MathOverflow Questions, Problems & Solutions : TransWikia.com ~ Page 19

What is the definition of the thermodynamic limit of a thermodynamic quantity?

Statistical mechanics is all about taking thermodynamic limits and, as far as I know, there are more than one way to define such limits. Consider the following theorem: Theorem: In...

Asked on 11/09/2021

1 answer

Solvable Lie algebra whose nilradical is not characteristic

Say that an ideal in a Lie algebra is characteristic if it is invariant under every derivation of the algebra.It is well known that the nilradical of a finite-dimensional Lie...

Asked on 11/07/2021 by David Towers

1 answer

Latent Dirichlet allocation and properties of digamma function

In the paper Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent Dirichlet Allocation. Journal of Machine Learning Research, 3(4–5), 993–1022. http://www.jmlr.org/papers/volume3/blei03a/blei03a.pdf let ...

Asked on 11/07/2021 by sunxd

1 answer

Existence of a subcover with large boundary

Let $mathscr{C}$ be a cover of $mathbf{N}={1,2,dotsc,N}$ by finite subsets $Sin mathscr{C}$ with $2leq |S|leq K$, where we write $|S|$ for the number of elements...

Asked on 11/07/2021

0 answer

Computing the integral $int_{-1}^1 dx , |x| J_0(alpha sqrt{1 - x^2}) P_ell(x)$

I would like to compute the following integral: $$I_ell(alpha) := int_{-1}^1 dx , |x| J_0(alpha sqrt{1 - x^2}) P_ell(x)tag{1}label{1}$$ where $alpha geq 0$, ...

Asked on 11/07/2021 by JCGoran

1 answer

Variance of random variable decreasing in parameter

I did quite a few numerical computations and think the following is true, but I cannot prove it: Let $varphi(x):=sum_{i=1}^n varphi_i(x_i)$ where $x=(x_1,...,x_n) in mathbb{R}^n$ and ...

Asked on 11/07/2021

1 answer

How to solve a system of quadratic equations?

Suppose we have a system of $p$ quadratic equations about $mathbf{x} in mathbb{R}^3$ and $mathbf{x} > 0$ $$ left{ begin{array}{lr}...

Asked on 11/07/2021 by heng

0 answer

There is no general method to construct n-regular polygon such that the given n-polygon inscribed the n-regular polygon

Conjecture 1: With $nge 5$, given general n-polygon, there is no general method to construct n-regular polygon such that the given n-polygon inscribed the n-regular polygon (with one and...

Asked on 11/07/2021 by Đào Thanh Oai

1 answer

English translation of "Une inégalité pour martingales à indices multiples et ses applications"

Does anyone know of a English translation of "Une inégalité pour martingales à indices multipleset ses applications" by Renzo Cairoli. Or could translate the statement of the martingale convergence...

Asked on 11/07/2021

1 answer

There is a 3-connected 5-regular simple $n$-vertex planar graph iff $n$ satisfies....?

Is there any characterization on the set of integers $n$ such that there is a 3-connected 5-regular simple $n$-vertex planar graph?...

Asked on 11/07/2021 by Xin Zhang

2 answer

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