2620 papers
This paper establishes necessary and sufficient conditions for the compactness of the embedding on the half-space with general singular weights, proving that compactness holds if and only if the measure has finite mass and satisfies a global tightness condition characterized by coercive tail inequalities and, in singular cases, weighted Hardy inequalities.
This paper investigates the Bott-Chern and Aeppli cohomologies of twistor spaces associated with compact self-dual 4-manifolds to characterize the validity of the -lemma, while explicitly computing the Dolbeault cohomology for the twistor space of the flat 4-torus as a specific example where the lemma fails.
This paper derives exact formulas for the proportions of derangements and derangements of -power order in various affine classical groups, utilizing a new generating function for specific integer partitions in the unitary case and verifying -polynomial identities in the symplectic and orthogonal cases.
This paper advances the dimension theory of sets and measures by weakening Hochman's exponential separation condition, demonstrating the equivalence of modified and original definitions for homogeneous self-similar IFS on , and proving the density of specific subsets defined by Assouad, Hausdorff, and dimensions within their respective spaces.
This paper establishes that the filter quotient construction preserves model structures under suitable conditions, demonstrating that while the resulting model inherits properties like being simplicial or proper, it may not remain cofibrantly generated, and further proves its compatibility with filter quotient -categories.
This paper establishes that a field is large if and only if it has an elementary extension that is the fraction field of a non-field henselian local domain, a result derived from new findings showing that the étale-open topology refines or is refined by the newly introduced finite-closed topology depending on whether the field is perfect or bounded.
This paper proposes centralized and distributed heuristic ADMM frameworks that combine continuous relaxation with efficient tree-projection subproblems to solve large-scale nonconvex multicommodity flow design problems under spanning tree and hop-constraint requirements, yielding near-optimal solutions.
This paper introduces the higher spin -operator associated with the Rarita-Schwinger operator, investigates its norm estimates, mapping properties, and adjoint, and applies these results to establish the existence and uniqueness of solutions for a higher spin Beltrami equation.
This paper generalizes the Atiyah problem and the Atiyah–Sutcliffe conjectures by introducing the -amplitude function, a tensor-based geometric inequality defined on finite graphs that recovers the original conjectures when the graph is complete.
This paper proposes optimization-based and deep reinforcement learning (specifically DDQN) methods to achieve positive-rate keyless covert communications in Rayleigh block-fading channels by solving power and rate allocation problems under both non-causal and causal channel state information scenarios.
This paper initiates a comprehensive study of -free graph drawings by establishing tight upper and lower bounds on edge density for every combination of drawing style, graph type, and forbidden cell type, while also characterizing simple graphs that admit drawings avoiding specific cell types and improving existing bounds for quasiplanar drawings.
This paper employs the localization framework to improve existing upper bounds on the number of cliques in graphs with bounded maximum degree or path length, while also providing structural characterizations of the extremal graphs that attain these sharper bounds.
This paper establishes that for a set of phylogenetic trees with leaves, if is sufficiently small (specifically ), the trees can be constructed to have virtually no common structure, thereby forcing any network displaying them to require nearly the maximum possible number of reticulations, .
This paper establishes a compactness result for the -convergence of integral functionals on -free vector fields to prove stochastic homogenization without periodicity assumptions, demonstrating that the homogenized integrand arises from limits of minimization problems on large cubes and can be explicitly characterized via the subadditive ergodic theorem under stochastic periodicity.
This paper investigates the arithmetic properties of factorizations in finitely-presented monoids by analyzing how presentation relations influence factorization behavior, constructing non-commutative fully elastic monoids, and proving that finitely-presented cancellative normalizing monoids satisfy the Structure Theorem for Unions.
This paper establishes explicit formulas for a quantum invariant functor on projective varieties over number fields, with a detailed analysis of the specific case involving abelian varieties with complex multiplication.
This paper classifies and analyzes exactly solvable one-dimensional complex Schrödinger operators related to the Gauss hypergeometric equation, organizing them into three geometric families (spherical, hyperbolic, and deSitterian) to compute their spectra and Green functions while establishing transmutation identities and linking them to symmetric manifolds.
This paper provides a complete classification of integrally closed domains and finitely generated torsion-free -algebras for which the ring of integer-valued polynomials is a Prüfer domain, proving that in the semiprimitive case, this property holds if and only if is a commutative finite direct product of almost Dedekind domains with finite residue fields satisfying specific boundedness conditions.
This paper establishes the global Hölder continuity of solutions to the Dirichlet problem for the complex Monge-Ampère equation on strictly pseudoconvex domains or Hermitian manifolds, assuming the right-hand side belongs to and the boundary data are Hölder continuous.
This paper extends the concept of average expansivity to operators on locally convex spaces, providing complete characterizations for weighted shifts on Fréchet and Köthe sequence spaces while addressing a specific open problem posed by Bernardes et al. and exploring general properties and examples of various expansivity notions.