4174 papers
This paper generalizes the classical multiplicity of an ideal to graded families of ideals on Noetherian local rings, establishing that many fundamental theorems (such as Rees' theorem and the Minkowski inequality) hold for this new invariant through simple proofs based on intersection products on blow-up schemes, independent of volume theory and Okounkov bodies.
This paper introduces an extended 3-manifold topological model for high-contrast optical flow that resolves the limitations of previous torus-based approaches by identifying that the most significant motion patches are concentrated near binary step-edge circles rather than the torus, thereby offering new insights into the topological and geometric structures underlying visual data inference.
This paper presents a unified framework that proves the equivalence of variational, Green's function, and characteristic-based methods for constructing reproducing kernels, enabling a data-driven, mesh-free approach to learning kernels that accurately approximate Koopman eigenfunctions and solve various linear transport equations.
This paper classifies central extensions for the loop group of area-preserving diffeomorphisms of the 2-sphere and demonstrates that their associated Lie algebra cocycles emerge as fuzzy sphere limits of Kac-Moody cocycles for large in (twisted) loop algebras of , provided a specific rescaling by $6/k^3$.
This paper establishes the scattering rigidity of positively homogeneous Hamiltonian systems on manifolds with boundary by proving that the Hamiltonian is uniquely determined up to boundary-fixing canonical transformations via the inversion of X-ray and light ray transforms on Hamiltonian curves, a result applied to demonstrate semiglobal lens rigidity for non-trapping Finsler manifolds.
This paper proves that in a general round-robin tournament model with equally strong players, the largest scores are asymptotically almost surely distinct provided that grows to infinity while satisfying the condition .
This paper investigates sign changes in summatory functions of arithmetic functions and their Dirichlet inverses, demonstrating that convolving with specific "magic partition function" encodings can smooth oscillatory behavior to produce sequences with predictable sign properties under reasonable asymptotic bounds.
This paper proposes an efficient algorithm for minimizing total squared rate deviation in parallel Gaussian channels under a sum-power constraint by deriving a closed-form solution using the Lambert W function and a one-dimensional bisection method, which outperforms classical waterfilling and general-purpose solvers in both speed and target-tracking accuracy.
This paper introduces a Gauss-Newton method for large-scale PDE-constrained inverse problems, such as Full-Waveform Inversion, that achieves fast convergence without requiring additional PDE solves beyond those needed for gradient evaluation.
This paper establishes that the theory of lovely pairs of any complete strongly geometric field theory with quantifier elimination admits quantifier elimination when expanded with predicates for linear independence and corresponding coordinate functions, thereby generalizing Delon's results to include dense pairs of real closed and -adically closed fields.
This paper establishes conditional stability estimates and derives a priori error estimates for a finite element-based least-squares reconstruction of parameter identification problems governed by elliptic equations with power-type nonlinearity, extending and sharpening previous linear results under weaker regularity assumptions.
This paper extends the Stockwell transform to the setting of Gelfand pairs, investigates its key properties, and analyzes the associated localization operators within this framework.
This paper derives explicit formulas for general position polynomials of complete multipartite graphs and investigates their unimodality and log-concavity, demonstrating that these properties hold for balanced complete multipartite graphs with small part sizes and for coronas of various graph classes, while failing for larger part sizes.
This paper resolves an open question in convex optimization by proving that the gradient-evaluation sequence in Nesterov's accelerated gradient descent method, including in projection-based and non-Euclidean settings, achieves the optimal convergence rate for the objective function value, matching the performance of the standard solution sequence.
This paper extends previous results on the structure of the center of finite -algebras to a broader range of prime characteristics and demonstrates that their Zassenhaus varieties are rational affine schemes birationally equivalent to a good transverse slice.
This paper formalizes the goal of demonstrating positive treatment effects in adaptive experiments within a multi-armed bandit framework, proposing novel inference procedures for threshold testing and an adaptive allocation rule that optimizes signal-to-noise ratio with logarithmic regret.
This paper presents a numerical technique for discretizing higher-order powers of the spectral fractional Laplacian with by utilizing the polyharmonic extension approach.
This paper extends the geometric simplex method to linear programs in locally convex topological vector spaces by replacing algebraic pivoting with a generalized geometric framework, thereby establishing convergence conditions and proving that all such polytopes possess exposed extreme points connected by edge paths, including complex cases like the Hilbert cube.
This paper establishes a sharp rate of convergence for a free-boundary curve shortening flow within a convex domain in , demonstrating that the flow evolves to a round half-point in finite time.
This paper provides a geometric realization of the universal enveloping algebras of Borcherds-Bozec algebras and certain generalized Kac-Moody algebras by utilizing motivic semi-derived and Bridgeland's Hall algebras associated with quivers with loops and acyclic quivers, respectively.