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Feb
4
comment In a bipartite graph $G$ with bipartite sets $X$ and $Y$, prove that $\alpha'(G)=|X|-\max_{S \subset X}(|S|-|N(S)|) $
Could you please explain the notation $\alpha',N(S)$?
Jan
10
comment Zeilberger's determinant evaluation problem
Could you please present one of your spreadsheet examples?
Jan
7
awarded  Custodian
Jan
7
reviewed Approve suggested edit on Problem with simple Projectile motion formula
Jan
1
awarded  Yearling
Dec
22
awarded  Nice Answer
Dec
21
comment Gaussian process property
Whoops, dropped a $\sigma^2$, yep. In the multivariate case, the moments factor when everything is independent and has 0 covariance. Things become rather tricky if you have nonzero covariances. You'll need something akin to Isserlis's theorem: en.wikipedia.org/wiki/Isserlis%E2%80%99_theorem and even then you'll definitely have many cross-terms to deal with and I doubt something as elegant as the above would hold.
Dec
21
comment Gaussian process property
@gunbl4d3: You will need to relate the $k-2$ moment to the $k$ moment when $k$ is even. You'll need to perform integration by parts on $z^{k-2}e^{-z^2/2\sigma}$. As a hint, take $dv=z^{k-2}$, so $u=...$.
Dec
21
revised Gaussian process property
added 83 characters in body
Dec
21
comment eigenfunctions of hamiltonian in 'natural units'
@user108605: $\langle f_n,g_m \rangle= \overline{ \langle g_m,f_n \rangle}$, so if you consider one case such as $n>m$, then $n<m$ follows.You also need to know what $a_+f_n$ and $a_-f_n$ give in terms of $f_{n+1}$ and $f_{n-1}$ respectively.
Dec
21
answered Gaussian process property
Dec
21
answered what is a “Banach algebra” without the norm condition on a continuous multiplication?
Dec
21
answered eigenfunctions of hamiltonian in 'natural units'
Dec
17
comment Concrete Example of the Contraction Principle
@Lost: yes, just show that it's a contraction which means it must have a solution $f(x)=x$.
Dec
17
answered Concrete Example of the Contraction Principle
Dec
12
comment Can this ant find its way back to the nest?
For all intents-and-purposes, the ant nest intersects tangentially anywhere on a circle of radius 40ft from the current position of the ant. Then the naive solution would be to walk out 40ft to an arbitrary point and then traverse the circumference of the circle. However, this uses at worst 40+2\cdot \pi 40 ft which slightly exceeds 280ft. Try to somehow cover more ground, perhaps by stepping outside the circle.
Dec
12
answered Law of Large Numbers when $E|X|=\infty$
Dec
10
comment The limit of $ \displaystyle\lim_{n\to\infty} \exp(-1+\exp(-2+\exp(-3+\ldots\exp(-n)…)))$.
Here's a a half-hearted attempt to find the value of the limit, in the spirit of Ramanujan's nested square-roots: Define $F(x)=\exp(-1+x+\exp(-2+x+\exp(-3+\cdots)))$ to be the limit of the above expression with an extra parameter $x$. Then $\exp(F(x-1)+x-1)=F(x)$. Does anyone see a way to solve this functional equation? You could almost use Lambert's W function on this if we had $F(x)$ in the exponential instead.
Dec
10
comment power sum of $\sum_{n=1}^\infty 2^n x^{n^2}$
Write the sum as $\sum_{k=1}^\infty a_k x^k$ to apply the usual radius of convergence test.
Dec
10
comment True or false: Exchanging this limit and sum
@Did: Saw a left sided limit, whoops. Thanks for the correction!