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http://mathoverflow.net/questions/55867?sort=oldest | ## The canonical divisor of the Hilbert scheme $Hilb^n P^2$?
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Hey everyone,
I was wondering if anyone knows what the canonical divisor of the Hilbert scheme $Hilb^n P^2$ is --$Hilb^n P^2$ is the Hilbert scheme 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": 14, "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/29652/what-are-the-most-elegant-proofs-that-you-have-learned-from-mo | ## What are the most elegant proofs that you have learned from MO?
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One of the things that MO does best is provide clear, concise answers to specific mathematical questions. I have picked up ideas from areas 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": 43, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://all-science-fair-projects.com/science_fair_projects_encyclopedia/Sound | # 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": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/43028/symmetries-of-spacetime-and-objects-over-it | # Symmetries of spacetime and objects over it
I guess according to mathematical didactic, we first think of spacetime as a set and we reason about elements of its topology and then it's furthermore equipped with a metric. Appearently it is this Riemannian metric, which people consider to be the object, which induced 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": 9, "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/115636/properties-of-permutations-with-unknown-pattern-avoidance-descriptions/116699 | ## Background
Many properties of permutations can be stated in terms of classical patterns. For example:
• a permutation is stack-sortable if and only if it avoids 231 (Knuth 1975)
• a permutation corresponds to a smooth Schubert variety if and only if it avoids 1324 and 2143 (Lakshmibai and Sandhya 1990)
For other ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/109140-differentiability.html | # Thread:
1. ## Differentiability
I don't understand this question. Could I get some help with it. (Problem is attached)
Thanks
Attached Thumbnails
2. It asks you to prove that the derivative of f(x,y) in (0,0) in the direction of a generic vector v (directional derivative) exists. You can do this thinking of v as ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/129824-unbiased-estimator-theta.html | # Thread:
1. ## unbiased estimator of theta
I'm trying to find an estimator for $\theta.$ I have the following facts:
Where $v_{ij}$ is a matrix that was obtained by multiplying a standard normal matrix and an unspecified data matrix.
$P(sign(v_{1j}) = sign(v_{2j})) = 1 - \frac{\theta}{\pi}$
My problem is how 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/20717/how-to-find-solutions-of-linear-diophantine-ax-by-c/20727 | # How to find solutions of linear Diophantine ax + by = c?
I want to find a set of integer solutions of Diophantine equation: $ax + by = c$, and apparently $gcd(a,b)|c$. Then by what formula can I use to find $x$ and $y$ ?
I tried to play around with it:
$x = (c - by)/a$, hence $a|(c - by)$.
$a$, $c$ and $b$ are 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": 77, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/269032/understanding-two-similar-definitions-frechet-urysohn-space-and-sequential-spac | # Understanding two similar definitions: Fréchet-Urysohn space and sequential space
Here are the definitions:
Fréchet-Urysohn space: A topological space $X$ where for every $A \subseteq X$ and every $x \in \text{cl}(A)$, there exists a sequence $(x_{n})_{n \in \mathbb{N}}$ in $A$ converging to $x$.
Sequential space:... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-topics/199962-geometric-sequences-how-find-maximum-value.html | # Thread:
1. ## Geometric Sequences - How to find maximum value
This question legitimately confuses me.
I found that the formula for a geometric sequence is An=1800 x 0.9^(n-1)
How does one calculate the maximum value from that, however?
I do not understand how there is a maximum value for geometric sequences.
2. ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/112555/lp-and-l-infty | # $L^p$ and $L^\infty$
So I am trying to prove that for a set $E$ of finite measure, and for $1 \leq p < \infty$, $||f||_p \leq (m(E))^{1 - 1/p}||f||_{\infty}$. But I think I have proved the wrong thing. Can you help me see where I went wrong?
My proof is something like
$$||f||_p =\left(\int_E |f|^p\right)^{1/p} \le... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/167346/implicit-differentiation-question | # Implicit differentiation question
Differentiate given
$$\frac{y}{x-y}=x^2+1$$
Initially I wanted to use the quotient rule to solve this, but then I tried differentiating it as it is:
$$\frac {y_\frac{dy}{dx}}{1-y_\frac{dy}{dx}}=2x$$
$$\frac{dy}{dx}(y y^{-1})=2x$$
$$\frac{dy}{dx}=\frac{2x}{yy^{-1}}$$
$$\frac{dy... | {"extraction_info": {"found_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": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/114801/normal-subgroups-of-free-products | ## Normal Subgroups of Free Products
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Let $G=A\ast \mathbb{Z}$ be the free product of a group $A$ and the cyclic group $\mathbb{Z}$ and suppose $K$ is a subgroup of $G$. By Kurosh Subgroup Theorem we know that $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": 31, "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/294660/trying-to-prove-let-e-be-a-hilbert-a-module-then-e-langle-e-e-rangle-i | # Trying to prove: Let $E$ be a Hilbert $A$-module. Then, $E\langle E,E\rangle$ is norm dense in $E$.
Let $E$ be a Hilbert $A$-module. Then, $E\langle E,E\rangle$ is norm dense in $E$.
I am having trouble proving this. I believe $\langle E,E\rangle$ is a $C^*$-algebra. If I can show this, then the proof is easy since... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "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/117156/generators-and-subgroups-of-mathbf-z-15 | # Generators and subgroups of $\mathbf Z_{15}$
Could you help me with following excercise?
Find all generators of additive group Z15.
Find all sub-groups of additive group Z15.
Could you please explain how to do that and post a solution?
Thanks, Mark
-
1
In case this is a homework, please add the tag `(homework)... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/9981?sort=newest | ## Coarse moduli spaces over Z and F_p
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I would like to know to what extent it is possible to compare fibers over $\mathbb{F}_p$ of coarse moduli spaces over $\mathbb{Z}$, and coarse moduli spaces over $\mathbb{F}... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/27589/convert-state-vectors-to-bloch-sphere-angles?answertab=votes | # Convert state Vectors to Bloch Sphere angles
I think this question is a bit low brow for the forum. I want to take a state vector $\alpha |0\rangle + \beta |1\rangle$ to the two bloch angles. What's the best way? I tried to just factor out the phase from $\alpha$, but then ended up with a divide by zero when trying ... | {"extraction_info": {"found_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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=472541 | Physics Forums
## Kinetics of Particles work and energy; A moving car
1. The problem statement, all variables and given/known data
The 2Mg (i assumed mega-gram, not sure if that is the correct term) car has a velocity of v= 100km/h when the driver sees an obstacle in front of the car.
If it takes 0.75 s for him 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": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/48951-what-perpendicular-distance-pt-5-4-line-y-1-2x-6-a.html | # Thread:
1. ## What is the perpendicular distance from the pt 5, 4 to the line y = 1/2x + 6?
The title pretty much explains the question:
What is the perpendicular distance from the pt 5, 4 to the line y = 1/2x + 6?
If you could please tell the answer and explain how you got there that would be great. thanks
2. L... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 23, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/53465/what-is-the-proof-that-a-force-applied-on-a-rigid-body-will-cause-it-to-rotate-a/53696 | # What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass?
Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating about an axis 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": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikiversity.org/wiki/Advanced_elasticity/Stress-strain_relation_for_thermoelasticity | # Advanced elasticity/Stress-strain relation for thermoelasticity
From Wikiversity
Relation between Cauchy stress and Green strain Show that, for thermoelastic materials, the Cauchy stress can be expressed in terms of the Green strain as $\boldsymbol{\sigma} = \rho~\boldsymbol{F}\cdot\frac{\partial e}{\partial \bo... | {"extraction_info": {"found_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": 16, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/39042/proving-function-for-stirling-numbers-of-the-second-kind?answertab=active | # Proving function for Stirling Numbers of the Second Kind
I need to proof the following formula for Stirling Numbers of the Second Kind:
$\sum\limits_{n \geq 0} S(n,k) x^n = \frac{x^k}{(1-x)(1-2x)\cdots(1-kx)}$
It is used widely around formularies but I neither have found any proof nor was I able to figure it out o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "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/145248/limits-problem-in-integration | # Limits problem in Integration
please look at the following question,
Let $X$ denote the diameter of an armored electric cable and $Y$ denote the diameter of the ceramic mold that makes the cable. Both $X$ and $Y$ are scaled so that they range between $0$ and $1$. Suppose that $X$ and $Y$ have the joint density
$$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": 68, "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/189127/what-is-bayes-theorem-in-simplest-way | # What is Baye's Theorem in simplest way
I am currently planning to take a course on artificial intelligence, there Bayes theorem is the basic. Now I tried to understand bayes theorem so many times. But to understand that I have to understand conditional probability, joint probability and total probability. So can any... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/55865/why-does-this-method-for-solving-matrix-equations-work | Why does this method for solving matrix equations work?
I have this assignment:
Given:
$A = \begin{pmatrix} 2 & 4 \\ 0 & 3 \end{pmatrix}$
$C = \begin {pmatrix} -1 & 2 \\ -6 & 3 \end{pmatrix}$
Find all B that satisfy $AB = C$.
I know that one option is to say $B = \left( \begin{smallmatrix} a & b \\ c & d \end{sma... | {"extraction_info": {"found_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": 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=107476 | Physics Forums
## Applications of Integration-Volume
I'm asked to find the volume generated by rotating the region bounded by the given curves about the y-axis (using the method of cylindrical shells).
I'm given the functions $$y= 4(x-2)^2$$and $$y = x^2 - 4x +7$$.
I'm not sure how to word this properly...they don'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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.mathplanet.com/education/pre-algebra/probability-and-statistic/combinations-and-permutations | # Combinations and permutations
Before we discuss permutations we are going to have a look at what the words combination means and permutation. A Waldorf salad is a mix of among other things celeriac, walnuts and lettuce. It doesn't matter in what order we add our ingredients but if we have a combination to our padloc... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/19264/what-is-the-etymology-for-the-term-conductor | ## What is the etymology for the term conductor?
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This is related to the previous question of how to define a conductor of an elliptic curve or a Galois representation.
What motivated the use of the word "conduct... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/104583/exponentiating-4-by-4-matrix-analytically | ## Exponentiating 4 by 4 matrix analytically
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Does there exist an analytical method by which i can exponentiate a 4 by 4 matrix, in the same way as the general 2 by 2 matrix case in pauli matrix basis. I have dira... | {"extraction_info": {"found_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/251839/probabilities-for-unknown-finite-population-from-sample?answertab=active | # Probabilities for unknown finite population from sample?
If i have a known population ($N$ marbles of which $M$ are black) and draw $n$ samples without replacement the probability to draw $x$ black marbles is given by the hypergeometric distribution.
Is there a way to get probabilities for the total number of black... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/208726-group-theory-question-print.html | # Group theory question
Printable View
• November 29th 2012, 03:07 PM
Ant
Group theory question
Hi,
Let $H_{1}, H_{2}, H_{3}$ be subgroups of a group $G$ under addition. Moreover suppose $x\in H_{1}, y\in H_{2}, x+y \in H_{3}$
I'm wondering if it then follows that $H_{1} = H_{2} = H_{3}$
Could anyone offer any hel... | {"extraction_info": {"found_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": 70, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/129361-vector-2-a.html | # Thread:
1. ## vector 2
the vector $\vec{a}=(2,3)$ is projected onto the x=axis. what is the scalar projection? what is the vector projection?
what are the scalar and vector projections when $\vec{a}$ is projected onto the y-axis
2. Originally Posted by william
the vector $\vec{a}=(2,3)$ is projected onto the x=ax... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://terrytao.wordpress.com/tag/covariance-matrices/ | 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 ‘covariance matrices’ tag.
## Random covariance matrices: Universality of local statistics of eigenvalues
9 December,... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/15611?sort=oldest | ## To prove the Nullstellensatz, how can the general case of an arbitrary algebraically closed field be reduced to the easily-proved case of an uncountable algebraically closed field?
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In his answer to a question ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 130, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://nrich.maths.org/6575/note?nomenu=1 | ## 'Fix Me or Crush Me' printed from http://nrich.maths.org/
### Why do this problem?
This problem gives students the opportunity to explore the effect of matrix multiplication on vectors, and lays the foundations for studying the eigenvectors and kernel of a matrix, ideas which are very important in higher level alg... | {"extraction_info": {"found_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://math.stackexchange.com/questions/253432/improving-newtons-iteration-where-the-derivative-is-near-zero/253466 | # Improving Newton's iteration where the derivative is near zero?
I'm implementing a root-solver for finding x coordinates of a function f(x), after I have an y-coordinate. The function is periodic, roughly sinusoidal with constant amplitude but non-linearly varying frequency; for an inverse I don't have a closed-form... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 43, "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/55021/list | ## Return to Answer
2 added 4 characters in body
Ian's answer is very elegant, but in case you're looking for a more computational approach, you could use the Seifert form. Namely, if you take a Seifert surface $\Sigma$ for a knot, look at the form $\Theta\colon H_1(\Sigma)\otimes H_1(\Sigma)\to \mathbb Z$ given by $... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2012/02/09/the-propagation-velocity-of-electromagnetic-waves/?like=1&source=post_flair&_wpnonce=420e8d64d7 | # The Unapologetic Mathematician
## The Propagation Velocity of Electromagnetic Waves
Now we’ve derived the wave equation from Maxwell’s equations, and we have worked out the plane-wave solutions. But there’s more to Maxwell’s equations than just the wave equation. Still, let’s take some plane-waves and see what 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 11, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/40526/list | ## Return to Answer
4 the editings overlapped, apparently, it should be fixed now, sorry...
Here is a quick sketch (probably it can be made much cleaner). Using an inductive argument it should not be difficult to reduce to studying the case that `$(X,<_1)$` is isomorphic to a cardinal, say $\kappa$. For convenience, ... | {"extraction_info": {"found_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/260249/finding-the-lengths-of-lines-outside-of-a-circle-when-theyre-not-tangent?answertab=active | # Finding the lengths of lines outside of a circle when they're not tangent
I recreated the question in paint above ^ The line is not tangent to the circle.
-
## 1 Answer
They're geometrically powers, so it must be that 5·29=x·7, assuming 5 and x are the lengths from the intersection point to the point in which 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://stats.stackexchange.com/questions/34100/joint-distribution-of-mid-p-value-and-p-value | # Joint distribution of mid p-value and p-value
I have a question about the joint distribution of the mid p-value and p-value.
We know that, for right tailed test with discrete test statistic $X$ with distribution $F$, the p-value is defined as $P=Pr(X \geq observed~X)$ and the mid p-value is defined as $mid~P=Pr(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": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2009/05/18/galois-connections/?like=1&_wpnonce=d19428bcb3 | # The Unapologetic Mathematician
## Galois Connections
I want to mention a topic I thought I’d hit back when we talked about adjoint functors. We know that every poset is a category, with the elements as objects and a single arrow from $a$ to $b$ if $a\leq b$. Functors between such categories are monotone functions, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 34, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/82685/presheaves-on-a-complete-segal-space | ## Presheaves on a complete Segal space
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Let C be an $(\infty,1)$-category, incarnated as a complete Segal space, hence in particular a bisimplicial set. Is there a model structure on the slice category of bisimpl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/91928/ultrafilters-on-the-set-of-semialgebraic-subsets-of-r2 | ## Ultrafilters on the set of semialgebraic subsets of R^2
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Let $R$ be a real closed field and $f: R \to R$ a map. Then let $\textrm{F}(f)$ be the set of semialgebraic subsets of $R^2$, which contain $(t,f(t))$ 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": 25, "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/tagged/speed-of-light?page=5&sort=newest&pagesize=30 | # Tagged Questions
The speed of light is fundamental universal constant that marks the maximum speed at which information can propagate. Its value is $299792458\frac{\mathrm{m}}{\mathrm{s}}$.
4answers
582 views
### What if we could give photons some mass?
I was reading an article and these paragraphs got me wonderi... | {"extraction_info": {"found_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://mathoverflow.net/questions/64362/linear-programming-with-a-matrix-of-decision-variables | Linear programming with a matrix of decision variables [closed]
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Is it possible to use linear programming when the decision variables are not simply a vector? For example, say I have $n$ countries and $m$ different po... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/48914/independent-families-of-subsets-of-mathbb-n-of-size-continuum/77276 | ## Independent families of subsets of $\mathbb N$ of size continuum
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A family $\mathcal F$ of subsets of $\mathbb N$ is independent if for any two finite, disjoint subsets $\mathcal A,\mathcal B\subseteq\mathcal 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": 81, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://scicomp.stackexchange.com/questions/3314/whats-a-good-numerical-optimization-software-package-for-solving-the-2-d-optima | # What's a good numerical/optimization software package for solving the 2-D optimal stopping problem?
I am looking for a numerical software package to help me solve the 2-dimensional "free boundary" PDEs that arise in optimal stopping problems. In one dimension a standard optimal stopping problem in Economics is when ... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/19065-functions-properties.html | Thread:
1. Functions and properties
Hi guys, im am so frustrated right now. I suck at discrete math. I dont understand it at all, the proffesor talks to fast. Im on the vergre of tears. Plus theres no tutoring for this class, and i really need help. right now i have two problems
1. suppose g: A--->B and f: B---> C 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/248358/why-is-korns-inequality-not-trivial | # Why is Korn's inequality not trivial?
Let $\Omega \subset \subset \mathbb{R}^N$ have smooth boundary, $N \geqslant 2$ and
$$\mathcal{E} ( v) := \int_{\Omega} \sum_{i, j} \varepsilon_{i j} ( v) \varepsilon_{i j} ( v) \mathrm{d} x := \int_{\Omega} \sum_{i, j} \left( \frac{v_{i, j} + v_{j, i}}{2} \right)^2 \mathrm{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": 26, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/acceleration+free-fall | # Tagged Questions
1answer
189 views
### Gravity and free fall
In Wikipedia it's stated that "[..] gravity, is the natural phenomenon by which physical bodies appear to attract each other with a force proportional to their masses". Then I found many examples ...
3answers
233 views
### when an object moves downward,... | {"extraction_info": {"found_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://physics.stackexchange.com/tags/density/hot | # Tag Info
## Hot answers tagged density
14
### Why does a black hole have a finite mass?
If something is infinitely dense, must it not also be infinitely massive? Nope. The singularity is a point where volume goes to zero, not where mass goes to infinity. It is a point with zero volume, but which still holds mass,... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/109570?sort=oldest | ## Can the level set of a critical value be a regular submanifold?
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I know that there is a theorem that a non-empty level set of a regular value of a smooth function $f:M\rightarrow\mathbb{R}$ on a smooth manifold... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/115375?sort=oldest | ## Algebraic maximal extension and algebraic closure
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Let $K$ be a valued field. We say that $K$ is algebraic maximal if any algebraic extension of $K$ has either a bigger value group or a bigger residue field. Un... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/02/12/properties-of-irreducible-root-systems-iii-2/?like=1&source=post_flair&_wpnonce=f9365a8c97 | # The Unapologetic Mathematician
## Properties of Irreducible Root Systems III
Today we conclude with our series of lemmas on irreducible root systems.
If $\Phi$ is irreducible, then roots in $\Phi$ have at most two different lengths. Here I mean actual geometric lengths, as measured by the inner product, not the “l... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 39, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/1647-big-test-question.html | Thread:
1. Big test question
Well, my math teacher gave us this question that he told us would be on the math test tomarow. Im not too sure how to do it but I have an idea.
An underground cable runs from (-20,35) to (-10,-25). Jessica's house is at (40,5). Determine the shortest distance of cable required to connect... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/21527/equivalence-principle-and-radiation-from-falling-particle | Equivalence principle and radiation from falling particle
I am currently having a hard time solving a problem of GR from Lasenby's book. I can't make it more clear than by quoting the exercise:
7.2 A charged object held stationary in a laboratory on the surface of the Earth does not emit electromagnetic radiation. If... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/41026/list | ## Return to Answer
2 clarified: integral curve -> trajectory of gradient
When a function is very close to flat, the trajectories tend to be very erratic and wandering. The answer is NO, even if linear bounds are specified on the derivatives of the function.
To be more specific: in the unit sphere, draw any smooth 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": 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/calculus/87221-solved-optimization-problem-cost-function.html | # Thread:
1. ## [SOLVED] optimization problem (cost function)
I can find the cost function, but I don't know how to find minimum cost. Which should = \$329.34
A rectangular storage container with an open top is to have a volume of 20 m^3. The length of its base is twice the width. Material for the base costs \$15 pe... | {"extraction_info": {"found_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": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/76857-multiple-integral.html | # Thread:
1. ## Multiple integral
Need helping starting this problem find the volume bound by $x+2z=4$ and $2y+z=2$ in the postive octant.
Will this be a triangle based pyramid?
2. I think it will be a square based pyramid, which mean it's volume is uniquely determined by it's base area and it's height.
$V=\frac{1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/revisions/61784/list | 2 retagged
1
# cohomology of BG, G compact Lie group
It has been stated in several papers that $H^{odd}(BG,\mathbb{R})=0$ for compact Lie group $G$. However, I've still not found a proof of this. I believe that the proof is as follows:
--> $G$ compact $\Rightarrow$ it has a maximal toral subgroup, say $T$
--> the 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": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.nag.com/numeric/cl/nagdoc_cl23/html/G13/g13dnc.html | # NAG Library Function Documentnag_tsa_multi_part_lag_corr (g13dnc)
## 1 Purpose
nag_tsa_multi_part_lag_corr (g13dnc) calculates the sample partial lag correlation matrices of a multivariate time series. A set of ${\chi }^{2}$-statistics and their significance levels are also returned. A call to nag_tsa_multi_cross_... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 105, "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/m... |
http://math.stackexchange.com/questions/213451/prove-that-w-frac-sqrtz2z1z2-3z2-analytic-on-z1 | # Prove that $w=\frac{\sqrt{z^2+z+1}}{z^2-3z+2}$ analytic on $|z|<1$
I've self-learning of a complex analysis course. My first difficulties are in analytic functions. In that book, that I learning from, there is no even one example on how proving such problem, like in the title:
Prove that $w=\frac{\sqrt{z^2+z+1}}{z^... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "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/4810/price-of-a-cash-or-nothing-binary-call-option?answertab=votes | # price of a “Cash-or-nothing binary call option”
I'm stuck with one homework problem here:
Assume there is a geometric Brownian motion \begin{equation} dS_t=\mu S_t dt + \sigma S_t dW_t \end{equation} Assume the stock pays dividend, with the cont. compounded yield $q$.
a) Find the risk-neutral version of the proces... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/210354-graph-problem-print.html | # Graph problem
Printable View
• December 26th 2012, 12:48 PM
Franek222
Graph problem
I have big problem to solve, could someone help :)
Prove or disprove: If $G$ is a k-edge-connected graph and $v,v_{1},v_{2},...,v_{k}$ are $k+1$ distinct vertices of $G$ then for $i = 1,2,...k$ there exist $v-v_{i}$ paths $P_{i}$ 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": 25, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/88955/is-there-a-right-adjoint-to-the-contravariant-functor-hom-b-in-the-category-of/88958 | ## Is there a right adjoint to the contravariant functor Hom(-,B) in the category of Sets
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi, I apologise if this is the wrong place for this question but i need to ask it somewhere. The question is whether the 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": 30, "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/67602/how-to-calculate-point-y-with-given-point-x-of-a-angled-line | # How to calculate point y with given point x of a angled line
I dropped out of school to early I guess, but I bet you guys can help me here. I've got a sloped line starting from point a(0|130) and ending at b(700|0).
I need an equation to calculate the y-coordinate when the point x is given, e.g. 300. Can someone he... | {"extraction_info": {"found_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://nrich.maths.org/6959/solution | Modular Fractions
We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.
Readme
Decipher a simple code based on the rule C=7P+17 (mod 26) where C is the code for the letter P from the alphabet. Rearrang... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 43, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/67134-triangle-inequality-problem.html | # Thread:
1. ## Triangle Inequality Problem
Triangle TUV has sides TU, UV, and VT. TU=6x - 11, UV=3x - 1, and VT=2x + 3. Describe the possible values of x.
Any help is appreciated. I've been trying to figure this one out for a while.
2. Originally Posted by jstark
Triangle TUV has sides TU, UV, and VT. TU=6x - 11, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/54412/combining-two-finite-number-fock-spaces-into-one?answertab=active | Combining two finite number fock spaces into one
Say I have two separate systems of identical Bosons, one with N Bosons the other with M. System one is described by a state $|\psi_1\rangle$ the other with $|\psi_2 \rangle$ which are expressed in a Fock space like
$|\psi_1\rangle = \sum_{n_1,...,n_{max}} \alpha(n_1,..... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/31384/what-are-the-computationally-useful-ways-of-thinking-about-killing-fields/31425 | ## What are the computationally useful ways of thinking about Killing fields?
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One definition of the Killing field is as those vector fields along which the Lie Derivative of the metric vanishes. But for very many... | {"extraction_info": {"found_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://www.chemeurope.com/en/encyclopedia/Gas_in_a_box.html | My watch list
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• Gas_in_a_box
# Gas in a box
In quantum ... | {"extraction_info": {"found_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": 36, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/5784/why-is-there-a-breakdown-in-kolmogorov-scaling-in-turbulence?answertab=votes | # Why is there a breakdown in Kolmogorov scaling in turbulence?
Why is there a breakdown of Kolmogorov scaling in turbulence? What causes intermittency?
-
## 1 Answer
The basic Kolomogorov theory is a mean-field theory -- dissipation rate is considered to be constant over the whole volume of liquid. While the dissi... | {"extraction_info": {"found_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://mathhelpforum.com/differential-geometry/115646-finite-infinite-sets-denumerable.html | # Thread:
1. ## finite and infinite sets...denumerable
Given Q is denumerable, such that R is not denumerable. Show now that R\Q is not denumerable.
2. Find injective map from the union of two countable sets to the naturals.
3. Problem: Given that $\mathbb{Q}\cong\mathbb{N}$ and $\mathbb{R}$ is not, prove that $\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": 66, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/88417-fourier-series-cosine.html | # Thread:
1. ## Fourier series cosine
Hello can anybody help me with this problem?
Find the even (cosine) extension of the function given in
Q. 6 as a Fourier-series. Write down, without making any calculations, the odd extension as a Fourier
This is the fuction given in question 6
f
(x) = sin (x)
0 (less than or 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/5277/determine-whether-a-number-is-prime?answertab=active | # Determine whether a number is prime
How do I determine if a number is prime? I'm writing a program where a user inputs any integer and from that the program determines whether the number is prime, but how do I go about that?
-
4
If you down vote my question please let me know why so that I can improve my question ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/12822/examples-of-class-group/12829 | # Examples of Class Group
I am trying to better understand how unique factorization of algebraic integers in an algebraic number ring implies that the class number of that number ring is 1.
I am asking for some examples of this to get me started.
-
## 3 Answers
I'm not sure what you mean by giving you examples... ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 70, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/291823/changing-1-cosx-x-to-avoid-cancellation-error-for-0-and/291843 | # Changing $(1-\cos(x))/x$ to avoid cancellation error for $0$ and $π$?
I have to change this formula: $$\frac{1-\cos(x)}{x}$$ so that I can avoid the cancellation error. I can do this for 0 but not for $π$. So I get: $$\frac{\sin^2(x)}{x(1+\cos(x))}$$ which for $x$ close to $0$ gets rid of the cancellation error. But... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/210352/boolean-simplification?answertab=votes | Boolean Simplification
I'm having some trouble getting a handle with this course. We are starting Boolean algebra and my professor wants us simplify the following:
(AB)'+(A'+B')'=
(AB)'+BC+A'B'C'=
I am assuming the "()" with "'" means the over-score above the variables.
Forgive my ignorance but my professor does 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": 6, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/51925-big-o.html | # Thread:
1. ## Big-O
Hello,
I'm totally confused by Big-O notation. This is the definition that I was given:
I don't understand how "k" fits into this equation. I also don't understand the significance of "C" or the relationship between the two constants (or witnesses).
I'm still thinking through this...
To prov... | {"extraction_info": {"found_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://nanoexplanations.wordpress.com/tag/rectangular-partitioning/ | the blog of Aaron Sterling
# Tag Archives: rectangular partitioning
## Polygon rectangulation wrap up
Posted on January 6, 2012
Tying up loose ends from my three posts in December about rectangulation of orthogonal polygons.
1. Derrick Stolee requested in a comment a resolution of the computational complexity of t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 14, "mimetex.cgi": 0, "/images/ma... |
http://en.wikisource.org/wiki/Page:A_Treatise_on_Electricity_and_Magnetism_-_Volume_1.djvu/375 | # Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/375
From Wikisource
280.] 333
SYSTEM OF LINEAR CONDUCTORS.
radius of the sphere must diminish in order to maintain the potential constant when the charge is allowed to pass to earth through the conductor.
In the electrostatic system, therefore, the 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": 30, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/48963/asymptotic-expansion-of-an-integral | ## Asymptotic expansion of an integral
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am looking for an asymptotic expansion of J(n)
$J(n)=\frac {2} {\pi} \int_{0}^{\pi/n} \prod_{k=1}^n \frac {\sin kx} {\sin x} dx$, $n=2,3,4,\dots$ The first approximation ... | {"extraction_info": {"found_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://rip94550.wordpress.com/2008/08/04/pca-fa-malinowski-summary/ | # Rip’s Applied Mathematics Blog
## PCA / FA Malinowski Summary
August 4, 2008 — rip
Malinowski’s work is considerably different from everything else we’ve seen before.
First of all, he expects that in most cases one will neither standardize nor even center the data X. We can do his computations as an SVD of X, 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 15, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/conservation-laws+energy | # Tagged Questions
2answers
142 views
### Perpendicular Elastic Collision (different masses, different velocities)
I'm stuck on a mechanics problem and I can't make any headway past momentum and kinetic energy being conserved. Here is the problem: Two hover cars are approaching an intersection from ...
5answers
172 ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/tagged/factorial+approximation | # Tagged Questions
0answers
37 views
### Bound on Permutations [duplicate]
I am trying to prove the following inequality, $$n^{(l)} = n(n-1)\cdots(n-l+1) \geq \frac{n^l}{e}\quad\text{ for }\quad 2 \leq l \leq \sqrt{n}\;.$$ So my approach is to observe that \$n^{(l)} = ...
0answers
40 views
### Approximation of fact... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/1605/what-functional-form-describes-the-implied-volatility-curve/1612 | # What functional form describes the implied volatility curve?
It is often convenient to parametrize the implied volatility curve to allow easy interpolation of volatility for any strike or maturity. What functional form describes the implied volatility curve for options at varying strikes and fixed maturity?
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1
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": 2, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/286911/condition-so-that-ypxyqxy-0-can-be-converted-in-a-ode-with-constant-c | # Condition so that $y''+p(x)y'+q(x)y=0$ can be converted in a ODE with constant coefficients
I have to find a necessary and a sufficient condition for the functions $p$ and $q$ so that the linear differential equation : $y''+p(x)y'+q(x)y=0$ can be converted in a linear differential equation with constant coefficients... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/semiclassical+quantum-gravity | # Tagged Questions
0answers
87 views
### Hawking radiation for closely orbiting black holes
Suppose we have two black holes of radius $R_b$ orbiting at a distance $R_r$. I believe semi-classical approximations describe correctly the case where $R_r$ is much larger than the average black body ... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/48044/matrix-operation-in-dirac-matrices/48184 | Matrix operation in dirac matrices
If we define $\alpha_i$ and $\beta$ as Dirac matrices which satisfy all of the conditions of spin 1/2 particles , p defines the momentum of the particle, then how can we get the matrix form ? \begin{equation} \alpha_i p_i= \begin{pmatrix} p_z & p_x-ip_y \\ p_x+ip_y & -p_z \end{pmatri... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://psychology.wikia.com/wiki/Principal_component_analysis | # Principal components analysis
Talk0
31,735pages on
this wiki
## Redirected from Principal component analysis
Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 116, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/revisions/6340/list | Return to Answer
2 corrected spelling
It's my understanding that the octonians aren't associative enough to have a projective plane in the usual sense. That is, you'd want to define $\mathbb{O}P^{2}$ as the collection of Cayley lines in $\mathbb{R}^{16}$. However, "Cayley lines" in $\mathbb{R}^{16}$ doesn't make sens... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 64, "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/247395/limiting-distribution-and-initial-distribution-of-a-markov-chain | # Limiting distribution and initial distribution of a Markov chain
For a Markov chain (can the following discussion be for either discrete time or continuous time, or just discrete time?),
1. if for an initial distribution i.e. the distribution of $X_0$, there exists a limiting distribution for the distribution of $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": 20, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://rosettacode.org/wiki/Matrix_arithmetic | # Matrix arithmetic
From Rosetta Code
Matrix arithmetic
You are encouraged to solve this task according to the task description, using any language you may know.
For a given matrix, return the determinant and the permanent of the matrix.
The determinant is given by
$\det(A) = \sum_\sigma\sgn(\sigma)\prod_{i=1}^n 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=3635350 | Physics Forums
## Left coset of a subgroup of Complex numbers.
1. The problem statement, all variables and given/known data
For H $\leq$ G as specified, determine the left cosets of H in G.
(ii) G = $\mathbb{C}$* H = $\mathbb{R}$*
(iii) G = $\mathbb{C}$* H = $\mathbb{R}$$_{+}$
3. The attempt at a solution
I have... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/100368?sort=newest | ## Idempotent homomorphisms of von Neumann algebras
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Is there any description of unital idempotent ($F^2(x)=F(x)$) morphisms of a von Neumann algebra into itself? Or, equivalently, of weakly closed subalgebras whi... | {"extraction_info": {"found_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/2686 | Gold Again
Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.
Pythagorean Golden Means
Show that the arithmetic mean, geometric mean and harmonic mean of a and b can be the lengths of the sides of a right-angles triangle if and only if a = bx^3, where x is 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": 7, "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/79681?sort=votes | ## Fourier transform of a real-valued function.
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My chemist roommate asked me the following question. Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a real-valued function and $F$ its 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": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://chempaths.chemeddl.org/services/chempaths/?q=book/Thermodynamics%3A%20Atoms%2C%20Molecules%20and%20Energy/2173/internal-energy | # Internal Energy
Submitted by jwmoore on Sat, 03/26/2011 - 11:42
When matterAnything that occupies space and has mass; contrasted with energy. absorbs or releases heatEnergy transferred as a result of a temperature difference; a form of energy stored in the movement of atomic-sized particles. energyA system's capaci... | {"extraction_info": {"found_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": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/tagged/integral-inequality+measure-theory | # Tagged Questions
1answer
67 views
### Prove that $L^1$ is a Banach algebra with multiplication defined by convolution
To be more specific, prove that $L^1(\mathbb{R}^n)$ with multiplication defined by convolution: $$(f\cdot g)(x)=\int_\mathbb{R^n}f(x-y)g(y)dy$$ is a Banach algebra. All the properties of Banach ...... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
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