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arXiv:2601.19230v1 Announce Type: new Abstract: The Graph Minors Structure Theorem (GMST) of Robertson and Seymour states that for every graph $H,$ any $H$-minor-free graph $G$...
arXiv:2601.19242v1 Announce Type: new Abstract: Given $\lambda\in (0,1/2)$, let \begin{equation*} C_\lambda=\set{(1-\lambda)\sum_{i=1}^\infty d_i\lambda^{i-1}:d_i\in\set{0,1}} \end{equation*} be the middle Cantor sets with convex hull $[0, 1]$. We are...
arXiv:2601.19250v1 Announce Type: new Abstract: Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale...
arXiv:2601.19252v1 Announce Type: new Abstract: In this paper we characterize concircular helices in $R^3$ by means of a differential equation involving their curvature and torsion....
arXiv:2601.19253v1 Announce Type: new Abstract: The main goal of this paper is to show that helix surfaces and the Enneper surface are the only surfaces...
arXiv:2601.19272v1 Announce Type: new Abstract: We obtain an improved lower bound for the restricted reverse weak-type estimate of the Hardy-Littlewood maximal operator $M$. This result...
arXiv:2601.19274v1 Announce Type: new Abstract: We study variable elliptic structures in the plane defined by a smoothly varying quadratic relation i^2 + beta(x,y) i +...
arXiv:2601.19282v1 Announce Type: new Abstract: The Integrate-and-Fire model is a Fokker-Planck equation arising in neuroscience. It describes the evolution of the probability density of the...
arXiv:2601.19283v1 Announce Type: new Abstract: We prove the existence of secondary terms of order $X^{5/6}$ in the asymptotic formulas for the average size of the...
arXiv:2601.19288v1 Announce Type: new Abstract: This article is the first in a series devoted to computing the class groups of real quadratic fields. We present...
arXiv:2601.19299v1 Announce Type: new Abstract: This paper studies the continuous-time q-learning (the continuous time counterpart of Q-learing) for Markov switching system under Tsallis entropy regularization....
arXiv:2601.19301v1 Announce Type: new Abstract: The product matrix of a finite commutative ring $R=\{x_1,x_2,\ldots,x_n\}$ and an element $u \in R$ is the matrix $A_u(R)=[a_{ij}]$, where...
arXiv:2601.19307v1 Announce Type: new Abstract: We consider a multiscale stochastic compartmental model with three types of cells (stem cells, immature cells and mature cells) which...
arXiv:2601.19308v1 Announce Type: new Abstract: We study composition operators between weighted Bergman spaces of the polydisc induced by smooth symbols. We prove a general result...
arXiv:2601.19317v1 Announce Type: new Abstract: This paper investigates the well-posedness of linear elliptic equations, focusing on the divergence-free transformation introduced in the author's recent work...
arXiv:2601.19319v1 Announce Type: new Abstract: We prove that the average error term when counting square-free values of polynomials is the quartic root of the main...
arXiv:2601.19323v1 Announce Type: new Abstract: It is often asserted in the literature that one should expect positive autocorrelation for random walk Metropolis-Hastings (RWMH), especially if...
arXiv:2601.19327v1 Announce Type: new Abstract: In recent progress on the union-closed sets conjecture, a key lemma has been Boppana's entropy inequality: $h(x^2)\ge\phi xh(x)$, where $\phi=(1+\sqrt5)/2$...
arXiv:2601.19330v1 Announce Type: new Abstract: It is of significant interest to understand whether a noise will speed up or prevent blow up. Under certain nondegenerate...
arXiv:2601.19355v1 Announce Type: new Abstract: We show that for a weighted Lipschitz operator $\omega\widehat{f}$, certain linear properties are equivalent. Specifically, we prove that compactness, strict...
arXiv:2601.19357v1 Announce Type: new Abstract: This work develops a polygonal cell-based smoothed finite element method for steady-state, transient, and free-surface seepage in saturated porous media....
arXiv:2601.19358v1 Announce Type: new Abstract: In this article, we study acylindrical graphs of groups, local quasiconvexity, and Cannon-Thurston maps in the setting of totally disconnected...
arXiv:2601.19359v1 Announce Type: new Abstract: We consider a monomial Caffarelli-Kohn-Nirenberg inequality, find the optimal constant and classify the optimizers under an integrated curvature dimension condition....
arXiv:2601.19370v1 Announce Type: new Abstract: Vehicular platooning refers to coordinated and close movement of vehicular users (VUs) traveling together along a common route segment, offering...