MathOverflow Questions, Problems & Solutions : TransWikia.com ~ Page 22

Higher derivatives of weighted zeta function and continuation to $s=1$

Is it possible to analytically continue to weighted reciprocal zeta function $frac{1}{zeta_{a}(s)}$ to the point $s=1$ by bounding the quantitybegin{equation}left|frac{d^n}{dx^n}prod_{kin S}left(1-frac{1}{k^x}right)right|tag{1}end{equation}for real ...

Asked on 11/03/2021 by Milo Moses

0 answer

Distance properties of the permutations of a set of points in a Euclidean space

We are given a set of $n$ distinct points $S={mathbf{x}_1, mathbf{x}_2, ldots, mathbf{x}_n}$ in a Euclidean space $mathbb{R}^d$, where the distance between two points $mathbf{x}_i,mathbf{x}_jin S$...

Asked on 11/03/2021

0 answer

Roots of determinant of matrix with polynomial entries — a generalization

For $1 le i, j le k$, consider $rho_{ij}$ which are equal to either zero or one such that $rho_{ii}=1$ and $rho_{ij}=0$ if and only if...

Asked on 11/03/2021

0 answer

Laplacian coupled with another equation over a two-dimensional rectangular region

I have the two-dimensional Laplacian $(nabla^2 T(x,y)=0)$ coupled with another equation which is: $$frac{partial t}{partial x}+alpha(t-T)=0 tag 1$$ where it is known that $t(x=0)=t_i$. The Laplacian is...

Asked on 11/03/2021

0 answer

Is there a finite equational basis for the join of the commutative and associative equations?

I asked this on math stack exchange, but I was told to post it on mathoverflow. Consider the lattice of equational theories of a single binary operation $*$....

Asked on 11/03/2021

0 answer

Looking for sufficient conditions for positive Fourier transforms

I am looking for some sufficient conditions for an even, continuous, nonnegative, non-increasing, non-convex function to be non-negative definite. In other words$$int_0^infty f(x)cos(xomega) , dxge 0,...

Asked on 11/03/2021 by Tanya Vladi

3 answer

What are some examples of proving that a thing exists by proving that the set of such things has positive measure?

Suppose we want to prove that among some collection of things, at least oneof them has some desirable property. Sometimes the easiest strategy is toequip the collection of...

Asked on 11/03/2021 by Tom Leinster

9 answer

Literature and history for: lifting matrix units modulo various kinds of ideal

This is not so much a mathematics question as a cross between a "history of mathematics" question and a reference request. My PhD student has been working on some problems...

Asked on 11/03/2021 by Yemon Choi

0 answer

Smallest family of subsets that generates the discrete topology

If $X$ is a finite set, what is the smallest (in cardinality) family of open subsets $mathcal Usubseteq 2^X$ such that $mathcal U$ generates the discrete topology,...

Asked on 11/03/2021 by user175348

2 answer

A global mathematics library

Just for personal interest, I am not (yet) professionally involved in it. My question is about the state of arts in digitalization of mathematics and to what extent it is...

Asked on 11/03/2021

3 answer

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