MathOverflow Questions, Problems & Solutions : TransWikia.com ~ Page 36

Does the lemma remain valid in b-metric space?

Let $(X,d)$ be a complete metric space. $$CB(X)={A : A text{ is a nonempty closed and bounded subset of }X },$$$$D(A,B)=inf {d(a,b) : ain A ,...

Asked on 01/04/2021 by Seddik Merdaci

0 answer

A determinant identity

The following identity involving determinants essentially appears in E.L. Ince's book on Ordinary Differential Equations: Let $A$ be an $n times n$ matrix, $n geq 3$. Denote...

Asked on 01/04/2021 by Vassilis Papanicolaou

1 answer

Extending continuous functions from dense subsets to quasicompacts

$DeclareMathOperatorcl{cl}$I am interested under what assumptions one can always extend continuously a function defined on a dense subset; the range of the function is compact but not necessarily Hausdorff....

Asked on 01/03/2021 by user97621

1 answer

Top and bottom composition factors of $M$ are isomorphic

Let $k$ be a field and $N$ a finite group. Let $M$ be a projective indecomposable $kN$-module. Since the algebra $kN$ is symmetric, it follows...

Asked on 01/02/2021 by user666

1 answer

Widely accepted mathematical results that were later shown to be wrong?

Are there any examples in the history of mathematics of a mathematical proof that was initially reviewed and widely accepted as valid, only to be disproved a significant amount of...

Asked on 01/02/2021 by Roman Starkov

47 answer

Anti-concentration of Gaussian quadratic form

Let $X_1,dots,X_n$ denote i.i.d. standard Gaussian random variables. My question is: Do there exist absolute constants $C,c>0$ such that for every $epsilon>0$ and positive real numbers $a_1,dots,a_n>0$, we have the...

Asked on 01/01/2021 by Mitch

3 answer

Convergence of solving an OP $ minlimits_{x, alpha} sum_i alpha_i f_i(x) + g(alpha)$

Consider the optimization problem$$ minlimits_{x, alpha} sum_i alpha_i f_i(x) + g(alpha). $$I solved the above problem by alternating fixing $x$ solve for $alpha$ and vice...

Asked on 01/01/2021 by user263322

0 answer

Quadrature for numerical integration over infinite intervals

I am looking for book recommendations or hints on numerical integration over infinite intervals. I am particularly interested in integrals of the form $intlimits_{-infty}^{+infty} g(x) exp(p_d(x)) mathrm{d} x$, where...

Asked on 12/31/2020 by BernieD

1 answer

When is ${b^2 - {b-1}_2}_2=1$ with odd $b$? (The bracket-notation explained below)

For the complete extraction of the factor $p$ and its powers from a natural number $n$let's define the notation $$ {n}_p := { n over p^{nu_p(n)}}...

Asked on 12/30/2020 by Gottfried Helms

4 answer

How to recognize a vector bundle?

Given a connected topological space $E$, under which conditions is it possible to find a subspace $B$ such that $E$ can be regarded as a (rank ...

Asked on 12/30/2020 by user163840

2 answer

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