7423 papers
This paper establishes that for monomial ideals in polynomial rings with two or three variables, the Castelnuovo–Mumford regularity of the integral closure is bounded by that of the ideal itself, and characterizes ideals generated in a single degree as having regularity equal to that degree if and only if they possess linear quotients.
This paper demonstrates that the population-size distribution of supercritical Galton-Watson branching processes, in the asymptotic regime where the mean offspring number approaches one, can be effectively approximated by a compound Poisson-gamma distribution, a finding supported by numerical experiments and applicable to modeling cascaded multiplication processes.
This paper establishes the first proof of the persistence of spatial analyticity for solutions to the Majda-Biello and Hirota-Satsuma coupled KdV systems when initialized with analytic data.
This paper investigates the natural action of the Galois group on the class group of a Galois number field through a direct approach, utilizing the class groups of overrings and the arithmetic of normsets to elucidate the relationship between these algebraic structures.
This paper constructs two confluent rewriting systems in noncommutative polynomials to establish an algebraic basis for polyzetas, demonstrating that irreducible polyzetas are transcendental and algebraically independent over the rationals, thereby proving that is algebraically independent from odd zeta values.
This paper classifies, up to topological equivalence, the actions of the abelian group on compact Riemann surfaces of genus that yield a quotient of genus zero with a signature consisting of branch points of order .
This paper introduces composite Lp-quantile regression and near quantile regression as robust, high-efficiency alternatives to existing methods for high-dimensional data with infinite error variance, while also establishing their oracle model selection properties and developing a unified, efficient algorithm for their implementation.
This paper establishes Plancherel-type identities and proves the surjectivity of the Fourier transform for certain unbounded dual tiling sets in , demonstrating that an open set tiles the real line by the finite set if and only if it admits a spectrum given by the Lebesgue measure on .
This paper introduces a novel radial and tangential decomposition framework for analyzing transient reactivity in two-dimensional linear ODEs, offering new geometric insights into state-space dynamics, orthovector structures, and the accumulation of transient amplification in nonautonomous systems.
This paper establishes a rigorous operator-level necessity result proving that in closed, unforced kinetic systems, the first-order Chapman-Enskog deviatoric stress arises if and only if the first-order distribution correction is nonzero, thereby filling a critical gap in the kinetic-to-continuum literature by demonstrating that vanishing precludes the emergence of stress under precise functional-analytic conditions.
This paper characterizes stable equivalences between centralizer matrix algebras over arbitrary fields using a new matrix equivalence relation, demonstrating that such equivalences induce Morita-type stable equivalences that preserve key homological dimensions and validate the Alperin–Auslander/Auslander–Reiten conjecture in this context.
This paper extends the complete census of orientable cusped hyperbolic 3-manifolds to 10 tetrahedra, identifying 150,730 new manifolds and their triangulations to determine 439,898 exceptional Dehn fillings, discover 1,849 new simplest hyperbolic knot exteriors, and provide the first example of such a manifold containing a closed totally geodesic surface.
This paper establishes a metric for categorical random variables based on entropy and symmetrical uncertainty, demonstrating that the resulting quotient space possesses a natural commutative monoid structure compatible with the induced topology.
This paper investigates the fractional heat equation with a Riesz potential nonlinearity, establishing a Fujita-type critical exponent that deviates from standard scaling predictions, thereby confirming a hypothesis by Mitidieri and Pohozaev and extending their nonexistence results to general convolution operators.
This paper derives an exact analytical three-dimensional channel impulse response for a fully absorbing spherical receiver under uniform drift by utilizing joint first-hitting time-location statistics and a Girsanov-based measure change to overcome previous symmetry-breaking limitations.
This paper introduces PANDAExpress, a novel algorithm that eliminates the impractical polylogarithmic factor of the original PANDA framework by employing a new probabilistic inequality and a dynamic hyperplane partitioning scheme, thereby achieving optimal, specialized-algorithm-level runtimes for conjunctive queries and disjunctive datalog rules under arbitrary degree constraints while maintaining full generality.
This paper presents a multiscale optimization framework for Lipschitz continuous functions that accelerates convergence and reduces computational costs by solving coarse-grid problems to warm-start fine-grid iterations, achieving provably tighter error bounds and significant speedups in applications like probability density estimation.
This paper establishes a unified theoretical framework for CUR matrix approximation and the Nyström method by deriving determinant-based error bounds that connect local projection errors to global quality and quantify the benefits of oversampling through volume sampling.
This paper proposes a stochastic gradient descent algorithm that dynamically maximizes revenue in a single-server queue with balking customers by using a novel Infinitesimal Perturbation Analysis procedure to estimate effective arrival rates based solely on observable joining behavior, thereby converging to the optimal price under mild regularity conditions.
This paper demonstrates that designs minimizing variance under a bias constraint, or minimizing bias under a variance constraint, are equivalent to minimax designs with appropriately tuned constants, and conversely, any minimax design solves these constrained optimization problems for suitable bounds.