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http://math.stackexchange.com/questions/139575/can-someone-explain-cremer-mcleans-astonishing-result-in-auction-theory/139576 | # Can someone explain Cremer-Mclean's astonishing result in auction theory?
In mechanism design/auction theory, there is a famous result by Cremer and Mclean that if agents'/bidders' valuations are even slightly correlated, then all the surplus can be extracted by the principal/auctioneer. This is what makes auction t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 41, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/32111/compactness-and-covering-spaces/32112 | ## Compactness and Covering Spaces
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Let p : Y -> X be an n-sheeted covering map, where X and Y are topological spaces. If X is compact, prove that Y is compact.
I realize that this seems like a very simple proble... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 56, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/120525-spread-disease.html | # Thread:
1. ## Spread of a disease
Under certain circumstances, the rate at which a disease spreads through a population of P individuals is proportional to the product of the number I of people infected and the number not infected
a) Write and equation for dI/dt
b) Invert to get dt/dI
c) Find t as a function of ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/44185/what-is-the-characteristic-length-of-a-cylinder?answertab=votes | # What is the characteristic length of a cylinder
I have a cold cylinder that is submerged in hot water and I need to find the convective heat transfer coefficient. I can do the whole process but I am stuck finding the characteristic length. I found that the characteristic length of an object is $$L_{c}=\frac{A}{P}$$
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/43720/minimum-population-size-for-chi-square-test | # Minimum population size for chi-square test?
I'm analyzing data from an experiment in which two independent groups were exposed to an experimental setup without and with treatment.
I am testing whether treatment changed the second group's behaviour by performing a chi-square test that compares group 2 (the observed... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/108953?sort=votes | ## Motivic generalisation of Neron-Ogg-Shaferevich criterion
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Given a variety $X$ over $\mathbb{Q}$ with good reduction at $p$, proper smooth base change tells us that its $l$-adic cohomology groups are unramified... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 69, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/88300/if-fx-is-continuous-on-a-b-and-m-max-fx-is-m-lim-limits-n/88309 | If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$?
Let $f(x)$ be a continuous real-valued function on $[a,b]$ and $M=\max\{|f(x)| \; :\; x \in [a,b]\}$. Is it true that: $$M= \lim_{n\to\infty}\left(\int_a^b|f(x)|^n\,\mathrm dx\ri... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/98869/list | ## Return to Question
3 added 63 characters in body
I am writing a paper for game theorists where I use (countable) amenable groups to do some things. So I am writing up a preliminary section about countable amenable groups whose main purpose is to convince the reader that invariant means are the generalization of th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/319137/determine-k-if-using-a-factor-of-x2 | # Determine $k$ if using a factor of $(x+2)$
$f(x)=2x^3-5x^2=kx-20$ Help is appreciated.
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Welcome to MSE! It helps to share what you have tried, and where you are stuck, so people can take it from there. – gnometorule Mar 3 at 3:46
I see you have some answers, but I cannot understand really what your question is. –... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/75031/solving-quadratic-diophantine-equations | # Solving quadratic diophantine equations
I hope it's not inappropriate asking this here. I stumbled upon this site recently while researching a Project Euler problem, now I figure I'd use it to ask about a recurring theme in these problems: quadratic Diophantine equations.
I've recently boiled down another Project E... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=663388 | Physics Forums
Please help with calculation involve solid angle.
This is only an example from Kraus Antenna 3rd edition page 404. The question is really a math problem involves calculation of ratio of solid angles. Just ignore the antenna part. this is directly from the book:
Example 12-1.1 Mars temperature
The inc... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/39312?sort=votes | ## Smallest non-isomorphic strongly regular graphs
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Motivation: I want to see how the 3-dimensional Weisfeiler-Lehman algorithm (see Logical complexity of graphs, p. 14) distinguishes between two non-isomorphic st... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/5955/how-can-we-determine-if-two-discrete-logarithms-are-equal/5957 | How can we determine if two discrete logarithms are equal?
Let $p$ be a prime number, and let $g_{1},g_{2},...,g_{n}$ be $n$ generator of $Z^{*}_{p}$. We have a list $y_{1},y_{2},\dotsc,y_{n}$ of elements in $Z^{*}_{p}$ such that for every $i\in \lbrace1,2,\dotsc,n \rbrace$ we have $y_{i}=g_{i}^{x_{i}} \bmod p$ for so... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/31629/advantages-of-working-with-cw-complexes-spaces-over-kan-complexes-simplicial-sets/31638 | ## Advantages of working with CW complexes/spaces over Kan complexes/simplicial sets?
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Many topologists express a clear preference for working with CW complexes instead of simplicial sets.
One of the reasons is t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://quant.stackexchange.com/questions/1833/duality-between-constant-rebalanced-portfolio-crp-and-corresponding-derivative/1922 | # Duality between constant rebalanced portfolio (CRP) and corresponding derivative
One of the greatest achievements of modern option pricing theory is finding corresponding dynamical trading strategies in linear instruments with which you can replicate and by that price derivative instruments; of course the most promi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/280876/definition-of-a-peculiar-quotient-group-of-isometries | # Definition of a peculiar quotient group of isometries
I just wrote a text file to sum up my ideas about the Riemann Hypothesis. This text is a draft, and I don't expect people here to say if this approach is interesting or not (but if by chance you think so, please let me know). My question is about the definition o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 104, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/tagged/banach-spaces+real-analysis | # Tagged Questions
1answer
70 views
### Is $(\ell^1 , \| \cdot \| )$ a Norm space?
Suppose $x= \{x_n \} \in \ell^ 1$ and $\| x \| = \sup | \sum_{k=1}^n x_k |$, let $\|x\|_1 = \sum_{n=1}^{\infty} |x_n |$ is a norm for $\ell^1$ . Is $(\ell^ 1 , \| \cdot \| )$ a Normed ...
0answers
35 views
### Integration for functio... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 220, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://stats.stackexchange.com/questions/1478/testing-implementation-of-anderson-darling-test-for-uniform-rv/1510 | # Testing implementation of Anderson-Darling test for uniform RV
I am trying to write unit tests for a whole mess of statistics code. Some of the unit tests take the form: generate a sample following a null hypothesis, use code to get a p-value under that null, repeat hundreds of times, then look at all the p-values: ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/MSbar_scheme | # Minimal subtraction scheme
(Redirected from MSbar scheme)
In quantum field theory, the minimal subtraction scheme, or MS scheme, is a particular renormalization scheme used to absorb the infinities that arise in perturbative calculations beyond leading order, introduced independently by 't Hooft (1973) and Weinberg... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/41795?sort=oldest | ## Self homeomorphisms of $S^2\times S^2$
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Every matrix $A\in SL_2(\mathbb{Z})$ induces a self homeomorphism of $S^1\times S^1=\mathbb{R}^2/\mathbb{Z}^2$. For different matrices these homeomorphisms are not homoto... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/199967/how-can-i-compute-a-posterior-distribution-using-bayes | # how can I compute a posterior distribution using Bayes?
This may be a silly question, but I cannot figure out a convincing (to myself) answer to it. Suppose that you want to buy a new car. Let $v$ be the value you attach to the car. Before visiting the dealer, you cannot tell for sure how much you value the car, i.e... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 63, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/121097/spectrum-of-a-laplacianized-matrix/121101 | ## Spectrum of a Laplacianized matrix
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Suppose that $A$ is a positive matrix and that we let $R$ be the diagonal matrix of $A$'s row-sums. What can be said about the spectrum of $R-A$? I am particularly interested... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/17157-greatest-product-sum-print.html | # Greatest product from a sum
Printable View
• July 23rd 2007, 11:33 PM
DivideBy0
Greatest product from a sum
The sum of n positive integers is 19. What is the maximum possible product of these n numbers?
Can you also please explain why this is so?
• July 24th 2007, 11:30 PM
CaptainBlack
Quote:
Originally Posted by... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 26, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/6841/list | ## Return to Answer
Post Undeleted by D. Savitt
2 deleted 255 characters in body; added 8 characters in body
Here's a strategy that I've been toying with. It seems unlikely to me that it works, but perhaps it'll inspire someone to have a better idea. Fix an embedding of $\overline{\mathbb{Q}}$ into $\mathbb{C}$, ther... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/287058/how-to-choose-x-evenly-distributed-points-from-within-an-n-ball | How to choose $x$ evenly distributed points from within an n-ball
I would like to know how to choose $x$ evenly distributed points from within an n-ball. I think a formal way of defining this is that we want to choose $x$ points from within the n-ball such that we maximize the closest distance between any two points. ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/133689/an-algebra-of-nilpotent-linear-transformations-is-triangularizable | # An algebra of nilpotent linear transformations is triangularizable
How to prove "An algebra of nilpotent linear transformations is triangularizable" using linear algebra only?
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What do you mean by triangularizable? That each element can be represented by a triangular element? – Manos Apr 19 '12 at 1:23
@Manos: Yes... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 62, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/users/17907?tab=recent | # René Pannekoek
1,092 Reputation
631 views
## Registered User
Name René Pannekoek
Member for 1 year
Seen 16 mins ago
Website
Location Leiden, The Netherlands
Age
| | | ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 110, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/87303/best-algorithm-software-for-solving-a-planar-transportation-problem | ## Best algorithm/software for solving a planar transportation problem ?
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I am looking for software (open-source or otherwise) or an implementable algorithm for solving a continuous transportation problem. The inp... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/142142/about-the-order-of-groups | # About the Order of Groups
Is there any theorem that states the all the finite groups of order n are the same? or some sort of theorem that refers to the order of two finite groups? If anyone can post a reference to this topic will be great... 10x in advance
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4
This is boldly not true for $n=4$. – Asaf Karagila Ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/53381/statistical-mechanic?answertab=active | # Statistical Mechanic
One can define entropy as $$S=k\log{\omega(E)},$$ where $\omega(E)$ is the numbers of states with energy equal $E$; and the canonical partition function for a set of N particles is defined as$$Z_N=\sum_{\phi}e^{-\beta E[\phi]}=e^{-\beta F(\beta,N)},$$ where the sum run on states $\phi$ and the f... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/102900/free-modules-over-integers/102901 | ## Free modules over integers
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After the course of linear algebra I'm more familiar with vector spaces rather than modules so my question may seem to be silly but I think it's quite natural for someone who thinks ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/4170/is-the-z-boson-one-entity-or-are-there-as-many-entities-as-decay-pairs-but-they | is the Z boson one entity or are there as many entities as decay pairs, but they are equivalent and lumped together
just wondering if it is a distinction without a difference - it seeming a bit weird that one thing can decay into different things.
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Ok, I am givin a bounty to someone able to answer setup and answer ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathforum.org/mathimages/index.php?title=The_Golden_Ratio&diff=35107&oldid=33491 | # The Golden Ratio
### From Math Images
(Difference between revisions)
| | ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/number-theory/98565-any-number-can-divides-infinity.html | # Thread:
1. ## any number can divides infinity???
Definition: An integer $b$ is said to be divisible by an integer $a \neq 0$, in symbols $a|b$, if there exists some integer $c$ such that $b=ac$.
If b is infinity $\infty$, then what are the possible a?
I think $a$ can be any number. Is it true?
2. ## according to... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 18, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/75675-binomial-expansion.html | # Thread:
1. ## Binomial expansion
Two positive integers , p and q are connected by p=q+1 . By using the binomial expansion , show that the expression $p^{2n}-2nq-1$ can be divided exactly by $q^2$ for all positive integers of n .
2. Originally Posted by thereddevils
Two positive integers , p and q are connected by ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/24822/percolation-in-a-2d-ising-model?answertab=oldest | # Percolation in a 2D Ising model
For a 2D Ising model with zero applied field, it seems logical to me that the phases above and below T_c will have different percolation behaviour. I would expect that percolation occurs (and hence there is a spanning cluster) below T_c and that it does not occur (no spanning clusters... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/192189/integrating-with-infinite-radius-semicircle | # integrating with infinite-radius semicircle
Sorry, I'm really confused on this one.... My math physics class is having us evaluate closed contours, where the contour is on the real line and at the infinities we turn towards the upper half of the space (i.e. for $z=a+ib$ we have $b>0$), anyway, the semicircle is esse... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 39, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/285030/random-walk-with-zero-drift/285045 | # Random walk with zero drift
Let $X_{k+1} = X_k+\xi_k$ be a random walk on $\Bbb R$ starting from $0$ and such that $\mathsf E\xi_0 = 0$, $\mathsf{Var}[\xi_0]>0$. Is that true that $$-\infty = \liminf_nX_n<\limsup_nX_n=\infty\quad \mathsf P\text{-a.s.}?$$
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## 1 Answer
If the variance is finite, the law of the ite... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/117131-conditions-process-martingale.html | # Thread:
1. ## Conditions for a process to be a martingale
Hi !
I'll give the introduction but it's not the main problem.
We have E a countable space of states. Q is an irreducible transition matrix. Let $(\Omega,\mathcal{F},(X_n)_n,\mathbb{P}_x)$ ( $\mathbb{P}_x$ denotes the initial probability) be the canonical M... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/7778/how-can-you-tell-if-a-critical-energy-density-is-actually-a-black-hole | # How can you tell if a critical energy density is actually a black hole?
Here's a question inspired by Edward's answer to this question.
It's my understanding that the average energy density of a black hole in its rest frame is $\rho_\text{BH}(A)$, a function of surface area. I calculated $3c^2/2GA$ for a Schwarzsch... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/8940/how-can-gravitational-forces-influence-time | # How can gravitational forces influence time?
How does it work that gravitational forces can affect time and what usable applications could arise from this?
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5
+1 good question, can we get Einstein in here? – Mark Schultheiss Apr 20 '11 at 14:48
You may be interested in the classic experiment that verified the exi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/dimensional-analysis+density | # Tagged Questions
1answer
103 views
### Gaussian integration and dimension argument
I made a mistake recently regarding the Gaussian density, by putting the determinant of the variance to the power $\frac{d}{2}$. Would the following argumentation be valid to highlight it should be to ...
3answers
92 views
### Cent... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/dimensional-analysis+symmetry | # Tagged Questions
1answer
239 views
### Understanding units and the units of the derivative operator
Suppose that $f$ is a function from unit $A$ to $B$, then what is the unit of $f'(x)$?. We can do $f'(x)\Delta x$ to get an estimate of $f(x + \Delta x)$. Since the latter has unit $B$, so has the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/133999/can-one-construct-a-non-measurable-set-without-axiom-of-choice | # Can one construct a non-measurable set without Axiom of choice?
Is axiom of choice required to show the existence of non-measurable sets? Is there a Lebesgue non-measurable set that can be constructed without axiom of choice?
Related question on MO says it is consistent: http://mathoverflow.net/questions/73902/axio... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/66613?sort=oldest | ## A toy model for the t-section problem
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Let $S(x)$ be the area of the yellow curvilinear triangle. I'd like to find a graph for which $S(x)=H(x)$ where $H$ is some prescribed function (small, smooth, vanishing n... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/78232/is-there-a-combinatorial-interpretation-of-this-triangle-sequence-is-there-a-si | ## Is there a combinatorial interpretation of this triangle sequence? Is there a “simpler” formula?
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Hi.
`$$a_{n,k} = \sum_{1 = m_1 < m_2 < \cdots < m_k = n}\ \prod_{j=2}^k S(m_j, m_{j-1})$$.
where the $S(n, k)$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 51, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/40518/subsets-of-products-of-trees/40546 | ## subsets of products of trees
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A subset of a geodesic metric space is called convex if for every two points in the subset one of the geodesics connecting these points lies in the subset. Is it true that every co... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 58, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/165979-covariance-normal-vector-x-y-distribution-z-x-2y-1-a.html | # Thread:
1. ## covariance, a normal vector (X,Y) and the distribution of Z = X - 2Y + 1
hi, I am preparing for a final in my least favorite class and could use a little help with this preparation problem.
Initially X and Y were normal with given mean and variance, and it asked for the distribution of the same Z = h... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathematica.stackexchange.com/questions/21454/how-to-define-functions-for-a-parameter-dependent-recursive-sequence | # How to define functions for a parameter-dependent recursive sequence
I am trying to generate a two variable recursive sequence
For instance on Mathematica, I did
````z[1] := {1, 1}
B := {{t, 1}, {-1, t}}
z[n_, t_] := B.z[n - 1, t]
````
When I tried to see `z[2]`, I get a bunch of gibberish.
$n$ is the variable t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/tagged/pattern-recognition+ring-theory | Tagged Questions
0answers
75 views
Multiplication structure for finite abelian rings of order $p^2$.
Consider an odd prime $p$ and a positive integer $a$ as close to 2 as possible that is not a quadratic residue $mod$ $p$. If we extend the ring $mod$ $p$ with the element $b = a^{\frac{1}{2}}$ then ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/71257/can-asymptotes-be-imaginary/71320 | # Can asymptotes be imaginary?
I'm currently learning about asymptotes and I'm trying to work out the following example:
$$f(x)=\frac{1}{x^2+1}$$
To find the vertical asymptotes, the book I'm following says that after factoring completely, you should set each factor of the denominator to $0$ and:
Every solution you... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://wikipedia.sfstate.us/Nonlinearity | edit
# Nonlinear system
(Redirected from Nonlinearity)
Not to be confused with Non-linear editing system.
This article describes the use of the term nonlinearity in mathematics. For other meanings, see nonlinearity (disambiguation).
In mathematics, a nonlinear system is one that does not satisfy the superposition pr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 32, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/20791?sort=votes | ## isomorphism of abelian varieties
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Let $A, B, C$ and $D$ be abelian varieties (over $\mathbb{C}$) such that $A \times B \cong C \times D$, and $A \cong C$. From the irreducibility of abelian varieties, we can sa... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/271205/whats-the-reason-why-this-sequence-of-function-doesnt-converge-uniformly-to-f | # What's the reason why this sequence of function doesn't converge uniformly to $f$?
Consider $f_n = \sqrt[n]{x}$ on $[0,1]$
So it converges to the step function $f = 0$ if $x = 0$ and $f=1$ otherwise
I could see why it doesn't converge if i draw an epsilon rectangle over one part since for each $n$, $f_n$ lies comp... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 121, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://crypto.stackexchange.com/questions/5345/breaking-rsa-given-a-special-kind-of-oracle-that-decrypts-related-ciphertexts-f | # Breaking RSA, given a special kind of oracle that decrypts related ciphertexts for us
Let $c=E^{RSA}_{e}(w)$ be the ciphertext belonging to the plaintext $w$ if an $RSA$ system is used. Assume that the public exponent $e$ satisfies $e \le 10$. Furthermore, assume there is an oracle that, on input $r>0$, responds wit... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/38701?sort=newest | Which group does not satisfy the Tits alternative?
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A group is said to satisfy the Tits alternative if every finitely generated subgroup of $G$ is either virtually solvable or contains a nonabelian free subgroup.
Tit... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/4749/is-there-any-physics-that-cannot-be-expressed-in-terms-of-lagrange-equations | # Is there any physics that cannot be expressed in terms of Lagrange equations?
A lot of physics, such as classical mechanics, General Relativity, Quantum Mechanics etc can be expressed in terms of Lagrangian Mechanics and Hamiltonian Principles. But sometimes I just can't help wonder whether is it ever possible (in t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues/2706 | # Making sense of principal component analysis, eigenvectors & eigenvalues
In today's pattern recognition class my professor talked about PCA, eigenvectors & eigenvalues.
I got the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 107, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://quant.stackexchange.com/questions/7202/what-do-eigenvalues-eigenvectors-of-the-yield-forward-rates-covariance-matrices/7204 | # What do eigenvalues/eigenvectors of the yield/forward rates covariance matrices mean?
I have 5 bonds (with maturities 1,2,3,4,5 years) which I calculated the yield curve for 10 days. I also calculated the forward rates from the yield rates. Now I've been told to calculate the covariance of the yield rates and the fo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/home-experiment+experimental-physics | # Tagged Questions
0answers
73 views
### Easy question about magnetism?
I have to build a simple electric motor by attaching a magnet to a battery, extending the terminals of the battery (with stiff wires so they could act as supports), and placing a coil of wire on top ...
1answer
85 views
### Whistling on bottle ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/82492?sort=newest | ## Nontrivial algorithm to check for polynomial symmetry?
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Hi.
As is known, a polynomial `$P \in K[x_1, \dots, x_n]$` is symmetric when permuting its variables always yields the same polynomial. This immediately ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/156316-solving-delta-epsilon-proof-given-epsilon-print.html | # Solving Delta Epsilon Proof (Given Epsilon)
Printable View
• September 15th 2010, 03:29 PM
penguinpwn
1 Attachment(s)
Solving Delta Epsilon Proof (Given Epsilon)
I read over the guide stickied at the top of the forum, but I did not understand the section on solving proofs when given a particular epsilon value. Coul... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/138502/what-is-the-form-of-fx/138531 | # what is the form of $f(x)$
Given that area of OPB and OPA are same, could any one help me to find the the $f(x)$
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It depends whether you are supposed to use Fundamental Theorem of Calculus. Easiest to guess answer will be $kx^2$, calculate, get $k=4/3$. – André Nicolas Apr 29 '12 at 18:12
## 2 Answers
I will th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/112258/express-weierstrass-g-2-and-g-3-in-terms-of-theta-functions-of-the-periods/112282 | ## Express Weierstrass' g_2 and g_3 in terms of theta-functions of the periods
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If E is a complex elliptic curve defined as the quotient of C over a lattice generated by w_1 and w_2, then it can be also written in... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/106522?sort=newest | ## Why can’t an explicit well-ordering of the reals be ruled out in ZF?
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The statement A = "There exists a well-ordering of the reals" is independent of ZF. My understanding is that the statement B = "There exists... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/37601/vector-calculus-integral-over-vector | # vector calculus - Integral over vector
Our physics prof wrote the following equation:
$\int\frac{\vec{r}}{r^3}d\vec{r} = \int\frac{1}{r^2}dr$
This is logical as long as I argue that $\vec{r}$ and $d\vec{r}$ are parallel, which is why the dot product evaluates as $|\vec{r}||d\vec{r}| = r dr$ However then i tried to... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/39413/list | ## Return to Question
2 added 193 characters in body; edited title; added 1 characters in body
# Intuitive Proof of Cramer's Decomposition Theorem
Cramer's Theorem decomposition theorem states that if $X$ and $Y$ are independent real random variables and $X+Y$ has normal distribution, then both $X$ and $Y$ are norma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.openwetware.org/index.php?title=User:Timothee_Flutre/Notebook/Postdoc/2012/01/02&oldid=607238 | # User:Timothee Flutre/Notebook/Postdoc/2012/01/02
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## Learn about the multivariate Norma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 40, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/107904/the-odds-3-or-more-group-elements-commute/108392 | ## The Odds 3 (or More) Group Elements Commute
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Some time ago I asked about the odds 2 group elements commute. I wonder about the odds that 3 group elements commute. Is there a "closed" formula for the sum
$$\fra... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/147840-trig-identities.html | # Thread:
1. ## Trig identities
14. a) Which equations are not identities? Justify your answers.
b) For those equations that are identities, state any restrictions on the variables.
i) $(1 - cos^2x)(1 - tan^2x) = \frac{sin^2x - 2sin^4x}{1 - sin^2x}$
Left Side
$= (1 - cos^2x)(1 - tan^2x)$
$= 1 - tan^2x - cos^2x + (-... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 77, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/5710/how-to-generate-a-random-integer-in-interval-1-2n-1-from-random-integer-in | # How to generate a random integer in interval $[1, 2^n-1]$ from random integer in interval $[0, 2^n-1]$?
For a project I am working on, I have access to a CSPRNG that outputs a random integer in the interval $[0, 2^n-1]$ for any integer $n$ greater than 0. I cannot use the zero values, so I have my RNG code in a `whi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 43, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/31247/why-do-we-need-higgs-field-to-re-explain-mass-but-not-charge | # Why do we need Higgs field to re-explain mass, but not charge?
We already had definition of mass based on gravitational interactions since before Higgs. It's similar to charge which is defined based on electromagnetic interactions of particles.
Why did Higgs need to introduce concept of universe-wide Higgs field to... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/3888/why-eg-gn-1-in-bilinear-pairings-holds?answertab=active | why $e(g,g)^N=1$ in bilinear pairings holds?
I can't get the point of prime order bilinear pairings:$\mathbb{G}\times\mathbb{G}\rightarrow\mathbb{G}_T$,$g=$ generator of $\mathbb{G}$ , $N=p*q$, $p$ and $q$ primes and $e(g,g)^N=1$. why $e(g,g)^N=1$ holds? Why is it 1?
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1 Answer
If $N$ is the order of the group $\ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/67708/depth-of-intersection | ## depth of intersection
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Hi let $I$ be an ideal in $S=K[x_1,...,x_n]$. Can we compute depth $( I \cap K[x_1,...,x_r])$ with $r \leq n$ ?? Is there any relation between depth $I$ and depth $( I \cap K[x_1,...,x_r]... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/8400/when-is-use-of-the-effective-mass-concept-appropriate | # When is use of the 'effective mass' concept appropriate?
In textbooks the characteristic length scale of an exciton, or an electron bound to dopant atom, in silicon is calculated by analogy to the vacuum case.
Bohr radius in vacuum:
$$a_0 = \frac{4 \pi \varepsilon_0 \hbar^2}{m_0 e^2} = 0.53\ {\rm Å}$$
where $\var... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/1402/is-it-possible-to-separate-the-poles-of-a-magnet/3560 | # Is it possible to separate the poles of a magnet?
It might seem common sense that when we split a magnet we get 2 magnets with their own N-S poles. But somehow, I find it hard to accept this fact.(Which I now know is stated by Gauss's Law)
I have had this doubt ever since reading about the quantum-field-theory and ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/156975/solving-p-vs-np-with-computer/157493 | # Solving P vs NP with computer
Is it possible to build a computer program that would (eventually) bring a solution to the P vs. NP question?
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## 3 Answers
Nobody knows. I suppose if there is a polynomial-time algorithm for 3-SAT (or some other NP-complete problem) then a computer could find it and prove P = NP. A... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/13831?sort=newest | ## Limit for divergent sequences
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Sorry for the title, but I think it's funny. Can you write down a homomorphism (of additive groups)
$\mathbb{R}^\mathbb{N} \to \mathbb{R}$,
which is nontrivial and whose kernel ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-math-topics/203120-prove-four-vectors-coplanar.html | # Thread:
1. ## Prove that four vectors are coplanar
I am given four vectors, A, B, C, and D, and need to show that they are coplanar.
I don't really know what to do. If it were three vectors, I know that I should scalar triple product them showing that the parallelepiped formed has zero volume, but when they add a ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/43560/understanding-the-exponential-distribution | Understanding the exponential distribution
I'm trying to wrap my head around the Exponential distribution and the meaning of its parameter. The parameter is the rate, right? So take, e.g., $$X\sim \exp(0.05)\,.$$ Now the probability of failure during the first time period is: $$P(X\le1)=1-P(X>1)=1-e^{-0.05}=0.04877\,.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/59563?sort=oldest | ## Configuration space of little disks inside a big disk
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The space of configurations of $k$ distinct points in the plane $$F(\mathbb{R}^2,k)=\lbrace(z_1,\ldots , z_k)\mid z_i\in \mathbb{R}^2, i\neq j\implies z_i\... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 32, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/9274/isomorphism-between-0-1-to-0-1 | # Isomorphism between [0,1] to (0,1)
I need to find an isomorphism between [0,1] to (0,1) can you help me with this please?
thanks. benny
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– Nuno Nov 26 '10 at 15:28
Also let me know if the tag elementary-set-theory here is inappropriate. – Nuno Nov 26 '10 at 15:36
## 6 Answers
The easiest way (if you can apply ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/2412/finding-the-lfsr-and-connection-polynomial-for-binary-sequence | # Finding the LFSR and connection polynomial for binary sequence.
I have written a C implementation of the Berlekamp-Massey algorithm to work on finite fields of size any prime. It works on most input, except for the following binary GF(2) sequence:
$0110010101101$ producing LFSR $\langle{}7, 1 + x^3 + x^4 + x^6\rang... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/250154/why-the-sets-defined-in-the-cumulative-hierarchy-transitive?answertab=oldest | # Why the Sets defined in the Cumulative Hierarchy transitive?
On Page 64, Set Theory, Jech(2006), define the following, by transfinite induction:
• $V_0=\emptyset$,
• $V_{\alpha+1}=P(V_{\alpha})$,
• $V_{\alpha}=\bigcup_{\beta<\alpha}V_\beta$, if $\alpha$ is a limit ordinal.
How can we prove $V_{\alpha}$ is transiti... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 46, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://correll.cs.colorado.edu/?p=1052 | Robots are systems that sense, actuate, and compute. So far, we have studied the basic physical principles of actuation, i.e., locomotion and manipulation. Understanding these principles is necessary to make and implement plans, e.g., using the A* or RRT for calculating shortest path for a mobile robot to travel on . S... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 3, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/2650/conjugacy-classes-in-finite-groups-that-remain-conjugacy-classes-when-restricted/2655 | Conjugacy classes in finite groups that remain conjugacy classes when restricted to proper subgroups
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In a forthcoming paper with Venkatesh and Westerland, we require the following funny definition. Let G be a finite ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/52332/linear-ode-roots-of-characteristic-equation-having-multiplicity-1 | # Linear ODE, roots of characteristic equation having multiplicity $>1$
I know the method. For a linear homogeneous ordinary differential equation with a root of the characteristic polynomial in $\alpha$ has multiplicity $k$, then $y=x^me^{\alpha x}$ with $m=0,1,\cdots k-1$ is a solution. This however was learnt from ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 14, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/differential-geometry/137644-showing-absolute-minimum.html | # Thread:
1. ## Showing absolute minimum
Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be defined by $f(x) = 2x^4+x^4\sin{1/x}$ for $x\neq0$ and $f(0)=0$ .
Show that f has an absolute minimum at $x=0$, but that its derivative has both positive and negative values in every neighborhood of 0 .
2. Originally Posted by french... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://gilkalai.wordpress.com/2009/07/17/the-polynomial-hirsch-conjecture-a-proposal-for-polymath3/?like=1&source=post_flair&_wpnonce=671450efa2 | Gil Kalai’s blog
## The Polynomial Hirsch Conjecture: A proposal for Polymath3
Posted on July 17, 2009 by
This post is continued here.
Eddie Kim and Francisco Santos have just uploaded a survey article on the Hirsch Conjecture.
The Hirsch conjecture: The graph of a d-polytope with n vertices facets has diameter a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 17, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/141424/creating-ways-to-encode-recursive-function?answertab=votes | # Creating ways to encode recursive function.
This is from an exercise in Boolos' Computability text. My problem is as follows:
I am looking for a method that encode numbers for recursive functions. Then given such an encoding for recursive functions by natural numbers, let d(x) = 1 if the one-place recursive functi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/43709?sort=oldest | ## Is the cut locus of a generic point in a hyperbolic manifold a generic polyhedron?
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Let $p\in M$ be a point in a closed riemannian manifold $M$. Recall that the cut locus of $p$ is the subset of $M$ consisting ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 64, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/44519/grovers-quantum-search-algorithm/44527 | ## Grover’s Quantum Search Algorithm
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I am confused about an extremely basic point concerning Grover's quantum search algorithm; my confusion suggests to me that maybe I've missed the entire point.
My understandi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/169584/completion-of-c-cx-with-respect-to-cdot-infty | # Completion of $C_c(X)$ with respect to $\|\cdot\|_\infty$
Notation:
All functions here are from $X$ to $\mathbb R$.
$C_c(X)$ = compactly supported continuous functions.
$C_b(X)$ = bounded continuous functions.
$B(X)$ = bounded functions.
$C_0(X)$ = continuous functions that tend to zero (so $X$ has to be locall... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 69, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://sbseminar.wordpress.com/2007/09/18/berkovich-spaces-i/ | Berkovich spaces I September 18, 2007
Posted by Scott Carnahan in characteristic p, Number theory, representation theory.
trackback
Around 1990, Berkovich discovered a rather elegant refinement of the notion of scheme that is particularly well-suited to non-archimedean analytic geometry. I feel that the ideas here... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 94, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/8649/list | ## Return to Answer
2 added 766 characters in body; added 91 characters in body; deleted 5 characters in body
For many questions, the easiest way to see the nuts and bolts of a projective variety $V \subseteq P^n$ is to look at its cone $CV \subseteq A^{n+1}$. After all, the graded ring whose Proj is $V$ is the same ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cs.stackexchange.com/questions/6771/lr1-items-look-ahead | LR(1) - Items, Look Ahead
I am having diffuculties understanding the principle of lookahead in LR(1) - items. How do I compute the lookahead sets ?
Say for an example that I have the following grammar:
S -> AB A -> aAb | b B -> d
Then the first state will look like this:
````S -> .AB , {look ahead}
A -> .aAb, {loo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/121066/inequality-with-eulers-totient-function/121100 | ## Inequality with Euler’s totient function
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Numerical analysis of the first several hundred n suggests the following inequality:
$\varphi(3^n-2) \ge 2\cdot3^{n-1}$
-
Up to a small additive factor, your inequali... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/56589/calculating-the-mass-equivalency-of-a-song?answertab=oldest | # Calculating the mass equivalency of a song?
I've recently become fascinated with the idea of sound energy having a theoretical equivalent mass. I've read over this thread:
Do light and sound waves have mass
I understand this part: $m_{eq}=E/c^2$ and $E=A\rho \xi^2\omega^2$
Where I am getting tripped up is the way... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/54758/does-the-following-series-converge/54892 | ## Does the following series converge?
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Does the following series converge? $\sum_{n=1}^{\infty} \vert \sin n \vert ^{n}$
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1
Probably not. If instead of taking sin n, you take at the n'th stage sin x_n where x_... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 35, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/103470/how-can-i-find-the-number-of-the-shortest-paths-between-two-points-on-a-2d-latti | # How can I find the number of the shortest paths between two points on a 2D lattice grid?
How do you find the number of the shortest distances between two points on a grid where you can only move one unit up, down, left, or right? Is there a formula for this?
Eg. The shortest path between $(0,0)$ and $(1,1)$ can be ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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