2088 papers
This paper investigates the split Grothendieck group of a -rigid subcategory within an extriangulated category, establishing isomorphisms between the Grothendieck group of the ambient category and specific subcategory groups for silting and -cluster tilting cases, while also determining the explicit structure of the Grothendieck group for -cluster categories of type .
This paper establishes a new characterization of regular Noetherian algebraic spaces via quasi-perfect blowups and demonstrates that the quasi-perfectness of proper morphisms is an étale-local property, thereby proving that the locus of such points is Zariski open.
This paper proposes a novel seasonal vegetation model to demonstrate that the duration and intensity of grazing cycles critically determine both the persistence of single populations and the competitive outcomes between species in semi-arid ecosystems.
This paper extends Pechenik's K-theoretic promotion operator () from tableaux to general posets and rooted trees, establishing divisibility properties for orbit sizes and completely determining these sizes for specific tree structures under certain conditions.
This paper extends the harmonic analogue of Rouché's Theorem to non-circular critical curves to determine that the complex-valued harmonic function possesses either or zeros, which are confined to two explicit annuli under specific conditions on the parameters and .
This paper provides a complete classification of when two continuous wavelet systems associated with matrix groups in two dimensions generate identical scales of coorbit spaces, thereby offering a rigorous framework for comparing their approximation-theoretic properties.
This paper establishes the theoretical consistency of sample average approximation and Karush–Kuhn–Tucker conditions for stochastic optimization problems with almost sure conic constraints in infinite-dimensional Banach spaces, providing a rigorous foundation for numerical methods across diverse applications such as operator learning, optimal transport, and PDE-constrained optimization.
This paper presents a residual-driven multiscale method within the GMsFEM framework that reformulates Darcy flow in perforated domains into a pressure-only system using velocity elimination and adaptive online enrichment to achieve high accuracy with significantly reduced computational costs.
This paper establishes new, concrete, and explicitly numerical conditional bounds for the residue at of the Dedekind zeta-function associated with a number field.
This paper provides rigorous theoretical guarantees for the existence and uniqueness of physically correct hydraulic states in water distribution systems by solving the underlying non-linear equations, thereby establishing a foundational basis for the reliability of hydraulic simulators and extending beyond previous approximation-based observability analyses.
This paper investigates the enumeration of numerical semigroups of genus with a fixed ordinarization number by interpreting the problem as counting integer points in rational polyhedral cones using Ehrhart theory, while deriving specific formulas and geometric characterizations for cases involving ordinarization numbers 1 and 2, two-generated semigroups, supersymmetric semigroups, and interval-generated semigroups.
This paper establishes a sharp upper bound of $2D_\mathrm{span} + 1\beta_{\mathrm{field}}D_\mathrm{span}$ in both coprime and non-coprime characteristics.
This paper establishes a geometric group theory framework for right quasigroups by introducing graph markings and invariants to characterize their Cayley (di)graphs, thereby proving that all racks are realizable by their full Cayley graphs and providing graph-theoretic characterizations for various algebraic structures.
This paper investigates the sum of the squares of irreducible character degrees not divisible by a prime and its relation to the corresponding quantity in a -Sylow normalizer, thereby proving a recent conjecture by E. Giannelli for the case and several other instances.
This paper introduces a scalable and parameter-robust solver for a cell-by-cell poroelasticity model of brain tissue, utilizing a three-field formulation with norm-equivalent preconditioning and Algebraic Multigrid approximations to efficiently simulate complex physiological processes like cellular swelling in detailed biological geometries.
This paper characterizes all possible infinite linear configurations that exist within the shift of any set of positive upper Banach density, thereby unifying and generalizing Szemerédi's theorem on arithmetic progressions and the recent density finite sums theorem.
This paper investigates a novel notion of polytope rigidity where edge lengths and face planarity are preserved while face shapes may vary, proving that convex polytopes are generically rigid in dimension three and conjecturing this holds for all dimensions .
This paper proves that for knots containing specific components like the -torus knot or the figure-eight knot, no compactly supported Hamiltonian diffeomorphism can move their conormal bundles to intersect the zero section cleanly along an unknot, a result established by deriving a unique algebraic constraint on the augmentation variety over the rational numbers using symplectic field theory.
This paper provides explicit equations describing Lipman's desingularization for double covers of regular surfaces, thereby establishing a concrete algorithm to resolve their singularities.
This paper establishes sharp local well-posedness up to critical regularity and proves global existence with scattering for small initial data in critical Sobolev spaces for hyperbolic nonlinear Schrödinger equations on , relying fundamentally on sharp endpoint Strichartz estimates.