Stability theorem and extremum conditions for abnormal problems

2015 ◽  
Vol 291 (1) ◽  
pp. 4-23 ◽  
Author(s):  
E. R. Avakov
Keyword(s):  
Stability Theorem ◽  
Abnormal Problems ◽  
Extremum Conditions

scholarly journals Why (some) abnormal problems are “normal”

2021 ◽  
Vol 154 ◽  
pp. 104971
Author(s):  
Dieter Grass ◽  
Gustav Feichtinger ◽  
Peter M. Kort ◽  
Andrea Seidl
Keyword(s):  
Abnormal Problems

scholarly journals A stability theorem for the obstacle problem

1975 ◽  
Vol 17 (1) ◽  
pp. 34-47 ◽  
Author(s):  
David G Schaeffer
Keyword(s):  
Obstacle Problem ◽  
Stability Theorem

Stability of elliptical horizontally inhomogeneous rodons

2000 ◽  
Vol 416 ◽  
pp. 29-43
Author(s):  
RENÉ PINET ◽  
E. G. PAVÍA
Keyword(s):  
Formal Analysis ◽  
Detailed Examination ◽  
Stability Theorem ◽  
Homogeneous Case ◽  
Density Distributions ◽  
Formal Stability ◽  
Inhomogeneous Density ◽  
Loss Of Mass ◽  
The Stability ◽  
Main Effects

The stability of one-layer vortices with inhomogeneous horizontal density distributions is examined both analytically and numerically. Attention is focused on elliptical vortices for which the formal stability theorem proved by Ochoa, Sheinbaum & Pavía (1988) does not apply. Our method closely follows that of Ripa (1987) developed for the homogeneous case; and indeed they yield the same results when inhomogenities vanish. It is shown that a criterion from the formal analysis – the necessity of a radial increase in density for instability – does not extend to elliptical vortices. In addition, a detailed examination of the evolution of the inhomogeneous density fields, provided by numerical simulations, shows that homogenization, axisymmetrization and loss of mass to the surroundings are the main effects of instability.

scholarly journals New Generalizations and Results in Shift-Invariant Subspaces of Mixed-Norm Lebesgue Spaces \({L_{\vec{p}}(\mathbb{R}^d)}\)

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 227 ◽  
Author(s):  
Junjian Zhao ◽  
Wei-Shih Du ◽  
Yasong Chen
Keyword(s):  
Invariant Subspace ◽  
Type Inequality ◽  
Invariant Subspaces ◽  
Minkowski Inequality ◽  
Hölder Inequality ◽  
Stability Theorem ◽  
Mixed Norm ◽  
Lebesgue Spaces

In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces Lp→(Rd). We obtain a mixed-norm Hölder inequality, a mixed-norm Minkowski inequality, a mixed-norm convolution inequality, a convolution-Hölder type inequality and a stability theorem to mixed-norm case in the setting of shift-invariant subspace of Lp→(Rd). Our new results unify and refine the existing results in the literature.

A dual to Lyapunov's stability theorem

2001 ◽  
Vol 42 (3) ◽  
pp. 161-168 ◽  
Author(s):  
Anders Rantzer
Keyword(s):  
Stability Theorem

scholarly journals Persistence in expansive systems

1983 ◽  
Vol 3 (4) ◽  
pp. 567-578 ◽  
Author(s):  
Jorge Lewowicz
Keyword(s):  
Structural Stability ◽  
Compact Manifold ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Dynamical Features

AbstractWe give some sufficient conditions for an expansive diffeomorphism ƒ of a compact manifold to be such that every neighbouring diffeomorphism shows, roughly, all the dynamical features of ƒ. These results are then applied to prove a structural stability theorem for pseudo-Anosov maps.

scholarly journals A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Mei Zhang ◽  
Danling Wang ◽  
Lequan Min ◽  
Xue Wang
Keyword(s):  
Discrete Time ◽  
Chaotic Map ◽  
Stability Theorem ◽  
Pseudorandom Number Generator ◽  
Generalized Synchronization ◽  
Key Space ◽  
Chaos System ◽  
Definition Of ◽  
Study Designs ◽  
Generalized Stability

Firstly, this study introduces a definition of generalized stability (GST) in discrete-time nonautonomous chaos system (DNCS), which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a novel 4-dimensional discrete chaotic map. Numerical simulations show that the dynamic behaviors of this map have chaotic attractor characteristics. As one application, we design a chaotic pseudorandom number generator (CPRNG) based on the GST DNCS. We use the SP800-22 test suite to test the randomness of four 100-key streams consisting of 1,000,000 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm, and a 6-dimensional CGS-based CPRNG, respectively. The numerical results show that the randomness performances of the two CPRNGs are promising. In addition, theoretically the key space of the CPRNG is larger than 21116. As another application, this study designs a stream avalanche encryption scheme (SAES) in RGB image encryption. The results show that the GST DNCS is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs.

A Path-Planning Strategy for Overhead Cranes With High Hoisting Speed

2002 ◽  
Author(s):  
Ho-Hoon Lee
Keyword(s):  
Path Planning ◽  
High Performance ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Control Laws ◽  
Planning Strategy ◽  
Overhead Cranes ◽  
Time Control ◽  
Small Load ◽  
Load Swing

This paper proposes a path planning strategy for high-performance anti-swing control of overhead cranes, where the anti-swing control problem is solved as a kinematic problem. First, two anti-swing control laws, one for hoisting up and the other for hoisting down, are proposed based on the Lyapunov stability theorem. Then a new path-planning strategy is proposed based on the concept of minimum-time control and the proposed anti-swing control laws. The proposed path planning is free from the usual constraints of small load swing, slow hoisting speed, and small hoisting distance. The effectiveness of the proposed path planning is shown by computer simulation with high hoisting speed and hoisting ratio.

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