2748 papers
This paper establishes the existence and uniqueness of solutions to G-SVIEs under time-varying and integral-Lipschitz conditions using Picard iteration, while also proving the continuity of solutions with respect to parameters in the Lipschitz case.
This paper presents three families of modular Nahm sums for symmetrizable matrices of indices and with arbitrary rank , extending previous results for low ranks and utilizing these families to construct two vector-valued automorphic forms.
This paper proposes unfolding-free majorization-minimization algorithms for nonnegative CP and Tucker tensor decompositions under -divergences, utilizing tensor contractions and joint update strategies to achieve theoretical convergence guarantees and significant computational speedups over traditional unfolding-based methods.
This paper presents a polynomial-time algorithm for testing the isomorphism of finite groups that are extensions of abelian groups by -generated groups (including abelian-by-cyclic and abelian-by-simple cases), achieved through a novel method for computing the unit group of a finite ring.
This paper classifies free graph braid groups using cubical structures and demonstrates that, under specific conditions, the large-scale geometry of graph 2-braid groups is determined by the union of maximal product subcomplexes, yielding new examples of groups that are and are not quasi-isometric to right-angled Artin groups.
This paper surveys recent developments in the arithmetic of power monoids—structures formed by finite subsets of a monoid—and highlights their role in advancing factorization theory, particularly within non-cancellative and non-commutative settings.
This paper investigates the binomial sum by expressing it in terms of powers of for specific sequences like Fibonacci numbers and various polynomials, while also establishing its properties, probabilistic interpretations, and generating functions in relation to and Appell polynomials.
This paper provides explicit closed formulae for the even polynomials and , which represent the ratios and , by expressing them in terms of Eulerian numbers and analyzing their structural properties to aid future investigations into the arithmetic nature of these ratios.
This paper investigates homotopy decompositions of classifying spaces of compact connected Lie groups via a relative fiber-cofiber construction, establishing rational sharpness and Cohen-Macaulay properties for the resulting spaces under specific cohomological conditions while providing explicit cohomological and K-theoretic computations for examples involving maximal tori and commuting elements.
This paper establishes the quantitative stability of Kantorovich potentials and optimal transport maps on metric measure spaces with lower Ricci curvature bounds, confirming a recent conjecture by Kitagawa, Letrouit, and Mérigot through a novel proof using heat kernel-regularized -transforms that avoids reliance on linear structures or sectional curvature bounds.
This paper formalizes the order-dependence of the moving-range sigma estimator by decomposing its total variance into order-invariant and adjacency-specific components via random permutation, revealing that under normal sampling, the adjacency effect accounts for the majority of its efficiency loss relative to the standard deviation estimator.
This paper introduces a general determinantal framework for analyzing coalescing random walks on a line, providing exact finite-dimensional distributions for survivor systems and deriving known results like the Rayleigh spacing density and joint gap distributions through a unified method applicable to arbitrary nearest-neighbor walks and their Brownian limits.
This paper generalizes the spacetime positive mass theorem to multiple time dimensions, proving that energy remains nonnegative and bounded by the trace norm of linear momenta, with equality implying a foliation by flat submanifolds and, under an umbilicity assumption, an isometric embedding into a generalized pp-wave.
This paper introduces a scalable multitask Gaussian process model with a fully separable kernel structure that effectively handles functional covariates and correlated tasks, demonstrating superior accuracy and computational efficiency over single-task approaches in predicting the behavior of complex mechanical systems like riveted assemblies with limited data.
This paper establishes global well-posedness in the critical energy space and proves almost periodicity in time for the half-wave maps equation on the one-dimensional torus by leveraging its integrable Lax pair structure to derive explicit solution formulae and a general stability principle that extends to matrix-valued cases and companion results on the real line.
Conditional on Zywina's effective Serre uniformity conjecture, this paper establishes a natural parameterization of non-CM rational points on all modular curves using finitely many such curves, thereby confirming Mazur and Ogg's philosophy that these points arise from the geometry of modular curves.
Inspired by Katz's work, this paper investigates the converse of the known property regarding rational torsion injection into reductions for -type abelian varieties and proposes a conjectural list of possible torsion orders for modular abelian varieties over with dimension up to 5.
This paper establishes sharp bounds and asymptotic equivalences among the Albertson, Sombor, and Sigma indices for trees, demonstrating that the Sombor index serves as an intermediate descriptor linking global degree dispersion and local edge irregularity through precise -relationships.
This paper establishes and provides an algorithmic method to verify a new criterion ensuring that a quasi-finite, flat morphism with locally constant geometric fibers between real algebraic varieties induces a covering map on their real points in the Euclidean topology.
This paper introduces "bipredictability" (P) as a fundamental, bounded measure of shared information between observations, actions, and outcomes to distinguish mere agency from true intelligence, demonstrating that current AI systems lack the self-monitoring feedback loops necessary for adaptive learning and proposing a thalamocortical-inspired architecture to restore it.