Desingularization of double covers of regular surfaces
This paper provides explicit equations describing Lipman's desingularization for double covers of regular surfaces, thereby establishing a concrete algorithm to resolve their singularities.
🔢 Category
math
2549 papers
Topological constraints on clean Lagrangian intersections from -valued augmentations
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.
Rigidity of polytopes with edge length and coplanarity constraints
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 .
Infinite linear patterns in sets of positive density
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.
Parameter-robust preconditioners for a cell-by-cell poroelasticity model with interface coupling
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.
Sum of the squares of the -character degrees
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.
Graph quandles: Generalized Cayley graphs of racks and right quasigroups
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.
Generic orbits, normal bases, and generation degree for fields of rational invariants
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.
Ordinarization numbers of numerical semigroups
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.
Existence and Uniqueness of Physically Correct Hydraulic States in Water Distribution Systems -- A theoretical analysis on the solvability of non-linear systems of equations in the context of water distribution systems
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.
Explicit conditional bounds for the residue of a Dedekind zeta-function at
This paper establishes new, concrete, and explicitly numerical conditional bounds for the residue at of the Dedekind zeta-function associated with a number field.
Two-Stage Stochastic Capacity Expansion in Stable Matching under Truthful or Strategic Preference Uncertainty
This paper introduces a two-stage stochastic capacity expansion model for many-to-one matching markets that accounts for both exogenous preference uncertainty and endogenous strategic misreporting, proposing sample average approximation-based heuristics to optimize school capacities and improve student outcomes compared to deterministic approaches.
A residual driven multiscale method for Darcy's flow in perforated domains
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.
Sample-Based Consistency in Infinite-Dimensional Conic-Constrained Stochastic Optimization
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.
Classifying Wavelet Coorbit Spaces in Dimension 2
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.
Counting Zeros of Complex-Valued Harmonic Functions via Rouché's Theorem
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 .
K-promotion on m-packed labelings of posets
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.
Impacts of the duration and intensity of grazing cycle on vegetation population dynamics in semi-arid ecosystems with seasonal succession
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.
A note on quasi-perfect morphisms
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.
The Grothendieck group of an extriangulated category
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 .