数学
This article is devoted to the study of the Davis--Wielandt shell and the Davis--Wielandt radii of elements in a $C^*$-algebra. Utilizing a state-space approach, several geometric properties of the algebraic Davis--Wielandt shell are…
In this paper, we present a linearly implicit, second-order block-centered finite difference (BCFD) prediction-then-projection scheme for the multi-species Keller-Segel chemotaxis system on non-uniform spatio-temporal grids. The proposed…
Jin and Rubinstein asked whether the fixed-level equivariant Tian's alpha invariant equals the fixed-level equivariant global log canonical threshold, and proved this equality for toric varieties. In this paper we provide a positive answer…
We introduce a chain map from quandle homology to relative group homology, and construct several quandle cocycles through the chain map. We also relate this chain map to triangulations of Seifert (hyper)surfaces of 1- and 2-dimensional…
We prove that an action by $C^1$ diffeomorphisms of a lattice in a simple $p$-adic group on a compact manifold is finite, provided the dimension is less than the rank. We extend this statement to lattices in totally disconnected…
A long-standing conjecture of Lapidus asserts that under certain conditions a self-similar fractal set is not Minkowski measurable if and only if it is of lattice-type. For self-similar sets in $\mathbb{R}$, the Lapidus conjecture has been…
This work presents a goal-oriented a posteriori error estimator based on the Dual Weighted Residual (DWR) method together with space-time mesh adaptivity for the Navier--Stokes equations. The resulting nonlinear algebraic systems on the…
This paper studies an inverse boundary value problem for a coupled Stokes-Darcy system modeling fluid-porous medium interaction, with an unknown solid object embedded in the free-flow region. We simultaneously recover the viscosity…
Deep neural networks show great promise for high-dimensional PDEs, yet enforcing essential boundary conditions remains challenging, especially as penalty parameters require problem-specific retuning with increasing dimensionality. In this…
In this article, we study the P\'olya group of a new family of quintic fields, namely Lecacheux quintic fields. We show that the associated P\'olya groups can be arbitrarily large elementary abelian \(5\)-groups. Using density arguments, we…
We extend the analysis of nonrepetitive sequences of Entringer et al. [Journal of Combinatorial Theory, 1974] to relaxations of equality testing under nonstandard equivalence relations, in particular parameterized equivalence and…
Autoencoders (AEs) have emerged as powerful tools for non-linear dimensionality reduction, often surpassing traditional linear methods such as Proper Orthogonal Decomposition (POD) in scenarios characterized by slowly decaying Kolmogorov…
The Sinkhorn algorithm is the de facto standard method for numerically solving entropy-regularized optimal transport problems over finite sets. In this work, we investigate a phenomenon arising when Sinkhorn is applied with a small…
This paper studies the asymptotic behaviour of a structured population model on the space of nonnegative Radon measures. Such formulations naturally arise when solutions develop concentration phenomena or when the population is represented…
We study the Schr\"odinger problem on metric graphs and its different formulations. Starting from a static version, we introduce an equivalent reformulation as entropic optimal transport and show $\Gamma$-convergence towards static optimal…
It was recently established by Perepechko and Zaidenberg that the automorphism group of a normal affine surface is finite-dimensional if and only if the surface admits no non-trivial action of the additive group of the base field. We extend…
We provide a recurrence for computing the terms of the OEIS sequence A393920, introduced in \cite{KS}. We also describe a surprising connection between A393920 and the Fibonacci sequence A000045, obtain non-trivial lower and upper…
In a previous work, we defined (type A) c-Birkhoff polytopes and showed that they were unimodularly equivalent to order polytopes of heap posets. In this note we answer the question: What about type B?
Multi-task regression aims at jointly solving multiple regression problems, called tasks. Compared to solving each task separately, better performances can be achieved as long as the tasks are sufficiently related. Full-conformal prediction…
The notion of depth two and higher mock modular forms have found important applications in mathematical physics and enumerative geometry since their inception through indefinite theta functions with general signature. These theta functions…