6227 papers
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 and proposing a conjecture that could extend this approach to an infinite family of similar equations.
This paper proposes a nonlinear conjugate gradient method with Wolfe line search for solving unconstrained multiobjective interval optimization problems, providing proofs of global convergence for general and specific algorithmic parameters (Fletcher-Reeves, Conjugate Descent, Dai-Yuan, and modified Dai-Yuan) alongside numerical performance evaluations.
This paper computes Donaldson-Thomas invariants and their descendants for the local Calabi-Yau 4-fold over the Mukai-Umemura variety using localization formulas, thereby verifying the predictions of Cao, Maulik, and Toda under the assumption that genus-one Gopakumar-Vafa invariants vanish.
The paper establishes a sharp inequality relating the Alexander-Taylor capacity to the functional capacity within complex Sobolev spaces on compact Kähler manifolds.
This paper presents a simplified extension of Birkhoff's representation theorem to locally-finite distributive lattices, establishing an isomorphism between such a lattice and the order ideals of the poset of its prime filters that differ from a specific ideal by a finite set.
This paper establishes a necessary and sufficient condition for decomposing the complete graph on vertices into isomorphic copies of a Cayley graph on a CI-group , while also providing a constructive method for such factorizations.
This paper resolves two longstanding problems from 1990 regarding indefinite integral ternary quadratic forms, highlighted by Margulis and initiated by Serre, by developing new tools to handle high ramification in sums weighted by diophantine invariants.
This paper investigates the long-time asymptotic behavior of multivariate Hawkes processes with power-law decaying interactions, employing a combination of short-range interaction techniques, -stable law properties, and Tauberian theorems to model realistic systems like neural networks with long-range connections.
This paper constructs a presheaf of Koszul complexes on weighted finite subsets of Euclidean space, utilizing linearized coefficients and change-of-coordinates maps to form a Čech-Koszul bicomplex whose degree-0 cocycles capture homotopical relationships between locally defined least squares solutions on data overlaps.
This paper proves that augmented admissible sets in Iwahori-Weyl groups are dual EL-shellable, thereby resolving a conjecture of Görtz and establishing the Cohen-Macaulayness of special fibers for local models with parahoric level structure—including previously open cases in residue characteristic 2 and non-reduced root systems—through a characteristic-free, intrinsic construction that yields an explicit shelling and inductive building procedure.
This paper demonstrates that while the "spectral density" derived from Gurau's resolvent trace yields valid probability measures on average for certain random tensor ensembles, it fails to correspond to a probability measure for individual deterministic tensors, thereby proving it is not a pointwise-defined probability distribution.
This paper introduces a Bayesian framework for linear programming under learned uncertainty that integrates data-driven posterior updates with robust optimization and scenario-based strategies to provide rigorous, finite-sample feasibility guarantees and improved decision safety compared to naive approaches.