Theory Of Causal Differential Equations
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Theory Of Causal Differential Equations
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Author : S. Leela
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-01
Theory Of Causal Differential Equations written by S. Leela 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 2010-01-01 with Mathematics categories.
The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework.
Theory Of Causal Differential Equations
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Author : V. Lakshmikantham
language : en
Publisher: Atlantis Studies in Mathematic
Release Date : 2009
Theory Of Causal Differential Equations written by V. Lakshmikantham and has been published by Atlantis Studies in Mathematic this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The theory of causal differential equations (CDE) includes several types of dynamic systems such as ordinary differential equations, functional differential equations, integro-differential equations (with or without memory), differential equations with anticipation and retardation. This is the first book which describes the theory of CDE as an independent discipline, incorporating the recent general theory of CDE and introducing several new ideas. This book is a timely introduction to the subject in a more generalised frame work. The present monograph collects recent works in this broad area and provides possible extensions to other dynamic systems involving causal operators such as CDE in abstract spaces, CDE with memory, CDE with fractional derivatives and causal set differential equations-giving initial apparatus, for further study in this important branch of nonlinear analysis.
Theory Of Causal Differential Equations
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Author : S. Leela
language : en
Publisher:
Release Date : 2010
Theory Of Causal Differential Equations written by S. Leela and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Differential equations categories.
The theory of causal differential equations (CDE) includes several types of dynamic systems such as ordinary differential equations, functional differential equations, integro-differential equations (with or without memory), differential equations with anticipation and retardation. This is the first book which describes the theory of CDE as an independent discipline, incorporating the recent general theory of CDE and introducing several new ideas. This book is a timely introduction to the subject in a more generalised frame work. The present monograph collects recent works in this broad area and provides possible extensions to other dynamic systems involving causal operators such as CDE in abstract spaces, CDE with memory, CDE with fractional derivatives and causal set differential equations-giving initial apparatus, for further study in this important branch of nonlinear analysis.
Theory Of Impulsive Differential Equations
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Author : Vangipuram Lakshmikantham
language : en
Publisher: World Scientific
Release Date : 1989-05-01
Theory Of Impulsive Differential Equations written by Vangipuram Lakshmikantham and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-05-01 with Mathematics categories.
Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems.
Theories Of Causality
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Author : John Losee
language : en
Publisher: Routledge
Release Date : 2017-07-28
Theories Of Causality written by John Losee and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-28 with Philosophy categories.
What types of entities qualify as causes and effects? What is the relationship between cause and effect? How are causal claims to be assessed? The first question deals with the structure of the world; the second is about theories that interpret the relationship of causes to effects; while the third has to do with proper procedure in science and everyday life. This volume is a wide-ranging history of answers that have been given to these three questions, and their relationship to scientific understanding.Losee presents a number of theories of causality within a historical survey that emphasizes the interrelationship between these theories and developments in science. His analysis displays the strengths and weaknesses of these theories so as to contribute to our present understanding of causal relatedness.Among the positions discussed are those of Aristotle, Hume, Kant, Mill, Salmon, Lewis, and Woodward. Losee's analysis displays the strengths and weaknesses of theories that identify causal relatedness with regularity of sequence, probability increase, energy transfer, exchange of a conserved quantity, counterfactual dependence, and inferability.These theories are judged, in part,by their ability to resolvedifficulties posed by instances of overdetermination,causation by omission, preventive causation, and causation by disconnection. Since applications of the theories to these instances disagree, a strategy of employing multiple concepts of causation is examined.Theories of Causality also describes the particular difficulties for causal analysis posed by quantum mechanics. One such difficulty is the prohibition against combining a causal analysis of a quantum process with a spatio-temporal description of that process.
Time Causality And The Quantum Theory
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Author : S. Mehlberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Time Causality And The Quantum Theory written by S. Mehlberg 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 2012-12-06 with Science categories.
An intermittent but mentally quite disabling illness prevented Henry Mehlberg from becoming recognized more widely as the formidable scholar he was, when at his best. During World War II, he had lived in hiding under the false identity of an egg farmer, when the Nazis occupied his native Poland. After relatively short academic appointments at the University of Toronto and at Princeton University, he taught at the University of Chicago until reaching the age of normal retirement. But partly at the initiative of his Chicago colleague Charles Morris, who had preceded him to a 'post-retirement' profes sorship at the University of Florida in Gainesville, and with the support of Eugene Wigner, he then received an appointment at that University, where he remained until his death in 1979. In Chicago, he organized a discussion group of scholars from that area as a kind of small scale model of the Vienna Circle, which met at his apart ment, where he lived with his first wife Janina, a mathematician. It was during this Chicago period that the functional disturbances from his illness were pronounced and not infrequent. The very unfortunate result was that colleagues who had no prior knowledge of the caliber of his writings in Polish and French or of his very considerable intellectual powers, had little incentive to read his published work, which he had begun to write in English.
Functional Equations With Causal Operators
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Author : C. Corduneanu
language : en
Publisher: CRC Press
Release Date : 2002-09-05
Functional Equations With Causal Operators written by C. Corduneanu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-05 with Mathematics categories.
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with cau
Time Causality And The Quantum Theory
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Author : Henry Mehlberg
language : en
Publisher: Springer Science & Business Media
Release Date : 1980
Time Causality And The Quantum Theory written by Henry Mehlberg 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 1980 with Causality (Physics) categories.
Theory And Examples Of Ordinary Differential Equations
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Author : Chin-Yuan Lin
language : en
Publisher: World Scientific
Release Date : 2011
Theory And Examples Of Ordinary Differential Equations written by Chin-Yuan Lin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This book presents a complete theory of ordinary differential equations, with many illustrative examples and interesting exercises. A rigorous treatment is offered in this book with clear proofs for the theoretical results and with detailed solutions for the examples and problems. This book is intended for undergraduate students who major in mathematics and have acquired a prerequisite knowledge of calculus and partly the knowledge of a complex variable, and are now reading advanced calculus and linear algebra. Additionally, the comprehensive coverage of the theory with a wide array of examples and detailed solutions, would appeal to mathematics graduate students and researchers as well as graduate students in majors of other disciplines. As a handy reference, advanced knowledge is provided in this book with details developed beyond the basics; optional sections, where main results are extended, offer an understanding of further applications of ordinary differential equations.
Theory Of Semiconductor Lasers
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Author : Minoru Yamada
language : en
Publisher: Springer
Release Date : 2014-04-10
Theory Of Semiconductor Lasers written by Minoru Yamada and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-10 with Science categories.
This book provides a unified and complete theory for semiconductor lasers, covering topics ranging from the principles of classical and quantum mechanics to highly advanced levels for readers who need to analyze the complicated operating characteristics generated in the real application of semiconductor lasers. The author conducts a theoretical analysis especially on the instabilities involved in the operation of semiconductor lasers. A density matrix into the theory for semiconductor lasers is introduced and the formulation of an improved rate equation to help understand the mode competition phenomena which cause the optical external feedback noise is thoroughly described from the basic quantum mechanics. The derivation of the improved rate equation will allow readers to extend the analysis for the different types of semiconductor materials and laser structures they deal with. This book is intended not only for students and academic researchers but also for engineers who develop lasers for the market, as the advanced topics covered are dedicated to real problems in implementing semiconductor lasers for practical use.