Results 251 to 260 of about 6,925,642 (276)

Convolutions With Slowly Varying Functions in the Complex Domain

Integral Transforms and Special Functions, 2005
We prove a theorem concerning asymptotic behavior of general complex-valued kernel convolutions with slowly varying functions in the sense of Karamata. In applications, we show that the content of some classical theorems can be naturally extended on some parts of complex z-plane.
Slavko Simić
exaly   +2 more sources

Stabilization of Nonlinear Systems With a Slowly Varying Parameter by a Control Lyapunov Function

ISA Transactions, 2010
Based on a control Lyapunov function (CLF) strategy, a novel approach for designing a controller for a slowly varying nonlinear system is proposed. The approach may be thought of as being in between the time-invariant and time-varying CLF techniques.
Mohammad-Javad Yazdanpanah, Mohammad Hossein Shafiei, M J Yazdanpanah   +2 more
exaly   +3 more sources

Slowly Varying Functions in the Zygmund Sense and Generalized Regular Variation

Journal of Mathematical Analysis and Applications, 2019
The author analyzes the fundamental role of slowly varying functions (SVF) in the Zygmund sense. Specifically: (1) He derives a necessary and sufficient condition for a positive measurable function to be slowly varying in the Zygmund sense; (2) analytical equivalences involving Zygmund SVF's in probabilistic setting are related to necessary and ...
Eugene Seneta
exaly   +3 more sources

A FAST-MANIFOLD APPROACH TO MELNIKOV FUNCTIONS FOR SLOWLY VARYING OSCILLATORS

International Journal of Bifurcation and Chaos, 1996
A new approach to obtaining the Melnikov function for homoclinic orbits in slowly varying oscillators is proposed. The present method applies the usual two-dimensional Melnikov analysis to the “fast” dynamics of the system which lie on an invariant manifold. It is shown that the resultant Melnikov function is the same as that obtained in the usual way
Chen, Shyh-Leh, Shaw, Steven W.
openaire   +1 more source

Sharp Hardy Inequalities of Fractional Order Involving Slowly Varying Functions

Journal of Mathematical Analysis and Applications, 2012
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Petr Gurka, Bohumir Opic
exaly   +3 more sources

Perturbation methods and the Melnikov functions for slowly varying oscillators

Chaos, Solitons & Fractals, 2005
A new approach based on the Lindstedt-Poincaré method is proposed to obtain the Melnikov function for homoclinic orbits in slowly varying oscillators. The goal of the authors is to show that without dealing explicitly with the complicated geometry related to the three-dimensional distance measured in a Poincaré section, the same Melnikov function can ...
Lakrad, Faouzi, Charafi, Moulay Mustapha
openaire   +1 more source

Limiting reiteration for real interpolation with slowly varying functions

Mathematische Nachrichten, 2004
AbstractWe present reiteration formulae with limiting values θ = 0 and θ = 1 for a real interpolation method involving slowly varying functions. Applications to the Lorentz–Karamata spaces, the Fourier transform and the Riesz potential are given. In particular, our results yield improvements of limiting Sobolev‐type embeddings due to Trudinger, Hansson,
Gogatishvili, A. (Amiran), Opic, B. (Bohumír), Trebels, W.   +2 more
openaire   +3 more sources

Measure of Non-Compactness and Limiting Interpolation With Slowly Varying Functions

Banach Journal of Mathematical Analysis
AbstractWe give estimates for the measure of non-compactness of an operator interpolated by the limiting methods involving slowly varying functions. As applications we establish estimates for the measure of non-compactness of operators acting between Lorentz–Karamata spaces.
Fernando Cobos
exaly   +4 more sources

Slowly varying linear functional differential equations

IEEE Transactions on Automatic Control, 1972
Several authors have studied the stability behavior of slowly varying linear systems of ordinary differential equations. These studies have yielded a sufficient condition for uniform exponential stability. In this work this result is extended to slowly varying linear functional differential equations.
openaire   +2 more sources

Slowly varying, linear, neutral, functional, differential equations†

International Journal of Control, 1973
Abstract For a slowly varying, linear, neutral, functional, differential equation, a sufficient condition is derived which ensures uniform exponential stability.
openaire   +1 more source