数学

Interval graphs are a special class of chordal graphs, and hence have connections to commutative algebra via Fr\"oberg's theorem that characterizes linear resolutions of squarefree quadratic ideals. In recent years, several hypergraphic…

We present a fast algorithm for evaluating conditionally convergent Coulomb lattice sums, governed by the Laplace equation with periodic boundary conditions on arbitrary unit cells (oblique in 2D, triclinic in 3D) and arbitrary particle…

Let $[0, 1]^{n} \subseteq \mathbb{R}^{n}$ be endowed with its pointwise order, and let $k$ be a positive integer. A subset $A$ of $[0, 1]^{n}$ is said to be a \emph{$k$-antichain} if $\operatorname{card}(A \cap C) \leq k$ for each chain $C…

Packing problems form a central theme in graph theory, owing to their relevance in modeling conflict-free resource allocation, network design, and communication constraints. Motivated by applications in wireless networks where each device…

This paper constructs a framed real monopole Floer homology for three-manifolds with involutions, marked with multiple basepoints. The relative gradings of these Floer homologies depend on the framing information and the paper gives a…

We prove a generalization for commuting $n$-tuples of unbounded self-adjoint operators and the Lorentz $(n,1)$ ideal,$n \ge 3$, of the Kato-Rosenblum theorem. The result is derived from earlier work for bounded operators [8]. Also, a very…

The main theme of approximation theory is to understand how well a general function $f$ can be approximated by a simpler function $g$ such as a polynomial or spline. In many applications, one wants $g$ to retain known properties of $f$ such…

In this work, we propose a robust Sparse Identification of Nonlinear Dynamics (SINDy) pipeline for handling datasets corrupted by noise and outliers. The method decouples outlier filtering from sparse regression by combining Iterative Least…

The Padovan sequence $\{P_{m}\}_{m\ge 0}$ is a ternary recurrence sequence with companion polynomial $X^{3}-X-1$ and initial conditions $P_{0}=P_{1}=P_{2}=1$. The Perrin sequence $\{R_{m}\}_{m\ge 0}$ is defined by the same companion…

We study a logarithmically hyperviscous Navier-Stokes model on the three-dimensional torus with Lie-transport noise, which includes both transport and stretching. We prove that, for noise of sufficiently large intensity and high frequency,…

This article treats kernel approximation and interpolation on embedded manifolds of $\mathbb{R}^N$using restrictions of positive and conditionally positive definite kernels. The main challenge is to develop an approximation theory that…

Systems defined by linear and complementarity constraints (SLCCs) arise frequently in engineering, economics, and other related fields. They also appear in the optimality conditions of many challenging optimization models, such as bilinear…

In this article, we introduce a new noise model for data-driven control. The model can be interpreted as a generalization of a Frobenius norm bound on the matrix of noise samples. For instantaneously bounded noise, the proposed model…

In this paper we study the structure of complex nilmanifolds $X$ admitting some special classes of Hermitian metrics, namely, astheno-K\"ahler, strongly Gauduchon and balanced metrics. We prove that, in complex dimension 4, the existence of…

Scalar objective functions are required when a multi-criteria optimization problem must yield a single preferred design rather than only a Pareto set. The choice of scalarization influences which compromise is selected, how preference…

Maranca and Rosenberg (2024) devised a ranking scheme for unlabeled multifurcating rooted trees, in which the trees are bijectively associated with the positive integers. Here, generalizing earlier results for bifurcating trees, we…

Slowness surfaces are algebraic varieties arising from propagation of elastic waves. In dimensions $2$, we completely classify the types of singularities slowness surfaces can have. The two types of possible singularities are a transversal…

In the full transformation semigroup $T_n$ on a finite chain $X_n$, let $D_n=\{\alpha \in T_n:(\forall x \in X_n) \ x\alpha \leq x\}$ be the subsemigroup of all order-decreasing maps of $T_n$, and let $O_n=\{\alpha \in T_n:(\forall x ,y\in…

We classify Boolean cubic forms in ten variables up to GL(10,2)-equivalence. The catalog contains all 3691560 nonzero orbits. For every orbit we provide a representative with small monomial count, the stabilizer order, and the alternating…

We show that the category of lax involutive $n$-Frobenius algebras is Quillen equivalent to the category of right comodules of the $n$-Poisson cooperad. It follows in particular, that the cohomology of a parallelized $n$-manifold is…