Results 51 to 60 of about 892 (193)

Initial State Privacy of Nonlinear Systems on Riemannian Manifolds

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT In this paper, we investigate initial state privacy protection for discrete‐time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances.
Le Liu, Yu Kawano, Antai Xie, Ming Cao
wiley   +1 more source

Maximal symplectic torus actions

Bulletin of the London Mathematical Society, EarlyView.
Abstract There are several different notions of maximal torus actions on smooth manifolds, in various contexts: symplectic, Riemannian, complex. In the symplectic context, for the so‐called isotropy‐maximal actions, as well as for the weaker notion of almost isotropy‐maximal actions, we give classifications up to equivariant symplectomorphism.
Rei Henigman
wiley   +1 more source

A note on the magnetic Steklov operator on functions

Mathematika, Volume 71, Issue 4, October 2025.
Abstract We consider the magnetic Steklov eigenvalue problem on compact Riemannian manifolds with boundary for generic magnetic potentials and establish various results concerning the spectrum. We provide equivalent characterizations of magnetic Steklov operators which are unitarily equivalent to the classical Steklov operator and study bounds for the ...
Tirumala Chakradhar, Katie Gittins, Georges Habib, Norbert Peyerimhoff   +3 more
wiley   +1 more source

Projection methods for some constrained systems [PDF]

Rendiconti di Matematica e delle Sue Applicazioni, 2003
This article is concerned with a geometric tool given by a pair of projector operators defined by almost product structures on finite dimensional manifolds, polarized by a distribution of constant rank and also endowed with some geometric structures ...
Paulo Pitanga, Paulo R. Rodrigues
doaj  

The porous medium equation: Large deviations and gradient flow with degenerate and unbounded diffusion

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1609-1655, September 2025.
Abstract The problem of deriving a gradient flow structure for the porous medium equation which is thermodynamic, in that it arises from the large deviations of some microscopic particle system is studied. To this end, a rescaled zero‐range process with jump rate g(k)=kα,α>1$g(k)=k^\alpha, \alpha >1$ is considered, and its hydrodynamic limit and ...
Benjamin Gess, Daniel Heydecker
wiley   +1 more source

On an evolution equation in sub-Finsler geometry

Analysis and Geometry in Metric Spaces
We study the gradient flow of an energy with mixed homogeneity, which is at the interface of Finsler and sub-Riemannian geometry.
Garofalo Nicola
doaj   +1 more source

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source

Global and microlocal aspects of Dirac operators: Propagators and Hadamard states

Mathematische Nachrichten, Volume 298, Issue 9, Page 2942-2974, September 2025.
Abstract We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy‐compact globally hyperbolic 4‐manifolds. We realize the Cauchy evolution operator as the sum of two invariantly defined oscillatory integrals—the positive and negative Dirac propagators—global in space and in time, with ...
Matteo Capoferri, Simone Murro
wiley   +1 more source

Stochastic Multisymplectic PDEs and Their Structure‐Preserving Numerical Methods

Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.
ABSTRACT We construct stochastic multisymplectic systems by considering a stochastic extension to the variational formulation of multisymplectic partial differential equations proposed in Hydon [Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461 (2005): 1627–1637].
Ruiao Hu, Linyu Peng
wiley   +1 more source

Closed geodesics and the first Betti number

Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.
Abstract We prove that, on any closed manifold of dimension at least two with non‐zero first Betti number, a C∞$C^\infty$ generic Riemannian metric has infinitely many closed geodesics, and indeed closed geodesics of arbitrarily large length. We derive this existence result combining a theorem of Mañé together with the following new theorem of ...
Gonzalo Contreras, Marco Mazzucchelli
wiley   +1 more source