Mathematics

The aim of this short note is to prove an analogue of the existential part of the Schur--Zassenhaus Theorem for finite skew braces: we show that every Hall ideal of a finite skew brace admits a sub-skew brace complement. As an application…

Many solution methods for linear discrete ill-posed problems with error-contaminated data (right-hand side) apply Tikhonov regularization to compute a meaningful approximate solution. This solution depends on a regularization parameter. It…

We present a quantum spectral solver for the steady incompressible Stokes equations on a two-dimensional periodic domain. The method uses the Quantum Fourier Transform as a coherent change of basis and exploits the resulting spectral…

We consider local hypersurface measures in ${\mathbb R}^3$ whose density is allowed to have a weight function constructed from real analytic functions in a broad sense. We prove $L^p$ Sobolev smoothing theorems for convolutions with such…

We study a two-dimensional Ornstein-Uhlenbeck system where only the first coordinate is observed, whereas the second coordinate remains hidden. Our goal is the estimation of the coupling parameter in the drift of the observed coordinate.…

We introduce a generalized continuous-time compartment model of ethanol metabolism in the human body that extends a recently developed framework. In the proposed model, we replace the Michaelis-Menten mechanism of the liver's ethanol…

We study the spatially homogeneous, massless Boltzmann equation in Minkowski spacetime for a certain range of hard and soft interactions. For hard interactions, we derive a Povzner-type inequality for massless particles and show that…

Let $Q = \{q_n\}_{n \ge 1}$ be a sequence of integers with $q_n \ge 2$ for all $n \in\mathbb{N}$. For any real number $x \in [0,1)$, it can be expanded into the following infinite series: $$x =\frac{\varepsilon_1(x)}{q_1}+…

We construct a simple and useful sufficient condition, based on actions on a lattice of idempotents, for monoids admitting homomorphisms to the monogenic free inverse monoid $\mathrm{FIM}(1)$ to not be of type $\mathrm{FP}_2$. This recovers…

Lu's first pinching theorem states that a closed minimal $n$-dimensional submanifold of the unit sphere satisfying $0\le S+\lambda_2\le n$ is one of the standard first-gap models; here $S$ is the squared norm of the second fundamental form…

We consider the problem of estimating numerically integrals of the shape $$ \int_P \frac{dt}{t_1 \dotsb t_k} $$ where $P \in {\mathbb R}_{>0}^k$ is a convex polytope, $t=(t_1,\dotsc, t_k)$ and $d t$ is the Lebesgue measure. This type of…

We examine how the Rasmussen invariant, satellite operations, and null-homologous twists can be used to establish infinite order of knots in the smooth concordance group. As an application, we show that the Conway knot has infinite…

Given a set $R$ of positive integers, an $R$-graph $H = (V, E)$ is a hypergraph where the cardinality of each hyperedge belongs to $R$. If $R = \{r\}$, we sometimes refer to the hypergraph as an $r$-graph rather than an $R$-graph. For a set…

Let $R$ be a local ring of prime characteristic $p$, and let $R^\infty$ denote the perfect closure of $R$. We prove that a finitely generated $R$-module $N$ has finite injective dimension if and only if $\operatorname{Ext}_R^i(R^\infty, N)…

Let $\epsilon_{ij}, i,j\geq 1$ be independent Rademacher variables. We prove \begin{equation*} \mathbb{E} \max_{1\leq j\leq p}\left|\frac{1}{n}\sum_{i=1}^n\epsilon_{ij}\right| \geq \min\left\{\frac{255}{256},\frac{1}{\sqrt{2\log…

Cohen, Manin, and Zagier recovered the Rankin-Cohen bracket for modular forms from an action of the modular group on pseudodifferential operators whose coefficients are holomorphic functions on the Poincar\'e upper half plane. We…

We present the entropy-degree theorem for Lipschitz maps between Alexandrov spaces with curvature bounded below, extending the classical Besson--Courtois--Gallot entropy-rigidity results to this singular setting. The proof requires a new…

The marginal degree of sums in dimension \(n\) is the smallest integer \(k\) such that the joint distributions of all subcollections of at most \(k\) coordinates of a real-valued random vector \(\left(X_1,\ldots,X_n\right)\) determine the…

This paper is concerned with the time-harmonic wave scattering problems in three dimensional poroelastic media. By introducing an intermediate variable $p$, the original $\mathbf{u}-\mathbf{w}$ system is equivalently transformed into a…

Farkas, Pandharipande, and Sammartano constructed non-rational irreducible components of Hilbert schemes of points in affine space $\mathbb{A}^n$ for all $n \geq 12$. Their construction starts from Hilbert schemes of curves in…