3690 papers
This paper generalizes the spacetime positive mass theorem to multiple time dimensions, proving that energy remains nonnegative and bounded by the trace norm of linear momenta, with equality implying a foliation by flat submanifolds and, under an umbilicity assumption, an isometric embedding into a generalized pp-wave.
This paper introduces a scalable multitask Gaussian process model with a fully separable kernel structure that effectively handles functional covariates and correlated tasks, demonstrating superior accuracy and computational efficiency over single-task approaches in predicting the behavior of complex mechanical systems like riveted assemblies with limited data.
This paper establishes global well-posedness in the critical energy space and proves almost periodicity in time for the half-wave maps equation on the one-dimensional torus by leveraging its integrable Lax pair structure to derive explicit solution formulae and a general stability principle that extends to matrix-valued cases and companion results on the real line.
Conditional on Zywina's effective Serre uniformity conjecture, this paper establishes a natural parameterization of non-CM rational points on all modular curves using finitely many such curves, thereby confirming Mazur and Ogg's philosophy that these points arise from the geometry of modular curves.
Inspired by Katz's work, this paper investigates the converse of the known property regarding rational torsion injection into reductions for -type abelian varieties and proposes a conjectural list of possible torsion orders for modular abelian varieties over with dimension up to 5.
This paper establishes sharp bounds and asymptotic equivalences among the Albertson, Sombor, and Sigma indices for trees, demonstrating that the Sombor index serves as an intermediate descriptor linking global degree dispersion and local edge irregularity through precise -relationships.
This paper establishes and provides an algorithmic method to verify a new criterion ensuring that a quasi-finite, flat morphism with locally constant geometric fibers between real algebraic varieties induces a covering map on their real points in the Euclidean topology.
This paper introduces "bipredictability" (P) as a fundamental, bounded measure of shared information between observations, actions, and outcomes to distinguish mere agency from true intelligence, demonstrating that current AI systems lack the self-monitoring feedback loops necessary for adaptive learning and proposing a thalamocortical-inspired architecture to restore it.
This paper introduces calculus rules for computing Kurdyka-Łojasiewicz exponents via rank theorems and Lie group actions, offering a smoothness-free framework to establish linear convergence for diverse algorithms in matrix factorization and neural networks, particularly for nonisolated local minima.
This paper establishes the detailed structure of oscillatory shock waves for the KdV-Burgers equation and proves their -contraction and uniform stability under arbitrarily large perturbations, thereby confirming the existence of zero viscosity-dispersion limits where Riemann shocks remain orbitally stable.
This paper establishes a combinatorial proof that the basin walls of coalescing particles on a line form a Pfaffian point process for any skip-free dynamics, deriving exact correlation formulas, proving a central limit theorem via indecomposability, and identifying a checkerboard duality between these walls and the surviving particles of a dual process.
This paper investigates the asymptotic behaviors of randomly weighted sums with upper tail asymptotically independent increments under new conditions without requiring moment assumptions on the weights, deriving uniform asymptotics and applying them to estimate finite-time ruin probabilities in discrete-time risk models.
This paper proves the strong monodromy conjecture for defining polynomials of projective hypersurfaces with weighted homogeneous isolated singularities in the specific cases where the hypersurface is a reduced curve or has homogeneous singularities in dimension at least four, demonstrating that an "amazing cancellation" prevents potential counterexamples.
This paper provides a self-contained tutorial on finite block length rate-distortion theory for a Bernoulli source with Hamming distortion, deriving the classical rate-distortion function, illustrating its computation via the Blahut-Arimoto algorithm, and analyzing finite-length refinements governed by rate-distortion dispersion with accompanying numerical examples.
This paper presents a new proof of the generalized Chapple-Euler relation for triangles inscribed in a circle and circumscribed about a central conic, establishing that the sum of the squared side lengths of such Poncelet triangles is invariant if and only if the circle is centered at either the conic's center or one of its foci.
This paper details a previously unrecorded error in Guy and Kelly's 2004 heuristic argument for the no-three-in-line problem, identified by Gabor Ellmann, and presents the resulting correction to their conjectured upper bound.
This paper introduces a new method utilizing syzygies to demonstrate that certain numerical semigroups are not Weierstrass, notably providing the first known examples of non-Weierstrass semigroups with multiplicity 6 and genus 13.
This paper establishes faster minimax convergence rates for a binary plug-in classification procedure applied to time-homogeneous SDE paths with space-dependent coefficients under low-noise conditions, by deriving a crucial exponential inequality and analyzing the lower bound on the empirical classifier's excess risk.
This paper constructs fractional Sobolev spaces with variable orders on arbitrary time scales and their product domains, establishing their functional-analytic properties and trace frameworks to derive Euler-Lagrange equations for variational problems involving variable-order Riemann-Liouville and Caputo fractional operators.
This paper establishes the global well-posedness and uniform exponential stabilization of the critical quintic wave equation in a 3D bounded domain with locally distributed Kelvin-Voigt damping by combining frequency-space Littlewood-Paley analysis, critical Strichartz estimates, and microlocal defect measures to overcome derivative loss and geometric obstructions.