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http://mathhelpforum.com/calculus/96978-acceleration-problem.html | # Thread:
1. ## Acceleration problem
The position equation for the movement of a particle is given by $s(t) = \sqrt{t^3 +1}$ where s is measured in feet and t is measured in seconds. Find the acceleration when t = 2 seconds.
I know that I have to get y'', I got ${3t^2/2} -\sqrt{t^3+1}$, but when trying to get y'' 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": 32, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.factbites.com/topics/Double-pendulum | Where results make sense
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Topic: Double pendulum
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Double Elliptical Pendulum Harmonograph
I was most interested in the Double Elliptical Pendulum Harmonograph because of the striking complexity of the patterns it could produce.
The hands... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/30877/what-is-relation-between-time-and-space-in-general-relativity/30887 | what is relation between time and space in general relativity?
there is a relation between time and space in special theory of relativity: $$t^2c^2-L^2=\tau^2.c^2$$ what is relation between time and space in general relativity?
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1
– David Zaslavsky♦ Jun 27 '12 at 21:07
1
– user1504 Jun 27 '12 at 21:29
-1: This is ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/39622/calculating-force-required-to-stop-bungee-jumper/39627 | Calculating force required to stop bungee jumper
Given that:
• bungee jumper weighs 700N
• jumps off from a height of 36m
• needs to stop safely at 32m (4m above ground)
• unstretched length of bungee cord is 25m
Whats the force required to stop the jumper (4m above ground)
First what equation do I use?
$F = ma$? ... | {"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": 17, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/121231-baffling-integral.html | # Thread:
1. ## a baffling integral
∫ 1 / (x^6 – 1) dx
Thanks in advance.
2. Originally Posted by niz
∫ 1 / (x^6 – 1) dx
Thanks in advance.
Are you familiar with the method of partial fractions? Notice that the denominator is the difference of two squares $(x^3-1)(x^3+1)$. Now use the formulae for the cubes. You ... | {"extraction_info": {"found_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/55264/how-to-measure-a-solid-solid-surface-energy?answertab=active | # How to measure a solid-solid surface energy?
Many techniques exist to measure the surface energy between a liquid and a liquid or a liquid and a gas (see e.g. the wiki page).
Methods to measure the surface energy between a solid and a fluid are rare, but still there is a method developed by Zisman (see e.g. here) 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": 4, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.scholarpedia.org/article/Galactic_dynamics | # Galactic dynamics
From Scholarpedia
George Contopoulos and Christos Efthymiopoulos (2011), Scholarpedia, 6(5):10670.
Curator and Contributors
1.00 - Christos Efthymiopoulos
0.40 -
Eugene M. Izhikevich
0.20 -
Benjamin Bronner
0.20 -
Alessandra Celletti
0.20 -
George Contopoulos
Galactic dynamics is the stu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 49, "mathjax_display_tex": 340, "mathjax_asciimath": 4, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathhelpforum.com/differential-geometry/202742-b-c-vectors-how-prove-vector-b-c-given-b-c-axb-axc.html | # Thread:
1. ## a,b,c are vectors. How to prove vector b = c, given a.b = a.c and axb = axc?
a,b,c are vectors. How to prove vector b = c, given a.b = a.c and axb = axc?
2. ## Re: a,b,c are vectors. How to prove vector b = c, given a.b = a.c and axb = axc?
I think we need an additional assumption that $\mathbf{a} \... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/64377/birthday-attack-problem-calculate-exact-numbers?answertab=oldest | # Birthday attack/problem, calculate exact numbers? [duplicate]
Possible Duplicate:
Birthday-coverage problem
An example of what I wish to do is the following: http://stackoverflow.com/questions/4681913/substr-md5-collision/4785456#4785456
How would I calculate how many people would be required, as in the link above... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/88066?sort=votes | ## Polygons uniquely inducing arrangements
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
A beautiful, relatively recent result is that,
Every simple arrangement $\cal{A}$ of $n$ lines in the plane is induced by a simple $n$-gon $P$.
In a simple arrangement... | {"extraction_info": {"found_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/318614/composition-of-continuous-functions/318616 | # composition of continuous functions
I was wondering if a function $f:[a,b]\rightarrow[c,d]$ is continuous, $g:[c,d]\rightarrow\mathbb{R}$ is continuous, does it necessarily imply that $g\circ f$ is continuous? Are there counterexamples? What is the necessary and sufficient condition for $g\circ f$ to be 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": 75, "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/7776/universal-property-for-collection-of-epimorphisms | ## Universal property for collection of epimorphisms
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Question Is there a nice universal property which captures the notion of "collection of all epimorphisms out of a given object". Of course I will have to consi... | {"extraction_info": {"found_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://math.stackexchange.com/questions/158758/what-is-the-result-of-sum-sum-limits-i-0n-2i/158767 | # What is the result of sum $\sum\limits_{i=0}^n 2^i$ [duplicate]
Possible Duplicate:
the sum of powers of $2$ between $2^0$ and $2^n$
What is the result of $$2^0 + 2^1 + 2^2 + \cdots + 2^{n-1} + 2^n\ ?$$
Is there a formula on this? and how to prove the formula?
(It is actually to compute the time complexity of a F... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 61, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/72922/cohomology-of-locally-indicable-groups | # Cohomology of Locally Indicable groups
Let $G$ be a locally indicable group (i.e. there is a non trivial homomorphism from $G$ to the real additive group $(\mathbb{R},+)$) and $l^2(G)$ be the Hilbert space with the base $G$. Is it true that $H^1(G,l^2(G))$ does not vanish?
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1
I think locally indicable generally 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": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://ams.org/bookstore?fn=20&arg1=tb-aa&ikey=GSM-131 | New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Ana... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Bernoulli's_principle | Bernoulli's principle
This article is about Bernoulli's principle and Bernoulli's equation in fluid dynamics. For Bernoulli's theorem in probability, see law of large numbers. For an unrelated topic in ordinary differential equations, see Bernoulli differential equation.
A flow of air into a venturi meter. The kinetic... | {"extraction_info": {"found_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": 56, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/272380/int-0-infty-2xe-2x-dx-221-22-how-to-find-this-result-of-the-inte | # $\int_0^\infty 2xe^{-2x} \: dx=Γ(2)2(1/2)^2$ how to find this result of the integral?
$$\int_0^\infty 2xe^{-2x} \: dx=Γ(2)2(1/2)^2$$
I don't understand. How can we write this? Please can you explain this clearly?
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Is there a reason you write the constant as $2(1/2)^2$ instead of $1/2$? – Christopher A. Wong Jan ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/117959/laurent-polynomials/117960 | Laurent Polynomials
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Let $R$ be a commutative ring with identity. Is there any characterization for invertible elements of $R[x,x^{-1}]$ ?
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3 Answers
I have read about this somewhere. I think it was as follows: $\... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.aps.org/articles/print/v4/43 | # Viewpoint: Finally, results from Gravity Probe B
, McDonnell Center for the Space Sciences and Department of Physics, Washington University, St. Louis, One Brookings Drive, St. Louis, MO 63130, USA
Published May 31, 2011 | Physics 4, 43 (2011) | DOI: 10.1103/Physics.4.43
Nearly fifty years after its inception, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 20, "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://mathhelpforum.com/differential-equations/172958-inhomogeneous-linear-second-order-ode-constant-coefficients.html | # Thread:
1. ## Inhomogeneous linear second-order ODE (constant coefficients)
y''(x) +3(y'(x))+2y=4e^(2x)+7
this is my ODE, it is inhomogeneous linear and second order with constant coefficients.
have i got this correct in saying the general solution is:
y=(1/3)*e^(2x)+7/2 ???
please could someone verify this qui... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/38241/normalization-of-a-spin-like-quantity-in-matrix-mechanics | # Normalization of a spin-like quantity in matrix mechanics
Suppose that there is a quantity in Heisenberg picture as the following:
$A=u_1\Sigma_1 + u_2\Sigma_2 +u_3\Sigma_3$
I am not sure why $u_1,u_2,u_3$ is normalized to be ${u_1}^2 + {u_2}^2 + {u_3}^2 =1$. (The matrices $\Sigma$ are the Pauli matrices.)
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Wha... | {"extraction_info": {"found_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://nrich.maths.org/384/clue | ### Set Square
A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?
### Biggest Bendy
Four rods are hinged at their ends to form a quadrilateral with fixed side lengths. Show that the quadrilateral has a maximum area when it is cycl... | {"extraction_info": {"found_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://math.stackexchange.com/questions/126897/the-decimal-expansion-of-the-quotient-of-two-integers | # The decimal expansion of the quotient of two integers
It is an exercise in a book on discrete mathematics.How to prove that in the decimal expansion of the quotient of two integers, eventually some block of digits repeats. For example: $\frac { 1 }{ 6 } =0.166\dot { 6 } \ldots$ and $\frac { 217 }{ 660 } =0.328787\do... | {"extraction_info": {"found_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://mathhelpforum.com/number-theory/123514-quadratic-nonresidues-residues.html | # Thread:
1. ## quadratic nonresidues and residues
How can I show that the number of quadratic residues modulo m is equal to the number of quadratic nonresidues modulo m in the set of reduced residue system modulo m?
2. Note that $1^2\equiv (p-1)^2(\bmod.p)$, $2^2\equiv (p-2)^2(\bmod.p)$, ...
So that the only distin... | {"extraction_info": {"found_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/38780/odd-number-of-second-class-constraints?answertab=oldest | # Odd number of second class constraints (!)
For my thesis, I have calculated the constraints for a system using Dirac method of constraint analysis. The problem is I got odd number of second class constraints (!), which gives me unusual numbers of degrees of freedom in phase space. I might have made some mistakes.
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": 13, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://scicomp.stackexchange.com/questions/2974/drawing-3d-projection-of-complex-surface | # Drawing 3d projection of complex surface
I have a complex surface (real dimension 2) in $\mathbb{C}^2$ with coordinates $(z,w)$ given explicitely: for any $\xi \in \mathbb{C}$ I know points $w(\xi)$ of intersection of surface with complex line $z = \xi$. I have to draw it's projection on fixed 3d plane. Please help ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://shlomifish.org/MathVentures/dodeca.html | Shlomi Fish (שלומי פיש) is an Israeli programmer, essayist, and humorist.
He is passionate about open source, open content, and freedom and openness in general.
It is easy to reach Shlomi using a large number of online means, including E-mail.
WWW
shlomifish.org
Puzzles Section Menu
If you like this site, I would ... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/19591?sort=newest | ## Dimension of subalgebras of a matrix algebra
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If n is given and A is a subalgebra of M_n(C), the algebra of n-by-n matrices with entries in the field of complex numbers, then what are the possible values of dim... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Talk:Orthogonality | # Talk:Orthogonality
WikiProject Mathematics (Rated B-class, Mid-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 17, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2011/03/29/tangent-vectors-at-a-point/?like=1&source=post_flair&_wpnonce=e94a57fbb5 | # The Unapologetic Mathematician
## Tangent Vectors at a Point
Tangent vectors are a very important concept in differential geometry, and they’re one of the biggest stumbling blocks in comprehension. There are two major approaches: one more geometric, and one more algebraic. I find the algebraic approach a bit more 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": 63, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/33006/relation-between-the-dedekind-zeta-function-and-quadratic-reciprocity | # Relation between the Dedekind Zeta Function and Quadratic Reciprocity
I was trying to learn a little about the Dedekind zeta function. The first place I looked at was obviously the Wikipedia article above. So my question comes from a sentence by the end of the article in the section on relations to other L-functions... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 51, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Polarization_(waves) | # Polarization (waves)
For other uses, see Polarization.
Polarization on rubber thread. (Circularly→linearly polarized standing wave.)
Polarization (also polarisation) is a property of waves that can oscillate with more than one orientation. Electromagnetic waves, such as light, and gravitational waves exhibit polari... | {"extraction_info": {"found_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": 25, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://lowentropymusings.wordpress.com/ | # Encrypted USB drives with eCryptfs
I’ve got several USB flash drives that I carry around with me on a regular basis, and it’s nice to be able to use those for small backups of important things, in addition to my usual system-wide backups that get dumped onto a couple external hard drives. This way, even if something... | {"extraction_info": {"found_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": 12, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/21919/pushing-with-a-lorentz-contracting-stick | # Pushing with a lorentz contracting stick
If I use a stick to push and accelerate an object, my hand pushes one end of the stick distance $x$, while the other end of the stick pushes the object distance $y$.
Distance $y$ is smaller than distance $x$, because of Lorentz contraction of the stick.
My hand does work $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": 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/183248/convergence-in-l1-problem | # Convergence in $L^1$ problem.
Problem: Let $f \in L^1(\mathbb{R},~\mu)$, where $\mu$ is the Lebesgue measure. For any $h \in \mathbb{R}$, define $f_h : \mathbb{R} \rightarrow \mathbb{R}$ by $f_h(x) = f(x - h)$. Prove that: $$\lim_{h \rightarrow 0} \|f - f_h\|_{L^1} = 0.$$
My attempt: So, I know that given $\epsilon... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 32, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/39762/vopenkas-principle-at-small-cardinals | ## Vopenka’s Principle at Small Cardinals
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I'm trying to understand Vopěnka's Principle, which is a large cardinal axiom. One version of the principle is that there does not exist a proper class of directed graphs... | {"extraction_info": {"found_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://mathforum.org/mathimages/index.php?title=Straight_Line_and_its_construction&diff=28278&oldid=13907 | # Straight Line and its construction
### 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": 217, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.scholarpedia.org/article/Neuropercolation | # Neuropercolation
From Scholarpedia
Robert Kozma (2007), Scholarpedia, 2(8):1360.
Curator and Contributors
1.00 - Robert Kozma
Neuropercolation is a family of stochastic models based on the mathematical theory of probabilistic cellular automata on lattices and random graphs and motivated by structural and dynamica... | {"extraction_info": {"found_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": 167, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/tagged/classical-physics+homework | # Tagged Questions
1answer
69 views
### Standing Waves: finding the number of antinodes
A string with a fixed frequency vibrator at one end forms a standing wave with 4 antinodes when under tension T1. When the tension is slowly increased, the standing wave disappears until tension T2 is ...
2answers
87 views
### C... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/37237-express-curve-standard-form.html | # Thread:
1. ## Express curve in standard form
Use an orthogonal transformation and a translation to express in standard form the curve given by the equation
2. Originally Posted by matty888
Use an orthogonal transformation and a translation to express in standard form the curve given by the equation
You will want 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": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/43303/relationship-between-hierarchy-problem-and-higgs-fine-tuning?answertab=votes | # Relationship between hierarchy problem and higgs fine tuning?
I often hear of hierarchy problem being used synonymous with Higgs fine tuning (esp with regards with motivations for SUSY). What exactly is the relationship between the two problems? As I understand it, the quadratic divergence from the Higgs self coupli... | {"extraction_info": {"found_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/standard-model?page=3&sort=active&pagesize=15 | # Tagged Questions
A model of the basic particles and forces featuring six quarks, three charged leptons, three massless neutral leptons and four fundamental force carrying bosons. The twelve fermions are arranged into three generations, while the bosons serve to explain the electromagnetic interaction plus the strong... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cs.stackexchange.com/questions/7098/is-1-in-k-sat-np-complete-for-k-3 | # Is 1-in-k SAT NP-complete for k > 3
It is well-known that 1-in-k SAT is NP-complete for k=3. What about for k > 3?
-
3
Indeed it is NP-Complete. – Geekster Dec 1 '12 at 3:08
## 1 Answer
It's still in NP by using a truth assignment as a proof.
You can reduce 1-in-3 SAT to 1-in-$k$ SAT to show hardness as follows... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/16353/why-is-time-order-invariant-in-timelike-interval/16355 | # why is time order invariant in timelike interval?
why do two observers measure the same order of events if we are inside the light cone?
(e.g. if ds^2 > 0 time order is preserved according to the class mech book I am reading, but it doesn't give any proof of this) I assume there is some simple geometrical argument ... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/83691/list | ## Return to Answer
2 added 371 characters in body
This is more of a longish comment explaining why I believe that the answer should be yes, and that a confirmation should be within reach using current technology.
Let $K$ be the field of $n$-th roots of unity, and $\zeta_p$ a primitive $p$-th root of unity for some ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 32, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/58732?sort=oldest | ## Torus based cryptography
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In cryptography one needs finite groups $G$ in which the discrete logarithm problem is infeasible. Often they use the multiplicative group $\mathbb{G}_m(\mathbb{F}_p)$ where $p$ is a 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": 96, "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/190709/graph-theory-adjacency-vs-incident/190712 | # Graph theory: adjacency vs incident
Okay, so I think if 2 vertices are adjacent to each other, they are incident to each other....or do I have it wrong? Is this just different terminology. I thought I was totally clear on this for my class, but now I am doubting myself reading the book and looking at my notes. I jus... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/159193-writing-up-recurrence-relation-problem.html | # Thread:
1. ## Writing up a Recurrence Relation Problem...
I know how to solve Recurrence Relation problems, I just need help writing up the equation:
Assume that the deer population of Rustic County is 200 at time
n = 0 and 220 at time n = 1 and that the increase from time n-1 to time n is twice the increase from... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/55789-question-what-kind-diff-eq.html | # Thread:
1. ## Question: what kind of diff. eq is that?
What kind of diff.eq. is that? I don't have any idea from where to begin with
2. Originally Posted by JrShohin
What kind of diff.eq. is that? I don't have any idea from where to begin with
The solution to the equation,
$y'' + y = 0$
Is given by $y=c_1\sin 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": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://terrytao.wordpress.com/tag/weak-turbulence/ | 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 ‘weak turbulence’ tag.
## Weakly turbulent solutions for the cubic defocusing nonlinear Schrödinger equation
14 Augus... | {"extraction_info": {"found_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": 43, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Integers | # Integer
(Redirected from Integers)
Symbol often used to denote the set of integers (see List of mathematical symbols)
Group theory
• Integers (Z)
• Lattice
Modular groups
• PSL(2,Z)
• SL(2,Z)
• General linear GL(n)
• Special linear SL(n)
• Orthogonal O(n)
• Euclidean E(n)
• Special orthogonal SO(n)
• Unitary U(n)
• ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 23, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/34803/can-two-positive-integers-be-uniquely-recovered-from-their-difference-and-xor?answertab=votes | # Can two positive integers be uniquely recovered from their difference and XOR?
As part of an answer to a Stack Overflow question I made the assumption that if I choose two distinct positive integers $m$ and $n$, them give you $m - n$ and $m$ XOR $n$, then you can uniquely determine what $m$ and $n$ were. For all 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": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/6668/how-to-obtain-a-one-value-share-in-shamirs-secret-sharing | How to obtain a one-value share in Shamir's secret sharing
This is a trivial question, but I had to ask:
since each generated share in a Shamir's secret sharing scheme initially consists of a pair of values (representing the coordinates of a point on the plane), how do I reduce the two values to one, so that the shar... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/76483/limit-of-a-prime-sequence?answertab=votes | # limit of a prime sequence
Let $p[n]$ be the $n$-th prime. Let $0 \leq m < k$.
Prove
$$\lim_{n\rightarrow\infty}\frac{ p[(n+k)^2] - p[(n+m)^2] }{ p[n]} = 4(k-m)\;.$$
This is a generalization of something I looked at a while ago. I have some empirical evidence for it but cannot prove it. I think it is hard (and 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": 30, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/tagged/black-scholes?sort=votes&pagesize=50 | # Tagged Questions
Black-Scholes is a mathematical model used for pricing options.
6answers
2k views
### Paradoxes in quantitative finance
Everyone seems to agree that the option prices predicted by the Black-Merton-Scholes model are inconsistent with what is observed in reality. Still, many people rely on the mode... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/70289?sort=newest | ## laplacian for metrics on $S^n$
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It is true that the restiction of the Laplace operator on $\mathbb R^n$ to functions on the sphere is the Laplacian for the round metric on the sphere. Is this true for any Riema... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/206099-dense-itself-set-print.html | # Dense-in-itself set
Printable View
• October 25th 2012, 05:40 PM
xinglongdada
Dense-in-itself set
Let $E\subset \mathbb{R}^1$ be a non-empty countable set. Suppose $E$ has no isolated points, prove that $\bar E\backslash E$ is dense in $\bar E.$
It is difficult, isn't it?
• October 25th 2012, 08:51 PM
hollywood
Re... | {"extraction_info": {"found_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": 79, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/23279/why-does-a-coin-falls-faster-when-its-flipping-as-well | # Why does a coin falls faster when it's flipping as well?
From my experiments with measuring how fast a coin falls, I have consistently measured a faster falling rate for a coin that flips as it falls.
As an example, a coin dropping on its edge from height of $45 \:\rm{cm}$ hits the ground $20 \:\rm{ms}$ later 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": 5, "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/188842-implicit-differentiation-word-problem.html | Thread:
1. Implicit differentiation word problem
I have a written assignment in which one specific word problem is confusing me greatly. I just recently learned implicit differentiation but haven't gotten much into depth with it. The question is as follows:
"Each time we use implicit differentiation, we are able 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 21, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/12829/convex-polyhedra | ## Convex Polyhedra
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Exactly what set of mathematical tools (means: set of areas of mathematical knowledge) are appropriate to begin with to analyse (to enumerate face vectors associated with polyhedron, to calcul... | {"extraction_info": {"found_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/58718?sort=oldest | Degree reduction argument in Guth-Katz’sproof of Erdos distinct distance problem in the plane
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In the middle of page 9 of http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.4105v1.pdf.
They said " Now we select a random 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": 57, "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/107530?sort=oldest | ## Fusion category and Hopf algebra
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Let $H$ be a semisimple Hopf algebra over an algebraically closed field of characteristic zero. Further, let $K\subseteq H$ be a normal Hopf subalgebra. As we all know, $H$ 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": 10, "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/14436/how-do-you-prove-s-sum-p-ln-p?answertab=votes | # How do you prove $S=-\sum p\ln p$?
How does one prove the formula for entropy $S=-\sum p\ln p$? Obviously systems on the microscopic level are fully determined by the microscopic equations of motion. So if you want to introduce a law on top of that, you have to prove consistency, i.e. entropy cannot be a postulate. ... | {"extraction_info": {"found_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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/forces | Tagged Questions
This tag is for the classical concept of forces, i.e. the quantities causing an acceleration of a body. It expands to the strong/electroweak force only insofar as they act comparable to ‘classical’ forces. Use [tag:particle-physics] for decay channels due to forces and [tag:newtonian-mechanics] 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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/17202/sum-of-the-first-k-binomial-coefficients-for-fixed-n/69153 | ## Sum of ‘the first k’ binomial coefficients for fixed n
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I am interested in the function $\sum_{i=0}^{k} {N \choose i}$ for fixed $N$ and $0 \leq k \leq N$. Obviously it equals 1 for $k = 0$ and $2^{N}$ for $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": 69, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/22548/21-dimensional-physics-theory-of-our-universe?answertab=votes | # $2+1$ dimensional physics theory of our universe?
Is there any physics theory that depicts our universe as $2+1$ dimensional?
I heard that black holes seem to suggest that the world might be $2+1$ dimensional, so I am curious whether such theory exists?
Just for curiosity.
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2
– David Zaslavsky♦ Mar 19 '12 at 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": 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/discrete-math/199323-scheduling-integer-programming-question-desperate.html | # Thread:
1. ## Scheduling - integer programming question [desperate]
Question:
Vicky is attending a summer school where she must study four units. She must do a one-hour lecture for each of the units every day. There are 6 one hour time slots in a day. As there are way too many students, repeating lectures for each ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/22903/list | ## Return to Answer
3 added 760 characters in body
As Robin as pointed out, for all primes $p$, $\mathbb{Q}_p$ is rigid, i.e., has no nontrivial automorphisms. It is sort of a coincidence that you ask, since I spent much of the last $12$ hours writing up some material on multiply complete fields which has application... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 93, "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/31264/what-is-the-principle-behind-centrifugation?answertab=votes | What is the principle behind centrifugation?
What is the principle behind centrifugation?
I understand the idea that you spin something around the centripetal force will cause an apparent force on the spinning system. However I don't quite grasp how particles (in the non subatomic sense) with different density should... | {"extraction_info": {"found_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/pre-calculus/187167-finding-interval-expression-having-two-quadratic-equations-print.html | Finding the interval of expression having two quadratic equations.
Printable View
• September 2nd 2011, 06:59 PM
sumedh
Finding the interval of expression having two quadratic equations.
What will be the values of 'm' so that the range of the equation
$y= \frac{mx^2+3x-4}{-4x^2+3x+m}$
will be all real values( i.e. $... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.aps.org/articles/v2/57 | # Viewpoint: Electrons in graphene: an interacting fluid par excellence
, Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Published July 6, 2009 | Physics 2, 57 (2009) | DOI: 10.1103/Physics.2.57
Along with the quark gluon plasma and cold atom gasses, graphene is establis... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 50, "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://mathoverflow.net/questions/77778?sort=votes | Bound of dimension of $H^1$ of certain line bundle
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Let $X$ be a smooth variety over a field $k=\bar k$, $\rm char$ $k=0$. Assume that $\mathcal{L}$ is a nef and big line bundle. Is there some bound saying that $$h^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": 18, "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/93069/when-are-conformal-maps-holomorphic/93070 | ## When are conformal maps holomorphic?
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It is a standard fact from elementary complex analysis that a holomorphic function $f:\mathbb{C}\to \mathbb{C}$ is a conformal mapping. Now, suppose I have a map $f':\mathb... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2011/06/18/brackets-and-flows/ | # The Unapologetic Mathematician
## Brackets and Flows
Now, what does the Lie bracket of two vector fields really measure? We’ve gone through all this time defining and manipulating a bunch of algebraic expressions, but this is supposed to be geometry! What does the bracket actually mean? It turns out that the bracke... | {"extraction_info": {"found_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": 41, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/202412-algorithm-finding-arrangement-5-variables-eqn-b-w-satisfy.html | # Thread:
1. ## Algorithm for finding arrangement of 5 variables in eqn with +/- b/w to satisfy it
Hi all
My friend gave me a riddle (very well known) in which I had to break a 40kg block in 4 pieces ( of integral weight) such that using all those pieces one can measure all weights in range 1 - 40 on a physical bala... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/newtonian-gravity+star | # Tagged Questions
1answer
130 views
### How to calculate gravity inside the star?
Gravity must decrease due to less effective mass when going inside the object but also must increase with depth inside the star due to its higher density. Is there a model or formula approximating ...
0answers
367 views
### Calculati... | {"extraction_info": {"found_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/124509/how-do-i-prove-the-following-statement-about-a-summation-of-a-series/124521 | # How do I prove the following statement about a summation of a series?
I have not been able to completely solve this problem and it's driving me crazy. Could you please help.
The question is to show that, $$\sum_{n=1}^N \frac{\sin n\theta}{2^n} =\frac{2^{N+1}\sin\theta+\sin N\theta-2\sin(N+1)\theta }{2^N(5-4\cos\thet... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/30176/statistic-hypothesis-testing-standard-deviation-less-than-0-4 | # Statistic hypothesis testing - Standard deviation less than 0.4
There was too much snow on the highways, so the mayor of the town sent snowplows to spread some chemicals on them. There is a standard of how much of one specific substance should be present in the compound that is used for spreading... We measured 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": 7, "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/202397-geometric-series-easy.html | # Thread:
1. ## Geometric series [easy]
Hey guys,
Just wondering if anybody could help me identify the r value in the following geometric series (sorry it's in image form, I'm no good at tex):
Anyway, I had one similar just before where the coefficient was 1, meaning my a and r terms were both x - which made it eas... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/80027?sort=oldest | Obstructions to being a hyperplane section or a fibre of a Lefschetz pencil
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Given a smooth projective variety $X$, when could $X$ fail to be a hyperplane section in some other variety $Y$, or fail to be the fibre 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": 28, "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/2009/03/05/uniqueness-of-jordan-normal-forms/?like=1&_wpnonce=84af3d0b4c | # The Unapologetic Mathematician
## Uniqueness of Jordan Normal Forms
So we’ve got a Jordan normal form for every linear endomorphism $T:V\rightarrow V$ on a vector space $V$ of finite dimension $d$ over an algebraically closed base field $\mathbb{F}$. That is, we can always pick a basis with respect to which the 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 18, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/187543-inequality-prove-involving-convex-notions.html | Thread:
1. Inequality to prove involving convex notions
Hi everyone,
Here's an exercice I have trouble with.
Let $a = (a_1,\dots,a_n)\in\mathbb{R}^n_+$ and define $G(a) = (a_1\dots a_n)^{\frac{1}{n}}$
I have to show that, assuming $a,b\in\mathbb{R}^n_+, G(a+b) \geqslant G(a) + G(b)$.
I have already tried a looooot... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/commutator+measurement-problem | # Tagged Questions
1answer
851 views
### Compatible Observables
My QM book says that when two observables are compatible, then the order in which we carry out measurements is irrelevant. When you carry out a measurement corresponding to an operator $A$, 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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Number_theory | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathematica.stackexchange.com/questions/tagged/complex+polynomials | # Tagged Questions
3answers
433 views
### Solving cubic equation for real roots
I'm looking to solve the following cubic equation for x: $\beta\, x^3 - \gamma \,x = c$. I have plugged in some sample values ($\beta = 2$, $\gamma = 5$ and $c = 2$). When I try to solve this ...
6answers
2k views
### Finding real roots... | {"extraction_info": {"found_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/55318/where-does-energy-go-in-destructive-interference/55326 | # Where does energy go in destructive interference? [duplicate]
This question already has an answer here:
• What happens to the energy when waves perfectly cancel each other? 10 answers
I have read that when two light waves interfere destructively, the energy contained within is transferred to other parts of the wav... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/21351/neutrino-oscillations-and-conservation-of-momentum | # Neutrino Oscillations and Conservation of Momentum
I would like to better understand how neutrino oscillations are consistent with conservation of momentum because I'm encountering some conceptual difficulties when thinking about it. I do have a background in standard QM but only rudimentary knowledge of particle ph... | {"extraction_info": {"found_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/93930/meaning-of-affine-transformation?answertab=oldest | # Meaning of affine transformation
From Wikipedia, I learned that an affine transformation between two vector spaces is a linear mapping followed by a translation.
But in a book Multiple view geometry in computer vision by Hartley and Zisserman:
An affine transformation (or more simply an affinity) is a non-singular... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/98515/what-is-the-optimal-growth-of-the-constant-in-bdg | ## What is the optimal growth of the constant in BDG?
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Let $X$ be a continuous local martingale, and $\langle X \rangle$ be its quadratic variation process. The "standard" proof of Burkholder-Davis-Gundy inequalit... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/138478-poisson-s-distribution-problem.html | # Thread:
1. ## Poisson's distribution problem
If a random variable is Poisson's distributed with a mean of 5.2 determine (a) standard deviation (b) the probability that random variable will have a value of three or less (c) the probability that random variable will have a value of more than 6 .
2. st dev=square roo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/20740/is-there-an-introduction-to-probability-theory-from-a-structuralist-categorical-p/25647 | ## Is there an introduction to probability theory from a structuralist/categorical perspective?
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The title really is the question, but allow me to explain.
I am a pure mathematician working outside of probability... | {"extraction_info": {"found_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/295545/sam-has-to-go-to-work-from-home-sam-moves-either-south-or-east-when-going-to-wo | # Sam has to go to work from home. Sam moves either SOUTH or EAST when going to work. How many distinct routes are there for sam to go to work?
The following figure depicts the paths from home to work. SAM never travels through the park when going to work.
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manual counting gives 8 ways. Is there a mathematical proce... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/28573/blocking-and-confounding-in-replicated-2k-factorial-design | # Blocking and confounding in replicated $2^k$ factorial design
Consider the $2^6$ factorial in 8 blocks of eight each runs with ABCD, ACE and ABEF as the independent effects chosen to be confounded with blocks. Generate a design. Find the other effect of confounding.
I can solve the second part of the question. I fo... | {"extraction_info": {"found_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://cogsci.stackexchange.com/questions/tagged/linguistics+reading | # Tagged Questions
1answer
99 views
### Judgments of similarity between samples of writing
I was thinking last night about the possibility of an experiment that investigates the factors contributing to peoples' judgments of 'stylistic similarity' between two samples of writing. For example, ...
5answers
296 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": 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/18491/watercooling-performance-and-amount-of-water-or-liquid-in-the-loop | # Watercooling performance and amount of water or liquid in the loop
Imagine a watercooling system. It consist of a reservoir, pump, tubes and a radiator. We all know how it works.
My question is, only inreasing the reservoir's volum, say from 1 liter to 2, will actually increase the performance?
I do remember some... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/246144/what-is-the-nth-derivative-of-dfrac1-sqrt1-x2 | # What is the nth derivative of $\dfrac{1}{\sqrt{1 + x^2}}$
I'm trying to find a general formula for the $n$th derivative of $$\dfrac{1}{\sqrt{1 + x^2}}$$ I got up to, \begin{eqnarray*} g^{(0)}(x) &=& g(x) \\ g^{(1)}(x) &=& \dfrac{1}{(1 + x^2)^{1/2}} \\ g^{(2)}(x) &=& \dfrac{-x}{(1 + x^2)^{3/2}} \\ g^{(3)}(x) &=& \dfr... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/2032/is-duration-really-the-slope-of-the-price-yield-curve | # Is Duration really the slope of the Price-Yield curve?
When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve. But is that really right?
Duration is (change in price) divided by (price times change in yield). That's hardly the slope of 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": 8, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/3441/how-can-i-calculate-the-number-of-potential-combinations-in-a-password | # How can I calculate the number of potential combinations in a password?
If I create a 10 digit password with the following requirements:
• At least one uppercase letter A-Z - 26
• At least one lowercase letter a-z - 26
• At least one digits 0-9 - 10
• At least one common symbol (#,\$,%,etc) - 32
By inclusion-exclu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/98563/distance-between-points-in-two-disjoint-compact-sets-closed | distance between points in two disjoint Compact sets [closed]
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let $S$ and $T$ be two disjoint compact nonempty sets. Show that there are points $x_0$ in $S$ and a point $y_0$ in $T$ such that |$x$−$y$|≥|$x_0$−$y_0$| ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.haskell.org/haskellwiki/index.php?title=User:Michiexile/MATH198/Lecture_4&diff=30783&oldid=30782 | # User:Michiexile/MATH198/Lecture 4
### 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": 32, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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