4012 papers
This paper establishes a logarithmic Bott localization formula for global holomorphic sections of on a compact complex manifold with a simple normal crossings divisor, extending the theory to non-isolated zero schemes that are local complete intersections and providing a current-theoretic formulation that identifies the local residue with a Coleff-Herrera current.
This paper establishes conditions for the distance integrality of specific graph families constructed via joins with cycles and for the distance Laplacian integrality of a particular class of dumbbell graphs.
This paper extends Kajiura's construction of noncommutative deformations of holomorphic line bundles on complex tori by viewing them through the lens of twisted trivial bundles and investigates their mirror duals within the SYZ framework.
This paper establishes a universal approximation theorem proving that shallow neural networks with inputs in a topological vector space and outputs in a Hausdorff locally convex space are dense in the space of continuous mappings on compact subsets, thereby generalizing existing scalar-valued results to include Banach and Hilbert-valued approximations.
This paper presents an elementary, self-contained proof of the Lovász Local Lemma that eliminates the need for conditional probabilities by relying solely on unconditional probability inequalities.
This paper establishes the unique determination of both linear and nonlinear coefficients in a semilinear Helmholtz equation from Neumann-to-Dirichlet boundary measurements using higher-order linearization and provides a Bayesian numerical reconstruction framework with uncertainty quantification.
This paper introduces shifted quantum affine symmetric pairs of split simply-laced type and constructs their GKLO representations, providing a complete proof that the proposed formulas define a valid representation.
This paper determines the values of the weighted zero-sum constants , , and for the specific case where the weight sets are and in the cyclic group .
This paper defines and analyzes a class of continuous functions on constructed via an infinite stochastic matrix and specific parameters, establishing criteria for their monotonicity, differentiability, and singularity while investigating the properties of their level sets.
This paper establishes a necessary and sufficient condition for the convergence of infinite products of rational inner functions on the polydisk and extends the concepts of Malmquist-Takenaka bases and unwinding to higher dimensions.
This paper investigates a one-parametric family of left-invariant, SO(1,1)-symmetric Lorentzian structures on the universal covering of SL(2,R), analyzing their global geodesic optimality and examining how these properties deform into those of a limiting sub-Lorentzian structure.
This paper establishes sufficient conditions for the existence of longest arcs in left-invariant three-dimensional contact sub-Lorentzian structures on solvable Lie groups and the universal cover of SL(2, R), addressing the nontrivial existence question inherent in such optimal control problems with unbounded control sets.
This paper establishes a comparison between the Segre motivic Chern classes of open projected Richardson varieties and affine Schubert cells via the affine Grassmannian using Demazure–Lusztig operators, while also relating these classes to twisted Kazhdan–Lusztig R-polynomials and providing a combinatorial formula for the Grassmannian case.
This paper resolves the non-uniqueness of maximal ancillary -fields by introducing a sequence-based asymptotic framework that enables semiparametrically efficient inference through finite-sample nuisance elimination, specifically utilizing center-outward residual ranks and signs to construct distribution-free restrictions of locally asymptotically normal experiments without requiring nuisance parameter estimation.
This paper characterizes the fundamental group of disjointly tree-graded spaces in terms of the fundamental groups of their constituent pieces, establishing an embedding into an inverse limit of free products even when local simple connectivity is absent.
This paper proposes sum rules for the moments of permutations with a fixed number of fixed points involving Stirling numbers of the first kind, while also deriving related identities for binomial coefficients and outlining connections to Bell numbers.
This paper establishes four equivalent combinatorial conditions proving that the maximum number of Hamiltonian sets of polygonal paths in a simple assembly graph of size is , a bound achieved exclusively by graphs known as tangled cords.
This paper establishes a combinatorial sufficient condition based on multinet structures for the Milnor fiber of a complex hyperplane arrangement to be non-1-formal and uses this criterion to construct an infinite family of monomial arrangements with non-formal Milnor fibers.
This paper establishes that Metropolis–Hastings algorithms with non-geometrically ergodic proposals and high acceptance rates at large states fail to be geometrically ergodic, while further demonstrating that guided walk variants converge twice as fast as random walk versions for polynomial-tailed targets but exhibit similar ballistic speeds to random walks for strictly convex potentials.
This survey reviews the computation of Weil-Petersson and Masur-Veech volumes for moduli spaces of Riemann surfaces, highlighting their profound impact on combinatorial enumeration, intersection theory, and recursion relations, while drawing parallels between the methods used to calculate these two distinct types of volumes.