6198 papers
This paper establishes that the homotopy type of the independence complex of a generalized Mycielskian graph is determined by the homotopy types of the independence complexes of the original graph and its Kronecker double cover, and applies this result to compute these types for paths, cycles, and categorical products of complete graphs.
This paper formulates a bilinear local smoothing conjecture for Fourier integral operators in all dimensions , demonstrates that the linear conjecture implies this bilinear version, and establishes the conjecture for dimension and all odd dimensions .
This paper constructs noncontinuous, strictly increasing, bisymmetric binary operations on real intervals using Cantor-type sets to demonstrate that continuity is not guaranteed for non-reflexive operations of a specific form, while also proving that such operations become continuous and quasi-arithmetic if they are reflexive at two points.
This paper demonstrates that for point perturbations of the Laplacian on a compact Riemannian manifold, the high-frequency eigenfunctions exhibit semiclassical measures invariant under the geodesic flow, provided the scatterers satisfy a non-focality condition ensuring that returning geodesics form a set of zero measure.
This paper presents a novel, computationally efficient integral solution for the mechanical response of a viscoelastic Kelvin-Voigt medium to pulse excitations, offering a simpler alternative to complex inverse Laplace transform methods and enabling straightforward asymptotic analysis.
This paper introduces a novel class of single- and multi-level Fourier-RQMC algorithms that leverage frequency-domain integration and randomized quasi-Monte Carlo sampling to achieve superior accuracy and computational efficiency in estimating multivariate shortfall risk and optimal capital allocations compared to traditional Monte Carlo methods.
This paper investigates a once-reinforced random walk on the half-line and establishes the limiting behaviors for all moments of its range.
This paper provides an alternative proof that certain links are not smoothly slice in and explores the implications of this result for detecting exotic smooth structures on .
This paper proves that the homeomorphic speedup of a linearly recurrent two-sided subshift preserves the property of linear recurrence, thereby demonstrating that this strong form of minimality is invariant under such time changes.
This paper revisits the golden sieve to demonstrate its generation of Wythoff pairs from natural numbers, establishes its connection to hiccup sequences and Fraenkel's partitions when applied to arithmetic progressions, and introduces a new extraction sieve governed by affine transformations of hiccup parameters.
The paper establishes that for any automorphism of order greater than 2 in a sporadic simple group, at most three of its conjugates are sufficient to generate a subgroup divisible by a fixed prime divisor of the group's order, with the sole exception of the Suzuki group where a specific class of elements requires four conjugates to generate a subgroup divisible by 11.
This paper proposes randomized stochastic gradient schemes with smoothing techniques to solve nonconvex nonsmooth stochastic potential games under uncertainty, achieving optimal sample complexity and asymptotic convergence without relying on stringent growth conditions or local convexity.
StochasticBarrier.jl is an open-source Julia toolbox that efficiently synthesizes Stochastic Barrier Functions for verifying the safety of discrete-time stochastic systems using Sum-of-Squares and piecewise constant optimization methods, demonstrating superior speed, scalability, and safety bounds compared to state-of-the-art tools across over 30 case studies.
This paper investigates the homotopy types and connectivity of total cut complexes and their Alexander duals for various graph families, including powers of cycles, complete multipartite graphs, and Cartesian products, thereby resolving specific conjectures regarding these structures.
This paper establishes a general mathematical framework for variational problems in quantum thermodynamics with measurement constraints, leveraging non-commutative optimal transport to analyze dual formulations and zero-temperature limits while tailoring the approach to quantum state tomography and developing convergent computational algorithms.
This paper improves the known bounds for the constant , which represents the minimum proportion of a Sidon subset guaranteed within any -set of size , by establishing that through a reformulated extremal problem and an explicit construction.
This paper establishes that the inversion walk on tournaments exhibits total-variation cutoff at time and characterizes the state space of the -restricted inversion walk as a coset of a subgroup whose codimension depends solely on .
This paper proves that for a smooth complex projective curve of genus , the Fourier–Mukai transform of a semistable vector bundle with slope greater than , when twisted by the principal polarization of the Jacobian, satisfies the property.
This paper investigates the finite-one structure within the many-one degrees of -rigid sets, demonstrating that such degrees typically contain a least finite-one degree and infinitely many pairwise incomparable finite-one degrees, thereby providing partial solutions to open problems posed by Richter, Stephan, and Zhang.
This paper introduces a notion of semistability for intrinsic reductions of non-archimedean rational functions at non-classical points in the Berkovich projective line and computes the resulting loci for quadratic rational iterations via a slope formula, demonstrating that these loci exhibit precise stationarity analogous to the polynomial case.