Actions of a group of prime order without equivariantly simple germs
The paper proves that equivariantly simple invariant singularities can only exist for real representations and certain "almost real" representations of a group of prime order.
🔢 Category
math
4188 papers
Analog Error Correcting Codes with Constant Redundancy
This paper establishes an upper bound and a simple single-error decoder for analog error-correcting codes with unit-norm columns, and constructs a new family of such codes with constant redundancy three that achieves a smaller height profile than existing MDS constructions.
Global Weak Solutions of a Navier-Stokes-Cahn-Hilliard System for Incompressible Two-phase flows with Thermo-induced Marangoni Effects
This paper establishes the existence of global weak solutions for a Navier-Stokes-Cahn-Hilliard system modeling thermo-induced Marangoni effects in two-phase incompressible flows with variable physical parameters and singular potentials in both two and three dimensions, while also proving solution uniqueness in the two-dimensional case under matched density conditions.
Enhancing User Fairness in Two-Layer RSMA: A Movable Antenna Approach
This paper proposes a novel movable antenna approach for two-layer rate-splitting multiple access (RSMA) systems that employs a two-loop iterative algorithm to jointly optimize beamforming, user clustering, common rate allocation, and antenna positions, thereby significantly enhancing user fairness compared to existing benchmark schemes.
Quadratic form of heavy-tailed self-normalized random vector with applications in -heavy Mar\v cenko--Pastur law
This paper establishes that the asymptotic distribution of quadratic forms for self-normalized heavy-tailed random vectors is determined solely by the diagonal entries of the matrix and the stability index , a result applied to derive the atom-free nature of the -heavy Marčenko--Pastur law for heavy-tailed sample correlation matrices.
Second-order geometry and Riemannian Newton's method for optimization on the indefinite Stiefel manifold
This paper presents a detailed implementation of Riemannian Newton's method for optimization on the indefinite Stiefel manifold by deriving the Levi-Civita connection and analytically computing the Hessian under two existing metrics, then solving the resulting Newton equation in the tangent space via the linear conjugate gradient method to achieve fast local convergence.
Quantitative Fluctuation Analysis for Continuous-Time Stochastic Gradient Descent via Malliavin Calculus
This paper establishes a quantitative Central Limit Theorem for continuous-time Stochastic Gradient Descent by employing Malliavin calculus and second-order Poincaré inequalities to derive explicit Wasserstein convergence rates driven by the learning rate magnitude, a result validated through numerical experiments.
On linear -quotients
This paper investigates linear -quotients on affine spaces by employing explicit stacky resolutions to classify their singularity types and compute stringy motivic invariants, thereby reducing a conjecture by the authors and Fabio Tonini—which posits that these invariants match those of linear -quotients—to a computationally verified equality of multi-sets.
English translation of Sophie Kowalevski's "On the problem of the rotation of a rigid body about a fixed point"
This paper presents an English translation and digitization of Sophie Kowalevski's 1889 French publication on the rotation of a rigid body about a fixed point, which introduced the famous Kovalevskaya Top.
Inexact Bregman Sparse Newton Method for Efficient Optimal Transport
The paper introduces the Inexact Bregman Sparse Newton (IBSN) method, a novel algorithm that combines a Bregman proximal point framework with a sparse Newton solver and Hessian sparsification to efficiently compute exact Optimal Transport distances for large-scale datasets while guaranteeing global convergence and outperforming existing state-of-the-art methods in both speed and precision.
A simple, high-order and compact WENO limiter based on control volume for spectral volume method
This paper introduces a novel, simple, and compact control volume-based high-order limiter for the spectral volume method that effectively suppresses oscillations in discontinuous problems while preserving high-order accuracy and resolution through a nonlinear weighting reconstruction strategy.
Resolution of the Skolem Problem for -Generalized Lucas Sequences
This paper resolves Skolem's problem for -generalized Lucas sequences by characterizing their zero-distribution at negative indices and proving that the zero-multiplicity is exactly for all .
A base change framework for tensor functions
This paper establishes a base change framework to extend tensor function results from specific fields to general fields, thereby proving that slice rank is linearly bounded by geometric rank and is quasi-supermultiplicative for any 3-tensors over any field.
Construction of Multicyclic Codes of Arbitrary Dimension via Idempotents: A Unified Combinatorial-Algebraic Approach
This paper presents a unified combinatorial-algebraic framework for constructing multicyclic codes of arbitrary dimension over by utilizing -dimensional primitive idempotents and multidimensional cyclotomic orbits to establish a direct equivalence between algebraic and combinatorial descriptions, derive a natural polynomial basis, and generalize BCH and Reed-Solomon bounds through an efficient constructive algorithm.
Anderson localization and Hölder regularity of IDS for analytic quasi-periodic Schrödinger operators
This paper establishes both Anderson localization and Hölder continuity of the integrated density of states for quasi-periodic Schrödinger operators on with non-constant analytic potentials and fixed Diophantine frequencies in the perturbative regime, utilizing a novel multi-scale analysis approach to control Green's functions.
Limit theorems for anisotropic functionals of stationary Gaussian fields with Gneiting covariance function
This paper establishes Gaussian and non-Gaussian limit theorems for non-linear additive functionals of stationary Gaussian fields with Gneiting-class non-separable covariance structures over anisotropically growing domains, demonstrating that these covariances are asymptotically separable in a cumulant sense to explicitly characterize convergence to either Gaussian or 2-domain Rosenblatt distributions based on long-range dependence conditions.
Lefschetz filtration and Perverse filtration on the compactified Jacobian
This paper proves that the Lefschetz filtration and the perverse filtration on the cohomology of the compactified Jacobian of a complex integral curve with planar singularities are opposite to each other, thereby confirming a conjecture by Maulik and Yun.
Online Bidding for Contextual First-Price Auctions with Budgets under One-Sided Information Feedback
This paper proposes a novel bidding algorithm for repeated contextual first-price auctions with budget constraints under one-sided information feedback, utilizing a robust regression method based on conditional quantile invariance to learn unknown competitor bid distributions and achieving order-optimal regret.
Necessary conditions for existence of tensor invariants for general nonlinear dynamical systems
This paper establishes necessary conditions for the existence of tensor invariants in general nonlinear dynamical systems, with a specific focus on semi-quasihomogeneous systems, thereby extending the foundational work of Poincaré and Kozlov on integrability.
Nontrivial automorphisms of in Cohen models
This paper establishes that nontrivial automorphisms of the Boolean algebra exist in Cohen extensions of a model for any number of added reals , and extends this result to under additional hypotheses involving sage Davies trees.