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Newton's method applied to rational functions: Fixed points and Julia sets

arXiv:2503.08498v2 Announce Type: replace Abstract: For a rational function $R$, let $N_R(z)=z-\frac{R(z)}{R'(z)}.$ Any such $N_R$ is referred to as a Newton map. We determine all...

Quantum Computing Mathematics

Local average in the Hyperbolic sphere problem

arXiv:2503.20455v2 Announce Type: replace Abstract: We consider a local average in the hyperbolic lattice point counting problem for the Picard group $\Gamma$ acting on the...

Adaptive hyper-reduction of non-sparse operators: application to parametric particle-based kinetic plasma models

arXiv:2504.00604v2 Announce Type: replace Abstract: This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic...

Software Technology

Acceleration via Perturbations on Low-resolution Ordinary Differential Equations

arXiv:2504.01497v2 Announce Type: replace Abstract: Recently, the high-resolution ordinary differential equation (ODE) framework, which retains higher-order terms, has been proposed to analyze gradient-based optimization algorithms....

Non-Birkhoff periodic orbits in symmetric billiards

arXiv:2504.03574v2 Announce Type: replace Abstract: We study non-Birkhoff periodic orbits in symmetric convex planar billiards. Our main result provides a quantitative criterion for the existence...

Policy Software

Logarithmic Crystalline Representations

arXiv:2504.14246v2 Announce Type: replace Abstract: In 1989, Faltings proved the comparison theorem between \'etale cohomology and crystalline cohomology by studying Fontaine-Faltings modules and crystalline representations....

Differentially Private Sampling via Reveal-or-Obscure

arXiv:2504.14696v2 Announce Type: replace Abstract: We introduce a differentially private (DP) algorithm called Reveal-or-Obscure (ROO) to generate a single representative sample from a dataset of...

Mathematics Engineering

Minimal Surfaces via Complex Quaternions

arXiv:2504.17377v2 Announce Type: replace Abstract: Minimal surfaces play a fundamental role in differential geometry, with applications spanning physics, material science, and geometric design. In this...

A filtered finite difference method for a highly oscillatory nonlinear Klein--Gordon equation

arXiv:2504.19359v2 Announce Type: replace Abstract: We consider a nonlinear Klein--Gordon equation in the nonrelativistic limit regime with highly oscillatory initial data in the form of...

Unitary ensembles with a critical edge point, their multiplicative statistics and the Korteweg-de-Vries hierarchy

arXiv:2504.20721v2 Announce Type: replace Abstract: We study the multiplicative statistics associated to the limiting determinantal point process describing unitary random matrices with a critical edge...

Mathematics Psychology

Existence of variational solutions to doubly nonlinear systems in nondecreasing domains

arXiv:2505.00148v2 Announce Type: replace Abstract: For $q \in (0, \infty)$, we consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form \begin{align*} \partial_t \big(...

On The Relative Cohomology For Algebraic Groups

arXiv:2505.00833v4 Announce Type: replace Abstract: Let $G$ be an algebraic group over a field $k$, and $M$ and $N$ be $G$-modules. In 1961, Hochschild showed...

Towards Riemannian diffeology

arXiv:2505.04170v3 Announce Type: replace Abstract: We introduce a framework for Riemannian diffeology. To this end, we use the tangent functor in the sense of Blohmann...

Technology Policy

On free arrangements of three conics

arXiv:2505.20025v2 Announce Type: replace Abstract: We give a complete classification of free arrangement of three smooth conics on complex projective plane admitting only ${\rm ADE}$...

Policy

Efficient Quadratic Corrections for Frank-Wolfe Algorithms

arXiv:2506.02635v4 Announce Type: replace Abstract: We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended conditional gradients, blended pairwise conditional gradients, and...

A Complete-Electrode-Model-Based Forward Approach for Transcranial Temporal Interference Stimulation with Linearization: A Numerical Simulation Study

arXiv:2506.18436v2 Announce Type: replace Abstract: Background and Objective: Transcranial temporal interference stimulation (tTIS) is a promising non-invasive brain stimulation technique in which interference between electrical...

Technology Neuroscience

On vector-valued functional equations with multiple recursive terms

arXiv:2507.01871v2 Announce Type: replace Abstract: In this work, we study vector-valued functional equations with multiple recursive terms that arise naturally when we are dealing with...

Branching space of multipointed d-space

arXiv:2507.08377v4 Announce Type: replace Abstract: Using the notion of short directed path, we introduce the branching space of a multipointed $d$-space. We prove that for...

Software Finance

Joint Deformations of Manifolds, Coherent Sheaves and Sections

arXiv:2507.20276v4 Announce Type: replace Abstract: We describe a differential graded Lie algebra controlling infinitesimal deformations of triples $(X,\mathcal{F},\sigma)$, where $\mathcal{F}$ is a coherent sheaf on...

Accelerating Conjugate Gradient Solvers for Homogenization Problems with Unitary Neural Operators

arXiv:2508.02681v2 Announce Type: replace Abstract: Rapid and reliable solvers for parametric partial differential equations (PDEs) are needed in many scientific and engineering disciplines. For example,...

Engineering Software

Structure constants of Peterson Schubert calculus

arXiv:2508.05457v2 Announce Type: replace Abstract: We give an explicit, positive, and type-uniform formula for all equivariant structure constants of the Peterson Schubert calculus in arbitrary...

Branching space of precubical set

arXiv:2508.14839v4 Announce Type: replace Abstract: Using the notion of short natural directed path, we introduce the homotopy branching space of a precubical set. It is...