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http://mathoverflow.net/questions/91604/does-regularity-of-the-boundary-imply-interior-sphere-condition | ## Does regularity of the boundary imply interior sphere condition
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In the article of Massari presented here there is a trace inequality which is said to be true for domains which satisfy the interior sphere condi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 40, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://logiciansdoitwithmodels.com/2010/09/ | # Logicians do it with Models
A self-guided jaunt in philosophical logic
## Archive for September, 2010
### Determination and Definability: Newtonian Mechanics & Statistical Dynamics
September 30, 2010
The last determination-without-reduction example I’ll talk about from Hellman is the one he gives regarding class... | {"extraction_info": {"found_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": 227, "mimetex.cgi": 0, "/images/m... |
http://unapologetic.wordpress.com/2012/07/17/the-higgs-mechanism-part-2-examples-of-lagrangian-field-equations/?like=1&source=post_flair&_wpnonce=ae4d6bb289 | # The Unapologetic Mathematician
## The Higgs Mechanism part 2: Examples of Lagrangian Field Equations
This is part two of a four-part discussion of the idea behind how the Higgs field does its thing. Read Part 1 first.
Okay, now that we’re sold on the Lagrangian formalism you can rest easy: I’m not going to go thro... | {"extraction_info": {"found_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": 43, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/280178/approximate-a-function-over-the-interval-0-1-by-a-polynomial-of-degree-n?answertab=oldest | # Approximate a function over the interval $[0, 1]$ by a polynomial of degree $n$ (or less).
To approximate a function $G$ over the interval $[0,1]$ by a polynomial $P$ of degree $n$ (or less), we minimize the function $f:R^{n+1} \to R$ given by $F(a) = \int_0^1 (G(x) - P_a(x))^2\,dx$, where $P_a(x) = a_nx^n+a_{n-1}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": 41, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/278935/can-a-sum-of-square-roots-be-an-integer | # can a sum of square roots be an integer?
Can a sum of a finite number of square roots of integers be an integer? if yes can a sum of two square roots of integers be an integer?
The square roots need to be irrational.
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6
like $\sqrt{9} + \sqrt{16} = 7$? – Jonathan Christensen Jan 14 at 23:07
If you choose only 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": 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/50066/list | ## Return to Answer
3 edited body
This is not exactly what you wanted, but in algebraic geometry it is often easier to prove something for a particular object by considering the moduli space parametrizing such objects. The example I have in mind is the following: Suppose you picked some random elliptic curve over $\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": 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/66650?sort=votes | ## Connectifications?
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Like many of my questions, this question is actually aimed at $p$-adic analysis. One of the main obstacles in doing analysis $p$-adically ist that the $\mathbb{Q}_p$ is totally disconnected.... | {"extraction_info": {"found_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://mathoverflow.net/questions/71137/regular-conditional-probability-given-a-natural-filtration-of-a-stochastic-proces/71141 | ## Regular Conditional Probability given a natural filtration of a stochastic process
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OK, this is kind of re-posting, but I think I can clarify the question more, so it's worth a shot.
Consider a real valued pro... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/93462/the-facial-structure-of-the-convex-hull-of-a-family-of-characteristic-functions | ## The facial structure of the convex hull of a family of characteristic functions
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Let $S$ be a finite set and let $\mathcal{A} \subset\mathcal{P}(S)$ be a family of subsets of $S$. Consider the convex polytope 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": 41, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/40134-applications-calculus.html | # Thread:
1. ## Applications of Calculus
Question:
The acceleration of a particle is given by a = 3x+1 (where a is acceleration, x is displacement from origin). If the particle is initially at the origin and moving at a velocity of $15ms^{-1}$, find its velocity after 3s.
What I've done:
$a = v\frac{dv}{dx} = 3x -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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 34, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/112657/maximal-subgroups-of-finite-simple-groups/112713 | ## maximal subgroups of finite simple groups
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Is it possible to determine the structure of maximal subgroups of finite simple groups?(Even if in special cases such as minimal simple groups, alternating groups,...)... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "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/180441/product-of-right-cosets-equals-right-coset-implies-normality-of-subgroup | # Product of right cosets equals right coset implies normality of subgroup
I cannot seem to find a way to prove that if $H$ is a subgroup of $G$ such that the product of two right cosets of $H$ is also a right coset of $H,$ then $H$ is normal in $G.$
(This is from Herstein by the way.)
Thank you.
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There might 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": 56, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/203941-what-do-i-need-do-equation.html | # Thread:
1. ## What do I need to do with this equation?
20x -10 = 6+12x
Maths was never my best subject!
Thanks!
2. ## Re: What do I need to do with this equation?
20x -10 = 6+12x
You have to solve for x, so you need to isolate x, to do that, you can subtract 12x from both sides: $20x-10-12x =6+12x-12x$ and you... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.mathplanet.com/education/algebra-1/discovering-expressions,-equations-and-functions/representing-functions-as-rules-and-graphs | # Representing functions as rules and graphs
Let's begin by looking at an example:
At a store the carrots cost \$2.50/lb. The prize the customer pays is dependent on how many pounds of carrots that he buys. Another way to say this is to say that the total cost is a function of the pounds bought. We can write this as ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/116797/constructive-proof-of-projective-implies-proper/116805 | Constructive proof of “Projective implies proper”
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For every ring $A$, the structural morphism of schemes $\pi_A : {\bf P}^n_{A} \to {\rm Spec}{A}$ is a closed map. The usual proof of this fact is not constructive : g... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.nag.com/numeric/cl/nagdoc_cl23/html/X02/x02intro.html | # NAG Library Chapter Introductionx02 – Machine Constants
## 1 Scope of the Chapter
This chapter is concerned with parameters which characterise certain aspects of the computing environment in which the NAG C Library is implemented. They relate primarily to floating point arithmetic, but also to integer arithmetic, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 65, "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://mathhelpforum.com/advanced-statistics/60148-consistent-unbiased-estimator.html | # Thread:
1. ## Consistent and unbiased estimator.
Let $Y_1, Y_2 , . . . \dotso Y_n$ denote a random sample from the uniform distribution on the interval $(\theta,\ \theta+1)$. Let
$\hat{\theta_1} = \overline{Y}-\frac{1}{2}$ and $\hat{\theta_2} = Y_{(n)} -\frac{n}{n+1}$
a) show that both $\hat{\theta_1}$ and $\hat{... | {"extraction_info": {"found_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": 113, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/96651/the-approximation-to-perturbed-kdv-equation/101617 | The approximation to perturbed KdV Equation
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Consider the perturbed KdV Equation $$u_t-6uu_x+u_{xxx}=\epsilon u$$,I want to use perturbative expansion to construct the solution as the form $$u=u(x,t;\epsilon)=\sum_{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": 3, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/celestial-mechanics+reference-request | # Tagged Questions
2answers
127 views
### How to learn celestial mechanics?
I'm a PhD student in math and am really excited about celestial mechanics. I was wondering if anyone could give me a roadmap for learning this subject. The amount of information about it on the ...
0answers
169 views
### Simple model of 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": 1, "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/20604/are-rings-really-more-fundamental-objects-than-semi-rings | ## Are rings really more fundamental objects than semi-rings?
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The discovery (or invention) of negatives, which happened several centuries ago by the Chinese, Indians and Arabs, has of course be of fundamental imp... | {"extraction_info": {"found_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-algebra/165335-please-help-clarify-galois-proof.html | # Thread:
1. ## Please help clarify this Galois proof
I more or less copied the following notes from my professor:
Find the Galois group of $x^4-2$ over $\mathbb{Q}$.
Solution: $x^4-2$ has roots $\pm\sqrt[4]{2},\pm i\sqrt[4]{2}$. Note that since $G$ acts on the four roots, $G$ is isomorphic to a subgroup of $S_4$. ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 58, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikisource.org/wiki/On_the_Electrodynamics_of_Moving_Systems_II | # On the Electrodynamics of Moving Systems II
From Wikisource
On the Electrodynamics of Moving Systems II (1904) by Emil Cohn, translated by Wikisource
In German: Zur Elektrodynamik bewegter Systeme II, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, Zweiter Halbband (43): 1404–1416, Source... | {"extraction_info": {"found_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": 174, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://nrich.maths.org/4835/note?nomenu=1 | ## 'Squares in Rectangles' printed from http://nrich.maths.org/
### Why do this problem?
This problem is a context for systematic number work, geometrical thinking and problem solving.
It is an excellent example of a situation where the thinking involved in analysing one rectangle can be applied directly to other rec... | {"extraction_info": {"found_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://mathhelpforum.com/number-theory/41324-help-algebraic-number-theory.html | # Thread:
1. ## Help with Algebraic Number Theory
Hello
I'm currently working through a text titled 'Introductory Algebraic Number Theory' by Saban Alaca and Kenneth S. Williams, and I'm having trouble with some of the practise exercises throughout the text.
The first problem I've been trying to figure out is 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 101, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.impan.pl/cgi-bin/dict?pick | ## pick
Pick the first arc of length 1 in this sequence.
We can continue to pick elements of $B$ as above. But there are only finitely many such, a contradiction.
Go to the list of words starting with: a b c d e f g h i j k l m n o p q r s t u v w y z
Copyright © 2011 by Jerzy Trzeciak, Warszawa 2011. All rights re... | {"extraction_info": {"found_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://www.openwetware.org/index.php?title=User:Pranav_Rathi/Notebook/OT/2010/08/18/CrystaLaser_specifications&diff=prev&oldid=674782 | # User:Pranav Rathi/Notebook/OT/2010/08/18/CrystaLaser specifications
### From OpenWetWare
(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": 12, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/35332?sort=newest | ## Does there exist a potential which realizes this strange quantum mechanical system?
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I have done some courses on quantum mechanics and statistical mechanics in the past. Since I also do math, I wonder about con... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/55348/what-are-the-ux-and-vx-y | What are the U(x) and V(x-y)
Srednicki in his QFT book introduces the the Hamiltonian operator of the quantum field theory (equation 1.32). Here what are $U \bf(x)$ and $V\bf(x-y)$?
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2
He explains what they are just above Eq. (1.30). He is describing a set of particles, each of which is subject to some potential $U... | {"extraction_info": {"found_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/116860/spectrum-of-the-normal-operator-associated-to-compact-supported-spectral-measures | ## Spectrum of the Normal Operator associated to compact supported spectral measures
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Let $\mathcal{H}$ be a Hilbert space and $E:\Sigma\to\mathcal{L}(\mathcal{H})$ be a compactly supported spectral on the Borel $... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/157692-trigonometric-sum-identity.html | # Thread:
1. ## trigonometric sum identity
I'm looking for a hint on how to prove that
$\sum \limits _{k=1}^n \cos \left[(2k-1)\theta\right]=\dfrac{\sin \left(2n \theta\right) }{2\sin \theta}$
I know I'm on here a lot but I really have no one to go to for guidance and am trying to learn this material on my own 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 59, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/122728/abelian-group-objects-category/122742 | ## abelian group objects category
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Suppose that $\mathcal{C}$ is a cartesian closed category. When is the category of abelian group objects $\mathcal{Ab}(\mathcal{C})$ a symmetric monoidal closed with respect to 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": 21, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/04/02/regular-outer-measures/?like=1&source=post_flair&_wpnonce=8cb43e0c56 | # The Unapologetic Mathematician
## Regular Outer Measures
As usual, let $\mathcal{R}$ be a ring of sets, $\mathcal{S}(\mathcal{R})$ be the smallest $\sigma$-algebra containing $\mathcal{R}$, and $\mathcal{H}(\mathcal{R})$ be the smallest hereditary $\sigma$-algebra containing $\mathcal{R}$. We’ve asked about the rel... | {"extraction_info": {"found_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": 38, "mimetex.cgi": 0, "/images/ma... |
http://polymathprojects.org/2012/07/12/minipolymath4-project-imo-2012-q3/?like=1&_wpnonce=76a2d9cd23 | # The polymath blog
## July 12, 2012
### Minipolymath4 project: IMO 2012 Q3
Filed under: research — Terence Tao @ 10:00 pm
Tags: mini-polymath4
This post marks the official opening of the mini-polymath4 project to solve a problem from the 2012 IMO. This time, I have selected Q3, which has an interesting game-theor... | {"extraction_info": {"found_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": 266, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/advanced-algebra/83479-irreduclible-polynomials.html | # Thread:
1. ## Irreduclible polynomials
Show that $f(x)=x^4+bx^2+d$ is irreducible over
$\mathbb Q(\sqrt{d(b^2-4d)})[x]$
2. Originally Posted by ZetaX
Show that $f(x)=x^4+bx^2+d$ is irreducible over $\mathbb Q(\sqrt{d(b^2-4d)})[x]$
this can't be right! did you mean reducible?
3. No this is correct, it is irreduci... | {"extraction_info": {"found_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": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/99736/beautiful-descriptions-of-exceptional-groups/99744 | ## Beautiful descriptions of exceptional groups
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I'm curious about the beautiful descriptions of exceptional simple complex Lie groups and algebras (and maybe their compact forms). By beautiful I mean: simple (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": 189, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/advanced-algebra/105059-abstract-algebra-groups.html | # Thread:
1. ## Abstract Algebra-Groups
puzzled by this problem. Suppose that a is a group element and a^(6)=e. What are the possibities for |a|?
Intuitively I want to say that the answer is 6 because of the definition of order of an element.
However another wants to say infinite...
Suggestions?
2. Originally Posted... | {"extraction_info": {"found_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://gilkalai.wordpress.com/2010/09/29/polymath-3-polynomial-hirsch-conjecture/?like=1&source=post_flair&_wpnonce=eb9f8a7f00 | Gil Kalai’s blog
## Polymath 3: Polynomial Hirsch Conjecture
Posted on September 29, 2010 by
I would like to start here a research thread of the long-promised Polymath3 on the polynomial Hirsch conjecture.
I propose to try to solve the following purely combinatorial problem.
Consider t disjoint families of subsets... | {"extraction_info": {"found_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": 597, "mimetex.cgi": 0, "/images/m... |
http://www.physicsforums.com/showthread.php?t=420820 | Physics Forums
Thread Closed
Page 1 of 3 1 2 3 >
## Why time is a separate physical quantity
Hi!
I have a question about time.
I don't understand why everyone thinks of a time as some coordinate like x,y,z. I don't get it. From my point of view the time as some physical quantity doesn't exist. Because 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": 0, "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/77639/left-and-right-cosets?answertab=votes | # Left and Right Cosets
Let $H$ be a subgroup of a group $G$ and let $a, b \in G$. I need to give a counterexample or proof of the following statement:
If $aH = bH$, then $Ha = Hb$
Proof:
For every $h \in H, ah = bh$
$\begin{align} ah &= bh \newline ahh^{-1} &= bhh^{-1} \newline a &= b \newline ha &= hb \end{align... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "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/52353/wanted-chain-of-nowhere-dense-subsets-of-the-real-line-whose-union-is-nonmeagre | ## Wanted: chain of nowhere dense subsets of the real line whose union is nonmeagre, or even contains intervals
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $X$ be a topological space. When I call a set nowhere dense, meagre or similar without qualifica... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/advanced-algebra/67161-help-me-invariant-subspace-please-print.html | # help me on invariant subspace please
Printable View
• January 7th 2009, 05:12 AM
Kat-M
help me on invariant subspace please
let T denote a linear operator on a vector space V. suppose that every subspace of V is invariant under T. prove that T is a scalar multiple of the identity map.
• January 7th 2009, 06:54 AM
... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/43511/force-of-a-particles-on-a-potential-barrier | # Force of a particles on a Potential Barrier [closed]
A particle confined by a potential wall exerts some pressure on it. More specifically, suppose that the particle moves in this potential:
$$V(x) ~=~\left\{ \begin{array}{lcc}\text{finite function}&\text{if}& x > b, \\ V_0 &\text{if} &x < b,\end{array}\right.$$ wh... | {"extraction_info": {"found_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/advanced-algebra/192461-only-non-abelian-simple-group-order-60-a_5-a.html | Thread:
1. The only non-abelian simple group of order 60 is A_5
Hi, assuming that a simple non-abelian group $G$ of order 60 can be embedded in $S_6$, I want to prove that $G$ cannot contain an odd permutation and is therefore a subgroup of $A_6$ (and then from that I can deduce that as it is order 60 it is $A_5$). 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": 23, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.digplanet.com/wiki/Integer_factorization | digplanet beta 1: Athena
Share digplanet:
Integer factorization
Computational hardness assumptions > Integer factorization Unsolved problems in computer science > Integer factorization Integer factorization algorithms > Integer factorization
Sections
Agriculture
Applied sciences
Arts
Belief
Chronology
Culture... | {"extraction_info": {"found_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://motls.blogspot.com.es/2012/08/atlas-released-10-papers-today.html?m=1 | # The Reference Frame
Our stringy Universe from a conservative viewpoint
## Monday, August 13, 2012
### ATLAS released 10 papers today
Update: Wow, by the end of the day, there would be 15 new papers posted but the extra five are on lead-lead collisions and will be ignored below.
The ATLAS collaboration at the LHC... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/242527/how-to-prove-periodicity-is-a-class-property | # How to prove periodicity is a class property?
It is said that in a Markov chain, if state $i$ has period $d$ and state $i$ and $j$ are communicate, then state $j$ also has period $d$.
I wonder how to prove it?
-
## 1 Answer
One way to define the period of state $i$ is as the largest integer $p$ such that you 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": 76, "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/55080/probability-question-regarding-brownian-motion/55081 | ## probability question regarding brownian motion
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Given a BM $dX_t=\mu t+\sigma dB_t$, having started at $X_0=0$. What is the probability that $X_t$ does not hit 0 in the time interval $[a,T]$ where $0\le a\le 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": 24, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/1740/stretching-a-random-seed-to-maximize-entropy?answertab=votes | # Stretching a random seed to maximize entropy
I'm using a random number generator that requires me to pass it a big (several kilobytes) pool of random data for initialization.
I've gathered entropy from various system metrics (free memory, system clock, mac address .etc) and generated a 64-bit seed value which I nee... | {"extraction_info": {"found_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://etna.mcs.kent.edu/volumes/1993-2000/vol2/abstract.php?vol=2&pages=1-21 | ## An implicitly restarted Lanczos method for large symmetric eigenvalue problems
D. Calvetti, L. Reichel, and D. C. Sorensen
### Abstract
The Lanczos process is a well known technique for computing a few, say $k$, eigenvalues and associated eigenvectors of a large symmetric $n\times n$ matrix. However, loss of orth... | {"extraction_info": {"found_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/69440/blowing-up-along-an-ideal-in-the-product-of-projective-varieties | # Blowing up along an ideal in the product of projective varieties
I am looking for information on blowing up along an ideal in a product of varieties. After extensive searching through several textbooks I cannot find an explicit method for doing so. Specifically, I am trying to blow up along the diagonal in the produ... | {"extraction_info": {"found_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://mathforum.org/mathimages/index.php?title=The_Golden_Ratio&diff=34261&oldid=31891 | # 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": 117, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/121105/which-functor-does-the-projective-space-represent | # Which functor does the projective space represent?
I hope this question isn't too silly. It is certainly fundamental, so the answer is likely contained at least implicitly in most sources out there, but I haven't seen it done this way (that is, in this particular functorial manner) in a way which is overt enough for... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 68, "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/30220/abstract-thought-vs-calculation/32106 | ## Abstract Thought vs Calculation
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Jeremy Avigad and Erich Reck in their remarkable historical paper "Clarifying the nature of the infinite: the development of metamathematics and proof theory" claim that one 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": 110, "mathjax_display_tex": 6, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/tagged/asymptotics?page=1&sort=votes&pagesize=15 | # Tagged Questions
Questions involving asymptotic analysis, including growth of functions, Big-O notation, Big-Omega and Big-Theta notations.
1answer
6k views
### How many fours are needed to represent numbers up to $N$?
The goal of the four fours puzzle is to represent each natural number using four copies of 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": 133, "mathjax_display_tex": 27, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathoverflow.net/questions/81553/orthogonal-polynomials-functions-on-the-interval-0-1-but-with-same-weight-as-ge/81555 | ## Orthogonal polynomials/functions on the interval [0,1] but with same weight as Gegenbauer polynomials
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I am looking for an othogonal basis of functions over the interval $[0,1]$ with weight function $(1-x^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": 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/questions/103395/isotopy-in-3-manifolds | ## Isotopy in 3-manifolds
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Assume $\Sigma_1$ and $\Sigma_2$ are two embedded compact surfaces (say orientable) in an orientable 3-manifold $M$. Assume $\Sigma_1$ and $\Sigma_2$ are homotopic in $M$. Then are they ... | {"extraction_info": {"found_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://mathhelpforum.com/number-theory/116487-quadratic-residue.html | # Thread:
1. ## Quadratic Residue
Prove that if c is odd, then $(\frac{2}{c}) = (-1)^{\frac{(c^{2}-1)}{8}}$.
I know I'm supposed to use the theorem that states $(\frac{2}{p}) = (-1)^{\frac{p^{2}-1}{8}}$, where p is an odd prime. But I'm not confident that stating that c is simply an odd prime is enough to satisfy 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": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/7436/lebesgue-integral-basics?answertab=oldest | # Lebesgue integral basics
I'm having trouble finding a good explanation of the Lebesgue integral. As per the definition, it is the expectation of a random variable. Then how does it model the area under the curve? Let's take for example a function $f(x) = x^2$. How do we find the integral of $f(x)$ under $[0,1]$ usin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 92, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/30898/ways-to-prove-an-inequality/30906 | ## Ways to prove an inequality
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It seems that there are three basic ways to prove an inequality eg $x>0$.
1. Show that x is a sum of squares.
2. Use an entropy argument. (Entropy always increases)
3. Convexity.
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 70, "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/13089/why-do-so-many-textbooks-have-so-much-technical-detail-and-so-little-enlightenmen/13090 | ## Why do so many textbooks have so much technical detail and so little enlightenment? [closed]
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I think/hope this is okay for MO.
I often find that textbooks provide very little in the way of motivation or conte... | {"extraction_info": {"found_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/34489/can-all-quantum-superpositions-be-realized-experimentally | # Can all quantum superpositions be realized experimentally?
When textbooks in QM give example of finite dimensional Hilbert spaces they give examples of photon polarizations or of 2-states systems and sometimes they mention how one can achieve superposition in such cases experimentally.
On the other hand when they 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": 19, "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/15052/graphene-space-elevator-possible?answertab=active | # Graphene space elevator possible?
I just read this story on MIT working on industrial scale, km^2 sheet production of graphene.
A quick check of Wikipedia on graphene and Wikipedia on space elevator tells me
Measurements have shown that graphene has a breaking strength 200 times greater than steel, with a tensile ... | {"extraction_info": {"found_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://directed-procrastination.blogspot.com/2011/06/versioned-arrays.html | directed procrastination
Wednesday, June 15, 2011
Versioned Arrays
I just learned of a method of creating functional data structures from mutable types called versioning. Basically, if you have mutable data like an array, you can implement functional changes of the data structure by storing the differences between 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": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2009/11/05/an-example-of-a-parallelogram/?like=1&source=post_flair&_wpnonce=5b12459335 | # The Unapologetic Mathematician
## An Example of a Parallelogram
Today I want to run through an example of how we use our new tools to read geometric information out of a parallelogram.
I’ll work within $\mathbb{R}^3$ with an orthonormal basis $\{e_1, e_2, e_3\}$ and an identified origin $O$ to give us a system 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": 0, "wp_latex": 68, "mimetex.cgi": 0, "/images/ma... |
http://outofthenormmaths.wordpress.com/tag/continued-fractions/ | # Tag Archives: continued fractions
March 13, 2012 · 7:21 pm
## Percentages for sceptics: part III
I wanted to do some self-criticism of my previous two posts in this series:
1. You can calculate the minimum of responses from a single percentage by hand (no need for computer programmes or look-up tables).
2. I’ve 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": 0, "wp_latex": 12, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-puzzles/152662-interesting-problem-please-help.html | # Thread:
1. ## Interesting Problem, Please Help
Hello.
I came up with an interesting problem that I am now trying to figure out.
Imagine a plane in space, and within that plane two parallel lines. From the perspective of any point outside of the plane (i.e. if your eye was there), the parallel lines would appear t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 73, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://sbseminar.wordpress.com/category/representation-theory/ | ## Hall algebras are Grothendieck groupsApril 18, 2011
Posted by Ben Webster in hopf algebras, representation theory.
13 comments
I’ve been attending a seminar/class run by Nick Proudfoot preparing for his workshop this summer on canonical bases. In conversations with Nick and graduate students, and there’s been some... | {"extraction_info": {"found_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": 88, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/48576?sort=oldest | ## When can the group von Neumann algebra of a one-relator group be isomorphic to a free group factor?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $G=\langle a,b | R \rangle$ be a one-relator group. When can the left group von Neumann algebra $LG$ be 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": 22, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Superconductor | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/214469/are-projective-modules-over-an-artinian-ring-free?answertab=votes | # Are projective modules over an artinian ring free?
Quoting a comment to this question:
By a theorem of Serre, if $R$ is a commutative artinian ring, every projective module [over $R$] is free. (The theorem states that for any commutative noetherian ring $R$ and projective module $P$ [over $R$], if $\operatorname{ra... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 61, "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/183051/tate-models-and-subgroups-of-typem-m-re-silverman-hindry-88 | # Tate models and subgroups of type$(m,m)$ - re Silverman, Hindry 88
I need help in understanding a passage in a paper by Hindry and Silverman, "The Canonical Height and Integral Points on Elliptic Curves". (re. page 439)
Let $E(K)$ be an elliptic curve with multiplicative reduction at a valuation $\nu$, and K a func... | {"extraction_info": {"found_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://mathoverflow.net/questions/81958/complement-of-a-simply-connected-domain | ## Complement of a simply connected domain [closed]
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Whether the unbounded connected component of the complement of the closure of a bounded simply connected domain in the extended complex plane $\overline C$ is 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": 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/289137/calculate-201234567-mod-251/289140 | # Calculate $20^{1234567} \mod 251$
I need to calculate the following
$$20^{1234567} \mod 251$$
I am struggling with that because $251$ is a prime number, so I can't simplify anything and I don't have a clue how to go on. Moreover how do I figure out the period of $[20]_{251}$? Any suggestions, remarks, nudges in 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": 12, "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/213336/noether-normalization-over-mathbbz | # Noether normalization over $\mathbb{Z}$
I would like to know what is a correct analogue of Noether normalization theorem for rings finitely generated over $\mathbb Z$. Obviously, Noether normalization can not hold "literately" in this case since, for example the ring $\mathbb Z_2[X]$ does not contain a polynomial su... | {"extraction_info": {"found_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://ams.org/bookstore?fn=20&arg1=ficseries&ikey=FIC-59 | New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Ana... | {"extraction_info": {"found_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/entropy?sort=faq&pagesize=15 | # Tagged Questions
A important property of all systems in thermodynamics and statistical mechanics. Entropy characterizes the degree to which the energy of the system is *not* available to do useful work
3answers
1k views
### How do you prove $S=-\sum p\ln p$?
How does one prove the formula for entropy $S=-\sum p\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": 9, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/26903?sort=oldest | ## When are entire functions surjective?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Is there some useful criterion to determine whether or not an entire function is surjective?
-
## 1 Answer
Maybe Picard's theorem is of help http://en.wikipedia.org/wik... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Confidence_intervals | # Confidence interval
(Redirected from Confidence intervals)
See also: Confidence distribution
In statistics, a confidence interval (CI) is a type of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval (i.e. it is calculated from the observati... | {"extraction_info": {"found_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": 25, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/16031?sort=votes | ## Suppose C and D are Morita equivalent fusion categories, can you say anything about R I: C->Z(C)=Z(D)->D?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
If C and D are (higher) Morita equivalent fusion categories, then the Drinfel'd centers Z(C) and Z(D) 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": 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/calculus/193284-application-derivative.html | # Thread:
1. ## Application of derivative
Hi guys, i have got a few question that needs help before my exams next week
The surface area of a cube with side x cm, is increasing at a rate of 16cm2/s
Whnt the total surface area of the cube reaches 216cm2
a)show that the volume of the cube is 216cm3
b) find the rate wh... | {"extraction_info": {"found_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://math.stackexchange.com/questions/36667/how-can-i-find-all-increasing-sequences-a-i-i-1-infty-such-that-dx | # How can I find all increasing sequences $\{a_i\}_{i=1}^{\infty}$ such that $d(x_1+x_2+\cdots+x_k)=d(a_{x_{1}}+a_{x_{2}}+\cdots + a_{x_{k}})$?
How can one find all increasing sequences $\{a_i\}_{i=1}^{\infty}$ such that $$d(x_1+x_2+\cdots+x_k)=d(a_{x_{1}}+a_{x_{2}}+\cdots + a_{x_{k}}),$$ holds for all $k$-tuples $(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": 26, "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/41653/a-special-residually-finite-group/41659 | ## A special residually finite group
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Is there an example of a finitely generated (infinite) residually finite group $\Gamma$ for which every linear representation of $\Gamma$ has finite image?
-
By linear repre... | {"extraction_info": {"found_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/11012/characterizing-free-modules-by-exterior-power?answertab=votes | # characterizing free modules by exterior power
Assume $M$ is a (finitely generated) $A$-module such that $\wedge^n M$ is free of rank $1$ for some $n \geq 1$. Does it follow that $M$ is free of rank $n$? Or at least locally free of rank $n$?
In general, is there a way of characterizing local free modules via exterio... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "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/275638/transformation-of-symplectic-structure-by-a-matrix?answertab=active | # transformation of symplectic structure by a matrix
Suppose that in canonical symplectic basis $e_1,e_2,f_1,f_2$ we have $$\Omega=pf_1^*\wedge f_2^*+qe_1^*\wedge e_2^*+r(e_1^*\wedge f_2^*+e_2^*\wedge f_1^*)+s(e_1^*\wedge f_1^*-e_2^*\wedge f_2^*)$$ Let $A_t$ be transformation of symplectic structure that depend on 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": 8, "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/2009/10/26/tensor-and-symmetric-algebras/?like=1&_wpnonce=122935e828 | # The Unapologetic Mathematician
## Tensor and Symmetric Algebras
There are a few graded algebras we can construct with our symmetric and antisymmetric tensors, and at least one of them will be useful. Remember that we also have symmetric and alternating multilinear functionals in play, so the same constructions will... | {"extraction_info": {"found_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": 56, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/definite-integral+integration | # Tagged Questions
0answers
61 views
### Why Riemann integration is needed? [closed]
What is the necessity of the notion of "Riemann Integration" ? Why is normal definite integral is not good enough ?
0answers
51 views
### Integral involving exponential, power and Bessel function
Is there any formula for calculati... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 72, "mathjax_display_tex": 37, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/86495/recurrence-relations-binary-substrings/86499 | # Recurrence relations - binary substrings
Let $S_n$ be the number of binary strings of length = $n$ which do not contain the sub-string $010$.
Find a recurrence relation for $S_n$.
edit:
I tried for $n=4$. There are two positions in string, how to place $010$.
[]010 or 010[] ... so last place is choosen from 2 po... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/24927/what-are-the-ramifications-of-the-fact-that-the-first-homotopy-group-can-be-non | # What are the ramifications of the fact that the first homotopy group can be non-commutative, whilst the higher homotopy groups can't be?
Does this mean that the first homotopy group in some sense contains more information than the higher homotopy groups? Is there another generalization of the fundamental group that ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 72, "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/54704/finding-the-smallest-positive-integer-a | # Finding the smallest positive integer a
Can we find the smallest positive integer $a$ such that $1971|50^n+a.23^n$ where n is odd?
Source:Problem Solving Strategies by Arthur Engel
-
Presumably you want this to hold for all odd values of $n$? Is that period between $a$ and $23^n$ a multiplication sign? The TeX-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": 30, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/5627/index?nomenu=1 | ## 'Quaternions and Rotations' printed from http://nrich.maths.org/
### Show menu
In this question we see how quaternions are used to give rotations of ${\bf R^3}$.
(1) Consider the quaternion $$q = {1\over \sqrt 2} + {1\over \sqrt 2}{\bf i} + 0{\bf j} + 0 {\bf k}.$$ (a) Show that the multiplicative inverse of $q$ 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": 18, "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/tagged/convolution?page=1&sort=unanswered&pagesize=30 | # Tagged Questions
Questions on the (continuous or discrete) convolution of two functions.
0answers
183 views
### Is there a closed form solution of $f(x)^2+(g*f)(x)+h(x)=0$ for $f(x)$?
When $g(x)$ and $h(x)$ are given functions, can $f(x)^2+(g*f)(x)+h(x)=0$ be solved for $f(x)$ in closed form (at least with some 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": 101, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/29805/richtmyer-meshkov-instability-in-mhd/29809 | # Richtmyer Meshkov instability in MHD
In magnetohydrodynamics, the Richtmyer Meshkov instability is found to get suppressed by application of longitudinal magnetic field. Exactly what happens at the interface? Why instability gets suppressed? (How one can get the physical intuition of what is happening?)
-
Yes, I 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://math.stackexchange.com/questions/240635/examination-of-convergence-of-a-few-series/240706 | # Examination of convergence of a few series
Determine whether the following series converge and whether they even converge absolutely:
1. $\displaystyle\sum\limits_{k=2}^\infty\frac{(-1)^k}{(\log(k))^k}$
2. $\displaystyle\sum\limits_{k=1}^\infty\left(\frac{1}{k!}-\frac{3}{(k+1)!}\right)$
3. $\displaystyle\sum\limits... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 48, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/23865-please-help-final-tom-word-problem.html | # Thread:
1. ## Please Help Final Tom!! Word Problem
Can someone please explain how to set up the equation for the following word problem,
-Express the surface area (S) of a rectangular box with a square base and of volume 100 ft.3 in terms of the length (x) of the square base.
2. Originally Posted by B1GG13
Can som... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?p=1874946 | Physics Forums
Blog Entries: 3
## Composition of Inverse Functions
In Micheal C. Gemignani, "Elementary Topology" in section 1.1 there is the following exercise
2)
i)
If $$f:S \rightarrow T$$ and $$G: T \rightarrow W$$, then $$(g \circ f)^{-1}(A) = f^{-1}(g^{-1}(A))$$ for any $$A \subset W$$.
I think the above 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": 19, "mathjax_display_tex": 18, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://unapologetic.wordpress.com/2010/09/23/reducibility/?like=1&source=post_flair&_wpnonce=d0199d491e | # The Unapologetic Mathematician
## Reducibility
We say that a module is “reducible” if it contains a nontrivial submodule. Thus our examples last time show that the left regular representation is always reducible, since it always contains a copy of the trivial representation as a nontrivial submodule. Notice that we... | {"extraction_info": {"found_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": 54, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/26420/cup-product-well-definedness | # cup product well definedness
So the cup product is not well defined over co-chain groups, but all the books claim it is well defined over co-homology groups. The only thing I am not clear on is invariance under ordering/re-ordering of simplices when we go to the co-homology level. Every book seems to gloss over this... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2009/08/17/the-singular-value-decomposition/?like=1&source=post_flair&_wpnonce=eb8d9d939c | # The Unapologetic Mathematician
## The Singular Value Decomposition
Now the real and complex spectral theorems give nice decompositions of self-adjoint and normal transformations, respectively. Each one is of a similar form
$\displaystyle\begin{aligned}S&=O\Lambda O^*\\H&=U\Lambda U^*\end{aligned}$
where $O$ is 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": 0, "codecogs_latex": 0, "wp_latex": 72, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/statistics/27665-quick-coin-flip-question.html | # Thread:
1. ## quick coin flip question
A professor flips two balanced coins. Both fall to the floor and roll under his desk. A student informs the professor that he can see only one coin and it shows tails. What is the probability that the other coin is also tails?
Is it 1/2? I said it was 1/2 because they are ind... | {"extraction_info": {"found_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": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/109443/fourier-transform-of-eit-xi-alpha/109457 | ## Fourier transform of $e^{it|\xi|^{\alpha}}$
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Consider the fourier transform of $e^{it|\xi|^{2\alpha}}$ ($\alpha>0$)in $\mathbb{R}^n$,let $K_{\alpha}=\mathcal{F}(e^{it|\xi|^{\alpha}})$,so $K$ is a tempered distr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 40, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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