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http://math.stackexchange.com/questions/172762/can-two-collections-of-different-size-have-same-a-m-g-m-and-h-m?answertab=votes | # Can two collections of different size have same A.M., G.M. and H.M?
After following Can two sets have same AM, GM, HM? and the sublime answer of Micah, I am tempted ask the solution of the same question when size of these two sets are not same.
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4
There is a trivial answer to your question, but I hope you'll do 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": 12, "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/27557/list | ## Return to Answer
2 added additional content
This can be rephrased as follows.
Let $X$ and $Y$ be independent random variables with the same, continuous, distribution. Is it true that $E(X)\le E(|X-Y|)$.
1. Is this likely?
2. Is it true for a discrete distribution?
3. If one has a discrete counterexample, can 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": 7, "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/189649/uncountable-minus-countable-set-is-uncountable | # Uncountable minus countable set is uncountable
Problem statement
Prove that if $A$ is an uncountable set and $B$ is a countable set, then $A\setminus B$ must be uncountable.
What I think
The statement does not mention $A$ and $B$ relationship. I think there are two possibilities:
• If $A \cap B = \emptyset$, 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": 40, "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/98171?sort=oldest | ## What is the relation between Quasicrystals, Riemann Hypothesis, and PV numbers?
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Could somebody explain to me, from a mathematical stand-point, what is a quasi-crystal, and how it relates to the set of Pisot nu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "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/Hilbert-style_deduction_system | # Hilbert system
(Redirected from Hilbert-style deduction system)
In mathematical physics, Hilbert system is an infrequently used term for a physical system described by a C*-algebra.
This article needs attention from an expert in Mathematics. See the talk page for details. WikiProject Mathematics (or its Portal) may... | {"extraction_info": {"found_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": 55, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/19063/reference-for-the-existence-of-a-shapovalov-type-form-on-the-tensor-product-of-in | ## Reference for the existence of a Shapovalov-type form on the tensor product of integrable modules
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Shapovalov and Jantzen showed us how to construct a nice inner product on finite dimensional representations 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": 43, "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/20502/angular-velocity-omega-by-v?answertab=votes | # Angular velocity $\omega$ by $v$
We have two girls, with mass (M). They become close to each other in speed of V. The distance between them is 3L.
I was asked to calclute the Angular velocity (w) of the two girls. So I set the rotation axis in the middle (where the distance between the two girls and the axis is 1.5... | {"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": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://programarcadegames.com/index.php?chapter=introduction_to_graphics | # Program Arcade GamesWith Python And Pygame
< Previous Home Next >
# Chapter 5: Introduction to Graphics
Now that you can create loops, it is time to move on to learning how to create graphics. This chapter covers:
• How the computer handles x, y coordinates. It isn't like the coordinate system you learned in 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": 7, "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/spin-model+ising-model | # Tagged Questions
1answer
249 views
### A simple model that exhibits emergent symmetry?
In a previous question Emergent symmetries I asked, Prof.Luboš Motl said that emergent symmetries are never exact. But I wonder whether the following example is an counterexample that has exact ...
1answer
69 views
### Random 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": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/32370/what-pdf-should-be-fit-to-a-rank-histogram | # What PDF should be fit to a rank histogram?
A Rank Histogram (or Talagrand Diagram) is a neat way of measuring whether your numerical model is giving appropriate variance. It's used for weather and climate forcasting, where you only have one observational series, and many model series (an ensemble). It's described 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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cs.stackexchange.com/questions/tagged/formal-methods | # Tagged Questions
a particular kind of mathematically-based technique for the specification, development and verification of software and hardware systems.
3answers
98 views
### Binary decision diagram for a six-figure Boolean function
Let $p$ be the six-figure Boolean function with the following definition: \$p(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": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/22250/list | ## Return to Answer
2 edited body
Wilfrid Hodges has shown that it is consistent with ZF that there be is an algebraic closure $L$ of the rational field $\mathbb{Q}$ with no nontrivial automorphisms. Obviously $|Aut(L)\smallsetminus {1}| = 2^{\aleph_{0}}$.
See: W. Hodges, Läuchli's algebraic closure of $\mathbb{Q}$.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2010/10/21/inner-products-in-the-character-table/?like=1&source=post_flair&_wpnonce=966197e62c | # The Unapologetic Mathematician
## Inner Products in the Character Table
As we try to fill in the character table, it will help us to note another slight variation of our inner product formula:
$\displaystyle\langle\chi,\psi\rangle=\frac{1}{\lvert G\rvert}\sum\limits_K\lvert K\rvert\overline{\chi_K}\psi_K$
where 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": 0, "wp_latex": 16, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/tagged/sha-2+preimage-resistance | # Tagged Questions
1answer
161 views
### Is the last step of an iterated cryptographic hash still as resistant to preimage attacks as the original hash?
Considering a cryptographic hash, such as MD5 or SHA2, denoted by the function $H(m)$ where $m$ is an arbitrary binary string, there is a lot of material available ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/6576/index?nomenu=1 | ## 'Cross with the Scalar Product' printed from http://nrich.maths.org/
### Show menu
Consider the vector
{\bf v}=\pmatrix{1\cr 2\cr 3}
Investigate the properties of vectors ${\bf u}$ such that ${\bf u}\cdot {\bf v}=0$.
Describe geometrically the set of all such vectors ${\bf u}$.
Now explore the possibilities for... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=160088 | Physics Forums
## Intersection between a plane and a line
Hi all:
Given a plane ax+by+cz+d = 0, and a straight line, X = X0 + vt. What is an efficient way to compute the intersection point please? Also, is there any efficient method to determine if two points are located on the same side of the plane or on the 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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://motls.blogspot.com.au/2012/09/astronomical-unit-au-redefined.html?m=1 | # The Reference Frame
Our stringy Universe from a conservative viewpoint
## Wednesday, September 19, 2012
### Astronomical unit (AU) redefined
We visited an old astronomer yesterday: I could see the sunspots exactly as you can see them on the web, except that the image was left-right-reflected and somewhat rotated.... | {"extraction_info": {"found_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://math.stackexchange.com/questions/260280/what-is-a-normalized-valuation-corresponding-to-a-valuation-ring | # What is a “normalized valuation” corresponding to a valuation ring?
I encountered the phrase "normalized valuation" similar to the following:
Let $A_i$ be the valuation ring $k[x_1,...,x_n]_{\langle x_i\rangle}$ and $v_i$ be the normalized valuation defined by $A_i$.
I didn't know this term before, and a short int... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 69, "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/11017/is-this-algorithm-for-simulating-a-quantum-computer-accurate/11019 | # Is this algorithm for simulating a quantum computer accurate?
I'm very new to quantum mechanics. I'm thinking of writing a quantum computer simulator, would the following work?
• Each qubit is stored as a single bit,
• For each operation, the qubits involved are transformed into a complex vector of amplitudes of si... | {"extraction_info": {"found_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/84384-integral-x-4-4-x-5-1-2-a.html | # Thread:
1. ## Integral x^4(4+x^5)^1/2
$\int x^4\sqrt{4+x^5}$
Do I make $u=4+x^5$ in order to solve this problem?
2. Originally Posted by cammywhite
$\int x^4\sqrt{4+x^5}$
Do I make $u=4+x^5$ in order to solve this problem?
Yes! Just remember to factor $\frac{1}{5}$ out of your integral!
3. Originally Posted by ... | {"extraction_info": {"found_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": 39, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/1589/toy-sheaf-cohomology-computation?answertab=oldest | # Toy sheaf cohomology computation
One thing that really helped in learning the Serre SS was doing particular computations (like $H^*(CP^{\infty})$)
I am curious, as a sort of followup if anyone can suggest: 1. a reference where small computations are carried out? or 2. a specific computation to do with a small enoug... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/102068?sort=newest | ## Intersection forms of 4-manifolds with boundary
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Let $X$ be any simply connected smooth 4-manifold with a fixed Euler characteristic $e$, signature $\sigma$ and boundary $Y$. Assume that the determinant of the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/218020/finite-free-rings-over-complete-local-rings-are-direct-products-of-local-rings | # Finite free rings over complete local rings are direct products of local rings
I came across the following statement: Let $R$ be a complete local Noetherian commutative ring. If $A$ is a commutative $R$-algebra that is finitely generated and free as a module over $R$, then $A$ is a semi-local ring that is the direct... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 47, "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/2220/note | ### Pebbles
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
### It Figures
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find?... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/92683?sort=votes | ## Finiteness conditions and Veronese subrings
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Consider a commutative group $G$ of finite type, a subgroup of finite index $H\subseteq G$, a noetherian commutative ring $A$, and a $G$-graded $A$-algebra $R=\bigop... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/136716/program-for-eigenvalue-calculation/136728 | # program for eigenvalue calculation
I have a n x n matrix. I would like to
(a) take successively higher powers of the matrix and then multiply by projection vectors until the resulting vectors differ by only a scalar factor.
(b) calculate the dominant eigenvalue of the matrix to compare to (a)
and (c) calculate, 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": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/34470/how-does-the-holographic-principle-imply-nonlocality | # How does the holographic principle imply nonlocality?
For example in the discussions here and here there are comments by Ron Maimon:
Your complaint about locality would be more serious if holography didn't show the way--- the CFT in AdS/CFT produces local AdS physics, even though the description is completely and 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": 3, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/trigonometry/209091-show-me-steps-solving-complex-numbers-involving-e.html | # Thread:
1. ## Show me the steps to solving complex numbers involving e?
My teacher didn't go into too much detail on these equations and they were on a test, so I'd like to know how to solve these equations for my final.
Z=
Can someone show me the steps how to get this complex number into algebraic form answer Z=... | {"extraction_info": {"found_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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/172409-find-specified-value-r-n.html | # Thread:
1. ## find the specified value for r and n
can anybody here help me on this problem.... i've been trying to solve them with the use of the formula of geometric sequence and geometric series. but i could not make it to the answer.
Given: 1. S sub 5 = 31/4 ; r = 1/2 ; what is first term?
2. S sub n = 94.5 ... | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/30408/how-much-are-reduced-powers-different/100141 | ## How much are reduced powers different ?
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Given two infinite sets $X$ and $I$, and a filter ${\cal F}$ on $I$, one defines as usual the equivalence relation $\approx_{\cal F}$ on $X^I$ and obtains the reduced po... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 60, "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/179267-double-integration.html | # Thread:
1. ## Double Integration
Use double integration to calculate the area that liew between the curves
$\sqrt{x} + \sqrt{y} = \sqrt{a}$ $and x + y = a, a > 0$This is what i have done , between the limits on the y = a-x and y = 0 and for x = a and 0 $\iint dy dx \int a- x dx = ax - \frac{{x}^{ 2} }{2 } = {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": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/36223/would-it-be-economical-to-add-a-counterweight-to-rocket-launches?answertab=votes | # Would it be economical to add a counterweight to rocket launches?
It seems a large amount of rocket fuel during launches is spent to get the mass moving; indeed according to QuickLaunch, Inc. it takes 40% of the rocket fuel to get to Mach 1.3. It seems as though the engines are firing quite a while before liftoff, 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": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://medlibrary.org/medwiki/Minkowski%E2%80%93Bouligand_dimension | Minkowski–Bouligand dimension
Welcome to MedLibrary.org. For best results, we recommend beginning with the navigation links at the top of the page, which can guide you through our collection of over 14,000 medication labels and package inserts. For additional information on other topics which are not covered by our da... | {"extraction_info": {"found_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": 20, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/38019/zeros-of-gradient-of-positive-polynomials/38634 | ## Zeros of Gradient of Positive Polynomials.
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It was asked in the Putnam exam of 1969, to list all sets which can be the range of polynomials in two variables with real coefficients. Surprisingly, the set $(0,\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": 6, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.scholarpedia.org/article/Attractor_reconstruction | Attractor reconstruction
From Scholarpedia
Timothy D. Sauer (2006), Scholarpedia, 1(10):1727.
Curator and Contributors
1.00 - Timothy D. Sauer
0.50 -
Eugene M. Izhikevich
Attractor reconstruction refers to methods for inference of geometrical and topological information about a dynamical attractor from observatio... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/47629-consecutive-heads-tails-weighted-coin-toss.html | 1Thanks
• 1 Post By awkward
# Thread:
1. ## Consecutive Heads/Tails in weighted coin toss
Hi,
Supposing you have a weighted coin which lands heads up 70% of the time and tails up 30% of the time.
Q. What is the probability that it lands on tails 20 or more times in a row if I did this 1000 times?
*Also could I ha... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 18, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/128521/number-of-decompositions-into-k-powers-of-p-counting-functions | # “Number of Decompositions into $k$ Powers of $p$”-Counting Functions
Let $a_j\in \mathbb{N}$, with $0< a_{j-1}<a_j$. My question is:
What is known about the counting functions $\sigma_{k,p}(n)$, counting how many numbers, less than $n$, have a decomposition into a sum of $k$ $p$-powers of $a_j$?
So for every $x\le... | {"extraction_info": {"found_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://mathbabe.org/2012/09/09/nyc-parks-datadive-update-does-pruning-prevent-future-fallen-trees/ | # mathbabe
Exploring and venting about quantitative issues
Home > data science > NYC Parks datadive update: does pruning prevent future fallen trees?
## NYC Parks datadive update: does pruning prevent future fallen trees?
September 9, 2012
After introducing ourselves, we subdivided our pruning problem into 5 proble... | {"extraction_info": {"found_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": 8, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/313282/finding-a-counterexample-to-a-prime-factorization-conjecture | # Finding a counterexample to a Prime Factorization Conjecture
Let $\mathbb{Z}_{\geq 2}$ be the set of natural numbers starting at 2:
$$\mathbb{Z}_{\geq 2}= \{2, 3, 4, 5,\ldots\}.$$
An natural number's prime factorization is odd if the total number of primes in its factorization is odd. It is even if the total numbe... | {"extraction_info": {"found_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/questions/91944/flattening-a-corner-in-a-convex-d-polytope-into-d-1-dimensions-without-over | ## Flattening a corner in a convex $d$-polytope (into $d-1$ dimensions, without overlap)?
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I'm interested in the following question, which seems to be assumed all over the place (at least for 3 dimensions) in conv... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=60863 | Physics Forums
## infinetely many primes of the form 3n+1
prove that there are infinetely many primes of the form
3n+1
we used :
Assume there is a finitely # of primes of the form 3n+1
let P = product of those primes.. which is also of the form 3A+1 for some A.
Let N = (2p)^2 + 3.
Now we need to show that N has a pr... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/199044/rational-number-solution-for-an-equation/199064 | # Rational number solution for an equation
Does there exist $v=(a,b,c)\in\mathbb{Q^3}$ with none of $v$'s terms being zero s.t. $a+b\sqrt[3]2+c\sqrt[3]4=0$ ?
And I was doing undergraduate algebra 2 homework when I encountered it in my head. At first It seemed like it can be proved there can be no such $v$ like how $\... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.reference.com/browse/representable | Definitions
# Representable functor
In mathematics, especially in category theory, a representable functor is a functor of a special form from an arbitrary category into the category of sets. Such functors give representations of an abstract category in terms of known structures (i.e. sets and functions) allowing one... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "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://en.wikipedia.org/wiki/Circular_motion | # Circular motion
"Radial motion" redirects here. It is not to be confused with radial velocity or rotational speed.
Classical mechanics
Branches
Formulations
Fundamental concepts
Core topics
Scientists
In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a cir... | {"extraction_info": {"found_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": 76, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/9468/riemannian-geometry/9487 | ## Riemannian Geometry
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I come from a background of having done undergraduate and graduate courses in General Relativity and elementary course in riemannian geometry.
Jurgen Jost's book does give somewhat of an 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": 79, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.reference.com/browse/Boolean+logic | Definitions
# Boolean logic
Boolean logic is a complete system for logical operations. It was named after George Boole, who first defined an algebraic system of logic in the mid 19th century. Boolean logic has many applications in electronics, computer hardware and software, and is the base of digital electronics. In... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 40, "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://www.conservapedia.com/Momentum | # Momentum
### From Conservapedia
Momentum is the "quantity of motion" an object possesses. In classical physics, the linear form of momentum is defined as the product of mass and velocity:
$\mathbf{p} = m\mathbf{v}$
Hence, the faster an object goes, or the more mass it posesses, the more momentum it has. Momentum ... | {"extraction_info": {"found_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": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/95557-very-complicated-algebra.html | # Thread:
1. ## very complicated algebra
Could someone help me with the following algebraic fraction:
$<br /> <br /> \frac {(a-b)(a^2+b^2)-a+b}{(a^3b^3)-(a^2-ab+b^2)+1}<br />$
2. I think you have a typo somewhere because the denominator does not factor. The numerator factors to be
$(a-b)(a^2+b^2-1)$
So if there 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2007/06/20/ | # The Unapologetic Mathematician
## The Existence Theorem for Limits
Of course, though we’ve defined limits, we don’t know in general whether or not they exist. Specific limits in specific categories have been handled in an ad hoc manner. We show that the Cartesian product is a product in $\mathbf{Set}$, or 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": 0, "wp_latex": 39, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/200839-domain-function-true-false.html | # Thread:
1. ## Domain and function True/False ?
True or false,
The domain of the function f(x) = x^2-9/x is {X|X /= +/-3}. I don't understand this question. Also, what does X|X mean? Thanks.
2. ## Re: Domain and function True/False ?
Originally Posted by kmerr98277
True or false,
The domain of the function f(x) = ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/98228?sort=oldest | ## Is it known that every PDF continuous in all $R^n$ has a maximum? [closed]
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I'm working with maximum a posteriori estimation and managed to show that every probability density function that is continuous in all... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "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/52532/cardinality-of-local-bases-in-the-non-standard-reals | ## cardinality of local bases in the non-standard reals
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Given a index set $S$ together with a ultrafilter $\mu$ on $S$ (such that no set of cardinality $< |S|$ has measure $1$). Let the ordered field $\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": 39, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/10.4153/CMB-2005-019-9 | Canadian Mathematical Society
www.cms.math.ca
| | | | |
|----------|----|-----------|----|
| | | | | | |
| Site map | | | CMS store | |
location: Publications → journals → CMB
Abstract view
The Distribution of Totatives
Read article
[PDF: 136KB]
http://dx.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/20396/energy-required-to-reach-1-wavelength/20398 | # Energy required to reach 1 wavelength [closed]
I was curious if there was a forumla to find the energy required to reach 1 wavelength in a given substance. (or a vacumn if that's too hard).
I am also wondering if this number can tell us anything about the way the wave acts?
My knowledge of electromagnetic radiatio... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-equations/207158-how-apply-langrange-equations-case.html | # Thread:
1. ## how to apply the Langrange equations in this case
In the proof to Theorem 7.3 from this paper on FNTFs, the authors invoke the so-called "Langrange equations." I assume they mean the Euler-Lagrange equations. (But maybe not...?) Unfortunately I'm not at all familiar with the Euler-Lagrange equations, ... | {"extraction_info": {"found_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://nrich.maths.org/981/index?nomenu=1 | On a digital $24$ hour clock, at certain times, all the digits are consecutive (in counting order). You can count forwards or backwards. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-math-topics/195737-disconnected-graphs.html | # Thread:
1. ## Disconnected Graphs
Let G be disconnected graph. Prove that if u and v are any two vertices of G complement then $d_{\overline{G}}(u,v) = 1 \;\; or \;\; 2$
therefore if G is disconnected graph then $diam(\overline{G} ) \leq 2$ . | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://polylogblog.wordpress.com/2012/07/29/data-streaming-in-dortmund-day-3/ | # Data Streaming in Dortmund: Day 3
July 29, 2012 in conference report
Continuing the report from the Dortmund Workshop on Algorithms for Data Streams, here are the happenings from Day 3. Previous posts: Day 1 and Day 2.
Michael Kapralov started the day with new results on computing matching large matchings in the 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/37740/projective-dimension-of-zero-module/113917 | ## Projective dimension of zero module
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Is there any consensus on what the projective dimension of the zero module should be? Here are three statements one commonly encounters in textbooks, sometimes with or witho... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 88, "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/93704?sort=oldest | ## Checking if one polytope is contained in another
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Hi,
I have two sets of inequalities, say, $Ax \leq 0$ and $Bx \leq 0$. I would like to know if they both define the same polytope. Or, even, whether one is con... | {"extraction_info": {"found_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/87865?sort=newest | ## What is the name for a finite-group representation that is the sum of all the irreducibles (once)?
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I vaguely remember seeing a paper studying the concept of a totally multiplicity-one representation of a finit... | {"extraction_info": {"found_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://calculus7.org/2012/03/31/diameter-vs-radius-part-ii/ | being boring
## Diameter vs radius, part II
Posted on 2012-03-31 by
A set $A$ in a metric space $X$ has diameter $\mathrm{diam}\, A=\sup_{a,b\in A} |a-b|$ and radius $\mathrm{rad}\, A = \inf_{x\in X}\sup_{a\in A} |a-x|$. It’s easier to find the radius by expressing it in a different form: the smallest (or infimal) v... | {"extraction_info": {"found_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": 19, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/234103/questions-about-assigning-a-probability-to-a-randomly-chosen-large-integer-n-b | # Questions about assigning a probability to a randomly chosen large integer $n$ being prime
I heard this question a few days ago, so reciting from memory:
If I were to randomly choose an arbitrarily large positive integer $n$, could I write a function that determines the likelihood of it being prime?
Intuitively, 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": 17, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/users/6764/71ga?tab=activity | # 71GA
reputation
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bio
website ziga-lausegger.netau.net/…
location Slovenia
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I love to program and crosscompile baremetal C programs for ARM based microcontrollers, I love physics and i love writing science 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": 62, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/139865-maclaurin-series.html | # Thread:
1. ## Maclaurin Series
How can I find the Maclaurin series for (z/z^3 + 8) and find the radiance of convergence?
2. Originally Posted by ihr02
How can I find the Maclaurin series for (z/z^3 + 8) and find the radiance of convergence?
One way to do it is this:
$\frac{z}{z^3+8}=\frac{z}{8}\cdot\frac{1}{1+\le... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/flow+viscosity | # Tagged Questions
1answer
495 views
### What is the shear stress of a fluid?
One book defines the shear stress $\tau$ of a (Newtonian) fluid as $$\tau = \eta \frac{\partial v}{\partial r}$$ where $\eta$ is the viscosity. There is not much context, so I've made some guesses. ... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/81800/the-lagrangian-formulation-of-mechanics-without-going-through-variational-princip | ## The Lagrangian formulation of mechanics without going through variational principles.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In some texts on classical mechanics and not only, the Euler--Lagrange equations of motion are directly obtained as solutio... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4003831 | Physics Forums
## The color of an apple (light absorption and emission)
From my textbook (explaining why an apple is red):
We imagine that the red apple in the picture is illuminated by daylight, IE light which contains all the wavelengths of the visible spectrum. The apple is red because the main part of the light ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/38970-distinct-value.html | # Thread:
1. ## distinct value of
given $cos ^2 \frac {4k\pi\pm\pi}{12}$
how can i find the three distinct values of it beside putting k = 1,2,3,4,5..... to evaluate it's value to see they are the same or not?
2. Originally Posted by afeasfaerw23231233
given $cos ^2 \frac {4k\pi\pm\pi}{12}$
how can i find the three ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/212560-positive-definite-symmetric-matrix-has-maximal-elements-diagonal.html | # Thread:
1. ## Positive definite symmetric matrix has maximal elements on diagonal
Let A be a positive definite symmetric matrix. Prove that for any column (or row) the maximal element of that list is on the diagonal. I've only been able to prove the weaker statement a_(i,i)+a_(j,j)>2*a_(i,j) for i not equal to 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathematica.stackexchange.com/questions/tagged/list-manipulation+combinatorics | # Tagged Questions
0answers
33 views
### Generating partitions of a set with a specified size of the parts [duplicate]
I tried the following (inspired by the answer here) myList = {a, b, c}; Needs["Combinatorica`"]; SetPartitions[myList] and I got this answer, ...
2answers
128 views
### Partition a set into $k$ non... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "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/9017/could-the-precisiongoal-for-ndsolve-be-a-negative-number/9018 | # Could the PrecisionGoal for NDSolve be a negative number?
The help of Mathematica doesn't say so much about the `PrecisionGoal` for `NDSolve`, and I never considered much about it even after I met the warning message
NDSolve::eerr
for several times when I was trying to solve a set of PDEs these days: every time 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": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/108899/how-close-are-these-events | # How close are these events?
I'm a computer programmer and we're running into a weird error on our website.
We have a large number users who do a certain task. Between the entire set of users, this task happens about once every 20 seconds, but of course each user is unique.
We're seeing a strange problem about once... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/11009/including-the-interaction-but-not-the-main-effects-in-a-model/11022 | # Including the interaction but not the main effects in a model
Is it ever valid to include a two-way interaction in a model without including the main effects? What if your hypothesis is only about the interaction, do you still need to include the main effects?
-
1
My philosophy is run lots of models, check their 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": 28, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.cfd-online.com/W/index.php?title=Reynolds_number&direction=next&oldid=13668 | [Sponsors]
Home > Wiki > Reynolds number
# Reynolds number
### From CFD-Wiki
Revision as of 09:15, 3 January 2012 by Peter (Talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
The Reynolds number characterises the relative importance of inertial and viscous forces in a flow. ... | {"extraction_info": {"found_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": 19, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/47224/what-does-a-sphere-moving-close-to-the-speed-of-light-look-like/47245 | What does a sphere moving close to the speed of light look like?
What shape does the viewer in a reference frame with $v=0$ perceive? I suppose that since the sphere moves in one direction only (oX only, not oY) its section would change into an ellipse, where the horizontal diameter would be shorter.
However, my text... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/7002/derive-a-short-rate-model-from-hjm/7005 | # Derive a short rate model from HJM
Suppose we are assuming the HJM framework. My question is, if it is possible to derive for different choices of the volatility function $\sigma$ (and hence of the drift function) the most common short rate models, i.e. Vasicek, CIR,Dothan, Ho-Lee,Hull-White? I know if we choose 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": 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/139936/paradox-of-general-comprehension-in-set-theory-other-than-russells-paradox | # Paradox of General Comprehension in Set Theory, other than Russell's Paradox
As is well known, the General Set Comprehension Principle (any class is a set) leads to the Russell Paradox (the class $x \notin x$ cannot be a set). As a result, set theories must restrict the Comprehension Principle to avoid self-referenc... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Boltzmann_equation | # Boltzmann equation
For other uses, see Boltzmann's entropy formula, Stefan–Boltzmann law, and Maxwell–Boltzmann distribution.
In physics, specifically non-equilibrium statistical mechanics, the Boltzmann equation or Boltzmann transport equation describes the statistical behaviour of a fluid not in thermodynamic 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": 41, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/education | # Tagged Questions
How is physics taught and learned. Teaching strategies, class examples and demonstrations; learning resources, career advice, etc. For explicit problems, use the 'homework' tag instead.
5answers
276 views
### Theoretical physics and education: Does it really matter a great deal about what happens ... | {"extraction_info": {"found_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/51815/where-inside-a-large-uniformly-dense-symmetrical-sphere-would-its-gravity-towar/51817 | # Where inside a large uniformly dense, symmetrical sphere would its gravity toward the center be the strongest?
Imagine a sphere of uniform density with similar volume and average density of our Earth. There is a bore leading to the center of the sphere from the surface with a scale at regular intervals. At what part... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/108503/constant-averages-along-orbits | ## constant averages along orbits
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
What should one say to describe the situation in which a function $T$ from some set $X$ to itself, and a function $f$ from $X$ to some characteristic-zero field $K$, have the 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": 107, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/revisions/114775/list | ## Return to Question
2 added 93 characters in body
Hi
I have a function F:R^n->R^n $F:\mathbb{R} ^ n\rightarrow \mathbb{R}^n$ for which I know there exist a unique fixed point $x ^ *$ (say). I also know that the Jacobian of F $F$ at each point x $x$ in R^n $\mathbb{R} ^ n$ has all of its eigenvalues in [0,1) $[0,1)... | {"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": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://motls.blogspot.com/2012/12/prediction-isnt-right-method-to-learn.html?m=1 | # The Reference Frame
Our stringy Universe from a conservative viewpoint
## Monday, December 31, 2012
### Prediction isn't the right method to learn about the past
Happy New Year 2013 = 33 * 61!
The last day of the year is a natural moment for a blog entry about time. At various moments, I wanted to write about 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": 0, "mathjax_display_tex": 33, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/71957-stoke-s-theorem-jacobian-problem.html | # Thread:
1. ## Stoke's Theorem - Jacobian Problem
Question asks to evaluate the surface integral for the given $F$ and $S$ with stokes theorem.
$F= [z^2, x^2, y^2], s: z^2 = x^2 + y^2$ for $y >= 0$, $0<=z<=2$
My question is that in transformation from x,y to u,v shouldn't there be jacobian multiplied ? I dont see ... | {"extraction_info": {"found_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://cs.stackexchange.com/questions/7406/intuitive-meaning-of-modal-mu-calculus-formula | # Intuitive meaning of modal $\mu$-calculus formula
I am solving one of the past exams and I am not certain with my solution to one of the exercises. The exercise is asking to give intuitive meaning to modal $\mu$-calculus formula:
$$\phi = \mu Z. \langle - \rangle tt \wedge [-a]Z$$
According to an article Modal log... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 51, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/213152-cot-x-3cot-2x-1-0-a.html | 2Thanks
• 1 Post By ILikeSerena
• 1 Post By ibdutt
# Thread:
1. ## cot(x) + 3cot(2x) - 1 = 0
Hello this question looked straight forward enough, but I'm stuck and would really appreciate some help.
Solve on the interval $0\leq x \leq\2\pi$
$\cot\theta + 3\cot2\theta-1=0$
I tried writing it in terms of $\cos\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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/1110 | nrich enriching mathematicsSkip over navigation
### Polydron
This activity investigates how you might make squares and pentominoes from Polydron.
### Symmetry Challenge
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to 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": 8, "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/algebraic-manipulation?sort=votes&pagesize=15 | Tagged Questions
The art of manipulating an algebraic expression into the desired form.
6answers
2k views
Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)
Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], M... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/3878/constructing-secure-key-exchange-protocol/3879 | # Constructing secure key exchange protocol
I have $\Pi=(Gen,Enc,Dec)$ and let it be semantically secure public-key encryption scheme. Security parameter is $n$, then the message space of plaintext is always $\lbrace 0, 1 \rbrace^n$.
By using $\Pi$ I want to construct key exchange protocol $\Theta$. There should be 2... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/tag/heat-flow/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Tag Archive
You are currently browsing the tag archive for the ‘heat flow’ tag.
## Random matrices: The Universality phenomenon for Wigner ensembles
2 February, 2012 in math.PR, 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-geometry/195066-converge-diverge-plus-show-why.html | # Thread:
1. ## Converge or diverge plus show why
show why the con/diverge:
$\sum_{r=1}^{\infty}\frac{r^{2}-1}{r^{2}+1}$
i think she diverges. because the terms get bigger (closer to 1 each) so you are just adding almost 1 + 1 +1 +1 ... it tails off to infinity... diverge... but i think i need to use a rigurous 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/40979/proof-of-quantum-mechanical-position-uncertainty?answertab=active | # Proof of quantum mechanical position uncertainty
How can you prove the uncertainty for position is:
$$\Delta{x} =\sqrt{\langle x^2\rangle-\langle x\rangle^2}$$
$\Delta{x}$, taken to be the root mean square of x.
$$\Delta{x} =\sqrt{\langle \left(x-\langle x\rangle\right)^2\rangle}$$
$$\Delta{x} =\sqrt{\langle \le... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/150270/preparing-for-exam-and-dont-understand-how-to-calculate-this-integral-via-integ | # Preparing for exam and don't understand how to calculate this integral via integrating by parts twice
It seems to be a pretty simple integral but I am blanking out on how to find this integral:
$$\int_0^1 e^{-x}\cos(n\pi x) \;dx$$
I tried Mathematica, but it seems to use some formula instead of integrating by part... | {"extraction_info": {"found_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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/265/clue | ### Just Rolling Round
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
### Rotating Triangle
What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?
### ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/37172/what-are-some-open-problems-in-algebraic-geometry/37203 | ## What are some open problems in algebraic geometry?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
What are the open big problems in algebraic geometry and vector bundles?
More specifically, I would like to know what are interesting problems related to mod... | {"extraction_info": {"found_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://nrich.maths.org/5816 | ### Rationals Between
What fractions can you find between the square roots of 56 and 58?
### Root to Poly
Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.
### Consecutive Squares
The squares of any 8 consecutive numbers can be arranged into tw... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=281663 | Physics Forums
## State of an electron, including spin
In the quantum mechanics book I have, they first cover the mechanics of a generic particle (say an electron), without ever considering the spin. They encode the state of the electron as a function F in L2, where the F^*F is the probability density for the locatio... | {"extraction_info": {"found_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://blog.drskippy.com/2012/05/14/dimension-reduction-for-machine-learning-simple-example-of-svd-pca-pathology/ | Of the fast and loose practices in machine learning that I cringe at, throwing one’s favorite tool at high-dimensional data and expecting algorithms to learn to generalize well.
Part of the problem is we don’t always know if the features we chose are meaningful to the learning problem. Another part of the problem is t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 3, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/general-relativity?page=3&sort=unanswered&pagesize=15 | # Tagged Questions
A theory that describes how matter produces and responds to the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.
2answers
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### Does a Weak 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": 6, "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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