding $5 blackjack on the Strip on a weekend. You’ll probably have to settle for a low-roller casino like the Riviera, Sahara, Frontier, or Circus Circus. It will be a lot easier downtown. Let It Ride is slowly fading away, but if you find it the minimum unit is usually $5.
Kevin from Philadelphia
Here in Nevada there is a state law that an electronic representation of playing cards must have the same probabilities as if a human being were dealing the game. To do business in Nevada a game maker must abide by this law in every machine it places anywhere in the world. So if they use major U.S. brands like IGT or Bally I’m sure the games are fair. However if the games are low-budget imports then I can make no assurances. As with a live game, check the rules before you play. Most importantly, avoid games that pay even money on blackjack.
Mike from Olympia
So there are 30 black, 30 red, and 4 green numbers. That would make the probability of black 30/64, red 30/64 and green 4/64. If the probability of an event is p then the fair odds are (1-p)/p to 1. So fair odds for any red would be (34/64)/(30/64) = 34 to 30 = 17 to 15. Same for black. The fair odds on green are (60/64)/(4/64) = 60 to 4 = 15 to 1. For a specific number the fair odds are (63/64)/(1/64) to 63 to 1.
I suggest paying 1 to 1 on red and black, 14 to 1 on green, and 60 to 1 on any individual number. One formula for the house edge is (t-a)/(t+1), where t is the true odds, and a is the actual odds. In this case the house edge on the red or black bet is (63-60)/(63+1) = 3/64 = 4.69%. On the green bet the house edge is (15-14)/(15+1) = 1/16 = 6.25%. On individual numbers the house edge is (63-60)/(63+1) = 3/64 = 4.69%.
Tom from Aurora, CO
For the beneit of other readers, my blackjack appendix 10 explains, the house edge in a five-deck game is 0.028% less if a continuous shuffler is used, as opposed to a hand shuffle. The difference between five decks and two decks, all other rules being equal, is 0.18%. So the two-deck game without a shuffler would be much better. Let’s compare a 5-deck continuous shuffler game to a 4-deck hand shuffled game. As my blackjack calculator show difference in house edge between four decks and five decks is 0.0329%. So the benefit of a continuous shuffler is worth less than removing a single deck.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948609.41/warc/CC-MAIN-20230327060940-20230327090940-00498.warc.gz
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CC-MAIN-2023-14
| 6,078 | 42 |
http://www.yorkprepsc.org/classes/22683
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math
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What is AP Calculus?
AP Calculus AB is a course designed by college board to give students the opportunity to experience a college level Calculus course. The class is taught so that students will not only be successful on the AP exam but in college as well. Calculus AB is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The courses emphasize a multirepresentational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations also are important. Topics include an in-depth study of functions, limits, derivatives, application of derivatives, integration and application of integration.
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https://deepai.org/publication/variational-extrapolation-of-implicit-schemes-for-general-gradient-flows
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math
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We are concerned with numerical schemes for evolution equations that arise as gradient flow (steepest descent) for an energy , where is a Hilbert space with inner product :
) may represent a (scalar or vectorial) ordinary or partial differential equation. Our focus is on unconditionally energy stable, high order in time discretizations. To be precise, by energy stable we mean the following dissipation property:
where denotes the approximation to the solution at the -th time step. Thus, in the context of PDEs, where is infinite dimensional, we are concerned with discrete in time, continuum in space schemes.
The backward Euler method for the abstract equation (1), with time step size , reads
As is well known and immediate to see, a solution for the implicit scheme (3) can be found via the following optimization problem
Energetic formulation (4) of the backward Euler scheme (3) is often referred to as minimizing movements. It enables extending numerical schemes for the stationary optimization problem to the dynamic, evolutionary problem (1) provided an additional, typically quadratic term in the cost function can be accommodated. The quadratic term in (4) is often referred to as the movement limiter, as it opposes deviation from the current configuration . It encodes the inner product with respect to which the gradient flow is being generated. Beyond numerical analysis and computation, minimizing movements approximation of gradient flows have been instrumental in the analysis of evolution equations of the form (1), e.g. in defining and finding weak solutions beyond the formation of singularities when classical notions of solution cease to exist.
There are many general purpose numerical methods that can certainly be used for solving Eq. 1. For instance, among high order schemes, some of the most well known are linear multi-step methods and Runge-Kutta methods, which can be regarded as special cases of the wider class of generalized linear methods [butcher2016numerical]. However, the energy stability of such general purpose numerical schemes is not immediate, and needs to be studied on a case by case basis. Among methods that focus on unconditional energy stability are convexity splitting [eyre1998unconditionally] and the more recent scalar auxiliary variable approach [shen2018scalar]. The following combination of desirable properties distinguish the new schemes introduced in this paper:
Complete generality. There is no assumption (e.g. convexity) on the energy in (1) beyond sufficient differentiability.
Unconditional energy stability.
High (at least up to third) order accuracy.
Each time step requires a few standard minimizing movements solves, equivalent to backward Euler substeps, or optimization of the associated energy plus a quadratic term.
Property 4 is perhaps the most unique and appealing aspect of the new framework: There are many existing schemes that can be recognized as some form of minimizing movements, sometimes relying on efficient optimization algorithms to solve (3) via (4). Our contribution shows how to painlessly jack up the order of accuracy of these schemes while preserving unconditional stability, relying only on a black-box implementation of the standard backward Euler scheme. In that sense, our new schemes can be understood as a variational analogue of Richardson extrapolation on Eq. 3, which in its standard form lacks the stability guarantees of our new schemes.
The rest of the paper is organized as follows:
Section 2 presents the general framework for the new scheme, focusing on unconditional energy stability.
Section 3 focuses on consistency, showing how to attain 2nd and 3rd order accuracy.
Section 4 gives 2nd and 3rd order examples of the new schemes.
Section 5 presents numerical convergence studies on a number of well-known ordinary and partial differential equations that are gradient flows.
2 The New Schemes: Stability
In this section, we formulate a wide class of numerical schemes that are energy stable by construction. We thus place stability front and center, leaving consistency to be dealt with subsequently. It is therefore important to allow many degrees of freedom in the scheme at this stage, in the form of a large number of coefficients, that will eventually be chosen, in the next section, to attain consistency at a high order of accuracy.
Our method is a linear -stage scheme of the following form:
where the intermediate stages , for , are given by
with the proviso . Notice that the proposed scheme Eq. 6 & Eq. 7, as promised, merely requires the solution of exactly the same type of problem at every time step as the standard backward Euler scheme: minimization of the associated energy plus a quadratic term.
At this point, it is not clear why a scheme such as Eq. 6 & (7) should dissipate energy at every iteration as in Eq. 2. However, in this section we establish quite broad conditions on the coefficients that ensure energy dissipation Eq. 2; this is the essential observation at the heart of the present paper. To demonstrate the idea, consider the following two-stage special case of scheme (6) & (7):
and impose the conditions
on the parameters. Set . Note that (9) is equivalent to
As we will see in Section 3, the conditions on the parameters of scheme (6) & (7) imposed in Claim 1 are loose enough to enable meeting consistency conditions to high order. We will establish Claim 1 with the help of the following couple of lemmas:
Let the auxiliary quantities , and be defined as in Theorem 1. We have
Let the auxiliary quantities , be given in Theorem 1 and let for . Then
3 The New Schemes: Consistency
We now turn to the question of whether the coefficients in scheme Eq. 6 and Eq. 7 can be chosen to ensure its high order consistency with the abstract evolution law Eq. 1. From Eq. 7, each stage satisfies the Euler-Lagrange equation:
The consistency equations for the ’s are found by Taylor expanding around (or equivalently ). Set . We will calculate the one-step error. For , let denote the multilinear form given by
so that the linear functional may be identified with an element of , and so on.
We begin with the Taylor expansion of the exact solution around :
We now present the error at each stage of the multi-stage algorithm, Eq. 6 and Eq. 7, and the conditions required to achieve various orders of accuracy: Let and be given in Eq. 6 and Eq. 7. The Taylor expansion of at each stage has the same form as Eq. 15, namely:
where the coefficients obey the following recursive relation
with . Furthermore, the following conditions for in scheme Eq. 6 are necessary and sufficient for various orders of accuracy:
|First Order:||Second Order:||Third Order:|
We first will Taylor expand around in Eq. 19:
Now we plug in an ansatz for the expansion on around , , and solve for , and :
Matching terms of the same order we get
completes stage one.
First we are going to solve for in Eq. 20:
Now Taylor expand around in Eq. 21:
Plug in the ansatz for and equation Eq. 16 for , and retaining up to terms of third order, we have that
Solving for , , by matching terms of the same order in Eq. 22, we arrive at:
completing the induction step.
4 The New Schemes: Examples
In this section, we exhibit second order and third order examples of scheme Eq. 6 that satisfy concurrently the hypothesis guaranteeing unconditional energy stability (Theorem 1) and the consistency equations (Section 3) up to second and third order. We found the ’s numerically and then sought a nearby algebraic solution to the consistency equations that still satisfied the conditions in Theorem 1.
4.1 Second order examples
It can be shown that there is no unconditionally energy stable second order two-stage method. However, it turns out that three stages are sufficient for unconditional stability:
This choice of ’s that endows the three-stage method Eq. 6 and Eq. 7 with unconditional stability and second order accuracy is by no means unique; indeed, here is another that has the additional benefit of having each one of its stages depend only on the previous one and :
4.2 Third order examples
We now exhibit a six stage version of scheme Eq. 6 and Eq. 7 that concurrently satisfies the conditions for unconditional energy stability (Theorem 1) as well the consistency equations (Section 3) up to third order:
The exact values of ’s above are given in the appendix (Section 7); they are all rational numbers but with long fractional representations. Again, we cannot rule out other solutions for , possibly with fewer stages.
5 The New Schemes: Numerical Tests
In this section, we will apply the second order Eq. 23 and third Eq. 25 order accurate unconditionally stable schemes to a variety of gradient flows. We found Eq. 23 before Eq. 24 and therefore ran all our numerical tests with the former. The gradient flows considered span linear and non-linear ordinary and partial differential equations. The corresponding energies include convex and non-convex forms. Careful numerical convergence studies are presented in each case to verify the anticipated convergence rates of previous sections.
5.1 Ordinary Differential Equations
Our first test is on the simple equation that corresponds to gradient flow for the scalar energy with respect to the standard inner product on . We take the initial condition in our numerical tests, so that the exact solution is . Table 1 and Table 2 show the error in the solution at time computed by the second order scheme (6), (7) & (23) and the third order scheme (6), (7) & (25), respectively, at various choices of the time step size. The anticipated order or convergence is clearly observed for both schemes.
Next, for a less trivial example, we turn to the ODE with the corresponding energy . With initial condition , the exact solution is . The errors for the two new schemes are tabulated in Table 3 and Table 4, and once again bear out the anticipated convergence rates.
For PDEs, we start with a preliminary test on the one dimensional heat equation on subject to periodic boundary conditions with initial data . This is gradient flow with respect to the inner product for the energy . The exact solution is . The spatial domain is discretized into a uniform grid of 2048 points, and a high order accurate discretization for the Laplacian is chosen so that the contribution to the error from spatial discretization is negligible. Table 5 and Table 6 show the error in the approximate solution at , computed via the second order accurate scheme (6), (7) & (23), and the third order accurate scheme (
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CC-MAIN-2021-43
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http://jabsto.com/Tutorial/topic-104/Microsoft-Excel-2013-Formulas-62.html
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math
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Microsoft Office Tutorials and References
In Depth Information
• Worksheet functions and their arguments: These include functions such as SUM or AVERAGE and their
arguments. Function arguments appear in parentheses and provide input for the function's calculations.
• Parentheses: These control the order in which expressions within a formula are evaluated.
Entering a formula
When you type an equal sign into an empty cell, Excel assumes that you are entering a formula because a for-
mula always begins with an equal sign. Excel's accommodating nature also permits you to begin your formula
with a minus sign or a plus sign. However, Excel always inserts the leading equal sign after you enter the for-
As a concession to former Lotus 1-2-3 users, Excel also allows you to use an “at” symbol (@) to begin a for-
mula that starts with a function. For example, Excel accepts either of the following formulas:
However, after you enter the second formula, Excel replaces the @ symbol with an equal sign.
If your formula uses a cell reference, you can enter the cell reference in one of two ways: Enter it manually or
enter it by pointing to cells that are used in the formula. I discuss each method in the following sections.
Entering a formula manually
Entering a formula manually involves, well, entering a formula manually. You simply activate a cell and type an
equal sign (=) followed by the formula. As you type, the characters appear in the cell as well as in the Formula
bar. You can, of course, use all the normal editing keys when typing a formula. After you insert the formula,
When you type an array formula, you must press Ctrl+Shift+Enter rather than just Enter.
An array formula is a special type of formula, which I discuss in Part IV.
After you press Enter, the cell displays the result of the formula. The formula itself appears in the Formula bar
when the cell is activated.
Entering a formula by pointing
The other method of entering a formula that contains cells references still involves some manual typing, but you
can simply point to the cell references instead of typing them manually. For example, to enter the formula
=A1+A2 into cell A3, follow these steps:
1. Move the cell pointer to cell A3.
2. Type an equal sign ( = ) to begin the formula.
Notice that Excel displays Enter in the left side of the status bar.
3. Press twice.
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https://www.e-education.psu.edu/ebf483/node/704
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math
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9.1.1 Reactive Power
Reactive power is a very complicated concept to understand technologically, but a fairly simple one economically. Here we will focus on the economics, but to do so we'll need to understand a little bit of the physics. If you want to know more about the mysterious nature of reactive power, I strongly encourage you to read Alexandria von Meier's excellent book Power Systems: A Conceptual Introduction.
Recall from the beginning of the term that electric power actually has two components: current and voltage. In an alternating current power system, the current and voltage that are produced are not constant. Both are sine waves with a frequency of 60 cycles per second or 60 Hertz (this "frequency" is an important concept that we'll come back to later in this lesson). If the voltage and current waves peak at exactly the same time, as shown in panel (a) of the figure below, they are said to be "in phase." If the voltage and current waves do not peak at exactly the same time, as shown in panel (b) of the figure below, then they are said to be "out of phase."
Power systems need the voltage and current to be as close to being "in phase" as possible. If the only devices that were connected to power systems were simple resistors (like a light bulb or basic toaster oven), then it would not be that difficult to keep the power system in phase. Some types of everyday devices, such as air conditioners, refrigerators, pool pumps, or anything else that uses an electric motor, can actually knock the voltage and current out of phase. These devices are sometimes called "inductive loads" because they draw current but can reduce voltage, or they produce a weak electromagnetic field that can push the voltage out of phase with the current.
If the voltage winds up out of phase with the current, this reduces the amount of power that can be delivered (remember that power = voltage times current) and some of those inductive loads may not work as well (and light bulbs may not be as bright, and so forth). The difference in the phase between the voltage and current, or what additional voltage would be needed to restore the system to being in phase, is known as reactive power.
The power that we actually consume (voltage times current) is sometimes called "real power" to differentiate it from reactive power. In this class, if we simply use the term "power" then that will always refer to real power.
This leads us to the first economic principle of reactive power: Real power and reactive power are complements in consumption. Many devices that use electricity require not only real power to perform their basic functions but reactive power to compensate for the effect that these devices have on the voltage.
When the power grid needs more reactive power, this can be effectively produced at the power plant. Remember that most power plants produce electricity through a coil of wire that is rotating in a magnetic field. (How quickly does that coil rotate? 60 times per second, or 60 Hertz, which is the same frequency as the voltage and current wave forms.) If the voltage and current waves are out of phase, that can be corrected by adjusting the strength of the magnetic field, which a power plant operator can do by moving the coil of wire ever so slightly. This is what we call the "production" of reactive power. The word "production" here is kind of misleading since reactive power is neither a thing (like a molecule of gas or drop of oil) nor a force (like electricity). But we use the term as a kind of short-hand.
There is a catch, however, which leads us to the second economic principle of reactive power: Reactive power and real power are substitutes in production. If a power plant wants to produce more reactive power, it has to reduce its production of real power by a little bit. Exactly how much is determined by the engineering design of the power plant. Since reactive power is neither an object nor a force, there is no direct cost involved in producing reactive power. There is, however, an opportunity cost to the power plant in the form of foregone real power production.
Some specialized devices, like capacitor banks, can also provide reactive power. At the margin, however, it is often cheaper to produce reactive power from an existing power plant than to build a new capacitor bank. Many such capacitor banks do exist in real power systems, particularly close to cities where building power plants may be difficult.
Prior to electricity restructuring, electric utilities would adjust the output of power plants when more reactive power was needed. The economic costs of that were internalized by the utility - if the system needed so much reactive power that it significantly increased the cost of generating real power, those costs would show up in the form of higher electric rates.
In areas that have undergone electricity restructuring, however, no power plant would voluntarily provide reactive power because that would mean less real power that it could sell in the market. PJM and other market operators have generally solved this problem by requiring generators to produce reactive power when requested, with any foregone real power consumption compensated based on opportunity cost. For example, if a generator is asked to reduce output by 1 MWh to increase reactive power, and if the market price is $25/MWh, then the generator would be compensated $25 for that action to increase reactive power.
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https://www.ask.com/web?q=What+Is+a+Scale+in+Math%3F&oo=2603&o=0&l=dir&qsrc=3139&gc=1&qo=popularsearches
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math
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In mathematics, the idea of geometric scaling can be generalized. The scale between two mathematical objects need not be a fixed ...
Math explained in easy language, plus puzzles, games, quizzes, worksheets and ... Scale. The ratio of the length in a drawing (or model) to the length of the real ...
Definition of Scale (On A Graph) explained with illustrated examples. Also, practice lots of math problems with fun math worksheets at Splash Math.
In this drawing of the horse anything with the size of 1 inch would have the size of 10 inches in the real world, so a measurement of 150mm on the drawing ...
An urban planner needs your help in creating a scale drawing. Let's use our knowledge about scale factor, length, and area to assist.
Understand how a scale drawing is converted into real numbers using the scale factor. ... The missions are in the subject where the math is. Chose any grade.
See how we solve a word problem by using a scale drawing and finding the scale factor.
Since it is not always possible to draw on paper the actual size of real-life objects such as the real size of a car, an airplane, we need scale drawings to represent ...
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https://link.springer.com/book/10.1007%2F978-0-387-77487-9
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math
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About this book
Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science.
Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well-selected additional bibliography of over 1250 papers and books which makes this a fine work for students, instructors, and researchers in the field.
"This book will certainly be, in the years to come, the basic reference to the subject."
--- The American Mathematical Monthly (First Edition)
"In this reviewer's opinion [the author] has more than succeeded in his aim. The problems at the end of each chapter are well-chosen; there are more than 650 of them. The book is especially suitable for self-study, as the author frequently provides ample explanation not only of what he is proving, but also of how and why he is proving it. As a reference work for the specialist or a text for the student, the book is highly recommended."
--- Mathematical Reviews (First Edition)
"Since the first day of its appearance in 1968, this book has been the standard reference in universal algebra, and no book since has reached its quality."
--- Journal of Symbolic Logic (Second Edition)
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| 1,530 | 9 |
https://goka-finance.com/definiciones-sucesion-de-K0H
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math
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In mathematics, the Fibonacci sequence (sometimes wrongly called the Fibonacci series) is the infinite sequence of natural numbers.
The sequence begins with the numbers 0 and 1, and from these, each element is the sum of the previous two. The elements of this sequence are called Fibonacci numbers. This sequence was described in Europe by Leonardo de Pisa, a 13th century Italian mathematician also known as Fibonacci.
It has numerous applications in computer science, mathematics, and game theory. It also appears in biological configurations, such as in the branches of trees, in the arrangement of the leaves on the stem, in the flora of the artichoke and in the arrangement of a cone.
The fundamental concept of the Fibonacci sequence is that each element is the sum of the previous two. In this sense, the sequence can be expanded to the set of integers such that the sum of any two consecutive numbers is the immediately following.
Applications of the Fibonacci sequence
Fibonacci sequences have their application in the stock market study, they are considered a very important indicator to see the magnitude of the retracements in the Stock Market:
Upon confirmation of a decline in the price, we will seek to calculate the probable magnitude of the movement. To achieve this, certain percentages obtained from the Fibonacci sequence are applied to the total magnitude of the previous trend.
The percentages used are the following:
- 61.8%: Also known as the golden ratio, or golden number, it is the limit of the quotient obtained from the division of one element of the Fibonacci sequence by the next, as the series tends to infinity.
- 50.0%: It is the most commonly accepted retracement, equivalent to half the advance of the main trend.
- 38.2%: It is obtained by subtracting 61.8% from the unit (1.000 - 0.618 = 0.382).
- 100%: Equivalent to the total magnitude of the main trend.
Considerations to take into account of the Fibonacci sequence
The percentages of retracement in the stock market analysis should be calculated only after the end of a trend has been confirmed, never while the trend continues.
Taking into account that trends are always part of a longer-term trend and in turn are made up of shorter-term trends, the question is: On which of these trends should I calculate the setbacks? It may not have a simple answer. In general terms, we must calculate the setbacks on that trend that has given clear signs of termination.
It is considered that a weak trend may have a 31.8% retracement, while a very strong trend may have a 61.8% retracement, before returning to its original direction.
Some books mention a critical zone of 33 to 38.2%, and 61.8 to 67%, instead of the specific levels.
The most important criticisms against Fibonacci retracements are based on random walk theory, arguing that there is no justification for assuming that price action has any reason to respect predetermined retracement levels.
Fibonacci retracements form an important part of the Elliott Wave Theory.
Below we can see a graphic example of the Fibonacci zones:
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http://slideplayer.com/slide/4167330/
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math
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Presentation on theme: "Inventory Models Planned Shortage Models. PLANNED SHORTAGE MODEL Assumes no customers will be lost because of stockouts Instantaneous reordering –This."— Presentation transcript:
PLANNED SHORTAGE MODEL Assumes no customers will be lost because of stockouts Instantaneous reordering –This can be modified later using standard reorder point analyses Stockout costs: –C b -- fixed administrative cost/stockout –C s -- annualized cost per unit short Acts like a holding cost in reverse Reorder when there are S backorders
PROPORTION OF TIME IN/OUT OF STOCK T 1 = time of a cycle with inventory T 2 = time of a cycle out of stock T = T 1 + T 2 = time of a cycle I MAX = Q-S = total demand while in stock. T 1 /T = Proportion of time in stock. Multiplying by D/D gives T 1 D/TD = (Demand while in stock)/(Demand for cycle) = (Q-S)/Q T 2 /T = Proportion of time out of stock Multiplying by D/D gives T 2 D/TD = (Demand while out of stock)/(Demand for cycle) = S/Q
Average Inventory Average Number of Backorders Average Inventory =Average Inventory = (Avg. Inv. When In Stock)(Proportion of time in stock) (Q-S) 2 /2Q =(I MAX /2)((Q-S)/Q) = ((Q-S)/2)((Q-S)/Q) = (Q-S) 2 /2Q Average Backorders =Average Backorders = (Average B/O When Out of Stock)(Proportion of time out of stock) S 2 /2Q = (S/2)(S/Q) = S 2 /2Q
TOTAL ANNUAL COST EQUATION TC(Q,S) = C O (Avg. Cycles Per Year) + C H (Average Inv.) + C s (Average Backorders) + C b (Number B/Os Per Cycle) (Avg. Cycles Per Year) + CD = C O (D/Q) + C h ((Q-S) 2 /2Q) + C s (S 2 /2Q) + C b S(D/Q) + CD
OPTIMAL ORDER QUANTITY, Q* OPTIMAL # BACKORDERS, S* Take partial derivatives with respect to Q and S and set = 0. Solve the two equations for the two unknowns Q and S.
EXAMPLE SCANLON PLUMBING Saunas cost $2400 each (C = 2400) Order cost = $1250(C O = 1250) Holding Cost = $525/sauna/yr.(C h = 525) Backorder Goodwill Cost $20/wk (C S =1040) Backorder Admin. Cost = $10/order (C b = 10) Demand = 15/wk(D = 780)
Using the Template Planned Shortage Worksheet Input Parameters Optimal Values
REORDER POINT ANALYSIS Reorder point can be affected by lead time. If lead time is fixed at L years, order is placed accounting for the fact that LD items would be demanded during lead time. Thus order is places when there are S*-LD backorders. –If this is a negative number, this implies an order is placed when there are LD - S* items left in ventory.
Example What If Lead Time Were 4 Weeks? Demand over 4 weeks = 4(15) = 60 –4 weeks =.07692 years (for template) Want order to arrive when there are 20 backorders. Thus order should be placed when there are 60 - 20 = 40 saunas left in inventory
Using Template Reorder Point = 40 Enter Lead Time
Review In planned shortage models there can be both time-dependent and time-independent shortage costs There are 2 unknowns which are found by taking partial derivatives of the total cost equation –Q* -- the amount to order –S* -- the number of backorders when order is placed The actual reorder point may be adjusted for lead time. Use of template
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https://ruudjanse.com/qa/what-is-linear-and-non-linear-model.html
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math
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- What are the example of linear model?
- What makes something linear?
- What is linear and nonlinear in English?
- How do you know if its linear or nonlinear?
- Is linear model appropriate?
- What is not a linear model?
- How do you identify a linear model?
- What is a simple linear regression model?
- What is a linear model?
- What is the common features of linear?
- What are the 2 other name of linear model?
- Why linear regression is called linear?
- What is the difference between linear and nonlinear functions?
- What are the characteristics of linear model?
- How do linear models work?
- How do you solve linear models?
- How do you calculate linear regression line?
What are the example of linear model?
The linear model is one-way, non-interactive communication.
Examples could include a speech, a television broadcast, or sending a memo.
In the linear model, the sender sends the message through some channel such as email, a distributed video, or an old-school printed memo, for example..
What makes something linear?
Linear functions are those whose graph is a straight line. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. a is the constant term or the y intercept.
What is linear and nonlinear in English?
Linear text refers to traditional text that needs to be read from beginning to the end while nonlinear text refers to text that does not need to be read from beginning to the end.
How do you know if its linear or nonlinear?
Plot the equation as a graph if you have not been given a graph. Determine whether the line is straight or curved. If the line is straight, the equation is linear. If it is curved, it is a nonlinear equation.
Is linear model appropriate?
To determine whether a linear model is appropriate, we examine the residual plot. … If a linear model is appropriate, the histogram should look approximately normal and the scatterplot of residuals should show random scatter . If we see a curved relationship in the residual plot, the linear model is not appropriate.
What is not a linear model?
A nonlinear model is nonlinear because it’s not linear in parameters. … In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables.
How do you identify a linear model?
Remember from algebra, that the slope is the “m” in the formula y = mx + b. In the linear regression formula, the slope is the a in the equation y’ = b + ax. They are basically the same thing. So if you’re asked to find linear regression slope, all you need to do is find b in the same way that you would find m.
What is a simple linear regression model?
Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.
What is a linear model?
A linear model is an equation that describes a relationship between two quantities that show a constant rate of change.
What is the common features of linear?
Answer. An increasing linear function results in a graph that slants upward from left to right and has a positive slope. A decreasing linear function results in a graph that slants downward from left to right and has a negative slope. A constant linear function results in a graph that is a horizontal line.
What are the 2 other name of linear model?
Answer: In statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used in time series analysis with a different meaning.
Why linear regression is called linear?
Linear Regression Equations In statistics, a regression equation (or function) is linear when it is linear in the parameters. While the equation must be linear in the parameters, you can transform the predictor variables in ways that produce curvature.
What is the difference between linear and nonlinear functions?
Linear FunctionA linear function is a relation between two variables that produces a straight line when graphed. Non-Linear FunctionA non-linear function is a function that does not form a line when graphed.
What are the characteristics of linear model?
CHARACTERISTICS OF A LINEAR MODELIt is a model, in which something progresses or develops directly from one stage to another.A linear model is known as a very direct model, with starting point and ending point.Linear model progresses to a sort of pattern with stages completed one after another without going back to prior phases.More items…•
How do linear models work?
Linear Regression is the process of finding a line that best fits the data points available on the plot, so that we can use it to predict output values for inputs that are not present in the data set we have, with the belief that those outputs would fall on the line.
How do you solve linear models?
Using a Given Input and Output to Build a ModelIdentify the input and output values.Convert the data to two coordinate pairs.Find the slope.Write the linear model.Use the model to make a prediction by evaluating the function at a given x value.Use the model to identify an x value that results in a given y value.More items…
How do you calculate linear regression line?
For simple linear regression, the least squares estimates of the model parameters β0 and β1 are denoted b0 and b1. Using these estimates, an estimated regression equation is constructed: ŷ = b0 + b1x .
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https://fr.slideserve.com/naeva/warm-up-powerpoint-ppt-presentation
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math
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Central Angle Angle = Arc
Inscribed Angle • Angle where the vertex in ON the circle
160 The arc is twice as big as the angle!! 80
Find the value of x and y. 120 x y
J K Q S M Examples 1. If mJK= 80 and JMK = 2x – 4, find x. x = 22 2. If mMKS = 56, find m MS. 112
Find the measure of DOG and DIG D 72˚ G If two inscribed angles intercept the same arc, then they are congruent. O I
If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.
Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY B A D C
If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. diameter
Q D 3 J T 4 U Example 3 In J, m3 = 5x and m4 = 2x + 9. Find the value of x. x = 3
Example 4 In K, GH is a diameter and mGNH = 4x – 14. Find the value of x. 4x – 14 = 90 H K x = 26 N G Bonus: What type of triangle is this? Why?
Example 5 Find y and z. z 110 110 + y =180 y y = 70 85 z + 85 = 180 z = 95
Homework WS Inscribed Angles Choose even or odd. Everyone does the last problem.
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https://writerspmaj.web.app/kilbane18449zu/getting-help-with-math-207.html
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math
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http://laujet.com/index.php/laujet/article/view/61
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math
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PERFORMANCE EVALUATION OF 1 kW HORIZONTAL AXIS WIND TURBINE FOR RESIDENTIAL USE IN ABEOKUTA
The conventional energy sources are mainly use in Nigeria to generate electricity and yet, there is a critical challenge of electric power deficit. Therefore, design, modeling and simulation of 1 kW horizontal axis wind turbine as alternative power supply for residential use is considered. This paper presents the design, modeling and simulation of horizontal axis type wind turbine with power output of 1 kW at a wind speed of 4 m/s. Analysis of wind power capacity in W/m2 was done based on the obtained wind data using Weibull probability distribution function. The results showed that the average exploitable wind power density between 4 W/m2 and 14.97 W/m2 was realizable. The wind turbine blades were modeled using blade element momentum theory. The rotational speed of the blades was increased by using airfoil. Mathematical equations were used to determine the tip speed ratio, lift and drag forces and the power output. The MATLABTM AND SIMULINKTM scientific computer program was used to simulate the model of the wind turbine. The model with its required input parameters, pitch angle, rotational speed of the rotor, angle of attack, and wind speed were varied above and below its actual settings. The results showed that when the parameters were decreased, there was no power output and with the parameters values above the actual settings, the output power was increased to 2.5 kW at a wind speed of 8 m/s and generator speed of 620 rpm. The capacity is small and it is affordable for many household applications in Nigeria.
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https://www.arxiv-vanity.com/papers/math/0509060/
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math
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Hamiltonian symmetries and reduction in generalized geometry
A closed -form defines an extension of by . This fact leads to the definition of the group of -twisted Hamiltonian symmetries as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold. The Hamiltonian reduction in the category of generalized complex geometry is then constructed. The definitions and constructions are natural extensions of the corresponding ones in the symplectic geometry. We describe cutting in generalized complex geometry to show that it’s a general phenomenon in generalized geometry that topology change is often accompanied by twisting (class) change.
Generalized complex structure was introduced by Hitchin and developed by Gualtieri in his thesis . Much more work has been done since. This new structure specializes to complex and symplectic structures on two extremes and it is regarded as the natural category in which to consider constructions pertaining to both, e.g. mirror symmetry.
The group of Hamiltonian diffeomorphisms occupies a prominent place in symplectic geometry. Reduction via group actions and related constructions have been proved fruitful whenever they exist. The existence of such notions and constructions in generalized geometry would definitely be desired (e.g. ). The notion of infinitesimal Hamiltonian symmetry in (untwisted) generalized geometry is given by , in remark and proposition . We obtain the following analogues of these notions from symplectic geometry in (twisted) generalized complex geometry:
Theorem 3.6. Let be an -twisted generalized complex manifold, be the subgroup of -twisted generalized symmetries preserving . Then , the set of time- generalized complex symmetries generated by time-dependent Hamiltonian functions is a subgroup of .
Theorem 4.4. Let be a compact Lie group. Suppose is an -twisted generalized complex manifold with a Hamiltonian -action with moment map , so that is a regular value of and the geometrical action of is free on . Then there is a natural extended complex structure on the reduced space .
We describe the content of the article in the following. The generalized geometry studies structures on the generalized tangent bundle with the structure of Courant algebroid given by a closed three form . When , it’s shown in that the group of symmetries of the Courant algebroid is given by the semi-direct product
The Lie algebra structure on is
which can be seen as the trivial extension of by the module :
In the presence of twisting , let and be the respective symmetry group and Lie algebra. We show in §2 that is the extension of by the module defined by the -cocyle
Let with the Lie bracket (1.1). Then the inclusion
is an inclusion of Lie algebra (proposition 2.3).
The inclusion comes into play, for example, when we integrate a generalized field, i.e. a section of , into a symmetry of the -twisted Courant algebroid structure:
Similar to symplectic geometry, we define (following ) the generalized Hamiltonian field generated by on an (-twisted) generalized complex manifold to be
The generalized Hamiltonian symmetry generated by is then as above. This enables us to define in §3 the notion of generalized Hamiltonian action by a Lie group and the group of generalized Hamiltonian symmetries , completely parallel to the corresponding definitions in symplectic geometry.
We then consider reduction in our Hamiltonian framework in §4. The induced Courant algebroid structure on the reduced manifold is again exact, while there is no canonical identification to with twisted Courant bracket, unless the group action factors through , in which case, explicit identification can be written down (upto a choice of connection form) (cf. corollary 4.7). One notable fact of the construction is that the twisting form upstairs is not required to descend to the reduced manifold. Furthermore, the Ševera class of the reduced structure (which is the class when a splitting is chosen) does not depend on either the choice of the connection form or invariant -field action on the original manifold. We also prove some minor facts, such as the reduction of a generalized Calabi-Yau manifold (as in ) is again generalized Calabi-Yau manifold in the same sense; and when the group is torus, the twisting form of the reduced structure satisfies a Duistermaat-Heckman type formula in a component of regular values of the moment map. In §4.5, we compute the example of with nontrivially twisted generalized complex structure.
With the generalized complex reduction in hand, other related constructions and phenomena exhibit themselves, such as coupling structure, cutting, wall crossing (at least for -action) etc. As in the case of symplectic geometry, we may also weaken the condition of free action and instead have orbifold as reduced space. These we postpone to a later work. Here we only describe cutting (§5), along the line of cutting constructions of [33, 34, 13], to show that operations in the generalized geometry share a common feature, i.e. change of topology is accompanied by change of twisting (class).
In the appendix, we collect various definitions and theorems on Lie and Courant algebroids and some facts on Lie algebra extensions.
The early version of this work appeared on the arXiv along with the works of Lin-Tolman , Bursztyn-Cavalcanti-Gualtieri as well as Stienon-Xu around the same time. In Hitchin described an example of generalized Kähler reduction. Another version of generalized complex reduction is given in , which is based on a notion of generalized holomorphic map. In particular, the fibers over regular values of such maps carry natural complex structure. Another point of view is provided by , which discusses three related stuctures on .
The reduction described in this article also fits into bigger picture of reduction theory. We give a very brief and extremely incomplete recount of related works in the following. More may be found in the references of the works mentioned below. First of all, our construction is a direct generalization of the Marsden-Weinstein reduction in symplectic geometry to generalized complex category. As shown in , generalized complex structures can also be defined as complex Dirac structures with real index . In fact, any generalized (as well as extended) complex structure provides the manifold with a Poisson structure (see §3.1 and the references therein) and the reduction constructed here coincides with the Poisson reduction defined by , when seen in the Poisson category. More generally, the reduction of Dirac structures (without twisting) was done in the control community, e.g. [9, 10], where integrability is not required while the reduced structure will be integrable if the original one is so. These are the so called Hamiltonian point of view. Another point of view on reduction of Dirac structures comes from the relation with variational principles, see for example [42, 43]. The reduction in singular cases for the Poisson and Dirac structures are also known, e.g. , , as well as the excellent book , where many more references may be found. Group valued moment maps are discussed in for , for torus and for general case. The related reduction and further theory can be found in for example [4, 5], . Reduction of symplectic structure by action of Poisson Lie group was also discussed, e.g. in . In there the moment map would have target space the dual Poisson Lie group instead of dual of the Lie algebra. Relation among different sorts of reductions of symplectic structures with or without moment map is discussed in the paper and the references therein. For the relation of symplectic reduction to algebraic geometry, the survey article and the references therein are excellent sources. Of other geometrical structures, to name just a few, such as Kähler, hyper-Kähler [25, 38, 37], Sasakian, locally conformal symplectic or Kähler geometries and contact geometry, etc, the various reductions were considered as well. Because of the limited scope of this paper, we only mention some recent developements of these, from which more references can be found: Kähler [26, 27, 28, 29, 6], hyper-Kähler [8, 52, 49], contact [2, 17, 57], Sasakian [21, 16], Vaisman structure , locally conformal Kähler , locally conformal symplectic , complex Poisson etc. The very incomplete list above could not and was not meant to capture the vast literature on and the span of the reduction theory. Instead, it only shows partly how much more the author needs to learn in this fascinating field of mathematics.
Acknowledgement. I’d like to thank François Lalonde and DMS in Université de Montréal for generous support and excellent working conditions, which made this work possible. I’d like to thank Tudor Ratiu for his patience and very helpful comments that brought this work into perspective with respect to general reduction constructions. Of course, the omissions and mistakes on the literature are all due to the author’s ignorance in the subject. I thank Mainak Poddar and B. Doug Park for invitation to Waterloo, when many enlightening talks were given on generalized complex geometry during the workshop of mirror symmetry at the Perimeter Institute, especially those of Hitchin and Gualtieri, and for helpful discussions that kick-started this project. I thank Sam Lisi for helpful discussions. I’d like to thank Yi Lin for initial discussions and providing with an early draft of their paper . The current work is partially inspired by their paper. I would also like to thank the referee for many valuable suggestions. Special thanks go to my family: Aihong, Henry and Catherine for their support and understanding.
A note on the notations: There are lots of brackets in the following. We did not try to make them all look different, for which there would be too much clutter of notations. Instead, except in the appendix where various bundles are involved and we distinguish them by bundle subscripts, we only make the distinction of -twisted brackets by adding subscript . As to the spaces on which the brackets are defined, it should be clear from the context.
2. Generalized symmetries
2.1. Symmetry group of Courant brackets
The symmetry group of we’ll consider is the group of generalized symmetries , whose action on is defined as push-forward by the following, where and :
We recall the definition of -twisted Courant bracket on :
The action of on the twisted Courant bracket gives the following:
The -form is the -field of the generalized symmetry . The action of is also called a -field transformation. Another convention for the action of is also valid, i.e. , while they give the same infinitesimal action. We write down the composition law (in our chosen convention for the action):
We have the extension sequence of groups:
Let be an -parameter subgroup of , then is an -parameter subgroup of diffeomorphisms generated by a vector field . Let then we have
The Lie algebra of is then with the bracket:
In other words, is the trivial extension of the standard Lie algebra by , where the module structure is given by (cf. appendix §6.2):
More generally, let be a smooth path, starting from the identity, in and the time-dependent vector fields generating . Then the infinitesimal symmetry generating is the path in , where:
The infinitesimal action of on is given by
A -form defines a -valued -cochain on the Lie algebra :
We have where is the differential of the Lie algebra cohomology. Thus, we obtain the following map
Given , the Lie algebra is the extension of by defined by the -cocycle . Equivalently, is with the following -twisted Lie bracket (cf. (6.14)):
can also be viewed as a -valued -cochain, which defines an extension of Lie algebra by . This extension is obviously trivial since defines another -valued -cochain on by and we can see that .
Let be the subgroup of generalized symmetries that preserve the Courant bracket and a path in . Let be the infinitesimal symmetry, then (2.2) gives
Consider the linear map . Then
and is an inclusion of Lie algebra.
Proof: Straightforward computation shows the equality, from which the last statement on follows.
2.2. Generalized complex structures
The data on together with the natural projection to defines a structure of Courant algebroid as in definition 6.3. We then rephrase the definition of generalized complex structure given in [23, 22] as follows:
The Courant algebroid will be called an extended tangent bundle and denoted when we forget the paticular splitting into the direct sum . The bracket will then be denoted simply as . An extended almost complex structure on is an almost complex structure on which is also orthogonal in the inner product . Furthermore, is integrable and is called an extended complex structure if the -eigensubbundle of is involutive with respect to the bracket .
In , the notion of exact Courant algebroid is used for the Courant algebroid here, since it fits into the exact sequence:
Let be a splitting with isotropic image (with respect to ), then it defines the -form , which is closed. Then identifies the Courant algebroid with with the -twisted Courant bracket. When such a splitting is chosen, we will use the notations , , etc, and say that we have the corresponding generalized structures. The set of splittings is a torsor over . The class does not depend on the choice of splitting and is called the Ševera characteristic class of .
The subgroup of generalized symmetries which preserve an extended complex structure is . Choose an (isotropic) splitting of and let be the corresponding twisting form, then we have .
2.3. Action on spinors
As shown in , each maximally isotropic subbundle corresponds to a pure line subbundle of the spin bundle :
where stands for the Clifford multiplication. A (nowhere vanishing) local section of is called a pure spinor associated to the subbundle . The integrability of with respect to the -twisted Courant bracket is equivalent to the condition , where via Clifford multiplication. More explicitly, there is a unique local section of , so that
where we use the same convention for as that in . For a generalized complex structure , we say that defines iff is the pure spinor defining the -eigenbundle of .
Let be a spinor, and define . Correspondingly, the infinitesimal action of on is
Suppose that defines a generalized complex structure , then defines the generalized complex structure . We also have .
Proof: Straightforward computation from the definitions.
3. Hamiltonian symmetries
3.1. Infinitesimal action
As shown by Gualtieri , the infinitesimal Hamiltonian fields on a generalized complex manifold can be defined by a complex valued function as , where is the Lie algebroid differential defined on (see (6.4)), and the infinitesimal symmetry is generated by . It’s straight forward to check that in the decomposition , . Write , then
Let , then the infinitesimal symmetry is when , in which there is no contribution from . For general , we take into account of the embedding and obtain
Let . The generalized symmetry preserving the -twisted Courant bracket generated by is . Let be a smooth function on an -twisted generalized complex manifold . The Hamiltonian field generated by is and is a Hamiltonian function defining the generalized Hamiltonian symmetry .
Similar arguments as those in Chapter of then imply that .
For , let . Then is a Poisson bracket and is canonically a Poisson manifold. We have
Proof: Since , we find that . Separating the real and imaginary parts and we have the first equation in (3.1).
To show that is Poisson bracket, we compute the -twisted Courant bracket of sections of the form in , without assuming :
It follows that and , proving the second equation in (3.1). The rest of the lemma then follows easily from these.
3.2. Group of Hamiltonian symmetries
Let (resp. ) be time-dependent Hamiltonian function on , with (resp. ), which generates infinitesimal symmetries (resp. ) and path of generalized symmetries (resp. ). Then and are paths in (cf. remark 3.2).
The path of generalized symmetries is generated by .
Proof: Let and . By (2.6), we have and . Consider where and generates . We only need to show that with . We first compute
It follows that
By definition, we have as well as , then
It follows that . The lemma then follows from checking
Completely parallel to symplectic case, we have the following:
Let be -twisted generalized complex manifold. The group of generalized Hamiltonian symmetries is the set of time- generalized symmetries generated by time-dependent Hamiltonian functions.
3.3. Hamiltonian action
We assume in the following that the Lie group is connected.
The action of Lie group on -twisted generalized complex manifold is given by a group homomorphism to . It is Hamiltonian with moment map if the induced geometric action on the Poisson manifold is Hamiltonian with equivariant moment map , so that the -action is generated by , where .
Let the -action on be Hamiltonian with moment map . Let be -transformed generalized complex structure where . Then the same -action is Hamiltonian with respect to iff , for which case the moment maps coincide.
Proof: We only need to check the condition for all , where and . It’s equivalent to .
The following is obvious:
For , let be -twisted generalized complex manifold, with Hamiltonian -action whose moment map is . Then is -twisted generalized complex manifold, with Hamiltonian -action whose moment map is . When , the diagonal action is Hamiltonian with moment map .
4. Reduction by Hamiltonian action
4.1. General construction
Let be a compact Lie group. Let be -twisted generalized complex manifold with a Hamiltonian action with moment map . Let and for . A few words on the notations below. The subscript means that the associated object is valued in (except those for and such) so that pairing with gives the cooresponding object associated to . An expression such as , with being -valued connection form, invokes also the pairing between and . Another equivalent way of unwinding is to choose dual basis and of and and express and , then .
We list the assumptions that we’ll use:
action is preserves a splitting, i.e. for all ,
is a regular value of ,
(the geometric part of) action is free on ,
We’ll drop the (the geometric part of) in condition and simply say that action is free on . We note the similarity of the condition to the exactness for Hamiltonian action in symplectic case, where . They both imply existence of an equivariantly closed extension, which is here and in symplectic geometry.
Let and be a linear generalized complex structure. Let denote the annihilating space in the pairing . Given subspace , we assume
Then, descends to and descends to on the sub-quotient as generalized complex structure. fits into the exact sequence, which splits non-canonically:
where is induced from projection and . Moreover, if
, where is the projection ,
the splitting map can be defined by an element of .
Proof: The subspace is obviously closed under . By the first assumption, is well defined. The pairing descends to a nondegenerate pairing since is the null-space of the restriction of . Also descends to on and is again generalized complex with respect to . With assumption , we have direct sum . The projection induces
The fact that is surjective follows from the second assumption. Note that is isotropic with respect to and it follows that is maximally isotropic with respect to .
Let be a basis of and , then is a basis of . Choose so that , then the sequence is split by the map induced by . If furthermore, , then we define and the map splits the sequence.
With the assumptions 4.1 and , there is a natural extended complex structure on the quotient . Moreover, the extension sequence splits when pulled back to , with the choice of a connection form on .
Proof: We first carry out the linear algebra for the bundles and . Consider the bundles over :
The assumption of lemma 4.3 is given by the assumption 4.1-. To see that is well defined, we note that for all . Then on gives assumption of lemma 4.3. Thus lemma 4.3 implies that and descends to and gives almost generalized complex structure with respect to on the bundle. We also have the exact sequence:
The bundle is -equivariant since both and are -equivariant subbundles of . The bundle with the structure descends to the bundle with the structure on . Obviously, is both complex and symplectic with respect to . Since naturally identifies with , the exact sequence above descends:
The image of , i.e. is maximally isotropic in the induced pairing. To split the pull-back sequence on , we choose a connection form on and define:
Let and be invariant sections of , i.e. the following vanishing is true (see (2.10)):
and ditto for . Direct computation shows that satisfies the above vanishing equations, i.e. is again invariant and in . It’s easy to see that and we compute:
We point out that the computations in this paragraph only use the vanishing equations. Now (6.7) implies
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https://www.thegreatcoursesplus.com/algebra-ii/conic-sections-mdash-circles-and-ellipses
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math
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Conic Sections—Circles and Ellipses
Lecture no. 18 from the course: Algebra II
Taught by Professor James A. Sellers | 31 min | Categories: The Great Courses Plus Online Mathematics Courses
Investigate the algebraic properties of the other two conic sections: ellipses and circles. Ellipses resemble stretched circles and are defined by their major and minor axes, whose ratio determines the ellipse's eccentricity. Circles are ellipses whose eccentricity = 1, with the major and minor axes equal.
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https://scholar.archive.org/work/mtk46wwdlna7fjj2x326xqzzmi
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math
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A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is
The first order language of graphs is a formal language in which one can express many properties of graphs -known as first order properties. The classic Zero-One law for random graphs states that if p is some constant probability then for every first order property the limiting probability of the binomial random graph G(n, p) having this property is either zero or one. The case of sparse random graphs has also been studied in detail for the binomial random graph model. We obtain results fordoi:10.4310/joc.2010.v1.n4.a3 fatcat:ygdujdrtjvf27ifwlaokq7zoeq
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https://www.ajol.info/index.php/jonamp/article/view/127901
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math
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Modelling Convergence of Finite Element Analysis of Cantilever Beam
Convergence studies are carried out by investigating the convergence of numerical results as the number of elements is increased. If convergence is not obtained, the engineer using the finite element method has absolutely no indication whether the results are indicative of a meaningful approximation to the correct solution. There are two major methods of mesh refinement; h-refinement and prefinement.
The cantilever beam plate was modelled using Abaqus/CAE 6.12-1, a finite element analysis tool. The geometry consists of a 300 x 100 mm beam section, spanning 3m and fixed at one end. A load of 1kN was applied at the free end. Also the model was meshed using 2D plane stress linear and quadratic quadrilaterals elements (CPS4R and CPS8), triangular elements (CPS3 and CPS6) and refined. For the linear quadrilateral element, a total of 20, 40,160 and 2560 elements were used for the coarse, medium, fine and very fine mesh respectively. Total numbers of 33, 63, 205 and 2737 nodes were generated accordingly.
The maximum bending stresses and shear stresses occurred at the fixed end. Exact stress and maximum displacement value at the mid-top fibre and free end of the beam was 100 N/mm2 and-19.5122 mm respectively. Simulated results at these points were analysed using the four element types at different mesh refinement levels. The study shows that linear FE converges slower compared to quadratic elements. Also a finer mesh is required to predict accurate stresses than is needed to calculate accurate displacements.
Keywords: Cantilever beam, finite element, Abaqus, convergence, stress, strain
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- January 8, 2019
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https://batubecopuvowyrys.ekinanaokulu.com/function-spaces-book-23314ma.php
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math
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4 edition of Function spaces found in the catalog.
Includes bibliographical references.
|Other titles||Proceedings of the sixth conference, function spaces|
|Statement||editors, R. Grząślewicz ... [et al.].|
|LC Classifications||QA323 .I54 2001|
|The Physical Object|
|Pagination||viii, 274 p. :|
|Number of Pages||274|
|LC Control Number||2005299360|
See the book. Corollary. is complete. The space Metric Spaces Page 2. Definition. Let be a metric space. An open ball of radius centered at is defined as Definition. Continuous functions Metric Spaces Page 5. is a continuous function on iff - open, the . A central theme of the book is the structure of various vector spacesmost importantly, Hilbert spacesand expansions of elements in these spaces in terms of bases. Functions, Spaces, and Expansions is intended for graduate students, researchers, and practitioners in applied mathematics, physics, and engineering. Readers are expected to have.
Search the world's most comprehensive index of full-text books. My library. Intuitively, a Sobolev space is a space of functions possessing sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function. Sobolev spaces are .
Don't show me this again. Welcome! This is one of over 2, courses on OCW. Find materials for this course in the pages linked along the left. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum.. No enrollment or registration. The book originates from the author's Habilitation thesis, in which the by then intensively investigated semismooth approach for finite-dimensional complementarity problems and variational inequalities was extended to and investigated in a function space setting.
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Theory of Function Spaces IV book. Read reviews from world’s largest community for ekinanaokulu.coms: 0. Buy Function Spaces and Partial Differential Equations: Volume 1 - Classical Analysis (Oxford Lecture Series in Mathematics and Its Applications) on ekinanaokulu.com FREE SHIPPING on Function spaces book ordersAuthor: Ali Taheri.
Buy Function Spaces and Partial Differential Equations: 2 Volume set (Oxford Lecture Series in Mathematics and Its Applications) on ekinanaokulu.com FREE SHIPPING on qualified ordersCited by: 1. where p nfunctions /: / - > /. theBaskakovDurrmeyer operators are usually defined by.
provided that the right side of () makes sense . Some approximation properties of certain operators () for functions f e C(I) or / Author: Paulina Pych-Taberska, Grzegorz Nowak.
“This book is the third part in a famous series of books on the theory of function spaces by the same author. After an intriguing historical survey in the introductory chapter, the book presents thorough discussions of typical building blocks as non-smooth atoms, quarks, wavelet bases, and wavelet ekinanaokulu.com: Birkhäuser Basel.
The book deals with the two scales B s p,q and F s p,q of spaces of distributions, where ‑∞spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of ekinanaokulu.com: Hans Triebel.
About this book. Introduction. Function spaces, especially those spaces that have become known as Sobolev spaces, and their natural extensions, are now a central concept in analysis.
In particular, they play a decisive role in the modem theory of partial differential equations (PDE). my book or in Coifman and Rochberg's original paper .
As far as Bergman spaces are concerned, all results in the first edition were stated and proved for the unweighted case. As a result of the addi tional effort made in Chapter 4, these results have all been generalized to the weighted case.
Function Spaces A function space is a topological space whose points are functions. There are many difierent kinds of function spaces, and there are usually several difierent topologies that can be placed on a given set of functions. These notes describe three topologies that can be placed on the set of all functions from a set X to a space Y: the product.
generalized fourier series and function spaces 75 In three dimensions the unit vectors i, j, and k play an important role. Any vector in the three dimensional space can be written as a linear combi. Hans Triebel’s most popular book is Theory Of Function Spaces.
Hans Triebel has 18 books on Goodreads with 19 ratings. Hans Triebel’s most popular book is Theory Of Function Spaces. Myuna Farm has many function spaces you can hire for your events. Terms and conditions About the booking. Booking fees are non-refundable. Events can be moved to another date if given a minimum of 2 weeks’ notice before the existing event.
As a textbook that provides a deep understanding of central issues in mathematical analysis, Functions, Spaces, and Expansions is intended for graduate students, researchers, and practitioners in applied mathematics, physics, and engineering.
The relevant function spaces are often equipped with the structure of a Banach space and many of the central results remain valid in the more general setting of bounded linear operators between Banach spaces or normed vector spaces, where the specic properties of the concrete. In mathematics, a function space is a set of functions between two fixed sets.
Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set X into a vector space has a natural vector space structure given by pointwise addition and scalar multiplication.
Jan 21, · Analysis on Function Spaces of Musielak-Orlicz Type provides a state-of-the-art survey on the theory of function spaces of Musielak-Orlicz type.
The book also offers readers a step-by-step introduction to the theory of Musielak–Orlicz spaces, and introduces associated function spaces, extending up to the current research on the topicAuthor: Osvaldo Mendez, Jan Lang. More formally, a function space is a class X of functions (with fixed domain and range), together with a norm1 which assigns a non-negative number kfk X to every function f in X; this number is the function space’s way of measuring how large a function is.
It is common (though not universal) for the class X of functions. This note covers the following topics: Basic set theory, Products, relations and functions, Cardinal numbers, The real number system, Metric and topological spaces, Spaces with special properties, Function spaces, Constructions on spaces, Spaces with additional properties, Topological groups, Stereographic projection and inverse geometry.
analogous axiom of countability belongs borhood bounded set bounded support Cauchy Chapter compact support complete countably normed condition conjugate space constant contains continuous function continuous linear functional converges to zero converges uniformly converges weakly convolution countably normed space definition differentiable.
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| 8,902 | 50 |
http://pandora-bracelet.us/category/allacciare-visitors/
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math
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Tapia (1996) discovered a several-foundation solution regarding a keen exploratory grounds research which have restriction chances approach off removal and you may an effective varimax, orthogonal, rotation. The fresh names into things claimed have been mind-depend on, value of math, pleasure of mathematics, and you can desire. Based on one basis data siti sesso , the newest forty situations was categorized on four categories all of and that was represented from the a factor. A chemical rating for each and every class is actually determined by adding upwards most of the variety of the latest scaled responses to the factors belonging to this group. Cronbach leader coefficients have been computed into the millions of this new scales and were found to be .96 to own care about-rely on, .93 to possess well worth, .88 getting enjoyment, and .87 to possess inspiration.
The content was reviewed by using multivariate factorial design on five affairs as the mainly based variables: (1) self-depend on, (2) really worth, (3) excitement, and you can (4) motivation as well as 2 independent details: (1) intercourse and you will (2) level of math nervousness. Multivariate studies out-of variance (MANOVA) is performed by using SPSS.
Data were analyzed testing for interaction effect and main effect at the .05 level. Data analysis indicated that the two-way interaction effect of the two variables Gender* MathAnxiety on the four dependent variables self-confidence, value, enjoyment, and motivation was insignificant with small effect size (Wilks Lambda F = 1.117, p < .35, eta squared = .04). Hence, it was concluded that there was not enough evidence to indicate a two-way multivariate interaction. The results also showed that the main effect of gender was insignificant with small effect size ( Wilks Lambda F= 1.018, p < .40, eta squared = .03), but the main effect of mathematics anxiety was significant with large effect size ( Wilks Lambda F = 7.237, p < .00, eta squared = .19). So it was concluded that there was enough evidence to say that there was an effect of the variable level of math anxiety on the four dependent variables self-confidence, value, enjoyment, and motivation. Therefore, follow ups were conducted.
Examination of ranging from-topic consequences showed that the outcome out of mathematics nervousness to three of your four centered details are high which have higher impact size
There was enough evidence to say that there was an effect of math anxiety on the variables self-confidence ( F (3,121) = , p < .00, eta squared = .44) , enjoyment ( F (3,121) = 9.614, p < .00, eta squared = .19) , and motivation ( F (3,121) = , p < .00, eta squared = .25) . Continue reading The newest ATMI is actually administered in order to users throughout their math groups
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| 2,792 | 5 |
https://nebusresearch.wordpress.com/2015/06/05/a-summer-2015-mathematics-a-to-z-fallacy/
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math
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Mathematics is built out of arguments. These are normally logical arguments, sequences of things which we say are true. We know they’re true because either they start from something we assume to be true or because they follow from logical deduction from things we assumed were true. Even calculations are a string of arguments. We start out with an expression we’re interested in, and do things which change the way it looks but which we can prove don’t change whether it’s true.
A fallacy is an argument that isn’t deductively sound. By deductively sound we mean that the premises we start with are true, and the reasoning we follow obeys the rules of deductive logic (omitted for clarity). if we’ve done that, then the conclusion at the end of the reasoning is — and must be — true.
A deductively sound argument is a wonderful thing. It tells us something we know must be true. That something will be true not just here and now — the way we might know “today is the 5th of June” is true — but always. It would be true anytime, anywhere in the universe. For that matter it would be true in other universes, if they existed. If nothing existed then … well, it’s very hard to say what would be true if nothing existed. Let’s step cautiously back from talking about “nothing”.
If we start out from a premise that isn’t true, or if we use a reason that isn’t part of the rules of deductive logic, then the argument is fallacious. It’s simple as that.
That isn’t to say the conclusion is wrong, by the way. If I present to you the argument, “I am a competent mathematician and I tell you that 53 is a prime number. Therefore 53 is a prime number”, I am making a fallacious argument. The conclusion is correct, but the fact that I’m a competent mathematician doesn’t prove that. Among other things you don’t know that I actually am a competent mathematician and not just a madman with a blog. You also don’t know that I’m not making a mistake or a joke or playing a prank. (This is a good point to look up “Grothendieck’s Prime”.) I promise you I am at least competent, and not making a mistake or a joke, and that 53 is prime. (I suppose I should double-check that before publishing). But I’ve given only a fallacious argument to prove it to you.
A fallacious argument can still be convincing. If you write to the United States Department of State and ask, and they tell you that Samuel Tilden was never President of the United States, that would convince nearly everyone that Tilden never was President. Formally speaking, that’s a fallacious argument. It’s even the same kind of fallacy I made with 53 up there. But you’d be perverse to insist they might be wrong about this.
Now … any interesting mathematical conclusion has a lot of reasoning in it. Nobody ever identifies every single bit of logical deduction, because that requires breaking the argument down into so many steps, each making so little progress, that the argument would be unreadable. We write out instead an argument that we are confident can be proved logically sound. How do we know there isn’t a fallacious step somewhere in the argument?
Normally, we know because we build interesting mathematical arguments out of smaller, simpler arguments that we proved already. Sometimes we proved them as mathematics majors or as graduate students. Sometimes we proved them by finding a book where someone who wasn’t us actually proved it. Or we start from an argument that is very much like one of these smaller, simpler arguments already proved, and trust that however we varied things isn’t going to change the soundness of the argument.
Much of the time this works out. Sometimes we’re wrong, and erratas or withdrawn proofs follow, chased down by a lot of sulking and fuming. Sometimes we’re even lucky and the reason that our proof was wrong turns out to be interesting, and to lead to new discoveries. That happens most rarely, but it almost makes up for the pain of finding the fallacy.
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