4481 papers
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.
This paper demonstrates that the -convexification of Gowers' space yields Banach spaces with unique unconditional bases containing block bases with spreading models distinct from , , and , thereby resolving a long-standing open problem by Bourgain et al. and disproving the conjecture that such spaces must be isomorphic to their squares.
This paper extends Khovanov homology to links in 3-manifolds that are connected sums of orientable interval bundles over surfaces by constructing type D and type A tangle invariants that, when glued along a separating sphere, recover the link's Khovanov homology.
This paper establishes the integrability of a one-parameter family of coupled Dirac-scalar field theories in dimensions that interpolates between the Dirac-sinh-Gordon and Dirac-sine-Gordon systems by constructing an explicit -valued Lax pair, proving the physical non-triviality of the deformation, and deriving associated conserved densities.
This paper investigates the Laplace transform in general neighborhoods of to establish conditions for decomposing holomorphic functions into discrete sums of exponentials, addressing key properties such as continuity and resummation formulas.
This paper investigates the convergence of discrete exponential sums with positive exponents in neighborhoods of negative infinity, demonstrating that such sums can be effectively summed by grouping terms with similar exponents into "packages" to achieve massive cancellations, particularly when the sums are bounded within logarithmic neighborhoods.
This paper establishes the wellposedness and polynomial energy decay of solutions for a quintic defocusing wave equation with nonlinear, energy-dependent damping by combining Galerkin approximations, Strichartz estimates, and an adapted Nakao method to overcome critical nonlinearity challenges.
This paper summarizes existing results and open questions regarding isometric embeddings between Schatten classes, provides an overview of relevant methods, and establishes a new non-embeddability result using a novel approach.
This paper characterizes -matching, interchangeable, and totally compatible products specifically within the context of null-filiform associative algebras.
This paper extends A. Miller's -forcing framework to regular uncountable cardinals to construct models with diverse lengths for the -Borel hierarchy on subspaces of the generalized Baire space and to determine the exact -Borel complexity of certain well-founded tree classes.
This paper establishes a groupoid-equivariant formulation of the Fredholm index by constructing a natural KK-theory class for Fredholm operators within the unitary conjugation groupoid framework, demonstrating that its composition with the Calkin extension boundary map recovers the classical index.
This paper proposes a model-free predictive tracking algorithm for unknown nonlinear systems with Koopman linear embeddings that leverages Willems' fundamental lemma to achieve dynamic regret decaying exponentially with the prediction horizon, effectively bridging the performance gap between nonlinear and lifted linear counterparts.
This paper establishes that for sufficiently large , the non-real part of the closure of roots of restricted polynomials outside the unit disk is exactly the closure of a finite-capture locus, achieved by constructing canonical traps and proving uniform inclusion properties within a specific lens-shaped region.
This paper establishes sharp uniform bounds on the eigenvalues of time-frequency localization operators and coherent state transform localizations near their spectral phase transition, revealing a qualitative difference in their decay rates where the former exhibits a logarithmic dependence while the latter decays quadratically.
This paper establishes the global well-posedness, uniform-in-viscosity estimates, and optimal large-time decay rates for classical solutions to the three-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent friction, thereby rigorously justifying the global inviscid limit and proving the first global existence of classical solutions for the corresponding Euler-Vlasov-Fokker-Planck system.