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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...
arXiv:2601.19379v1 Announce Type: new Abstract: This paper considers the problem of asynchronous stochastic nonconvex optimization with heavy-tailed gradient noise and arbitrarily heterogeneous computation times across...
arXiv:2601.19381v1 Announce Type: new Abstract: This paper considers decentralized nonsmooth nonconvex optimization problem with Lipschitz continuous local functions. We propose an efficient stochastic first-order method...
arXiv:2601.19389v1 Announce Type: new Abstract: In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the...
arXiv:2601.19400v1 Announce Type: new Abstract: The Muon optimizer has recently attracted attention due to its orthogonalized first-order updates, and a deeper theoretical understanding of its...
arXiv:2601.19414v1 Announce Type: new Abstract: We give an explicit description of the arithmetic-geometric extension of iterated Galois groups of rational functions. This yields a complete...
arXiv:2601.19415v1 Announce Type: new Abstract: Let $\widetilde{\mathfrak g}$ be an affine Lie algebra of type $D_4^{(1)}$ and $L(\Lambda)$ its standard module of level $k$ with...
arXiv:2601.19416v1 Announce Type: new Abstract: It is known that Rodrigues formulas provide a very powerful tool to compute orthogonal polynomials with respect to classical weights....
arXiv:2601.19417v1 Announce Type: new Abstract: We prove Gaussian concentration inequalities for maximal displacement of compactly supported random walks on a compactly generated locally compact group...
arXiv:2601.19418v1 Announce Type: new Abstract: Consider the following story: A teacher announces to her students a test for the following week, such that the test...
arXiv:2601.19427v1 Announce Type: new Abstract: We establish an existence result for weak solutions to an aggregation-diffusion-reaction equation with a constraint, arising in the modelling of...
arXiv:2601.19429v1 Announce Type: new Abstract: In this paper, we introduce a class of Dirichlet series defined in terms of the Riemann zeta-function, motivated by the...
arXiv:2601.19441v1 Announce Type: new Abstract: Motivated by the fact that the classical Jacobi theta function $\vartheta$ is the exponential generating function of the Eisenstein series,...
arXiv:2601.19442v1 Announce Type: new Abstract: The main objective of this paper is to prove that if capillarity effect is taken into account then there exist...
arXiv:2601.19443v1 Announce Type: new Abstract: We prove that, if $G$ is a finite almost simple group and $H$ is a maximal subgroup of $G$, then...