5923 papers
This paper extends Serrin's symmetry theorem to the anisotropic setting by proving that for a bounded indecomposable set of finite perimeter with specific regularity conditions, the existence of a weak solution to the anisotropic overdetermined torsion problem implies that the domain must be a translate and dilation of the Wulff shape.
This paper establishes the existence and multiplicity of solutions for an asymptotically linear fractional equation driven by the spectral fractional Laplacian with mixed Dirichlet-Neumann boundary conditions, utilizing pseudo-index theory when the nonlinear term is odd and specific parameter-eigenvalue relations hold.
This paper establishes sufficient and, in some cases, necessary conditions for the continuity and compactness of embeddings between various scales of generalised Morrey smoothness spaces on bounded smooth domains, utilizing wavelet characterisations to generalise and improve upon existing results for classical smoothness Morrey spaces.
This paper proves that the star product for quantum symmetric pair coideal subalgebras is short, a result the authors use to provide new, elementary proofs of fundamental properties such as the existence of the bar involution and the intertwiner property of the quasi K-matrix without relying on the quasi K-matrix itself.
This paper extends the definitions of -biharmonic and bi--harmonic maps between Riemannian manifolds and investigates their fundamental properties.
This paper establishes that for any ball in the unit square, the Hausdorff dimension of the intersection with the set of weighted badly approximable vectors equals that of the corresponding set of weighted approximable vectors, providing an explicit formula for this dimension in terms of the weight parameters.
This paper investigates which finitely generated groups admit proper actions on finite products of locally finite trees, presenting evidence that hyperbolic surface groups possess such actions and providing an explicit embedding of the genus 2 surface group into for any prime .
This paper proposes a policy iteration algorithm for general entropy-regularized time-inconsistent stochastic control problems that converges exponentially to an equilibrium policy by proving the generated value functions form a Cauchy sequence, thereby establishing the global existence and uniqueness of a classical solution to the associated exploratory equilibrium Hamilton–Jacobi–Bellman equation.
This paper extends the theory of border bases from zero-dimensional to positive-dimensional homogeneous ideals by introducing the concept of homogeneous border bases relative to infinite order ideals and providing an effective criterion for their characterization using formal multiplication matrices that requires verification in only finitely many degrees.
This paper constructs new infinite families of Ramanujan complexes with distinct local structures by utilizing super-definite unitary groups over totally real number fields, yielding novel examples across various types and providing a fully explicit rank-5 construction that generates golden gates for the real Lie group .
This paper presents a systematic method to construct vector fields that realize hierarchical excitable networks, where lower-level dynamics form heteroclinic connection patterns and top-level transitions between these patterns are excitable with zero threshold, thereby extending the simplex realization method of Ashwin and Postlethwaite.
The paper proposes Alkaid, a provably secure steganographic scheme that achieves deterministic robustness against edit errors by integrating minimum distance decoding into the encoding process, thereby significantly outperforming state-of-the-art methods in decoding success rates, payload capacity, and encoding speed.
This paper analyzes the secrecy performance of continuous-aperture array (CAPA) systems over Rayleigh fading channels, deriving theoretical expressions for secrecy rate and outage probability across single, multiple independent, and multiple collaborative eavesdropper scenarios, and demonstrating that CAPA systems outperform traditional spatially-discrete arrays by achieving higher secrecy rates, lower outage probabilities, and a diversity order equal to the spatial degrees of freedom.
This paper proposes a framework for Haar-type measures on topological quasigroups by introducing quasi-invariant measures with modular cocycles, demonstrating how Moufang-type identities constrain these cocycles to suggest that Kunen's theorem reflects the collapse of modular defects into a loop structure.
This paper establishes a necessary and sufficient condition for the existence of an equivalent measurable version of a stochastic process on arbitrary probability spaces by characterizing measurability with respect to a specific -algebra larger than the product -algebra, thereby generalizing previous results on separable versions and liftings.
This paper establishes sharp nonasymptotic oracle inequalities and minimax optimal convergence rates for sparse Lasso and Slope estimators of high-dimensional drift matrices in Lévy-driven Ornstein--Uhlenbeck processes based on discrete observations, thereby extending high-dimensional statistical theory to systems driven by pure jump noise.
This paper investigates finiteness conditions on skew braces, specifically -skew braces with additive groups, by establishing structural analogs to finite conjugacy and demonstrating how these properties characterize infinite set-theoretic solutions of the Yang-Baxter equation that behave similarly to finite ones.
This paper investigates the poset of subgroup classes in finite groups sharing the same set of element orders, characterizing the groups for which this poset is a chain or specifically , and analyzing its lattice properties, including distributivity and modularity, for cyclic and dihedral groups.
This paper establishes the existence, uniqueness, and exponential mixing of an invariant measure for a stochastic generalized Constantin-Lax-Majda-DeGregorio model of turbulence featuring an anomalous enstrophy cascade, utilizing the Krylov-Bogoliubov argument and large viscosity conditions to advance the dynamical systems understanding of turbulent cascades.
This paper establishes a precise asymptotic transfer mechanism for critical recursive composition schemes in map enumeration, demonstrating how singular structures and associated central limit theorems for statistics on 2-connected maps propagate to the broader class of all maps.