Download or read book Differential Equations with Small Parameters and Relaxation Oscillations written by E. Mishchenko and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large amount of work has been done on ordinary differ ential equations with small parameters multiplying deriv atives. This book investigates questions related to the asymptotic calculation of relaxation oscillations, which are periodic solutions formed of sections of both sl- and fast-motion parts of phase trajectories. A detailed discussion of solutions of differential equations involving small parameters is given for regions near singular points. The main results examined were obtained by L.S. Pontryagin and the authors. Other works have also been taken into account: A.A. Dorodnitsyn's investigations of Van der Pol's equation, results obtained by N.A. Zheleztsov and L.V. Rodygin concerning relaxation oscillations in electronic devices, and results due to A.N. Tikhonov and A.B. Vasil'eva concerning differential equations with small parameters multiplying certain derivatives. E.F. Mishchenko N. Kh. Rozov v CONTENTS Chapter I. Dependence of Solutions on Small Parameters. Applications of Relaxation Oscillations 1. Smooth Dependence. Poincare's Theorem . 1 2. Dependence of Solutions on a Parameter, on an Infinite Time Interval 3 3. Equations with Small Parameters 4 Multiplying Derivatives 4. Second-Order Systems. Fast and Slow Motion.
Download or read book Differential Equations Containing Small Parameter and Relaxation Oscillations written by Evgeniĭ Frolovich Mishchenko and published by . This book was released on 1965 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relaxation Oscillations in Mathematical Models of Ecology written by A. I︠U︡ Kolesov and published by American Mathematical Soc.. This book was released on 1995 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents for the first time a systematic exposition of techniques for constructing relaxation oscillations and methods for investigating stability properties of certain classes of systems with delay. The authors bring out some of the distinctive features that have no analogues in relaxation systems of ordinary differential equations. The exposition provides analysis of significant examples from biophysics, mathematical ecology, and quantum physics that elucidate important patterns. Many unsolved problems are posed. The book would appeal to researchers and specialists interested in the theory and applications of relaxation oscillations.
Download or read book Selected Research Papers written by L.S. Pontryagn and published by CRC Press. This book was released on 2019-11-11 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the finest achievements in modern mathematics are two of L.S. Pontryagin's most notable contributions: Pontryagin duality and his general theory of characters of a locally compact commutative group. This book, the first in a four-volume set, contains the most important papers of this eminent mathematician, those which have influenced many generations of mathematicians worldwide. They chronicle the development of his work in many areas, from his early efforts in homology groups, duality theorems, and dimension theory to his later achievements in homotopic topology and optimal control theory. On 3 September 1983 Lev Semenovich Pontryagin was seventy-five. To mark this important event in the life of this outstanding contemporary mathematician we are beginning the publication of his scientific works in four volumes, according to a decision taken by the Mathematics Division of the USSR Academy of Sciences. The first volume contains the most important mathematical papers of L. S. Pontryagin and also includes a bibliography of his basic scientific works, the second is his well-known monograph Topological Groups, the third comprises two monographs, Foundations of Algebraic Topology and Smooth Manifolds and Their Applications in Homotopy Theory, and the fourth is a revised edition of The Mathematical Theory of Optimal Processes by L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko.
Download or read book Topological Groups written by R. V. Gamkrelidze and published by CRC Press. This book was released on 1987-03-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering the insights of L.S. Pontryagin, one of the foremost thinkers in modern mathematics, the second volume in this four-volume set examines the nature and processes that make up topological groups. Already hailed as the leading work in this subject for its abundance of examples and its thorough explanations, the text is arranged so that readers can follow the material either sequentially or schematically. Stand-alone chapters cover such topics as topological division rings, linear representations of compact topological groups, and the concept of a lie group.
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book Geometric Singular Perturbation Theory Beyond the Standard Form written by Martin Wechselberger and published by Springer Nature. This book was released on 2020-02-21 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.
Download or read book Analysis and Simulation of Chaotic Systems written by Frank C. Hoppensteadt and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and Simulation of Chaotic Systems is a text designed to be used at the graduate level in applied mathematics for students from mathematics, engineering, physics, chemistry and biology. The book can be used as a stand-alone text for a full year course or it can be heavily supplemented with material of more mathematical, more engineering or more scientific nature. Computations and computer simulations are used throughout this text to illustrate phenomena discussed and to supply readers with probes to use on new problems.
Download or read book Nonlinear Dynamics of Electronic Systems written by Valeri M. Mladenov and published by Springer. This book was released on 2014-06-30 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 22nd International Conference on Nonlinear Dynamics of Electronic Systems, NDES 2014, held in Albena, Bulgaria, in July 2014. The 47 revised full papers presented were carefully reviewed and selected from 65 submissions. The papers are organized in topical sections on nonlinear oscillators, circuits and electronic systems; networks and nonlinear dynamics and nonlinear phenomena in biological and physiological systems.
Download or read book L S Pontryagin Selected Works written by Lev Semenovich Pontri︠a︡gin and published by . This book was released on 1986 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the finest achievements in modern mathematics are two of L.S. Pontryagin's most notable contributions: Pontryagin duality and his general theory of characters of a locally compact commutative group. This book, the first in a four-volume set, contains the most important papers of this eminent mathematician, those which have influenced many generations of mathematicians worldwide. They chronicle the development of his work in many areas, from his early efforts in homology groups, duality theorems, and dimension theory to his later achievements in homotopic topology and optimal control theory.
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Artificial Systems for Medicine and Education V written by Zhengbing Hu and published by Springer Nature. This book was released on 2022-01-01 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book broadly covers a scope of the latest advances for the development of artificial intelligence systems and their applications in various fields from medicine and technology to education. The proceedings comprise refereed papers presented at the Fifth International Conference of Artificial Intelligence, Medical Engineering, and Education (AIMEE2021), which took place at the Mechanical Engineering Institute of the Russian Academy of Sciences, Moscow, Russia, on 1–3 October 2021. Given the rapid development of artificial intelligence systems, the book emphasizes the need for the intensification of training of a growing number of relevant specialists, in particular, in medical engineering to increase the effectiveness of medical diagnosing and treatment. In digital artificial intelligence systems, scientists endeavour to reproduce the innate intellectual abilities of humans and other organisms, and the in-depth study of genetic systems and inherited biological processes can provide new approaches to create more and more effective artificial intelligence methods. Topics of the included papers concern thematic materials in the following spheres: mathematics and biomathematics; medical approaches; technological and educational approaches. The book is a compilation of cutting-edge research papers in the field, covering a comprehensive range of subjects that are relevant to business managers and engineering professionals alike. The breadth and depth of these proceedings make them an excellent resource for asset management practitioners, researchers, and academics, as well as undergraduate and postgraduate students who are interested in artificial intelligence, bioinformatics systems, also their expanding applications. The intended readership includes specialists, students, and other circles of readers who would like to know where artificial intelligence systems can be applied in the future with great benefit.
Download or read book Technological Concepts and Mathematical Models in the Evolution of Modern Engineering Systems written by Mario Lucertini and published by Springer Science & Business Media. This book was released on 2003-11-27 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of historical research studies covers the evolution of technology as knowledge, the emergence of an autonomous engineering science in the Industrial Age, the idea of scientific managment of production and operation systems, and the interaction between mathematical models and technological concepts. The book is published with the support of the UNESCO Venice Office - Regional Office for Science & Technology in Europe as an activity of the Project: The evolution of events, concepts and models in engineering systems.
Download or read book Selected Papers of Norman Levinson written by J.A. Nohel and published by Springer Science & Business Media. This book was released on 1997-12-18 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential & integral equations, harmonic, complex & stochas tic analysis, and analytic number theory during more than half a century. Yet, the extent of his contributions has not always been fully recognized in the mathematics community. For example, the horseshoe mapping constructed by Stephen Smale in 1960 played a central role in the development of the modern theory of dynami cal systems and chaos. The horseshoe map was directly stimulated by Levinson's research on forced periodic oscillations of the Van der Pol oscillator, and specifi cally by his seminal work initiated by Cartwright and Littlewood. In other topics, Levinson provided the foundation for a rigorous theory of singularly perturbed dif ferential equations. He also made fundamental contributions to inverse scattering theory by showing the connection between scattering data and spectral data, thus relating the famous Gel'fand-Levitan method to the inverse scattering problem for the Schrodinger equation. He was the first to analyze and make explicit use of wave functions, now widely known as the Jost functions. Near the end of his life, Levinson returned to research in analytic number theory and made profound progress on the resolution of the Riemann Hypothesis. Levinson's papers are typically tightly crafted and masterpieces of brevity and clarity. It is our hope that the publication of these selected papers will bring his mathematical ideas to the attention of the larger mathematical community.
Download or read book Asymptotic Methods for Relaxation Oscillations and Applications written by Johan Grasman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: In various fields of science, notably in physics and biology, one is con fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.
Download or read book Singularity Theory and Some Problems of Functional Analysis written by Semen Grigorʹevich Gindikin and published by American Mathematical Soc.. This book was released on 1992 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of singularity theory marks the return of mathematics to the study of the simplest analytical objects: functions, graphs, curves, surfaces. The modern singularity theory for smooth mappings, which is currently undergoing intensive developments, can be thought of as a crossroad where the most abstract topics (such as algebraic and differential geometry and topology, complex analysis, invariant theory, and Lie group theory) meet the most applied topics (such as dynamical systems, mathematical physics, geometrical optics, mathematical economics, and control theory). The papers in this volume include reviews of established areas as well as presentations of recent results in singularity theory. The authors have paid special attention to examples and discussion of results rather than burying the ideas in formalism, notation, and technical details. The aim is to introduce all mathematicians - as well as physicists, engineers, and other consumers of singularity theory - to the world of ideas and methods in this burgeoning area.
