arXiv preprints from January 1, 2026 through September 6, 2026 — 14:34:26 EST
We prove that the coefficient of the star $\mathfrak{st}_{21^{n-2}}$ in the chromatic symmetric function $X_G$ determines whether a connected graph $G$ is $2$-connected. We also prove new linear relations on other star coefficients of chromatic symmetric functions. This allows us to find new bases for certain spans of chromatic...
Ball, Ortega--Moreno, and Prodromou asked whether, for every odd prime $p$, one can find a $1$-factor of the complete graph $K_{p+1}$ with some arithmetic restrictions related to quadratic residues. This problem is motivated by $1$-factorizations that are compatible with the sign pattern of certain Paley-type matrices. Recently,...
This paper is concerned with the design and analysis of symmetric low-regularity integrators for the semilinear Klein-Gordon equation. We first propose a general symmetrization procedure that allows for the systematic construction of symmetric schemes from existing explicit (non-symmetric) integrators. Applying this procedure, we...
In this note, we give an alternative construction of the $G_2(2)$-graph from a $U_3(2)$-geometry.
We study an optimal boundary control problem associated to the boundary obstacle problem for the couple conformal Laplacian and conformal Robin operator on n-dimensional compact Riemannian manifolds with boundary and with n\geq 3. When the Cherrier-Escobar invariant of the compact Riemannian manifold with boundary is positive, we show...
We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within an uncertainty set. Unlike in classical MFGs, model uncertainty renders the population...
Genetic mutations frequently disrupt protein structure, stability, and solubility, acting as primary drivers for a wide spectrum of diseases. Despite the critical importance of these molecular alterations, existing computational models often lack interpretability, and fail to integrate essential physicochemical interaction. To...
The doubly degenerate nutrient taxis system \begin{equation}\label {0.1} \left\{ \begin{aligned} &u_{t}=\nabla \cdot (uv\nabla u)-χ\nabla \cdot (u^αv\nabla v)+\ell uv,&x\in Ω,\, t>0,\\ & v_{t}=Δv-uv,&x\in Ω,\, t>0,\\ \end{aligned} \right. \end{equation} is considered under zero-flux boundary conditions in a smoothly bounded domain...
This paper systematically investigates the properties and characterization of interval B-tensors and interval double B-tensors. We propose verifiable necessary and sufficient conditions that allow for determining whether an entire interval tensor family belongs to these classes based solely on its extreme point tensors. The study...
This paper examines the large-time behavior of solutions to a one-dimensional conservation law featuring a non-convex flux and an artificial heat flux term regulated by Cattaneo's law, forming a 2$\times$2 system of hyperbolic equations. Under the conditions of small wave strength and sufficiently small initial perturbations, we...
We provide several characterizations of Sobolev multiplier spaces of Lorentz type and their preduals. Block decomposition and Köthe dual of such preduals are discussed. As an application, the boundedness of local Hardy-Littlewood maximal function on these spaces will be justified.
Interlocking interfaces are commonly employed to mitigate relative sliding under shear.Indeed, Their geometry is typically selected on grounds of fabrication convenience rather than analytical optimality. There is no reason to suppose that circular or polygonal profiles minimize localized stress concentration under fixed geometric...
In this paper, we consider the following principal eigenvalue problem with a large divergence-free drift: \begin{equation}\label{0.1} -\varepsilonΔφ-2α\nabla m(x)\cdot\nabla φ+V(x)φ=λ_αφ \,\ \text{in}\, \ H_0^1(Ω),\tag{0.1} \end{equation} where the domain $Ω\subset \mathbb{R}^N (N\ge 1)$ is bounded with smooth boundary $\partialΩ$,...
We consider a possibly multiply connected bounded open subset $Ω$ of ${\mathbb{R}}^n$ of class $C^{\max\{1,m\},α}$ for some $m\in {\mathbb{N}}$, $α\in]0,1[$ and we plan to solve both the Dirichlet and the Neumann problem for the Helmholtz equation in $Ω$ and in the exterior of $Ω$ in terms of acoustic layer potentials. Then we turn to...
This paper provides a complete proof of Simon-Lukic conjecture for orthogonal polynomials on the unit circle. For a probability measure $dμ= w(θ) \frac{dθ}{2π} + dμ_s$ with Verblunsky coefficients $α=\{α_n\}_{n=0}^\infty$, distinct singular points $(θ_k)_{k=1}^{\ell}$, and multiplicities $(m_k)_{k=1}^{\ell}$, we establish the...
In this paper, we introduce the bivariate exponential generating function $F_l(x,y)$ for the number of level-$l$ faces of an exponential sequence of arrangements (ESA), and establish the formula $F_l(x,y)=\big(F_1(x,y)\big)^l$ with a combinatorial interpretation. Its specialization at $x=0$ recovers a result first obtained by Chen et...
We prove a relative GAGA theorem for perfect and pseudo-coherent complexes in non-archimedean analytic geometry, allowing bases given by Fredholm analytic rings, including those associated from affinoid perfectoid spaces. This answers a question raised in \cite{heuer2024padicnonabelianhodgetheory}. As an application, we show that for...
We develop a topological approach to prove the generalized Lax conjecture using the fact that determinants of sufficiently big symmetric linear pencils are able to express the rigidly convex sets of RZ polynomials of any degree $d$. Monicity of the representation is assessed through a topological argument that allows us to perturbate...
The disjoint amalgamation property (DAP), which asserts that all spans of a class of models can be amalgamated with minimal intersection, is an important property in the context of abstract elementary classes, with connections to both Grossberg's question and Shelah's categoricity conjecture. We prove that, in a nice AEC $\mathbf{K}$...
We construct infinite families of nonzero classes in $H_d(GL_n(F_2);F_2)$ along lines of the form $d =\frac{2}{3}n +$(constant), thereby showing that the known slope $\frac{2}{3}$-stability for these homology groups are optimal. Using the new stability Hopf algebra perspective of Randal-Williams, our computations in addition recover...
We show a localization estimate for local solutions to the parabolic equation $-\partial_t u+\mbox{div} (A\nabla u)=0$ with zero Neumann data, assuming that the $L^p$ Neumann problem and $L^{p'}$ Dirichlet problem for the adjoint operator are solvable in a Lipschitz cylinder for some $p\in(1,\infty)$. Using this result, we establish...
Resource Balance Analysis (RBA) is a framework for predicting steady-state cellular growth under resource constraints. However, classical RBA formulations are static and do not capture the dynamic regulation of biosynthetic resources or macromolecular turnover, which is particularly important in eukaryotic cells. In this work, we...
Given $2n \times 2n$ real symmetric positive semidefinite matrix $A$ with symplectic kernel, there exists a real $2n \times 2n$ \emph{symplectic matrix} $M$ such that $M^TAM= D \oplus D$, where $D$ is an $n \times n$ non-negative diagonal matrix which is unique up to permutation of its diagonal entries. The diagonal entries of $D$...
We study a finite index inclusion of simple unital C*-algebras and construct a canonical completely positive coproduct on the second relative commutant, thereby endowing it with a natural coalgebra structure. Motivated by this construction, we introduce the notion of a weak quantum hypergroup, a generalization of the quantum...
Slow and costly communication is often the main bottleneck in distributed optimization, especially in federated learning where it occurs over wireless networks. We introduce BiCoLoR, a communication-efficient optimization algorithm that combines two widely used and effective strategies: local training, which increases computation...