4476 papers
This paper addresses an Erdős-Herzog-Piranian problem by proving that the maximum product of distances for diameter-2 point sets can be found among convex polygons, providing improved constructions over regular -gons and demonstrating that a general characterization of extremal polygons is impossible for even orders.
This paper develops a comprehensive Malliavin calculus for the Dirichlet–Ferguson process on a general phase space by deriving explicit chaos expansions, establishing fundamental operators and rules, and applying the framework to characterize the Fleming–Viot process and prove a Poincaré inequality.
This paper generalizes the Peter-Weyl Theorem by demonstrating that functions on locally compact groups with large nontrivial compact open subgroups can be approximated by locally representative functions.
The paper proves that equivariantly simple invariant singularities can only exist for real representations and certain "almost real" representations of a group of prime order.
This paper establishes an upper bound and a simple single-error decoder for analog error-correcting codes with unit-norm columns, and constructs a new family of such codes with constant redundancy three that achieves a smaller height profile than existing MDS constructions.
This paper establishes the existence of global weak solutions for a Navier-Stokes-Cahn-Hilliard system modeling thermo-induced Marangoni effects in two-phase incompressible flows with variable physical parameters and singular potentials in both two and three dimensions, while also proving solution uniqueness in the two-dimensional case under matched density conditions.
This paper proposes a novel movable antenna approach for two-layer rate-splitting multiple access (RSMA) systems that employs a two-loop iterative algorithm to jointly optimize beamforming, user clustering, common rate allocation, and antenna positions, thereby significantly enhancing user fairness compared to existing benchmark schemes.
This paper establishes that the asymptotic distribution of quadratic forms for self-normalized heavy-tailed random vectors is determined solely by the diagonal entries of the matrix and the stability index , a result applied to derive the atom-free nature of the -heavy Marčenko--Pastur law for heavy-tailed sample correlation matrices.
This paper presents a detailed implementation of Riemannian Newton's method for optimization on the indefinite Stiefel manifold by deriving the Levi-Civita connection and analytically computing the Hessian under two existing metrics, then solving the resulting Newton equation in the tangent space via the linear conjugate gradient method to achieve fast local convergence.
This paper establishes a quantitative Central Limit Theorem for continuous-time Stochastic Gradient Descent by employing Malliavin calculus and second-order Poincaré inequalities to derive explicit Wasserstein convergence rates driven by the learning rate magnitude, a result validated through numerical experiments.
This paper investigates linear -quotients on affine spaces by employing explicit stacky resolutions to classify their singularity types and compute stringy motivic invariants, thereby reducing a conjecture by the authors and Fabio Tonini—which posits that these invariants match those of linear -quotients—to a computationally verified equality of multi-sets.
This paper presents an English translation and digitization of Sophie Kowalevski's 1889 French publication on the rotation of a rigid body about a fixed point, which introduced the famous Kovalevskaya Top.
The paper introduces the Inexact Bregman Sparse Newton (IBSN) method, a novel algorithm that combines a Bregman proximal point framework with a sparse Newton solver and Hessian sparsification to efficiently compute exact Optimal Transport distances for large-scale datasets while guaranteeing global convergence and outperforming existing state-of-the-art methods in both speed and precision.
This paper introduces a novel, simple, and compact control volume-based high-order limiter for the spectral volume method that effectively suppresses oscillations in discontinuous problems while preserving high-order accuracy and resolution through a nonlinear weighting reconstruction strategy.
This paper resolves Skolem's problem for -generalized Lucas sequences by characterizing their zero-distribution at negative indices and proving that the zero-multiplicity is exactly for all .
This paper establishes a base change framework to extend tensor function results from specific fields to general fields, thereby proving that slice rank is linearly bounded by geometric rank and is quasi-supermultiplicative for any 3-tensors over any field.
This paper presents a unified combinatorial-algebraic framework for constructing multicyclic codes of arbitrary dimension over by utilizing -dimensional primitive idempotents and multidimensional cyclotomic orbits to establish a direct equivalence between algebraic and combinatorial descriptions, derive a natural polynomial basis, and generalize BCH and Reed-Solomon bounds through an efficient constructive algorithm.
This paper establishes both Anderson localization and Hölder continuity of the integrated density of states for quasi-periodic Schrödinger operators on with non-constant analytic potentials and fixed Diophantine frequencies in the perturbative regime, utilizing a novel multi-scale analysis approach to control Green's functions.
This paper establishes Gaussian and non-Gaussian limit theorems for non-linear additive functionals of stationary Gaussian fields with Gneiting-class non-separable covariance structures over anisotropically growing domains, demonstrating that these covariances are asymptotically separable in a cumulant sense to explicitly characterize convergence to either Gaussian or 2-domain Rosenblatt distributions based on long-range dependence conditions.
This paper proves that the Lefschetz filtration and the perverse filtration on the cohomology of the compactified Jacobian of a complex integral curve with planar singularities are opposite to each other, thereby confirming a conjecture by Maulik and Yun.