English
Related papers

Related papers: Generalized definitions of discrete stability

200 papers

Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class…

Optimization and Control · Mathematics 2025-07-16 Boris S. Mordukhovich , Peipei Tang , Chengjing Wang

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…

Dynamical Systems · Mathematics 2011-06-20 Marianne Akian , Stephane Gaubert , Bas Lemmens

Self-similarity of systems is very popular and intensively developing field during last decades. To this field belong so-called stable distributions and their generalization. In Klebanov and Sl\'amov\'a (2014) there was given an approach to…

Probability · Mathematics 2014-08-19 Lev B. Klebanov , Lenka Slámová , Ashot Kakosyan , Gregory Temnov

The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…

Statistical Mechanics · Physics 2009-11-10 Sumiyoshi Abe , G. Kaniadakis , A. M. Scarfone

Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…

Dynamical Systems · Mathematics 2022-10-10 Hana Krakovská , Christian Kühn , Iacopo P. Longo

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

Dynamical Systems · Mathematics 2016-12-14 Nicholas Apostolopoulos , Fernando Ortega , Grigoris Kalogeropoulos

We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of $\delta$-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay…

Computational Geometry · Computer Science 2015-05-08 Jean-Daniel Boissonnat , Ramsay Dyer , Arijit Ghosh

Novel criteria for global asymptotic stability of nonlinear uncertain finite-dimensional systems are presented. The results are obtained by a combination of the "discretization approach" and the ideas contained in the proof of the original…

Optimization and Control · Mathematics 2009-07-24 Iasson Karafyllis

The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…

Systems and Control · Electrical Eng. & Systems 2022-08-12 Francesco Ferrante , Giorgio Valmorbida

We explore set-stabilizability by constrained controls, and both controllability and stabilizability can be regarded as the special case of set-stabilizability. We not only clarify how to define an equilibrium point of Schr$\ddot{o}$dinger…

Quantum Physics · Physics 2014-01-21 Ming Zhang , Zairong Xi , Tzyh-Jong Tarn

The usual definition of the stability region of implicit multistep methods often implies that there are some isolated points of stability within the region of instability of the numerical method. These isolated stable points may appear when…

Numerical Analysis · Mathematics 2019-01-30 Lajos Lóczi

In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…

General Relativity and Quantum Cosmology · Physics 2016-11-15 M. I. Wanas , M. A. Bakry

Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…

Probability · Mathematics 2023-04-11 C. Houdré , R. Kawai

We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any…

Machine Learning · Computer Science 2020-01-01 Katrina Ligett , Moshe Shenfeld

Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…

Statistics Theory · Mathematics 2017-05-24 Holger Rootzén , Johan Segers , Jennifer L. Wadsworth

A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with…

Operator Algebras · Mathematics 2021-04-21 Søren Eilers , Tatiana Shulman , Adam P. W. Sørensen

This paper introduces the concept of dimensional stability for spline spaces over T-meshes, providing the first mathematical definition and a preliminary classification framework. We define dimensional stability as an invariant within the…

Numerical Analysis · Mathematics 2025-08-11 Bingru Huang , Falai Chen

We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.

Logic · Mathematics 2014-02-10 Itaï Ben Yaacov

After some historical remarks we discuss different criteria of dynamical stability of stars, and properties of the critical states where dynamical stability is lost, leading to collapse with formation of the neutron star or a black hole. At…

Astrophysics · Physics 2007-05-23 G. S. Bisnovatyi-Kogan

Complex networks with expanding dimensions are studied, where the networks may be directed and weighted, and network nodes are varying in discrete time in the sense that some new nodes may be added and some old nodes may be removed from…

Chaotic Dynamics · Physics 2007-05-23 Yuming Shi , Guanrong Chen