2549 papers
This paper establishes Morawetz-type estimates for the elastic wave equation with singular weights, demonstrating that space-time weights allow for stronger singularities and weaker initial data regularity requirements compared to purely spatial weights .
This paper introduces two new families of multirate time step adaptivity controllers and a set of fifth-order embedded MERK methods, demonstrating their superior performance and flexibility in efficiently solving problems with multiple time scales through adaptive simulations.
This paper proposes a simple, merit-function-free first-order algorithm for full-rank equality constrained optimization that adaptively selects between tangent and infeasibility-reducing steps without evaluating the objective function, achieving an O(1/sqrt{k}) convergence rate and demonstrating robust performance in noisy environments.
This paper establishes that the diameter of the dual graph of an arrangement of topological disks is bounded by a function of and the maximum number of connected components in any pairwise intersection, providing a tight bound of for two disks and an bound for disks by analyzing the count of maximal faces.
This paper establishes dimension-free -estimates for operator-valued maximal spherical means over cyclic groups by extending the Nevo-Stein spectral technique to the noncommutative setting, thereby proving a noncommutative spherical maximal inequality for automorphism actions on von Neumann algebras.
This paper rigorously establishes the exponential convergence to equilibrium for a system of Fokker-Planck equations modeling predator-prey interactions by introducing Energy-type distances that reveal how the dissipative interaction term governs the emergence of stable equilibrium configurations.
This paper presents one geometric and two combinatorial formulas for computing the equivariant Chern-Schwartz-MacPherson classes of open quiver loci in type quiver representations, introducing "chained generic pipe dreams" and providing streamlined versions of known formulas for the associated quiver polynomials.
This paper investigates the dimension statistics of representations for finite groups, demonstrating that for reductive groups over finite fields and symmetric groups, quantities such as representation dimensions and conjugacy class sizes exhibit asymptotically constant or log-constant behavior as the field size or group rank tends to infinity.
This paper proves that for any real and constants satisfying necessary conditions, there exist infinitely many triples of Piatetski-Shapiro primes satisfying a specific linear Diophantine inequality with mixed powers, provided the exponent is sufficiently close to 1.
This paper investigates dual variants of the Erdős distinct distances and unit distance problems by analyzing the maximum numbers of unit, extremal, and distinct-volume -simplices formed by arrangements of hyperplanes in .
This paper outlines the educational framework and practical examples of the Moscow Mathematical Conference for High School Students, demonstrating how non-novel research projects can effectively guide adolescents through the complete scientific process—from developing intuition and peer review to receiving formal recognition.
This paper proposes a movable-antenna-assisted Rate-Splitting Multiple Access (RSMA) framework integrated with a Reconfigurable Intelligent Surface (RIS) to maximize sum rate by jointly optimizing beamforming, reflection coefficients, rate splitting, and antenna positions, demonstrating significant performance gains over conventional fixed-antenna systems.
This paper investigates the existence of -designs (decompositions of complete graphs into edge-disjoint copies of a grid graph ), proving that such designs exist for toroidal grids when is an odd prime or its square, and for the path-grid (which relates to scrambling Connections puzzles), while showing that admits no such design.
This paper proposes a generalized Fermat's conjecture within the framework of arithmetic dynamics, provides supporting evidence for it, and introduces a multi-indexed version of the conjecture.
This paper establishes sufficient conditions for the infinite direct product of a continuous self-map on a compact metric space to be -chaotic and applies these findings to construct examples of unusual -chaotic maps.
This paper extends the concept of -mixing to set-valued random sequences in Banach spaces and establishes several strong laws of large numbers for such sequences, demonstrating the naturalness and sharpness of the underlying hypotheses through illustrative examples.
This paper establishes improved minimum degree conditions that guarantee the existence of Hamiltonian transversals and Hamiltonian connectivity in both balanced and nearly balanced bipartite graph collections, thereby advancing previous results in the field.
This paper classifies all tame integer tilings and hypertilings by developing a geometric model based on generalised Farey graphs in the hyperbolic plane, which connects these structures to triangulated polygons, friezes, and the Cayley hyperdeterminant.
This paper characterizes the gauge profiles of sets of reals defined by effective dimension and demonstrates a separation between these sets and -well approximable numbers using Hausdorff measure.
This paper proves the long-standing Erdős Matching Conjecture, establishing that the maximum size of a family of -sized subsets of containing no pairwise disjoint sets is bounded by the larger of two canonical extremal constructions.