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http://physics.stackexchange.com/questions/27441/pauli-villars-pv-regularisation-breaks-supersymmetry-how-to-see-that?answertab=oldest | # Pauli-Villars (PV) regularisation breaks supersymmetry. How to see that?
Does the PV regulator breaks SUSY?
Take for instance the 1-loop (top/stop loops) correction to the Higgs squared-mass parameter in the MSSM, and you'll get something like,
$$\delta m^2_{h_u} = - 3Y_u^2/(4 \pi^2) m_{\tilde{t}}^2 ln (\frac{\Lam... | {"extraction_info": {"found_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://www.scholarpedia.org/article/Yarkovsky_and_YORP_effects | # Yarkovsky and YORP effects
From Scholarpedia
David Vokrouhlicky and William F. Bottke (2012), Scholarpedia, 7(5):10599.
Curator and Contributors
1.00 - David Vokrouhlicky
Prof. David Vokrouhlicky accepted the invitation on 22 February 2010 (self-imposed deadline: 22 August 2010).
The Yarkovsky effect describes 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": 26, "mathjax_display_tex": 294, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://wiki.stat.ucla.edu/socr/index.php?title=Probability_and_statistics_EBook&oldid=10188 | # Probability and statistics EBook
### From Socr
Revision as of 20:44, 4 June 2010 by Jenny (Talk | contribs)
This is a General Statistics Curriculum E-Book, which includes Advanced-Placement (AP) materials.
## Contents
This is an Internet-based probability and statistics E-Book. This EBook, and the materials, too... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/74943?sort=oldest | ## Constructible sheaves and dg-modules
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Let $M$ be a smooth manifold, $A_M$ the de Rham algebra of $M$, $D_{A_M}$ the derived category of the category of differential graded (dg) $A_M$-modules and `$D^+_c(M)$` 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": 72, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/14486/list | ## Return to Question
Post Made Community Wiki by Harry Gindi
8 oops
## Speculation and background
Let $\mathcal{C}:=CRing^{op}_{Zariski}$, the affine Zariski site. Consider the category of sheaves, $Sh(\mathcal{C})$.
According to nLab, schemes are those sheaves that "have a cover by Zariski-open immersions of aff... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 66, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/169176-problem-integrating-factor.html | Thread:
1. Problem with Integrating Factor
I'm trying to solve the differential equation dy/dx + (2-3x^2)(x^-3)y = 1. I've integrated (2-3x^2)(x^-3) and taken the exponential of this to give an integrating factor of (x^-3)e^(x^2). However, when I differentiate the integrating factor multiplied by y, I don't end up wi... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?s=eb5f721862ebf984eca45b3331b57b52&p=4173662 | Physics Forums
## Symmetry and conservation law
This is my first post, so hello everybody. I don't have university background and english is not my native language, so please forgive me if what I'm writing is hard to understand sometimes. I'll do my best to be clear.
I've always loved physics in general, but recently... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/51302/hamiltonian-and-non-conservative-force | Hamiltonian and non conservative force
I have to find the Hamiltonian of a charged particle in a uniform magnetic field; the potential vector is $\vec {A}= B/2 (-y, x, 0)$.
I know that $$H=\sum_i p_i \dot q_i -L$$ where $p_i$ is conjugated momentum, $\dot q_i$ is the velocity and $L$ is the Lagrangian.
The result 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": 22, "mathjax_display_tex": 15, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/206527/is-c-0-infty-dense-in-lp/206533 | # Is $C_0^\infty$ dense in $L^p$?
I have a question concerning the Lebesgue spaces: Is $C_0^\infty$ dense in $L^p$ ?
And if yes, why?
Thanks!
-
Over what set? What is the measure you are working with? – Siminore Oct 3 '12 at 11:40
## 3 Answers
Yes. First of all, it is enough to see that any function in $L^p$ wit... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 32, "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/176198-convergence-divergence.html | # Thread:
1. ## Convergence/divergence
Can someone help me with the following problem...I'm stuck!
Find whether the following series converges/diverges using one of the following tests: Nth Term Test for Divergence, Integral Test, Alternating Series Test, Absolute Convergence, Geometric Series, P-Series, Comparison ... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2009/07/10/symmetric-antisymmetric-and-hermitian-forms/?like=1&source=post_flair&_wpnonce=39170bc4ce | # The Unapologetic Mathematician
## Symmetric, Antisymmetric, and Hermitian Forms
The simplest structure we can look for in our bilinear forms is that they be symmetric, antisymmetric, or (if we’re working over the complex numbers) Hermitian. A symmetric form gives the same answer, an antisymmetric form negates the a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 17, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/99969/cosheaf-homology-and-a-theorem-of-beilinson-in-a-paper-on-mixed-tate-motives/119381 | Cosheaf homology and a theorem of Beilinson (in a paper on Mixed Tate Motives)
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I'm trying to understand the proof of Theorem 4.1 in the paper Multiple Polylogarithms and Mixed Tate Motives by AB Goncharov (http://arx... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/90191/list | ## Return to Question
2 deleted 2 characters in body
in aubin's book on page 104 theorem 4.7 there is the theorem: Let $(M,g)$ be a compact $C^{\infty}$ Riemannian manifold. There exists a weak solution $\varphi \in H_{1}$ of $\Delta \varphi = f$ if and only if $\int f dvol = 0$. The solution is unique up to a consta... | {"extraction_info": {"found_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/tagged/co.combinatorics | ## Tagged Questions
0answers
99 views
### One element not belong to at least half of the subsets [closed]
Let $F$ be a collection of subsets of a finite set that is closed under intersection (meaning that the empty set is an element of $F$). Is it true that there must exist one element …
1answer
97 views
### Genera... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/82756-turning-points.html | # Thread:
1. ## Turning points
I dont know if this goes in here but this is a question from my pre-calc class that i could not solve
Find a polynomial whose turning points are at -1, (3 + √7)/4 , and (3 - √7)/4
Any help will be appreciated.
2. Originally Posted by mathprob
I dont know if this goes in here but 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/141970-using-geometry-calculate-volume-solid-under-z-sqrt-64-x-2-y-2-a.html | # Thread:
1. ## Using geometry, calculate the volume of the solid under z = \sqrt{ 64 - x^{2} - y^{2}
Using geometry, calculate the volume of the solid under and over the circular disk .
2. $x^2+y^2+z^2 = 64$ is the equation of a sphere with radius 8........... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/33767/classical-limit-of-schrodinger-equation | # Classical Limit of Schrodinger Equation
There is a well-known argument that if we write the wavefunction as $\psi = A \exp(iS/\hbar)$, where $A$ and $S$ are real, and substitute this into the Schrodinger equation and take the limit $h \to 0$, then we will see that $S$ satisfies the Hamilton-Jacobi equation (for exam... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://simple.wikipedia.org/wiki/Computer_Algebra_System | # Computer Algebra System
A computer algebra system (CAS) is a large computer program that helps people with mathematics and algebra. It changes and moves around (manipulates) mathematical equations and expressions containing numbers and symbols called variables. Variables can stand for known or unknown values that ca... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/67303/list | ## Return to Answer
2 added 1 characters in body
It is easy to see that whenever a space has an unconditional basis then the space of diagonal operators of the basis is equivalent to $\ell_\infty$. If $c_0$ embeds in $K(X,Y)$ then $K(X,Y)$ is not complemented in $B(X,Y)$. One reference for this is: M. FEDER. On subsp... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/22896/why-is-compressible-flow-near-the-choke-point-so-efficient | # Why is compressible flow near the choke point so efficient?
Imagine a steady state, one-dimensional, compressible flow in a horizontal pipe of constant cross sectional area. This flow can be isothermal, adiabatic (Fanno), or diabatic (Rayleigh). As an example, the relevant macroscopic energy balance for Fanno flow 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": 4, "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/198160/subgroups-of-mathbb-z-times-mathbb-z-n-mathbb-z?answertab=oldest | # Subgroups of $\mathbb Z \times(\mathbb Z/n\mathbb Z)$
So I am dealing with a problem from Dummit (specifically 2.1.7) and am having some issues. The part of the problem in question is:
Prove the set of elements of the direct product $\mathbb{Z} \times (\mathbb{Z} / n \mathbb{Z})$ of infinite order together 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": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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photoelectric effect
Definition/Summary... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/87238/morse-kelley-set-theory-consistency-strength/100699 | ## Morse-Kelley set theory consistency strength
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I've come across several references to MK (Morse-Kelley set theory), which includes the idea of a proper class, a limitation of size, includes the axiom schema of 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": 80, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/84134-negative-exponent.html | # Thread:
1. ## negative exponent
-0.0583 = x^-2
Solve for x.
What do you have to do to -0.0583 to find x?
2. Just remember that $x^{-a} = \frac {1}{x^a}$.
So you need to solve $-0.0583 = \frac {1}{x^2}$. Which should be pretty easy.
Hope that helps!
EDIT: Just noticed there's a wrinkle here, since the answer 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/278902/proving-convergence-of-sequence-with-induction | # Proving convergence of sequence with induction
I have a sequence defined as $a_{1}=\sqrt{a}$ and $a_{n}=\sqrt{1+a_{n-1}}$ and I need to prove that it has an upper bound and therefore is convergent. So i have assumed that the sequence has a limit and by squaring I got that the limit is $\frac{1+\sqrt{5}}{2}$ only $\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": 52, "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/63465/is-there-a-closed-form-for-the-nth-integral-of-a-polynomial | # Is there a closed form for the $n$th integral of a polynomial?
Say I have some polynomial $p(x)$ and want to express its $n$th integral, is there a closed form for this?
-
4
It doesn't have a unique $n^{th}$ integral; this is only well-defined up to a polynomial of degree $n-1$. – Qiaochu Yuan Sep 11 '11 at 3:45
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": 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/33095?sort=oldest | ## How/where are semi-log resolutions used?
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In the paper, by János Kollár there is problem 19 (page 8). It is one more strict resolution. A resolution that leaves untouched the semi-simple-normal-crossings singul... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/22801-finding-exact-area-definite-integral.html | # Thread:
1. ## Finding exact area with the Definite Integral
Okay i was busy trying to figure these things out and then i got stuck.
Now using the Riemann notation to calculate the area under the graph $x^2 + 1$ we get the following:
$R_{6} = \sum_{i = 1}^{6} [ f(x_{i}) \cdot ( \frac{3-0}{6})]$
(I calculated $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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3888245 | Physics Forums
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## Bianchi's entropy result--what to ask, what to learn from it
Quote by fzero ... Since the BH is not a pure state, the correct way to do the computation is to compute the energy from (9) in an ensemb... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/203003-re-armstrong-s-basic-topology-pg-70-definition-not-clear.html | 3Thanks
• 1 Post By Deveno
• 1 Post By johnsomeone
• 1 Post By johnsomeone
Thread:
1. Re: Armstrong's Basic Topology. Pg 70. definition not clear.
On pg 70 in Armstrong's Basic Topology book, the author writes:
" We introduce the disjoint union $X+Y$ of spaces $X,Y,$ and the function $j:X+Y \rightarrow X \cup Y$ 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": 44, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/29128/why-determinant-of-a-2-by-2-matrix-is-the-area-of-a-parallelogram | # Why determinant of a 2 by 2 matrix is the area of a parallelogram?
Let $A=\begin{bmatrix}a & b\\ c & d\end{bmatrix}$ be a two by two matrix where the first row of $A$ is $a, b$ and the second row of $A$ is $c, d$. How could we show that $ad-bc$ is the area of a parallelogram with vertex $(0, 0),\ (a, b),\ (c, d),\ (... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/20011/can-the-mic-algorithm-for-detecting-non-linear-correlations-be-explained-intuiti | # Can the MIC algorithm for detecting non-linear correlations be explained intuitively ?
More recently, I read two articles. First one is about the history of the correlation and second is about the new method called Maximal Information Coefficient (MIC). I need your help regarding to understand the MIC method to esti... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method | # Quasi-Monte Carlo method
[Pseudorandom sequence]
[Low-discrepancy sequence (Sobol sequence)]
256 points from a pseudorandom number source, Halton sequence, and Sobol sequence (red=1,..,10, blue=11,..,100, green=101,..,256). Points from Sobol sequence are more evenly distributed.
In numerical analysis, quasi-Monte 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": 17, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/72382-solved-combining-functions.html | # Thread:
1. ## [SOLVED] Combining functions
Given the graph of a function with a few clear ordered pairs. Call it f(x). Can one use those given points on the graph, to sketch (f+f)(x)? Add y values? Add x values? Both?
2. Originally Posted by EyesForEars
Given the graph of a function with a few clear ordered pairs.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2007/04/10/endomorphism-rings/?like=1&source=post_flair&_wpnonce=5d5a17dad5 | # The Unapologetic Mathematician
## Endomorphism rings
Today I want to set out an incredibly important example of a ring. This example (and variations) come up over and over and over again throughout mathematics.
Let’s start with an abelian group $G$. Now consider all the linear functions from $G$ back to itself. 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 21, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/51285/qubit-initial-state | # Qubit initial state
Suppose that a qubit in an initial state that we don't know was measured, and the result was 1. Is it possible to know the initial state of the qubit by the result measured? And if the result would have been 0?
-
## 1 Answer
No. The only thing you know is that $\langle \psi | 1\rangle\neq 0$.
... | {"extraction_info": {"found_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/tagged/yang-mills+lattice-model | Tagged Questions
0answers
78 views
SU(2) critical point and volume dependence
I am doing multi-dimensional plots of $\beta_j$ for SU(2) for infinite volume to understand the flow behavior and I was wondering, before I go too much further, if anyone knew off the top of their ...
1answer
85 views
What evidence do 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": 1, "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/87731/list | ## Return to Answer
2 punctuation and spelling: two extra comments
My answer is in agreement with Grothendieck that topological spaces may be seen as inadequate for many geometric, and in particular, homotopical purposes. Round about 1970, I spent 9 years trying to generalise the fundamental groupoid of a topological... | {"extraction_info": {"found_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": 4, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/156097-solve-y.html | # Thread:
1. ## Solve for y...
I'm doing differential equations and got stuck on this part.
How do I solve for y if I have the equation:
-siny = x^2 + C
Thanks
2. Originally Posted by jzellt
I'm doing differential equations and got stuck on this part.
How do I solve for y if I have the equation:
-siny = x^2 + 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": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://programmingpraxis.com/2011/01/11/two-integrals/?like=1&source=post_flair&_wpnonce=6c7ec013d9 | # Programming Praxis
A collection of etudes, updated weekly, for the education and enjoyment of the savvy programmer
## Two Integrals
### January 11, 2011
The exponential integral appears frequently in the study of physics, and the related logarithmic integral appears both in physics and in number theory. 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": 0, "wp_latex": 2, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/16074/how-to-analyse-this-data-obtained-from-a-simple-physics-experiment-on-attractive/16079 | # How to analyse this data obtained from a simple physics experiment on attractive forces?
I did a simple physics experiment that measures the attractive force a plate experiences towards the other plate as a function of the applied voltage and distance between the plates. Now I have to know whether the gathered data ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/6495/a-differential-equation | # A differential equation
Think of $t$ and $r$ as two independent variables.
• Suppose $E$ be a function of $r$ and $V~$ be a function of $(t,r)$ such that both go to $0$ at $r=0$.
• There exists a positive function $M(r)$ such that $M(0)=0$ and $V(t,r) = -\dfrac{M(r)}{R(t,r)}$ where $R$ is another positive function... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 63, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/87956/unionnew-intersection-of-any-number-of-open-sets-is-also-open/87959 | # union(new: intersection) of any number of open sets is also open
I've just begun reading Spivak's Calculus on Manifold and attempted to proof this simple result.
-I've updated my proof-
My proof are as follows,
My proof for the intersection case still looks kinda dubious though.
@Devan Ware, the notation $N_{\ep... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/13404/capacitance-of-two-cocentric-spheres-contradicting-results | # Capacitance of two cocentric spheres, contradicting results
Suppose we are given two conducting, cocentric spheres of radius $a_1$ and $a_2$ respectively. The inner sphere with charge $q$, the outer sphere with charge $-q$.
I can calculate the capacitance of this system by calculating the potential difference $U$ 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": 14, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-math-topics/19705-sequences.html | # Thread:
1. ## Sequences
1a) Define $(x_n)$ as being the sequence:
$x_1 = 3$
$x_{n+1} = \frac{1}{2}\cdot (x_n + \frac{3}{x_n})$
Prove $x_n$ converges and find the lim.
b) Let $b > 1$ and define $(x_n)$ as being the sequence:
$x_1 = b$
$x_(n+1) = \frac{1}{2}\cdot (x_n + \frac{b}{x_n})$
Prove $x_n$ converges an... | {"extraction_info": {"found_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": 35, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/3003?sort=votes | ## In what sense are fields an algebraic theory?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Since there is no "free field generated by a set", it would seem that
1) there is no monad on Set whose algebras are exactly the fields
and
2) there is no Lawve... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/tagged/multivariable-calculus+integral | # Tagged Questions
0answers
31 views
### A little help integrating this torus?
Let $\mathbf{F}\colon \mathbb{R}^3 \rightarrow \mathbb{R}^3$ be given by $$\mathbf{F}(x,y,z)=(x,y,z).$$ Evaluate $$\iint\limits_S \mathbf{F}\cdot dS$$ where $S$ is the surface of the torus ...
1answer
79 views
### How to integrate $\cos\... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 111, "mathjax_display_tex": 25, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://sciencehouse.wordpress.com/2009/03/27/the-gigabit-machine/ | Scientific Clearing House
Carson C. Chow
The gigabit machine
There are plenty of amazing things about the brain but one of the most mind boggling is that it can be coded by a genome of only 3 billion base pairs or 6 gigabits. If we consider a brain with about $10^{11}$ neurons each receiving something like $10^4$ 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 10, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/26864/what-is-the-use-of-a-universal-not-gate/26865 | # What is the use of a Universal-NOT gate?
The universal-NOT gate in quantum computing is an operation which maps every point on the Bloch sphere to its antipodal point (see Buzek et al, Phys. Rev. A 60, R2626–R2629). In general, a single qubit quantum state, $|\phi\rangle = \alpha |0\rangle + \beta | 1 \rangle$ 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": 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/statistics/210701-help-null-alternative-hypothesis-z-test-proportions.html | # Thread:
1. ## Help with null/alternative hypothesis in Z-test of proportions
I have a clinical trail where all the patients sufferd from a stroke.
I need to assess the efficacy of the drug treatment (drug/placebo) for the entire sample by using the z-test in excel.
I have the values if the drug treatment was a 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/91648?sort=newest | Simple and general relation between continuant polynomials
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Continued fraction $[a_0,a_1,...,a_n]$ may be expressed as quotient of two polynomials of $(a_0,a_1,...,a_n)$, named continuants (see http://en.wikipedia.org... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2007/04/07/the-first-isomorphism-theorem-for-rings/?like=1&source=post_flair&_wpnonce=3fdfac1636 | # The Unapologetic Mathematician
## The First Isomorphism Theorem (for rings)
Just like we had for groups, there is an isomorphism theorem for rings. In fact, the demonstration goes much the same as it did there.
Any subring $S$ of a ring $R$ comes equipped with an inclusion homomorphism $\iota_{(R,S)}:S\rightarrow ... | {"extraction_info": {"found_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": 49, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/35301?sort=votes | ## P/poly algorithm for polynomial identity testing
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
By the Schwartz–Zippel lemma, "Is this arithmetic formula identically zero?" is in coRP $\subseteq$ BPP $\subset$ P/poly, with the second inclusion by Adleman'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": 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/38771?sort=newest | ## Dual Schroeder-Bernstein theorem
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This question was motivated by the comments to http://mathoverflow.net/questions/38754/dual-of-zorns-lemma
Let's denote by the Dual Schroeder-Bernstein theorem (DSB) the state... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2009/02/11/repeated-eigenvalues/?like=1&source=post_flair&_wpnonce=18b5244a97 | # The Unapologetic Mathematician
## Repeated Eigenvalues
So we’ve got a linear transformation $T$ on a vector space $V$ of finite dimension $d$. We take its characteristic polynomial to find the eigenvalues. If all of its roots are distinct (and there are $d$ of them, as there must be if we’re working over an algebra... | {"extraction_info": {"found_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": 13, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/88001?sort=newest | ## Relative generic flatness.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
It is known that any morphism is flat at an open set of points. I'd like to know if there is a relative version of this fact.
Let $f: X \rightarrow Y$ and $g:Y \rightarrow S$ be mor... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://alanrendall.wordpress.com/2011/05/ | # Hydrobates
A mathematician thinks aloud
## Archive for May, 2011
### Is half of what is in immunology textbooks wrong?
May 31, 2011
Yesterday I heard a talk by Rolf Zinkernagel who won a Nobel prize together with Peter Doherty in 1996 for the discovery of the MHC restriction in the T cell recognition of antigens... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 7, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/102214-problem-limits.html | # Thread:
1. ## Problem on Limits
Can anyone give guidance and point me in the right direction for this problem? I've tried a couple approaches that have lead to dead ends and am not sure what to do. Thanks.
(SqRT(10x+9)-SqRT(79))/x-7
Limit x->7
2. Originally Posted by JP22
Can anyone give guidance and point me 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/41334/list | Return to Question
3 Corrected well-ordered to well-founded
Symmetric Proof that Product is Well-OrderedWell-Founded
This is a fairly minor, technical question, but I'll toss it out in case someone has a good idea on it.
Suppose $(X,<_X)$ and $(Y,<_Y)$ are well-orderings well-founded orderings (not necessarily line... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 91, "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/150732/asymptotic-expansion-of-x-n-x-n-frac1-tanx-n | # Asymptotic expansion of $x_{n}$, $x_{n}=\frac{1}{\tan(x_{n})}$
I would like to find a two-term or a three-term asymptotic expansion of $x_{n}$ the unique solution of $$x_{n}=\frac{1}{\tan(x_{n})}$$ on the interval $]n\pi,n\pi+\pi[$
We have: $$x_{n}=n\pi+\arctan(\frac{1}{x_{n}})$$
So $$x_{n} \sim_{n\rightarrow \inf... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/30714/list | ## Return to Answer
2 added 67 characters in body
Q/Z
$\mathbb{Q}/\mathbb{Z}$ is a pretty terrible abelian group, or a rather hard one, there may be better injective resolutions to work with. It would certainly be easier to do the projective resolution, use $0 \to Z \mathbb{Z} \to Z \mathbb{Z} \to Z/n \mathbb{Z}/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": 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/27662/extend-an-alternative-definition-of-limits-to-one-sided-limits/27679 | # extend an alternative definition of limits to one-sided limits
The following theorem is an alternative definition of limits. In this theorem, you don't need to know the value of $\lim \limits_{x \rightarrow c} {f(x)}$ in order to prove the limit exists.
Let $I \in R$ be an open interval, let $c \in I$, and let $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": 111, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/algebra/26681-how-do-i-find-sides-triangle.html | # Thread:
1. ## How do i find the sides of this triangle?
Heres the question:
On the banks of a river, surveyors marked locations A, B, and C. The measure of angle ACB=70 degrees and the measure of angle ABC=65 degrees. Which expression shows the relationship between the lengths of the sides of this triangle?
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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/40075/chain-complexes-and-linear-infinity-categories | Chain Complexes and Linear Infinity-Categories
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A statement I heard recently is that "chain complexes are the same thing as strict linear $\infty$-categories". Can someone explain how to see this?
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The cochain comp... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "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/Limit_of_a_sequence | Limit of a sequence
n n sin(1/n)
1 0.841471
2 0.958851
...
10 0.998334
...
100 0.999983
As the positive integer n becomes larger and larger, the value n sin(1/n) becomes arbitrarily close to 1. We say that "the limit of the sequence n sin(1/n) equals 1."
In mathematics, the limit of a sequence is the value that 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": 86, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/180782-inequality-proof.html | # Thread:
1. ## Inequality proof.
I need to mathematically prove that:
(a + b)/(c + d) lies between (a / c) and (b / d).
a,b,c,d are all real and >0
Any ideas?
(also, if necessary you can assume that b>a and d>c but preferably not)
2. We don't need to assume $b\geq a$ (or the other way), but we do have to assume... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-algebra/156643-subgroup-question.html | # Thread:
1. ## subgroup question
Q: Find all possible finite subgroups of the non negative rational numbers under multiplication.
I can only think of the singleton set containing the identity element which would be of order 1. All other sets would be of infinite order. I feel there is more to this though.
thanks
... | {"extraction_info": {"found_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": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/40/is-it-possible-to-invoke-the-oeis-from-mathematica?answertab=active | # Is it possible to invoke the OEIS from Mathematica?
I had always wondered if there might be a way to write a function, which I'll call `OEISData[]`, that more or less works as a curated data function for The On-Line Encyclopedia of Integer Sequences.
I would imagine that the usage might be a little something like 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": 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/geometry/105216-finding-measure-angles.html | # Thread:
1. ## Finding the measure of angles...
For an acute angled triangle,all its angles have measure in integral degree.The smallest angle has a mesure 1/5th the measure of largest.Find all the measures of triangle>>
2. Hello anshulbshah
Originally Posted by anshulbshah
For an acute angled triangle,all its angl... | {"extraction_info": {"found_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": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://tcsmath.wordpress.com/2009/06/ | # tcs math – some mathematics of theoretical computer science
## June 19, 2009
### Lecture P1. From Integrality Gaps to Dictatorship Tests
Filed under: CSE 599S — Tags: discrete harmonic analysis, hardness of approximation, invariance principle — James Lee @ 2:25 pm
Here are Prasad Raghavendra‘s notes on one of tw... | {"extraction_info": {"found_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": 107, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/33453/complex-analysis-differentiablity-continuity-analyticity | # Complex analysis: differentiablity/continuity/analyticity
Suppose I have a real-valued function f defined on a complex open connected set D. Am I right in saying that: f is analytic on D if and only if f is n times continuously differentiable on D?
Or does this only apply if f is complex valued?
thanks
-
1
What ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/139584/whats-the-most-straight-forward-way-to-prove-walrass-law?answertab=active | # What's the most straight-forward way to prove Walras's Law?
Walras' Law states that summation of pi Ei(p) = 0 for all pi. We define Ei(p) = xi(p) - qi(p) - Ri. What are the next steps that I should take?
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I don't quite know what your notation is. The proof starts by asserting LNS preferences and claiming walras' ... | {"extraction_info": {"found_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/questions/11044?sort=newest | ## What is the probability that 4 points determine a hemisphere ?
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Given 4 points ( not all on the same plane ), what is the probability that a hemisphere exists that passes through all four of them ?
-
Related 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": 22, "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/96760?sort=newest | Schemes associated to vector spaces
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Let $k$ be a field. Let $F$ be a covariant functor on the category of $k$-algebras to the category of sets. Assume that the opposite functor $F^{op}$ on the category of affine $k$-... | {"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": 40, "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/84074/undecidable-sentences-of-first-order-arithmetic-whose-truth-values-are-unknown | ## undecidable sentences of first-order arithmetic whose truth values are unknown
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Godel's undecidable sentences in first-order arithmetic were guaranteed to be true, by construction. But are there examples of spe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 108, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/73368-finding-velocity-function.html | # Thread:
1. ## Finding the velocity function
I thought acceleration was the change in velocity or in other words the derivative of the velocity function, and thus am trying to solve the problem I've attached keeping this in mind but it's not working. Any helpful hints?
Attached Thumbnails
2. Originally Posted by fa... | {"extraction_info": {"found_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": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/86679?sort=newest | ## Why the notation $\mathcal{O}(\mathcal{L})$ for line bundles $\mathcal{L}$
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Let $X$ be a complex manifold. If $D$ is a divisor on $X$, then $\mathcal{O}(D)$ denotes the (up to isomorphic) line bundle $\mathcal{... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 43, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/29949/what-is-the-shortest-program-for-which-halting-is-unknown/29953 | ## What is the shortest program for which halting is unknown?
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In short, my question is:
What is the shortest computer program for which it is not known whether or not the program halts?
Of course, this depends ... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.chemeurope.com/en/encyclopedia/Refractive_index.html | My watch list
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# Refractive index
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": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/tags/string-theory/info | Tag info
About string-theory
String theory is an research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything, a self-contained mathematical model that describes all fundamental forces and forms of matter. String theory posits... | {"extraction_info": {"found_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://math.stackexchange.com/questions/168786/how-to-approach-integrals-as-a-function/168835 | # How to approach integrals as a function?
I'm trying to solve the following question involving integrals, and can't quite get what am I supposed to do:
$$f(x) = \int_{2x}^{x^2}\root 3\of{\cos z}~dz$$ $$f'(x) =\ ?$$
How should I approach such integral functions? Am I just over-complicating a simple thing?
-
7
Are ... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/27428/does-the-axiom-of-choice-or-any-other-optional-set-theory-axiom-have-real-wor/29192 | ## Does the Axiom of Choice (or any other “optional” set theory axiom) have real-world consequences? [closed]
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Or another way to put it: Could the axiom of choice, or any other set-theoretic axiom/formulation whic... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/20454-word-prob.html | # Thread:
1. ## Word prob.
A particle in a magnetic field travels in a straight line. The force (in Newtons) acting upon it is given by the function
F(s) = square root of (s) −s^2, where s = f(t), the position of the particle in meters, changes with time t. At what rate is the force changing with respect to time at a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/65405?sort=newest | ## Induced pretopologies on sSet
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Recall that the geometric realisation functor $| - |: sSet \to Top$ preserves products (choosing $Top = k Space$ or similar). Thus any given singleton Grothendieck pretopology on ... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/101014/fundamental-problems-whose-solution-seems-completely-out-of-reach/101075 | ## Fundamental problems whose solution seems completely out of reach [closed]
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In many areas of mathematics there are fundamental problems that are embarrasingly natural or simple to state, but whose solution seem... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 157, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/50186?sort=votes | ## If the Riemann Hypothesis fails, must it fail infinitely often?
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That is must there either be no non-trivial zeros off the critical line or infinitely many?
I'm sure that no one believes otherwise, but I've ne... | {"extraction_info": {"found_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://math.albany.edu/~hammond/mmlmisc/bordermx2t.html | # Another BorderMatrix Example
Make the whole thing a $4×4$ ordinary table using table rules with inline math in the cells except for the first row and first column:
| | | ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 7, "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/revisions/35090/list | ## Return to Question
4 deleted 16 characters in body
Normally a 2-sided error randomized algorithm will have some constant error $\varepsilon < 1/2$. We know that we can replace the error term for any inverse polynomial. And the inverse polynomial can be replace replaced for an inverse exponential. Say that we 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": 30, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cs.stackexchange.com/questions/8970/how-to-prove-a-problem-is-np-complete | How to prove a problem is NP-complete?
Consider the following problem: Given two graphs $G_1 = (V_1, E_1)$ and $G_2 = (V_2, E_2)$ and some non-negative integer $k \in \mathbb{N}$, is it possible to delete at most $k$ vertices from $G_1$ to obtain $G_1'$ such that $G_1' \cong G_2$, i.e. the resulting graph is isomorphi... | {"extraction_info": {"found_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/79927/which-n-maximize-gn-frac-sigmann-log-log-n | ## Which $n$ maximize $G(n)=\frac{\sigma(n)}{n \log \log n}$?
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By Robin's theorem
$$G(n)=\frac{\sigma(n)}{n \log \log n}$$
is bounded by $e^\gamma \approx 1.78107241799$ for $n>5040$ assuming Riemann hypothesis ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 102, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://en.wikipedia.org/wiki/Beer-Lambert_law | Beer–Lambert law
(Redirected from Beer-Lambert law)
An example of Beer–Lambert law: green laser light in a solution of Rhodamine 6B. The beam intensity becomes weaker as it passes through solution
In optics, the Beer–Lambert law, also known as Beer's law or the Lambert–Beer law or the Beer–Lambert–Bouguer law (named... | {"extraction_info": {"found_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": 44, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/275115/why-fourier-transformation-use-complex-number | # Why fourier transformation use complex number?
I know that the Fourier transform is as follows:$$\hat{f}(\xi)= \int_{-\infty}^{\infty}\exp(-\mathrm ix\xi)f(x)\mathrm{d}x$$ but I couldent understand why should use complex number $i$ in the integration. Is that means I have a real number function and after fourier tra... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/84846/joint-distribution-of-sum-of-independent-normals | Joint distribution of sum of independent normals [closed]
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Suppose we have three independent normally distributed random variables $$X_0 \sim \mathcal{N}(\mu_0, \sigma_0^2),$$ $$X_1 \sim \mathcal{N}(\mu_1, \sigma_1^2)... | {"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": 13, "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/14418/can-one-canonical-conjugate-variable-be-considered-to-be-the-frequency-of-the | # Can one canonical conjugate variable be considered to be the “frequency” of the other one? (which could be a “wavelength”)?
So, from http://en.wikipedia.org/wiki/Conjugate_variables#Derivatives_of_action, we have...
• The energy of a particle at a certain event is the negative of the derivative of the action along ... | {"extraction_info": {"found_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/33942/do-the-base-3-digits-of-2n-avoid-the-digit-2-infinitely-often-what-is-the-s | ## Do the base 3 digits of $2^n$ avoid the digit 2 infinitely often — what is the status of this problem?
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I believe this question is due to Erdős and Graham, and I think it is still open: does the base 3 expansio... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/82270/reference-request-gluing-manifolds-along-pieces-of-boundary | ## Reference request: gluing manifolds along pieces of boundary
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I've been asked for a reference for the following construction and since I didn't know one, I thought I'd ask here if anyone did.
Consider two smoo... | {"extraction_info": {"found_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://aquantumoftheory.wordpress.com/ | # A Quantum Of Theory
Exploring new paths in quantum physics
### Quantum theory – A view from the inside – Part VI
The last post gave a possible answer to a very interesting question, namely “Why does the wave function collapse and where does the randomness come from?”. But we have also left out a few important deta... | {"extraction_info": {"found_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": 55, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/55691?sort=newest | ## For what reductive groups $G$ over $K$ are the inner forms classified by $H^1(K, G^{ad})$?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Suppose $G$ is a connected reductive algebraic group over an arbitrary field $K$; let $Z$ be the center of $G$. The 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": 42, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://catalog.flatworldknowledge.com/bookhub/reader/4309?e=averill_1.0-ch96appE | # General Chemistry: Principles, Patterns, and Applications, v. 1.0
by Bruce Averill and Patricia Eldredge
Study Aids:
Click the Study Aids tab at the bottom of the book to access your Study Aids (usually practice quizzes and flash cards).
Study Pass:
Study Pass is our latest digital product that lets you take not... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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://physics.stackexchange.com/questions/32427/how-convincing-is-the-evidence-for-dark-matter-annihilation-at-130-gev-in-the-ga?answertab=votes | # How convincing is the evidence for dark matter annihilation at 130 GeV in the galactic center from the Fermi Satellite data?
I listened to Christoph Weniger present his results at SLAC today. See his paper is here: http://arxiv.org/abs/1204.2797 and also see a different analysis here: http://arxiv.org/abs/1205.1045.... | {"extraction_info": {"found_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... |
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