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The ideas of Elie Cartan are combined with the tools of Felix Klein and Sophus Lie to present in this book the only detailed treatment of the method of equivalence. An algorithmic description of this method, is presented for the first time.
Book Synopsis The Method of Equivalence and Its Applications by : Robert B. Gardner
Download or read book The Method of Equivalence and Its Applications written by Robert B. Gardner and published by SIAM. This book was released on 1989-01-01 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ideas of Elie Cartan are combined with the tools of Felix Klein and Sophus Lie to present in this book the only detailed treatment of the method of equivalence. An algorithmic description of this method, is presented for the first time.
The ideas of Elie Cartan are combined with the tools of Felix Klein and Sophus Lie to present in this book the only detailed treatment of the method of equivalence. An algorithmic description of this method, which finds invariants of geometric objects under infinite dimensional pseudo-groups, is presented for the first time. As part of the algorithm, Gardner introduces several major new techniques. In particular, the use of Cartan's idea of principal components that appears in his theory of Repere Mobile, and the use of Lie algebras instead of Lie groups, effectively a linear procedure, provide a tremendous simplification. One must, however, know how to convert from one to the other, and the author provides the Rosetta stone to accomplish this. In complex problems, it is essential to be able to identify natural blocks in group actions and not just individual elements, and prior to this publication, there was no reference to block matrix techniques. The Method of Equivalence and Its Applications details ten diverse applications including Lagrangian field theory, control theory, ordinary differential equations, and Riemannian and conformal geometry. This volume contains a series of lectures, the purpose of which was to describe the equivalence algorithm and to show, in particular, how it is applied to several pedagogical examples and to a problem in control theory called state estimation of plants under feedback. The lectures, and hence the book, focus on problems in real geometry.
Book Synopsis The Method of Equivalence and Its Applications by : Robert B. Gardner
Download or read book The Method of Equivalence and Its Applications written by Robert B. Gardner and published by SIAM. This book was released on 1989-01-01 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ideas of Elie Cartan are combined with the tools of Felix Klein and Sophus Lie to present in this book the only detailed treatment of the method of equivalence. An algorithmic description of this method, which finds invariants of geometric objects under infinite dimensional pseudo-groups, is presented for the first time. As part of the algorithm, Gardner introduces several major new techniques. In particular, the use of Cartan's idea of principal components that appears in his theory of Repere Mobile, and the use of Lie algebras instead of Lie groups, effectively a linear procedure, provide a tremendous simplification. One must, however, know how to convert from one to the other, and the author provides the Rosetta stone to accomplish this. In complex problems, it is essential to be able to identify natural blocks in group actions and not just individual elements, and prior to this publication, there was no reference to block matrix techniques. The Method of Equivalence and Its Applications details ten diverse applications including Lagrangian field theory, control theory, ordinary differential equations, and Riemannian and conformal geometry. This volume contains a series of lectures, the purpose of which was to describe the equivalence algorithm and to show, in particular, how it is applied to several pedagogical examples and to a problem in control theory called state estimation of plants under feedback. The lectures, and hence the book, focus on problems in real geometry.
Physical Properties Mathematics and its Application(English Version) By: Chen Shuxuan Chen Shuxuan（陈叔瑄) was born on March 30, 1936 in Fuzhou, Fujian Province. He graduated from the Department of Physics at Xiamen University. He has been engaged in teaching and scientific research for many years in colleges and universities. He has taught courses such as electrician principle, electronic circuit, pulse circuit, digital logic, computer composition principle, computer application, assembly language programming, and so on. Based on many years of teaching experience, he compiled the IBM Microcomputer System and Assembly Language Programming guide which was published by Xiamen University Press in March 1990. In addition to teaching, he has made great efforts to develop the application of scientific theory and technology, participated in the development of many electronic circuits and computer applications projects, and published many research papers and works. Among them, "MM-1000 Friction Testing Machine Microcomputer System" software and hardware development, passed provincial technical appraisal in December 1987.The system plays an important role in the research of wet friction and wear testing technology and it has won the third prize of the Ministry of Electricity. Before retirement, he was an associate professor in the Department of Computer Science, Xiamen University.
Book Synopsis Physical Properties Mathematics and its Application (English Version) by : Chen Shuxuan
Download or read book Physical Properties Mathematics and its Application (English Version) written by Chen Shuxuan and published by Dorrance Publishing. This book was released on 2020-04-17 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physical Properties Mathematics and its Application(English Version) By: Chen Shuxuan Chen Shuxuan（陈叔瑄) was born on March 30, 1936 in Fuzhou, Fujian Province. He graduated from the Department of Physics at Xiamen University. He has been engaged in teaching and scientific research for many years in colleges and universities. He has taught courses such as electrician principle, electronic circuit, pulse circuit, digital logic, computer composition principle, computer application, assembly language programming, and so on. Based on many years of teaching experience, he compiled the IBM Microcomputer System and Assembly Language Programming guide which was published by Xiamen University Press in March 1990. In addition to teaching, he has made great efforts to develop the application of scientific theory and technology, participated in the development of many electronic circuits and computer applications projects, and published many research papers and works. Among them, "MM-1000 Friction Testing Machine Microcomputer System" software and hardware development, passed provincial technical appraisal in December 1987.The system plays an important role in the research of wet friction and wear testing technology and it has won the third prize of the Ministry of Electricity. Before retirement, he was an associate professor in the Department of Computer Science, Xiamen University.
Book Synopsis Problems of Life and Mind: The method of science and its application to metaphysics. The rules of philosophising. Psychological principles. The limitations of knowledge by : George Henry Lewes
Download or read book Problems of Life and Mind: The method of science and its application to metaphysics. The rules of philosophising. Psychological principles. The limitations of knowledge written by George Henry Lewes and published by . This book was released on 1874 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Chaotic behavior arises in a variety of control settings. In some cases, it is beneficial to remove this behavior; in others, introducing or taking advantage of the existing chaotic components can be useful for example in cryptography. Chaos in Automatic Control surveys the latest methods for inserting, taking advantage of, or removing chaos in a variety of applications. This book supplies the theoretical and pedagogical basis of chaos in control systems along with new concepts and recent developments in the field. Presented in three parts, the book examines open-loop analysis, closed-loop control, and applications of chaos in control systems. The first section builds a background in the mathematics of ordinary differential and difference equations on which the remainder of the book is based. It includes an introductory chapter by Christian Mira, a pioneer in chaos research. The next section explores solutions to problems arising in observation and control of closed-loop chaotic control systems. These include model-independent control methods, strategies such as H-infinity and sliding modes, polytopic observers, normal forms using homogeneous transformations, and observability normal forms. The final section explores applications in wireless transmission, optics, power electronics, and cryptography. Chaos in Automatic Control distills the latest thinking in chaos while relating it to the most recent developments and applications in control. It serves as a platform for developing more robust, autonomous, intelligent, and adaptive systems.
Book Synopsis Chaos in Automatic Control by : Wilfrid Perruquetti
Download or read book Chaos in Automatic Control written by Wilfrid Perruquetti and published by CRC Press. This book was released on 2018-10-03 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaotic behavior arises in a variety of control settings. In some cases, it is beneficial to remove this behavior; in others, introducing or taking advantage of the existing chaotic components can be useful for example in cryptography. Chaos in Automatic Control surveys the latest methods for inserting, taking advantage of, or removing chaos in a variety of applications. This book supplies the theoretical and pedagogical basis of chaos in control systems along with new concepts and recent developments in the field. Presented in three parts, the book examines open-loop analysis, closed-loop control, and applications of chaos in control systems. The first section builds a background in the mathematics of ordinary differential and difference equations on which the remainder of the book is based. It includes an introductory chapter by Christian Mira, a pioneer in chaos research. The next section explores solutions to problems arising in observation and control of closed-loop chaotic control systems. These include model-independent control methods, strategies such as H-infinity and sliding modes, polytopic observers, normal forms using homogeneous transformations, and observability normal forms. The final section explores applications in wireless transmission, optics, power electronics, and cryptography. Chaos in Automatic Control distills the latest thinking in chaos while relating it to the most recent developments and applications in control. It serves as a platform for developing more robust, autonomous, intelligent, and adaptive systems.
Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships. A mapping principle is presented to connect many of the methods. The eigenvalue problems studied are linear, and linearization is shown to give important information about nonlinear problems. Linear vector spaces and their properties are used to uniformly describe the eigenvalue problems presented that involve matrices, ordinary or partial differential operators, and integro-differential operators.
Book Synopsis Variational Methods for Eigenvalue Approximation by : H. F. Weinberger
Download or read book Variational Methods for Eigenvalue Approximation written by H. F. Weinberger and published by SIAM. This book was released on 1974-01-01 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships. A mapping principle is presented to connect many of the methods. The eigenvalue problems studied are linear, and linearization is shown to give important information about nonlinear problems. Linear vector spaces and their properties are used to uniformly describe the eigenvalue problems presented that involve matrices, ordinary or partial differential operators, and integro-differential operators.
Book Synopsis Multilevel Projection Methods for Partial Differential Equations by : Stephen F. McCormick
Download or read book Multilevel Projection Methods for Partial Differential Equations written by Stephen F. McCormick and published by SIAM. This book was released on 1992-01-01 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathemati
Book Synopsis Using the Mathematics Literature by : Kristine K. Fowler
Download or read book Using the Mathematics Literature written by Kristine K. Fowler and published by CRC Press. This book was released on 2004-05-25 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathemati
Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.
Book Synopsis Techniques of Differential Topology in Relativity by : Roger Penrose
Download or read book Techniques of Differential Topology in Relativity written by Roger Penrose and published by SIAM. This book was released on 1972-06-01 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.
This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.
Book Synopsis The Cahn–Hilliard Equation: Recent Advances and Applications by : Alain Miranville
Download or read book The Cahn–Hilliard Equation: Recent Advances and Applications written by Alain Miranville and published by SIAM. This book was released on 2019-09-09 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.
