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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...
arXiv:2601.19455v1 Announce Type: new Abstract: Polylogarithmic functions (polylogs) in $n$ variables can be viewed as elements of $(U\mathfrak{p}_{m})^*$, the dual of the universal enveloping algebra...
arXiv:2601.19456v1 Announce Type: new Abstract: There has been significant recent interest in understanding the dependence on the wavenumber, $k$, of boundary integral operators (BIOs), supported...
arXiv:2601.19459v1 Announce Type: new Abstract: We prove a central limit theorem for a class of H\"older continuous cocycles with an application to stricly convex and...
arXiv:2601.19460v1 Announce Type: new Abstract: Recently Baranyai described a necessary combinatorial characterisation of graph rigidity for dimension 3. In this short note we provide a...
arXiv:2601.19465v1 Announce Type: new Abstract: Sums of powers $S_p(n)=\sum_{k=1}^n k^p$ can be described by Faulhaber's formula in terms of the Bernoulli numbers. The first cases...
arXiv:2601.19471v1 Announce Type: new Abstract: Let $\rho : \Gamma \longrightarrow G$ be a Zariski dense irreducible convex representation of the hyperbolic group $\Gamma$, where G...
arXiv:2601.19478v1 Announce Type: new Abstract: This note is devoted to some nonlocal, nonlinear elliptic problems with an emphasis on the computation of the solution of...
arXiv:2601.19485v1 Announce Type: new Abstract: We show that the Kuperberg invariant of the Weeks manifold with any framing is a gauge invariant of finite-dimensional Hopf...
arXiv:2601.19511v1 Announce Type: new Abstract: This paper assumes a robust stochastic model where a set $\mathcal{P}$ of probability measures replaces the single probability measure of...
arXiv:2601.19512v1 Announce Type: new Abstract: We prove two weak compactness criteria in Musielak-Orlicz spaces for $N$-functions satisfying the $\Delta_2$-condition. They extend criteria from And\^o for...