Newest Questions
165,205 questions
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Divisibility relations among degrees of irreducble factors of a binomial
Suppose $K$ is an algebraic number field, and $a \in K$. Let $n$ be a positive integer. The polynomial $t^n - a \in K[t]$ splits as a product of irreducible factors of degrees $d_1, \dots, d_r$.
Is it ...
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Lattice-to-Continuum Tightness for Uniformly Strongly Log-Concave Gibbs Measures
Let $A_n$ be a lattice field defined on a sequence of meshes on a fixed compact domain, say the $d$-dimensional torus $\mathbb T^d$, with lattice spacing $a_n \to 0$.Suppose $A_n$ is distributed ...
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Formal completion along affine closed subscheme
Let $X$ be a scheme, $Z$ be a closed subscheme. If $Z$ is affine, is the formal completion $\hat X$ of $X$ along $Z$ necessarily an affine formal scheme?
I have heard this claim (at least when $Z$ is ...
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A surjective homomorphism of $\mathbb R$-groups that is not surjective on $\mathbb R$-points
$\newcommand{\R}{{\mathbb R}}
\newcommand{\C}{{\mathbb C}}
$I have asked this question on MSE, but got no answers or comments, so I decided to try my luck on MO.
Consider a non-connected reductive ...
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Continuity of perimeter of sets
Let $\Omega$ be a bounded open set in $\mathbb{R}^n$ with $C^1$-boundary. For any $r>0$, define $$\Omega_r=\{x\in\Omega: 0<d(x,\partial\Omega)<r\}.$$
Under what minimal regularity assumptions ...
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Closed form for a polytope integral in analytic number theory
In Theorem 1.1 of this paper a constant is defined by a massive polytope integral, which is subsequently evaluated for certain values of $r$ using a computer algebra system. My question is whether ...
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Morse function for quotient of manifold?
I have a closed (compact without boundary) manifold M and a compact Lie group G that acts on it. I want to understand the topology of $M/G$, at least compute its singular homology groups. The action ...
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An explicit "easily" computable-and-invertible mapping between permutations?
TL;DR version: With the magician's back turned, a spectator shuffles a standard deck of $n=52$ playing cards and selects and arranges $m=27$ of them face-up in a row left to right. The magician's ...
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What is this vague time in the terminology of topology? [closed]
Okay, loosely speaking, a homeomorphism is a continuous, bijective, and invertible mapping. A homotopy is a continuous deformation of a topological space with a parameter. An isotopy is a homotopy ...
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Polynomial conditions on cycle space of simple graph
Let $G=(V,E)$ be a simple graph and $\Phi:=\lbrace \phi\rbrace$ a set of cycles such that for every edge $e\in E$ there is a $\phi\in \Phi$ such that $e\in \phi$. We say that $\Phi$ covers $G$. Assume ...
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Justifying the Robbins-Monro procedure using Dvoretzky's theorem on stochastic approximation
A colleague and I are trying to understand some results in stochastic approximation theory with a view to gaining quantitative information about rates of convergence of certain processes. We have done ...
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How to project a function represented by a neural network into finite element spaces
Suppose we trained a neural network to fit a solution of a PDE, but we want to do something in a Finite Element Space, so we need transform our neural network to the latter. What is the way to do this ...
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Conditions for a Fourier-windowed quadratic form to define a finite-range or exponentially decaying interaction?
Let $A: \mathbb T^4 \to \mathfrak{su}(2)$ be a smooth gauge potential on the 4-torus. We consider a quadratic functional $Q[A]$ defined via a decomposition using a wavelet-type frame $\{\psi_{j,k}\}$:$...
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What can be computed without collapsing $\omega_1$
Below work in $\mathsf{ZFC+CH}$ for simplicity.
Say that a (set) forcing notion $\mathbb{P}$ captures a map $f:\mathbb{R}\rightarrow\mathbb{R}$ iff there is some $\mathbb{P}$-name for a real $\nu$ ...
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Spiral visualizations of Riemann Zeta function sampled at arithmetic progressions: has this been studied? [closed]
While experimenting with visualizations of the Riemann zeta function on the critical line, I constructed the following object, which I have not seen discussed in the literature, and I would like to ...
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