5427 papers
This paper establishes new Ore-degree conditions that guarantee the existence of matchings in -uniform hypergraphs by proving upper bounds on the Ore-degree for intersecting hypergraphs and demonstrating that exceeding a specific threshold ensures the presence of pairwise disjoint edges.
This paper establishes the existence of nontrivial nonnegative weak solutions to a semilinear Grushin-Schrödinger equation in with controlled potentials by proving the embedding of the associated energy space into a weighted Lebesgue space and deriving subsequent regularity results.
This paper investigates rigid-ruling folding motions of curved creases by deriving conditions for the foldability of developable semi-discrete conjugate nets and applying these findings to enable the sequential construction of foldable patterns and characterize the compatibility of planar and constant fold-angle creases.
This paper establishes that a notion of higher-order normality, derived from iterated Lie brackets, is sufficient to prevent infimum gaps in impulsive extensions of control-affine systems under an -control topology, thereby extending existing no-gap results beyond the more common -trajectory framework.
This paper confirms Martin's conjecture for a broad subclass of weakly quasi-o-minimal theories.
This paper characterizes the monogenicity of irreducible trinomials of the form (where is prime) by classifying them according to their Galois groups, thereby extending the authors' previous research.
This paper demonstrates that, unlike the Casten-Holland and Matano theorem for interior reactions, nonconstant stable solutions for boundary reactions can exist in convex domains such as squares and regular polygons (but not circles), with their existence and the location of boundary singularities determined by a new renormalized energy function derived from the domain's conformal structure.
This paper explores the recursive structure of integer partitions by demonstrating how Sylvester waves, which represent partitions as sums of polynomial and quasiperiodic components, rely on integer weights that are themselves sums of partitions into smaller sets of integers.
This paper establishes and proves the tightness of the optimal bounded stepsize limits for Popov's algorithm in solving generalized monotone variational inequalities, demonstrating a bound of for constrained cases and an improved for unconstrained cases through a novel Lyapunov-type function analysis.
This paper demonstrates that in o-minimal structures, every definable mapping that is Lipschitz with respect to the inner metric can be approximated by (or if the structure admits smooth cell decomposition) mappings with arbitrarily close derivative bounds, a result achieved through the construction of partitions of unity with sharp derivative estimates and extended to outer Lipschitz mappings.
This paper solves the Snellius-Pothenot problem by determining the number of points in the plane of a fixed triangle that correspond to any given point on the surface defined by the cosines of the angles subtended by the triangle's sides.
This paper establishes local Schauder estimates for flat viscosity solutions to a class of non-convex fully nonlinear elliptic PDEs with Dini continuous data and linear drift terms using geometric tangential techniques, while also deriving an Evans-Krylov type estimate and characterizing the nodal sets of such solutions.
This paper establishes the necessary and sufficient conditions under which a heavy-tailed random variable can be paired with an independent heavy-tailed variable such that their minimum results in a light-tailed distribution, characterizing the specific "segmented" structure required for this phenomenon.
This paper establishes simple left-inverse characterizations of the singularity invariants , , and for equidimensional varieties and utilizes a trace morphism to prove their descent under finite surjective morphisms.
This paper presents explicit examples of K3 surfaces over with geometric Picard rank 1, specifically constructing degree 10 surfaces as intersections of hyperplanes, a quadric, and the Grassmannian in , as well as a degree 6 example.
This paper establishes that under upper timelike sectional curvature bounds in Lorentzian length spaces, the space of directions at a point exists as a metric space with curvature bounded above by , while its metric cone forms a Lorentzian length space with non-positive timelike sectional curvature, thereby extending synthetic comparison geometry to causal settings.
This paper establishes the existence, uniqueness, and moment bounds for a generalized spatial model of Muller's ratchet with density-dependent rates and deleterious mutations, utilizing a sequence of approximating processes and a delicate coupling argument to overcome challenges posed by non-monotonicity and non-local interactions.
This paper establishes an explicit second-order expansion for the volume dimension of the Julia sets of holomorphic skew products in as a perturbation parameter approaches zero, extending the classical Ruelle-McMullen results on Hausdorff dimension to non-conformal higher-dimensional dynamical systems.
This paper establishes a functional law of large numbers for a spatial model of Muller's ratchet, proving that the system converges to an infinite system of partial differential equations that rigorously determine population spreading speeds and demonstrate that deleterious mutations can indeed surf deterministic population waves.
This paper combines additive combinatorics and Diophantine geometry to establish a uniform sum-product phenomenon for one-dimensional algebraic groups over , thereby resolving Bremner's conjecture on arithmetic progressions in elliptic curve coordinates and improving upon existing results by Bays--Breuillard regarding Elekes--Szabó-type theorems.