Author: Robert B. Gardner
Publisher: SIAM
ISBN: 0898712408
Category : Mathematics
Languages : en
Pages : 131
Book Description
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 Method of Equivalence and Its Applications
Author: Robert B. Gardner
Publisher: SIAM
ISBN: 0898712408
Category : Mathematics
Languages : en
Pages : 131
Book Description
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.
Publisher: SIAM
ISBN: 0898712408
Category : Mathematics
Languages : en
Pages : 131
Book Description
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 Method of Equivalence and Its Applications
Author: Robert B. Gardner
Publisher: SIAM
ISBN: 9781611970135
Category : Mathematics
Languages : en
Pages : 134
Book Description
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.
Publisher: SIAM
ISBN: 9781611970135
Category : Mathematics
Languages : en
Pages : 134
Book Description
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.
Some Applications of Cartan's Method of Equivalence to the Geometric Study of Ordinary and Partial Differential Equations
Author: Mark Eric Fels
Publisher:
ISBN:
Category :
Languages : en
Pages : 208
Book Description
"We also characterize invariantly under point transformations some equivalence classes of parabolic quasi-linear second order partial differential equations, and examine their point symmetry groups. We are able to make our characterizations by proving a reduction theorem for principal fibre bundles." --
Publisher:
ISBN:
Category :
Languages : en
Pages : 208
Book Description
"We also characterize invariantly under point transformations some equivalence classes of parabolic quasi-linear second order partial differential equations, and examine their point symmetry groups. We are able to make our characterizations by proving a reduction theorem for principal fibre bundles." --
The Cahn–Hilliard Equation: Recent Advances and Applications
Author: Alain Miranville
Publisher: SIAM
ISBN: 1611975921
Category : Mathematics
Languages : en
Pages : 216
Book Description
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.
Publisher: SIAM
ISBN: 1611975921
Category : Mathematics
Languages : en
Pages : 216
Book Description
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.
Physical Properties Mathematics and its Application (English Version)
Author: Chen Shuxuan
Publisher: Dorrance Publishing
ISBN: 1646103637
Category : Education
Languages : en
Pages : 444
Book Description
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.
Publisher: Dorrance Publishing
ISBN: 1646103637
Category : Education
Languages : en
Pages : 444
Book Description
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.
Problems of Life and Mind: The method of science and its application to metaphysics. The rules of philosophising. Psychological principles. The limitations of knowledge
Author: George Henry Lewes
Publisher:
ISBN:
Category : Knowledge, Theory of
Languages : en
Pages : 456
Book Description
Publisher:
ISBN:
Category : Knowledge, Theory of
Languages : en
Pages : 456
Book Description
The method of science and its application to metaphysics. The rules of philosophising. Psychological principles. The limitations of knowledge
Author: George Henry Lewes
Publisher:
ISBN:
Category : Knowledge, Theory of
Languages : en
Pages : 512
Book Description
Publisher:
ISBN:
Category : Knowledge, Theory of
Languages : en
Pages : 512
Book Description
Cartan's Equivalence Method and an Application to Second Order Evolution Equations
Author: Roberto T. Murrillo
Publisher:
ISBN:
Category :
Languages : en
Pages : 182
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 182
Book Description
Adapting Tests in Linguistic and Cultural Situations
Author: Dragoş Iliescu
Publisher: Cambridge University Press
ISBN: 1107110122
Category : Education
Languages : en
Pages : 711
Book Description
This book provides a practical but scientifically grounded step-by-step approach to the adaptation of tests in linguistic and cultural contexts.
Publisher: Cambridge University Press
ISBN: 1107110122
Category : Education
Languages : en
Pages : 711
Book Description
This book provides a practical but scientifically grounded step-by-step approach to the adaptation of tests in linguistic and cultural contexts.
Ten Lectures on Wavelets
Author: Ingrid Daubechies
Publisher: SIAM
ISBN: 0898712742
Category : Science
Languages : en
Pages : 369
Book Description
Mathematics of Computing -- Miscellaneous.
Publisher: SIAM
ISBN: 0898712742
Category : Science
Languages : en
Pages : 369
Book Description
Mathematics of Computing -- Miscellaneous.