MathOverflow Questions, Problems & Solutions : TransWikia.com ~ Page 12

Polytope with most faces

Fix $m,n in mathbb{N}$ with $m ge n+1$. Take $m$ points in general position in $mathbb{R}^n$ and let $P$ be their convex hull. What is...

Asked on 12/01/2021 by zjs

1 answer

Algebraization of arithmetic and stronger theories?

Intuitionistic and classical propositional logic, and even classical first-order logic with identity, have algebraic counterparts. Algebraizable logics, 1989, by Willem J. Blok and Don Pigozzi, is a classical reference. Is...

Asked on 12/01/2021 by Frode Alfson Bjørdal

0 answer

Vector field along an immersion whose covariant derivative is the differential

Let $(M,g)$ be a Riemannnian manifold and let $f:Sigmato M$ be a smooth immersion. Then the vector bundle $f^ast TMtoSigma$ has a natural bundle metric and metric-compatible...

Asked on 12/01/2021 by Quarto Bendir

1 answer

Condition for block symmetric real matrix eigenvalues to be real

I have a $2n times 2n$ block symmetric matrix that in the simplest case ($n=2$) looks like: $$M_2 = begin{bmatrix}a_1 & 0 & b_{1,2} &...

Asked on 11/29/2021

1 answer

Canonical forms for block-positive-definite matrices

Suppose we are given a block $2times 2$ matrix that is positive-definite, and let's suppose for simplicity that the blocks along the main diagonal are the identity. So...

Asked on 11/29/2021 by Laurent Lessard

0 answer

Form of a block upper triangular matrix of finite order

If I take a diagonalizable block upper triangular matrix whose diagonal blocks are of finite order, is it true that away from the leading block diagonal, the matrix is zero?...

Asked on 11/29/2021 by user44128

1 answer

Determinant of block tridiagonal matrices

Is there a formula to compute the determinant of block tridiagonal matrices when the determinants of the involved matrices are known? In particular, I am interested in the case ...

Asked on 11/29/2021

2 answer

Full measure properties for Zariski open subsets in $p$-adic situation

Let $F$ be a $p$-adic field and let $X$ be a smooth integral variety over $F$ (I am chiefly interested in the case when $X$...

Asked on 11/29/2021 by Alex Youcis

0 answer

Prove $int_{0}^{infty} cos(omega x) exp(-x^{alpha}) , {rm d} x ge {alpha^2 sqrt{pi} over 8} exp left( -frac{omega^2}{4} right)$

I would like to prove that $$int_{0}^{infty} cos(omega x) exp(-x^{alpha}) , {rm d} x ge{alpha^2 sqrt{pi} over 8} exp left( -frac{omega^2}{4} right)$$ for any $omega >...

Asked on 11/29/2021

0 answer

Prove of the shape-derivative identity relating the shape and material derivative of a shape-dependent function

I've started reading about shape optimization. Most of the concepts I've encountered so far (such as the shape derivatives of domain and boundary integrals and the corresponding) seem to be...

Asked on 11/29/2021

1 answer

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