A characterization of Fano type varieties
The paper presents a new characterization of Fano type varieties.
🔢 Category
math
2921 papers
A Finite-Blocklength Analysis for ORBGRAND
This paper presents a finite-blocklength analysis for Ordered Reliability Bits GRAND (ORBGRAND) by deriving a random-coding union bound and characterizing its decoding metrics to establish a second-order achievable-rate expansion with a normal approximation, thereby quantifying its performance at short-to-moderate blocklengths where prior results were limited to asymptotic regimes.
The Kerr-Newman two-twistor particle
This paper presents an all-orders worldline effective action for Kerr-Newman black holes within twistor particle theory and identifies exact hidden symmetries in self-dual backgrounds.
Representations of shifted super Yangians and finite -superalgebras of type A
This paper investigates the representation theory of shifted super Yangians and finite -superalgebras of type A by establishing a criterion for the finite dimensionality of irreducible modules, deriving an explicit Gelfand-Tsetlin character formula for Verma modules, and proving that the centers of these algebras associated with even nilpotent elements are isomorphic to the center of the universal enveloping superalgebra.
Fundamental Groups of Genus-$0$ Quadratic Differential Strata via Exchange Graphs
This paper utilizes exchange-graph techniques and weighted mixed-angulations to derive explicit presentations of the fundamental groups for genus-zero strata of meromorphic quadratic differentials, generalizing known relations to include higher-order zeroes.
Topological, metric and fractal properties of one family of self-similar sets
This paper investigates the topological, metric, and fractal properties of a specific family of homogeneous self-similar sets parameterized by , proving that each set is a Cantorval with a non-empty interior and fractal boundary, while also determining its Lebesgue measure and the Hausdorff dimension of its boundary.
Subnormality of the quotients of -invariant Hilbert modules
This paper investigates the subnormality of quotients of -invariant Hilbert modules by homogeneous polynomials, establishing that such quotients are subnormal only if the polynomial is square-free and of degree at most one for standard spaces like the Hardy and Drury-Arveson modules, while also demonstrating that higher-degree examples exist for specific invariant modules like the Dirichlet module.
Validity of the Strong Version of the Union of Uniform Closed Balls Conjecture in the Plane
This paper proves the validity of the strong version of the union of uniform closed balls conjecture in the plane.
Local Laplacian: theory and models for data analysis
This paper introduces the persistent local Laplacian formalism, a theoretically grounded and highly parallelizable framework that overcomes the sensitivity and scalability limitations of traditional topological data analysis by establishing a generalized persistent Hodge isomorphism and unitary equivalence to efficiently extract fine-grained local structural signatures from large-scale datasets.
Peacock's Principle as a Conservative Strategy
This paper argues that Peacock's principle of permanence was not invalidated by Hamilton's non-commutative algebras, but rather correctly understood as a conservative strategy—rooted in Hume's philosophy—that permits exceptions like non-commutativity only when the reasons for violating established laws of reasoning outweigh the reasons for preserving them.
Proceedings Eighth International Conference on Applied Category Theory
This paper presents the proceedings of the Eighth International Conference on Applied Category Theory (ACT2025), held at the University of Florida in June 2025, which featured a diverse collection of contributions spanning pure and applied disciplines such as computer science, quantum computation, and chemistry.
On the 2-Linkage Problem for Split Digraphs
This paper resolves a problem posed by Bang-Jensen and Wang by proving that every 6-strong split digraph is 2-linked, and further establishes that every 5-strong semicomplete split digraph is 2-linked, a bound shown to be tight.
Inverse Robin Spectral Problem for the p-Laplace Operator
This paper investigates an inverse Robin spectral problem for the nonlinear -Laplace operator by establishing a thin-coating asymptotic limit, proving the uniqueness of the Robin coefficient via linearization and unique continuation, and deriving a conditional local Hölder-type stability estimate.
Existence, Sharp Boundary Asymptotics, and Stochastic Optimal Control for Semilinear Elliptic Equations with Gradient-Dependent Terms and Singular Weights
This paper establishes the existence, uniqueness, and sharp boundary asymptotics of large solutions to semilinear elliptic equations with gradient-dependent terms and singular weights, while also proving their strict convexity and identifying them as value functions for infinite-horizon stochastic optimal control problems.
Explicit affine formulas for distances between tuples in classical discrete structures
This paper answers a question posed by Ben Yaacov, Ibarlucía, and Tsankov by demonstrating an explicit construction of an affine formula using quantifier alternations to calculate distances between -tuples in -valued -structures.
Regularization of Hyperbolic Stochastic Partial Differential Equations By Two Fractional Brownian Sheets
This paper establishes the existence and uniqueness of strong solutions for a stochastic differential equation driven by the sum of two correlated fractional Brownian sheets with distinct Hurst parameters, demonstrating that the additive noise regularizes the system to ensure well-posedness even under weak drift assumptions.
On algebro-geometric solutions to the Gelfand--Dickey hierarchy
This paper presents a simple construction of algebro-geometric solutions to the Gelfand–Dickey hierarchy using an -type infinite ODE system and Dubrovin's method, while also deriving a formula for the -point function of the associated Riemann -function.
Sign-changing solutions for a Yamabe type problem
This paper establishes the existence of sign-changing solutions to a critical elliptic equation involving a Yamabe type operator on a compact manifold with boundary, contingent upon specific geometric conditions.
Oscillatory Interference in Dirichlet L-Functions and the Separation of Primes
This paper constructs simplified oscillatory reconstructions based on the nontrivial zeros of Dirichlet L-functions to visualize how interference patterns act as analytic filters that separate primes into congruence classes, thereby providing a visual bridge between the zero distributions of L-functions and the algebraic structure of cyclotomic fields.
Extreme value theorem for geodesic flow on the quotient of the theta group
This paper establishes an extreme value theorem for the geodesic flow on the hyperbolic surface associated with the theta group by introducing a spliced continued fraction algorithm, proving its dynamical equivalence to the flow's first return map, and deriving a Galambos-type extreme value law for maximal cusp excursions via spectral analysis of the transfer operator.