Mathematics

In this paper, we introduce and study the notion of S-filters in bounded distributive lattices.

We propose a new algorithm for approximating the metric projection onto a superelliptic disk of order $p>1$, i.e., the convex hull of a superellipse (Lam\'e curve), and prove its convergence.

Schauder Orlicz-type estimates are derived for weak solutions to second-order linear elliptic equations in divergence form with lower-order terms. The Orlicz setting $X=L^\psi$ is treated first. Under suitable assumptions on the Young…

The second Eulerian numbers are defined via the descent enumerator of Stirling permutations, a class of permutations introduced by Gessel and Stanley. We give a simple and conceptual proof of two identities relating the Bernoulli numbers…

We investigate Fourier multipliers associated with the Strichartz Fourier transform on the Heisenberg group. In particular, we establish H\"ormander-type $L^{p}-L^{q}$ boundedness results for the range $1<p\leq 2\leq q<\infty$. The analysis…

Let $({X}, \omega)$ be a compact $n$-dimensional K\"ahler orbifold, the stabilizer groups of which are abelian and have rank at most two. Let ${E}$ be an orbi-ample vector bundle of rank $2$ over ${X}$ and let $H$ be a Hermitian metric on…

In this paper, we introduce the notion of $t$-tone edge coloring. A $t$-tone edge $k$-coloring of a graph $G$ assigns to each edge of $G$ a set of $t$ distinct colors from $\{1,\dots,k\}$ such that any two edges at distance $d$ share fewer…

This paper is devoted to the study of strong solutions for the compressible Navier-Stokes/Allen-Cahn system in bounded domain $\Omega\subset\mathbb R^3$, allowing for the presence of initial vacuum. A characteristic of this system is the…

Matrix measures induced by vector norms are widely used in contraction theory of nonlinear dynamical systems. A natural and important robustness question is whether negativity of a matrix measure is preserved under arbitrary nonnegative…

We characterize the potential V (x) that minimizes the fundamental spectral gap of weighted Schr\"odinger operators on the interval [0,{\pi}] subject to Dirichlet boundary conditions, under the constraint that the potential V (x) is convex…

Recently, Qiu, Xu, Ye and Yu proved that for product system of finitely many minimal systems, the maximal $\infty$-step pro-nilfactor of the system is the topological characteristic factor. In this paper, we extend the result to…

Return panels, covariances, and large feature matrices evolve one observation or one entry at a time, yet downstream models require an up-to-date low-rank factorization $A_t \approx U_t \Sigma_t V_t^\top$ on every tick -- a regime where…

Pipedreams and bumpless pipedreams are two combinatorial models that compute double Grothendieck polynomials. While studying matrix Schubert varieties, Pechenik, Speyer, and Weigandt defined a permutation statistic$\mathsf{rajcode}(\cdot)$…

We revisit a conjecture of Mubayi that was proposed as a hypergraph analogue of the Li--Li algebraic proof of Tur\'{a}n's theorem. The conjecture compares a polynomial ideal generated by multipartite 3-graphs with a differentiated…

If a self-map $\sigma \colon \mathcal{X} \rightarrow \mathcal{X}$ has a dynamical zeta function with nonzero radius of convergence $1/\Lambda$ and the Ces\`aro mean $B$ of $ \# \mathrm{Fix}(\sigma^k)/\Lambda^k$ exists and is positive, we…

We study a finite-horizon stochastic control criterion for non-convex optimization in which Brownian exploration is balanced against a quadratic control cost. Rather than emphasizing the classical Hopf--Cole representation, we isolate the…

We study a singularly perturbed Dirichlet problem for the $p$-Laplacian with competing superlinear terms, \[ -\varepsilon \Delta_p u = a(x)|u|^{q-2}u - b(x)|u|^{\gamma-2}u, \qquad u|_{\partial\Omega}=0, \] where $1<p<q<\gamma<p^*$, $a\geq…

Let $n, m \ge 4$. We classify the Zappa--Sz\'ep products $G = HK$ with $H = \langle x\rangle \rtimes \langle y\rangle \cong \mathrm{SD}_{2^n}$ and $K = \langle z\rangle \rtimes \langle w\rangle \cong \mathrm{SD}_{2^m}$, according to the…

Ring-like communication graphs appear in UAV formations, cyclic patrols, perimeter monitoring, and other multi-agent tasks in which agents exchange information mainly with neighboring vehicles along a closed route. When measurement and…

Let $\mu_p$ be the generalized Gaussian distribution on $\mathbb{R}^n$ with density $e^{-\frac{|x|^p}{p}}$ multiplied by a constant depending on $p\ge 1$ and $n$, and $\alpha_p(n)$ be the largest number such that the Brunn-Minkowski type…