6623 papers
This paper establishes the almost sure Hausdorff dimension of the images and graphs of a broad class of random complex series, which encompasses famous deterministic functions like the Weierstrass and Riemann functions, thereby providing a probabilistic framework to predict the exact dimension values of their deterministic counterparts.
This paper introduces two numerical frameworks—a strong-competition penalty method with damped Gauss-Seidel iterations and a projected gradient method with an accelerated variant—to solve elliptic systems governed by nonconvex partial segregation constraints where three nonnegative components must have a vanishing pointwise product.
This paper advances the study of outer length billiards by proving 3- and 4-periodic versions of the Ivrii conjecture and demonstrating the existence of functional spaces of billiard tables with invariant curves of -periodic points, including an explicit geometric parameterization for the centrally symmetric case.
This paper proposes a Newton-based algorithm with an Armijo-like line search strategy to solve multiobjective interval optimization problems by establishing a link between weakly Pareto optimal and Pareto critical points, proving its convergence, and validating its effectiveness through numerical experiments and a portfolio optimization application.
This paper establishes a sharp topological dichotomy for slices of the Sierpinski tetrahedron, demonstrating that slices at dyadic rational heights possess finitely many connected components with infinite first Čech homology, whereas slices at non-dyadic rational heights are totally disconnected with vanishing positive-degree homology.
This paper determines all -biderivations for the Witt algebra, the Virasoro algebra, the -algebras , and their universal central extensions , and subsequently presents applications of these results.
This paper constructs a new class of simple weight modules for the twisted Heisenberg-Virasoro algebra and gap- Virasoro algebras by utilizing restricted modules over their positive part subalgebras, yielding novel results particularly for the mirror Heisenberg-Virasoro algebra when .
This paper characterizes the spectrum of values for weak uniform Diophantine exponents associated with lattices in arbitrary dimensions.
This paper establishes the existence and uniqueness of a non-negative, piecewise smooth, and symmetric potential in that maximizes the sum of the first two Dirichlet eigenvalues for Sturm-Liouville operators, demonstrating that its nonzero part is determined by the solution to the pendulum equation via measure differential equations and weak convergence.
This paper proposes a physically consistent signal model and an alternating optimization framework for downlink sum-rate maximization in STAR beyond-diagonal RISs with per-element amplification, achieving substantial performance gains over conventional passive systems while ensuring hardware feasibility and passivity.
This paper establishes the first large deviation principle for convolutional neural networks in the infinite-channel regime, characterizing the asymptotic behavior of conditional covariance matrices and posterior distributions under Gaussian priors while also providing streamlined proofs for their Gaussian equivalence and concentration.
This paper constructs an arbitrary-order asymptotic expansion for the quantum evolution of coherent states in self-interacting bosonic field theories, refining previous leading-order results by applying Hepp's method to both spatially cutoff models and non-polynomial analytic interactions.
This paper establishes a unified framework using symplectic field theory functorial properties to generate finite algebraic (planar) torsions, thereby confirming a conjecture by Latschev and Wendl regarding stably fillable examples in dimensions five and higher and demonstrating the ubiquity of tight, non-weakly fillable contact structures on spheres in those dimensions.
This paper proves Oort's conjecture that the automorphism group of a generic principally polarized supersingular abelian variety in characteristic is , except for the specific cases of genus 2 or 3 with , while also providing an explicit description of the -locus in the corresponding Rapoport-Zink space and establishing analogous results for supersingular -divisible groups.
This paper establishes an explicit characterization of irregular Hodge numbers for twisted de Rham cohomology groups in terms of classical Hodge numbers, demonstrating their independence from the choice of non-degenerate functions and providing a concrete formula for unipotent non-degenerate cases.
This paper constructs analytic symplectomorphisms on the sphere, disk, and cylinder that exhibit minimal ergodicity with exactly three ergodic measures by generalizing a principle introduced by Berger based on the Anosov-Katok approximation by conjugacy method.
This paper provides a comprehensive update on stochastic rounding research from 2022 to 2026, with a specific focus on the new limited-precision variant, while offering insights into its industrial applications and future hardware implementation.
This paper establishes the consistency and asymptotic normality of the Whittle estimator for Lévy-driven CARMA models observed at renewal times, demonstrating that the integrated periodogram-based approach remains robust under mild conditions even when the driving noise exhibits heavy tails and jumps.
This paper defends the significance of Bezboruah and Shepherdson's incompleteness result regarding the weak theory against Kreisel's objections, compares it with Pudlák's extension of the Second Incompleteness Theorem, and provides a new proof based on sequence coding insights from Nielsen and Markov.
This paper defines the topological pressure of continuous functions for holomorphic correspondences on the Riemann sphere using open covers and proves that this definition is equivalent to the existing approach based on separated and spanning families of orbits.