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http://physics.stackexchange.com/questions/23316/how-fast-is-heat-transferred-by-conduction | # How fast is heat transferred by conduction?
How fast is heat transferred by conduction? Is there some simple, but quantitative way that starts from some properties of the material (e.g. its thermal conductivity) and makes rough predictions, for example about how much time is needed for temperature to change at one e... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/122308/when-a-riemannian-manifold-is-of-hessian-typ | ## When a Riemannian manifold is of Hessian Typ
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When a Riemannian manifold is of Hessian Type (i.e., a Riemannian manifold which its metric is Hessian)
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1
This doesn't seem to be a question. – HW Feb 19 at 14:... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/213607/a-mapping-function-is-requested | # a mapping function is requested
I have $n$ data points in $d$-dimensional space, i.e $x_1,x_2,...x_n$ where $x_i\in R^d$. I want an interpolation function $f:R^d-> R$ on these data points to map them to $y_1,y_2,...,y_n$, where $y_i=f(x_i)$. In other words, I require an extension to Lagrange interpolation method 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": 17, "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/199530/probability-limit-of-a-decreasing-uncountable-family-of-sets/199541 | # Probability limit of a decreasing (uncountable) family of sets.
Let $t^*\in(0,1)$ and $(\Omega,\mathcal{F},P)$ be a probability space. Suppose I have set $A\in\mathcal{F}$ and an uncountable family of sets $(B_t : t\in[0,1])\subset\mathcal{F}$ with the following properties:
1. $P(A)>0$ and $P(B_t)=p$ where $p>0$ 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": 30, "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/tagged/internal-energy?sort=active&pagesize=15 | # Tagged Questions
The internal-energy tag has no wiki summary.
1answer
41 views
### Why doesn't intensity of light affect the emission of electrons?
So electrons of specific atoms have a minimum amount of energy needed to escape the atom, called the work function, W. Now let's say that you emit a certain frequency... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-geometry/161797-uniform-continuity-proof.html | # Thread:
1. ## Uniform Continuity Proof
Hi,
I'm not sure how to prove this statement:
Suppose f is uniformly continuous on the set S and let T be the image of S under f. Also assume that the function g is uniformly continuous on T. Prove that g o f is uniformly continuous on S?
Thanks a lot!
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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/18770?sort=newest | ## Is there a name for this property of a topology?
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This property seems like it should have a nice name, but I can't find one anywhere. Does anyone know a name for this?
For each non-empty open set $U$, there ex... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/98272/on-the-vector-product/98279 | # on the vector product
Can the product(element to element) of two vector $\vec{a}$ and $\vec{b}$ with the same dimension be written as the usual vector(or matrix) product?
Say $\vec{a}=[2,3],\vec{b}=[4,5]$ and $\vec{a}~\text{product(element to element)}~\vec{b}=[8,15]$
Thank you!
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if you mean dot product ,then 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": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://gowers.wordpress.com/2012/11/ | # Gowers's Weblog
Mathematics related discussions
## Archive for November, 2012
### What maths A-level doesn’t necessarily give you
November 20, 2012
I had a mathematical conversation yesterday with a 17-year-old boy who is in his second year of doing maths A-level. Although a sample of size 1 should be treated 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": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/234832/show-that-e-x2-is-the-solution-to-the-initial-value-problme-y2-4x2y | # Show that $e^{-x^2}$ is the solution to the initial value problme $y''+(2-4x^2)y=0$ $y(o)=1$ $y'(0)=0$
I have already worked out a lot of stuff already from previous parts of the questions and I think I've got to work from the fact that $a_{2k+1}=0$ and $a_{2k}= (-1)^k/k!$ for k>0 satisfies the recurrence relation o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/298543/how-to-show-ln-lnk1-ln-lnk-frac1k-lnk-forall-k-in-mathbbn | How to show $\ln(\ln(k+1))-\ln(\ln(k))<\frac{1}{k \ln(k)},\forall K\in \mathbb{N}, K\geq 2.$
How can I show the inequality $\ln(\ln(k+1))-\ln(\ln(k))<\dfrac{1}{k\ln(k)},\forall K\in \mathbb{N}, K\geq 2.$
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1
Welcome to MSE! If this is homework, please tag it as such, people will help you anyway. And please try and 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": 8, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/111541/nth-roots-and-e | # $n^{th}$ roots and $e$.
In Churchill's book on complex variables, the $n^{th}$ root of $e$ is defined to be $e^{1/n}$. A comment is made that in this respect $e$ is treated differently than the $n^{th}$ roots of other complex numbers (in the sense that there are typically n roots of the nth root of a number in compl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 46, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/38738/a-question-on-the-prime-divisors-of-p-1/49562 | ## A question on the prime divisors of p-1
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For each positive integer n we may define the convergent sum $$s(n)=\sum_{p}\frac{(n,p-1)}{p^2}$$ where the summation is over primes p and $(a,b)$ denotes the greatest 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": 39, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/101780-absolute-value-inequality.html | # Thread:
1. ## Absolute value inequality
Solve the inequality |x^2 - x| - |x| < 1 analytically.
2. $\left| x \right|\left| x-1 \right|-\left| x \right|-1<0.$
Three cases to solve this:
• $x\le0.$
• $0\le x\le1.$
• $x\ge1.$
3. Hmm how did you come up with the second case, $0 \leq x \leq 1$? In the past for all equ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 36, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/39923/can-a-self-adjoint-operator-have-a-continuous-set-of-eigenvalues/77406 | ## Can a self-adjoint operator have a continuous set of eigenvalues?
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This should be a trivial question for mathematicians but not for typical physicists.
I know that the spectrum of a linear operator on a Banach... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/45451/spring-coupled-platforms-conservation-of-momentum-can-it-be-solved-with-fres/45468 | Spring coupled platforms & conservation of momentum - can it be solved with freshman physics?
This question came up as an exercise in a first year undergraduate course I was a TA for. It turned out to be a lot more difficult (impossible?) than anticipated...
Two platforms of mass $M_1$ and $M_2$ ($M_1\neq M_2$) are 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": 15, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=148386 | Physics Forums
Recognitions:
Homework Help
## An introduction to the analysis of statically indeterminate systems
It is assumed that the reader is familiar with the basic concepts of structural analysis. Further on, I am aware of the possible inconsistencies and errors in this writing, and hereby invite all who 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": 84, "mathjax_display_tex": 38, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/28108/calculating-mass-of-object-by-lifting-edge | # Calculating mass of object by lifting edge
Assuming a solid rectangular plate, hinged along one edge. How does one calculate the mass of the plate if the force necessary to lift the opposite edge is known?
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Something's missing in your problem... – Pygmalion May 10 '12 at 12:35
@Pygmalion What are you thinking 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": 8, "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/39317/maximum-principle-fails-when-uc-cant-find-example/39327 | Maximum Principle fails when u∉C²(Ω)? Can’t find example.
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I would like an example where the maximum principle fails in a bounded smooth domain $\Omega$ where one has a solution which is not $C^2(\Omega)$ to $Lu=0$ 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": 21, "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/17522/are-there-rules-of-logic-dealing-with-the-implies-operator | # Are there rules of Logic dealing with the implies operator?
I'm just beginning a course in discrete mathematics and I'm learning a few of the basic laws to prove propositions. I understand how to use propositions that use the logical connectives, AND , OR, NOT. However I'm not sure how to prove a proposition that ha... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/3005/derivation-of-maxwells-equations-from-field-tensor-lagrangian/3006 | Derivation of Maxwell's equations from field tensor lagrangian
I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$ (where $F^{\mu\nu} = \partial^\mu A^\nu - \partial^\nu... | {"extraction_info": {"found_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": 20, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://crypto.stackexchange.com/questions/5694/public-keys-and-their-protocols/5850 | # Public keys and their protocols
I'm having difficulties understanding exactly what this protocol means:
$S \to D : \{N_S , S\}K_D$
$D \to S : \{N_S , N_D \}K_S$
$S \to D : \{N_D \}K_D$
"where $S$ represents the supervisor’s console and $D$ represents the door controller and the other symbols have their usual sec... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 35, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/200423/show-that-the-set-w-is-a-countable-set/200426 | # Show that the set W is a countable set.
Q: Let the alphabet A be a finite set of $n$ letters such that A=${a_1, a_2,...,a_n}$ and let W be the set of all possible words written from this finite alphabet (here a word is a finite concatenation of letters). Show that W is countable.
I don't know how to do this...?
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... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/22295?sort=newest | ## (∞,1) vs Category weakly enriched over spaces
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What is the difference between:
($\infty,1$) categories - in which have for two objects you have an ($\infty,0$) category of morphisms (i.e. a space of morphisms)... | {"extraction_info": {"found_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://mathoverflow.net/revisions/60398/list | ## Return to Answer
2 notation error.
I'm pretty certain the answer is no provided $n \geq 3$. Let $X$ be the Whitehead manifold: http://en.wikipedia.org/wiki/Whitehead_manifold
It's a contractible open 3-manifold which is not homeomorphic to $\mathbb R^3$.
$X^2$ I claim is homeomorphic to $\mathbb R^6$. I don't ha... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/31142/does-the-fundamental-frequency-in-a-vibrating-string-not-necessarily-have-the-st/31157 | # Does the Fundamental Frequency in a Vibrating String NOT Necessarily Have the Strongest Amplitude?
I am doing some experiments on musical strings (guitar, piano, etc.). After performing a Fourier Transform on the sound recorded from those string vibrations, I find that the fundamental frequency is not absolutely 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": 9, "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/50693/stable-motivic-cohomology-with-finite-coefficients | ## Stable motivic cohomology with finite coefficients?
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In this question, which attracted no responces so far, I've asked whether it is possible to extend the Beilinson-Lichtenbaum etale descent rule for motivic 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": 6, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/tagged/probability?sort=votes&pagesize=15 | # Tagged Questions
A probability provides a quantitative description of the likely occurrence of a particular event.
7answers
18k views
### What is the difference between “likelihood” and “probability”?
The wikipedia page claims that likelihood and probability are distinct concepts. In non-technical parlance, "like... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/69321/list | ## Return to Answer
4 added 184 characters in body
I don't understand the questions for the following reason: If the image of $X$ is complemented in $E_1$ then the extension is split. Indeed, if $P$ is a projection of $E_1$ onto the image of $X$ then $1-P$ is a projection onto an isomorph of $Y$ by the open mapping 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": 73, "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/144332/interesting-recurrence-relation-tn-t-sqrtn-tn-sqrtn-n | # Interesting Recurrence Relation $T(n) = T(\sqrt{n}) + T(n-\sqrt{n}) + n$
I found an interesting recurrence that I do not know how to solve. I think this has to do with quicksort with pivots at rank $\sqrt{n}$. I do not know how to approach this problem nor found any helpful resources about it.
Here is the recurrenc... | {"extraction_info": {"found_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://mathoverflow.net/questions/37202?sort=votes | ## Derived algebraic geometry via dg rings?
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Jacob Lurie's stuff seems to develop derived algebraic geometry via $E_\infty$ rings and/or maybe something like simplicial commutative rings. Ben Wieland's comment 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": 5, "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/29359/list | ## Return to Answer
1 [made Community Wiki]
Of course, the Cayley Hamilton Theorem is not really hard, and there are many many proofs of it. But you have to admit that, at least when you first step into linear algebra, it's rather surprising that it's enough to proof the theorem for diagonal matrices (which is a very... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/70645-integrals.html | # Thread:
1. ## Integrals
find the following indefinite integral (using u substitution):
$\int x \sqrt[3]{x+1} dx$
evaluate the following definite integrals using the Fundamental Theorem of the Calculus (u sub involved):
$\int_{0}^{\frac{\pi}{4}} (1 + tan^2 x)sec^2 x dx$
$\int_{0}^{2|b|} \frac{x}{\sqrt{x^2 + b^2}... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/122201/is-this-function-on-the-surface-smooth?answertab=votes | # Is this function on the surface smooth?
Consider the following functions $F_{ij}:S\subset{\mathbb R}^3\to{\mathbb R}$, $$F_{ij}(y) = \begin{cases} \frac{(y_i-x_i)(y_j-x_j)(y-x)\cdot n(y)}{|y-x|^3},&y\neq x; \\ 0,& y=x.\end{cases} \quad i,j = 1,2,3$$ where $S$ is a surface which has a continuously varying normal vect... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/81789/is-this-a-subcase-of-the-fundamental-lemma | Is this a subcase of the fundamental lemma?
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Let $F$ be a local field and $G= GL(n,F)$.
Assume that $\gamma$ is an element of $G$ and $G_\gamma$ is its centralizer. The orbital integral is defined as $$O_\gamma^G( \p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 84, "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/tagged/action?sort=faq&pagesize=15 | # Tagged Questions
The action tag has no wiki summary.
5answers
1k views
### Hamilton's Principle
Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum). Why should the action integral be stationary? On ...
2answers
1k views
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.maths.usyd.edu.au/u/pubs/publist/preprints/2010/thomas-26.html | ## Infinite generation of non-cocompact lattices on right-angled buildings
### Anne Thomas and Kevin Wortman
#### Abstract
Let $\Gamma$ be a non-cocompact lattice on a locally finite regular right-angled building $X$. We prove that if $\Gamma$ has a strict fundamental domain then $\Gamma$ is not finitely generated. ... | {"extraction_info": {"found_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/167752/bipartite-simple-graph-matching-proof/270259 | # bipartite simple graph matching-proof
Prove that if $G$ is a bipartite simple graph and every vertex has the same degree $k$, then the edges of $G$ can be partitioned into $k$ matchings. Can we then prove the same if every vertex has degree $\le k$?
-
It's not clear in your statement of the problem whether or not e... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 96, "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/35408?sort=oldest | ## Naturally occuring groups with cardinality greater than the reals.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In group theory, the single most important piece of information about a group is its cardinality, which is of course either finite, countably ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/25513?sort=oldest | ## Zariski closed sets in C^n are of measure 0
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This is related to another question in which it is proved that Zariski open sets are dense in analytic topology.
But it is intuitive that something more is true. Na... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 59, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/6009/solution | ### Folium of Descartes
Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
### Witch of Agnesi
Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.
### Quick Route
What is the quickest route across a ploughed field when 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": 30, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physicspages.com/2011/09/26/gausss-law/ | Notes on topics in science
## Gauss’s Law
Required math: vectors, calculus
Required physics: electrostatics
Reference: Griffiths, David J. (2007) Introduction to Electrodynamics, 3rd Edition; Prentice Hall – Sec 2.2.
Gauss’s law in electrostatics is a relation between the charge contained by a closed surface and 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": 0, "wp_latex": 22, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/26402?sort=oldest | ## {transcendental numbers} \ {computable transcendental numbers}
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I know Chaitin's constant Ω is not computable (and therefore transcendental). Are there other specific, known noncomputable numbers? I am trying 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": 37, "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/7687?sort=oldest | ## Clifford algebra as an adjunction?
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Background
For definiteness (even though this is a categorical question!) let's agree that a vector space is a finite-dimensional real vector space and that an associative 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": 101, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/discrete-math/73672-binomial-expansion.html | # Thread:
1. ## Binomial expansion
In each of the following expansions , find the term as stated .
(1) $(1+x)^{10}$ , 5th term
(2) $(2a+b)^{12}$ , 10th term
(3) $(x-\frac{1}{x})^6$ , constant term
2. Originally Posted by thereddevils
In each of the following expansions , find the term as stated .
(1) $(1+x)^{10}... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/32701/comparing-observed-data-to-simulated-data | # Comparing observed data to simulated data?
I have a set of observed values (shown with black dots in the figure) that I would like to compare to some simulated data (100 simulated datasets shown as box plots with quartiles, extremes (excluding outliers) as whiskers, and outliers as white dots).
The observed values ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "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/49979?sort=votes | ## Statistics of a simple Markov chain
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Imagine a two-state Markov chain which hops between the states $\pm 1$ with probability $p<1/2$, so that the autocorrelation function after $k$ steps is
$\rho_k = (2p-1)^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": 70, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/118893-jordan-form-help.html | # Thread:
1. ## Jordan form help...
I stumbled across this question, and I'm not quite sure how to go about and find the Jordan form of this kind of question. Any help on how to get started?
Let
N be an element of L(P4(C)), defined by N(p(z)) = zp'''(z)+p'(z).Show that N is nilpotent and find the Jordan form of N.
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/math-topics/162723-physics-multiple-choices-question.html | # Thread:
1. ## Physics ( Multiple choices question)
How do i find which force creates the largest moment about the pivot?
What is the Pole on the point of the solenoid with an arrow pointing towards it drawn by me as induced by the other circuit?
Any help is appreciated. I am looking for the reasoning behind not o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/13832/integrals-of-motion?answertab=votes | # Integrals of Motion
Landau writes in chapter 2 of his Mechanics book "The number of independent integrals of motion for a closed mechanical system with s degrees of freedom is 2s-1". Then he goes on to show how -- "Since the equations of motion for a closed system do not involve time explicitly, the choice of the 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": 6, "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/representation-theory | # Tagged Questions
The representation-theory tag has no wiki summary.
learn more… | top users | synonyms
2answers
80 views
### When are there enough Casimirs?
I know that a Casimir for a Lie algebra $\mathfrak{g}$ is a central element of the universal enveloping algebra. For example in $\mathfrak{so}(3)$ the gener... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/56641-got-class-30-mins-3-problems-i-dont-know-how-solve.html | Thread:
1. Got class in 30 mins, 3 problems I dont know how to solve
These are incredibly difficult
2) A fourth degree polynomial f(x) with real coefficients and leading coefficient of 1 has zeroes of -1, 2,1 -i. Write the polynomial as a product of linear and quadratic factors with real coefficients that are irredu... | {"extraction_info": {"found_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/13838/what-kind-of-vector-space-does-the-set-of-complex-real-solutions-of-the-follow/13858 | # What kind of vector space does the set of (complex/real) solutions of the following differential equation form?
I'm doing a multiple choice exercise and I'm stuck at a question, where there are two possible answers (may be both or none correct).
Consider the differential equation
$$y''+y'+y=0$$
for $y(x)$. Which ... | {"extraction_info": {"found_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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/5553/bent-combining-functions/5554 | # Bent Combining Functions
Bent functions are boolean functions with maximum nonlinearity and are widely studied for their potential applications in cryptography. Lets say you wanted to use a simple two input AND gate as a nonlinear combiner for the outputs of two Linear Feedback Shift Registers . Because a two input ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/101062/list | ## Return to Answer
1 [made Community Wiki]
It is very common in set theory to prove that a particular model or structure is well-founded by mapping it into a fixed well-founded structure. The point is that if $j:\langle M,{\in^M}\rangle\to \langle N,{\in}\rangle$ is $\in$-preserving, then any instance of ill-founded... | {"extraction_info": {"found_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/17152/given-an-infinite-number-of-monkeys-and-an-infinite-amount-of-time-would-one-of/17156 | # Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet?
Of course, we've all heard the colloquialism "If a bunch of monkeys pound on a typewriter, eventually one of them will write Hamlet."
I have a (not very mathematically intelligent) friend who presented it as if it 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": 39, "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/129610-banach-algebras-question-4-a.html | # Thread:
1. ## Banach algebras question 4
I've the lats three questions about maximal ideals in Banach algebras.
How can I show the following (in red shape) part of proof?
2. Originally Posted by Arczi1984
I've the lats three questions about maximal ideals in Banach algebras.
How can I show the following (in red ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/194916-asymptotic-variance-print.html | Asymptotic Variance
Printable View
• January 4th 2012, 07:41 AM
Duke
Asymptotic Variance
What is the asymptotic variance of an estimator? There seems to be several definitions on the web but I know the one I'm after includes the expectation of the second derivative of the log-likelihood.
• January 4th 2012, 10:01 PM
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/225697/is-this-the-correct-way-to-prove-exists-y-forall-x-px-vee-qy-equiv-f?answertab=oldest | Is this the correct way to prove $\exists y \forall x (P(x) \vee Q(y)) \equiv \forall xP(x) \vee \exists x Q(x)$?
$\exists y \forall x (P(x) \vee Q(y)) \equiv \forall xP(x) \vee \exists x Q(x)$
If the LHS is true, then there are two cases: P(x) is true, in which case $\forall$ P(x) is true and the RHS is true, and Q(... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "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/12201/why-dont-waves-with-different-wavelengths-interfere-with-each-other-in-white-li/12204 | # Why don't waves with different wavelengths interfere with each other in white-light?
The book I'm reading about optics says at some point that "each color (wavelength) contained in the white light interferes only with itself". But why is this so?
Edit: I moved the rest of the question elsewhere.
-
Closely related... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=190540 | Physics Forums
Thread Closed
Page 1 of 2 1 2 >
## Wavefunction collapse: is that really an axiom
Can the wavefunction collapse not be derived or is it really an axiom?
How can the answer to this question (yes or no) be proven?
If it is an axiom, is it the best formulation, is it not a dangerous wording?
Let... | {"extraction_info": {"found_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": 16, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/topology+cosmology | # Tagged Questions
2answers
160 views
### Excluding big bang itself, does spacetime have a boundary?
My understanding of big bang cosmology and General Relativity is that both matter and spacetime emerged together (I'm not considering time zero where there was a singularity). Does this mean that ...
2answers
262 vie... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/285390/computation-of-laplace-beltrami-operator-in-a-conformally-equivalent-metric/287026 | # Computation of Laplace-Beltrami operator in a conformally equivalent metric
Could anyone tell me where I'm wrong with the following elementary calculation? Given a smooth Riemannian manifold $(M, g)$, I'd prove that if $\tilde{g}$ is conformally equivalent to $g$ (that is, $\tilde{g} = e^{2w}g$ for some smooth funct... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?s=2816695dae063360286660dc07995d2d&p=4027645 | Physics Forums
## Having trouble understanding/accepting the definition of work. Thought exercise...
One concept in physics that has never set well with me is the way work and energy are defined.
According to all the physics sources I've looked at, work is defined as:
$$W = \vec{F} \cdot \vec{d}$$
(for a constant ... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/50135-domain-problem.html | # Thread:
1. ## Domain Problem
What's the domain of G(t) = ln(t^4-1)?
How did you get the answer, the answer in the book says that it's (-infinity, -1) union (1, infinity) but I don't really understand why.
2. For $x \in \left[ { - 1,1} \right]\quad \Rightarrow \quad \ln \left( {x^4 - 1} \right) \mbox{ is meaningle... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/123910/let-p-be-a-prime-prove-that-p-divides-abpbap-for-all-integers-a-and/123914 | # Let $p$ be a prime. Prove that $p$ divides $ab^p−ba^p$ for all integers $a$ and $b$.
Let $p$ be a prime. Prove that $p$ divides $ab^p−ba^p$ for all integers $a$ and $b$.
(This is not a homework)
-
Hint: It helps to think of it as $ab^p \equiv ba^p \mod p$. – Tara B Mar 24 '12 at 12:47
Oh, I see that while I was la... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/82781/hodge-decomposition-of-a-symplectic-form | ## Hodge decomposition of a symplectic form.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Can anyone explain to me what the Hodge decomposition form of a symplectic form in a special symplectic manifold looks like?
-
What exactly are you asking? What does... | {"extraction_info": {"found_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/24426?sort=oldest | ## What do people mean by “subcategory”?
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Mac Lane defines a subcategory as a subset of objects and a subset of morphisms that form a category. But the first rule of category theory is that you do not talk about e... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 49, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/34595/is-there-an-intuitive-interpretation-of-a-negative-variogram-nugget-value | Is there an intuitive interpretation of a negative variogram “nugget” value?
A variogram plots the variance of the difference between sample pairs on a field (any dimensionality) against spatial separation (the "lag") of those samples.
The extrapolation from observed small-lag variances to a zero-lag variogram value ... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-algebra/60127-sysmetric-tridiagonal-matrix-print.html | # sysmetric tridiagonal matrix
Printable View
• November 17th 2008, 04:57 PM
tinng
sysmetric tridiagonal matrix
For the following symmetric matrix A, find a symmetric tridiagonal matrix T, such that A and T have the same eigenvalues.
A=
[ 2 1 0 0
1 1 2 2
0 2 0 -1
0 2 -1 4]
• November 18th 2008, 10:49 AM
Opalg
Quote:... | {"extraction_info": {"found_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/72800/every-real-function-has-a-dense-set-on-which-its-restriction-is-continuous | ## Every real function has a dense set on which its restriction is continuous
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The title says it all: if $f\colon \mathbb{R} \to \mathbb{R}$ is any real function, there exists a dense subset $D$ of $\mathbb{R}$ 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": 13, "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/55227/how-many-orders-of-magnitude-in-energy-spans-the-domain-of-validity-of-the-stand | How many orders of magnitude in energy spans the domain of validity of the Standard Model?
I am wondering if it makes sense to state that the upper limit is roughly 1012 eV (up to know the physics probed by the LHC seems to be pretty consistent with the SM) and the lower one is ... the upper bound for the photon mass ... | {"extraction_info": {"found_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://nrich.maths.org/6972 | ### The Numbers Give the Design
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
### Straight to Curves
How can you make a curve from straight strips of paper?
### Colouring Curves Game
In this game, try not to colour two adjacent regions the same ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cs.stackexchange.com/questions/9964/how-to-construct-this-generalized-xor-without-needing-an-extra-vector | # How to construct this generalized xor without needing an extra vector?
## Operator - Generalized Symmetric Difference
If you take binary xor and generalize it to other radices you can do so by the absolute value of the difference of each element in a radix vector. However this doesn't have the same properties as 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": 15, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/196446-finding-separatrix.html | # Thread:
1. ## Finding the separatrix
I have a pair of differential equations:
$\frac{dx}{dt} = x (3 - x - 2 y)$
$\frac{dy}{dt} = y (2 - x - y)$
We can see that there are equilibrium points at $(0,0), (0,3), (2,0), (1,1)$ which we can further determine are respectively unstable, stable, stable and a saddle point. 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/53767/constructions-unique-up-to-non-unique-isomorphism/53781 | ## Constructions unique up to non-unique isomorphism
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1) Fields have algebraic closures unique up to a non-unique isomorphism.
2) Nice spaces (without base point) have universal covering spaces unique up to a non... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 104, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/16526/can-a-photon-passing-by-an-open-space-barycenter-of-a-system-of-masses-be-model | Can a photon passing by an open space barycenter of a system of masses be modeled as if all the system's mass is at the barycenter?
To be clear, this example can't apply to the Solar System, since the barycenter is within the Sun, similarly the Earth/Moon system's barycenter is within the Earth.
But, given a system... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/7864/what-am-i-doing-wrong-when-i-try-to-make-this-unit-conversion/7892 | # What am I doing wrong when I try to make this unit conversion?
I am trying to reconcile data that I have found in one publication (Allen 1969) with data that I found in another publication (George 2003) that synthesized this data. The data is root respiration rate, it was originally measured at $27\ ^\circ C$.
## 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": 55, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/statistics/174036-probability-union-independent-events-proof-induction-argument.html | # Thread:
1. ## Probability of the union of independent events proof (induction argument)
I am trying to prove the following:
If $E_1, E_2, ... , E_n$ are mutually independent events, then
$<br /> P(E_1 \cup E_2 \cup ... \cup E_n) = 1 - \Pi^{n}_{i=1} [1 - P(E_i)|<br />$
This is true for $n=2$
$<br /> P(E_1 \cup E_... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.cfd-online.com/W/index.php?title=Turbulence_free-stream_boundary_conditions&diff=5438&oldid=5437 | [Sponsors]
Home > Wiki > Turbulence free-stream boundary conditions
# Turbulence free-stream boundary conditions
### From CFD-Wiki
(Difference between revisions)
| | ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Binocular_disparity | # Binocular disparity
Binocular disparity refers to the difference in image location of an object seen by the left and right eyes, resulting from the eyes' horizontal separation (parallax). The brain uses binocular disparity to extract depth information from the two-dimensional retinal images in stereopsis. In compute... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/98105/why-are-smooth-manifolds-defined-to-be-paracompact?answertab=oldest | # Why are smooth manifolds defined to be paracompact?
The way I understand things, roughly speaking, the importance of smooth manifolds is that they form the category of topological spaces on which we can do calculus. The definition of smooth manifolds requires that they be paracompact. I've looked all over, but I hav... | {"extraction_info": {"found_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://gilkalai.wordpress.com/2008/05/26/natis-influence/?like=1&source=post_flair&_wpnonce=bbf4ba6a50 | Gil Kalai’s blog
Nati’s Influence
Posted on May 26, 2008 by
When do we say that one event causes another? Causality is a topic of great interest in statistics, physics, philosophy, law, economics, and many other places. Now, if causality is not complicated enough, we can ask what is the influence one event has on 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": 0, "wp_latex": 53, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/158894-show-injective-surjective.html | # Thread:
1. ## Show Injective/surjective
f: A x b --> A defined by f(x,y) = x
Injective: Here's what I did
Suppose f(x,y) = f(a,b). Then x = a. Thus not injective
Is this the correct approach?
surjective: Not sure how to go about this... Any advice? Thanks
2. For injective, you need to say that $b$ is not equal 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": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/91138/field-constructions/91143 | ## Field constructions
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If $F$ is a field of characteristic $p$ prime, how can one create a field $K$ such that $K$ is created from $F$ (either by modding out or by taking a product which includes $F$ or by some o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 59, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/18854/list | ## Return to Question
2 added homology tag
1
# Homology of Surfaces with Holes
The classification theorem for surfaces says that the complete set of homeomorphism classes of surfaces is
{ $S_g : g \geq 0$ } $\cup$ { $N_k : k \geq 1$ },
where $S_g$ is a sphere with $g$ handles, and $N_k$ is a sphere with $k$ crossc... | {"extraction_info": {"found_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://mathoverflow.net/questions/94402?sort=votes | ## Changing the Type of a Module in MAGMA
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I am currently working with irreducible $k[G]$-modules in MAGMA for finite fields $k$ and finite groups $G$. To construct these modules, I am using the commands Irreducib... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://dsp.stackexchange.com/questions/3557/shape-of-structuring-elements-for-morphological-gradients | # Shape of structuring elements for morphological gradients
I am looking to understand recommended shapes of structuring elements used in calculating morphological gradients. According to Pierre Soille: Morphological Image Analysis:
Only symmetric structuring elements containing their origin are considered. By doing ... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/34303/what-criteria-distinguishes-causality-from-retrocausality/34362 | # What criteria distinguishes causality from retrocausality?
The brilliant philosopher David Hume remarked that if two events are always found to be correlated to each other with one event happening prior to the other, we call the earlier event the cause and the latter event the effect. However, it has been pointed ou... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/differential-geometry/112632-help-proving-some-facts.html | # Thread:
1. ## Help with proving some facts
Hi,
I have to prove the following facts, but I am not sure if I figured them out correctly:
f : X --> Y and F : P(X) --> P(Y )
1) If A1 is a subset of A2, then F(A1) is a subset of F(A2)
For this one, I have the following:
For all x that are elements of A1 and A2
(there... | {"extraction_info": {"found_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://dsp.stackexchange.com/questions/tagged/frequency-response | # Tagged Questions
Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system.
0answers
18 views
### Frequency cut-offs for guitar amp tone [migrated]
I am wanting to know what the typical frequency cu... | {"extraction_info": {"found_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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/153019-vector-spaces-problem.html | # Thread:
1. ## Vector spaces Problem
Let V1 = span {(1 0 2)}, and V2 = span{(0 0 1)} (they are colomn, not row)
Observe that V1 and V2 are both vector spaces. A new set of vectors, S, is constructed by taking any vector from V1 and any vector from V2 and adding these 2 vectors together.
why S will also be a vector... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 18, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/101031?sort=oldest | ## Kervaire invariant: Why dimension 126 especially difficult?
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Is there any resource that might help non-experts gains some understanding of why the Kervaire invariant problem remains open now only in dimension $... | {"extraction_info": {"found_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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/47043/quantum-field-theories-with-asymptotic-freedom?answertab=oldest | # Quantum field theories with asymptotic freedom
QCD is the best-known example of theories with negtive beta function, i.e., coupling constant decreases when increasing energy scale. I have two questions about it:
(1) Are there other theories with this property? (non-Abelian gauge theory, principal chiral field, non-... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/4165/why-does-the-adjusted-closing-price-take-into-account-dividends | Why does the adjusted closing price take into account dividends?
I'm trying to get an intuition as to why the adjusted closing price includes a dividend adjustment:
\begin{equation} 1 - \frac{dividend}{close} \end{equation}
I understand why the adjusted closing price "undoes" the effect of a split on a stock. A stoc... | {"extraction_info": {"found_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/22950/why-isnt-the-mobius-band-an-algebraic-line-bundle | ## why isn’t the mobius band an algebraic line bundle?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
When I hear the phrase "line bundle" the first thing that pops into my head is a mobius band. But this is a bad picture from an algebraic point of view since... | {"extraction_info": {"found_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://mathoverflow.net/questions/19942/rank-of-aba-where-b-is-positive-definite/19954 | ## Rank of ABA where B is positive definite
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I have a n-by-k matrix A and a n-by-n matrix B, where B is positive definite. I can form the matrix $M = A^t B A$. Playing around, I always found $rk(M) = rk(A)$ but I ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/70692/why-is-the-chebyshev-function-relevant-to-the-prime-number-theorem/70835 | ## Why is the Chebyshev function relevant to the Prime Number Theorem
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Why is the Chebyshev function
$\theta(x) = \sum_{p<=x}\log p$
useful in the proof of the prime number theorem. Does anyone have a conceptual... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 54, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/cjm/v64/n3/ | Canadian Mathematical Society
www.cms.math.ca
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location: Publications → journals → CJM
« Vol. 64 No. 2 Vol. 64 No. 4 »
Volume 64 Number 3 (Jun 2012)
Looking for a pri... | {"extraction_info": {"found_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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/36611-growth-model-word-problem-w-differential-equations.html | # Thread:
1. ## Growth model word problem w/differential equations
Instructions:
Biology. A population of eight beavers has been introduced into a new wetlands area. Biologists estimate that the maximum population the wetlands can sustain is 60 beavers. After 3 years, the population is 15 beavers. If the population ... | {"extraction_info": {"found_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": 36, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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