5207 papers
This paper introduces new techniques to provide a unified framework for computing the metric entropy of ellipsoids in Banach spaces, delivering precise asymptotic expansions with explicit constants, improved second-order terms, and the first exact characterization for infinite-dimensional bodies, with significant applications to function classes in Sobolev and Besov spaces and machine learning.
This paper establishes the global well-posedness of the elastic-viscous-plastic (EVP) sea-ice model under inviscid Voigt-regularization, thereby resolving the long-standing issue of handling viscosity coefficients without cutoff that has hindered the analysis of related sea-ice models.
This paper establishes the existence, energy decay, and blow-up behavior of solutions for a three-dimensional piezoelectric beam model with nonlinear dampings and supercritical sources by utilizing nonlinear semigroups, the potential well method, and differential inequality techniques, while removing restrictive conditions on model coefficients.
This paper advances the theory of holonomic D-modules by establishing the invariance of Euler characteristics under localization and regular singular twists, proving local generic vanishing theorems via twisting with differential forms, and providing a direct construction of the Laplace transform for Stokes-filtered sheaves that completes the correspondence with holonomic D-modules.
This paper introduces and analyzes a divide-and-conquer algorithm for quantizing one-dimensional probability distributions, establishing a universal Wasserstein-1 error bound and demonstrating through numerical experiments that the method achieves optimal convergence rates while offering superior stability under arithmetic operations compared to existing schemes.
This paper investigates the geometric properties of tetrahedra with a fixed base by characterizing the closure and boundary of the set formed by the cosines of the face angles at the apex.
This paper establishes explicit criteria, based on Yavicoli-thickness, -uniformity, and Newhouse thickness conditions, under which compact subsets of (particularly in the plane) are guaranteed to contain similar copies of any linear 3-point configuration or any triangle.
This paper investigates the asymptotic symmetry structure of Jackiw-Teitelboim supergravity within a BF framework, demonstrating how the dilaton supermultiplet dynamically reduces the affine symmetry to a specific subalgebra with an abelian ideal, thereby providing a consistent bulk-based framework for studying boundary dynamics beyond the Schwarzian regime.
This paper establishes a non-unitary version of the Bisognano-Wichmann property and proves Haag duality for nets of smeared Wightman fields by deriving Tomita-Takesaki-like results directly from Wightman axioms, thereby extending these fundamental algebraic quantum field theory concepts to non-unitary theories where traditional Hilbert space functional analysis tools are unavailable.
This paper provides an explicit description of the phase space stratification for Calogero-Moser-Sutherland systems associated with , demonstrating that each positive-dimensional symplectic stratum is symplectomorphic to and admits natural action-angle coordinates.
This paper applies Sandqvist's semantics for classical logic without bivalence to metamathematics, demonstrating how this anti-realist framework resolves -incompleteness, establishes induction as meaning-constitutive, and provides an elementary consistency proof for Peano Arithmetic without relying on transfinite ordinals or transcendent truth.
This paper establishes a sharper upper bound for the amenability constant of the Fourier algebra of discrete groups and uses it to calculate explicit values for new classes of discrete and compact groups, thereby providing further evidence for the conjecture that Runde's lower bound is an equality.
This paper formulates a ten-dimensional holomorphic supergravity on a Calabi-Yau five-fold that reproduces heterotic moduli equations, exhibits factorized anomalies reconstructing a double-extension complex for moduli counting, and is conjectured to be an -twisted version of supergravity related to the Costello-Li theory.
This paper theoretically analyzes the Bergman determinantal point process to optimize its simulation by constructing restricted variants, establishing optimal transport inequalities for truncation errors, determining the optimal number of points with deviation bounds, and providing general deviation results for determinantal point processes.
This paper advances Mazur's Program B for elliptic curves over by proving that the genus-69 modular curve has no non-CM rational points, a result achieved by linking these points to solutions of a generalized Fermat equation and reducing the complete classification of 7-adic Galois representations to finding rational points on a single plane quartic.
This paper proposes a new omnibus goodness-of-fit test for univariate continuous distributions that leverages the full covariance structure of trigonometric moments to achieve a well-calibrated asymptotic null distribution, offering a unified, plug-and-play framework with demonstrated accuracy and power across 11 common parametric families.
This paper introduces the concept of the Hamiltonian path index as the minimum number of iterations required for a graph's line graph to contain a Hamiltonian path, proving its existence for all graphs and determining its exact value for trees while discussing its properties in graphs with Hamiltonian 2-connected blocks.
This paper introduces a unified framework for analyzing wireless network utility regions based on the spectral radius of nonlinear mappings, offering a powerful mathematical tool to characterize feasible regions, derive tractable conditions for convexity, and optimize sum-rate maximization across cellular, cell-less, and hybrid architectures.
This paper proves that for any reversible Finsler metric on the two-sphere, the number of prime closed geodesics grows quadratically with respect to length, utilizing improved versions of Franks' theorem and cylindrical contact homology.
This paper characterizes product identities of the form among Hecke eigenforms over totally real number fields, proving that such identities occur exclusively for the field with exactly two instances, while also demonstrating their non-existence when both factors are Eisenstein series of distinct weights.