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http://physics.stackexchange.com/questions/46277/general-question-on-aligning-a-quantization-axis?answertab=oldest | # General question on aligning a quantization axis
I have a general question on how to work with quantization axis. Here is the setup:
I am looking at a single two-level atom placed at the origin $(0, 0, 0)$, which is unperturbed in the sense that no magnetic field is applied to it.
I now send in a coherent EM-field... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/26921/physical-interpretation-to-the-category-of-cfts?answertab=oldest | # Physical interpretation to the category of CFTs
This question comes from reading Andre's question where I wandered whether that question even makes sense physically. In mathematics, VOAs form a category, does this category as a whole have a physical interpretation?
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I think a good question should be self-contai... | {"extraction_info": {"found_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/differential-geometry/112574-summation-print.html | # Summation
Printable View
• November 5th 2009, 06:17 AM
Talamari
Summation
Thanks for taking the time to look at this, it's going to be one of those problems where I'm either missing something really obvious, or there's no simple way to approach it, so I thought I'd post it up on see if anyone has any ideas:
From t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/129452-defining-isomorphism.html | # Thread:
1. ## Defining an isomorphism....
Prove that the field R of real numbers is isomorphic to the ring of all 2x2 matrics of the form (0 0; 0 a) with a a real number.
It says to let f(a)=(0 0; 0 a), but I don't know how to show that this is one to one and onto.
Thanks.
2. Originally Posted by zhupolongjoe
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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/21565?sort=oldest | ## Is it true that the only interesting topologies are metric topologies and weak topologies?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In "Infinite dimensional analysis, A hitchhikers guide" by Aliprantis and Border, they write that these 2 classes of 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": 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/differential-geometry/27506-1-manifolds.html | # Thread:
1. ## 1-manifolds
Hi to all!
I'm a new member, my name is Riccardo.
I've a problem with 1-manifolds, i have to prove a proposition but i can't do it.
Here is the extract of the book with notation and the proposition 1 that i have to prove:
//
DEFINITION. A 1-manifold is a second countable Hausdorff topolo... | {"extraction_info": {"found_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/32133?sort=oldest | ## Expressing adj(A) as a polynomial in A?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Suppose $A\in R^{n\times n}$, where $R$ is a commutative ring. Let $p_i \in R$ be the coefficients of the characteristic polynomial of $A$: $\mathop{\mathrm{det}}(A-xI) ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 229, "mathjax_display_tex": 16, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathoverflow.net/questions/10957/a-hands-on-description-of-a-completion-of-the-free-commutative-monoid-on-counta | ## A hands-on description of a “completion” of the free commutative monoid on countably many generators
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
This is basically an I'm-weak-at-algebraic-geometry question. I asked it as a warm-up question here, but Ily... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 82, "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=3999849 | Physics Forums
Page 2 of 2 < 1 2
Recognitions:
Science Advisor
Linearity of Maxwell's equations as a result of special relativity.
Quote by TrickyDicky The fact that in curved spacetime Maxwell eq. are also linear trivially reflects IMO the fact that the spatial part of curved spacetimes can be... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/29117/regression-technique-for-data-comprised-of-categorical-explanatory-variables-a | # Regression technique for data comprised of categorical explanatory variables & a continuous response variable
i suppose one way to characterize data is by a combination of the variable types that comprises it:
```` Continuous/Continuous | Continuous/Discrete
-----------------------|---------------------
Discret... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/3200/hash-function-from-narrower-block-cipher-operated-in-cbc-encryption-mode/4032 | # Hash function from narrower block cipher operated in CBC-encryption mode?
I am trying to build a public hash function (thus collision-resistant and preimage-resistant, and more generally behaving like a random oracle), with input a message $M$ of fixed size $|M|=m\cdot b$ bits, and output the hash $H(M)$ of fixed 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": 105, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/102983?sort=oldest | ## Reference Request: de Rham vs. Dolbeault
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Hi everyone. I need the following statement:
For a Kahler manifold $X$, the natural map `$H^n(X,\mathbb{C})\to H^n(X,\mathcal{O})$` (from the sheaf extension) coincide... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/16179/poles-wavefunctions-transmission | # Poles, wavefunctions, transmission
Why is it said that $\operatorname{sech}x$ (a transmission amplitude) has a simple pole on the imaginary axis? Thanks.
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1
Can you give some context? sech has no poles as far as I can tell, as it is a continuous, strictly positive, bound function. I would vote down but I can'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": 11, "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/43510/bound-states-in-a-double-delta-function-potential | # Bound States in a Double Delta Function Potential [closed]
Let $V(x) = −u \delta(x) - v \delta(x − a)$ where $u, v > 0$ correspond to a potential with two $\delta$ wells. Let $v > u$. If $a$ is very large, there is certainly a bound state: the particle sits in the $\delta$-well. As $a$ decreases to a certain critica... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/250998/diffeomorphism-on-the-torus | # Diffeomorphism on the torus
Let $S : \mathbb{R}^n → \mathbb{R}^n$ be linear invertible map, then $S$ projects to $\mathbb{T}^n$ diffeomorphism if and only if $S ∈ GL_n(\mathbb{Z})$.
I can't prove the right to left implication.
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That $S$ projects to a diffeo of $T^n$ means that $S$ is $\mathbb{Z}^n$-equivariant. ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 66, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/34731-value-sin-x-different-intervals.html | # Thread:
1. ## Value of sin x for different intervals
I have been asked what the average value of the sin x for the interval greater or equal to 0 and less than or equal to 2 pi. I just plugged in the two end values and since both are = 0 the answer is, of course, 0.
Then I was asked what the average value of this ... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2009/05/21/arml-scrimmage-power-question-2/?like=1&source=post_flair&_wpnonce=3fdfac1636 | # The Unapologetic Mathematician
## ARML Scrimmage Power Question
I helped the Howard County and Baltimore County ARML teams practice tonight by joining the group of local citizens and team alumni to field a scrimmage team. As usual, my favorite part is the power question. It follows, as printed, but less the (unnece... | {"extraction_info": {"found_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": 99, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/101294-basic-diff-eq-question-finding-function-given-properties.html | Thread:
1. Basic Diff EQ question: finding a function with given properties
Find a function f(y) with the property that: for each solution y(x) of dy/dx = f(y), the limiting value lim as x-> +inf of y(x) equals 3 if y(0) > 0.
Any help?
2. A possible solution of the problem is a function $y(x)$ with the following de... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/82116-fields-rings-homomorphisms.html | # Thread:
1. ## Fields, Rings and Homomorphisms
Let F be a field and R a ring and suppose phi: F --> R is a homomorphism.
Prove that either phi is one-to-one or phi is the trivial homomorphism (that is, phi(a) = 0 for all a in F).
2. Originally Posted by Coda202
Let F be a field and R a ring and suppose phi: F --> 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": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/3654/malleability-attacks-against-encryption-without-authentication?answertab=votes | # Malleability attacks against encryption without authentication
Suppose there is a message that is encrypted with AES-128-CBC. The message is as follows, new lines are used to delimit the 16 byte boundary for each block:
````Wire funds from:
Alice to Bob in
the amount of $
1
````
Because this message is encrypted... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2008/12/19/the-symmetrizer-and-antisymmetrizer/?like=1&_wpnonce=34114a6dfa | # The Unapologetic Mathematician
## The Symmetrizer and Antisymmetrizer
Today we’ll introduce two elements of the group algebra $\mathbb{F}[S_n]$ of the symmetric group $S_n$ which have some interesting properties. Each one, given a representation of the symmetric group, will give us a subrepresentation of that repre... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 27, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/20212/expansion-of-helmholtz-energy/20214 | # Expansion of Helmholtz energy
To get an expansion of Helmholtz energy of
a) an ideal gas b) a Van der waals gas
we must integrate
$\left ( \frac{\delta A }{\delta V} \right )_{T}=-P$
I saw the solution is :
Can you explain why is that?
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## 1 Answer
Consider just part (a). we use the ideal gas law for $P$, 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": 5, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/2125/whats-the-difference-between-correlation-and-simple-linear-regression/30760 | # What's the difference between correlation and simple linear regression?
Is it cheating if I know the answer, but ask it anyways?
I figure it's good for people to know :)
In particular, I am referring to the Pearson product-moment correlation coefficient
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3
I have no idea what this question is about. – Robby McK... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/gravity?sort=votes&pagesize=30 | # Tagged Questions
Gravity is an attractive force that affects and is effected by all mass and - in general relativity - energy, pressure and stress. Prefer newtonian-gravity or general-relativity if sensible.
13answers
5k views
### How does gravity escape a black hole?
My understanding is that light can not escape... | {"extraction_info": {"found_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/25509/effectively-closed-computable-functions | ## Effectively closed computable functions
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I've recently been interested in the following type of functions. A total computable function f:N→N is effectively closed if there is a computable function p such that 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": 88, "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/38204/morphisms-of-frobenius-manifolds-definitions-and-examples/38257 | ## Morphisms of Frobenius manifolds: Definitions and examples?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Frobenius manifolds arise in the study of quantum cohomology and mirror symmetry -- roughly they are manifolds (or varieties or whatever) such that 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": 21, "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/24680/a-conceptual-problem-with-euler-bernoulli-beam-theory-and-euler-buckling | A conceptual problem with Euler-Bernoulli beam theory and Euler buckling
Euler-Bernoulli beam theory states that in static conditions the deflection $w(x)$ of a beam relative to its axis $x$ satisfies
$$EI\frac{\partial^4}{\partial x^4}w(x)=q(x)\ \ \ \ (1)$$
where $E$ is Young's modulus, $I$ is the second moment 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": 18, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://gowers.wordpress.com/2007/10/04/when-are-two-proofs-essentially-the-same/?like=1&_wpnonce=9e687b4e3a | # Gowers's Weblog
Mathematics related discussions
## When are two proofs essentially the same?
A couple of years ago I spoke at a conference about mathematics that brought together philosophers, psychologists and mathematicians. The proceedings of the conference will appear fairly soon—I will give details when they ... | {"extraction_info": {"found_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": 438, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/114484?sort=votes | ## subgroups of a $p$-solvable group and complete reducibility
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
1.
Let $G$ be a $p$-solvable group and $V$ be a finite dimensional faithful $kG$-module, where the characteristic of $k$ is $p$. But $V$ is not a se... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/100230/list | ## Return to Answer
2 added 193 characters in body
The answer was given by Samuel Blank in his Brandeis 1967 phd dissertation, on which Poenaru gave a Bourbaki seminar.
Then Peter Shor and C. J. Van Wyk gave a polynomial time algorithm to decide if there is an extension.
EDIT: Blank's method already gave a polynomi... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2009/12/17/iterated-integrals-ii/ | # The Unapologetic Mathematician
## Iterated Integrals II
Let’s get to proving the assertions we made last time, starting with
$\displaystyle{\int\limits_-}Rf(x,y)\,d(x,y)\leq{\int\limits_-}_a^b{\int\limits^-}_c^df(x,y)\,dy\,dx\leq{\int\limits^-}_a^b{\int\limits^-}_c^df(x,y)\,dy\,dx\leq{\int\limits^-}Rf(x,y)\,d(x,y)... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 38, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4276763 | Physics Forums
Quick question about Dirac delta functions
What does the square of a Dirac delta function look like? Is the approximate graph the same as that of the delta function?
PhysOrg.com science news on PhysOrg.com >> Front-row seats to climate change>> Attacking MRSA with metals from antibacterial clays>> 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": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://hilbertthm90.wordpress.com/2010/03/11/the-grothendieck-spectral-sequence/ | # The Grothendieck Spectral Sequence
March 11, 2010 by | 1 Comment
Well, I meant to do lots more examples building up some more motivation for how powerful spectral sequences can be in some simple cases. But I’m just running out of steam on posting about them. Since we’ve done spectral sequences associated to a doubl... | {"extraction_info": {"found_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": 26, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/144768-constrained-optimisation-problem.html | # Thread:
1. ## constrained optimisation problem
(a) Write down the objective function and the constraint equation for aconstrained optimisation problem which is to minimize the total surface area of a rectangular box with the constraint that its volume is fixed to be 1. (Hint: Let the box have length x, width y 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/Arrhenius_equation | # Arrhenius equation
Arrhenius' equation is a simple, but remarkably accurate, formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist J. H. van't Hoff who had noted in 1884 that van't Hoff's equation for the temperature depend... | {"extraction_info": {"found_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": 27, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/32108/how-is-riemannstieltjes-integral-a-special-case-of-lebesguestieltjes-integral | # How is Riemann–Stieltjes integral a special case of Lebesgue–Stieltjes integral?
Thanks for reading! My questions are based on the following quotes from Wikipedia:
1. About the existence of Lebesgue–Stieltjes integral:
The Lebesgue–Stieltjes integral $\int_a^b f(x)\,dg(x)$ is defined when ƒ : [a,b] → R is Borel-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": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/243171/is-mathematics-the-only-language-that-is-not-subject-of-interpretation?answertab=votes | # Is mathematics the only language that is not subject of interpretation?
Do you know any other "language" that is used by people except mathematics and is not subject of interpretation? By subject of interpratation I mean e.g. that 1 000 000 people will undertand that 1 + 1 = 2 and never 3. E.g. when you say that "Th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/221402/how-can-we-make-mathbbrn-into-a-multiplicative-group | # How can we make $\mathbb{R}^n$ into a multiplicative group?
Are there any sorts of multiplicative group structures we can put on set $\mathbb{R}^n$? By multiplicative, I mean that it should be compatible with the natural scalar multiplication on $\mathbb{R}^n$; that is, for any $x,y \in \mathbb{R}^n$ and $c \in \mat... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/62053/list | ## Return to Answer
2 added 1481 characters in body
I think the answer to the question is yes, but it is very unlikely that it can be proved without using the classification of finite simple groups.
Note that $A_5$ of order 60 is the only simple group order for which this statement is true, because for all higher or... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-puzzles/168742-divided-square.html | # Thread:
1. ## Divided square
Hey guys i found a problem in the MENSA book, i've tried to use basic algebra to this this problem but i think i'm on the wrong track.
Can anyone suggest any techniques to do this problem?
The answers are at the back of the book although i do want to know how to do it.
THE IMAGE IS AT... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/06/27/the-rank-nullity-theorem/?like=1&source=post_flair&_wpnonce=fe7f791e1e | # The Unapologetic Mathematician
## The Rank-Nullity Theorem
Today we start considering how a given linear transformation acts on a vector space. And we start with the “rank-nullity” theorem. This sounds really fancy, but it’s actually almost trivial.
We already said that $\mathbf{Vect}(\mathbb{F})$ (also $\mathbf{F... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 23, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/69488?sort=votes | ## Are surface bundles over a surface with non-zero signature necessarily complex (or algebraic)?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
By "surface bundle over a surface" I mean a compact, oriented 4-manifold $X$ which is the total space of an orient... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 46, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/131919/eigenfunctions-of-the-adjoint-of-an-operator/131956 | # eigenfunctions of the adjoint of an operator
If the eigenfunctions of a linear operator are known, is there a way to calculate the eigenfunctions of the corresponding adjoint operator based on the known eigenfunctions? In other words, what's the relation between the eigenfunctions of an operator and its adjoint?
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": 14, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/294132/which-problems-do-you-recommend-it-to-me-to-solve-it | # which problems do you recommend it to me to solve it? [closed]
i study abstract algebra from dummit and foote .
i started to solve some problems in section 3 in chapter 4
there is 36 problems
i study the subject myself , so there is no proffesor to recommend or instructor !
so , i hope that you help me to recomm... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/2887/difference-between-encrypting-something-and-hashing-something/2898 | # Difference between encrypting something and hashing something
What is the difference between encrypting something and hashing something? in what situations would I want one or the other?
-
1
@moderation: please, make this question a sugested similar question to every new question that asks about encryption or hash... | {"extraction_info": {"found_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://meta.math.stackexchange.com/questions/1652/what-do-we-do-with-users-who-post-numerous-unlabeled-homework-questions/1661 | # What do we do with users who post numerous unlabeled homework questions?
User student has, quite impressively, recognized that all of user6560's questions are homework questions from the ongoing course Math 620 at the University of Buffalo. I just went through, downvoted all the questions and left an explanatory 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": 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/256864/solve-the-sde-by-applying-ito-formula | # Solve the SDE by applying Ito formula
Solve the SDE $d\delta_{t}=\mu\delta_{t}dt+\sigma\delta_{t}dW_{t}$ by applying the Ito formula and the final solution should be in the form of $\delta_{t}=\delta_{0}\exp\left((\mu-\frac{1}{2}\sigma^{2})t+\sigma W_{t}\right)$
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## 1 Answer
The useful form of Ito's lemma is 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": 12, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-challenge-problems/94701-crazy-integral-print.html | # Crazy integral
Printable View
• July 9th 2009, 12:10 AM
simplependulum
Crazy integral
Determine which integral is more crazy ...
$\int \frac{dx}{1 + \sin^3{x}}$
and
$\int \frac{dx}{1+\sin^6{x}}$
3 or 6 ? The answer is 3 ! It is very interesting that although 6 is greater than 3 , the integral $\int \frac{dx}{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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/115471-chi-square-test.html | # Thread:
1. ## [SOLVED] Chi-Square Test
Two different teaching procedures were used in two different groups of students. Each group had 100 students of similiar ability. These are the results:
Group A B C D F
I 15 25 32 17 11
II 9 18 29 28 16
Data is independent from two respective multinomial distribution with k ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=3924927 | Physics Forums
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## Classic Papers in Astronomy and Cosmology
Hellfire requested that I post a list of classic papers that one could use for reference when trying to understand the current state of astronomy and cosmology. I'll do so here... | {"extraction_info": {"found_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://mathforum.org/mathimages/index.php?title=Prime_spiral_(Ulam_spiral)&diff=32702&oldid=14449 | # Prime spiral (Ulam spiral)
### From Math Images
(Difference between revisions)
| | ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 90, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.haskell.org/haskellwiki/index.php?title=User:Michiexile/MATH198/Lecture_1&diff=29929&oldid=29928 | # User:Michiexile/MATH198/Lecture 1
### From HaskellWiki
(Difference between revisions)
| | | | ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/53338/confusion-regarding-photons/53339 | # Confusion regarding photons?
I'm still in high school, and while I can't complain about the quality of my teachers (all of them have done at least a bachelor, some a masters) I usually am cautious to believe what they say straight away. Since I'm interested quite a bit in physics, I know more about it than other sub... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/255590/spherical-coordinates-to-cartesian-coordinates | # Spherical coordinates to cartesian coordinates.
I want to find out the distance between the centers of $2$ circles. Say, circle $1$ $(\theta,\phi)$ circle $2$ $(\theta,\phi)$
The radius of this circle is found using $d\tan(\theta)$ where $d$ is the range (different from radius)
$$cd=\sqrt{(x_1-x_2)^2 + (y_1-y_2)^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": 25, "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/114963/tangent-space-of-the-stack-overline-mathcalm-g-nx-beta | ## Tangent space of the stack $\overline{\mathcal{M}}_{g,n}(X,\beta)$.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $\overline{\mathcal{M}}_{g,n}(X,\beta)$ be the moduli stack of stable maps $f$ from genus $g$, $n$-marked curve $C$ to a variety $X$ i nt... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.appropedia.org/Pulser_pump | Appropriate technology • Construction • Energy • Food & Agriculture • Green living • Health & Safety • Medical Devices • Projects • Service learning • Solar • Transport • Water
# Pulser pump
From Appropedia
Status
This OSAT has been designed but not yet tested - use at own risk.
This OSAT has been modeled.
This... | {"extraction_info": {"found_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": 11, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/fractals?sort=active&pagesize=15 | # Tagged Questions
Questions on fractals, irregular-looking mathematical objects that display the property of self-similarity.
1answer
52 views
+50
### Reverse Hölder Continuity and Hausdorff dimension
Let $f$ be a function on $[0,1]$. Say that $f$ is reverse Hölder continuous of exponent $\beta > 0$ if there is a ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 52, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/2666/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?
### Great Squares
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
### Square Areas
Can you work... | {"extraction_info": {"found_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://math.stackexchange.com/questions/36609/what-is-the-nature-of-this-sequence | # what is the nature of this sequence?
$3, 4, 10, 33, 136$
what will be next most appropriate value? I tried finding any relation in the sequence but i couldn't.
$a.276$
$b.539$
$c.612$
$d.685$
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2
Is this just a puzzle or do you have some context you can provide? – Aryabhata May 3 '11 at 6:15
I have got option... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/52081/how-do-i-correctly-express-the-work-required-to-put-an-object-with-positive-buoy | # How do I correctly express the work required to put an object with positive buoyancy down into a certain depth (of water)?
It seems to me that I can express the work required to put an object under water in the same way that I express lifting an object up against gravity. I. e., in both cases I increase the potentia... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2011/07/13/the-lie-derivative-on-forms/?like=1&source=post_flair&_wpnonce=18b5244a97 | The Unapologetic Mathematician
The Lie Derivative on Forms
We’ve defined the Lie derivative $L_XY$ of one vector field $Y$ by another, $X$. This worked by using the flow of $X$ to compare nearby points, and used the derivative of the flow to translate vectors.
Well now we know how to translate $k$-forms by pulling 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 29, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/23706/reductive-lie-algebra-of-a-lie-group | ## Reductive Lie algebra of a Lie group
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In the answer of my question:
http://mathoverflow.net/questions/23085/on-the-full-reducibility-of-representations-of-reductive-lie-algebras
James E. Humphreys replied to ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/263691/simple-equation-misunderstanding | # Simple equation misunderstanding
Im trying to use an equation on this page
http://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics
The angle of lean, $\theta$, can easily be calculated using the laws of circular motion
$$\theta = \arctan\left(\frac{v^2}{gr}\right)$$
where $v$ is the forward speed, $r$ is 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": 7, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/19055/is-there-really-no-meaning-in-potential-energy-and-potential/19059 | # Is there really no meaning in potential energy and potential?
I have been told all my physics life that potential energy between two mass/charge has no meaning and only their difference has meaning. The same goes for electric potential, only the difference matter.
Perhaps I am not understanding it correctly, but be... | {"extraction_info": {"found_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": 14, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/305011/regular-compact-domains-of-a-riemannian-manifolds | # Regular compact domains of a Riemannian manifolds
In a Riemannian manifold $M$ a regular compact domain $D$ is a compact subset of $M$ with non empty interior and such that for every $p \in \partial D$ there exists $\left(U,\varphi\right)$ coordinate neighbourhood of $p$ such that $\varphi(U\cap \partial D)\subseteq... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 43, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/43423/determine-when-a-light-is-going-into-the-object/43427 | # Determine when a light is going into the object [closed]
Please look at this image: (http://mypages.iit.edu/~smart/acadyear/refract.gif)
How can I determine when light is going into the object?
Actually, if there is, what is the simplest way to determine whether light is going into the object or not?
NOTE: I coul... | {"extraction_info": {"found_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/algebra/179699-cube-root-5-a-print.html | # Cube root of 5
Printable View
• May 6th 2011, 02:14 AM
mathguy80
Cube root of 5
Hi Guys,
Need a little hint on this one.
Expand $(1 + x)^{\frac{1}{3}}$ in ascending powers of $x$ as far as the term in $x^3$, simplifying the terms as much as possible. By substituting 0.08 for $x$ in your result obtain an approxima... | {"extraction_info": {"found_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://www.abstractmath.org/Word%20Press/?tag=formula | Gyre&Gimbleposts about math, language and other things that may appear in the wabe
Conceptual blending
2012/06/18 — SixWingedSeraph
This post uses MathJax. If you see formulas in unrendered TeX, try refreshing the screen.
A conceptual blend is a structure in your brain that connects two concepts by associating par... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 194, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/119074/system-of-4-equations-3-of-them-linear-what-can-be-said-about-the-solution-s?answertab=oldest | # System of 4 equations (3 of them linear) - What can be said about the solution set
I have a homework at linear algebra and we have this system of linear equations:
$x+y+z+w=0$
$x+2*y+9*z+13*w=0$
$4*x+41*y+6*z+656*w = 0$
And we add this equation:
$x^3 + y^4 + 8* z^5 + 8* w^6 = 0$
What can be said about the soluti... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/297351/implicit-derivative-and-related-rates | # Implicit derivative and related rates
I'm having a bit of trouble with this assignment. I had to miss a couple class, and I'm afraid the teacher talked about this. I have the notes, but they are not of much help and don't talk about related rates at all. I tried looking around, I found lots of PDF from different uni... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/advanced-statistics/31821-continous-random-variable.html | # Thread:
1. ## continous random variable
Y has a distribution function:
$F(y) = \left\{ \begin{array}{rcl} 0 & \mbox{for} & y \leq 0 \\ <br /> \\<br /> \frac{y}{8} & \mbox{for} & 0 < y < 2 \\<br /> \\<br /> \frac{y^2}{16} & \mbox{for} & 2 \leq y < 4 \\<br /> \\<br /> 1 & \mbox{for} & y \geq y 4<br /> \end{array}\ri... | {"extraction_info": {"found_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/16386/a-wonky-gravitational-potential-and-its-critical-points | # A wonky gravitational potential and its critical points
I have tough problem I am not sure how to solve:
For this question, we are confined to a plane. Consider a gravitational field that is proportional to $\frac{1}{r^3}$ instead of $\frac{1}{r^2}$, and consider its potential which is then proportional to $\frac{1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 71, "mathjax_display_tex": 26, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://conservapedia.com/Golden_ratio | # Golden Ratio
### From Conservapedia
(Redirected from Golden ratio)
The golden ratio is a number, commonly known as phi ($\varphi$), defined to be the larger of the two solutions to $\varphi^2 = \varphi + 1$. The value of phi is
$\frac{1 + \sqrt{5}}{2}$
Phi is an irrational number. Its decimal expansion begins
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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/quantum-field-theory+general-relativity | # Tagged Questions
1answer
95 views
### proper variation of action term
I have a term I want to vary by a field, $\phi$. $$`S' = \frac{-1}{2}\,\sqrt{-g}\,g^{\mu\,\nu}\,\delta\left[h(\phi)\,\partial_{\mu}\phi\,\partial_{\nu}\phi \right].$$ Is it correct to get this? ...
1answer
100 views
### Why is $R^2$ gravity not... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/157066-prove-phi-1-w-v-isomorphism.html | # Thread:
1. ## Prove that Phi^-1:W->V is an isomorphism
Suppose $V$ and $W$ are vector spaces over a field $F$.
Now suppose $\varphi :V\rightarrow W$ is an isomorphism. The inverse of this is defined as $\varphi^{-1}:W\rightarrow V$. Prove that $\varphi^{-1}:W\rightarrow V$ is an isomorphism, by verifying that it 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": 52, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/71587/what-are-the-different-theories-that-the-motivic-fundamental-group-attempts-to-un | ## What are the different theories that the motivic fundamental group attempts to unify?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I must preface by confessing complete ignorance in the subject. I've read introductory texts about the theory of motives, 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": 41, "mathjax_display_tex": 0, "mathjax_asciimath": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/16777/when-does-energy-turn-to-matter/16779 | # When does energy turn to matter?
I always hear about matter converting to energy - fusion, fission...
When does it go the other way around? What conditions lead to it? Are there reproducible experiments on this topic?
-
I was going to write an answer about how endothermic nuclear reactions (in which energy turns ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/295173/fibonnaci-identity | # Fibonnaci identity
Here's a problem that is leading me in circles.
Consider the Fibonacci number $F_n$ defined by $F_0 = 0$, $F_1 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for all $n \geq 2$.
Prove that $F_{2n-1} = F_{n}^2 + F_{n-1}^2$.
Tried an induction proof that lead me nowhere fast. So far we have only been given 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": 14, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/8999/discrete-harmonic-function-on-a-planar-graph/9050 | ## Discrete harmonic function on a planar graph
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Given a graph $G$ we will call a function $f:V(G)\to \mathbb{R}$ discrete harmonic if for all $v\in V(G)$ , the value of $f(v)$ is equal to the average of the value... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 68, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/26082/bootstrap-variance-of-squared-sample-mean | # Bootstrap variance of squared sample mean
The following is question 8 of chapter 8 in Wasserman's All of Statistics:
Let $T_n = \overline{X}_n^2$, $\mu = \mathbb{E}(X_1)$, $\alpha_k = \int|x - \mu|^kdF(x)$, and $\hat{\alpha}_k = n^{-1}\sum_{i=1}^n|X_i - \overline{X}_n|^k$.
Show that $$v_{\mathrm{boot}} = \frac{4\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": 19, "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/37136/classification-of-finite-groups-of-isometries/37152 | ## Classification of finite groups of isometries
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Consider the problem of classifying the finite groups of isometries of R^n. --For n=2 it is cyclic and dihedral groups. --For n=3 they are well known, probably fro... | {"extraction_info": {"found_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://math.stackexchange.com/questions/178940/proofs-that-every-mathematician-should-know/219528 | # Proofs that every mathematician should know? [closed]
There are mathematical proofs that have that "wow" factor in being elegant, simplifying one's view of mathematics, lifting one's perception into the light of knowledge etc.
So I'd like to know what mathematical proofs you've come across that you think other 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": 82, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/differential-operators+differential-geometry | # Tagged Questions
0answers
54 views
### Complex differential geometric form of the Grothendieck–Hirzebruch–Riemann–Roch theorem
From the wikipedia article, it seems that there should be a differential geometric form of the Grothendieck-Riemann-Roch theorem with schemes replaced by complex manifolds and quasi-cohere... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/32178/liquid-crystal-polarizes-light-reflection-question | # Liquid crystal polarizes light reflection question
I was hoping someone could help me with understanding why a row of polarizes reflects a light wave when the whole row is the same length as the wavelength of the light.
I pretty much get the physics behind the rest, just don't understand this little part. Why only ... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/geometry+string-theory | # Tagged Questions
5answers
127 views
### Why is the world sheet of an open string a cylinder?
I went to a lecture a few weeks ago and was told the following: The world sheet of a closed string is a normal, standing cylinder. The world sheet of an open string is a cylinder on its side. This ...
2answers
160 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": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/157763-derivative-problem.html | # Thread:
1. ## Derivative Problem
Would someone tell me how would you solve the following:
1) Find $\frac{\partial z}{\partial y}$
$z=sin(x^3 e^{y}-4y^5)$
this is what i have done, but i don't think its correct.
$\frac{\partial z}{\partial y}=x^3 e^y-20y^4cos(x^3 e^{y}-4y^5)$
P.S
2. $z = \sin{(x^3e^y - 4y^5)}$.
... | {"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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://scicomp.stackexchange.com/questions/1982/problems-that-can-be-reduced-to-the-traveling-salesman-problem | # Problems that can be reduced to the Traveling Salesman Problem
Which search/optimization problems can be reduced to the famous "Traveling Salesman Problem"? For instance, I have a collection of N particles, in 3D, and there is a function (Van der Waals energy) which depends on their coordinates. I want to find which... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/92119/duality-of-eta-product-identities-a-new-idea | ## Duality of eta product identities: a new idea?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Looking at the collection of Eta Function Product Identities by Michael Somos, it seems like generally those identities come in pairs: let's call two eta product ... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/6052/why-work-in-a-subgroup-qrn-of-an-rsa-group-z-n?answertab=oldest | Why work in a subgroup QR(n) of an RSA group $Z^*_n$?
I sometimes read in papers that a (sub-)group generator $g$ is taken from $\mathrm{QR}(n)$ instead of $\mathbb{Z}^*_n$, where $n = p \cdot q$ and $p$ and $q$ are prime. Is there a reason for this? What properties does $\mathrm{QR}(n)$ have? Is it an especially big ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/153238/finding-a-point-on-the-line-joining-two-points-in-cartesian-coordinate-system?answertab=votes | # Finding a point on the line joining two points in Cartesian coordinate system
Given a point A with coordinates (a,b) ; a point B with coordinates (c,d) , I want to find a point C's coordinate (x,y) ,with C lying on the line joining A and B and C is at a distance Dist from point A. This is the representation
-
## 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": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/207725-partial-fractions.html | 1Thanks
• 1 Post By hollywood
# Thread:
1. ## Partial fractions
Please explain the step in the green box(#5), I remember doing this in algebra 2 but not this specifically.
Attached Thumbnails
2. ## Re: Partial fractions
Which bit don't you understand?
Incidentally substituting x=i (as well as x=0 and x=1) is quit... | {"extraction_info": {"found_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/138090/solving-quadratic-residue/138100 | # Solving quadratic residue
Suppose we have $25x^2 + 70x + 37 \equiv 0 \pmod{13}$. Since it doesn't factor we obviously have to subtract/add $(ax + b)$ from both sides of the congruence. However I'm getting different answers. What is the proper way to approach solving for all residues that solve this congruence?
Than... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/19213?sort=newest | Changing the orientation of a Landweber exact cohomology theory
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let the ring R be a MU`*`-module via a ring homomorphism φ and suppose it satisfies the condition of the Landweber exact functor theorem such that we ob... | {"extraction_info": {"found_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/18058/ | ## On statements provably independent of ZF + V=L
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Are there any known statements that are provably independent of $ZF + V=L$? A similar question was asked here but focusing on "interesting" statements and all exa... | {"extraction_info": {"found_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/96007/integration-involving-product-of-inverse-error-and-polynomial-functions | # Integration involving product of inverse error and polynomial functions
I am stuck with the following integral: $$\int_{x \ge 1} \frac{18 \exp \left(-\frac12 \left(\phi^{-1}[1 - \frac{1}{x^3}]\phi^{-1}[1 - \frac{1}{(z-x)^3}] \right) \right)}{\sqrt{3}x^3 (z-x)^4} dx$$ where $z$ is a constant and $\phi^{-1}$ is the 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": 2, "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/48123/regarding-a-feature-of-multivariate-real-function | ## Regarding a Feature of Multivariate Real Function
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Any real function can be expressed as a function of the sum of two monotonic real functions?
More precisely, for real function p(x, y), there exist continuous... | {"extraction_info": {"found_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://math.stackexchange.com/questions/156094/construct-a-new-relation-from-several-relations/156099 | # Construct a new relation from several relations
Let $f_0,\dots,f_{n-1}$ are relations, where $f_i$ is a relation of arity $m_i$ for every $i=0,\dots,n-1$.
How to construct an $(m_0+\dots+m_{n-1})$-ary relation from them?
For my previous erroneous attempt to do this see here: Name for product of relations
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If al... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/259047/solving-a-trig-equation | # Solving a trig equation?
How would I solve the following equation? $$1+ \sin (x)=2 \cos(x)$$ I am having difficult with it.
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## 5 Answers
We have $1 + \sin(x) = 2 \cos(x)$. Recall that $1 - \sin^2(x) = \cos^2(x)$. Hence, we get that $$(1 + \sin(x))(1- \sin(x)) = \cos^2(x)$$ i.e. $$2 \cos(x) (1 - \sin(x)) = \cos^... | {"extraction_info": {"found_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": 18, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/16664/how-do-i-rearrange-de-dt-to-find-an-electrons-half-life-due-to-synchrotron-ra | # How do I rearrange dE/dt to find an electron's 'half-life' due to synchrotron radiation?
I know that $-\frac{\mathrm{d}E}{\mathrm{d}t} \propto E^2$ for an electron losing energy to synchrotron radiation, but I can't find how to arrange this to give the time it would take for the electron to lose half of its original... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/120352/list | ## Return to Answer
2 added 13 characters in body
You can just prove it yourself directly in local holomorphic coordinates. Indeed, the $\overline{\partial}$ Laplacian on functions is equal to $\Delta_{\overline{\partial}}f=g^{i\overline{j}}\partial_i \partial_{\overline{j}}f$. Apply this to $|\partial f|^2=g^{k\over... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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