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http://physics.stackexchange.com/questions/14181/do-stationary-states-with-higher-energy-necessarily-have-higher-position-momentu?answertab=oldest | # Do stationary states with higher energy necessarily have higher position-momentum uncertainty?
For simple potentials like square wells and harmonic oscillators, one can explicitly calculate the product $\Delta x \Delta p$ for stationary states. When you do this, it turns out that higher energy levels have higher val... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=522640 | Physics Forums
## Biot-Savart law and Poisson's equation
Dear colleagues,
I have questions regarding Biot-Savart law. From [1], it is shown that the equation (Biot-Savart) is derived from the solution to Poisson's equation (assuming here div A=0)
\begin{equation}
\vec{\nabla}^2 \vec{A} = -\mu \vec{J}
\end{equation}
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/16841-midpoint-theorum-help.html | Thread:
1. Midpoint Theorum Help!!
I need help in this sum.
Q: In the adjoining figure, ABCD is a square and BCPQ is a parallelogram. If M is the midpoint of DC and PM produced meets AN at N, prove that AN=1/2 AD. If BD meets MN at R, prove that BQ=1/2 AC.
I have no problem with the first part of the question but 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/28968/examples-of-piecewise-smooth-dynamical-systems/29049 | # Examples of piecewise smooth dynamical systems [closed]
I have recently been studying continuous dynamical systems whose phase space can be divided into a number of regions. Inside each of these the flow is smooth, but there is a discrete jump in the flow just at the boundaries. In the mathematical description, 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": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://terrytao.wordpress.com/tag/open-mapping-theorem/ | 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 ‘open mapping theorem’ tag.
The closed graph theorem in various categories
20 November, 2012 in expository, math.AG, ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 137, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/24031/dimension-of-module | ## Dimension of module
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Does dimension of a module (say, dimension of its support) have anything to do with the supremum length of chains of prime submodules like rings? Let's restrict to finitely generated module... | {"extraction_info": {"found_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://math.stackexchange.com/questions/35409/determining-the-balance-equations-for-a-poisson-process/35474 | # Determining the balance equations for a Poisson Process
I'm trying to do an exercise (not homework) and I fail to understand the solution the reader is giving me.
Consider a gas station with one gas pump. Cars arrive at the gas station according to a Poisson process with an arrival rate of 20 cars per hour. An arri... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/game-theory?sort=faq&pagesize=15 | # Tagged Questions
The study of competitive and non-competitive games, equilibrium concepts such as Nash equilibrium, and related subjects. Combinatorial games such as Nim are under (combinatorial-game-theory), and algorithmic aspects (e.g. auctions) are under (algorithmic-game-theory).
4answers
773 views
### Probab... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 53, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/Events/winter10/abs/cp.html | 2010 CMS Winter Meeting
Coast Plaza Hotel and Suites, Vancouver, December 4 - 6, 2010 www.cms.math.ca//Events/winter10
Contributed Papers
Org: Martin Barlow (UBC)
[PDF]
BHAGWAN AGGARWALA, University of Calgary
Entry Inhibitors of HIV [PDF]
Entry Inhibitors of HIV (Fuzeon is an example) have been approved by FDA (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": 76, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/20855/show-that-the-energy-levels-of-a-particle-in-a-specific-potential-are-e-n-n-f?answertab=votes | # Show that the energy levels of a particle in a specific potential are $E_n=(n+\frac{1}{2})h\omega-\frac{1}{2}\frac{F^2}{m\omega^2}$ [closed]
A particle of mass m moves on the x-axis under the influence of the potential $$V(x)=\frac{1}{2}m\omega^2x^2+Fx$$ Can anyone help me, using Schrödinger's equation in one dimensi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/8408 | # Number Spirals
##### Stage: 2 Challenge Level:
Let's explore making spirals from the middle outwards.
We'll use a short list of numbers repeated over and over again.
Here we see one I've explored a bit. I used the numbers $1$ to $6$ and went anticlockwise.
I noticed that often when I got to the number $6$ I had co... | {"extraction_info": {"found_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/24743/does-exceptionalism-persist-as-sample-size-gets-large | # Does exceptionalism persist as sample size gets large?
Which of the following is more surprising?
1. In a group of 100 people, the tallest person is one inch taller than the second tallest person.
2. In a group of one billion people, the tallest person is one inch taller than the second tallest person.
Put more pr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 140, "mathjax_display_tex": 17, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://math.stackexchange.com/questions/58576/how-to-show-martingale-is-bounded-in-l1 | # How to show martingale is bounded in $L^1$?
Fix a filtered probability space $(\Omega,\mathcal{F},(\mathcal{F}_n)_{n\geq 0},\mathbb{P})$ and an $L^1$-bounded submartingale $X_n$.
We can show that, for $n\geq 0$, the sequence $(\mathbb E[X^+_p|\mathcal{F}_n],p\geq n)$ is increasing and converges to an a.s. limit $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": 28, "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/283591/hyperbola-is-a-pair-of-straight-lines | # Hyperbola is a pair of straight lines?
I'm confused by this question:
If $f(x) = 2x^2 - 6y^2+xy+2x-17y-12=0$ is to represent a pair of straight lines, one of which has equation $x+2y+3=0$, what must be the equation of the other line? Verify that $f(x)=0$ does, indeed, represent a pair of straight lines.
Given the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/2263/how-to-cluster-stocks-and-construct-an-affinity-matrix?answertab=active | # How to cluster stocks and construct an affinity matrix?
My goal is to find clusters of stocks. The "affinity" matrix will define the "closeness" of points. This article gives a bit more background. The ultimate purpose is to investigate the "cohesion" within ETFs and between similar ETFs for arbitrage possibilities.... | {"extraction_info": {"found_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.physicsforums.com/showthread.php?s=7400154d1617519c275ecb052f9c2382&p=3953927 | Physics Forums
## Fourier transform capabilities in reconstructing missing data
Hi,
I know this topic is more suited for Computing & Technology, but it has even more to do with general questions about Fourier transform capabilities. I have a question about sample restoration in Discrete Fourier Transform. Suppose we... | {"extraction_info": {"found_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": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/2359-isomorphism.html | # Thread:
1. ## Isomorphism
Let n be a positive integer. Define f : Z ! Zn by f(a) = [a]. Is f a homomorphism? One-to-one? Onto? An isomorphism? Explain.
Can any one help? Thanks very much.
2. Originally Posted by suedenation
Let n be a positive integer. Define f : Z ! Zn by f(a) = [a]. Is f a homomorphism? One-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": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/1664/how-many-explanatory-variables-is-too-many/1681 | # How many explanatory variables is too many?
When researching any sort of predictive model, whether using ordinary linear regression or more sophisticated methods such as neural networks or classification and regression trees, there seems to always be a temptation to add in more explanatory variables/factors. 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": 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/91940/intuition-around-why-domain-of-x-of-arcsine-and-arccosine-is-11-for-real-re/91941 | # Intuition around why domain of x of arcsine and arccosine is [-1;1] for “real result” & domain for arctangent is all real numbers
Context
I'm working my way through basic trig (this question has a focus on inverse trig functions, specifically arcsine, arccosine and arctangent ), using Khan Academy, wikipedia and so... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 51, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/205201/how-to-show-that-this-logical-argument-is-valid/259197 | # How to show that this logical argument is valid?
I am asked to show the following argument is valid:
I know you need to use the rules of inference like modus ponens/converse fallacy but I'm confused because it doesn't look like any of the forms I've learned about?
$$N\to B\lor S\\ S\to W\lor A \\ M\to N\land W \\ ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/130870-proof-limits-sequences.html | # Thread:
1. ## Proof: Limits of Sequences
Supply a proof for the following theorem: Suppose that f is continuous at a and that x(subscript)n tends to a as n goes to infinity. Then there is an integer N such that f(x(subscript)n) is defined for all integers n > N; furthermore, f(x(subscript)n) tends to f(a) as n goes... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/30762/model-selection-for-linear-mixed-models-over-alternative-sets-of-parameters-nlm | # Model-selection for linear mixed models over alternative sets of parameters (nlme function in R)
My models look like:
````lme1 = lme(y~X+Y+V, random=~1|Subject, data=mydata, method ="ML")
lme2 = lme(y~X+Y+V2+V3, random=~1|Subject, data=mydata, method ="ML")
lme3 = lme(y~X+Y+V4, random=~1|Subject, data=mydata, metho... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/157866/derivative-for-matrix-function?answertab=active | # Derivative for Matrix function
I have a matrix kernel function which I am trying to find the derivative to. Function is K = c * exp[-1/2 * (P(X1 - X2))' * P(X1 -X2)] where uppercase are matrices and lower case are scalars (and ' denotes transpose). I'm trying to find dK/dP. I'm pretty rusty on matrix calculus, can 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": 10, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/101476/radius-of-convergence-of-sum-n-geq2-fraczn-lnn | # Radius of convergence of $\sum_{n\geq2}\frac{z^{n}}{\ln(n)}$?
What is the R.O.C. of the following power series:
$$\sum_{n\geq2}\frac{z^{n}}{\ln(n)}\qquad?$$ Here is my attempt:
$$\lim_{n\rightarrow\infty}\left|\frac {z^{n+1}\ln(n)}{\ln(n+1)z^{n}}\right|=\lim_{n\rightarrow\infty}\left|\frac{z\ln(n)}{\ln(n+1)}\right... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/5968/plotting-implicitly-defined-space-curves | # Plotting implicitly-defined space curves
It is known that space curves can either be defined parametrically,
$$\begin{align*}x&=f(t)\\y&=g(t)\\z&=h(t)\end{align*}$$
or as the intersection of two surfaces,
$$\begin{align*}F(x,y,z)&=0\\G(x,y,z)&=0\end{align*}$$
Curves represented parametrically can of course be pl... | {"extraction_info": {"found_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://math.stackexchange.com/questions/296117/special-kaehler-manifolds | # Special Kaehler manifolds
If we have complex vector space $V=T^{*}C^{m}$ with standard complex symplectic form $\Omega =\sum_{i=1}^{m}dz^{i}\wedge dw^{i}$, and if $\tau : V\to V$ is standard real structure of $V$ with set of fixed points $V^{\tau }=T^{*}R^{m}$. Then $\gamma =\sqrt{-1}\Omega (.,\tau .)$ defines a Her... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/266928/sum-of-random-number-of-random-variables | # Sum of random number of random variables
Consider a sequence of independent and identically distributed random variables $X_1, X_2, \ldots$ such that $$\mathbb P(X_i\geqslant k)=\prod_{\ell=1}^{k-2}\frac{n-\ell}n \ \textrm{ for every } 2\leqslant k\leqslant n+1.$$
Consider also $$Z= \sum_{i=1}^Y X_i ,$$
where $Y$ ... | {"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": 15, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4176841 | Physics Forums
## Which of these interpretations of the modulus squared of wavefunction is right?
Does $|\psi(\mathbf{x},t)|^2d^3\mathbf{x}$ or $|\psi(\mathbf{x},t)|^2d^3\mathbf{x}dt$ give the probability of a particle to collapse at the point $\mathbf{x}$ at time $t$?
Griffiths sides with the former, but I'm having... | {"extraction_info": {"found_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/182581/prime-factorization-composite-integers/182595 | # Prime factorization, Composite integers.
Describe how to find a prime factor of 1742399 using at most 441 integer divisions and one square root.
So far I have only square rooted 1742399 to get 1319.9996. I have also tried to find a prime number that divides 1742399 exactly; I have tried up to 71 but had no luck. Su... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "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/1145/how-much-would-it-cost-in-u-s-dollars-to-brute-force-a-256-bit-key-in-a-year/1149 | # How much would it cost in U.S. dollars to brute force a 256 bit key in a year?
I am often told that any key can be broken and that it is only a matter of time and resources for any key to be broken. I know that this it technically true. However, I think that there is probably a point where it makes sense to say a ke... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 42, "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/118113/what-makes-elementary-functions-elementary/137236 | # What makes elementary functions elementary?
Is there a mathematical reason (or possibly a historical one) that the "elementary" functions are what they are? As I'm learning calculus, I seem to focus most of my attention on trigonometric, logarithmic, exponential, and $n$th roots, and solving problems that have solut... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/5982/burn-in-period-for-random-walk?answertab=oldest | # Burn-in period for random walk
We are trying to make simulation experiment involving a common stochastic trend, that is described by the random walk (or $I(1)$ process) $Y_t = Y_{t-1} + \varepsilon_t$, where innovations $\varepsilon_t$ ~ $N(0,1)$. However when could we be sure that the past innovations are more or 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": 39, "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/1775/why-is-there-no-absolute-maximum-temperature/1778 | Why is there no absolute maximum temperature?
If temperature makes particles vibrate faster, and movement is limited by the speed of light, then temperature must be limited as well I would assume. Why there is no limits?
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1
Forget SR considerations and lets focus on low velocity/KE particles. If I am standing, with... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/7169/solution | nrich enriching mathematicsSkip over navigation
### Consecutive Numbers
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
### 14 Divisors
What is the smallest number with exactly 14 divisors?
### Summing Consecutive Numbers
Many numbers can be expres... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/47851/action-of-the-lorentz-group-on-scalar-fields | # Action of the Lorentz group on scalar fields
The Lorentz groups act on the scalar fields as: $\phi'(x)=\phi(\Lambda^{-1} x)$
The conditions for an action of a group on a set are that the identity does nothing and that $(g_1g_2)s=g_1(g_2s)$. This second condition is not fulfilled because of the inverse on $\Lambda$.... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Exsecant | # Exsecant
exsecant (blue) and excosecant (green)
The trigonometric functions, including the exsecant, can be constructed geometrically in terms of a unit circle centered at O. The exsecant is the portion DE of the secant exterior to (ex) the circle.
The exsecant, also abbreviated exsec, is a trigonometric function d... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/70068?sort=oldest | ## Conic hulls and cones
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Suppose I have a number of vectors in $\mathbb{R}^n.$ The first question is: what is the most efficient algorithm to compute their "conic hull" (the minimal convex cone which contains 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": 47, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/7670/clue | ### Integration Matcher
Match the charts of these functions to the charts of their integrals.
### Brimful
Can you find the volumes of the mathematical vessels?
### Lennard Jones Potential
Investigate why the Lennard-Jones potential gives a good approximate explanation for the behaviour of atoms at close ranges
# ... | {"extraction_info": {"found_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://www.contrib.andrew.cmu.edu/~ryanod/?p=877 | ## Analysis of Boolean Functions
by Ryan O'Donnell
Fall 2012 course at Carnegie Mellon
# §5.3: The Fourier coefficients of Majority
In this section we will analyze the Fourier coefficients of $\mathrm{Maj}_n$. In fact, we give an explicit formula for them in Theorem 16 below. But most of the time this formula is no... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 89, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/62282/mathbbpn-is-simply-connected | ## $\mathbb{P}^n$ is simply connected
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In his chapter about Hurwitz' theorem for curves, Hartshorne shows that $\mathbb{P}^1$ is simply connected, i.e. every finite étale morphism $X \to \mathbb{P}^1$ is a finite ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 131, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.r-bloggers.com/simulated-powerprecision-analysis/ | ## R-bloggers
R news and tutorials contributed by (452) R bloggers
# Simulated Power/Precision Analysis
February 21, 2013
By BioStatMatt
(This article was first published on BioStatMatt » R, and kindly contributed to R-bloggers)
I cringe when I see research proposals that describe a sophisticated statistical appro... | {"extraction_info": {"found_math": true, "script_math_tex": 3, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Rule_of_inference | # 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": 11, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/93780/list | ## Return to Answer
2 added 294 characters in body
A subgroup of maximal rank of maximal dimension is certainly a maximal subgroup of maximal rank. Maximal connected subgroups of maximal rank in $Spin(n)$ correspond to maximal reductive Lie subalgebras of maximal rank in $so(n)_{\mathbf{C}}$. Such subalgebras in semi... | {"extraction_info": {"found_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://headinside.blogspot.com/2012/07/estimating-square-roots.html?m=0 | 3
## Estimating Square Roots
Published on Sunday, July 08, 2012 in fun, math, self improvement
I've shown how to find square roots of perfect squares in past tutorials, but how do you handle numbers that aren't perfect squares?
In this tutorial, you'll learn how to quickly determine an approximate square root for 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": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2009/03/13/eigenpairs/?like=1&source=post_flair&_wpnonce=420e8d64d7 | # The Unapologetic Mathematician
## Eigenpairs
Well, Wednesday I was up at the University of Pennsylvania again, and yesterday I was making arrangements for a visit to San Diego in a couple weeks. And next week is an exam week, so I’ll have to inch forward today.
We’ve seen a lot about Jordan normal forms, which can... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 21, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2009/09/28/euclidean-spaces/?like=1&source=post_flair&_wpnonce=a34a077b61 | # The Unapologetic Mathematician
## Euclidean Spaces
In light of our discussion of differentials, I want to make a point here that is usually glossed over in most treatments of multivariable calculus. In a very real sense, the sources and targets of our functions are not the vector spaces $\mathbb{R}^n$.
Let’s think... | {"extraction_info": {"found_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": 10, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/303764/countably-generated-versus-being-generated-by-a-countable-partition | # Countably generated versus being generated by a countable partition
(1) Apparently a general term of a sigma-field generated by a countable partition can be written down. For example, if $\mathcal{B} = \sigma(B_n,n\ge 1)$ and $\{B_n\}_{n\ge1}$ is a partition of the ground set $\Omega$, then a general element of $\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": 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/87429/generators-of-a-certain-ideal | ## Generators of a certain ideal
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In view of Mariano Suárez-Alvarez's answer I see how badly phrased my question was, and decided to rewrite it. The drawback is that some comments of Martin Brandenburg are now inc... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/144314/orthogonal-vectors-question?answertab=votes | # Orthogonal vectors question
Can orthogonal vectors have some values that are the same? such as are (1,2,5) and (1,2,-5). orthogonal as the dot product is zero?
Thanks in advance!
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These two are not orthogonal :) – Artem May 12 '12 at 19:17
1
$(1,2,5) \cdot (1,2,-5) = 1 + 4 -25 = -20 \ne 0$, so they arent orthogo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/114691/natural-relations-between-substitutions | ## Natural relations between substitutions
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Consider two contexts $\Gamma,\Delta$ (from some background type theory), and substitutions $s_1,s_2:\Gamma\rightarrow \Delta$. In the case of $1$-element contexts, we g... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/352/volatility-pumping-in-practice?answertab=active | # Volatility pumping in practice
The fascinating thing about volatility pumping (or optimal growth portfolio, see e.g. here) is that here volatility is not the same as risk, rather it represents opportunity. Additionally it is a generic mechanical strategy that is independent of asset classes.
My question:
Do you kno... | {"extraction_info": {"found_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/8809/is-every-subgroup-of-an-algebraic-group-a-stabilizer-for-some-action/8831 | ## Is every subgroup of an algebraic group a stabilizer for some action?
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Suppose G is an algebraic group (over a field, say; maybe even over ℂ) and H⊆G is a closed subgroup. Does there necessarily exist an action... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2008/05/06/associativity-in-series-i/?like=1&source=post_flair&_wpnonce=a832ba55c5 | # The Unapologetic Mathematician
## Associativity in Series I
As we’ve said before, the real numbers are a topological field. The fact that it’s a field means, among other things, that it comes equipped with an associative notion of addition. That is, for any finite sum we can change the order in which we perform 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 30, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/184679/when-does-n-divide-ad1/184702 | # When does $n$ divide $a^d+1$?
$\newcommand{\ord}{\operatorname{ord}}$
For what values of $n$ will $n$ divide $a^d+1$ where $n$ and $d$ are positive integers?
Apparently $n$ can not divide $a^d+1$ if $\ord_n a$ is odd.
If $n\mid (a^d+1)\implies a^d\equiv -1\pmod n\implies a^{2d}≡1\pmod n \implies\ord_na\mid 2d$ bu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/27578/why-do-non-equioriented-asubn-sub-quivers-have-singularities-identical-to-the | ## Why do non-equioriented A<sub>n</sub> quivers have singularities identical to the singularities of Schubert varieties?
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In the general case, quiver cycles are of the form of orbit closures of $GL\cdot V_{\vec{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": 28, "mathjax_display_tex": 0, "mathjax_asciimath": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/tagged/homework+vector-calculus | # Tagged Questions
3answers
842 views
### Finding unit tangent, normal, and binormal vectors for a given r(t)
For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$. I've got Mathematica, but I've never used it before and I'm not sure how to coerce ... | {"extraction_info": {"found_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/advanced-algebra/192308-what-dimension-solution-set-nonhomogeneous-equation-system.html | # Thread:
1. ## What is the dimension of the solution set of a nonhomogeneous equation system?
I thought its dimension is equal to the dimension of the solution set of the same homogenous system. Am I right?
2. ## Re: What is the dimension of the solution set of a nonhomogeneous equation system?
Not necessarily. We... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/70748/model-of-a-group-in-category-of-rings/173613 | # Model of a group in category of rings
I'm curious, is a model for a theory of groups (in the sense of Lawvere's algebraic theories) in the category of rings a group ring? Similarly, is a model for a theory of rings in the category of groups a group ring?
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## 3 Answers
To address the question in a comment, there ... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/44430/momentum-and-energy-problem?answertab=active | # Momentum And Energy Problem
The information to the question is, "A $59.0~kg$ boy and his $38.0~kg$ sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity $3.00~m/s$ toward the west. Ignore friction."
The specific question I am working on 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": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/36034?sort=newest | ## Mod l local Galois representations (l different from p)
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My question is referred to the statement and proof of Prop. 2.4 of Diamond's article "An extension of Wiles' Results", in Modular Forms and Fermat Last 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": 26, "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/51886/hamiltons-equations-for-a-simple-pendulum | # Hamilton's equations for a simple pendulum
I don't get how to use Hamilton's equations in mechanics, for example let's take the simple pendulum with $$H=\frac{p^2}{2mR^2}+mgR(1-\cos\theta)$$ Now Hamilton's equations will be: $$\dot p=-mgR\sin\theta$$ $$\dot\theta=\frac{p}{mR^2}$$ I know one of the points of Hamilton... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2009/09/23/ | # The Unapologetic Mathematician
## Directional Derivatives
Okay, now let’s generalize away from partial derivatives. The conceptual problem there was picking a bunch of specific directions as our basis, and restricting ourselves to that basis. So instead, let’s pick any direction at all, or even more generally 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 38, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/08/17/associated-metric-spaces-and-absolutely-continuous-measures-ii/?like=1&source=post_flair&_wpnonce=3fdfac1636 | # The Unapologetic Mathematician
## Associated Metric Spaces and Absolutely Continuous Measures II
Yesterday, we saw that an absolutely continuous finite signed measure $\nu$ on a measure space $(X,\mathcal{S},\mu)$ defines a continuous function on the associated metric space $\mathfrak{S}$, and that a sequence of su... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 55, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/48655-question-about-proof-prime-number-theorem.html | # Thread:
1. ## A question about proof of prime number theorem
The following is the basic steps in one proof of the prime number theorem (many steps are left out)
$\pi(x)\sim \frac{x}{\ln(x)}\quad\text{iff}\quad \psi(x)\sim x$
Now,
$\psi_0(x)=-\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\zeta'(s)}{\zeta(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": 34, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/2701-div-grad-curl.html | Thread:
1. div, grad, curl
I have the following query:
I need to verfiy:
curl(AxB) = (B. $\nabla$)A - B(divA) - (A. $\nabla$)B + A(divB)
for A=(1,0,0) and B=(x,y,z).
I can do the left side and the div terms of the right side but I am unsure of how to go about working out the other two terms with the $\nabla$ in 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": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/61404?sort=oldest | ## Intersection probability for ‘N’ fixed-length rods in one- or two-dimensions
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Please consider the case where I have 'N' rods of length L (and width W) placed on a one- or two-dimensional surface with dimensions... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/tagged/locales | ## Tagged Questions
1answer
58 views
### On the openness of the map X^I -> X * X.
Hello ! Let $X$ be a locale or a topological spaces. $I$ denote the unit interval of the real numbers, and $X^I$ the space of function from $I$ to $X$ (The locale exponential if \$ …
0answers
211 views
### Are $\infty$-topoi determine... | {"extraction_info": {"found_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://math.stackexchange.com/questions/81119/compare-light-volume-of-two-light-bulbs-with-different-degree-spreads | # Compare light volume of two light bulbs with different degree spreads
I got two light bulbs, they are the same, but one spreads the light with an angle of 45 degrees, while the other 60 degrees.
I have measured their lux from a height of 1 meter, starting right below the light bulb an, then measured again, walking ... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Gauss's_law | # Gauss's law
This article is about Gauss's law concerning the electric field. For analogous laws concerning different fields, see Gauss's law for magnetism and Gauss's law for gravity. For Gauss's theorem, a mathematical theorem relevant to all of these laws, see Divergence theorem.
Electromagnetism
• Coulomb's law
•... | {"extraction_info": {"found_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": 35, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/119830?sort=newest | ## combinatorial lemma (is it well-known?)
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The following should be something well?-known, but i haven't seen it anywhere, neither have i met any references about.
Let $M^{n}$ be a $n$-dimensional oriented closed... | {"extraction_info": {"found_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://mathoverflow.net/questions/86549?sort=oldest | ## Schottky locus in genus 2
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Let $\phi_g : \mathcal{M}_g \rightarrow \mathcal{A}_g$ be the period mapping from the open moduli space of genus $g$ Riemann surfaces to the moduli space of $g$-dimensional principall... | {"extraction_info": {"found_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://mathoverflow.net/questions/92996/conjugate-function-for-matrix-mixed-norm/93251 | ## conjugate function for matrix mixed norm
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I am familiar with the conjugate function of the vector norm, which uses the concept of dual norm and is defined as follows:
$\|\mathbf{y}\|_p^*=\max_{\mathbf{x}}\left... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/260969/find-the-number-of-homomorphisms/260971 | # Find the number of homomorphisms
In each of the following examples determine the number of homomorphisms between the given groups:
$(a)$ from $\mathbb{Z}$ to $\mathbb{Z}_{10}$;
$(b)$ from $\mathbb{Z}_{10}$ to $\mathbb{Z}_{10}$;
$(c)$ from $\mathbb{Z}_{8}$ to $\mathbb{Z}_{10}$.
Could anyone just give me hints for... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://regularize.wordpress.com/category/math/regularization/ | # regularize
Trying to keep track of what I stumble upon
### Regularization
Archived Posts from this Category
March 26, 2013
## OPTPDE – A Collection of Problems in PDE-Constrained Optimization
Posted by Dirk under Math, Optimization, Regularization | Tags: Basis pursuit denoising, ill-posed problems, Optimal con... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 585, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/10220/can-the-speed-of-light-become-complex-inside-a-metamaterial/10900 | # Can the speed of light become complex inside a metamaterial?
The speed of light in a material is defined as $c = \frac{1}{\sqrt{\epsilon \mu}}$. There are metamaterials with negative permittivity $\epsilon < 0$ and permeability $\mu < 0$ at the same time. This leads to a negative refractive index of these materials.... | {"extraction_info": {"found_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://letterstonature.wordpress.com/category/statistics-and-metrics/ | # Letters to Nature
Feeds:
Posts
Comments
## How to win at the races
I’ve rambled about this before, but with the Melbourne Cup - “the race that stops a nation” – a few days away and Tom Waterhouse’s annoying face on TV too often, it’s worth repeating.
Don’t bet on the horse you think will win!
More precisely, don... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 32, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Weighing | # Weight
(Redirected from Weighing)
This page is about the physical concept. In law, commerce, and in colloquial usage weight may also refer to mass. For other uses see weight (disambiguation).
A spring scale measures the weight of an object.
SI unit: newton (N)
Derivations fr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/2672/calculation-of-the-cross-section | # Calculation of the cross section
Why, when we calculate the total cross section, we make the average other initial states and the sum over final states?
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## 2 Answers
The summing over final states and the averaging over initial states is a good observation that I always emphasize as the origin of the arrow of ti... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/280879/hypercube-problem?answertab=active | Hypercube problem
$B$ is an n-dimensional hypercube, considered as undirected graph. Let $A$ be a subset of the vertices of $B$ such that $|A| \gt 2^{n-1}$.
Let $H$ is a subgraph of $B$ induced by $A$. Prove that $H$ has at least $n$ edges.
Any help, would be greatly appreciated.
-
Why does it seem like a Ramsey-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": 34, "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/258879/how-many-fractional-digits-do-i-need-to-represent-a-number-of-base-m-in-base | # How many fractional digits do I need to represent a number of base $m$ in base $n$?
I have authored a web application RADIX, which for further optimisation needs to calculate the maximum number of places necessary to precisely represent the fraction part of a number of base $m$ in base $n$ (assuming a precise conver... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 177, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/138584/multiplication-of-taylor-series-expanding-2x-sinx | # Multiplication of Taylor series - expanding $2x\sin(x)$
I'm working on a problem for university Calculus 2. We're talking about Taylor series right now and I need to approximate an integral using one of a function that I think it should be easy to produce a series for, but I'm not 100% sure. This is the function:
$... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/10495/could-extra-dimensions-be-or-become-clustered/10505 | # Could extra dimensions be or become clustered?
String theory - for example - requires extra spatial dimension. Say for example in 10 dimensional string theory, what theoretically prevents clustering of the extra 6 dimensions in 2 timeless 3 dimensional (infinite) spaces?
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## 1 Answer
I will here only comment on ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 32, "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/6020/many-time-pad-attack/6026 | # Many time pad attack
I've already sent my correct solution to a programming question on an online class:
Let us see what goes wrong when a stream cipher key is used more than once. Below are eleven hex-encoded ciphertexts that are the result of encrypting eleven plaintexts with a stream cipher, all with the same st... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=4191522 | Physics Forums
## Can anyone give a common-sense explanation of singular values?
I've been reading a few mathematical definitions and I'm still not sure I grasp their significance. If Ax = b, then what do the singular values of A represent in terms of x and b? Why are they important?
I'm not looking for a formal def... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/1903/what-is-the-connection-between-default-probabilities-calculated-using-the-credit/4526 | # What is the connection between default probabilities calculated using the credit rating and the price of a CDS?
I'm working on a tool to price Credit Default Swaps. I've already done the standard pricing tools. I'm working on a pricing tool which uses the credit rating for the default probabilities used in the prici... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/114310/how-to-find-error-bounds-of-trapezoidal-rule/114314 | # How to find Error Bounds of Trapezoidal Rule?
I stack about Error Bounds of Trapezoidal Rule. The question says
How large should $n$ be to guarantee the Trapezoidal Rule approximation for $\int_{0}^{\pi}x\cos x\,dx$ be accurate to within 0.0001 ?
I used $|E_{T}| <= \frac{K(b-a)^3}{12n^2}$ On the process of this 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": 56, "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/291663/mean-value-theorem-help | Mean value theorem help?
So I am learning this chapter "mean value theorem", and there is an exercise.
Prove the inequality of $e^{x} \gt x+1$ for $x$ different from zero and the inequality of $2x \arctan x \ge \ln (x^2+1)$... I feel very retarded every time I read this exercise because I don't understand what theore... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 50, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/70339?sort=votes | ## Stone-Weierstrass theorem applied to Fourier series
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This is a question on Fourier series convergence. The problem is, in the applications of the Stone Weierstrass approximation theorem on wikipedia, there's st... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/202113/proof-of-chinese-remainder-theorem-for-ring | # proof of chinese remainder theorem for ring
Let $R$ be a ring(not necessary have "1") and let $I,J$ be ideals of $R$ such that $I+J=R$. I want to prove that there is a $x\in R$ such that $$x\equiv r ({\rm mod} I) \quad x \equiv s ({\rm mod} J) \quad \mbox{for any} ~~~r,s\in R$$
I prove that since $I+J=R$ $$r=r_i+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": 31, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/10.4153/CJM-2006-042-0 | Canadian Mathematical Society
www.cms.math.ca
| | | | |
|----------|----|-----------|----|
| | | | | | |
| Site map | | | CMS store | |
location: Publications → journals → CJM
Abstract view
# Partial $*$-Automorphisms, Normalizers, and Submodules in Monoton... | {"extraction_info": {"found_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": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/53742/frequency-of-an-electron | # Frequency of an Electron
My question is very simple. If frequency is defined as the cylces per unit time, Then what is meant by "Frequency of an Electron" ? If the rotation of electron around a nucleus is considered then, Which phenomena we consider for a free electron i.e: electron in a force field (unstable alone ... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/6114/ggm-prg-construction-why-do-we-need-to-change-keys-all-the-time-with-underlying/6141 | # GGM PRG construction: Why do we need to change keys all the time with underlying PRG
When constructing a PRF that has n bit input using the GGM PRG, why do we always have to recursively run the PRG using its previous output as a seed key n times. Instead, why don't we run the PRG n times, and use that as the output.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/51294/supervenience-in-mathematics/51295 | ## Supervenience in mathematics
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I'm not quite sure if this is the right place to ask, and if this is the right way to ask, but I dare.
In philosophy (of mind, e.g.) the concept of supervenience is used:
"Superv... | {"extraction_info": {"found_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/43771/find-the-quantity-of-charge-given-potential-function?answertab=active | Find the quantity of charge - given potential function
A potential function is given by $V(r)=\frac{Ae^{-\lambda r}}{r}$ Find charge density and hence charge.
I first took the gradient of potential to get $\vec{E}(r)=\frac{Ae^{-\lambda r}}{r}[\lambda+\frac{1}{r}] \hat{r}$
Now using Gauss's law $\nabla \cdot \vec{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": 17, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathbabe.org/2012/11/15/columbia-data-science-course-week-11-estimating-causal-effects/ | # mathbabe
Exploring and venting about quantitative issues
Home > data science, math education, open source tools, statistics > Columbia Data Science course, week 11: Estimating causal effects
## Columbia Data Science course, week 11: Estimating causal effects
November 15, 2012
The week in Rachel Schutt’s Data Scie... | {"extraction_info": {"found_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": 47, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/69800-tricky-question.html | Thread:
1. Tricky question
Morning Forum I am having issues with the following question any help would be appreciated:
Attached Thumbnails
2. Originally Posted by AlgebraicallyChallenged
Morning Forum I am having issues with the following question any help would be appreciated:
It might help if you write
$f\circ g(... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/32623?sort=votes | ## behavior of places of a function field under automorphism
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if $P_{1}$ and $P_{2}$ are distinct places of equal degree of the function field F/K, and $\sigma$ is a K-field automorphism, such that $\sigma(P_{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": 28, "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/21260/lim-limits-x-to-infty-frac-ln1000-xx5/21269 | $\lim\limits_{x \to \infty}\frac{\ln^{1000} x}{x^5}$
I'm trying to solve $$\lim\limits_{x \to \infty}\frac{\ln^{1000} x}{x^5}$$ Here's what I get: $$e^{\lim\limits_{x \to \infty}\ln{\frac{\ln^{1000}x}{x^5} }}$$ Dropping the $e$ for ease, $$\lim\limits_{x \to \infty} 1000\ln{(\ln{(x)})} - 5 \ln{x}$$
Now I have $\infty... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/159169/flipping-cards-probability | # Flipping Cards Probability
You have a deck of cards, 26 red, 26 black. These are turned over, and at any point you may stop and exclaim "The next card is red.". If the next card is red you win £10.
What's the optimal strategy? Prove this is the optimal strategy.
I feel like the optimal strategy is whenever you are... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/21999/list | ## Return to Answer
2 know--> no; currently known--> known
One way to answer this question is as follows: Ramanujan's conjecture is a special case of a much more general conjecture that any cuspdial automorphic representation of $GL_n$ over a number field is tempered. This is a technical but fundamental notion, 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": 18, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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