2549 papers
This paper investigates cohomological and motivic invariants of semisimple algebraic groups within the Freudenthal magic square, establishing a new isotropy criterion for strongly inner groups of type based on the Rost invariant and constructing a degree 5 cohomological invariant that detects isotropy for certain groups of type .
This paper computes the -graded Bredon cohomology of equivariant universal and classifying spaces with constant coefficients, providing an explicit description of the resulting coefficient ring and applying these results to study lifts of cohomology operations via equivariant complex projective spaces.
This paper presents a deterministic, realizability-preserving finite element framework for proton therapy dose calculation that solves the energy-dependent moment model backward in energy using a monolithic convex limiting strategy and Strang-type operator splitting to ensure physically admissible, accurate dose distributions.
This paper establishes a uniform upper bound for the eigenvalues of the Hodge Laplacian on closed Riemannian manifolds with lower bounds on Ricci curvature and injectivity radius, as well as an upper bound on diameter, thereby extending Cheng-type eigenvalue comparison theorems to differential forms without requiring sectional curvature bounds.
This paper proposes a noise-tolerant regularized quasi-Newton method with a relaxed Armijo-type line search that achieves a global convergence rate of for smooth nonconvex optimization under inexact function values, demonstrating superior robustness and competitive efficiency in experiments involving both artificial noise and low-precision arithmetic.
This paper utilizes the complexity function of invariant subsets in two-sided shift spaces to calculate the polynomial entropy of induced dynamics on hyperspaces of continua for specific one-dimensional systems and establishes a criterion for the induced map to possess infinite topological entropy.
This paper confirms the conjecture that every critical point metric is Einstein under the condition of constant norm of the traceless Ricci operator, and additionally proves it for the 3-dimensional case when the traceless Ricci operator satisfies a specific cubic trace inequality.
This paper establishes the first central limit theorems for the number of edges and unimodular triangulation edges in symmetric edge polytopes generated by Erdős–Rényi random graphs in high dimensions, utilizing the discrete Malliavin–Stein method to derive precise asymptotics and identify an atypical fluctuation regime where variance cancellation occurs.
This paper mathematically proves that in three-dimensional space, the Cauchy walk (Lévy exponent ) uniquely achieves scale-invariant, near-optimal detection across diverse target sizes and shapes by transitioning from volume-dominated to surface-area-dominated search strategies, thereby establishing a rigorous foundation for the Lévy flight foraging hypothesis in 3D.
This paper presents a classification over the field of real numbers of the parametric line congruences arising from trilinear birational maps, utilizing line geometry tools to analyze the space-filling families of straight lines associated with these mappings.
This paper establishes sufficient conditions, based on the admissibility of function classes and a smallness integrability condition, for the preservation of nonuniform exponential dichotomies under nonlocal perturbations.
This paper addresses the limitations of conventional multi-layer stacked intelligent metasurfaces (SIMs) by introducing and analyzing two-layer architectures (MF-SIM and FILM) that effectively balance signal processing performance with reduced structural complexity and power loss, thereby offering a practical pathway for 6G wireless systems.
This paper presents a polynomial-size representation and a corresponding polynomial-time construction algorithm for the family of all sets with a fixed value in integer-valued symmetric submodular functions, thereby generalizing low-rank structure theorems from graph cut-rank functions to broader connectivity functions and enabling efficient solutions to cardinality-constrained minimization problems.
This paper establishes that an affine transformation in is a product of two coninvolutions if and only if its linear part is -reversible, while also characterizing products of three coninvolutions and proving that every transformation with a linear part of unit determinant is a product of at most four coninvolutions.
This paper proves that the leading and penultimate leading coefficients of the error terms for the NRS(2) method applied to a cubic polynomial are positive-coefficient polynomials in the variables and , thereby simplifying and extending previous results.
This expository article explores the phenomenon where different definitions of fractal dimension yield conflicting results for simple examples and introduces "dimension interpolation" as a framework to unify these isolated numerical answers into a coherent geometric picture by viewing classical dimensions as boundary points of continuous families.
This paper evaluates and compares different auxiliary problem designs for homotopy continuation methods, demonstrating that a new approach based on the entropy solution offers a robust and systematic strategy for solving the nonlinear coupling challenges in multiphase flow within porous media.
The paper proves that for special alternating links where the classical signature provides a sharp lower bound for the unlinking number, this minimum is achieved by crossing changes in any alternating diagram, a result the authors use to determine new unknotting numbers for specific knots with 11 and 12 crossings.
This paper establishes that factors of smooth words are f-smooth and advances Sing's conjecture on their complexity by proving the asymptotic growth rate for even alphabets, confirming the lower bound for all binary alphabets, and improving the upper bound for odd alphabets.
This paper presents a Lanczos tau method for approximating and optimizing the -norm of delay differential algebraic systems, proving its convergence and stability under specific conditions while deriving efficient gradient formulas for robust controller synthesis and demonstrating accelerated convergence through spline-based extensions.