2145 papers
This paper establishes convex body domination results for generalized vector-valued commutators of operators that already admit such domination, deriving strong type estimates and characterizing the associated BMO spaces.
This paper refines the understanding of maximal faces in the cone of completely positive matrices by proving that the exact lower bound on their dimensions is for odd , and establishing a new upper estimate between and for even .
This paper surveys averaging techniques in stochastic gradient methods, covering their theoretical foundations, modern developments in machine learning applications, finite-sample behaviors, and future research directions.
This paper establishes that the space of infinite circle patterns in the Euclidean plane parameterized by discrete harmonic functions of finite Dirichlet energy forms an infinite-dimensional Hilbert manifold homeomorphic to the Sobolev space of half-differentiable functions, equipped with a Riemannian metric derived from a hyperbolic volume functional that relates to a symplectic form via an analogue of the Hilbert transform, thereby connecting these patterns to the Weil-Petersson class of the universal Teichmüller space.
This paper establishes that sufficiently large topologically generating sets in connected compact, amenable, and reductive algebraic groups are necessarily redundant, providing quantitative bounds linked to finite simple groups of Lie type and demonstrating that these findings partially resolve Gelander's conjectures by showing they follow from the Wiegold conjecture.
This paper investigates the fundamental structural properties and numerical prevalence of finite algebras within locally finite varieties of nonassociative linear algebras over finite fields, without assuming associativity or the Lie property.
This paper introduces LS-ReCoNN, a novel deep learning framework that solves parametric transmission problems by decomposing the solution into regular and singular components and employing a least-squares-based training strategy to accurately capture interface discontinuities and junction singularities across diverse parameter values.
This paper investigates Ulrich bundles on smooth toric threefolds with Picard number 2 by constructing resolutions and monads for bundles of arbitrary rank, classifying those pulled back from , and proving that these varieties are Ulrich wild.
This paper introduces ALMTON, a globally convergent third-order Newton method for unconstrained nonconvex optimization that achieves an complexity by using adaptive quadratic regularization to maintain a tractable cubic model solvable via a single semidefinite program per iteration, thereby outperforming existing third-order and second-order baselines in convergence consistency and robustness.
This paper revisits and expands the theory of Dunford-Pettis multilinear operators by introducing new classes, establishing their relationships with existing and emerging operator ideals, and analyzing inclusion and coincidence conditions.
This paper establishes the compactness and -convergence of a nonlocal phase transition functional involving the norm and surfactants to a local perimeter-type energy that accounts for both the interfacial surfactant density and the total variation of the surfactant measure away from the interface.
Motivated by the Schoen–Marques–Neves conjecture, this paper verifies a sufficient pointwise Ambrozio–Carlotto–Sharp inequality for minimal isoparametric hypersurfaces with positive Ricci curvature in unit spheres, thereby establishing a lower bound on the Morse index proportional to the first Betti number for closed embedded minimal hypersurfaces in these ambient manifolds.
This paper resolves the Deng-Robles problem for polarized variations of Hodge structure over smooth quasi-projective surfaces with one-dimensional pure period images by demonstrating that the obstruction to an intrinsic algebraic description of the completed period image is divisor-theoretic and proving the necessary Picard-generation statement.
This paper resolves the open case for in Pelczyński's theorem by constructing -injective but not -injective Banach spaces via an iterative "zero-sum" subspace technique, while also establishing a new upper bound of $9+6\sqrt{3}L_\infty[0,1]\ell_\infty$.
This paper extends the correspondence between automorphism groups and -categorical structures to the locally Roelcke precompact and locally -categorical settings by defining the latter, proving a Ryll-Nardzewski theorem, characterizing the associated groups via isometric actions, and establishing that bi-interpretability of structures is equivalent to the isomorphism of their automorphism groups.
This paper establishes that the convergence of the Flint Hills series is equivalent to the irrationality measure of being at most $5/2\zeta(3)L(3, \chi_{-3})$.
This paper establishes rigorous error estimates for the hyperbolic scaling limits of linear discrete kinetic models on networks by reformulating symmetric n-edge junctions into independent initial-boundary value problems and deriving asymptotic expansions via the energy method.
This paper introduces a flexible transformed minimization model with two adjustable parameters to enhance sparse signal recovery, establishing exact and stable recovery guarantees via the restricted isometry property, proposing an efficient IRLSTLp algorithm with convergence proofs, and demonstrating its superior performance and theoretical bounds through numerical experiments.
This paper proposes a model-free reinforcement learning algorithm that achieves almost sure convergence with an optimal rate of O(1/n) for solving long-run Conditional Value-at-Risk (CVaR) optimization problems in Markov decision processes using a single sample trajectory.
This paper establishes the existence and qualitative properties of steady states for a nonlinear integro-differential equation modeling polymer dynamics involving nucleation, transport, and multiplicative coagulation, demonstrating that a sufficiently strong decay rate for large polymers prevents gelation despite the coagulation kernel's tendency to cause it in isolation.