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http://math.stackexchange.com/questions/122080/grossone-the-arxiv-blogs-pick-of-the-day/122115 | # GrossOne? The arXiv blog's pick of the day.
The arXiv blog having chosen GrossOne for its daily pick of today, I read the arXiv paper concerned, and posted a comment there. The arXiv blog used to be quite high profile as these things go.
Is there an existing well-known (but not to me) mathematical construction 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": 1, "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/126126-lebesgue-integral.html | # Thread:
1. ## Lebesgue Integral
Let $f \in L_p(X)$,1 $\le p < \infty$ and let $\epsilon > 0$. Show that there exists a set $E_\epsilon \subseteq X$ with $m(E_\epsilon) < \infty$ such that if $F \subseteq X$ and $F \cap E_\epsilon = \phi$,then $\int_F |f|^p dm < \epsilon^p$
I let $E_\epsilon = \{ x \in X : |f(x)| \... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 33, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/173762-tricky-equation-first-order.html | # Thread:
1. ## A tricky equation of the first order
My teacher gave me a "bonus" assignment the other day, and I've been racking my brain trying to solve it. Here it is:
$xy'(ln(\frac{x}{y}) +1) = y(ln(\frac{x}{y}) - 1)$
So far I've figured that I should substitute $ln(\frac{x}{y})$ for $u(x)$, thus giving me $y =... | {"extraction_info": {"found_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": 21, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/72546/is-the-l-function-of-the-complex-cohomology-of-a-motive-equal-to-the-l-function | ## Is the “L-function of the complex cohomology” of a motive equal to the L-function of its l-adic realization?
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Let's say I have a motive in $\mathcal{M}_{num}(K)$ ($K$ a number field). For each prime $l$ there 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": 53, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://katlas.math.toronto.edu/wiki/The_Jones_Polynomial | # The Jones Polynomial
### From Knot Atlas
(For In[1] see Setup)
In[2]:= ?Jones
Jones[L][q] computes the Jones polynomial of a knot or link L as a function of the variable q.
In Naming and Enumeration we checked that the knots 6... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 14, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=318121 | Physics Forums
4-momentum of a massive scalar field in terms of creation and annihilation operators
Hi,
I'm trying to compute
$$P^{\mu} = \int d^{3}x T^{0\mu}$$
where T is the stress energy tensor given by
$$T^{\mu\nu} = \frac{\partial\mathcal{L}}{\partial[\partial_{\mu}\phi]}\partial^{\nu}\phi - g^{\mu\nu}\mathc... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 20, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/80469/list | ## Return to Answer
2 added 4 characters in body
Suppose you have any optimization problem that is symmetric. I somehow weaker question is: How much of the original symmetry carries over to the solutions? For the symmetric group $S_n$ if the degree $d$ of the polynomials that describe the problem is low (compared to ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/36113/was-the-universes-entropy-equal-to-zero-at-the-big-bang-is-zero-entropy-state?answertab=active | # Was the Universe's entropy equal to zero at the Big Bang? Is zero-entropy state unique?
It is postulated by many cosmologists that at the Big Bang time the universe was in an unusual low entropy state.
Does this claim specifically mean that the entropy of the initial universe was zero?
Is zero-entropy state unique... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/tagged/basic-concepts?sort=active&pagesize=15 | # Tagged Questions
The basic-concepts tag has no wiki summary.
1answer
61 views
### Interpretation of mean in this example
I recently presented a national test and the company in charge of preparing the test then does a standardization to provide the final scores for each person. These are the values they gave at t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/64211?sort=newest | ## Roth’s theorem and Behrend’s lower bound
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Roth's theorem on 3-term arithmetic progressions (3AP) is concerned with the value of $r_3(N)$, which is defined as the cardinality of the largest subset of the integer... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/87255/linear-equivalence-of-divisors-in-smooth-algebraic-surface | ## Linear equivalence of divisors in smooth algebraic surface
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Let's assume $X$ is a smooth algebraic surface and $C$ a curve containing a smooth point $p_0\in X$, then there exist divisors $H_1$ and $H_2$ non 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://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Shannon_capacity | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/95315-finding-basis.html | # Thread:
1. ## Finding a basis for...
This was a bonus question on my test yesterday (I hope I can remember it correctly).
Q: Let W be a subsapce of $P_{3}$ such that P(0)=0 and let U be a subspace of $P_{3}$ such that P(1)=0. Find a basis for both W and U.
A: For W I figured the basis ought to be $\{x,x^{2},x^{3}... | {"extraction_info": {"found_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": 25, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/2007/04/08/simons-lecture-iii-structure-and-randomness-in-pde/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Simons Lecture III: Structure and randomness in PDE
8 April, 2007 in math.AP, question, talk, travel | Tags: concentration compactness, nonlinear PDE, randomness, Ricci flow, Simons ... | {"extraction_info": {"found_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": 63, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/97980/an-inequality-involving-binomial-coefficients/97983 | # An inequality involving binomial coefficients
For $k\leq n$, how do I prove that ${2n \choose n}(1-\frac{k}{n})^{k}\leq{2n \choose n+k}$?
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## 1 Answer
Hint: If $0\lt a\leqslant b$, then $\dfrac{a}b\leqslant\dfrac{a+1}{b+1}$.
Application: The hint yields $\dfrac{n-k}n\leqslant\dfrac{n-k+i}{n+i}$ for every $i\geq... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/109426?sort=votes | ## On the representation of a (real) square matrix as a product of two symmetric matrices
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(For this queation, all matrices are real).
According to the ancient paper http://www.springerlink.com/content/l455p58221... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/tag/nonlinear-bound-states/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Tag Archive
You are currently browsing the tag archive for the ‘nonlinear bound states’ tag.
## A global compact attractor for high-dimensional defocusing non-linear Schrödinger 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": 0, "wp_latex": 10, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/13100/why-must-gluinos-be-spin-1-2-instead-of-3-2?answertab=votes | # Why must gluinos be spin 1/2 instead of 3/2?
Is there some condition in the N=1 SUSY algebra telling that the spin of the superpartners of gauge bosons (either for colour or for electroweak) must be less than the spin of the gauge boson? I am particularly puzzled because sometimes a supermultiplet is got from sugra ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/89752?sort=votes | ## Ax=0, estimate min(Hamming(x)) ? Equivalently: Bipartite graph. How to find (estimate) minimal number of vertices1 which are connected with EVEN number of vertices2 ? Equivalently: estimate minimal weight of error correcting code ?
### Remember to vote up questions/answers you find interesting or helpful (requires ... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/137635-power-series-representation-function.html | # Thread:
1. ## Power series representation for the function
Find a power series representation for the function and determine the interval of convergence
2. Originally Posted by racewithferrari
Find a power series representation for the function and determine the interval of convergence
Let $z=x^4$ then we have $\f... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/250713/the-symmetric-difference-of-two-recursive-recursively-enumerable-sets-is-recur | # The symmetric difference of two recursive (recursively enumerable) sets is recursive (recursively enumerable)
I want to prove it, but don't know how... (I've tried to resolve complement by defining characteristic function like this: $\chi_{\bar A} = 1 - \chi_A$) Any ideas please? :-)
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Why do you think it's true 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": 7, "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/74206/ray-class-group?answertab=votes | # Ray class group
Can someone please go through a proof of the fact that the ray class group of a number field is finite?
I just can't find a nice readable elementary one on the internet...
Thanks in advance.
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1
Just to put it out there... have you considered, I don't know, a book and/or a library? There is a wor... | {"extraction_info": {"found_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://mathhelpforum.com/discrete-math/189114-small-o-theta-questions.html | Thread:
1. Small-o and Theta questions
I have these questions from a book:
show that if f(n)=theta(log2 n) then f(n)=theta (log10 n)
show that if f(n)=o(g(n)) and g(n)=o(f(n)) then f(n)=theta(g(n))
how to prove? can anyone help me with it?
2. Re: please help me with these quetions
The first proposition, do you m... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Newtons_law_of_cooling | # Convective heat transfer
(Redirected from Newtons law of cooling)
See also: Heat transfer and convection
Simulation of thermal convection. Red hues designate hot areas, while regions with blue hues are cold. A hot, less-dense lower boundary layer sends plumes of hot material upwards, and likewise, cold material from... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 35, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/658/index?nomenu=1 | ## 'Plus Minus' printed from http://nrich.maths.org/
### Show menu
This problem follows on from What's Possible?
Jo has been experimenting with pairs of two-digit numbers. She has been looking at the difference of their squares.
Jo has collected together some answers which she found quite surprising:
$$55^2-45^2=1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/cosmology+big-bang | # Tagged Questions
1answer
58 views
### Assuming space is infinite can our observable universe be an island amongst an archipelego?
According to recent measurements our observable universe is roughly 93 billion light years in diameter; also it appears (according to WMAP measurements) that spacetime is flat. Supposin... | {"extraction_info": {"found_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://mathoverflow.net/questions/73006/tensor-product-in-k-linear-categories-how-canonical/73021 | ## tensor product in k-linear categories how canonical
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi,
my question is related to the tensor product in k-linear additive categories. If you have such a category, an object $A$ and a finite dimensional k-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": 35, "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/2012/02/ | # Hydrobates
A mathematician thinks aloud
## Archive for February, 2012
### Entrainment by oscillations
February 25, 2012
In the book of Goldbeter which I have mentioned in several recent posts a concept which occurs repeatedly is that of entrainment. While looking for some more information about this topic I foun... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/7189/3d-minimum-uncertainty-wavepackets?answertab=active | # 3D Minimum uncertainty wavepackets
Based on the 1D case mentioned in Griffiths, I decided to try looking at the features of 3D Gaussian wavefunctions, i.e. (position basis) wavefunctions of the form $\psi(\mathbf{r}) = Ae^{-\mathbf{r}^\dagger\mathsf\Sigma\mathbf{r}/4}$, where A is a normalization constant, r is posi... | {"extraction_info": {"found_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://mathoverflow.net/questions/14714/what-do-heat-kernels-have-to-do-with-the-riemann-roch-theorem-and-the-gauss-bonne/16770 | ## What do heat kernels have to do with the Riemann-Roch theorem and the Gauss-Bonnet theorem?
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I know the following facts. (Don't assume I know much more than the following facts.)
• The Atiyah-Singer index theo... | {"extraction_info": {"found_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": 27, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/algebra/137951-geometric-series-question.html | Thread:
1. Geometric series question
A large school board established a phone tree to contact all of its employees in case of emergencies. Each of the 3 superintendents calls 3 employees who each in turn calls 3 other employees and so on. How many rounds of phone calls are need to notify all 9840 employees?
The back... | {"extraction_info": {"found_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/18780/is-there-a-sensible-notion-of-abstract-constructible-space | ## Is there a sensible notion of abstract constructible space?
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In the past by the term "variety" people understood a subset of projective space locally closed for the Zariski topology. Now we have a more natural ... | {"extraction_info": {"found_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/27580/list | Return to Answer
Post Undeleted by Greg Kuperberg
2 added 324 characters in body
Ian Morris has it essentially correct in his comment. If you solve the equation `$x = (\sin \pi y/2)^2$` for $y$, then the orbit of $y \in \mathbb{R}/\mathbb{Z}$ under `$y \mapsto 2y$` is dense if and only if $y$ is 2-normal. In other wo... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/3967/rsa-encryption-input-range-plaintexts-that-map-to-ciphertexts?answertab=active | # RSA encryption input range - plaintexts that map to ciphertexts?
According to the wiki article on the RSA encryption function, the valid range of input $m$ is $0 \leq m \lt n$. However I have found that the following values of $m$ always return themselves when encrypted:
• $0$
• $1$
• $n - 1$
• $n - 2$
Have I impl... | {"extraction_info": {"found_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://mathoverflow.net/questions/99221?sort=oldest | ## relation with jacobifields in a small neighbourhood
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hi,
I have the following question: Let $(M,g)$ be a complete Riemannian manifold with all sectional curvatures non-positive. Let $p \in M$ and consider 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": 37, "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/286563/is-goedel-term-in-incomleteness-theorem-both-true-and-unproveable?answertab=oldest | # Is Goedel term (in incomleteness theorem) both true and unproveable?
In Goedel incompleteness theorem is Goedel term both true and unproveable, or just unproveable and truth neutral?
Can we add Goedel term to the theory as axiom and get new theory?
Can we add Goedel term negation to the theory and get a new theory... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 125, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bams/1183485660 | ### Determination of all systems of $\infty ^4$ curves in space in which the sum of the angles of every triangle is two right angles
Jesse Douglas
Source: Bull. Amer. Math. Soc. Volume 29, Number 8 (1923), 356-366.
First Page:
Full-text: Open access | {"extraction_info": {"found_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/questions/74450?sort=votes | ## proper action and amenable action
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We say that an action of a (discrete) group G on a locally compact space X is called proper if the map from $G\times X$ to $X\times X$ defined by $(g,x)\mapsto (gx,x)$ is prop... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/15664/how-to-test-for-differences-between-two-group-means-when-the-data-is-not-normall | How to test for differences between two group means when the data is not normally distributed?
I'll eliminate all the biological details and experiments and quote just the problem at hand and what I have done statistically. I would like to know if its right, and if not, how to proceed. If the data (or my explanation) ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/155528/a-center-of-a-graph-for-example-a-tree-lies-on-its-longest-path | # A center of a graph (for example a tree) lies on its longest path
Prove a center of a tree (or if not much harder, of any graph) lies on the longest path.
(I encountered this when I was reading an alternative proof for the property :"a tree has at most two centers")
-
## 2 Answers
I think it goes like this. 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": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/187877-synthetic-division.html | Thread:
1. Synthetic division
Find the values of real numbers $a$ and $b$ such that:
$x^4 +4x^3+ax^2-b$ is divisible by both $(x-1)$ and $(x+2)$
Do I need to extract the factors (x-1) and (x+2) FIRST and then try to solve for a and b or how do I start?
Also, the answers provided are a = 7 and b = 12 but when I try... | {"extraction_info": {"found_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://scientopia.org/blogs/skullsinthestars/2010/05/04/singular-optics-light-chasing-its-own-tail/ | Just another Scientopia Blogs site
# Singular Optics: Light chasing its own tail
(Title stolen shamelessly from my postdoctoral advisor, who I assume will forgive me.)
As I've noted numerous times in previous posts, one of the fundamental properties that characterizes wave behavior (i.e. that makes a wave a wave) 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": 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/170009/proving-fracabb2b1aba5b1-fracbcc2c1bcb5c1-f | # proving :$\frac{(ab+b)(2b+1)}{(ab+a)(5b+1)}+\frac{(bc+c)(2c+1)}{(bc+b)(5c+1)}+\frac{(ca+a)(2a+1)}{(ca+c)(5a+1)}\ge\frac{3}{2}$
Let $a,b,c, >0$ be real numbers such that $$\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\ge3$$
How to prove that :
$$\frac{(ab+b)(2b+1)}{(ab+a)(5b+1)}+\frac{(bc+c)(2c+1)}{(bc+b)(5c+1)}+\frac{... | {"extraction_info": {"found_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": 23, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://unapologetic.wordpress.com/2009/04/17/inner-products-and-angles/?like=1&_wpnonce=d19428bcb3 | # The Unapologetic Mathematician
## Inner Products and Angles
We again consider a real vector space $V$ with an inner product. We’re going to use the Cauchy-Schwarz inequality to give geometric meaning to this structure.
First of all, we can rewrite the inequality as
$\displaystyle\frac{\langle v,w\rangle^2}{\langl... | {"extraction_info": {"found_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": 23, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/11/15/tensors-over-the-group-algebra-are-invariants/?like=1&source=post_flair&_wpnonce=a832ba55c5 | # The Unapologetic Mathematician
## Tensors Over the Group Algebra are Invariants
It turns out that we can view the space of tensors over a group algebra as a subspace of invariants of the space of all tensors. That is, if $V_G$ is a right $G$-module and ${}_GW$ is a left $G$-module, then $V\otimes_G W$ is a subspace... | {"extraction_info": {"found_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": 34, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/115430?sort=oldest | ## What is the geometry of an undecidable diophantine equation?
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As an arithmetic algebraic geometer of the highest moral fiber, I am trained to look at Diophantine equations in terms of the geometry of the corres... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/81042/a-congruence-problem | # A congruence problem
Prove that if $\gcd(a,b)=d$ and $d$ divides $f$, then there is a an integer $k$ such that $a\cdot k \equiv f\pmod b$.
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7
you haven't said what k is. – user16697 Nov 11 '11 at 4:49
## 1 Answer
If $\gcd(a,b)=d$, then you can find integers $r$ and $s$ such that $ar+bs=d$. Since $d$ divides $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": 16, "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=283080 | Physics Forums
## Minimum Work needed?
1. The problem statement, all variables and given/known data
what is the minimum wirk neede to push a 1000kg car 300m up a 17.5o incline?
Part a. Ignore friction
2. Relevant equations
So we are allowed to use the general equation
W=FdCos $$\theta$$
3. The attempt at a soluti... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://electronics.stackexchange.com/questions/28058/design-considerations-for-powering-microcontrollers-with-a-100-m-cable | # Design considerations for powering microcontrollers with a 100 m cable
I'm currently doing some research for a project where I'd have a number of microcontrollers (say 5 ATtinys or if I manage to bring power consumption down, maybe even ATmegas) which I want to power from a single category 5e cable. I don't think 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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/2622/real-life-collision-when-only-using-truncated-hash/2626 | # Real life collision when only using truncated hash
For MD5 two different inputs are known that produce the same 128 bit hash value. However, these inputs are artificially created for this specific purpose.
For normal, real life inputs I believe no such collision is known?
When you only consider the first n bits 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": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=381056 | Physics Forums
## Lagrangians and conserved quantities
Hi,
I have a relatively straight forward question. If we have a Lagrangian that only depends on time and the position coordinate (and its derivative), how can I decide whether angular momentum is conserved?
That is, if the Lagrangian specifically does not have ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/149199-prove-equivalence-relation.html | # Thread:
1. ## Prove equivalence relation
Please critique the following proof and also let me know if I have defined the equivalence classes correctly.
Let $f:A\longrightarrow B$. Define a relation $\equiv$ on A by $a_{1}\equiv a_{2}$ iff $f(a_{1})=f(a_{2})$. Give a quick proof that this is an equivalence relation.... | {"extraction_info": {"found_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": 41, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.impan.pl/cgi-bin/dict?although | ## although
[see also: though]
Although [1] deals mainly with the unit disc, most proofs are so constructed that they apply to more general situations.
Although these proofs run along similar lines, there are subtle adjustments necessary to fit the argument to each new situation.
Although the definition may seem ar... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://electronics.stackexchange.com/questions/35293/calculating-an-r-rc-circuit | # Calculating an R-RC circuit
This is not homework. I have this circuit, and I want to calculate V2. I know it is equal to V1 at t=0, and equal to $V1 \cdot \frac{R2}{R1+R2}$ at t=$\infty$, but I don't know how to calculate the charging of the capacitor.
All I find on Google is charging of an RC, without the parallel... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/trees?sort=unanswered | # Tagged Questions
A tree is a graph that is connected but contains no cycles.
2answers
50 views
### How many vertices of degree 1 in a tree?
How many vertices of degree 1 are there in a tree with no vertices of degree more than 4? The only thing that I have right now is that the number of edges in a tree is n-1 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": 63, "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/90232/neumann-series-in-an-incomplete-normed-algebra?answertab=active | # Neumann series in an incomplete normed algebra
Let $\mathcal{A} \equiv (A, \|\cdot\|_A)$ be a unital (associative) normed algebra over the real or complex field, and assume that $\mathcal{A}$ is not complete. Provided $\mathcal{B}_\mathcal{A}$ is the open unit ball of $\mathcal{A}$, define $N$ to be the set of all $... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4155741 | Physics Forums
## Maximizing heat absorption through Radiation
Hi All,
I am currently investigating a method of absorbing heat from radiation. This is being done to harness heat from skin.
I was wondering what was the best method to do this?
Is there a particular material that is best suited to do this? I know 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": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/42430/two-questions-about-finiteness-of-ideal-classes-in-abstract-number-rings/43031 | ## Two questions about finiteness of ideal classes in abstract number rings
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Let us say that an abstract number ring is an integral domain $R$ which is not a field, and which has the "finite norms" property: for 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": 125, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/business-math/152543-economic-problem-based-constraint-scarce-product.html | # Thread:
1. ## Economic problem based on constraint of scarce product
Hi, so i'm trying to figure out how to do this question but I'm a bit lost.
I assume the answer to a) is 3P1 + P2 = K
after that, I'm not sure what to do.
Any help is greatly appreciated! Thanks in advance!!
p.s I'm not trying to make anyone do 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": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/19363?sort=newest | ## Background
Let $X$ and $S$ be simplicial sets, i.e. presheaves on $\Delta$, the so-called topologist's simplex category, which is the category of finite nonempty ordinals with morphisms given by order preserving maps.
How can we derive the structure of the face and degeneracy maps of the join from either of the 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": 76, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/97579?sort=votes | ## upper bounds on a certain matrix norm
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Is there some simple upper bound on $||(B^{-1}+A^{-1})^{-1}||$, where $A,B$ are $n \times n$ symmetric matrices?
-
2
What norm are you denoting by $||\cdot ||$? – Noah 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": 36, "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/278895/how-to-communicate-mathematics-by-computer-and-in-the-internet | # How to communicate mathematics by computer and in the internet?
I would like to know how can I exchange mathematical ideas with symbolic representations by computer, by e-mail or asking questions with formulas and mathematics symbols in the internet. For letters we have the keyboard but mathematics it is different 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": 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/52365/euler-method-on-differential-equation-problem?answertab=active | # Euler method on differential equation problem
I have this problem to solve. I want to compute the inclination of a plane $\theta(t)$ at every frame of a simulation given the following rule for its angular speed of rotation $\omega(t)$
$$\omega(t) = - \frac{\mathbf{V}\cdot\hat{\mathbf{n}}}{(||\mathbf{P}-\mathbf{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": 7, "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/222000/how-many-different-passwords-of-length-6-can-be-formed?answertab=votes | # How many different passwords of length 6 can be formed…
Each user on a computer system has a password, which is six characters long, where each character is an uppercase letter or digit. Each password must contain at least one digit. How many possible passwords are there?
Why am I incorrect in reasoning that the 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": 23, "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/224/note?nomenu=1 | ## Fair Exchange
In your bank, you have three types of coins. The number of spots shows how much they are worth.
| | | |
|----|----|----|
| | | |
| 1 | 2 | 5 |
Can you choose coins to exchange with the groups below to make the same total?
Full screen version
This text is usually replaced by 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": 16, "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/38404/how-is-gauss-law-integral-form-arrived-at-from-coulombs-law-and-how-is-the | # How is Gauss' Law (integral form) arrived at from Coulomb's Law, and how is the differential form arrived at from that?
On a similar note: when using Gauss' Law, do you even begin with Coulomb's law, or does one take it as given that flux is the surface integral of the Electric field in the direction of the normal 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": 12, "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/93382/a-modified-divisor-game | ## A modified divisor game
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Consider a two player game. There are N balls marked 1 to N. A move consists of removing a ball n and all other balls which are divisors of n (including 1). The players alternate the mo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/9340/bounding-the-series-sum-m-leq-x-m-neq-n-frac1-logm-n | # Bounding the series $\sum_{m\leq x,m\neq n}\frac{1}{|\log(m/n)|}$
I am trying to reproduce the following bound:
$\sum_{1\leq m\leq x, m\neq n}\frac{1}{|\log(m/n)|}=O(x\log(x))$,
for $x\geq 2$ and some $n$, $1\leq n\leq x$ (the implicit constant shouldn't depend on $n$).
I have tried to bound each term by $\frac{1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/112102/computing-a-density-function-for-the-integral-of-a-stochastic-process-given-its | ## Computing a density function for the integral of a stochastic process, given its transition function
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$P$ is a one-dimensional Markov stochastic process that runs on time interval $[0, t_f]$. I know its transit... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/39287/list | 2 edited title
1
# How to exact the diagonal from a bivariate generating function
Let $F(s,t)= \sum_{i,j} f(i,j) s^i t^j$, which is a bivariate generating funcion of the number $f(i,j)$ for some enumeration problem. Sometimes we know about $F(s,t)$, but what we really need is the number $f(i,i)$ with the generating ... | {"extraction_info": {"found_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/45272/necessary-condition-for-a-graph-to-be-non-hamiltonian | ## Necessary condition for a graph to be Non-Hamiltonian
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Let us denote the edges incident on vertices of valence 2 as "required" as these edges has to be covered by a Hamiltonian circuit, if one exists on that (u... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/608/solution | ### N000ughty Thoughts
Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the number of noughts in 10 000! and 100 000! or even 1 000 000!
### Fac-finding
Lyndon chose this as 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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/122298/getting-the-angles-of-a-non-right-triangle-when-all-lengths-are-known/122303 | # Getting the angles of a non-right triangle when all lengths are known
I have a triangle that I know the lengths of all the sides. But I need to know the angles. Needs to work with non-right triangles as well.
I know it is possible, and I could have easily done this years ago when I was in trig, but it has completel... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/190880/number-of-divisors?answertab=active | # Number of divisors
How can I find number of divisors of N which are not divisible by K.
($2 \leq N$, $k \leq 10^{15})$
One of the most easiest approach which I have thought is to first calculate total number of divisors of 'n' using prime factorization (by Sieve of Eratosthenes) of n and then subtract from it 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": 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/87877?sort=newest | ## Jacobi’s equality between complementary minors of inverse matrices
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What's a quick way to prove the following fact about adjugates of an invertible matrix $A$ and its inverse?
Let $A[I,J]$ denote the submatrix... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/34726/ados-theorem-for-metric-lie-algebras | ## Ado’s theorem for metric Lie algebras?
### Background
Ado's Theorem states that every finite-dimensional Lie algebra over a field of zero characteristic admits a faithful representation.
More precisely, if $\mathfrak{g}$ is a finite-dimensional Lie algebra over a field $K$ of zero characteristic, then there is a ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/7385-story-drop-problems.html | # Thread:
1. ## Story drop Problems
How do I solve these?
A stone is dropped from the edge of a roof, and hits the ground with a velocity of -165 feet per second. How high (in feet) is the roof?
and
A particle is moving with acceleration a(t) = 24t+4. Its position at time t=0 is s(0) = 14 and its velocity at time 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": 40, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/42277/limit-of-the-derivative-of-a-function-as-x-goes-to-infinity | # Limit of the derivative of a function as x goes to infinity
I've been trying to solve the following problem:
Suppose that $f$ and $f'$ are continuous functions on $\mathbb{R}$, and that $\displaystyle\lim_{x\to\infty}f(x)$ and $\displaystyle\lim_{x\to\infty}f'(x)$ exist. Show that $\displaystyle\lim_{x\to\infty}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": 57, "mathjax_display_tex": 9, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-topics/58419-turning-point-parabola.html | Thread:
1. Turning Point of a Parabola
Hello,
How do I find the turning point of a parabola?
Thanks in advance
2. Originally Posted by J4553
Hello,
How do I find the turning point of a parabola?
Thanks in advance
Complete the square.
Alternatively, use calculus.
Post a more specific question (and state your ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/56679?sort=oldest | ## Dual of a Basis for a Hopf Algebra Conatined in all Dually Paired Hopf Algebras
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For an infinite dimensional Hopf algebra $H$, a non-degenerate dually pairing Hopf algebra $H'$, and a choice of basis $e_i$ 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": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/3939/list | ## Return to Question
6 deleted 136 characters in body
Let me ask a more specific question.
Suppose P(x) $P(x)$ is a monic integer polynomial with roots r1, r2$r_1, ... rnr_n$ such that pk$p_k = r1k + r2kr_1^k + ... + rnkr_n^k$ is a non-negative integer for all k. positive integers $k$. Is P(x) $P(x)$ necessarily 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": 6, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://scicomp.stackexchange.com/questions/4952/numeric-solution-of-simple-but-possibly-singular-linear-system | # Numeric solution of simple but possibly singular linear system
I have a simple (and small) linear homogeneous system $Ax=0$, where the entries of the $N\times M$ matrix $A$ are small integers. I do not need fancy methods which efficiently solve almost singular matrices and treat roundoff errors etc. But I need to kn... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/60428/what-is-the-most-accurate-method-to-get-intersection-point-in-3d | # What is the most accurate method to get intersection point in 3D?
I have been given 3D point data, belonging to different planar segments. Points are not exactly laid on the planes so that I have fitted best planes using least square solutions. Now, I want to find the intersection point where more than 2 planes 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": 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/algebra/132898-multiplying-binomial-w-two-trinomials.html | # Thread:
1. ## multiplying binomial w/two trinomials
Sorry, I figured it out; I'd like to delete the thread can't seem to delete right now though.
2. Originally Posted by greatsheelephant
Here is the expression I'm supposed to find the product of:
$(4y^3+5y^2-12y)(-12-2)(7y^2-9y+12)$
To multiply it, does it matter... | {"extraction_info": {"found_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://mathoverflow.net/questions/24842?sort=votes | ## BSD conjecture and L functions with zeroes of order g
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If the group of rational points of $E$, which is finitely generated by the Mordell-Weil Theorem, has $g$ generators of infinite order, then the Birch-Swinn... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/semiclassical+scattering | # Tagged Questions
0answers
30 views
### equation for the potential in terms of the phase shift for a rotational invariant potential
let be a potential in 3d invariant under rotations so $V(r)$ in the WKB approximation the phase shifts are given by \delta _{l} (k)= \int_{a}^{\infty}dr ... | {"extraction_info": {"found_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/120829/an-infinite-group-such-that-every-proper-subgroup-is-finite | ## An infinite group such that every proper subgroup is finite?
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While reading about the Burnside problem, I thought of the following question:
```` If every proper subgroup of G is finite, does it follow that G ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/273546/what-is-the-difference-between-open-ball-and-neighborhood-in-real-analysis/273548 | # What is the difference between open ball and neighborhood in real analysis?
I'm learning real analysis.
Open ball: The collection of points $x \in X$ satisfying $|x - x_{0}| < r$ is called the open ball of radius $r$ centered at $x_{0}$
Neighborhood: A neighborhood of $x_{0} \in X$ is an open ball of radius r > 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": 27, "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/106417/solving-lyapunov-like-equation | ## solving Lyapunov-like equation
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The following matrix equation might be a Lyapunov-like equation, but it seems hard for me to develop a simpler way to solve it. From the computation effort, I need some help 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": 41, "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/80323?sort=votes | ## Logarithm of a hypergeometric series
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I am sorry if the answer to my question is well-known. I am quite new in this topic, so it will be also nice to have a reference, if it exists.
I was wondered if there exi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/41692/generate-correlated-ar-process-for-given-correlation-between-demand-series | # Generate correlated AR process for given correlation between demand series
How can I generate two correlated $AR(1)$ data series with given correlation between $d_{1,t}$ and $d_{2,t}$, $r_{12}$, where $\rho_{12}$ is correlation between the two error series $$d_{1,t}=\mu+\phi_1d_{1,(t−1)}+e_{1}(t)\quad\quad d_{2,t}=\... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Cost-of-living_index | # Cost-of-living index
A cost-of-living index is a theoretical price index that measures relative cost of living over time or regions. It is an index that measures differences in the price of goods and services, and allows for substitutions to other items as prices vary.[1]
There are many different methodologies 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": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/38795/borel-sets-on-rn | ## Borel Sets on R^n
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Define the Borel sigma-algebra on R^n as the smallest sigma-algebra containing all n-rectangles (a1, b1) x...x (an, bn).
Is it true that the Borel sigma algebra contains all sets of the form... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/103529/proof-of-a-combinatorial-identity-possibly-using-trigonometric-identities/103662 | ## Proof of a combinatorial identity (possibly using trigonometric identities)
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For integers $n \geq k \geq 0$, can anyone provide a proof for the following identity?
$$\sum_{j=0}^k\left(\begin{array}{c}2n+1\\ 2j... | {"extraction_info": {"found_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": 16, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/69815?sort=oldest | ## How to motivate and interpret the geometric solutions of Hamilton-Jacobi equation?
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Studying the Hamilton-Jacobi equation, I meet a generalization of the notion of its solutions, which is found already in the w... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 57, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/thermodynamics?sort=unanswered&pagesize=30 | # Tagged Questions
Covers the study of (mostly homogeneous) macroscopic systems from a heat/energy/entropy point of view. Maybe combine with [tag:statistical-mechanics].
learn more… | top users | synonyms
0answers
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### How is the logarithmic correction to the entropy of a non extremal black hole derived?
... | {"extraction_info": {"found_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://mathoverflow.net/questions/97769/approximation-theory-reference-for-a-bounded-polynomial-having-bounded-coefficien | ## Approximation theory reference for a bounded polynomial having bounded coefficients
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Let $P(x)$ be a real polynomial of degree at most $d$. Assume $|P(x)| \leq 1$ for $|x| \leq 1$. I would like a bound saying 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": 30, "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/250096/calculating-the-mean-of-a-discrete-r-v-in-a-question | # Calculating the mean of a discrete R.V in a question
I have the following HW question:
There are $N$ balls in a box, $m$ balls with an $S$ for success and $N-m$ balls with an $F$ for failure. Choose $n$ balls at random ($n\leq N$) and let $X$ = the number of successes.
a. Calculate the probability function $p(\cdo... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/12030/equation-of-motion-for-explicit-time-dependent-potential?answertab=oldest | # Equation of motion for explicit time dependent potential
What is the equation of motion for a single scalar field Lagrangian density in which the potential explicitly depends on time? For example: $$U(\phi,t)=\frac{1}{2}\phi^2 - \frac{1}{3} e^{t/T}\phi^3 + \frac{1}{8}\phi^4$$ where $T$ is a constant.
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## 1 Answer... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/129873-prove-lhs-rhs-using-only-properties-det.html | # Thread:
1. ## Prove that LHS=RHS using ONLY properties of Det.
Q) Without directly expanding the det., but using only the well-known properties, prove that:
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Tried solving many times but couldn't find a proper method/approach. Keep getting stuck every tim... | {"extraction_info": {"found_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": 22, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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