4517 papers
This paper establishes that two homotopic smooth embeddings of a closed surface into a closed oriented 5-manifold are isotopic if they share a common algebraic dual 3-sphere or if the ambient manifold is simply connected, by introducing a new invariant defined via the manifold's homotopy groups that classifies such isotopy classes.
This paper extends previous research on Poincaré and logarithmic Sobolev inequalities for perturbed measures to investigate analogous results for weaker functional inequalities, including weak and weighted variants, with applications to convolution products.
This paper presents a proof of a Ramanujan identity by expressing it in polar coordinates, which reduces the verification to an elementary trigonometric identity and yields several variations of the original result.
This paper establishes variational principles for pressure functions in discrete nonautonomous dynamical systems on compact metric spaces by applying methods from convex analysis to the thermodynamical formalism.
This paper develops an explicit invariant calculus for noncommutative linear differential operators using noncommutative Bell polynomials to derive universal formulas for gauge-covariant Wilczynski invariants and their projective counterparts, subsequently globalizing the framework to construct modular and Siegel modular differential operators on Riemann surfaces.
This paper establishes the existence of solutions for a class of integro-differential equations involving the difference between Laplacian and bi-Laplacian operators in unbounded domains by applying fixed point techniques and solvability conditions for non-Fredholm elliptic operators.
This paper partially answers Genevois's question regarding when hyperbolic graph braid groups arise as 3-manifold groups by demonstrating that is a 3-manifold group while for is not even quasi-isometric to one.
This paper presents a highly symmetric 6-dimensional polytope whose antipodal quotient yields a 24-vertex triangulation of , conjectured to be minimal, while also providing improved 45- and 49-vertex triangulations for .
This paper introduces combinatorics on words through the lens of low factor complexity in infinite words, exploring their minimal complexity, formalizing non-triviality, and presenting new algebraic proofs and consequences for classical theorems by Morse, Hedlund, and Tijdeman.
This paper generalizes the Micro-Transit Zoning Problem to incorporate a global budget and proposes an efficient Column Generation framework with pricing heuristics that outperforms existing enumeration-based approaches in solution quality and scalability across major U.S. cities.
This paper classifies the generating functions of genus zero lattice walks in the first quadrant with interacting boundaries by adapting a -difference equation method to show that, unlike the non-interacting case, these functions are typically hypertranscendental unless specific algebraic relations between the Boltzmann weights render them -algebraic or -rational.
This paper proposes Hadamard-NOMA, a robust downlink non-orthogonal multiple access scheme that leverages the Hadamard Transform at the source level to mitigate fading and channel state information imperfections, achieving significant bit error rate improvements over existing T-NOMA and Usman-NOMA schemes.
This paper establishes a measure-theoretic framework for constructing Arveson systems from stationary factorizing measure types, providing a rigorous characterization of spatiality and a robust mechanism for generating type III systems via infinite products, which is applied to derive explicit type III random-set systems from the zero sets of Brownian motion.
This paper establishes the foundational theory of covers and envelopes within proto-exact categories and applies these results to prove that categories of Banach modules over arbitrary Banach rings possess enough injectives.
This paper investigates the irreducible components of fixed point sets within the -character variety of a genus two surface under finite group actions, utilizing the genus two DAHA to identify geometric transitions that yield novel candidates for symmetry-reduced moduli spaces in 4d SCFTs.
This paper presents a fully device-resident, multi-GPU architecture that achieves near-zero host-device communication and 99.7% parallel efficiency through lock-free work-stealing and optimized shared-memory tiling, enabling the verification of Goldbach's conjecture up to $10^{13}$ in just 133.5 seconds on a four-GPU system with a 45.6× speedup over previous methods.
This paper demonstrates that partial differential equation propagation acts as a spectral preconditioner that improves Fourier ratio bounds, thereby enabling stable recovery of discretized fields from incomplete random spatial samples with sampling rates that are effectively independent of grid resolution.
This paper presents a simplified approach to the stable Hopf invariant by offering elementary proofs of the Cartan, Composition, and Transfer formulas, and extends these results to the stable category of -spaces for discrete groups.
This paper analyzes two coupled ODE models of political competition on probability simplices, demonstrating that a unique spectral threshold governs global stability and radicalization dynamics, where the baseline model precludes irreversible centrist decline while an extended model with disengaged voters reveals how cumulative structural shifts can trigger staircase radicalization.
This paper establishes a de Rham and Hyodo-Kato flip-flopping theorem for dual towers of rigid analytic spaces by utilizing pro-étale comparison theorems, and applies this result to prove the admissibility of the de Rham and Hyodo-Kato cohomologies of finite level coverings of Drinfeld spaces as representations of .