3729 papers
This paper demonstrates that under the condition of a tracially sequentially-split -homomorphism of order zero, key regularity properties including tracial -comparison, tracial -almost divisibility, and tracial nuclear dimension less than are preserved from a target unital -algebra to a source algebra .
This paper addresses open questions regarding strict spectral approximants by computing the subdifferential of the Ky Fan - norm to establish characterizations for best approximations and derive necessary and sufficient conditions for -orthogonality.
This paper establishes spectral upper bounds for the independence number of graphs and even uniform hypergraphs, extends the Hoffman bound to these structures, and provides a simple spectral condition to determine key graph parameters including the independence number, Shannon capacity, and Lovász number.
This paper proves the author's conjecture that every compact primitive of a Stepanov remotely almost periodic function with a minimal -limit set is itself remotely almost periodic, thereby resolving the problem of integrating such functions.
This paper presents new methods for constructing external subsets of nonstandard arithmetic models to demonstrate that while copies of the real numbers cannot be formed within an ultraproduct of finite fields using these techniques, such constructions can yield copies of the algebraic reals, hyperreal fields, or algebraically closed fields of continuum cardinality.
This paper proves a conjecture by Dong et al. regarding the negativity of the -th derivative of the logarithm of the chromatic polynomial with a negative variable for all and , where is the graph's maximum degree.
This paper establishes higher pointwise regularity for nonnegative classical solutions of fully fractional parabolic equations by providing a unified proof based on novel equivalent definitions of pointwise function spaces and the integral representation of the fractional heat kernel.
The paper presents a new characterization of Fano type varieties.
This paper presents a finite-blocklength analysis for Ordered Reliability Bits GRAND (ORBGRAND) by deriving a random-coding union bound and characterizing its decoding metrics to establish a second-order achievable-rate expansion with a normal approximation, thereby quantifying its performance at short-to-moderate blocklengths where prior results were limited to asymptotic regimes.
This paper presents an all-orders worldline effective action for Kerr-Newman black holes within twistor particle theory and identifies exact hidden symmetries in self-dual backgrounds.
This paper investigates the representation theory of shifted super Yangians and finite -superalgebras of type A by establishing a criterion for the finite dimensionality of irreducible modules, deriving an explicit Gelfand-Tsetlin character formula for Verma modules, and proving that the centers of these algebras associated with even nilpotent elements are isomorphic to the center of the universal enveloping superalgebra.
This paper utilizes exchange-graph techniques and weighted mixed-angulations to derive explicit presentations of the fundamental groups for genus-zero strata of meromorphic quadratic differentials, generalizing known relations to include higher-order zeroes.
This paper investigates the topological, metric, and fractal properties of a specific family of homogeneous self-similar sets parameterized by , proving that each set is a Cantorval with a non-empty interior and fractal boundary, while also determining its Lebesgue measure and the Hausdorff dimension of its boundary.
This paper investigates the subnormality of quotients of -invariant Hilbert modules by homogeneous polynomials, establishing that such quotients are subnormal only if the polynomial is square-free and of degree at most one for standard spaces like the Hardy and Drury-Arveson modules, while also demonstrating that higher-degree examples exist for specific invariant modules like the Dirichlet module.
This paper proves the validity of the strong version of the union of uniform closed balls conjecture in the plane.
This paper introduces the persistent local Laplacian formalism, a theoretically grounded and highly parallelizable framework that overcomes the sensitivity and scalability limitations of traditional topological data analysis by establishing a generalized persistent Hodge isomorphism and unitary equivalence to efficiently extract fine-grained local structural signatures from large-scale datasets.
This paper argues that Peacock's principle of permanence was not invalidated by Hamilton's non-commutative algebras, but rather correctly understood as a conservative strategy—rooted in Hume's philosophy—that permits exceptions like non-commutativity only when the reasons for violating established laws of reasoning outweigh the reasons for preserving them.
This paper presents the proceedings of the Eighth International Conference on Applied Category Theory (ACT2025), held at the University of Florida in June 2025, which featured a diverse collection of contributions spanning pure and applied disciplines such as computer science, quantum computation, and chemistry.
This paper resolves a problem posed by Bang-Jensen and Wang by proving that every 6-strong split digraph is 2-linked, and further establishes that every 5-strong semicomplete split digraph is 2-linked, a bound shown to be tight.
This paper investigates an inverse Robin spectral problem for the nonlinear -Laplace operator by establishing a thin-coating asymptotic limit, proving the uniqueness of the Robin coefficient via linearization and unique continuation, and deriving a conditional local Hölder-type stability estimate.