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http://mathoverflow.net/questions/77014/recovering-the-alexander-polynomial-from-ocneanus-homflypt/77023 | ## Recovering the Alexander Polynomial from Ocneanu’s HOMFLYPT
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Let $H_q(n)$ denote the Hecke algebra associated to the symmetric group $S(n)$: this is the $\mathbb{Z}[q^{\pm 1/2}]$ algebra generated by $T_1, \ldo... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/234562/domain-codomain-and-range/234565 | # Domain, codomain, and range
This question isn't typically associated with the level of math that I'm about to talk about, but I'm asking it because I'm also doing a separate math class where these terms are relevant. I just want to make sure I understand them because I think I may end up getting answers wrong when 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": 62, "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/100676/uniformity-on-a-convex-subspace-of-mathbbrn | Uniformity on a convex subspace of $\mathbb{R}^n$
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Let's consider a set of points (in cartesian coordinates) in a convex subspace of $\mathbb{R}^n$ and more precisely in a subspace of the standard (n-1)-simplex ($x_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": 7, "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/112079?sort=votes | ## What is Gödel’s pairing function on ordinals?
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I find many references to Gödel's pairing function on ordinals but I have not found a definition. What is it?
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## 3 Answers
Define an order on pairs of ordinal... | {"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": 73, "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/101676/proof-of-no-simple-group-of-order-992 | # Proof of no simple group of order 992
Prove there are no simple groups of order $992$.
Factorise it. $31 \times 2^5$ so you have $|G|=31 \times 2^5 \geq n_{31}(31-1)+ n_{2}(2^5-1)+1$
Putting it in Sylow theorem. So how do you get the contradiction? Or is this totally wrong.
I need to use Sylow theorem to prove 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": 50, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://maherararblog.com/ | LTE, WIMAX, MIMO, MATLAB
• ### Motorola’s 4TXx8RX LTE eNB May be the...
Since my last post I have been surfing the Internet looking for a commercial LTE basestation that would satisfy the bandwidth-hungry applications such as HD video conferencing and HD video streaming. Motorola seems to be the only company that has... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.nag.com/numeric/cl/nagdoc_cl23/html/G01/g01intro.html | # NAG Library Chapter Introductiong01 – Simple Calculations on Statistical Data
## 1 Scope of the Chapter
This chapter covers three topics:
• summary statistics
• statistical distribution functions and their inverses;
• testing for Normality and other distributions.
## 2 Background to the Problems
### 2.1 Summar... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 92, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/76820/why-t-mathbbs2-otimes-t-mathbbs2-is-trivial/76825 | # Why $T\mathbb{S}^{2}\otimes T\mathbb{S}^{2}$ is trivial?
I encountered this problem in an homework problem set of algebraic topology. Naturally I thought about Bott Periodicity which implies $K(\mathbb{S}^{2})\cong \mathbb{Z}$. But I am beware that we are working in $KO$ theory instead of $K$ theory, so this is not ... | {"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": 26, "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/29673/modeling-stochastic-process-with-frequency-dependent-power-spectrum | # Modeling stochastic process with frequency-dependent power spectrum
I'm trying to model of Johnson-Nyquist noise propagation in a nonlinear circuit. An ideal (linear) resistor can be modeled very nicely by the Fokker-Planck equation (equivalently, the drift-diffusion equation), where charge $V/R$ flows through the 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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/127377-prove-definition-e.html | # Thread:
1. ## Prove the definition of e
Prove that
$lim_{h-->0}$ $(1+h)^{1/h}$= e
given that: If g is continuous at c and f is continuous a g(c), then the composition f o g is continuous at c
2. Originally Posted by wopashui
Prove that
$lim_{h-->0}$ $(1+h)^{1/h}$= e
given that: If g is continuous at c and f is c... | {"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://math.stackexchange.com/questions/8157/if-a-set-contain-2n1-elements-and-if-the-number-of-subsets-which-contain-at | # If a set contain $(2n+1)$ elements and if the number of subsets which contain at most n elements is 4096, then what is the value of $n$?
If a set contain $(2n+1)$ elements and if the number of subsets which contain at most n elements is 4096, then what is the value of $n$?
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I recently found a nice proof for the 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": 13, "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/7914?sort=oldest | ## Torsion line bundles with non-vanishing cohomology on smooth ACM surfaces
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I am looking for an example of a smooth surface $X$ with a fixed very ample $\mathcal O_X(1)$ such that $H^1(\mathcal O(k))=0$ for all ... | {"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/31271/approximation-with-continuous-functions/31366 | ## Approximation with continuous functions
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Is it true that for every function $\mathbb{R} \to \mathbb{R}$ there exists a sequence of continuous functions $f_n(x): \mathbb{R} \to \mathbb{R}$ such that for any $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": 53, "mathjax_display_tex": 1, "mathjax_asciimath": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/tags/binary-options/hot | # Tag Info
## Hot answers tagged binary-options
10
### Do binary options make any sense?
The text of your question doesn't actually match the question title. The answer to your title is of course yes binary options make sense. And as others have pointed out with binary options your reward is limited, and conversely... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Continuum_hypothesis | # Continuum hypothesis
In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis, advanced by Georg Cantor in 1878, about the possible sizes of infinite sets. It states:
There is no set whose cardinality is strictly between that of the integers and that of the real numbers.
Establishing the truth or ... | {"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": 34, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/24295/relationship-between-the-angle-of-the-floor-and-the-angular-velocity-in-a-bank?answertab=oldest | # Relationship between the “angle of the floor” and the angular velocity in a banked turn?
Wel, imagine that you're in a carousel, and the floor is, let's say at $\theta=0$ so it's totally horizontal, if $\theta=90$ the floor would be vertically.
The object put above the floordoesn't move until the carousel starts.
... | {"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://m-phi.blogspot.com/2011/08/every-thing-is-what-it-is-and-not.html | # M-Phi
A blog dedicated to mathematical philosophy.
## Saturday, 13 August 2011
### "Every thing is what it is, and not another thing"
In general, I'm not keen on reductionism. Bad for the health. That isn't to say we don't know how to reduce $A$s to $B$s (or, reduce theory $T$ in $L$ to theory $T^{\prime}$ in $L^... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/7542/how-to-perform-goodness-of-fit-test-and-how-to-assign-probability-with-uniform/7547 | # How to perform goodness of fit test and how to assign probability with uniform distribution?
I have to demonstrate that a generator of VoIP calls generates calls uniformly distributed between callers. In particular the distribution is the uniform (min, max) one where the volume per caller distribution is uniformly ... | {"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://mathhelpforum.com/algebra/197463-finding-polynomials-lowest-possible-degree-satisfy-given-condition-print.html | # Finding polynomials of the lowest possible degree that satisfy a given condition
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• April 17th 2012, 03:23 PM
LJoe21
Finding polynomials of the lowest possible degree that satisfy a given condition
Hello there,
I need to find the polynomials $f(x)$ and $g(x)$, which are of the lowest possible degree ... | {"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://mathhelpforum.com/differential-geometry/130569-interior-compact-subet-c-0-empty.html | # Thread:
1. ## Is the interior of a compact subet of C^0 empty?
This question is very similar to one I asked here: http://www.mathhelpforum.com/math-he...ons-empty.html
Let C0 be the set of continuous functions (from [a,b] to R) and a subspace of Cb, the set of bounded functions (from [a,b] to R), defined with 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/24492/upper-critical-dimension-in-field-theory | # upper critical dimension in field theory
Is there field theory which describe a second order phase transition without upper critical dimension ? Mermin-Wagner says something about lower critical dimension but nothing about upper dimension.
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You need a way to declare that two field theories in different dimensions ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/business-math/177340-sinking-fund.html | # Thread:
1. ## Sinking fund
Hi,
I’m trying to solve this problem;
A bank has three types of account in which the interest rate depends on the amount invested. The ordinary account offers a return of 6% and is available to any customer. Extra account offers 7%, only available to customers with 5,000\$ or more to inv... | {"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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/110636/books-on-analytic-functions-on-banach-spaces-over-a-non-archimedean-field/110674 | ## Books on analytic functions on Banach spaces over a non-Archimedean field
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I'm looking for good textbooks on analytic functions on Banach spaces over a non-Archimedean field. If you know one(s), please let me 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": 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/69179/integration-by-parts-for-a-general-negative-definite-self-adjoint-operator/69648 | Integration by parts for a general negative-definite self-adjoint operator.
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I suspect I am asking a very stupid question.
Suppose you have self-adjoint negative-definite operator $L$ densely defined on a space $L^2(... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 80, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/10592/how-to-calculate-tridiagonal-approximate-covariance-matrix-for-fast-decorrelati/10638 | # How to calculate tridiagonal approximate covariance matrix, for fast decorrelation?
Given a data matrix $X$ of say 1000000 observations $\times$ 100 features, is there a fast way to build a tridiagonal approximation $A \approx cov(X)$ ?
Then one could factor $A = L L^T$, $L$ all 0 except $L_{i\ i-1}$ and $L_{i i}$, ... | {"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": 33, "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/21459/bourbaki-exercise-on-connected-sets | # Bourbaki exercise on connected sets
This is Exercise I.11.4 of Bourbaki's General Topology.
Let $X$ be a connected space.
a) Let $A$ be a connected subset of $X$, $B$ a subset of $\complement A$ which is both open and closed in $\complement A$. Show that $A\cup B$ is connected.
b) Let $A$ be a connected subset 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": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/173846-set-theory-show-these-equivalent-print.html | # Set theory: Show these are equivalent.
Printable View
• March 8th 2011, 07:34 AM
Showcase_22
Set theory: Show these are equivalent.
Quote:
Show that the following are equivalent:
a). $A$ is finite
b). $A$ admits a well order <whose inverse> is also a well-order.
c). The structure $(\mathcal{P}(A), \subset_{\mathc... | {"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": 32, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/38002-expanding-binomials-print.html | # expanding binomials
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• May 11th 2008, 01:52 PM
Nick87
expanding binomials
Promise no more questions today! ^_^
The reason I'm stuck on these is because I've completely forgotten what im doing, after returning to these from months ago.
I need to:
1) Express $x^2 - 8x + 15$ in the form $(x + a )^2 + ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 32, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/11904/why-arent-there-compression-waves-in-electromagnetic-fields | # Why aren't there compression waves in electromagnetic fields?
I just started learning about optics, and in the book I'm reading they explain how the electrical field caused by a single charged particle could be described by a series of field lines, and compare them to ropes, to provide an intuition of the concept.
... | {"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://math.stackexchange.com/questions/74298/different-results-for-row-reduction-in-matlab?answertab=votes | # Different results for row reduction in Matlab
Consider the following matrix: $\left[ \begin{array}{ccc} -0.05 & 0.45 & 0 \\ 0.05 & -0.45 & 0 \end{array} \right]$
Row reducing the above matrix in Matlab using the rref() function produces what I would expect (just adding top row to bottom row and scaling top row): $\... | {"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://physics.stackexchange.com/questions/32871/simple-pde-vs-string-theory?answertab=oldest | # Simple PDE vs String Theory
For the sake of simplicity, I’d like to believe that there is one master non-linear partial differential equation governing physics. In particular, consider a Klein-Gordon form:
$$\frac{\partial^2 f}{\partial t^2}=v^2 \left (\frac{\partial^2 f}{\partial x^2}+\frac{\partial^2 f}{\partial ... | {"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://mathhelpforum.com/number-theory/184931-another-quadratic-reciprocity-problem-print.html | # Another quadratic reciprocity problem
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• July 21st 2011, 04:02 PM
alexmahone
Another quadratic reciprocity problem
For which positive integers n do there exist integers x and y such with (x, n) = 1, (y, n) = 1, such that $x^2+y^2 \equiv 0\ (mod\ n)$?
• July 21st 2011, 05:04 PM
alexmahone
Re: Another q... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/217022/how-to-tackle-markov-chains-with-transition-cost | How to tackle markov chains with transition cost?
A simple example would be:
I have 3 states, A,B,C
The transition matrix for the chain is:
```` A B C
A 0.1 0.3 0.6
B 0.4 0.2 0.4
C 0.5 0.2 0.3
````
and the transition cost matrix is:
```` A B C
A 3 5 1
B 6... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://xianblog.wordpress.com/2012/09/13/abc-as-knn/ | # Xi'an's Og
an attempt at bloggin, from scratch…
## ABC as knn…
Gérard Biau, Frédéric Cérou, and Arnaud Guyader recently posted an arXiv paper on the foundations of ABC, entitled “New insights into Approximate Bayesian Computation“. They also submitted it to several statistics journals, with no success so far, 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/36268/list | ## Return to Answer
2 fix typo
(this is a variation on Darij's answer)
Note that "holomic" holonomic" generating functions $f(x)$, i.e. generating functions satisfying a linear differential equation with polynomial coefficients (in $x$) enjoy rich closure properties.
For a (very brief) summary, see Table 1 of a pape... | {"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://math.stackexchange.com/questions/161479/name-of-proof-that-area-of-squarearea-of-rectangle-of-the-same-perimeter/161639 | Name of proof that area of square>area of rectangle of the same perimeter
What is the proof called for the fact that the area of a square is always greater than the area of a non-square rectangle of the same perimeter?
-
1
How about this: "Proof of the fact that area of a square>area of a rectangle of the same perim... | {"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": 21, "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/24859/finding-the-union-of-n-random-circles-arbitrarily-or-conspiratorially-placed-on/96364 | ## Finding the union of N random circles arbitrarily (or conspiratorially) placed on a two-dimensional surface
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Please consider a two-dimensional surface populated with a set of Cartesian coordinates $(x_i, y_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": 10, "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/Canonical_ensemble | # Canonical ensemble
Statistical mechanics
• NVE Microcanonical
• NVT Canonical
• µVT Grand canonical
• NPH Isoenthalpic–isobaric
• NPT Isothermal–isobaric
• µVT Open statistical
Models
Scientists
This article . Relevant discussion may be found on Talk:Canonical ensemble. Please improve it by verifying the claims mad... | {"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": 78, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/68647/understanding-the-wiki-page-on-verdier-duality/94478 | ## Understanding (the wiki page on) Verdier duality
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My familiarity with concepts related to derived categories is only tangential, and little by little I intend to get more comfortable with them. I was playing ar... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/59180/list | ## Return to Answer
2 added 2 characters in body; deleted 6 characters in body
This is of the "to puzzle graduate students" variety, but I was taken enough with it to write it up in a short note:
Let $V$ be a vector space over a field $F$, of dimension at least $2$, and consider coverings $\mathcal{C} = \{W_i\}$(W_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": 13, "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/63278?sort=newest | ## Complexity of computing matrix rank over integers
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Does computing the rank of an integer matrix have complexity polynomial in the size of the input?
The Gaussian elimination algorithm is polynomial in the numb... | {"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://mathhelpforum.com/advanced-algebra/2466-when-lr-not-complete-space.html | # Thread:
1. ## When is lR NOT a complete space?
Hey all!
I was wondering... Everywhere I see examples of completes spaces, I also see that $\mathbb{R}$ is complete with the usual metric. That's fine with me, but I was wondering why I see no example of a metric for which $\mathbb{R}$ is not complete.
For those wond... | {"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://mathhelpforum.com/advanced-math-topics/174027-what-cyclonical-curve.html | # Thread:
1. ## What is a Cyclonical curve?
Hi everyone,
Recently in a problem I encountered the word cyclonical curve. Do you have any idea what this is? One of the ideas that I thought of is a cyclone can be approximated to a spiral. But then there are many different kind of spirals.......
2. 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": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/92747/list | Return to Answer
2 corrected two typos
The answer is no: for example, $k[[x]]\otimes_k k((x))$ is not noetherian.
Indeed, if it were, so would be $k((x))\otimes_k k((x))$.
But this would contradict the following interesting general theorem of Vámos:
Given an extension of fields $K/F$ the tensor product $K\otimes_F 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": 12, "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/61185/are-there-any-results-about-equation-over-rational-field-or-the-extension-qx | ## are there any results about equation over rational field or the extension Q[x]?
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Given a polynomial $p(x)\in \mathbb{Q}[x]$, it is known that its roots can be obtained in terms of the coefficients of the polyno... | {"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/revisions/19724/list | ## Return to Answer
1 [made Community Wiki]
Vague definition of canonical:
Let $X$ and $Y$ be collections (often sets) for which assumptions has been made (has been given structures and/or are related somehow). A function $f\colon X \to Y$ is canonical if it is given by a rule using only the already given structure.... | {"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://terrytao.wordpress.com/tag/russells-paradox/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Tag Archive
You are currently browsing the tag archive for the ‘Russell’s paradox’ tag.
## The “no self-defeating object” argument, and the vagueness paradox
2 November, 2010 in ex... | {"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": 1, "mimetex.cgi": 0, "/images/mat... |
http://mathinsight.org/conservative_vector_field_determine | # Math Insight
• Top
• Tests
• In threads
• Notation
When printing from Firefox, select the SVG renderer in the MathJax contextual menu (right click any math equation) for better printing results
### How to determine if a vector field is conservative
#### Suggested background
A conservative vector field (also calle... | {"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": 96, "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/24181?sort=oldest | ## Representations of Pin vs. Representations of Clifford
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This may be total nonsense. But I need to know the answer quickly and I am too tired to think about it thoroughly. Let $k$ be a positive integer. Roe's "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": 71, "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/57252/convex-polynomial-homogenization-and-convexity | ## Convex polynomial homogenization and convexity
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I have a polynomial that I know to be convex. If I homogenize the polynomial, is the resulting homogeneous polynomial also convex? I know that the perspective 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": 21, "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/Inertial_frames | # Inertial frame of reference
(Redirected from Inertial frames)
It has been suggested that be merged into this article. (Discuss) Proposed since March 2013.
Classical mechanics
Branches
Formulations
Fundamental concepts
Core topics
Scientists
In physics, an inertial frame of reference (also inertial reference frame... | {"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": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/21237/calculating-statistical-power | # Calculating statistical power
As I understand it, I need to know at least three aspects (out of four) of my proposed study in order to conduct power analysis, namely:
• type of test - I intend to use Pearson's r and ANCOVA/Regression - GLM
• significance level (alpha) - I intend to use 0.05
• expected effect size -... | {"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://en.wikipedia.org/wiki/Binary_symmetric_channel | # Binary symmetric channel
A binary symmetric channel (or BSC) is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit (a zero or a one), and the receiver receives a bit. It is assumed that the bit is usually transmitted correctly, but 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 219, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/47504?sort=votes | Intersection Cohomology of Coordinate Hyperplanes
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I'm trying to learn how to compute stalks of IC sheaves, and I was wondering about the following example:
Fix $n$. Let $X \subset \mathbb{C}^n$ be the variety cut ou... | {"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": 31, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/43984/list | Return to Answer
3 Corrected a switch between N and n in the Khovanskii bound
To expand on David's answer, the bound given by Khovanskii's theorem is of the form $2^{\binom{N}{2}} (N+1)^n$ n+1)^N\$ per quadrant (more or less). Incremental improvements on this bounds have been obtained http://arxiv.org/abs/1010.2962 b... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "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/35644/do-we-live-in-a-world-with-4-or-more-dimension | # Do we live in a world with 4 or more dimension?
A NOVA show have told the audience that we are live in 3 dimensional world, the world we lived in is compose by 3 element: the energy, matter, space. By the time Einstein have invented the 4-dimensional model including the time element, why no one claim that we actuall... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/homework+velocity | # Tagged Questions
0answers
36 views
### A space vehicle travelling at a velocity of 1296 (km/h) separates by a controlled explosion into two sections of mass 7276 (kg) and 236 (kg) [closed]
A space vehicle traveling at a velocity of 1296 (km/h) separated by a controlled explosion into two sections of mass 7276 (kg)... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/57153/conditional-density-of-two-jointly-gaussian-random-vectors | # Conditional density of two jointly gaussian random vectors
In my estimation theory textbook, the following is stated as a reminder without any further explanation:
Consider the gaussian random vector $\bf{z} = \begin{pmatrix}\bf{x} \\ \bf{y}\end{pmatrix}$ with mean $\hat{z} = \begin{pmatrix}\hat{x} \\ \hat{y}\end{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": 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/113250/the-area-of-the-superellipse?answertab=active | # The area of the superellipse
I'm watching this video, where D. Knuth explains the connection of $\pi$ and factorials, and other matters (it is very interesting). Almost at the end of the talk he says the area of the superellipse
$$x^{\frac{1}{\alpha}}+y^{\frac{1}{\alpha}}=1$$
is given by
$$A(\alpha) = \frac{2 \al... | {"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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/2615?sort=newest | Least number of charts to describe a given manifold
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Hello, I'm wondering if there is a standard reference discussing the least number of charts in an atlas of a given manifold required to describe it.
E.g. a circle ... | {"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/113858?sort=votes | ## Is there an algebraic geometry analogue of the closed graph theorem?
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In functional analysis, the closed graph theorem asserts that if a linear map $T: X \to Y$ between two Banach spaces $X, Y$ has a closed gra... | {"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://physics.stackexchange.com/questions/tagged/calabi-yau | # Tagged Questions
The calabi-yau tag has no wiki summary.
1answer
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### Is the opening of the NOVA program a Calabi-Yau space?
Is the opening of the NOVA program on PBS a Calabi-Yau space?
0answers
84 views
### Calabi Yau compactification based on U(1) charges
In Green-Schwarz-Witten Volume 2, chapter 15... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "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/2543/square-root-of-symmetric-matrix-and-transposition | square root of symmetric matrix and transposition
I have a symmetric matrix A. How do I compute a matrix B such that $B^tB=A$ where $B^t$ is the transpose of $B$. I cannot figure out if this is at all related to the square root of $A$.
I've gone through wikimedia links of square root of a matrix.
-
3
– alex Aug 15 ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/94691/why-is-the-pullback-completely-determined-by-d-f-ast-f-ast-d-in-de-rham-co | # Why is the pullback completely determined by $d f^\ast = f^\ast d$ in de Rham cohomology?
Fix a smooth map $f : \mathbb{R}^m \rightarrow \mathbb{R}^n$. Clearly this induces a pullback $f^\ast : C^\infty(\mathbb{R}^n) \rightarrow C^\infty(\mathbb{R}^m)$. Since $C^\infty(\mathbb{R}^n) = \Omega^0(\mathbb{R}^n)$ (the sp... | {"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/228954/an-inequality-like-the-triangle-inequality | # an inequality like the triangle inequality
Its easy question, but I cannot find the name of the inequality. Please provide me with it.
I am doing the following, let $a$ be $n$-dimentional vector. Let $b_i, i=1, \ldots, n$ be positive numbers. Then, $$\left(\left|\sum_{i=1}^n a_i\right|^p\right)^{1/p}=\left(\left|\s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/18321-polynominal-print.html | # Polynominal
Printable View
• September 1st 2007, 07:54 AM
Ununuquantium
Polynominal
Determine all polynominals $P(x)$ (real coeffitients of course) such that for arbitrary number $x$ there is:
$P(x^{2})\times P(x^{3}) = (P(x))^{5}$
• September 2nd 2007, 08:42 AM
ThePerfectHacker
Quote:
Originally Posted by Ununuqu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 79, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/44826/proca-equation-question?answertab=votes | # Proca equation question
i'm having trouble understanding the Proca equation
$$(g_{\mu\nu}(\Box+\mu^2)-\partial_{\mu}\partial_{\nu})\varphi^{\nu}=0$$
where $g_{\mu\nu}$ is the metric and $\mu$ is a parameter. Where is the wrong assumption?
$$(g_{\mu\nu}(\partial_{\mu}\partial^{\mu}+\mu^2)-\partial_{\mu}\partial_{\... | {"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": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/56077-gcd-polynomials.html | # Thread:
1. ## GCD of polynomials
Hello,
could you help me understand the procedure of finding the GCD of two polynomials step by step, using the Euclidean Algorithm?
For example
$a = x^3 - 3x +2 , b = x - 1$
Thanks.
2. Originally Posted by drthea
Hello,
could you help me understand the procedure of finding the GCD... | {"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://mathhelpforum.com/advanced-algebra/130887-prove-there-matrix-b-print.html | # Prove there is a matrix B
Printable View
• February 26th 2010, 09:24 AM
Runty
Prove there is a matrix B
Let $A$ be an $m\times n$ matrix and suppose that $X$ is an $n\times p$ matrix such that every column of $X$ is in the column space of $A$. Prove there is a matrix $B$ such that $AX=B$
[Hint: we know that the equ... | {"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://math.stackexchange.com/questions/198404/is-this-scenario-possible-and-if-so-find-the-equation-of-the-hill/198454 | # Is this scenario possible and if so, find the equation of the hill
Assume a ball is placed on a hill and the time is measured for the ball to reach the ground (y=0). If the time taken for the ball to reach the ground is independent on the position the ball is placed on the hill, determine the equation or set of poss... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/18890/how-to-visualize-points-on-a-high-dimensional-3-manifold | # How to Visualize points on a high dimensional (>3) Manifold?
Are there any ways to visualize(plot/draw) points on a high dimensional (ex: dimension = 5) manifold?
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4
Heh, there's a joke about that. An engineer goes with a mathematician friend to a geometry seminar. Afterwards, the mathematician asks him what he 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": 7, "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/59812/are-gits-good-categorical-quotients-just-locally-ringed-space-coequalizers | ## Are GIT’s good categorical quotients just locally ringed space coequalizers?
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Introduction: The definition of "good categorical quotient" in geometric invariant theory (given below) seems fairly ad hoc to me, 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": 49, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/statistics/203850-proof-semi-graphoid-symmetry-axiom.html | # Thread:
1. ## Proof of semi-graphoid symmetry axiom
I have some trouble understanding why this proof is a proof:
Lemma:
$I_p(X, Z, Y) \iff I_p(Y, Z, X)$
Proof:
$I_p(X, Z, Y) \iff P(C_x | C_y \land C_z) = P(C_x | C_z)$
Ok, this is just conditional independence, x independent of y given z.
$\iff \frac{P(C_x \land C... | {"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://mathoverflow.net/revisions/76500/list | ## Return to Answer
2 edited body
The dimension of $S_{21}(V)$ is $(n+1)n(n-1)/3$; it is only $8$ if $n=3$. The other half of Schur Weyl duality says that $S_{21}(V)$ is a $GL_n$ (not $S_n$) S_3$) irrep; namely, the one which is indexed by the partition$(2,1)$. Similarly,$\mathrm{Sym}^3(V)$and$\bigwedge^3 V$have dime... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/133800-vector-problem.html | # Thread:
1. ## vector problem
Describe the shape of the intersection of the plane z=-3 and the plane y=z in three space. I drew out a diagram of z=-3 but im not sure what to do with y=z i know that from what i've learned, every point on y is equal to a point on z and that the x coordinates can be any value.
2. Orig... | {"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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/178741/additive-quotient-group-mathbbq-mathbbz-is-isomorphic-to-the-multiplicat/178771 | # Additive quotient group $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the multiplicative group of roots of unity
I would like to prove that the additive quotient group $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the multiplicative group of roots of unity.
Now every $X \in \mathbb{Q}/\mathbb{Z}$ is of the form $\frac{p}{q} ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 54, "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/66954/collapsing-cyclic-quotient-singularities | ## Collapsing Cyclic quotient Singularities
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Let $X$ be a surface with cyclic quotient singularities, and let $f:X\rightarrow Y$ be a birational morphism with exceptional locus $E$. Assume $E\cong\mathbb{P}^{1}$, ... | {"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://physics.stackexchange.com/questions/21793/entropy-change-in-a-cycle-with-two-isochoric-and-two-adiabatic-processes?answertab=active | # Entropy change in a cycle with two isochoric and two adiabatic processes [closed]
Prove that the change of Entropy in a cycle with two isochoric and two adiabatic processes is 0. How can I prove that? Thanks!
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Welcome to Physics! This is a site for conceptual questions about physics, not general homework help. If... | {"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://nrich.maths.org/5952/solution?nomenu=1 | ## 'Escape from Planet Earth' printed from http://nrich.maths.org/
### Show menu
Steven from City of Sunderland College sent us in a wonderful, complete solution to this problem, which we recommend reading in full to any budding problem solver. The main points are as follows:
The gravitational potential energy of 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": 20, "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/81963/regular-functions-on-slodowy-slices | ## Regular Functions on Slodowy Slices
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I recently learned that there is a natural identification, given a simple Lie algebra,
Polynomial functions on the Slodowy slice of a regular nilpotent orbit $\simeq$ polyn... | {"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://math.stackexchange.com/questions/117351/the-lebesgue-differentiation-theorem-holds-for-any-measure | # The Lebesgue differentiation Theorem holds for any measure?
What are the assumptions to a measure to the Lebesgue Differentiation Theorem be True?
What is(if there is) a practical way to find the decomposition of a measure $\lambda$ in relation to a measure $\mu$?
OBS: I am only interested on non negative measure,... | {"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/53988/what-is-the-motivation-for-a-vertex-algebra/54029 | ## What is the motivation for a vertex algebra?
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The mathematical definition of a vertex algebra can be found here:
http://en.wikipedia.org/wiki/Vertex_operator_algebra
Historically, this object arose as an 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": 31, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/19911/list | ## Return to Answer
3 added 62 characters in body
Here is a general trick that you can use to make yourself look like you have an amazing memory.
Start with a finite abelian group $(G,+)$ in which you are comfortable doing arithmetic. Be sure to know the sum $$g^* = \sum_{g \in G} g.$$
Take a set $S$ of $|G|$ physi... | {"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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/174020/prove-or-disprove-lim-limits-n-to-infty-p-n1-p-n-sqrtp-n-0/175112 | Prove or disprove $\lim\limits_{n \to \infty} (p_{n+1} - p_{n})/\sqrt{p_n} = 0$
Can anyone prove or disprove the following statement?
$$\lim_{n \to \infty} \frac{p_{n+1} - p_{n}}{\sqrt{p_n}} = 0.$$
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13
I'm guessing $p_n$ is meant to the be $n$th prime? Ideally, one should not be forced to guess, though, and the go... | {"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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/754/is-the-following-statement-about-prg-true-or-false/789 | # Is the following statement about PRG true or false?
Is the following statement true?
If $G: \{0,1\}^k \rightarrow \{0,1\}^n$ is a PRG, then so is $G':\{0,1\}^{k+l} \rightarrow \{0,1\}^{n+l}$ defined as $$G'(x.x')=G(x).x'$$ where $x \in \{0,1\}^k$ and $x' \in \{0,1\}^l$. We are using $.$ to denote concatenation.
My... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/forces?page=3&sort=newest&pagesize=15 | # Tagged Questions
This tag is for the classical concept of forces, i.e. the quantities causing an acceleration of a body. It expands to the strong/electroweak force only insofar as they act comparable to ‘classical’ forces. Use [tag:particle-physics] for decay channels due to forces and [tag:newtonian-mechanics] or .... | {"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://mathoverflow.net/questions/14376?sort=votes | ## Why is addition of observables in quantum mechanics commutative?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am no expert in the field. I hope the question is suitable for MO.
Background/Motivation
I once followed a quantum mechanics course aimed at... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/34063/what-is-the-maximum-surface-charge-density-of-aluminum?answertab=active | # What is the maximum surface charge density of aluminum?
I understand that the maximum free charge carrier density for aluminum has been measured using the Hall effect (in the case of electric current). However, I'm not clear how to determine the maximum surface charge density to which aluminum (or any conductor) can... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/80949/monodromy-representations-of-families-of-hyperelliptic-jacobians/118601 | ## monodromy representations of families of hyperelliptic jacobians
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Let $k$ be a number field , $f \in k[x]$ of degree $2g$ with distinct roots, and $X$ the complex plane with the roots of $f$ removed. Then defin... | {"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": 42, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/102934/list | ## Return to Question
Post Made Community Wiki by aglearner
1
# Pedagogical notes on line bundles on complex projective manifolds
I would like to find some notes (or book), that explains on a very basic level what is a line bundle on a complex projective manifold. Maybe even, what is a line bundle on $\mathbb CP^n$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/39309/complete-lattices-and-sublattices-which-requirement-is-more-stringent?answertab=oldest | # Complete lattices and sublattices – which requirement is more stringent?
I'm studying from Michael Carter's "Foundations", and on page 29 he makes the comment, "Note that the requirement of being a sublattice is more stringent than being a complete lattice in its own right".
This seems counterintuitive. Some lattic... | {"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": 31, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/60458/list | ## Return to Answer
2 not knot
Note: This is a generalization in a different direction from what the question asked for (these references generalize in terms of finding volumes, but Koundinya Vajjha wanted a generalization in terms of finding the centroid). The higher dimensional version by Gray and Miquel linked 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": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Akaike_information_criterion | # Akaike information criterion
The Akaike information criterion is a measure of the relative quality of a statistical model, for a given set of data. As such, AIC provides a means for model selection. AIC is founded on information entropy: it offers a relative estimate of the information lost when a given model is use... | {"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": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/60749-partial-derivatives.html | # Thread:
1. ## Partial derivatives..
I'm looking for the indicated second-order partial derivative for the function f(x,y).
f(x,y)=(1+2xy^2)^8
What I have is:
fx=(2y^2)^8 fy=(4xy)^8
fxx=0 fyy=(4x)^8
fxy=(4y)^8 fyx=4^8
I'm not good at the language of math so I'm not sure if I need to go on and if so, if I have ... | {"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://terrytao.wordpress.com/2010/07/10/cayley-graphs-and-the-geometry-of-groups/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Cayley graphs and the geometry of groups
10 July, 2010 in expository, math.CO, math.GR | Tags: Cayley graphs, fibre bundles, normal subgroups, semi-direct products
In most undergrad... | {"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": 179, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/66450-mathematical-analysis-problem-please-help.html | # Thread:
1. ## mathematical analysis problem. please help.
suppose {x(n)} is a sequence such that
x(1)=1 and
x(n+1)=1+x(n)/(1+x(n+1)) ; n>=1
Prove that this sequence converges and find the limit.
I know how to find the limit of this sequence but dont know how to show that {x(n)} is a convergent sequence. Please he... | {"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": 37, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/60641?sort=oldest | ## In what sense is the étale topology equivalent to the Euclidean topology?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I have heard it said more than once—on Wikipedia, for example—that the étale topology on the category of, say, smooth varieties over $\... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/45036?sort=votes | ## Spectral sequences: opening the black box slowly with an example
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My friend and I are attempting to learn about spectral sequences at the moment, and we've noticed a common theme in books about spectral sequenc... | {"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": 77, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/17024/energy-non-conservation-for-time-dependent-potentials | # Energy non-conservation for time-dependent potentials
Written in a book I read that the "total energy is not preserved when the potential depends explicitly on time", i.e. $U=U(x,t)$. Is there any proof or explanation for this?
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– Qmechanic♦ Nov 16 '11 at 18:17
## 3 Answers
It is easy to understand on a "ball &... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2010/06/17/the-fatou-lebesgue-theorem/?like=1&source=post_flair&_wpnonce=39170bc4ce | # The Unapologetic Mathematician
## The Fatou-Lebesgue Theorem
Now we turn to the Fatou-Lebesgue theorem. Let $\{f_n\}$ be a sequence of integrable functions (this time we do not assume they are non-negative) and $g$ be some other function which dominates this sequence in absolute value. That is, we have $\lvert f_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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 14, "mimetex.cgi": 0, "/images/ma... |
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