4793 papers
This paper provides a characterization of Dedekind domains, including non-Noetherian ones, based on a specific property of their module homomorphisms, utilizing a homological algebra argument in its proof.
This paper presents the first weakly polynomial-time algorithms for the parametric submodular line search problem by exploiting a dual formulation and cutting-plane methods to reduce the number of calls to the exact submodular function minimization oracle.
This paper proves that every large connected Cayley graph with degree at least for some absolute constant contains a Hamilton cycle, thereby advancing the Lovász conjecture by improving previous density thresholds through a proof that utilizes an arithmetic regularity lemma tailored to Cayley graphs instead of Szemerédi's regularity lemma.
This paper derives general bright-dark soliton solutions to the coupled Sasa-Satsuma equation under mixed boundary conditions by constructing two-bright-two-dark solutions for the four-component Hirota equation via the KP reduction method and analyzing their dynamical behaviors.
This paper generalizes a lower bound for the log canonical threshold of -primary ideals to the -threshold in positive characteristic and provides a classification of homogeneous ideals that achieve this minimal singularity threshold, thereby resolving a conjecture by Bivià-Ausina.
This paper proposes a definition of asymptotically flat spacetimes consistent with gravitational scattering and proves three antipodal matching conditions at spatial infinity, which are reformulated as asymptotic conservation laws governing tails and the breaking of peeling.
This paper constructs a family of complex quasi-Hamiltonian G-spaces as moduli spaces of framed meromorphic connections on principal G-bundles over a disc, thereby providing a finite-dimensional framework for the symplectic structures of monodromy and Stokes data on arbitrary genus Riemann surfaces and offering a new proof of the symplectic nature of their isomonodromic deformations.
This paper resolves Grothendieck's localization problem for a specific class of rings from tight closure theory by utilizing a detailed analysis of the relative Frobenius map.
This paper establishes rigorous a priori bounds for the exact period of Rayleigh's stretched string equation to prove that Rayleigh's approximation overestimates the true period, providing explicit inequalities that demonstrate the relative error is directly proportional to the initial displacement and inversely proportional to the initial stretch.
This paper proves that any complete local domain of mixed characteristic possesses a weakly almost Cohen-Macaulay algebra by constructing it over the absolute integral closure using Fontaine rings and Witt vectors, thereby extending Heitmann's methods for the Monomial Conjecture.
This paper establishes the existence of big Cohen-Macaulay algebras in mixed characteristic for certain special cases by applying the almost purity theorem of Davis and Kedlaya to advance the homological conjectures.
This paper establishes that for a perfect -algebra satisfying property , the ring of Witt vectors of also possesses property , specifically proving this affirmative result for the property of being integrally closed under a mild condition.
This paper presents a new, elementary proof of the Cohen-Gabber theorem specifically for the equal characteristic case.
This informal note introduces the fundamental linear algebra concepts that underpin the complex structure of Higgs bundles and their moduli spaces, aiming to make this advanced mathematical topic accessible to a general audience.
This paper establishes that a compact polyhedron collapses to a subpolyhedron if and only if it admits a piecewise-linear free deformation retraction onto that subpolyhedron, while also addressing metric characterizations of collapsibility by correcting and providing a counterexample to a claim regarding injective metric spaces.
This paper rigorously establishes the gap property for linearized operators associated with the cubic nonlinear Schrödinger equation in three dimensions by proving, via a new comparison-based approach, that the interval contains no eigenvalues and that no resonances exist at the bottom of the essential spectrum, even in the fully non-radial case.
This paper demonstrates that twisted sectors in the vanishing cohomology of one-parameter deformations of Calabi-Yau type Fermat polynomial singularities, along with the genus zero Gromov-Witten generating series of the corresponding varieties, are components of automorphic forms for certain triangular groups, utilizing mixed Hodge structures, the Riemann-Hilbert correspondence, and genus zero mirror symmetry.
This paper reviews independence results within Norman Megill's finite axiom-schematization of classical first-order logic and demonstrates that a specific axiom scheme is independent despite all of its individual instances being provable from the remaining schemes.
This paper introduces a nonlinear potential theory problem to characterize Berezin densities for polynomial Bergman spaces and adapts a soft Riemann-Hilbert approach to study the asymptotics of planar orthogonal polynomials under exponentially varying weights, serving as a foundational step toward deriving explicit global expansions for the polynomial Bergman kernel and associated random normal matrix ensembles.
This paper introduces a novel collection of "deep zero problems" that focus on local properties at a small number of points, along with their associated uniqueness, sampling, and interpolation issues.