2549 papers
This paper proposes an efficient, unconditionally stable predictor-corrector algorithm combining orthogonal spline collocation finite elements with variable time stepping to achieve high-order accuracy and suppress numerical oscillations in solving the FitzHugh-Nagumo system.
This paper establishes a structure theorem for -labeled graphs that exclude a fixed -labeled immersion, demonstrating that such graphs admit a tree-cut decomposition where each bag contains either few high-degree vertices or is nearly signed over a proper subgroup of the finite group .
This paper systematically determines the circular chromatic indices of small graphs and multigraphs with maximum degrees up to 6, constructs infinite families of graphs with specific fractional indices, and refutes edge-connectivity variants of the "Upper Gap Conjecture."
For the planar three-body problem with positive masses, non-zero angular momentum, and fixed negative energy, the paper proves the existence of global solutions that maintain an arbitrarily large potential energy by featuring a single close approach to triple collision while evolving into a tight binary configuration with the third body diverging to infinity.
This paper introduces a determinantal method for computing minimal local generalized additive decompositions (GADs) of homogeneous polynomials by minimizing the rank of symbolic inverse systems, proving that this approach guarantees finding all minimal decompositions without tensor extensions whenever the local GAD-rank does not exceed the form's degree.
This paper establishes the existence and combinatorial characterization of the asymptotic v-number for Noetherian graded families of homogeneous ideals via Newton-Okounkov regions, while also proving its eventual quasi-linearity and strict inequalities with regularity and multiplicity.
This paper proposes a robust geometric early warning indicator based on the width of the stochastic separatrix in a two-state ecosystem model, which successfully predicts rapid under-ice phytoplankton blooms in the Arctic where conventional critical slowing down signals fail due to strong noise or limited data.
This paper generalizes the classical discrete -Hardy inequality to arbitrary integer orders to establish optimal discrete -Rellich and -Birman inequalities, utilizing a novel Copson inequality variant with a negative exponent and demonstrating how these results recover the continuous -Birman inequality.
This paper investigates the domination polynomial of the co-maximal graph by deriving explicit formulas for specific cases of , establishing structural connections for general , and analyzing the unimodality, log-concavity, and modulus bounds of its roots.
This paper constructs exotic Hecke correspondences between the special fibers of PEL-type Shimura varieties with potentially bad reduction by utilizing Pappas-Rapoport splitting models, thereby establishing new geometric Jacquet-Langlands correspondences and verifying generic instances of the Tate conjecture.
This paper investigates Max-Cut instances on complete graphs with geometrically decreasing edge weights, establishing a sharp phase diagram for the optimality of isolated cuts based on threshold polynomials and conjecturing their global optimality for sufficiently large .
This paper demonstrates that for approximately memoryless surjective POST channels, feedback does not increase channel capacity, thereby extending Shannon's classical result on discrete memoryless channels to a broader class of finite-state channels.
This paper proposes a novel -adaptive algorithm for the Poisson equation with fixed polynomial degree that guarantees -robust error contraction and optimal algebraic convergence rates under a verifiable a posteriori criterion, supported by numerical experiments.
This paper develops a linearized boundary control method to reconstruct unknown damping perturbations in the damped wave equation from the linearized Neumann-to-Dirichlet map, providing stability estimates and a validated numerical algorithm for constant backgrounds in any dimension while establishing increasing stability for non-constant backgrounds in dimensions three and higher.
This paper investigates the spectral properties of degree-based weighted adjacency matrices for complete and crown multipartite graphs, characterizes families with three distinct eigenvalues and integral spectra, corrects previous findings on energy changes after edge deletion, and resolves an open problem regarding ISI energy in multipartite graphs.
This paper establishes the first example of Batchelor's law for a passive scalar under deterministic forcing by proving that sufficiently smooth initial data in a specific time-periodic, Lipschitz velocity field converges to a limiting solution satisfying a cumulative form of the law.
The paper establishes that the consistency of with being measurable implies the consistency of where is simultaneously the least strongly regular and least measurable cardinal, while all uncountable cardinals below it have countable cofinality.
This paper establishes that for positive recurrent Lévy diffusions driven by scaled Brownian motion and -stable processes ($1<\alpha<2$) in the small noise regime, the large-time limiting behavior of the one-dimensional marginal distribution is determined by the optimal value of a deterministic control problem featuring both continuous and impulse controls.
This paper introduces a Bianchi-Calo type construction method for generating Bryant-type linear Weingarten surfaces within hyperbolic space.
This paper introduces the class of weakly Demi Dunford-Pettis applications, investigates their relationships with weakly Dunford-Pettis and Demi Dunford-Pettis operators, and analyzes their behavior within Banach Lattices.