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Author: C. Bardos Publisher: Springer Science & Business Media ISBN: 9400990049 Category : Science Languages : en Pages : 591
Book Description
One of the main ideas in organizing the Summer Institute of Cargese on "Bifurcation Phenomena in Mathematical Physics and Related Topics" was to bring together Physicists and Mathematicians working on the properties arising from the non linearity of the phenomena and of the models that are used for their description. Among these properties the existence of bifurcations is one of the most interesting, and we had a general survey of the mathematical tools used in this field. This survey was done by M. Crandall and P. Rabinowitz and the notes enclosed in these proceedings were written by E. Buzano a]ld C. Canuto. Another mathematical approach, using Morse Theory was given by J. Smoller reporting on a joint work with C. Conley. An example of a direct application was given by M. Ghil. For physicists the theory of bifurcation is closely related to critical phenomena and this was explained in a series of talks given by J.P. Eckmann, G. Baker and M. Fisher. Some related ideas can be found in the talk given by T. T. Wu , on a joint work with Barry Mc Coy on quantum field theory. The description of these phenomena leads to the use of Pade approximants (it is explained for instance in the lectures of J. Nuttall) and then to some problems in drop hot moment problems. (cf. the lecture of D. Bessis).
Author: C. Bardos Publisher: Springer Science & Business Media ISBN: 9400990049 Category : Science Languages : en Pages : 591
Book Description
One of the main ideas in organizing the Summer Institute of Cargese on "Bifurcation Phenomena in Mathematical Physics and Related Topics" was to bring together Physicists and Mathematicians working on the properties arising from the non linearity of the phenomena and of the models that are used for their description. Among these properties the existence of bifurcations is one of the most interesting, and we had a general survey of the mathematical tools used in this field. This survey was done by M. Crandall and P. Rabinowitz and the notes enclosed in these proceedings were written by E. Buzano a]ld C. Canuto. Another mathematical approach, using Morse Theory was given by J. Smoller reporting on a joint work with C. Conley. An example of a direct application was given by M. Ghil. For physicists the theory of bifurcation is closely related to critical phenomena and this was explained in a series of talks given by J.P. Eckmann, G. Baker and M. Fisher. Some related ideas can be found in the talk given by T. T. Wu , on a joint work with Barry Mc Coy on quantum field theory. The description of these phenomena leads to the use of Pade approximants (it is explained for instance in the lectures of J. Nuttall) and then to some problems in drop hot moment problems. (cf. the lecture of D. Bessis).
Author: Marvin Isadore Knopp Publisher: American Mathematical Soc. ISBN: 0821851551 Category : Mathematics Languages : en Pages : 624
Book Description
Emil Grosswald was a mathematician of great accomplishment and remarkable breadth of vision. This volume pays tribute to the span of his mathematical interests, which is reflected in the wide range of papers collected here. With contributions by leading contemporary researchers in number theory, modular functions, combinatorics, and related analysis, this book will interest graduate students and specialists in these fields. The high quality of the articles and their close connection to current research trends make this volume a must for any mathematics library.
Author: Kotik K. Lee Publisher: World Scientific ISBN: 9789971509651 Category : Science Languages : en Pages : 476
Book Description
The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.
Author: Jaime Angulo Pava Publisher: American Mathematical Soc. ISBN: 0821848976 Category : Mathematics Languages : en Pages : 272
Book Description
This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied include Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.
Author: Yuri Kuznetsov Publisher: Springer Science & Business Media ISBN: 1475739788 Category : Mathematics Languages : en Pages : 648
Book Description
Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
Author: Enayet U Tarafdar Publisher: World Scientific ISBN: 9814476218 Category : Mathematics Languages : en Pages : 627
Book Description
This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems.Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings.
Author: Mark H. Holmes Publisher: Springer Science & Business Media ISBN: 1461454778 Category : Mathematics Languages : en Pages : 447
Book Description
This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.
Author: C. Bardos
Author: C. Bardos
Author: Claude Bardos
Author: Marvin Isadore Knopp
Author: Ludwig Arnold
Author: Kotik K. Lee
Author: Jaime Angulo Pava
Author: Yuri Kuznetsov
Author: Enayet U Tarafdar
Author: Itzhak Bars
Author: Mark H. Holmes