2088 papers
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 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 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 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 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 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 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 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 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 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 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 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 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 establishes explicit formulas for the dimension and Bose distance of narrow-sense and certain non-narrow-sense BCH codes of length over within significantly expanded ranges of designed distance, thereby enabling the construction of several optimal linear codes.
This paper presents a fast direct boundary element solver for two-dimensional elastodynamic transmission problems that utilizes a mixed Burton-Miller and PMCHWT formulation with proxy-based low-rank approximation to achieve linear computational complexity and efficient handling of multiple right-hand sides, regardless of inclusion shape.
This paper provides an accessible, modernized proof of Ralph Seifert's 1971 result that no prime functional digraphs exist, thereby resolving a recent conjecture by Antonio E. Porreca.
This paper establishes necessary and sufficient conditions for reparametrizing nonholonomic mechanical trajectories as geodesics of a conformally modified Riemannian metric, while clarifying the relationships between these projective geodesic extensions and concepts like -simplicity, invariant measures, and Hamiltonization in Chaplygin systems.
This paper presents and analyzes a complex scaling-based integral equation method that enables the efficient, high-order, and exponentially accurate numerical solution of wave scattering problems involving the junction of two semi-infinite periodic structures by analytically continuing the formulation into the complex plane to overcome slow kernel decay and prove its well-posedness.
This paper constructs specific classes of strictly stationary, reversible Markov chains with finite second moments where the central limit theorem fails, thereby investigating the limited extent to which reversibility aids central limit theory under various mixing rates, particularly contrasting power-type and sub-exponential scenarios.
This paper introduces discrete approximate circle bundles as a data science analog to topological circle bundles, providing stable identification methods, cohomology invariants, and computational algorithms for coordinatization and dimensionality reduction, which are demonstrated through applications in computer vision and supported by an open-source software package.