7024 papers
This paper establishes a -equivariant analogue of Orlov's short exact sequence for derived categories of abelian varieties and utilizes this framework, along with splitting propositions, to lift derived equivalences of abelian surfaces to generalized Kummer varieties.
This paper presents an error analysis and a new regularization parameter selection strategy for the iterated Golub-Kahan-Tikhonov method applied to discretized ill-posed operator equations, demonstrating its superior accuracy over both standard Golub-Kahan-Tikhonov and iterated Arnoldi-Tikhonov methods, particularly for non-symmetric matrices.
This paper establishes the quasi-optimality of the Crouzeix-Raviart finite element method for nonlinear -Laplace-type problems by proving that its error is bounded by the best-approximation error and a data oscillation term, while also deriving a novel localized a priori error estimate for the conforming lowest-order Lagrange FEM.
This paper compares various recently proposed notions of non-rigidity for horizontal vectors in Carnot groups, which are motivated by the study of monotone sets and Whitney extension properties.
This paper proposes a kernel-based maximum causal entropy inverse reinforcement learning framework for infinite-horizon stationary mean-field games that models unknown rewards in a reproducing kernel Hilbert space to capture nonlinear structures, proves the algorithm's theoretical consistency via Fréchet differentiability, and demonstrates superior policy recovery performance over linear baselines in traffic routing scenarios while extending the approach to finite-horizon non-stationary settings.
This paper introduces a novel computational framework that utilizes Legendre time-dimensional reduction to transform the inverse initial-data problem for compressible anisotropic Navier-Stokes equations into a solvable system of elliptic equations, enabling the robust and accurate reconstruction of initial velocity fields from noisy boundary observations.
This paper establishes a standard Central Limit Theorem for the normalized number of triangles in a modified edge-triangle Exponential Random Graph model, valid across the entire analyticity region of the free energy and derived via a polynomial representation of the partition function.
This paper establishes elementary upper and lower bounds for the partition function and its generalizations by applying a geometric inequality in Euclidean space.
This paper establishes the rigorous convergence of hyperbolic approximations to various higher-order PDEs, including the KdV and Kuramoto-Sivashinsky equations, by proving that weak solutions of the approximations converge to smooth solutions of the limiting problems, a result supported by numerical evidence.
This paper establishes the well-posedness and -based Sobolev regularity for vector-valued fluid dynamics PDEs, including Stokes and Navier–Stokes equations, on closed manifolds of minimal regularity by developing a parametrization-free variational approach that decouples velocity and pressure variables.
This paper investigates Benford's law in stick and box fragmentation models by reducing multi-proportion stick fragmentation to a single-proportion case using combinatorial identities, establishing necessary and sufficient conditions for strong Benford convergence based on irrationality exponents, and proving that high-dimensional box fragmentation satisfies strong Benford behavior under mild conditions.
This paper introduces the concept of (W')-specification to prove that recurrence sets in a broad class of subshifts and piecewise expanding interval maps, which lack the standard specification property, possess full Hausdorff dimension.
This paper establishes Lipschitz and Hölder stability for semi-discrete inverse source and Cauchy problems associated with stochastic parabolic equations in arbitrary dimensions by deriving and applying three new global Carleman estimates for the semi-discrete stochastic parabolic operator.
This paper establishes the NP-completeness of determining whether graphs lacking efficient edge dominating sets possess at least two perfect edge dominating sets, while also presenting a cubic-time algorithm to find, count, and weight minimal perfect edge dominating sets in -free graphs.
This paper proposes an inertial accelerated primal-dual algorithm derived from a time-scaled second-order differential system to solve non-smooth convex optimization problems with linear equality constraints, establishing fast convergence rates for the primal-dual gap, feasibility violation, and objective residual, and validating its performance through numerical experiments.
This paper proposes a proximal stochastic gradient algorithm with adaptive step size and variance reduction for convex composite optimization, establishing its strong convergence, gradient error convergence, and an convergence rate under Lipschitz continuity, while validating its effectiveness through numerical experiments on Logistic and Lasso regression.
This paper introduces a novel approach using disintegration maps to establish criteria for identifying metric measure foliations based on the geometric arrangement of conditional measure supports in Wasserstein space, while also demonstrating the framework's application to studying perturbations of such foliations.
This paper demonstrates that the union of randomly digitally shifted Korobov polynomial lattice point sets achieves a star discrepancy with an inverse that depends linearly on the dimension, thereby narrowing the search for explicit constructions from a continuum to a finite set of candidates.
This paper introduces a novel matrix-based framework for deriving upper and lower bounds for the Permutation Flowshop Scheduling Problem, demonstrating significant improvements on standard benchmarks and providing new theoretical insights into makespan value estimates and asymptotic approximation ratios.
This paper establishes explicit upper bounds on the quadratic Wasserstein distance between trained single-layer neural networks and their Gaussian process limits, demonstrating that the approximation error decays polynomially with network width while accounting for the influence of architectural parameters and training dynamics.