arXiv preprints from January 1, 2026 through September 7, 2026 — 06:50:54 EST
The aim of this paper is to take the study of Dedekind braces, that is, left braces for which every subbrace is an ideal, started in a previous paper, further. Dedekind braces $A$ whose additive group is non-periodic are analysed. We prove sufficient conditions for $A$ to be abelian: it is enough that every element is $2$-nilpotent...
We establish an integral identity for functions on R^2 that are invariant under discrete diagonal translations. The identity shows that integration over the diamond-shaped region |x| + |y| <= L is exactly one half of the integral over the square domain [-L, L]^2, allowing diamond-domain integrals to be reduced to easier rectangular...
For a property $\mathcal{X}$ of integral domains, an integral domain $D$ is said to be a {\it locally $\mathcal{X}$-domain} if $D_P$ has the property $\mathcal{X}$ for every prime ideal $P$ of $D$. In this paper, we study the transfer of local properties of integral domains under several extensions and constructions, including flat...
Motivated by pioneering works of Bandle and Wagner, given a bounded Lipschitz domain $Ω\subset \mathbb R^d$ with $d\ge3$, we consider the Robin-Laplacian torsional rigidity $τ_α(Ω)$ with negative boundary parameter $α$ and we show that sharp inequalities for $τ_α(Ω)$ hold if $|α|$ is small enough. In particular, we prove that, if...
We establish a non-ergodic version of the Host-Kra-Ziegler structure theorem for measure-preserving $\mathbb{Z}^d$-actions. Our argument reduces the non-ergodic case to the ergodic theorem (for $d\ge 2$ due to Candela and Szegedy) via a measurable selection procedure. We also establish a non-ergodic vertical nilcharacter version of...
Banderier, Marchal, and Wallner considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. In this work, we prove a conjecture of Fuchs and Yu concerning the enumeration of two classes of three-row Young tableaux with walls. Combining with the work by...
Rubin's generalized Minkowski--Funk transforms $M_t^α$ on the sphere $\mathbb{S}^n$ give rise, for irrational radii $t=\cos(βπ)$, to a small denominator problem governed by the asymptotic behavior of their spectral multipliers. We show that for Lebesgue-almost every $β$ the corresponding two-sine small divisor inequality has...
For an associative algebra $A$ over a field of characteristic zero, let $P_n(A)$ and $P_n^z(A)$ denote the spaces of multilinear polynomials of degree $n$ modulo the polynomial identities and the central polynomials of $A$, respectively. We also write $Δ_n(A)$ for the space of multilinear central polynomials of degree $n$ modulo the...
One of the major advantages of $\infty$-category theory over classical $1$-category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of $\infty$-categories. However, it is both subtle and crucial to specify which variant of the $\infty$-category of $\infty$-categories is being used when...
Let $ρ$ be an $n$-dimensional representation of $\mathcal{G}_{\mathbb{Q}_p}$ over $\overline{\mathbb{F}_p}$. When $ρ$ is generic and a good conjugate, the article "Conjectures and results on modular representations of $\mathrm{GL}_n(K)$ for a $p$-adic field $K$", by Breuil-Herzig-Hu-Morra-Schraen, introduces the notion of...
Sweepstakes reproduction may be generated by chance matching of reproduction with favorable environmental conditions. Gene genealogies generated by sweepstakes reproduction are in the domain of attraction of multiple-merger coalescents where a random number of lineages merges at such times. We consider population genetic models of...
How many natural numbers below $X$ can be written as a sum of $k$ units of the ring of integers of a given number field? We give the asymptotics as $X$ gets large for quadratic number fields. This solves a problem of Jarden and Narkiewicz from 2007 for quadratic number fields.
We characterize projections among positive norm-one elements in unital C$^*$-algebras in pure geometric terms determined by the norm of the underlying Banach space. Concretely, let $A$ be a C$^*$-algebra (or a JB$^*$-algebra) whose positive cone and unit sphere are denoted by ${A}^+$ and $\mathrm{S}_{A}$, respectively. The positive...
We prove an infinite-dimensional version of "quantization commutes with reduction" in the framework of geometric quantization of Chern-Simons gauge theory, focusing on the genus one case. The proof is complex-analytic and relies on the Atiyah-Bott stack and the Chern-Simons line bundle.
For oriented surfaces $Σ$ with boundary, we consider the infinite-dimensional deformation space of projective structures on $Σ$ with nondegenerate boundary, up to isotopies fixing the boundary. We show that this space carries a natural symplectic structure, and is a Hamiltonian space for the symplectic groupoid integrating the...
While Kolmogorov's probability axioms are widely recognized, it is less well known that in an often-overlooked 1930 note, Kolmogorov proposed an axiomatic framework for a unifying concept of the mean -- referred to as regular means. This framework yields a well-defined functional form encompassing the arithmetic, geometric, and...
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations and propose ways to eliminate oscillations. A new approach for error analysis that requires...
The concepts of hypocoercivity and hypocontractivity and their relationship are studied for semi-dissipative continuous-time and discrete-time evolution equations in a Hilbert space setting. New proofs for the characterization of the short-time decay of the solution from the initial value are presented, that in particular characterize...
We consider the realisation problem for normal 1-types of 4-manifolds with a given boundary. More precisely, given a normal 1-type $ξ$ and closed 3-dimensional $ξ$-manifold $Y$, does there exist a compact 4-dimensional $ξ$-manifold with boundary $Y$? We describe a three stage obstruction theory for the existence of such a 4-manifold,...
We show that all smooth ring domains $Ω\subset \mathbb{R}^2$ that admit a solution to Serrin's classical problem $Δu+2=0$ with locally constant overdetermined boundary conditions along $\partial Ω$ can be described as algebro-geometric potentials of the mKdV hierarchy. The same result holds for periodic unbounded domains with two...
Deltoids provide a natural framework for studying defective (partial) matchings in abelian groups, and we develop both structure and existence results in this setting. Given finite subsets $A$ and $B$ of an abelian group $G$, a matching is a bijection $f:A\to B$ such that $af(a)\notin A$ for all $a\in A$, a definition motivated by the...
This paper analyzes and explicitly solves a class of long-term average impulse control problems and a related class of singular control problems. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The model is motivated by applications such as the optimal long-term management of renewable...
In this article, we prove that if $X$ is a complex manifold of dimension $n\geq 4$ such that there exists a $q$-convex with corners function $f\in F_{q}(X)$, then every holomorphic line bundle over $\{f>c\}$ extends uniquely to $X$ if $1\leq q\leq n-3$. This generalizes a well-known result obtained in \cite{ref5} for $q$-complete with...
The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved by Dikranjan, Goldsmith, Salce and Zanardo. It was later extended by Shlossberg to torsion nilpotent groups of class 2. As our main result, we prove the Addition Theorem for endomorphisms of torsion nilpotent groups of...
Reduced Order Models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity Computational Fluid Dynamics (CFD) for accelerating the design and optimization processes in engineering applications. Many industrial geometries feature repeating subdomains or contain sub-regions governed by distinct physical...