2088 papers
This paper introduces a local treatment of finite alignment for arbitrary higher-rank graphs by identifying a finitely aligned sub-constellation, which enables the construction of novel locally compact path and boundary-path groupoids that extend existing models and are proven to be amenable.
This paper introduces the concepts of strongly and weakly left Jacobson rings, establishes a one-sided noncommutative Nullstellensatz for polynomial rings over finite-dimensional algebras, and characterizes the Jacobson property for Azumaya algebras and algebras finitely generated over their centers.
This paper introduces a unified spectral decomposition system for analyzing spectral functions on Hilbert spaces and establishes a novel reduced minimization principle that constructively simplifies the evaluation of their convex analytical objects, such as conjugates, subgradients, and Bregman proximity operators.
This paper bridges the gap between theory and practice for randomized iterative methods like Gauss-Seidel and Kaczmarz by deriving tighter asymptotic performance bounds through new spectral radius techniques and Perron-Frobenius theory, while simultaneously resolving a 2007 open problem by quantifying the performance benefits of relaxation.
This paper introduces an operad of dependent directed wiring diagrams to enable the composition of instantaneous systems like Mealy machines and parameterized stock-and-flow diagrams, providing a formal algebraic framework and a semantic morphism that maps these diagrams into Mealy machines.
This paper establishes that the -category of normed algebras in genuine -spectra is modeled by strictly commutative algebras in -symmetric spectra, providing a higher-categorical description of ultra-commutative global ring spectra as a partially lax limit of genuine -spectra categories.
This paper disproves the conjecture that a high-order explicit time-stepping scheme introduced by Buvoli remains stable as accuracy approaches infinity, while simultaneously establishing its superior stability over classical methods, deriving a criterion for maximum permissible accuracy, and providing a unified -stability analysis for extensional PDEs under the CFL condition.
This paper proves that Ruzsa's conjecture on congruence-preserving sequences holds true if the associated generating function has at most two singular directions at the origin, thereby showing that any potential counterexample must exhibit at least three such directions.
This paper computes the first and second moments of sums of Hecke eigenvalues for holomorphic cusp forms averaged over large weights, revealing distinct size transitions at and within the regime where the sum length is smaller than .
This paper investigates a path-based variant of the Explorer-Director game on graphs, demonstrating that the resulting number of visited vertices can differ arbitrarily from the original distance-based version depending on the graph structure.
This paper establishes the continuity of asymptotic entropy for random walks on wreath products (where is any countable group and is a hyper-FC-central group with a cubic-growth subgroup) by proving the continuity of non-return probabilities and demonstrating that weak continuity of harmonic measures implies entropy continuity, thereby extending known results to new classes of groups including linear and groups.
This paper extends interior non-concentration estimates for Laplace eigenfunctions to the boundary of compact smooth manifolds with boundary, demonstrating that these bounds, combined with a generalized sup-norm estimate, immediately yield the sharp bounds established by Grieser.
This paper establishes new weighted Sobolev embedding theorems and a Pólya-Szegö type inequality derived from an isoperimetric problem to analyze a class of semilinear degenerate elliptic equations in a three-dimensional domain, thereby extending existing results to higher dimensions.
This paper introduces a novel subgradient definition based on Busemann functions for convex optimization on Hadamard spaces, enabling the generalization of stochastic and incremental subgradient methods with guaranteed complexity bounds to nonpositively curved metric spaces such as BHV tree space.
This paper computes the derived Witt groups of smooth proper curves over nondyadic local fields of characteristic not equal to 2 by utilizing reduction techniques and conducting a general study of the existence of Theta characteristics.
This paper establishes the meromorphic continuation and, in the specific case of the lattice, a precise functional equation for a Dirichlet series involving Fourier-Jacobi coefficients of cusp forms on orthogonal groups of signature by utilizing an integral representation derived from Klingen-type orthogonal Eisenstein series and their connections to Epstein and Siegel Eisenstein series.
This paper investigates long-range one-dimensional internal diffusion-limited aggregation, establishing that clusters formed by random walks with finite variance converge to a nearly symmetric contiguous block (improving previous moment conditions), while those driven by walks in the domain of attraction of symmetric -stable laws ($1 < \alpha < 2$) form a contiguous block that occupies only a fraction of the total sites.
This paper extends support variety theory from the compact to the non-compact part of a monoidal triangulated category in the noncommutative setting, establishing conditions under which the extended theory detects the zero object and thereby confirming a portion of a conjecture by the second author, Nakano, and Yakimov regarding central cohomological support in stable categories of finite tensor categories.
This paper revisits and improves upon Erdős and Rado's proof regarding well-quasi-ordered finite-image sequences of length to establish that the maximum linearization of such sequences is bounded by a function roughly -times exponential in the maximum linearization of the underlying well-quasi-order, a bound shown to be nearly tight for .
This paper investigates the horofunction boundaries of Carnot groups by proving that all horofunctions are piecewise-defined via Pansu derivatives and demonstrating that filiform Lie groups of dimension provide the first examples where the boundary dimension deviates from the expected .