Oscillators And Oscillatory Signals From Smooth To Discontinuous

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Oscillators and Oscillatory Signals from Smooth to Discontinuous

Author: Valery N. Pilipchuk
language: en
Publisher: Springer Nature
Release Date: 2023-09-23
This updated and enriched new edition maintains its complementarity principle in which the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford’s algebras, give rise to the essentially nonlinear “quasi-impact” methodology based on the idea of non-smooth temporal substitutions. In the years since “Nonlinear Dynamics: Between Linear and Impact Limits,” the previous edition of this book, was published, due to a widening area of applications, a deeper insight into the matter has emerged leading to the rudimentary algebraic view on the very existence of the complementary smooth and non-smooth base systems as those associated with two different signs of the algebraic equation j2 =± 1. This edition further includes an overview of applications found in the literature after the publication of first edition, and new physical examples illustrating both theoretical statements and constructive analytical tools.
Asymptotic Methods for Engineers

Asymptotic Methods for Engineers is based on the authors’ many years of practical experience in the application of asymptotic methods to solve engineering problems. This book is devoted to modern asymptotic methods (AM), which is widely used in engineering, applied sciences, physics, and applied mathematics. Avoiding complex formal calculations and justifications, the book’s main goal is to describe the main ideas and algorithms. Moreover, not only is there a presentation of the main AM, but there is also a focus on demonstrating their unity and inseparable connection with the methods of summation and asymptotic interpolation. The book will be useful for students and researchers from applied mathematics and physics and of interest to doctoral and graduate students, university and industry professors from various branches of engineering (mechanical, civil, electro-mechanical, etc.).
Advanced Topics in Electric Circuits

This book is addressed to researchers and practitioners in the theory and applications of electric circuits. It can also serve as a textbook for Ph.D. students examining applications of modern mathematics to important issues emerging nowadays more and more often in advanced electrical and electronic systems. The book offers effective tools to facilitate the study of all those circuits and systems increasingly penetrating our world, helping to discover their hidden beauty. The material is presented in twelve chapters divided into sections. Usually, first sections are of an introductory nature, explain studied phenomena and announce numerical results. More advanced investigations are presented in subsequent sections. The center of concern is set on existing modern methods as well as continuously emerging new methods of investigations useful for researchers, engineers and practitioners active in many interdisciplinary fields, where physics, electrochemistry, and electric circuits play a key role. Coverage includes: • Principles of optimal operations of electrical circuits; • The equilibrium state of the circuit as a stationary point of its power functional; • The Gibbs effect and its consequences for circuit analysis; • Accurate calculation of complex dynamic circuits operating in non-sinusoidal periodic states; • Energy hysteresis loops in non-sinusoidal periodic states of circuits; • Optimal transformations of elements in three-phase circuits; • Analog and digital filters; • Fractals and their structures and measures; • Fibonacci, Sierpiński and Cantor circuits; • Chaos in electrical circuits; •Electrochemical impedance spectroscopy; •Circuits with nanostructures and their properties; •Circuits of fractional orders; •AI in electrical circuits. This is the first extensive description of these topics and the interpretations of analytical results and those obtained from computer simulations with MATLAB environments. Special attention is paid to nonlinear electric circuits and finally the presentation is extended to effective applications of the achievements of modern AI. Numerous examples and exercises illustrate main results of the book. The book provides readers with a better understanding of origins and properties of many new circuit structures made possible by nanotechnology and atomic microscopy.