The Method Of Normal Forms
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The Method Of Normal Forms
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Author : Ali H. Nayfeh
language : en
Publisher: John Wiley & Sons
Release Date : 2011-08-29
The Method Of Normal Forms written by Ali H. Nayfeh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-29 with Science categories.
In this introductory treatment Ali Nayfeh presents different concepts from dynamical systems theory and nonlinear dynamics in a rigorous yet plan way. He systematically introduces models and techniques and states the relevant ranges of validity and applicability. The reader is provided with a clear operational framework for consciously use rather than focused on the underlying mathematical apparatus. The exposition is largely by means of examples, dealt with up to their final outcome. For most of the examples, the results obtained with the method of normal forms are equivalent to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging. The previous edition had a remarkable success by researchers from all over the world working in the area of nonlinear dynamics and their applications in engineering. Additions to this new edition concern major topics of current interest. In particular, the author added three new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems. In particular the latter has become of major importance in several applications, both in mechanics and in different areas. Accessible to engineers and applied scientist involved with nonlinear dynamics and their applications in a wide variety of fields. It is assumed that readers have a knowledge of basic calculus as well as the elementary properties of ordinary-differential equations.
Database Design And Relational Theory
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Author : C.J. Date
language : en
Publisher: "O'Reilly Media, Inc."
Release Date : 2012-04-17
Database Design And Relational Theory written by C.J. Date and has been published by "O'Reilly Media, Inc." this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-17 with Computers categories.
What makes this book different from others on database design? Many resources on design practice do little to explain the underlying theory, and books on design theory are aimed primarily at theoreticians. In this book, renowned expert Chris Date bridges the gap by introducing design theory in ways practitioners can understand—drawing on lessons learned over four decades of experience to demonstrate why proper database design is so critical in the first place. Every chapter includes a set of exercises that show how to apply the theoretical ideas in practice, provide additional information, or ask you to prove some simple theoretical result. If you’re a database professional familiar with the relational model, and have more than a passing interest in database design, this book is for you. Questions this book answers include: Why is Heath’s Theorem so important? What is The Principle of Orthogonal Design? What makes some JDs reducible and others irreducible? Why does dependency preservation matter? Should data redundancy always be avoided? Can it be? Databases often stay in production for decades, and careful design is critical for avoiding subtle errors and processing problems over time. If they’re badly designed, the negative impacts can be incredibly widespread. This gentle introduction shows you how to use important theoretical results to create good database designs.
Normal Forms Melnikov Functions And Bifurcations Of Limit Cycles
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Author : Maoan Han
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23
Normal Forms Melnikov Functions And Bifurcations Of Limit Cycles written by Maoan Han and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-23 with Mathematics categories.
Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior.
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems
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Author : Mariana Haragus
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-23
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems written by Mariana Haragus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-23 with Mathematics categories.
An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.
Normal Forms And Unfoldings For Local Dynamical Systems
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Author : James Murdock
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-10
Normal Forms And Unfoldings For Local Dynamical Systems written by James Murdock and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-10 with Mathematics categories.
The subject of local dynamical systems is concerned with the following two questions: 1. Given an n×n matrix A, describe the behavior, in a neighborhood of the origin, of the solutions of all systems of di?erential equations having a rest point at the origin with linear part Ax, that is, all systems of the form x ? = Ax+··· , n where x? R and the dots denote terms of quadratic and higher order. 2. Describethebehavior(neartheorigin)ofallsystemsclosetoasystem of the type just described. To answer these questions, the following steps are employed: 1. A normal form is obtained for the general system with linear part Ax. The normal form is intended to be the simplest form into which any system of the intended type can be transformed by changing the coordinates in a prescribed manner. 2. An unfolding of the normal form is obtained. This is intended to be the simplest form into which all systems close to the original s- tem can be transformed. It will contain parameters, called unfolding parameters, that are not present in the normal form found in step 1. vi Preface 3. The normal form, or its unfolding, is truncated at some degree k, and the behavior of the truncated system is studied.
Smooth Invariant Manifolds And Normal Forms
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Author : I. U. Bronshte?n
language : en
Publisher: World Scientific
Release Date : 1994
Smooth Invariant Manifolds And Normal Forms written by I. U. Bronshte?n and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book deals with the qualitative theory of dynamical systems and is devoted to the study of flows and cascades in the vicinity of a smooth invariant manifold. Its main purpose is to present, as completely as possible, the basic results concerning the existence of stable and unstable local manifolds and the recent advancements in the theory of finitely smooth normal forms of vector fields and diffeomorphisms in the vicinity of a rest point and a periodic trajectory. A summary of the results obtained so far in the investigation of dynamical systems near an arbitrary invariant submanifold is also given.
Methods Of Logic
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Author : Willard Van Orman Quine
language : en
Publisher: Harvard University Press
Release Date : 1982
Methods Of Logic written by Willard Van Orman Quine and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Philosophy categories.
This widely used textbook of modern formal logic now offers a number of new features. Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, W. V. Quine's new edition will serve admirably for both classroom and independent use.
Normal Forms And Stability Of Hamiltonian Systems
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Author : Hildeberto E. Cabral
language : en
Publisher: Springer Nature
Release Date : 2023-08-11
Normal Forms And Stability Of Hamiltonian Systems written by Hildeberto E. Cabral and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-11 with Mathematics categories.
This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics. This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of strongly stable systems. With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.
Poisson Structures And Their Normal Forms
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Author : Jean-Paul Dufour
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17
Poisson Structures And Their Normal Forms written by Jean-Paul Dufour and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-17 with Mathematics categories.
The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.
Discrete Mathematics
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Author : Dr. Vinay Kumar
language : en
Publisher: BPB Publications
Release Date : 2018-06-06
Discrete Mathematics written by Dr. Vinay Kumar and has been published by BPB Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-06 with Mathematics categories.
Description:This book is intended to be a textbook for the student pursuing B.E.B.Tech in Computer Science or MCAM Tech and NIELIT - B & C Level or equivalent courses. Topics included are self contained. Sequence is maintained in such a way that no prerequisite is necessary. This book contains topics ranging from set, relation, recurrence relation, generating function, posets, lattice, methods of proofs, Quine McKluskey Method, Floyd Warshall's algorithm, finite automata, bipartite graph etc. Only necessary theorems have been included, and wherever required, theirs applicability has been demonstrated using appropriate examples. Whenever required, a diagram is used to make the concept easily understood to the reader. It contains good number of solved examples and exercises for hands on practice.Table of Contents:Chapter 1 : Seti Chapter 2 : Relationi Chapter 3 : Number Theoryi Chapter 4 : Functioni Chapter 5 : Predicate Calculusi Chapter 6 : Poseti Chapter 7 : Latticei Chapter 8 : Finite Boolean Algebrai Chapter 9 : Recursive Equationsi Chapter 10 : Generating Functioni Chapter 11 : Method Of Proofsi Chapter 12 : Permutationsi Chapter 13 : Combinationsi Chapter 14 : Groupi Chapter 15 : Cyclic Groupi Chapter 16 : Permutationi Chapter 17 : Matrixi Chapter 18 : Graphi Chapter 19 : Path and Circuiti Chapter 20 : Graph Algorithmsi Chapter 21 : Formal Languagei Chapter 22 : Finite Automatai Chapter 23 : Galois Field