5016 papers
This paper introduces a dynamic programming framework to identify extremal general polyomino chains for degree-based topological indices, specifically resolving a 2015 open problem by characterizing the chains that maximize the generalized Randić index with based on the number of squares modulo 4.
This paper proves a conjecture by Brochier, Jordan, Safronov, and Snyder that characterizes fully-dualizable and invertible -algebras within higher Morita categories, thereby identifying the specific algebraic structures that generate -dimensional and invertible topological quantum field theories.
This paper characterizes strong -matroids corresponding to orientable ribbon graphs via the new concept of pseudo-orientable ribbon graphs, establishes a geometric construction linking them to orientable graphs, and derives significant results including the Matrix--Quasi-tree Theorem, Hurwitz stability, and log-concavity for quasi-tree generating polynomials.
This paper introduces color 2-switches to characterize -colored graphs with identical color degree matrices and defines several classes of neighborhood -balanced graphs to analyze their structural properties and minimum balance numbers across various graph families.
This paper demonstrates that combining a partial pivoted Cholesky approximation with a Vecchia approximation of the residual yields an exact Vecchia approximation of the original matrix with an augmented sparsity pattern, thereby unifying low-rank and sparse inverse Cholesky approximations under a single framework.
This paper introduces FlexTrace, a novel single-pass trace estimator that accurately computes the trace of matrix functions for large symmetric positive semi-definite matrices using only matrix-vector products with the original matrix, thereby overcoming the computational expense of existing methods that require products with the function of the matrix.
This paper investigates generalized b-weakly compact operators on locally convex-solid Riesz spaces by providing new characterizations and introducing KR-spaces to establish a factorization theory analogous to that of b-weakly compact operators through KB-spaces.
This paper presents the first part of a study on the generalized Honeymoon Oberwolfach Problem by establishing existence conditions for solutions involving multiple round tables, specifically for cases with two round tables under certain modular constraints and for cases with small round tables where the total number of non-spouse seats is at most 10.
This paper demonstrates that in the general framework of -boundaries, the boundary of an infinitely ended group admitting a splitting over finite subgroups is canonically homeomorphic to the dense amalgam of the limit sets of its factor subgroups.
This paper demonstrates that while topological classification of a specific "tears of the heart" polycycle unfolding suggests four invariants, a metrical perspective reveals that for Lebesgue almost all parameter values, only two such invariants exist.
This paper presents a specialized lock-free work-stealing queue designed for a master-worker framework in mixed-integer programming solvers that leverages restricted concurrency assumptions to support native bulk operations and achieve constant-latency push performance, significantly outperforming general-purpose implementations like C++ Taskflow in batch processing scenarios.
This paper introduces a novel frequency response formulation for nonlinear systems within the Koopman operator framework, deriving a generalized complex-valued function via Laplace transforms and resolvent theory to enable Bode plot analysis under specific existence conditions.
This paper proves that for connected outerplanar graphs containing at most one or two triangles, any precoloring of two or three non-adjacent vertices can be extended to a proper 3-coloring of the entire graph.
This paper establishes a new framework of Besov spaces on bounded domains with Neumann boundary conditions to prove the local well-posedness of the Navier-Stokes equations for initial data in a space that is strictly larger than any previously considered in bounded domains.
This paper provides a detailed Lie-algebraic analysis of the Heisenberg-Weyl Lie algebra by constructing explicit unitary intertwining operators for tensor products of its Schrödinger representations and proving that finite-dimensional irreducible representations of the symplectic Lie algebra yield a large family of finite-dimensional, nonunitary indecomposable representations when restricted to .
This paper investigates -twisted almost Hermitian structures, introducing a class of automorphisms called -Codazzi maps due to their relationship with Codazzi tensors, and applies these findings to prove a non-integrability result for the standard nearly Kähler structure on the 6-sphere.
This paper investigates the existence, stability, and multiplicity of ground states and stationary solutions for the defocusing nonlinear Schrödinger equation on noncompact metric graphs, establishing that while small masses always yield stable ground states, large masses lead to non-existence in the subcritical regime, with specific sharp thresholds and bifurcation behaviors identified under -type vertex conditions.
This paper provides a more elementary proof of the nonasymptotic universality laws established by Brailovskaya and van Handel, demonstrating that the spectral statistics of independent sums of random matrices mirror those of Gaussian matrices with matching first- and second-order moments, by utilizing a novel implementation of the method of exchangeable pairs.
This paper constructs and analyzes the birational geometry of a Kausz-type compactification of the space of symmetric matrices by realizing it as an evaluation fiber in the Kontsevich space of pointed conics on the Lagrangian Grassmannian, while also presenting analogous results for orthogonal Grassmannians.
This paper investigates a new elementary method by Luo and Lin for solving quartic equations, successfully applying it to provide a straightforward solution for Bumby's equation $3X^4-2Y^2=1$ and proposing a conjecture that could extend this approach to an infinite family of similar equations.