5870 papers
This paper establishes the functional framework and existence of weak solutions for quasilinear equations involving the fractional magnetic -Laplacian in three dimensions by employing variational methods and introducing a novel concentration compactness principle to address challenges posed by nonlocality, magnetic potentials, and critical nonlinearities.
This paper constructs Green currents associated with the dominant eigenspaces of holomorphic correspondences on compact Kähler manifolds under specific dynamical degree conditions, establishes the log-Hölder continuity of their super-potentials, and proves the exponential equidistribution of positive closed currents toward the main Green current when the correspondence exhibits simple cohomological action and satisfies a local multiplicity assumption.
This paper employs tropical geometry and Hamiltonian flows to derive explicit formulae for leaky Hurwitz numbers in genus 0 and prove that these invariants satisfy topological recursion under fixed leakiness, thereby establishing a partial inverse to recent results on KP -functions.
This paper generalizes the Newton-Puiseux Theorem to the context of planar real analytic vector fields by proving that every characteristic orbit of an isolated singularity admits a "power-log" asymptotic expansion.
This paper develops a spectral method to solve coupled kinetic and viscous half-space problems at network nodes, enabling the derivation of accurate macroscopic coupling conditions for the linearized BGK equation and its acoustic limit through detailed asymptotic analysis of interface layers.
The paper proves that transitive Anosov flows are abundant on fibered hyperbolic 3-manifolds by demonstrating that a finite index subgroup of the mapping class group consists of elements whose mapping tori carry such flows, thereby establishing that these manifolds have positive density within the set of all fibered hyperbolic 3-manifolds.
This paper establishes the discrete Rubio de Francia extrapolation theorem for pairs of quasi non-increasing sequences with weights and provides a weight characterization for the boundedness of the generalized discrete Hardy averaging operator on such sequences within the space .
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.