Classification of Nottingham algebras
This paper completes the classification of Nottingham algebras by establishing existence and uniqueness results that determine all such infinite-dimensional, positively graded thin algebras up to isomorphism.
🔢 Category
math
7210 papers
Robinson Splitting Theorem and Induction
This paper establishes that a weakened version of the Robinson Splitting Theorem, where lowness is replaced by superlowness, holds within models of the theory .
Non-Derivability Results in Polymorphic Dependent Type Theory
This paper establishes that in pure polymorphic dependent type theory (P2), parametric quotient types and strong coinduction principles are not definable, and that function extensionality is strictly necessary to prove induction principles, by constructing specific models where these principles fail.
Invariant measures and traces on groupoid -algebras
This paper establishes sufficient conditions for the existence and uniqueness of traces on the essential and full -algebras of (possibly non-Hausdorff) étale groupoids extending invariant measures, particularly linking uniqueness to essential freeness and amenability of isotropy groups, with applications to gauge-invariant algebras of finite-state self-similar groups.
Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images
This paper classifies the -adic Galois images of elliptic curves over with mod non-split Cartan images using -adic Hodge theory, providing a novel algorithm for the potentially supersingular case and deriving global consequences for elliptic curves over that sharpen bounds on their adelic images.
On the generalized circular projected Cauchy distribution
This paper establishes the relationship between the generalized circular projected Cauchy distribution and the wrapped Cauchy distribution, proposes a log-likelihood ratio test for comparing two angular means without assuming equal concentration parameters, and evaluates the test's performance through simulations when the underlying distribution is incorrectly assumed to be wrapped Cauchy.
Rapid stabilization of general linear systems with F-equivalence
This paper establishes simple sufficient conditions for the rapid stabilization of general linear systems with a Riesz basis of eigenvectors by employing an -equivalence approach via Fredholm transformations, thereby proving that such systems can be transformed into exponentially stable systems with arbitrarily large decay rates and improving existing results for non-parabolic operators.
A new ultrafilter proof of Van der Waerden's theorem
This paper presents a concise new proof of Van der Waerden's Theorem using algebra in the compact space of ultrafilters , distinguishing itself from existing proofs by avoiding the use of minimal or idempotent ultrafilters.
Differential Goppa Codes
This paper provides a rigorous generalization of Rosenbloom and Tsfasman's algebraic-geometric codes to arbitrary genus curves by defining differential Goppa codes via -jets and Hasse-Schmidt derivatives, analyzing their structural properties and distance variations, and establishing that they encompass all linear codes on while strictly generalizing classical Goppa codes.
Localization operators on Bergman and Fock spaces
This paper establishes that localization operators on weighted Bergman spaces converge weakly to those on Fock spaces under natural scaling as the parameter , a result leveraged to derive sharp norm estimates for Toeplitz operators, analyze windowed Berezin transforms, and prove Szegő-type theorems.
An Adaptive KKT-Based Indicator for Convergence Assessment in Multi-Objective Optimization
This paper proposes a robust adaptive reformulation of an entropy-inspired KKT-based convergence indicator, utilizing quantile normalization to effectively assess stationarity in multi-objective optimization without relying on external reference sets.
A scalar auxiliary variable-based semi-implicit scheme for stochastic Cahn--Hilliard equation
This paper proposes a novel semi-implicit numerical scheme based on a stochastic scalar auxiliary variable (SSAV) reformulation for the stochastic Cahn--Hilliard equation with multiplicative noise, which incorporates Itô correction terms to achieve optimal strong convergence of order one-half while preserving the energy evolution law.
Signed graphs with exactly two main eigenvalues: The unicyclic case
This paper extends the characterization of signed graphs with exactly two main eigenvalues from the case where the associated multigraph has a tree base to the case where the base graph is unicyclic, concluding with several proposed open problems.
Online Order Fulfillment with Replenishment
This paper investigates the relative impact of inventory replenishment policies versus real-time online fulfillment algorithms on system profit under demand uncertainty, demonstrating that cumulative regret remains stable over long cycles and introducing a novel look-ahead algorithm that outperforms myopic baselines while identifying specific regimes where optimizing one lever yields greater revenue gains than the other.
The Construction Principle and superstability of free objects in varieties of algebras
This paper establishes that if a variety of algebras satisfies a strong form of the Eklof-Mekler-Shelah Construction Principle, then almost all of its AEC-coverings of free objects are unsuperstable, with specific applications to -modules and groups.
Bilinear spherical maximal function on the Heisenberg group
This paper establishes sharp estimates for single-scale, full, and lacunary bilinear Nevo-Thangavelu spherical maximal operators on the Heisenberg group () by employing newly developed single-scale average estimates, Hopf's maximal ergodic theorem, and an adapted argument.
Limiting empirical spectral measure of the normalized Laplacian in preferential attachment graphs
This paper proves that the empirical spectral distribution of the normalized Laplacian for linear preferential attachment graphs in the Barabási-Albert regime converges weakly in probability to a deterministic measure on [0, 2], which is characterized by the expected diagonal Green function of the associated Pólya-point graph using a combination of resolvent methods, random-walk representations, and concentration inequalities.
Riemannian Gradient Method with Momentum
This paper introduces a Riemannian gradient method with momentum that extends a recent unconstrained optimization technique, proving an worst-case complexity bound for finding -stationary points and demonstrating competitive performance against state-of-the-art solvers through extensive numerical experiments.
Unweighted Hardy Inequalities on the Heisenberg Group and in Step-Two Carnot Groups
This paper establishes unweighted Hardy-type inequalities on step-two Carnot groups with one-dimensional vertical layers by employing a quantitative integration-by-parts mechanism that substitutes the non-horizontal Euler vector field with a controlled horizontal one, yielding explicit optimal constant bounds for the Heisenberg group and generalized non-isotropic structures.
Wasserstein Gradient Flows of semi-discret energies: evolution of urban areas anduniform quantization
This paper investigates the Wasserstein gradient flow of semi-discrete energies relevant to urban planning and uniform quantization by proving the convergence of the JKO scheme to a singularly coupled PDE-ODE system, analyzing its qualitative properties such as atomic convergence to Laguerre cell barycenters, and validating these findings through numerical simulations that reveal dynamic crystallization phenomena.