Mathematics

The goal of this note is twofold. First, we provide explicit examples of periodic (though not necessarily lattice) sets that give rise to Gabor systems failing to form frames. Our constructions depend only on the parity of the window…

In this note we prove a conjecture by Hasegawa stating that a simply connected, nilpotent Lie group of dimension $2n$ endowed with a left-invariant complex structure is biholomorphic to $\mathbb{C}^n$.

In this article, assuming Artin's (holomorphy) conjecture, we establish an explicit asymptotic formula for the number of non-trivial zeros, up to any given height $T\geq 1$, of Artin $L$-functions. As a consequence, our result yields an…

In this paper, we investigate the rate of convergence of the relative value iteration (RVI) algorithms for diffusions in $\mathbb{R}^d$ under both the conventional ergodic cost (CEC) and ergodic risk-sensitive cost (ERSC) criteria, and…

We introduce a geometric formulation of statistical feature learning for supervised regression. Feature learning is defined through a base--fiber decomposition: the base is the feature-side geometry produced by training, and the fiber is…

This paper proposes a modular vehicle system for passenger-freight integration along a bidirectional transit corridor. The system uses homogeneous units that can be coupled into vehicles and assigned to either passenger or freight service.…

This paper focuses on the analysis of an initial-boundary value (direct) problem for the Hallaire-Luikov moisture transfer equation involving the $\psi$-Prabhakar integral-differential operator of fractional order. We establish the…

Let $k$ be a non-archimedean local field of characteristic zero. We give sufficient conditions under which the Ginzburg-Rallis models of the induced representations of $\mathrm{GL}_6(k)$ from a parabolic subgroup of type $[2^3]$ are…

We study the image of a regular unipotent element under any finite-dimensional irreducible polynomial representations of $\mathrm{GL}_3(\mathbb{C})$. This problem is equivalent to decomposing certain compositions of irreducible…

We construct holomorphic differential forms of many degrees, including the minimum possible one, on the modular varieties associated to the even lattices of signature $(2, n)$ with $n\equiv 1, 3$ mod $8$ and discriminant $-2$ in the range…

We relate the hyperbolicity of a calibrated manifold $(X, \phi)$ to the analytic properties of the space of Smith immersions $\mathrm{SmIm}(B^k, X)$ from the Poincare $k$-ball into $X$. In particular, we establish the following calibrated…

In the siblings version of the coupon collector, a main collector stops when every coupon type has appeared once. Duplicates are passed successively to siblings, and $U_j^N$ denotes the number of empty spaces in the $j$th collector's album…

Low-rank matrix optimization is often carried out via the Burer-Monteiro (BM) formulation, but choosing the factorization rank $r$ is delicate and can substantially slow optimization. We propose a unified framework, termed…

Acoustic scattering arises in a wide range of applications, including medical imaging, geophysical exploration, acoustic metamaterials, etc. In this paper, we develop a fast and highly accurate algorithm for acoustic scattering by multiple…

A rainbow stacking of $m$ independent, uniformly random $r$-edge-colourings of $K_n$ is a tuple of vertex permutations that superimposes the colourings such that no two edges of the same colour overlap. The study of the critical palette…

In this article, we study bilinear Calder\'on--Zygmund operators on a Vilenkin group $G$. As a preliminary step, we establish a Grafakos--Torres-type endpoint weak-type result in our setting. Furthermore, we prove that such operators extend…

We provide an explicit construction of a Gabor orthonormal bases for a local field $K$ that provides maximal localization in both time and frequency. Such a localization is not true in case of $\mathbb{R}$ due to the uncertainty principle.…

Partial differential equations on unbounded domains are challenging because the exterior region must be represented without excessive truncation error. Truncation-based methods often require problem-dependent artificial boundary conditions,…

Let $p$ be a prime number, and let $k$ be a finite field of characteristic different from $p$. Let $X$ be a normal geometrically connected variety over $k$, let $\overline X$ be a compactification of $X$, and let $Z=\overline X\setminus X$.…

The aim of this paper is to show that the spectral theory based on the S-spectrum is particularly well suited for the Dirac operator on manifolds, even in cases where the operator is not self adjoint. Traditionally, for non-self adjoint…