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http://mathoverflow.net/questions/59020/where-can-i-find-a-modern-write-up-of-heegners-solution-of-gauss-class-number-1/59030 | ## Where can I find a modern write-up of Heegner’s solution of Gauss' class number 1 problem?
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In a recent MO question someone mentioned Heegner's solution of the Gauss "class number 1" problem which takes the fol... | {"extraction_info": {"found_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://amathew.wordpress.com/tag/fac/ | # Climbing Mount Bourbaki
Thoughts on mathematics
August 25, 2011
## Analytic spaces
Posted by Akhil Mathew under functional analysis | Tags: analytic spaces, coherent sheaves, FAC, Oka's theorem |
Consider the space ${\mathbb{C}^n}$ and the sheaf ${\mathcal{O}}$ of holomorphic functions on it. One should think of ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 16, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=1440733 | Physics Forums
## why solvable is solvable
When a Lie algebra is solvable, does it have something to do with actually solving something?
PhysOrg.com science news on PhysOrg.com >> Front-row seats to climate change>> Attacking MRSA with metals from antibacterial clays>> New formula invented for microscope viewing, ... | {"extraction_info": {"found_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/1491/can-i-parameterize-the-state-of-a-quantum-system-given-reduced-density-matrices?answertab=votes | # Can I parameterize the state of a quantum system given reduced density matrices describing its subparts?
As the simplest example, consider a set of two qubits where the reduced density matrix of each qubit is known. If the two qubits are not entangled, the overall state would be given by the tensor product of the on... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/49394/list | 2 LaTeX
# classificationClassification of real forms byupto inner automorphisms
I hope to know the classification of real forms of complex simple Lie algebras of types A, D, E $A$, $D$, $E$ up to inner automorphisms.
Let g_1 $\mathfrak{g}_1$ and g_2 $\mathfrak{g}_2$ be real forms of a complex simple Lie algebra 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": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.ugcs.caltech.edu/~srbecker/wiki/BP | # Category:Problems
### From SparseSolver
(Redirected from BP)
## Sparse approximation problems
### Best subset selection
This problem is in general NP-hard. Many of the algorithms presented on this wiki are attempts to solve this problem approximately, or to solve it in certain special cases. We denote the $\ell_... | {"extraction_info": {"found_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": 54, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/statistics/129665-expected-value.html | # Thread:
1. ## Expected Value
No idea where to start.
The owner of a small firm has just purchased a personal computer, which she expects will serve her for the next two years. The owner has been told that she "must" buy a surge suppressor to provide protection for her new hardware against possible surges or variat... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/55384?sort=oldest | ## Primes represented by two-variable quadratic polynomials
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I'm looking over a paper, "Primes represented by quadratic polynomials in two variables" [1] which attempts to characterize the density of the primes 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": 35, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/120010/list | ## Return to Answer
2 added 4 characters in body
I don't know how much about areas you want to prove, and how developed a background the audience is supposed to have, but here is a definition of area of a bounded planar region.
Take such a region $D$ in $\mathbb{R}^2$, $\newcommand{\bZ}{\mathbb{Z}}$ $\newcommand{\ve... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/304769/a-tough-series-sum-k-1-infty-frac-zeta2kk12k1-need-help | # A tough series: $\sum_{k=1}^{\infty}\frac{\zeta(2k)}{(k+1)(2k+1)}$, need help
I was doing a integral which ends up with a tough series part: $$\sum_{k=1}^{\infty}\frac{\zeta(2k)}{(k+1)(2k+1)}$$ Mathematica says $$\frac12$$ Which agrees with the anwer...Anyone know how to evaluate this?
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Isn't there an exact expres... | {"extraction_info": {"found_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": 16, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/30343/help-with-summing-a-power-series/30407 | # Help with summing a power series
I'd like to determine the function corresponding to the following power series: $$x + \sum_{n=1}^\infty (-1)^n\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n} \frac{x^{2n+1}}{2n+1},$$ where $|x|<1$.
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12
@bimol: Please do not ask questions in the imperative. Instead, explain... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 66, "mathjax_display_tex": 23, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/95408/elliptic-curves-over-rings/95409 | ## Elliptic Curves over Rings?
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So an elliptic curve $E$ over a field $K$ is a smooth projective nonsingular curve of genus $1$ together with a point $O \in E$.
I was reading Silverman's "Arithmetic of Elliptic 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": 18, "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/6811/can-peps-explain-the-holographic-principle-in-quantum-gravity | Can PEPS explain the holographic principle in quantum gravity?
Condensed matter physicists have shown using quantum information that in many condensed matter systems, entanglement entropy only scales as the area of the boundary, and not the volume. This is the basis for the density matrix renormalization group and Pro... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://jeremykun.com/2012/08/26/k-nearest-neighbors-and-handwritten-digit-classification/ | # K-Nearest-Neighbors and Handwritten Digit Classification
Posted on August 26, 2012 by
## The Recipe for Classification
One important task in machine learning is to classify data into one of a fixed number of classes. For instance, one might want to discriminate between useful email and unsolicited spam. Or one mig... | {"extraction_info": {"found_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": 27, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/9555/laplaces-equation | # Laplace's equation
I have got some mathematical difficulties in the following exercise :
Calculate the potential of the polarized sphere along the z-axis. There are no free charges.
For this, we need to solve Laplace's equation, by using the method of separation of variables.
$\phi (r, \theta, \phi) = R(r) \Theta... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 81, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-topics/205697-question-circles.html | Thread:
1. Question on circles
So, I've attached ye question and have completed the square to solve it. However, what do I do after doing so , what can I do to find the answer?<br>
<br>
Also for part b, how do I find the point of intersection?
Attached Thumbnails
2. Re: Question on circles
You have the right line 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": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/34713/fundamental-group-of-a-finite-set-with-discrete-topology/34715 | # Fundamental Group of a finite set with discrete topology
let S be a finite set with say n elements. Give it the discrete topology, Now what can we say about its fundamental group? Atleast can we determine the fundamental group of a set with two elements? Thanks
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## 2 Answers
Such a space is not path-connected, 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": 18, "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/15640/what-are-electron-holes-in-semiconductors | # What are “electron holes” in semiconductors?
I'm tutoring senior high school students. So far I've explained them the concepts of atomic structure (Bohr's model & Quantum mechanical model) very clearly. Now the next topic to be taught is semiconductors.
I myself am not conviced with the concept of electron holes. I... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/24418/ordinary-cohomology-of-stacks/24428 | ## Ordinary cohomology of stacks
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Let $\mathbf{X}$ be a stack over $Top$ (a lax sheaf of groupoids, or some such thing). If it admits a surjective representable map $F \to \mathbf{X}$ then one can form the iterate... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 52, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/267863/for-measurable-f-n-x-to-0-infty-show-that-sum-n-1-infty-f-n-inf/281734 | # For measurable $f_n : X \to [0, \infty)$ show that $\sum_{n=1}^\infty f_n < \infty$ almost everywhere
Let $f_n : X \to [0 \infty)$ be a sequence of measurable functions on the measure space $(X, \mathcal{F}, \mu)$. Suppose there is an $M > 0$ such that the functions $g_n = f_n\chi_{\{f_n \le M\}}$ satisfy $||g_n||_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": 30, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/106666-prove-if-g-abelian-group-then-s-order-least-6-a.html | # Thread:
1. ## Prove that if G is an abelian group then it's order is at least 6
I need to show that all groups of smaller orders are abelian but i'm not sure how to do this.
2. Originally Posted by Louise
I need to show that all groups of smaller orders are abelian but i'm not sure how to do this.
I'm almost sure... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/50890/mean-of-log-of-cdf | # Mean of log of cdf
Let $CDF$ be the cumulative distribution function for the standard normal distribution. Let $Z$ be a standard normal random variable.
Then $CDF(Z)$ is uniformly distributed on the unit interval, so by integration we can show that $E(ln(CDF(Z))) = -1$.
My question: there an easy way to compute $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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/32268/suppose-phi-is-a-weak-solution-of-delta-phi-f-in-mathcalh1-then | # Suppose $\phi$ is a weak solution of $\Delta \phi = f \in \mathcal{H}^1$. Then $\phi\in W^{2,1}$
I'm trying to prove the statement in the title in as simple a way as possible. It is Theorem 3.2.9 in Helein's book "Harmonic maps, conservation laws, and moving frames", although it is not proved there. The statement 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": 29, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/Events/summer12/abs/com | 2012 CMS Summer Meeting
Regina Inn and Ramada Hotels (Regina~Saskatchewan), June 2 - 4, 2012 www.cms.math.ca//Events/summer12
Combinatorics
Org: Karen Meagher (Regina) and Marni Mishna (SFU)
[PDF]
ROBERT BAILEY, University of Regina
Metric dimension of distance-regular graphs: an update [PDF]
A {\em resolving set}... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 94, "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/55885 | Why semigroups could be important?
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There is known a lot about the use of groups -- they just really appear a lot, and appear naturally. Is there any known nice use of semigroups in Maths to sort of prove they are ind... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/68387-union-u-intersection-n.html | # Thread:
1. ## Union (u) and Intersection (n)
the real number system
ImageShack - Image Hosting :: 16012009078os8.jpg
eg. Q n R = Q
Find?
1)Q u H
2)J u N
3)H n J
4)H n R
5)Q u R
6)H n Q
7)J n N
I cant understand how to do them ? please solve the above with explanation.
2. Originally Posted by mj.alawami
the real... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 34, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/43578/solving-time-dependent-schrodinger-equation-in-matrix-form?answertab=oldest | # Solving time dependent Schrodinger equation in matrix form
If we have a Hilbert space of $\mathbb{C}^3$ so that a wave function is a 3-component column vector $$\psi_t=(\psi_1(t),\psi_2(t),\psi_3(t))$$ With Hamiltonian $H$ given by $$H=\hbar\omega \begin{pmatrix} 1 & 2 & 0 \\ 2 & 0 & 2 \\ 0 & 2 & -1 \end{pmatrix}$$ ... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/30861/isotropy-and-noise/41801 | # Isotropy and Noise
If you have a field which value is just Gaussian noise plus a constant do you call it isotropic?
• there is no preferred direction
• however it is not "the same" in all directions if "the same" means "constant"
The question is about a definition of a word, thus obviously conflicting answers can ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "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/119866/find-all-solutions-to-the-equation-ez-i/119869 | Find all solutions to the equation $e^z = i$
I know that there is an equation for finding the nth roots of a complex number, which easily done once you have the modulus and argument of the complex number in question. There would be n roots. But how do I know how many solutions there are to an exponential raised to a 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": 23, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2011/04/26/tangent-spaces-and-regular-values/?like=1&source=post_flair&_wpnonce=c8d80d4293 | The Unapologetic Mathematician
Tangent Spaces and Regular Values
If we have a smooth map $f:M^m\to N^n$ and a regular value $q\in N$ of $f$, we know that the preimage $f^{-1}(q)=A\subseteq M$ is a smooth $m-n$-dimensional submanifold. It turns out that we also have a nice decomposition of the tangent space $\mathcal{... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 51, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/116257/list | ## Return to Answer
2 added 156 characters in body
You can look at the short paper by Conte, Marchisio end Murre On the k-unirationality of the cubic complex (2007).
It contains a proof of the unirationality of $V_6$ over a field $k$ of any characteristic $\neq 2,3$, under the assumption that $V_6$ has a $k$-rationa... | {"extraction_info": {"found_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://nrich.maths.org/472/index?nomenu=1 | Sketch the members of the family of graphs given by $$y = {a^3\over (x^2+a^2)}$$ for $a=1$, $2$ and $3$. | {"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": 3, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=587545&page=4 | Physics Forums
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## What exactly is an electron?
In post # 47, a minimum electron radius value, (3Gm/c^2) was noted. From this radius, a fundamental mass value is defined, using a ring shape with the angular momentum (h/4pi). The charge spins at light velocity so that the effecti... | {"extraction_info": {"found_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/216311/fourier-transform-and-sampling-time | # Fourier transform and sampling time
Given a signal $x(t)$ and the $X(\omega)$ obtained from $x(t)$ using a FFT with a sampling time $Ts$, I get a subset of $X(\omega)$: $Y(\omega)$ obtained from $X(\omega)$ taking it between $\omega_0$ and $\omega_1$, the question is: if I make the IFFT of $Y(\omega)$, does the new ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/25933/kleisli-monad-bijection/26044 | ## Kleisli Monad bijection
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For a monad $(T,\mu,\eta)$ if $T(A) = T(B)$, does this imply that $\mu_A = \mu_B$? I want to know because in the bijection between Kleisli triples and monads, given a monad, we define $... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/65256/problem-about-assasin-of-module | # Problem about Assasin of module
I found this problem and I don't understand the solution. I will appreciate your help. Let $A = \mathbb{Q}[X_1,...,X_n,...], a = (X_1^2,...,X_n^2,...)$ and $M = A/a$. Show that $Ass_A (M) = \emptyset$. Why isn't $Ass_A(M) = (X_1,...,X_n,...)$ ?
I'm writing this because the site is gi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 49, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/82726?sort=newest | ## The Plancherel Formula for SL2
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What are the important questions to start to study about Plancherel Formula for SL2? And what is the relation this topic and the Arthur's paper, "On some problems suggested 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": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/172911-evaluating-particular-product-sines.html | # Thread:
1. ## Evaluating a particular product of sines
I need to evaluate the product $\prod_{m=n-a}^{n-1} \sin \left( \pi m /n \right)$.
I've found this identity: $\prod_{m=1}^{n-1} \sin \left( \pi m /n \right) \equiv \frac{n}{2^{n-1}}$, which looks useful but isn't quite what I need.
Does anyone know of a genera... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/54847/ac-circuit-theory-maximum-power-transfer | # AC Circuit Theory Maximum Power Transfer
I am currently hitting a barrier with regards to the basics of this question.
A 50HZ supply is connected to various given impedance's, calculate the maximum power transfer.
Maximum power transfer I understand is basically the Thevenin/Norton equivalent.
Though THERE IS NO ... | {"extraction_info": {"found_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/216929/put-n-items-into-m-groups-such-that-the-sums-of-the-ns-in-every-m-are-as-even-a | Put N items into M groups such that the sums of the N's in every M are as even as possible
I have a `multiset`, `S`, that contains `N` items that I wish to place into `M` different groups so that the sum of all `N`'s in each group `M` is as evenly distributed as possible amongst all `M`'s.
For example:
If my multise... | {"extraction_info": {"found_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/math-topics/121793-quadratic-problem-help-print.html | # Quadratic Problem Help
Printable View
• December 28th 2009, 09:22 AM
andi01
Quadratic Problem Help
Thanks for your help in advance, here's the problem:
The path of a golf ball can be modeled by a quadratic equation. The path of a ball hit an angle of 10 degrees can be modeled by h=-0.002d^2+0.4d where h is the hei... | {"extraction_info": {"found_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://mathematica.stackexchange.com/questions/5563/how-to-load-a-package-without-naming-conflicts/5567 | # How to load a package without naming conflicts?
This question applies to any package, but I encountered this problem while working with graphs. There are symbols in the Combinatorica package (such as Graph, IncidenceMatrix, EdgeStyle, and others) that have the same name as analogous symbols in System. If I execute 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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 5, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Biorthogonal_system | Biorthogonal system
In mathematics, a biorthogonal system is a pair of indexed families of vectors
$\tilde v_i$ in E and $\tilde u_i$ in F
such that
$\langle\tilde v_i , \tilde u_j\rangle = \delta_{i,j} ,$
where E and F form a pair of topological vector spaces that are in duality, ⟨,⟩ is a bilinear mapping and $\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": 15, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/164989-secant-method-error-bound-between-kth-iteration-root.html | # Thread:
1. ## Secant Method - Error bound between kth iteration and root
Hey guys.
I know from the proof of the secant method that given the two initial values, [LaTeX ERROR: Convert failed] and [LaTeX ERROR: Convert failed] , are sufficiently close to the solution, [LaTeX ERROR: Convert failed] , then
[LaTeX ERR... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/74693/on-pseudo-rational-modular-forms-of-weight-2-and-level-n | ## On pseudo rational modular forms of weight 2 and level N
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So consider the $\mathbb{Q}$-vector space $V$ of functions which satisfy the following conditions
(1) $f:\mathbb{H}\rightarrow\mathbb{C}$ is holomorphi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 95, "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/tagged/sequences-and-series+combinatorics | # Tagged Questions
1answer
66 views
### effective way to get the integer sequence A181392 from oeis
the sequence A181392 are perfect squares and any digit in the sequence says "I am part of an integer in which you'll find d digits "d"" (see A108571, How can we call them? "digit-valid"?) How to get ...
3answers
30 vi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 117, "mathjax_display_tex": 32, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://www.physicsforums.com/showthread.php?p=810950 | Physics Forums
## Work Done "On" or "By" The System
Will someone help solidy this concept of Work 'On' a system and Work 'Done' by a system.
If I lift an object from some defined zero potential. Then the work BY the system is -mgh, because gravity 'g' is in the reverse direction as the displacement 'h', but work don... | {"extraction_info": {"found_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://understandinguncertainty.org/node/622 | # Quantifying the Risk of Natural Catastrophes
How do companies prepare for the financial impact of natural catastrophes? How can they possibly have an idea of what the potential cost can be for events that haven't yet happened? Shane Latchman explains the way companies in the insurance industry are using catastrophe ... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://euler.slu.edu/escher/index.php/Tessellations_by_Polygons | Tessellations by Polygons
Seville, Spain.
Explorations
The explorations for this section include:
Explorations using Geogebra
For those who have access to The Geometer's Sketchpad the following explorations are available. The first part of the Introductions to GSP Exploration is heavily based on and inspired by 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": 15, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/4049/meaning-of-the-anti-commutator-term-in-the-uncertainty-principle/4077 | # Meaning of the anti-commutator term in the uncertainty principle
What is the meaning, mathematical or physical, of the anti-commutator term? $\langle ( \Delta A )^{2} \rangle \langle ( \Delta B )^{2} \rangle \geq \dfrac{1}{4} \vert \langle [ A,B ] \rangle \vert^{2} + \dfrac{1}{4} \vert \langle \{ \Delta A, \Delta B ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "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/3141/can-has-string-theory-solved-cosmological-constant-problem | # Can/has string theory solved cosmological constant problem?
Can someone explain to me what the KKLT paper says, and what has and hasn't it achieved regarding the ability to construct solutions with a small positive or negative cosmological constant in string theory?
-
For starters, how about a link to the paper? –... | {"extraction_info": {"found_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/tagged/newtonian-mechanics?sort=active&pagesize=15 | # Tagged Questions
Newtonian mechanics covers the discussion of the movement of classical bodies under the influence of forces by making use of Newton’s three laws. For more general discussion of energy, momentum conservation etc., use classical-mechanics, for Newton’s description of gravity, use newtonian-gravity.
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": 44, "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/15292/why-cant-there-be-a-general-theory-of-nonlinear-pde | ## Why can’t there be a general theory of nonlinear PDE?
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Lawrence Evans wrote in discussing the work of Lions fils that
there is in truth no central core theory of nonlinear partial differential equations, nor 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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/87143?sort=votes | ## Algebraic function with extra condition, what can it be?
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I have an unknown function $\psi(\xi_1,\dots,\xi_n)$, such that $\psi$ satisfy an (unknown) polynomial equation with coefficients polynomials in the $\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": 36, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3932172 | Physics Forums
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## Why does light move?
Or how does light move?
There's a source of light, for example a torch but what is it that propelled the photons into my eye from the torch?
I'm new to this so I don't know, I mean I know light is a wave but it's also a photon init, so why does 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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/241525/generating-random-variables-from-standard-uniform-distribution-on-1-0?answertab=active | # Generating random variables from standard uniform distribution on $(1,0)$
A random number generator generates random values from the standard uniform distribution $\mathrm{Uniform}(0,1)$. Call this random variable $U$. Starting with a random value $u$ from $U$, show all the steps necessary to generate a random varia... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 58, "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/110404/when-does-a-distinguished-matching-exist/111309 | ## When does a `distinguished matching' exist?
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Suppose I have a bipartite graph on a pair of vertex sets $X$ and $Y$.
Definition: A distinguished matching is a subset $DX\subseteq X$ and a subset $DY\subseteq Y$... | {"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": 53, "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/97005?sort=votes | Planar sets closed under intersection of circles
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Let $P$ be the plane with a point at infinity. By plane, I mean the Euclidian plane, and therefore it has circles. A line is also a circle, though its center is at inf... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 63, "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/27849/branch-point-twist-fields-and-operator-insertions-on-a-riemann-manifold?answertab=votes | # Branch-point twist fields and operator insertions on a Riemann manifold
I am having trouble understanding how Eq (2.6) in this paper (PDF) $$Z[\mathcal{L},\mathcal{M}_{n}]\propto\langle\Phi(u,0)\tilde{\Phi}(v,0)\rangle_{\mathcal{L}^{(n)},\mathbb{R}^{2}}$$
generalizes to Eqn (2.7) $$\langle\mathcal{O}(x,y;\mbox{ she... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathforum.org/mathimages/index.php?title=Volume_of_Revolution&oldid=7780 | # Volume of Revolution
### From Math Images
Revision as of 15:14, 8 July 2009 by Lmasis1 (Talk | contribs)
Solid of revolution
This image shows a solid of revolution
Solid of revolution
Field: Calculus
Created By: Lizah Masis
# Basic Description
This image shows the solid formed after revolving the region bounded ... | {"extraction_info": {"found_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": 24, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/48287/earth-moves-how-much-under-my-feet-when-i-jump?answertab=active | Earth moves how much under my feet when I jump?
If I'm standing at the equator, jump, and land 1 second later, the Earth does NOT move 1000mph (or .28 miles per second) relative to me, since my velocity while jumping is also 1000mph.
However, the Earth is moving in a circle (albeit a very large one), while I, while j... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/17915/the-role-of-resistor-in-e-g-an-and-gate?answertab=active | # The role of resistor in e.g. an AND gate
What is the role of the resistor in e.g. an AND gate like this one? :
One often sees lots of resistors in electric circuits, but I haven't really understood their role.
-
This is rather more a technology question that one of physics per se. I'll ask the mods at Electronics.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/165465/do-function-with-the-following-property-have-special-name | Do function with the following property have special name?
I'm writing "a structure preserving surjection" way too much when I need to refer a function of the following property:
$$Y \subseteq Z, X \subseteq Z. g: Z \to A, g \text{ is some fixed function}.$$ $$\phi : X \to Y, \phi \text{ is a surjection, and } g(\phi... | {"extraction_info": {"found_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://www.reference.com/browse/Differential+equations+of+addition | Definitions
# Differential equations of addition
In cryptography, differential equations of addition (DEA) are one of the most basic equations related to differential cryptanalysis that mix additions over two different groups (e.g. additions over GF$\left(2^\left\{32\right\}\right)$ and GF$\left(2\right)$) and where ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 18, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/32152/number-of-realizations-of-particular-triad-type?answertab=votes | # Number of realizations of particular triad type
Given four types of triads (figure below) their probabilities in a random Bernoulli digraph are as follows:
• $T_{003}$: $(1-p)^6$
• $T_{012}$: $6p(1-p)^5$
• $T_{102}$: $3p^2(1-p)^4$
• $T_{111D}$: $6p^3(1-p)^3$
For example, for triad $T_{012}$ there are six realizati... | {"extraction_info": {"found_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/161770-solid-revolution.html | # Thread:
1. ## Solid of revolution
The area under the curve y= sin x, between x =0 and x = π
Show that the volume of the solid formed by rotating this area through 360 about the x-axis is exactly ½(π^2)
This is what I have after doing some of the work:
V = π (-cos^2x) limits π and 0
I am not sure how to take it any... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=621949 | Physics Forums
## Tough problem involving algebra
1. The problem statement, all variables and given/known data
Original problem asked me to prove $$\int_a^b \! x \, \mathrm{d} x = \frac{b^2-a^2}{2}$$ using Riemann sums. I've already seen a simpler formula using the left side of the rectangles but I'm curious as to ho... | {"extraction_info": {"found_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": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/22080/does-a-ski-racer-with-a-larger-mass-have-an-advantage | # Does a ski racer with a larger mass have an advantage?
Does a ski racer with a greater mass have an advantage over a racer with a lesser mass? If mass of one racer is 54 kg and the mass of a more slender racer is 44 kg I know the speed at which they descend should be equal if they were to fall in a vacuum. How 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": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathematica.stackexchange.com/questions/tagged/numerical-integration?page=3&sort=votes&pagesize=15 | # Tagged Questions
Questions on the use of numerical functions NIntegrate and NDSolve.
1answer
408 views
### Solving a PDE containing DiracDelta
I want to get the answer from a PDE: \begin{align*} \frac{\partial \rho(r,t)}{\partial t}&=Dr^{-2}\frac{\partial}{\partial r}r^2h(r)e^{-U(r)}\frac{\partial}{\partial ...
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": 13, "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/29082/would-time-freeze-if-you-can-travel-at-the-speed-of-light | # Would time freeze if you can travel at the speed of light?
I read with interest about Einstein's `Theory of Relativity` and his proposition about the speed of light being the speed limit for anything with mass. So, if I were to travel in a spacecraft at the speed of light, would I freeze and stop moving? Would the 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": 5, "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/785/is-there-a-general-formula-for-solving-4th-degree-equations?answertab=active | # Is there a general formula for solving 4th degree equations?
There is a general formula for solving quadratic equations, namely the Quadratic Formula.
For third degree equations of the form $ax^3+bx^2+cx+d=0$, there is a set of thee equations: one for each root.
Is there a general formula for solving equations 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": 62, "mathjax_display_tex": 30, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/37647/the-dold-thom-theorem-for-infinity-categories/37898 | ## The Dold-Thom theorem for infinity categories?
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Let $\mathcal{M}$ denote the category of finite sets and monomorphisms, and let $\mathcal T$ denote the category of based spaces. For a based space $X \in \mathca... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 41, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/258654/cyclic-vector-exists-for-symmetric-operator-iff-there-no-repeated-eigenvalues?answertab=oldest | # cyclic vector exists for symmetric operator iff there no repeated eigenvalues
Considering a symmetric operator $A$ acting on a finite dimensional Hilbert space $H$, we say $x\in H$ is a cyclic vector for $A$ if the set of finite linear combinations of $\{A^n x:n=0,1,2,...\}$ is equal to $H$. I am looking for a proof... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-topics/52799-circles-please-help.html | # Thread:
1. ## Circles - Please Help
Two circles touch internally at a point A and the smaller of the two circles passes through O, the centre of the larger circle. AB is any chord of the larger circle, cutting the smaller circle S. The tangents to the larger circle at A and B meet at a point T.
Prove:
i) AB is bi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/194865/inequality-3-leftia2ib2ic2-right-geq-ab2bc2ca2 | # Inequality. $3\left(IA^2+IB^2+IC^2\right) \geq AB^2+BC^2+CA^2$
(Korea 1998) Let $I$ be the incenter of a triangle $ABC$.Prove that:
$$3\left(IA^2+IB^2+IC^2\right) \geq AB^2+BC^2+CA^2.$$
Thanks :)
-
We prefer to avoid subjective titles. – Peter Tamaroff Sep 12 '12 at 19:26
Presumably you're looking at this in ord... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/14083/modular-forms-and-the-riemann-hypothesis/14161 | ## Modular forms and the Riemann Hypothesis
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Is there any statement directly about modular forms that is equivalent to the Riemann Hypothesis for L-functions?
What I'm thinking of is this: under the Mellin transf... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 48, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/103288?sort=votes | ## A combinatorial question
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This possibly easy question is related to this one. Let $s_1,...,s_n$ be a sequence of natural numbers (some of them may be equal to 0). Consider the following sequence of multisets 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": 68, "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/163792/convex-programming-when-the-problem-has-an-underlying-combinatorial-structure-th?answertab=active | # Convex programming when the problem has an underlying combinatorial structure that's a DAG
I have a nonlinear convex objective function to minimize. The function is defined on a set of variables: $\{ x_1,x_2, \ldots ,x_p \},$ where each $x_i$ is a number associated with a path in the DAG.
I'm wondering if there's 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": 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/189401/proving-that-a-n-and-b-n-relatively-prime-implies-ab-n-relatively-prime/189403 | # Proving that $a,n$ and $b, n$ relatively prime implies $ab,n$ relatively prime
Question:
Suppose $a,b \in \Bbb N$, $\gcd (a,n) = \gcd(b,n) = 1$. The question is to prove or give a counterexample: $\gcd(ab,n) = 1$.
My Work:
This is what I have so far (for $\alpha, \beta, \gamma, \delta \in \Bbb Z$): \begin{align*}... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 68, "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/112015?sort=newest | ## The history of the geometrization of closed surfaces
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1. Who first recognized that the torus supports a flat structure?
2. Who first characterized the moduli space of flat structures on the torus?
3. Who firs... | {"extraction_info": {"found_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/questions/95714/reduced-cyclic-homology-of-a-free-product-of-unital-algebras | ## (Reduced) cyclic homology of a free product of unital algebras
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Rather embarrassingly, the question is on how to prove something I used to know how to do... but I thought that the collective wisdom of MO might ... | {"extraction_info": {"found_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://all-science-fair-projects.com/science_fair_projects_encyclopedia/Complex_number | # 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": 39, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/95206-setup-help-print.html | # Setup help
Printable View
• July 15th 2009, 11:58 AM
Danneedshelp
Setup help
Q: Find all subsets of the set that forms a basis for $\mathbb{R}^{3}$.
$S=\{(1,3,-1),(-4,1,1),(-2,7,-3),(2,1,1)\}$
A: well, I did a similar one of these and got the same answer as book, but with a bunch of negative 1's unlike their stri... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://shreevatsa.wordpress.com/2012/10/ | # The Lumber Room
"Consign them to dust and damp by way of preserving them"
## The potions puzzle by Snape in Harry Potter and the Philosopher’s Stone
with one comment
Sometime this week, I reread the first Harry Potter book (after at least 10 years… wow, has it been that long?), just for contrast after reading Row... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/205280/sobolev-approximation-theorem-example | # Sobolev Approximation Theorem Example
The approximation theorem states that if $U$ is bounded, $u \in W^{1,p}(U)$ for some $1 \leq p < \infty$ then there are functions $u_m \in C^\infty(U) \cap W^{k,p}(U)$, such that $u_m \rightarrow u$ in $W^{k,p}(U)$.
This is probably very simple, but I'm trying to follow along 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": 36, "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/37682?sort=oldest | ## Computing equivalent vector of random variables from covarience matrix
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Given a covariance matrix, how can I construct a vector of expressions of randomly distributed variables whose covariance matrix is equal ... | {"extraction_info": {"found_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/50366/logdet-maximization-under-logdet-inequalitie-constraint | ## logdet maximization under logdet inequalitie constraint
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Consider the following convex problem $\max_{\mathbf{A}} \log |\mathbf{I} + \mathbf{CA} |$ subject to $\log |\mathbf{I} + \mathbf{FA} | \leq \xi$ where $... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/56988/set-theory-proving-statements-about-sets/56990 | Set Theory: Proving Statements About Sets
Let A, B, and C be arbitrary sets taken from the positive integers.
I have to prove or disprove that: A ∩ B ∩ C = ∅, then (A ⊆ ~B) or (A ⊆ ~C)
Here is my disproof using a counterexample:
If A = {} the empty set, B = {2, 3}, C = {4, 5}
With these sets defined for A, B, and ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/57061/will-we-feel-right-up-inside-the-airplane-if-the-airplane-accelerates-toward-ear/57076 | # Will we feel right up inside the airplane if the airplane accelerates toward earth at 20m/s^2?
Suppose you are in the airplane and the airplane falls toward the earth with acceleration of $20m/s^2$(double of gravitational acceleration $g$). This double acceleration by airplane will cancel the gravitational accelerat... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/5402/secure-mac-implies-that-probability-of-same-tags-on-different-messages-is-neglig?answertab=active | Secure MAC implies that probability of same tags on different messages is negligible
So let any secure MAC (message authentication code) be given.
Intuitively, I think it is clear that the probability of getting the same tag on two different messages is very small, i.e. negligible. I want to prove this statement math... | {"extraction_info": {"found_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-statistics/171161-conjugate-prior-gamma-distribution.html | # Thread:
1. ## Conjugate prior for gamma distribution
Conjugate prior for the gamma distribution (with parameters $\alpha,\beta$) is supposed to be:
$\frac{1}{Z}\frac{p^{\alpha -1}e^{-\beta q}}{{\gamma(\alpha)}^r \beta^{-\alpha s}}$
with the hyperparameters, p, q, r, s when both shape parameter and the scale param... | {"extraction_info": {"found_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://math.stackexchange.com/questions/150004/evaluate-int-bar-z-dz?answertab=active | # Evaluate $\int \bar z dz$
How would I evaluate $\int \bar z dz$, with
1: the contour $\gamma$ being the straight line segment from $0$ to $1+i$
2: the contour $\sigma$ being the straight line segment from $0$ to $1$, followed by the straight line segment from $1$ to $1+i$.
For the first one, I tried working it fr... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/92100-max-min-help-cant-find-critical-points.html | # Thread:
1. ## Max and Min, Help Cant find the critical points?
Hi
I would really appreciate if anyone could help me with the following exercises k, l, m, n. I cant seem to solve the derivatives to find the critical points. THANK VERY MUCH in advance.
Attached Thumbnails
2. You need to use partial differenitation... | {"extraction_info": {"found_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://nrich.maths.org/5749 | ### Plane to See
P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.
### Four Points on a Cube
What is the surface area of the tetrahedron with one vertex at O the vertex of a unit 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": 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/15444/the-phenomena-of-eventual-counterexamples/27550 | ## The phenomena of eventual counterexamples
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Define an "eventual counterexample" to be
• $P(a) = T$ for $a < n$
• $P(n) = F$
• $n$ is sufficiently large for $P(n) = T\ \ \forall n \in \mathbb{N}$ to be a 'reas... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 127, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/discrete-math/52812-q-ary-code-proof-using-spheres.html | # Thread:
1. ## q-ary code proof using spheres
Show that there is no q-ary code of length 5 and distance 3 with more than $\frac{q^5}{5q-4}$ codewords. You should prove this from first principles using spheres and without using known bounds on the number of codewords.
This is my working so far:
First prove that ther... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/27111/i-have-a-statistic-how-do-i-calculate-its-distribution | # I have a statistic, how do I calculate its distribution?
I am comparing images for correlation. The images are all correlated, but I would like to determine when one pair is much more highly correlated, relative to another pair. I am using as a statistic the difference in the logs of p-values produced by a Spearman ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/270752/lipschitz-continuity-result | # Lipschitz continuity result
Hi: I'm reading a proof in a convex optimization book and I don't understand something. The author states the following:
Let $Q$ be a subset of $R^{n}$. We denote by $C_{L}^{k,p}(Q)$, the class of functions with the following properties:
A) any $f \in C_{L}^{k,p}(Q)$ is $k$ times differ... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/31326/how-should-one-interpret-the-comparison-of-means-from-different-sample-sizes | # How should one interpret the comparison of means from different sample sizes?
Take the case of book ratings on a website. Book A is rated by 10,000 people with an average rating of 4.25 and the variance $\sigma = 0.5$. Similarly Book B is rated by 100 people and has a rating of 4.5 with $\sigma = 0.25$.
Now because... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.wikiwaves.org/Strip_Theory_Of_Ship_Motions._Heave_%26_Pitch | # Strip Theory Of Ship Motions. Heave & Pitch
From WikiWaves
Wave and Wave Body Interactions
Current Chapter Strip Theory Of Ship Motions. Heave & Pitch
Next Chapter Ship Roll-Sway-Yaw Motions
Previous Chapter Forward-Speed Ship Wave Flows
## Ship motions with forward speed
Ship advances in the positive x-direction ... | {"extraction_info": {"found_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": 154, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
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