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http://mathhelpforum.com/number-theory/164816-unique-integers.html | # Thread:
1. ## unique integers
what exactly does it mean for integers to be unique? if i am supposed to prove that there exists UNIQUE positive m and n integers under a condition, can m and n be equal at some conditions? for them to be unique, does it just mean there is only one m and only one n each time the condit... | {"extraction_info": {"found_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://electronics.stackexchange.com/questions/12865/is-a-current-limiting-resistor-required-for-leds-if-the-forward-voltage-and-supp/12866 | # Is a current-limiting resistor required for LEDs if the forward voltage and supply voltage are equal?
For blue LEDs with a forward voltage of 3.3 V and supply voltage of 3.3 V, is a series resistor still needed to limit current?
Ohm's Law in this case says 0 Ω, but is this correct in practice?
Perhaps just a small... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/1574-x-intercept-tangent-parabola.html | Thread:
1. x-intercept of tangent to parabola
Show that the tangent to the parabola Y=Ax^2 (for A does not equal 0) at the point where x = c will intersect the x axis at the point (c/2 , 0 . Where does it intersect the y axis.
2. Originally Posted by frozenflames
Show that the tangent to the parabola Y=Ax^2 (for A d... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=46093 | Physics Forums
## "classic" problem
Here is a problem I have been trying in Maple, but to no avail.
I am trying to calculate the theta that will result in maximum distance for a projectile fired from off the edge of plateau onto another, lower surface. The projectile can be considered to be fired from the exact corn... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.purplemath.com/learning/viewtopic.php?f=8&t=1906&p=5666 | The Purplemath Forums
Helping students gain understanding and self-confidence in algebra.
How do you go from a quadratic function in...
Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
3 posts • Page 1 of 1
How do you go from a quadratic function in...
by Abs... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 16, "/images/ma... |
http://math.stackexchange.com/questions/149139/explaining-why-sin-and-cos-are-not-at-right-angles?answertab=votes | Explaining why sin and cos are *not* at right angles
Disclaimer: I'm an engineer, not a mathematician
I recently had a fierce discussion (lots of blood) on electronics.stackexchange about phase shifts.
The impedance of a resistor is real, that of a coil imaginary ($j\omega L$), so that adding 3V across a resistor 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": 30, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/32360/what-entities-create-a-gravitational-field/32372 | What entities create a gravitational field?
It is well known that masses create a gravitational field. Photons are affected by gravitation, but do they generate a gravitational field as well? What about the other gauge bosons?
Do gravitons create a gravitational field?
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1
– Qmechanic♦ Jul 19 '12 at 10:57
3 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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://terrytao.wordpress.com/2011/08/04/localisation-and-compactness-properties-of-the-navier-stokes-global-regularity-problem/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Localisation and compactness properties of the Navier-Stokes global regularity problem
4 August, 2011 in math.AP, math.MP, paper | Tags: concentration compactness, energy estimates, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 227, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/76413/torsion-subgroups-in-families-of-twists-of-elliptic-curves/76416 | ## Torsion subgroups in families of twists of elliptic curves
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Here is the short version:
Fix an elliptic curve $E/\mathbb{Q}$. How does the torsion structure $E_d(\mathbb{Q})_{tors}$ vary, as $E_d$ runs through ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 113, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/190829/whats-the-right-way-to-make-a-change-of-variables-under-another-integral | # What's the right way to make a change of variables under another integral?
Here's something that has me a little perplexed. I'm missing some step in making a change of variables under a multiple integral, where the new variable depends on more than one of the original ones.
I can't think of a simplified example tha... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/tagged/current+electromagnetism | # Tagged Questions
2answers
70 views
### Can a current carrying loop or wire produces no magnetic field?
A current carrying wire produces magnetic field around it. We can find the direction by Fleming's Right hand rule. We know change in electric filed produces magnetic field and change on magnetic field ...
2answer... | {"extraction_info": {"found_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.reference.com/browse/wiki/Representation_theory_of_SL2(R) | Definitions
# Representation theory of SL2(R)
In mathematics, the main results concerning irreducible of the Lie group SL2(R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish-Chandra (1952).
## Structure of the complexified Lie algebra
We choose a basis H, X, Y for the complexification of the L... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 9, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/quantum-chromodynamics+standard-model | # Tagged Questions
2answers
83 views
### The status of $SU(3)_C$ symmetry in the Standard Model
In the Standard Model of Particle physics the $SU(2)_{EW}$ symmetry and the $SU(2)$ isospin symmetry are broken. What about $SU(3)_C$? Is it broken too? if YES, what breaks the symmetry? If NO, what ...
0answers
98 views
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "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/26888/on-shell-symmetry-from-a-path-integral-point-of-view/53070 | # On-shell symmetry from a path integral point of view
Normally supersymmetric quantum field theories have Lagrangians which are supersymmetric only on-shell, i.e. with the field equations imposed. In many cases this can be solved by introducing auxilary fields (field which don't carry dynamical degrees of freedom, 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": 20, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://thecodeabode.com/ | Probabilistic Compositions
Last time, I wrote a post about the odds of reaching a certain space in Monopoly. An interesting result ended up coming out of this, and it is a consequence of the relationship between a sequence of die rolls and a partition. First, some definitions: a partition is any way of writing a posit... | {"extraction_info": {"found_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": 89, "mimetex.cgi": 0, "/images/ma... |
http://www.absoluteastronomy.com/topics/Group_(mathematics) | Group (mathematics)
# Group (mathematics)
Overview
Discussion
Ask a question about 'Group (mathematics)' Start a new discussion about 'Group (mathematics)' Answer questions from other users Full Discussion Forum
Unanswered Questions
Encyclopedia
In mathematics
Mathematics
Mathematics is th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/number-theory/171644-multiplication-natural-numbers-proof.html | # Thread:
1. ## Multiplication of Natural Numbers proof
Let m be an element of the Natural Numbers and n be an element of the Integers. If m*n is an element of the Natural Numbers, then n is an element of the Natural Numbers.
Any help with the above proof would be appreciated!
2. Originally Posted by jstarks44444
L... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/117684?sort=newest | ## Are spectra really the same as cohomology theories?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $E \to F$ be a morphism of cohomology theories defined on finite CW complexes. Then by Brown representability, $E, F$ are represented by spectra, and 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": 70, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/86476/list | Return to Question
2 Added a missing _ in a formula
The short version:
Given non-zero real numbers $\alpha$ and $\beta$, can one prove the following estimate in a simple manner? Or does it follow from a well-known result on exponential sums? $$\sum_{n=1}^N \frac{1}{\sqrt{n}}e(\alpha n + \beta n \log n) = O_{\alpha,\... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 50, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/differential-geometry/118341-eigenspace-lambda-1-bounded-linear-operator-its-adjoint.html | # Thread:
1. ## Eigenspace of \lambda = 1 for a bounded linear operator and its adjoint
$H$ is a Hilbert space and $T \in B(H)$ is such that $||T||_{H} \leq 1$. Show that $Tx = x \iff T^{*}x = x$.
I have tried looking at this problem in several ways and I just cannot seem to see the significance of $||A|| \leq 1$ 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 21, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/standard-deviation | # Tagged Questions
In Probability and Statistics, the standard deviation of a statistical population or data set is a measure of how much variation or dispersion exists from its average value. It is defined as the square root of the variance.
2answers
27 views
### standard deviation of a certain distribution
If I h... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "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-challenge-problems/107413-number-puzzle-u.html | # Thread:
1. ## A number puzzle for u
There are two numbers with the difference of 3 between them and the difference of their squares is 51.
Can you find the numbers???
2. Spoiler:
Suppose the two numbers are $a$ and $b$, with $a<b$.
Then the problem says that $b-a=3$ and $b^2-a^2=51$. Note that $b^2-a^2=(b-a)(b+a)... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/67417/product-of-integrals?answertab=votes | # Product of Integrals
I'm given $\Psi(x,t)$ as a proposal for a wave function. $\Psi(x,t)=\int_{1}^{1+\Delta k} e^{i(kx-wt)} k^2 dk$
Now I try to compute $\Psi^*(x,t)\Psi(x,t)$ wich is the product
$(\int_{1}^{1+\Delta k} e^{-i(kx-wt)} k^2 dk) (\int_{1}^{1+\Delta k} e^{i(kx-wt)}k^2 dk)$
In wich way should I transfo... | {"extraction_info": {"found_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/78147/walks-that-cannot-hit-the-boundary/78151 | ## Walks that cannot hit the boundary
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I've casually proved, as application of some ideas that I am developing, a result that might be of interest in itself. I am completely new in this field and then I would like... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/25875/generators-of-a-maximal-ideal-of-kx1-xn | ## Generators of a maximal ideal of k[X1,…,Xn]
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi. Given $k$ an algebraically closed field, I know that that a maximal ideal $\mathfrak{m}$ of $A = k[X_1,\cdots,X_n]$ is just a $\langle X_1-a_1,\cdots,X_n-a_n \ra... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "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/intuition+integral | # Tagged Questions
4answers
496 views
### The Meaning of the Fundamental Theorem of Calculus
I am currently taking an advanced Calculus class in college, and we are studying generalizations of the FTC. We just started on the version for Line Integrals, and one can see the explicit symmetry ...
0answers
60 views
###... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2007/04/30/tensor-products-of-modules/?like=1&source=post_flair&_wpnonce=1ba466d084 | # The Unapologetic Mathematician
## Tensor products of modules
The notion of a tensor product also extends to modules, but the generalization is not quite as straightforward as it was for direct sums.
We start with a ring $R$ and consider a right $R$-module $A_R$ and a left $R$-modules ${}_RB$. We consider functions... | {"extraction_info": {"found_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": 58, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/254305/why-is-this-inequality-important | # Why is this inequality important?
I'm reading Courant's What is Mathematics?
In the beginning, he's showing some proofs, there's a proof about An Important Equality and this important equality is:
$$(1+p)^n\geq 1+np$$
The book's author states the proof but he doesn't say why the inequality is important, I had a 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": 24, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/118683-total-length-astroid.html | # Thread:
1. ## Total length of the astroid
This is the last section of my class and I just don't get it. I can't even get my calculator so graph it for me (probably my stupid though). Can anyone please explain how to answer this type of question? I have 5 questions on the length of a parametric curve to do. I just c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.m.wikibooks.org/wiki/Famous_Theorems_of_Mathematics/Logic | # Famous Theorems of Mathematics/Logic
## Gödel's completeness theorem
In the following, we state two equivalent forms of the theorem, and show their equivalence.
Later, we prove the theorem. This is done in the following steps:
1. Reducing the theorem to sentences (formulas with no free variables) in prenex 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 100, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/84749/transitivity-of-a-flow-and-its-time-1-map | ## Transitivity of a flow and its time-1 map
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Let $M$ be a closed manifold, $f:M\to M$ be a homeomorphism, and $\phi_t:M\to M$ be a flow. .
The map $f$ is said to be (point)-transitive if some orbit $\lbrace f^nx... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/29785/is-the-escape-velocity-at-geosynchronous-earth-orbit-0km-hr?answertab=active | # Is the escape velocity at Geosynchronous Earth Orbit 0km/hr?
Follow-up question to How long must escape velocity be maintained?
Is the escape velocity at GSO 0?
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1
What do you mean by GEO? – Bernhard Jun 8 '12 at 22:16
Geosynchronous Earth Orbit is what I had in mind (+: But we can do without the mention of Eart... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Cube_root | # Cube root
This article may be expanded with text translated from the corresponding article in the Catalan Wikipedia. (June 2012) Click [show] on the right to read important instructions before translating. Google's machine translation is a useful starting point for translations, but translators must revise erro... | {"extraction_info": {"found_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": 31, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Non-circular_gear | # Non-circular gear
Non-circular gear example
Another non-circular gear
A non-circular gear (NCG) is a special gear design with special characteristics and purpose. While a regular gear is optimized to transmit torque to another engaged member with minimum noise and wear and with maximum efficiency, a non-circular ge... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/106019/calculate-all-the-equivalent-martingale-measure/106244 | # calculate all the equivalent martingale measure
Under the assumption of no arbitrage without vanish risk, in an incomplete market $(\Omega,{\cal F}, P)$, the set of equivalent martingale measure is NOT empty, i.e. ${\cal P} = \{Q: Q \sim P\}\neq \emptyset.$
My question is: in the following simplified market with 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": 27, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/10064-graph.html | # Thread:
1. ## Graph
Graph y = sqrt{x^2}, y = x, y |x|, and y = (sqrt{x})^2, NOTING which graphs are the SAME.
NOTE:
What is the mirror-like image of the graph y = x?
2. Originally Posted by symmetry
Graph y = sqrt{x^2}, y = x, y |x|, and y = (sqrt{x})^2, NOTING which graphs are the SAME.
NOTE:
What is the mirr... | {"extraction_info": {"found_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": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/48587/how-to-calculate-the-darcy-weissbach-friction-factor-for-shear-thinning-laminar | # How to calculate the Darcy-Weissbach friction factor for shear thinning laminar flow in a pipe?
The Darcy-Weissbach friction factor for laminar flow would be $\frac{64}{Re}$
Now, having a shear thinning (non-newtonian) fluid where the viscosity is not constant how do I arrive at $Re$?
To know an apparaent viscosity... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Raoult's_law | # Raoult's law
Established by François-Marie Raoult in 1882,[1] Raoult's law states:
The vapour pressure of an ideal solution is directly dependent on the vapour pressure of each chemical component and the mole fraction of the component present in the solution.[2]
Once the components in the solution have reached 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": 24, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/unitarity?sort=active&pagesize=15 | # Tagged Questions
The unitarity tag has no wiki summary.
2answers
196 views
### Irreducible Representations Of Lorentz Group
In Weinberg's The Theory of Quantum Fields Volume 1, he considers classification one-particle states under inhomogeneous Lorentz group. My question only considers pages 62-64. He define stat... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/50544/some-dirichlet-series-questions/50688 | ## Some Dirichlet series questions.
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I asked this question on m.SE in an attempt to find out the right words to say for these questions I am about to ask.
In his great answer, Matthew Emerton explained that (cusp... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "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/32100/is-there-a-third-dimension-of-numbers/32103 | # Is there a third dimension of numbers?
Is there a third dimension of numbers like real numbers, imaginary numbers, [blank] numbers?
-
12
– Aryabhata Apr 10 '11 at 16:30
Wow, that is annoying. Are three-dimensional numbers even possible/necessary? – awesomeguy Apr 10 '11 at 16:42
1
Quaternions are four-dimensional... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/59717/non-linearity-of-the-consistency-strength-ordering-in-zf/59800 | ## (Non?)-linearity of the consistency strength ordering in ZF
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Much of the research taking place in set theory, is related to the classification of sentences according to their consistency strength relative to ZF... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/49474/list | ## Return to Question
6 added 762 characters in body; added 2 characters in body
Solutions to this equation, however, are not unique. If we fill any unit real interval with some function, then the equation entails the function at the whole real line (provided $f$ is defined there.). So there are as many solutions as ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 134, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/8951/what-are-the-ideal-centers-of-mass-and-rotation-for-a-steadicam | # What are the ideal centers of mass and rotation for a steadicam?
For those who don't know what a steadicam is, I'll explain it in two points to give a basic idea. If you know what a steadicam is, skip to point 3.
1) A steadicam is a stabilizing mount for a motion picture camera, which mechanically isolates the oper... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/16653/why-is-beta-negative-decay-more-common-than-beta-positive/16654 | # Why is beta negative decay more common than beta positive?
In simple terms, why is beta negative decay more common than beta positive?
I know it's something to do with occuring inside/outside the nucleus - but I can't find a simple, easy to understand explanation!
-
## 2 Answers
The beta-decay may be "locally" r... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/71970/quartic-diagonal-as-a-sum-of-squares-of-quadratic-forms/72058 | ## quartic diagonal as a sum of squares of quadratic forms
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I would appreciate if someone can point out to the literature related to characterizing the set of all different ways to write real quartic diagonal $\su... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/183100/computing-the-differential-of-the-map-phi-m-2-mathbbc-times-m-2-mathbbc?answertab=active | # Computing the differential of the map $\phi: M_2(\mathbb{C})\times M_2(\mathbb{C})\rightarrow M_2(\mathbb{C})$
Let $\phi: M_2(\mathbb{C})\times M_2(\mathbb{C})\rightarrow M_2(\mathbb{C})$ be the map $$(B_1,B_2)\mapsto [B_1,B_2]$$ which takes two $2\times 2$ matrices to its Lie bracket.
Then why does $d\phi_{(B_1,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": 21, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=1623716 | Physics Forums
Cosmology Question: Expansion of the Universe
1. The problem statement, all variables and given/known data
So the other day in my cosmology class we talked about whether smaller objects like a solar system, a star or a galaxy expand with the rest of the universe. While the answer is obviously no, sinc... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=149298 | Physics Forums
## Total energy of a damped oscillator
Is it possible to express the total energy of a damped linear oscillator as a function of time? I'm confused here. I'd like to find E(t). As the oscillation is damped, dE/dt should everywhere be negative (energy being dissipated as radiation or heat). By setting E... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/45363-solving-system.html | # Thread:
1. ## Solving system
I tried to simplify it down and go to this point:
I don't know if I did it right. From there, I have no idea what to do T_T The problem asks for a exact answer so everything must stay in radicals. I also don't know how to solve it using matrices...
2. from the first equation ...
$\sq... | {"extraction_info": {"found_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/229497/f-mathbfr-rightarrow-mathbfr-monotone-increasing-rightarrow-f-is/229502 | $f: \mathbf{R} \rightarrow \mathbf{R}$ monotone increasing $\Rightarrow$ $f$ is measurable
Problem. Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a monotone increasing function. Show that $f$ is measurable.
Solution. We know that the set of discontinuites of any monotone increasing function $f$ is measure zero (since... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 39, "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/122532/semiring-naturally-associated-to-any-monoid | ## Semiring naturally associated to any monoid?
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For any monoid $M$, we can naturally construct a semiring $S$ as follows:
1. Let the additive monoid of $S$ be the free commutative monoid on $M$
2. Let the multip... | {"extraction_info": {"found_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://mathhelpforum.com/algebra/207093-induction-proof-de-moivres-formula.html | # Thread:
1. ## induction proof of de moivres formula
Is this correct and enough proof
$(cosx+isinx)^n=cos(nx)+isinx$ is true so i put 1 and its true now ima prove for
$S(k+1) = (Cosx+isinx)^k+1= (Cosx+isinx)^k(cosx+isinx)$ now we can rewrite that ^k with a formula i cant remember as
$(coskx+isinkx)(cosx+isinx)$
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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Wormhole | # Wormhole
From Wikipedia, the free encyclopedia
Jump to: navigation, search
For other uses, see Wormhole (disambiguation).
"Einstein-Rosen Bridge" redirects here. For the EP by Venetian Snares, see Einstein-Rosen Bridge (EP).
General relativity
$G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}$
Introd... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=666594 | Physics Forums
## Vertical Spring
Let's say we have a vertical spring. As it oscillates, the energy bounces between gravitational potential energy, spring potential energy, and kinetic energy, right? Why does my lab say that spring potential energy = kinetic energy at any moment in time? Is that a mistake on their pa... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/37377-give-example-non-normal-subgroup-group.html | # Thread:
1. ## give an example of non-normal subgroup of a group
Give an example of a subgroup of a group that is not normal
2. Originally Posted by szpengchao
Give an example of a subgroup of a group that is not normal
Any subgroup of $S_5$ which is not $\{ e\}, A_5, S_5$ would not be normal. This provides a lot o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/88317/coproduct-on-coordinate-ring-of-finite-algebraic-group/88320 | ## Coproduct on coordinate ring of finite algebraic group
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I'm reading Mukai's book "An introduction to invariants and moduli", and I am having trouble understanding one of his examples. It is example 3.49 on page... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 49, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/11219/is-there-a-the-arithmetic-of-elliptic-curves-for-shimura-curves | ## What is a good roadmap for learning Shimura curves?
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I am interested in learning about Shimura curves. Unlike most of the people who post reference requests however (see this question for example), my problem 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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/97743-serious-trouble-finding-big-o-print.html | serious trouble finding big O
Printable View
• August 11th 2009, 06:27 PM
Roclemir
serious trouble finding big O
Original statement:
$f(n)=(n^3+4log_2 n)/(n+4)$
I'm sure the n+4 in both the denominator and numerator have something to do with it, but if i make $n$in the denominator a $n^3$, wouldn't that then make i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 26, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/271035/calculating-a-multivariate-integral-via-level-sets | # calculating a multivariate integral via level sets
I'm considering the possibility of calculating an integral of the form $\int_{S_n} f(x_1,\dots,x_n) dx_1\dots dx_n$ via level sets, where $S_n$ is the domain of integration. In my problem everything is real valued, and $f:R^n\to R$. Also, consider $f$ smooth, with 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": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/tagged/group-theory+graphs-and-networks | # Tagged Questions
3answers
497 views
### Find cycles of graphs with both directed and undirected edges
I need to enumerate all the simple cycles of a graph which has both directed and undirected edges, where we can treat the undirected edges as doubly directed. (Specifically, I am looking at the Cayley ...
1answer
... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Lucas_number | # Lucas number
Not to be confused with Lucas sequences, which are a generic class of sequences to which the Lucas numbers belong.
The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related 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": 23, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2011/06/15/the-lie-derivative/?like=1&source=post_flair&_wpnonce=c8d80d4293 | # The Unapologetic Mathematician
## The Lie Derivative
Let’s go back to the way a vector field on a manifold $M$ gives us a “derivative” of smooth functions $f\in\mathcal{O}M$. If $X\in\mathfrak{X}M$ is a smooth vector field it has a maximal flow $\Phi$ which gives a one-parameter family $\Phi_t$ of diffeomorphisms, ... | {"extraction_info": {"found_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": 40, "mimetex.cgi": 0, "/images/ma... |
http://johncarlosbaez.wordpress.com/2012/05/27/symmetry-and-the-fourth-dimension-part-2/ | Azimuth
Symmetry and the Fourth Dimension (Part 2)
The Coxeter group of the cube
Coxeter groups are a huge amount of fun. Normally their delights are reserved for people who have already studied group theory. But I don’t think that’s fair. You don’t need to know music theory to enjoy a piece by Bach. And you don’t n... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/6377/top-spun-up-with-string-under-tension-problem | # Top spun up with string under tension problem [duplicate]
Possible Duplicate:
I have a top with an unknown mass. It has a moment of inertia of 4.00 * 10^-7 kgm^2 a string is wrapped around the top and pulls it so that its tension is kept at 5.57 N for a distance of .8 m.
Could somebody help me derive some equation... | {"extraction_info": {"found_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/166792/need-a-formula-for-a-quadratic-spline | # Need a formula for a quadratic spline
I'm trying to reproduce some results from a paper and I need an explicit formula for a specific quadratic spline to do so.
The problem is, I've only got a plot of it. The quadratic spline is from figure 2 (a) of Stephane Mallats paper "Singularity Detection and Processing with ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 31, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/27230/from-vertex-function-to-anomalous-dimension | # From vertex function to anomalous dimension
• In a $d$ dimensional space-time, how does one argue that the mass dimension of the $n-$point vertex function is $D = d + n(1-\frac{d}{2})$?
• Why is the following equality assumed or does one prove that a function $f$ will exist such that, $\Gamma^n(tp,m,g,\mu) = f(t)\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": 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/87382?sort=oldest | ## Detecting equivalences of (infinity) categories by nerves
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I have two questions:
1. Is there a way to tell if a functor $F:C \to D$ between two small categories is an equivalence in terms of the map $$N(F):N(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": 35, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://bayesianthink.blogspot.com/2012/08/understanding-bayesian-inference.html | # Probability Puzzles
## Tuesday, August 21, 2012
### Understanding Bayesian Inference
Understanding Bayesian approaches to estimating probabilities are important. Often people don't get the full import of it and/or fail to see the consequences of not estimating it the right way. Most books that discuss it have conf... | {"extraction_info": {"found_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://mathhelpforum.com/differential-equations/58771-power-series-differential-equations.html | Thread:
1. Power Series/Differential Equations
Find the first four nonzero terms in each of two linearly independent power series solutions about the origin.
What do you expect the radius of convergence to be for each solution?
$(cosx)y^{''} +xy^{'} -2y=0$
Set the coefficients near zero and first terms to 1
I am ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/280070/simplex-volume-in-terms-of-the-radius-of-the-inscribed-sphere | # Simplex volume in terms of the radius of the inscribed sphere?
It is well known that for the area of a triangle $A$ we have $$A=r\cdot s,$$ where $s$ is the semiperimeter, and $r$ is the radius of the inscribed circle.
Is there an analogue for the higher-dimensional case. In other words, can I express the volume 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": 22, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/54929/list | ## Return to Question
2 added 1 characters in body; edited tags
Hi everyone. My recent work has me developing software to compute in $H^\ast(G/P)$, where $G$ is a complex connected semisimple algebraic group and $P$ is a standard parabolic subgroup (usually, $B$ or a maximal $P$). While my programs are built on sound... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/91789/non-linear-lie-group | ## Non-linear Lie group [closed]
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Possible Duplicate:
Complex Lie group without faithful real representations?
We know that for a matrix (linear) Lie group $G$, we define it to be a closed subgroup of $GL(n,\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": 13, "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/93055/hypercohomology-of-a-complex-of-sheaves-that-might-be-acyclic-or-might-not/93087 | ## Hypercohomology of a complex of sheaves that might be acyclic (or might not)
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Back again, check this out, let $X$ be a topological space and let $F^{\bullet}$ be a cochain complex of sheaves, I'm trying to comp... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "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/70594/list | ## Return to Answer
2 edited body
Hi,
Your Question:When are the dg-Lie algebra structures on Hochschild cochains: HCH∗(C∗(Ω(M),Q),C∗(Ω(M),Q))[1]≅HCH∗(C∗(M,Q),C∗(M,Q))[1] quasi-isomorphic ?
this is always true.
Step 1: From my paper with Felix and Thomas, looking at the proof, you can see that dg-Lie algebra struc... | {"extraction_info": {"found_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/pre-calculus/76247-absolute-values-question.html | # Thread:
1. ## Absolute Values Question?
ok so i have never been given a quesiton like this and im trying to figure it out for the first time. here it is
Solve |2x-3/4x+1| = > 2
2. Originally Posted by jamman790
ok so i have never been given a quesiton like this and im trying to figure it out for the first time. h... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/reference-request | # Tagged Questions
Use this tag for questions seeking a single specific paper or a short, non-open-ended list of references, like "What paper first discovered X?", "Where can I find the original derivation of X?", or "What is the canonical source for X?" etc.
0answers
56 views
### Relativistic canonical transformati... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/187022-confusion-about-total-derivative.html | Thread:
1. Confusion about Total Derivative
Hello everyone, I was a little confused about something and hope that someone can help me.
Let $U \subseteq \mathbb{R}$ be open, and if a function $f : U \rightarrow \mathbb{R}$ is differentiable on $U,$ then for each $u\in U$ there must exist a linear map $Df(u):\mathbb{R... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathpages.blogspot.com/2008/02/how-to-square-circle.html | # Math Pages Blog
God used beautiful mathematics in creating the world.
## Friday, February 15, 2008
### How to square a circle
A few days ago, I wrote a post in which I introduced a simple and elegant method to "square" a circle using only compass and straightedge. The solution in that post gave a value for $%5Cpi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 13, "/images/ma... |
http://mathoverflow.net/questions/80871/how-many-idempotent-elements-are-in-z-m-closed | ## How many idempotent elements are in Z_m [closed]
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How many idempotent elements are in Z_m or How many roots have this polynomial in Z_m
f(x)=x^2 +x procedure of proof is important for me.
-
That looks too mu... | {"extraction_info": {"found_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/163326/finding-a-subgroup-of-psl-211 | # Finding a subgroup of $PSL_2(11)$
Here is my problem:
Let $X=\begin{pmatrix} 10 & 8 \\ 8 & 1 \end{pmatrix}$ and $Y=\begin{pmatrix} 5 & 7 \\ 5 & 5\end{pmatrix}$ be two elements of $SL_2(11)$. Find a subgroup of $PSL_2(11)$ isomorphic to $A_5$.
I know that $A_5$ has a presentation as $$A_5=\langle x,y|x^2=y^3=(xy)^5... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/257712/a-problem-with-regard-to-wiener-process?answertab=votes | # A problem with regard to Wiener process
Let $W$ be a Wiener process and $U_x$ is the amount of time spent below $x$ during time interval $(0,1)$. Hence $U_x=\int\limits_0^1I_{\{W(t)<x\}}dt$. My question is: what is the probability density function of $U_x$? Thank you.
-
1
– TheBridge Dec 13 '12 at 12:12
@TheBridge... | {"extraction_info": {"found_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/8782/multidimensional-array-reduction-through-summation-over-one-of-its-dimensions?answertab=votes | # Multidimensional array reduction through summation over one of its dimensions
## 1. Introduction
I am using an array of dimension 3 (might become more) to store some values. I would like to implement a function that takes as argument the array and a couple of numbers smaller than the array dimension and returns a 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": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/88689-p-m-f.html | # Thread:
1. ## p.m.f.
Let x and y have the joint p.m.f. given by:
$<br /> \begin{pmatrix}&&&x&&\\y&1&2&3&4&5\\3&0.02&0.03&0. 06&0.15&0.07\\2&0.02&0.05&0.08&0.12&0.06\\1&0.05&0 .05&0.06&0.13&0.05\end{pmatrix}<br />$
a) Find the marginal p.m.f.s and the means and variances.
b) Are x and y independent? Why?
c) Find 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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/118985-finding-inverse-function.html | # Thread:
1. ## Finding inverse function
In the theory of relativity, the mass of a particle with velocity v is
$m=f(v)=\frac{m_{0}}{\sqrt{1-\frac{v^2}{c^2}}}$
where $m_{0}$ is the rest mass of the particle and c is the speed of light in vacuum. Find the inverse function of f.
I've tried to make v the subject 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/107885/parity-condition | # Parity Condition
In the proof for the NP-completeness of Edge-colouring (paper), there is an intermediate result used called the parity condition, which is formulated in a lemma.
Quoting from the paper:
Let $G$ be a cubic, 3-edge colored graph and $V' \subseteq V(G)$ a set of vertices in $G$. Let $E' \subseteq E(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": 27, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/167114-liminf-product-print.html | # liminf of a product
Printable View
• December 30th 2010, 12:57 AM
amheissan
liminf of a product
I am trying to prove the following:
$\underbrace{(\lim \inf f_n)}_f\underbrace{(\lim\inf g_n)}_g\leq \underbrace{\lim\inf (f_ng_n)}_k$.
Here's what I have so far:
FTSOC assume $fg>k$. We know that $f_n<f-\epsilon$ and $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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/symmetry+hamiltonian-formalism | # Tagged Questions
2answers
161 views
### Relativistic Hamiltonian Formulations [duplicate]
Possible Duplicate: Hamiltonian mechanics and special relativity? The Hamiltonian formulation is beautifully symmetric. It's a shame that the explicit time derivatives in Hamilton's ...
3answers
261 views
### What is the dif... | {"extraction_info": {"found_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://math.stackexchange.com/questions/222915/what-taking-gcd-of-two-even-numbers-gives | # What taking gcd of two even numbers gives
What does taking the gcd of two even numbers $y$ and $z$ give? Does it give another indefinite even number $x$?
-
without further knowledge about $y$ and %z$, all we can say, is that$\cgd(y,z)\$ is even. But that does not make it indefinite. – Hagen von Eitzen Oct 28 '12 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": 31, "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?p=4003030 | Physics Forums
## Developing Inner Product in Polar Coordinates via metric
Hey all,
I've never taken a formal class on tensor analysis, but I've been trying to learn a few things about it. I was looking at the metric tensor in curvilinear coordinates. This Wikipedia article claims that you can formulate a dot produc... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/44860?sort=oldest | ## orbits in locally compact group
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As everyone knows if $x\in S^1$, then the set ${ x^n }$ is either finite or dense. Under which condition is true for any other locally compact group, i.e if $G$ is a locally com... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/14440/how-can-i-conclude-that-i-live-in-a-solar-system/14447 | How can I conclude that I live in a solar system?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Well, this is an awkward question and I don't know if it is mathematical enough for MO (I'm sorry if not) but I'll try it: What observations in the coordinate system ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/metric-tensor+units | Tagged Questions
2answers
197 views
Einstein tensor in Friedmann equations : where is the missing $c^2$?
I would like to demonstrate the several forms of the Friedmann equations WITH the $c^2$ factors. Everything is fine ... apart that I have a missing $c^2$ factor somewhere. In all the following $\rho$ ... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/16281/what-is-the-probability-distribution-for-the-angle-of-an-approximate-laserbeam | # what is the probability distribution for the angle of an approximate laserbeam
I'm trying to simulate the light distribution characteristics from a Gaussian laser beam, but having difficulty with the angular distribution.
I need to generate a large number of points on an x/y plane, along with pointing vectors down ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/77175?sort=newest | ## Taking “Zooming in on a point of a graph” seriously.
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In calculus classes it is sometimes said that the tangent line to a curve at a point is the line that we get by "zooming in" on that point with an infinitel... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 74, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/215059/two-non-isomorphic-root-field-extension-of-the-field | # two Non isomorphic root field-extension of the field.
Does there exist two non isomorphic minimal field extension ( root field) of $f= \frac {x^{64}-x}{x(x-1)} \in F_2[x]$ .
I may be using wrong word here saying minimal field extension but in german its said as "minimal würzelkörper" .
Any help would be appreciate... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/25848?sort=oldest | ## Shortest Paths on fractals
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How can one find shortest paths between 2 specified points on fractals, or (since I'm pretty sure this is quite complicated) make useful generalizations about them?
Since the above ... | {"extraction_info": {"found_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://mathematica.stackexchange.com/questions/5519/solving-an-equation-and-finding-a-couple-of-results-given-that-they-are-integer/5520 | # Solving an equation and finding a couple of results given that they are integer
My problem is to find all solutions to an equation with 2 variables between two values that define the range of my search. e.g., $(x+y-y²)/(1-y-x²)=0$ with solutions ${x,y} \in \mathbb{Z}$.
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## 2 Answers
The following might be of use... | {"extraction_info": {"found_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://windowsontheory.org/2012/11/27/755/ | ## A Research Blog
by
Computational learning is full of problems that are deceptively simple to state but fiendishly hard to solve. Perhaps none more so than the problem of learning Juntas, posed by Avrim Blum and Pat Langley. Its the kind of problem which seems well suited for a polymath endeavor, Dick Lipton likes ... | {"extraction_info": {"found_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": 31, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/109707/lyapunov-function-on-chains | ## Lyapunov function on chains
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How can I prove that if $x R y$ (for each $e$ there is a $e$-chain from x to y) then for each lyapunov function $L$ we have $L(x)>= L(y)$.
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Homework? Read the FAQ – Anthony Quas ... | {"extraction_info": {"found_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... |
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