2888 papers
This paper extends previous results on the structure of the center of finite -algebras to a broader range of prime characteristics and demonstrates that their Zassenhaus varieties are rational affine schemes birationally equivalent to a good transverse slice.
This paper formalizes the goal of demonstrating positive treatment effects in adaptive experiments within a multi-armed bandit framework, proposing novel inference procedures for threshold testing and an adaptive allocation rule that optimizes signal-to-noise ratio with logarithmic regret.
This paper presents a numerical technique for discretizing higher-order powers of the spectral fractional Laplacian with by utilizing the polyharmonic extension approach.
This paper extends the geometric simplex method to linear programs in locally convex topological vector spaces by replacing algebraic pivoting with a generalized geometric framework, thereby establishing convergence conditions and proving that all such polytopes possess exposed extreme points connected by edge paths, including complex cases like the Hilbert cube.
This paper establishes a sharp rate of convergence for a free-boundary curve shortening flow within a convex domain in , demonstrating that the flow evolves to a round half-point in finite time.
This paper provides a geometric realization of the universal enveloping algebras of Borcherds-Bozec algebras and certain generalized Kac-Moody algebras by utilizing motivic semi-derived and Bridgeland's Hall algebras associated with quivers with loops and acyclic quivers, respectively.
This paper establishes sharp quantitative integral inequalities for a general family of conformally invariant extension operators and their adjoints by developing a refined analysis of hypergeometric functions, thereby extending previous results to the full admissible parameter range.
This paper establishes the equivalence between Bogomolov's instability theorem and the Miyaoka-Sakai theorem on surfaces in positive characteristic, demonstrating how their interplay yields partial vanishing results, new proofs for Kawamata-Viehweg vanishing on del Pezzo surfaces, and Reider-type results for Fujita's conjecture.
This paper constructs new cotorsion pairs in an abelian category by gluing cotorsion pairs from a recollement's outer components, establishes conditions for their coincidence and completeness, and applies these results to Morita rings while introducing a specific class of recollements with enhanced homological properties.
This paper establishes that quadratic congruences modulo hold for a wide range of half-integral weight cusp forms with the eta multiplier and an arbitrary Dirichlet character, extending previous results limited to real characters through the study of modular Galois representations and a new theorem on the existence of specific conjugacy classes in their images.
This paper introduces the class of -cuttable undirected phylogenetic networks as a computationally useful alternative to tree-child-orientable networks, demonstrating that they are recognizable in polynomial time and render the NP-hard Tree Containment problem solvable in polynomial time for .
This paper establishes the local and global well-posedness, quenching criteria, and asymptotic convergence rates (exponential or algebraic) of solutions to a second-order nonlocal parabolic MEMS equation by employing operator semigroups, Lojasiewicz–Simon inequalities, and numerical validation.
This paper introduces a novel Fréchet regression framework for multivariate distributional responses that leverages the nonparanormal transport metric to efficiently decompose the problem into marginal and dependence regressions, offering theoretical guarantees on convergence and dimensionality while demonstrating practical utility in continuous glucose monitoring.
This paper introduces a novel construction of local Morse homology to compute the homology of critical points in the Lagrange problem, thereby proving that linear critical points are either saddle points or degenerate, refining the previous conclusion that they must be saddle points if non-degenerate.
This paper provides a comprehensive survey of various Waring-type problems across the mathematical structures of groups, Lie algebras, and associative algebras.
This paper introduces the bicomplex Prabhakar derivative by extending fractional calculus to four-dimensional bicomplex spaces, establishing its fundamental operational properties and integral representations to provide a versatile framework for modeling complex phenomena with memory effects and multi-dimensional coupling.
This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations modeling Micro-Electro-Mechanical Systems (MEMS) under Dirichlet boundary conditions, establishing their convergence to equilibrium with rate estimates and supporting numerical simulations.
This paper develops a wave function renormalization scheme within the Hamiltonian formalism to construct the ground state representation of interacting Hamiltonians for non-relativistic particles coupled to quantized relativistic fields, thereby addressing ultraviolet and infrared singularities in models like the spin-boson and Nelson systems.
This paper proposes a unified calibration framework that integrates heterogeneous internal and auxiliary information into randomized experiments under covariate-adaptive randomization via convex optimization, ensuring asymptotic validity and a no-harm efficiency guarantee while accommodating scenarios with growing numbers of strata and information sources.
This short note refutes two natural conjectures regarding polynomial count varieties by demonstrating that a smooth variety with a point count of is not necessarily isomorphic to affine space, and that such varieties do not necessarily have vanishing Hodge numbers for .