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MathOverflow : Recent Questions and Answers (Page 27)

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Conditions for continuity of an integral functional

Let $X$ be a metric space, $nu,mu$ be Borel measures on $X$, $f:Xtimes mathbb{R}rightarrow [0,infty)$ be a measurable function. Under what conditions is the integral...

Asked on 11/03/2021 by James_T

2 answer

Best-approximation with tensors of rank $ge2$

Let $kinmathbb N$, $H_i$ be a (finite-dimensional, if necessary) $mathbb R$-Hilbert space for $iin I:={1,ldots,k}$, $H:=bigotimes_{iin I}H_i$ denote the tensor product$^1$...

Asked on 11/03/2021

1 answer

$x '(t) + g (x (t)) = f (t),quad forall tin mathbb R$ have periodic solution $iff; frac 1T int_0 ^ T f (t) dt in g (mathbb R) $

I have a research work concerning the equation: $$x '(t) + g (x (t)) = f (t),quad forall tin mathbb R$$f and g are defined and continuous in...

Asked on 11/03/2021

1 answer

Smooth projective surface with geometrically integral reduction

Let $S$ be a geometrically connected smooth projective surface over $mathbb{Q}_p$. Can it be put in a proper flat $mathbb{Z}_p$-scheme with a geometrically integral special fiber?...

Asked on 11/03/2021 by user158636

2 answer

On the difference between Malliavin derivative and Gross-Sobolev derivative

Let $W=C_0([0,1],mathbb R^d)$ be the classical Wiener space equipped with $mu$ the Wiener measure.If $F:Wtomathbb R$ is a cylindrical function of the form begin{align*}F(w)=f(W_{t_1}(w),cdots,W_{t_n}(w)),...

Asked on 11/03/2021

0 answer

Equivalent characterization of ordinary $F$-crystals

Let $k$ be a perfect field in characteristic $p$, let $W$ be its ring of Witt vectors. Let $A=W[[t_1,cdots,t_n]]$, let $A_0=A/pA$. Let $H$ be...

Asked on 11/03/2021 by Qixiao

0 answer

What subsystem of second-order arithmetic is needed for the recursion theorem?

In its simplest version, the recursion theorem states that for any $minmathbb{N}$ and any function $g:mathbb{N}rightarrowmathbb{N}$, there exists a function $f:mathbb{N}rightarrowmathbb{N}$ such that $f(0)=m$ and ...

Asked on 11/03/2021

1 answer

How to calculate possible arrangements of hexagons?

I was wondering someone could help. I've developed a board game which is made up of six, large hexagonal board pieces, which can be arranged in any order, and with...

Asked on 03/04/2021 by Matt Roberts

0 answer

Open affine subscheme of affine scheme which is not principal

I'm not sure whether this is non-trivial or not, but do there exist simple examples of an affine scheme $X$ having an open affine subscheme $U$ which is not principal...

Asked on 02/28/2021 by Wanderer

5 answer

Simple examples of equivariant cobordism

Let $Y$ be an oriented 3-manifold with a free action by a finite group $G$. If I understand correctly, there exists a multiple of $NY$ of ...

Asked on 02/25/2021 by user_501

0 answer

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