3268 papers
This paper proposes an equivalent formulation of the Twin Prime Conjecture based on a symmetric property observed within a specific sequence of arithmetic progressions defined for pairs of coprime integers.
This paper generalizes several topological results and concepts from ring theory to the setting of monoids.
This paper introduces and validates a novel semi-discrete optimal transport scheme for the compressible semi-geostrophic slice model that utilizes -exponential charts to efficiently construct -Laguerre tessellations, thereby enabling mass- and energy-conserving simulations of large-scale atmospheric dynamics while preserving key geometric structures.
This paper presents a concise and self-contained proof of Delahan's theorem, demonstrating that every simple graph with vertices appears as an induced subgraph of a Steinhaus graph with vertices by utilizing the concept of generating index sets for Steinhaus triangles.
This paper answers a question posed by Ellenberg regarding primitive elements of small height and uses this result to improve Heath-Brown's upper bounds for the -torsion part of class groups in purely cubic and general pure number fields of arbitrary odd degree.
This paper determines the minimum sizes of -completely hyperseparating set systems for general and of $2$-hyperseparating set systems, thereby generalizing recent results by Bat'iková, Kepka, and Němec.
This paper proves that as approaches infinity, the proportion of orientably-regular maps and hypermaps with automorphism groups or that are chiral tends to 1, establishing that chirality is generic for these structures.
This paper proves a sharp reverse isoperimetric inequality in three-dimensional space forms of constant curvature, demonstrating that among all -convex bodies with a fixed surface area, the -convex lens uniquely minimizes volume, thereby confirming Borisenko's Conjecture for non-zero curvature cases.
This paper establishes that the asymptotic accumulation of eigenvalues near unity for convolutions of indicator functions and density operators on locally compact groups occurs if and only if the group is unimodular and the underlying sets form a Følner sequence, thereby extending known results for the Heisenberg group to broader classes such as nilpotent and homogeneous Lie groups.
This paper introduces the -footrule coefficient, a new copula-based measure of negative association defined as the -distance to the countermonotonic copula, establishes its theoretical relationship with Gini's gamma and Spearman's footrule, and provides a statistically rigorous rank-based estimator with proven consistency and asymptotic normality.
This paper proposes a mixed-integer linear programming framework that discretizes the three-dimensional wiring diagram problem into structured network graphs to optimize cable or pipeline routing while satisfying complex industrial constraints such as obstacle avoidance, safety distances, and constructibility.
This paper characterizes primitive elements in the Ringel-Hall algebra of a tame hereditary algebra associated with a quiver with automorphism, providing a generalized description that improves upon previous results for tame quivers and constructing an explicit basis for the space of primitive elements via a new identity in the regular subalgebra.
This paper introduces the framework of "fat Lie theory" to establish a one-to-one correspondence between fat extensions and abstract 2-term representations up to homotopy, while demonstrating that fat extensions of groupoids correspond to general linear PB-groupoids and core extensions to vertically/horizontally core-transitive double groupoids, thereby upgrading existing correspondences to equivalences of categories.
This paper introduces a new family of -Berezin seminorms to establish refined inequalities for the Berezin radius and investigates the convexity of Berezin ranges for specific operators on weighted Hardy and Fock spaces.
This paper establishes a new pointwise estimate for rough operators in Ahlfors regular metric measure spaces by combining a subrepresentation formula involving modified Riesz potentials with a maximal function control, and subsequently derives a family of functional inequalities from this result.
This paper derives WKB-asymptotic expressions for multipoint Virasoro conformal blocks in the comb channel on the sphere by applying the WKB method to the classical BPZ equation, validating the results against known exact solutions and AGT correspondence while demonstrating their utility for generalizing Zamolodchikov's elliptic recursion and numerically evaluating minimal string theory amplitudes.
This paper presents a general scheme for constructing optimal and numerically stable generalized Schultz iterative methods with variable coefficients to efficiently compute matrix inverses, supported by theoretical derivation and numerical testing.
This paper presents a practical, step-by-step methodology for formulating finite elasto-plasticity in curvilinear coordinates using explicit basis changes rather than differential geometry, clarifying the treatment of deformation gradients, Jacobians, and shifters to enable robust finite element analysis of axisymmetric problems with large deformations.
This paper investigates the geometric relationship between hyperbolic, elliptic, and parabolic disks and their supporting half-distance bands within the Beltrami–Cayley–Klein model, aiming to define and quantify their "closeness" through precise approximations of area and circumference.
This paper establishes a toric analog of Yuan and Zhang's theory of adelic divisors to show that the arithmetic self-intersection number of a semipositive toric adelic divisor equals the integral of a concave function over a compact convex set, thereby enabling the computation of heights for toric arithmetic varieties with singular metrics.