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arXiv:2601.19790v1 Announce Type: new Abstract: We establish infinite families of congruences modulo arbitrary powers of $2$ for three restricted partition functions $M(n), T^\ast(n)$, and $P^\ast(n)$...
arXiv:2601.19797v1 Announce Type: new Abstract: We develop a general theory of nonlocal linear elasticity based on nonlocal gradients with general radial kernels. Starting from a...
arXiv:2601.19800v1 Announce Type: new Abstract: Indicator variograms and madograms are structural tools used in many disciplines of the natural sciences and engineering to describe random...
arXiv:2601.19801v1 Announce Type: new Abstract: This thesis studies qualitative properties of solutions to nonlinear elliptic equations of Poisson type with Dirichlet boundary conditions that arise...
arXiv:2601.19803v1 Announce Type: new Abstract: The aim of this paper is to consider the extensibility of the Diophantine triple $\{2,b,c\}$, where $2
arXiv:2601.19805v1 Announce Type: new Abstract: Building upon the work of Buczy\'nska et al., we study here tensor formats and their corresponding encoding of tensors via...
arXiv:2601.19807v1 Announce Type: new Abstract: We prove that the tail of the sets $$\mathbf S_x := \big\{\left\lfloor x^n\right\rfloor : n\in \mathbb N\big\}$$ are Sidon for...
arXiv:2601.19808v1 Announce Type: new Abstract: We consider an initial-boundary value problem for a class of nonlocal thin film equations governed by the spectral fractional Laplacian...
arXiv:2601.19813v1 Announce Type: new Abstract: The adaptive Antoulas-Anderson (AAA) algorithm for rational approximation is a widely used method for the efficient construction of highly accurate...
arXiv:2601.19817v1 Announce Type: new Abstract: We present a computational study of 200 composite integers of approximately 350 bits, engineered using the Arnault framework to pass...
arXiv:2601.19828v1 Announce Type: new Abstract: We present a unified framework for the analysis of space-time methods based on Galerkin-type time discretizations for parabolic and hyperbolic...
arXiv:2601.19830v1 Announce Type: new Abstract: We present a new cryptomorphic definition of orthogonal matroids with coefficients using Grassmann--Pl\"ucker functions. The equivalence is motivated by Cayley's...
arXiv:2601.19838v1 Announce Type: new Abstract: The year 2025 marks the 100 and 30 years anniversaries of the discovery of Bose--Einstein condensation and its successful experimental...
arXiv:2601.19840v1 Announce Type: new Abstract: An XC-algebra is the minimum algebraic structure needed to define a framed, oriented knot invariant and generalises Lawrence's invariant obtained...
arXiv:2601.19841v1 Announce Type: new Abstract: In this paper, we study oriented surfaces S in $\mathbb{R}^3$, called Surfaces with quadratic support function of harmonic type (in...
arXiv:2601.19845v1 Announce Type: new Abstract: We prove that for $k\ge 1$, all coefficients in the expansion of the series $$\sum_{n\ge 0} \frac{(q^{2n+2}, q^{2n+2k}; q^2)_\infty}{(q^{2n+1};q^2)_\infty^2} q^{2n}$$...
arXiv:2601.19846v1 Announce Type: new Abstract: We investigate a two-parameter hyperbolic relaxation approximation to the incompressible Navier-Stokes equations, incorporating a first-order relaxation and the artificial compressibility...
arXiv:2601.19855v1 Announce Type: new Abstract: We characterise non-Hermitian Fabry-P\'erot resonances in high-contrast resonator systems and study the properties of their associated resonant modes from continuous...
arXiv:2601.19860v1 Announce Type: new Abstract: Let $\mathcal G\simeq H\rtimes\Gamma$ be the semidirect product of a finite group $H$ and $\Gamma\simeq\mathbb Z_p$. Let $ F/\mathbb Q_p$...
arXiv:2601.19864v1 Announce Type: new Abstract: In this paper, we establish the properties of viscosity solutions in Martinet spaces, which lack both the algebraic group law...
arXiv:2601.19868v1 Announce Type: new Abstract: This study investigates component wise estimation of ordered variances of scale mixture of two normal distributions. For this study two...
arXiv:2601.19872v1 Announce Type: new Abstract: Nonlocal boundary value problems with Dirichlet or Neumann boundary are well-studied for nonlocal operators of the type $\mathcal{L}_\gamma u =...
arXiv:2601.19873v1 Announce Type: new Abstract: We show that for infinite Tychonoff spaces X and Y the weak*-dual of Ck(X x Y) contains a basic sequence;...
arXiv:2601.19874v1 Announce Type: new Abstract: Consider \[ \begin{cases} F(D^2 u,Du,u,x) = u^{-p}v^{-q},~\text{in}~\Omega\\ F(D^2 v,Dv,v,x)=u^{-r}v^{-s},~~\text{in}~~\Omega\\ u,v>0~~\text{in}~~\Omega\\ u=v=0~\quad~\text{on}~~\partial\Omega, \end{cases} \] where $\Omega$ is an open connected subset...