2099 papers
This paper establishes a universal method for solving the Poincaré center problem by proving that every analytic center admits a Laurent inverse integrating factor, thereby enabling a theoretical procedure to characterize centers in polynomial vector fields, including nontrivial families that have resisted previous approaches.
This paper resolves a conjecture from OEIS entry A005243 by proving that the greedy self-generating sequence defined by Hofstadter, where each term is the smallest integer greater than the previous one representable as a sum of at least two consecutive earlier terms, omits infinitely many positive integers.
This paper introduces a model-agnostic framework that improves function extrapolation by projecting baseline approximations onto feasible sets defined by anchor functions, thereby providing rigorous, proven bounds that guarantee error reduction in extrapolation regions.
This paper investigates the qualitative dynamics and wave-character transitions in radially symmetric isentropic Euler flows across outward supersonic, subsonic, and inward supersonic regimes, establishing structural restrictions, identifying novel asymmetric transition mechanisms, deriving conditions for finite-time singularity formation, and validating these theoretical findings through Semi-Discrete Lagrangian-Eulerian numerical simulations.
This paper introduces a two-phase approximation method that resolves singularities in three-dimensional harmonic Dirichlet problems by decomposing the solution into a singular component handled via Green's formula with high-order quadrature and a regular component recovered through collocation with a harmonic basis.
This paper proposes an efficient offline-online subspace decomposition preconditioner that leverages localized defect structures to robustly solve elliptic diffusion problems with multiscale heterogeneous coefficients, significantly reducing the computational cost of uncertainty quantification in Monte-Carlo simulations.
This paper establishes a generalized version of Reshetnyak's theorem for quasiregular values mapping from generalized -manifolds with controlled geometry to Euclidean space , extending prior results by Kangasniemi and Onninen from the Euclidean setting.
This paper revisits Kippenhahn's conjecture regarding the unitary equivalence of Hermitian matrix pairs with repeated characteristic polynomial factors by employing local spectral analysis to establish necessary and sufficient conditions for the conjecture's validity.
This paper extends fundamental homotopical concepts to -categories and presentable enriched categories by introducing homotopy posets indexed by categorical disk boundaries, which assemble into a Postnikov tower converging for -categories and characterize Postnikov complete -categories as the limit of -categories under truncation.
This paper reinterprets Gödel's second incompleteness theorem through proof-theoretic semantics by demonstrating that while certain arithmetical theories cannot prove their own consistency, they nonetheless semantically support it via a compositional notion of consequence based on inferential roles, thereby reframing incompleteness as a divergence between derivability and internal semantic support rather than a gap between syntax and external truth.
This paper presents a generalized framework for the SQIsign signature scheme by incorporating level structures into the isogeny challenge, which leads to a new explicit Deuring correspondence for supersingular elliptic curves and solutions to constrained norm equations.
This paper establishes the existence and nonexistence of finite-energy solutions to singular Einstein-scalar field Lichnerowicz equations on complete Riemannian manifolds with low-regularity coefficients, utilizing -regularization, mountain pass arguments, and Harnack's inequality under specific spectral, geometric, and integrability conditions.
This paper presents a theoretical algebraic framework for the Linear Code Equivalence problem using Plücker coordinates and invariant rational functions to construct polynomials with the underlying permutation matrix as a root, demonstrating the potential of algebraic geometry in cryptanalysis despite the resulting polynomials being computationally infeasible for practical attacks.
This paper introduces sparse linear inequalities that outer approximate the positive semidefinite cone to create an LP relaxation with bounds equivalent to semidefinite programming, demonstrating that these inequalities can accelerate branch-and-bound algorithms for solving nonconvex quadratic optimization problems.
This paper rigorously proves the fast dynamo conjecture for a pulsed-diffusion model on the 3-torus by constructing a specific hyperbolic velocity field and utilizing anisotropic Banach spaces to demonstrate that magnetic instability persists under small diffusivity.
This paper proves that for sloshing problems defined by the Laplace equation with mixed boundary conditions on a smooth bounded domain, all eigenvalues become simple under small perturbations of the domain.
This paper investigates optimization problems concerning the relationship between the first eigenvalue and torsional rigidity induced by general anisotropic seminorms, specifically analyzing the minimization and maximization of their product functional with respect to the seminorm control.
This paper establishes a finite-blocklength rate-distortion framework for heterogeneous random fields on finite lattices that explicitly incorporates tile-based processing constraints, providing non-asymptotic bounds and a second-order expansion to quantify the effects of spatial correlation, heterogeneity, and tile size on compression performance.
This paper investigates the well-posedness, simultaneous exact and approximate controllability, and polynomial stabilization of cascade coupled 1-d heat and wave systems within an abstract LTI framework, leveraging the cascade structure to overcome challenges associated with classical energy methods.
This paper introduces the family of -disjoint graphs as a generalization of non-König-Egerváry almost bipartite graphs, proving that they preserve key structural equalities while extending the relationship between the corona, core, and independence number to accommodate multiple disjoint odd cycles, thereby verifying a recent conjecture by Levit and Mandrescu.