The method of equivalence and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics
1989
|
| Schriftenreihe: | CBMS-NSF regional conference series in applied mathematics
58 |
| Schlagworte: | |
| Online-Zugang: | TUM01 UBW01 UBY01 UER01 Volltext |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references Equivalence problems -- Lifting of equivalence problems to G-spaces -- The structure equations -- Reduction of the structure group by normalization -- The inductive step -- e-structures -- Global results and involutive structure -- Serendipity -- Normal forms and generalized geometries -- Prolongation 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 |
| Beschreibung: | 1 Online-Ressource (vii, 127 Seiten) |
| ISBN: | 0898712408 9780898712407 |
| DOI: | 10.1137/1.9781611970135 |
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| 500 | |a Equivalence problems -- Lifting of equivalence problems to G-spaces -- The structure equations -- Reduction of the structure group by normalization -- The inductive step -- e-structures -- Global results and involutive structure -- Serendipity -- Normal forms and generalized geometries -- Prolongation | ||
| 500 | |a 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 | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Gardner, Robert B. 1939-1998 |
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| id | DE-604.BV039747287 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:10:18Z |
| institution | BVB |
| isbn | 0898712408 9780898712407 |
| language | English |
| lccn | 89021972 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024594818 |
| oclc_num | 873886422 |
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| physical | 1 Online-Ressource (vii, 127 Seiten) |
| psigel | ZDB-72-SIA |
| publishDate | 1989 |
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| publisher | Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | CBMS-NSF regional conference series in applied mathematics |
| series2 | CBMS-NSF regional conference series in applied mathematics |
| spelling | Gardner, Robert B. 1939-1998 Verfasser (DE-588)1089272758 aut The method of equivalence and its applications Robert B. Gardner Equivalence and its applications Philadelphia, Pa. Society for Industrial and Applied Mathematics 1989 1 Online-Ressource (vii, 127 Seiten) txt rdacontent c rdamedia cr rdacarrier CBMS-NSF regional conference series in applied mathematics 58 Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references Equivalence problems -- Lifting of equivalence problems to G-spaces -- The structure equations -- Reduction of the structure group by normalization -- The inductive step -- e-structures -- Global results and involutive structure -- Serendipity -- Normal forms and generalized geometries -- Prolongation 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 Geometry, Differential Invariants Transformations (Mathematics) Transformation Mathematik (DE-588)4060637-5 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Invariante (DE-588)4128781-2 gnd rswk-swf Invariante (DE-588)4128781-2 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Transformation Mathematik (DE-588)4060637-5 s Erscheint auch als Druck-Ausgabe, Paperback 0898712408 Erscheint auch als Druck-Ausgabe, Paperback 9780898712407 CBMS-NSF regional conference series in applied mathematics 58 (DE-604)BV046682627 58 https://doi.org/10.1137/1.9781611970135 Verlag Volltext |
| spellingShingle | Gardner, Robert B. 1939-1998 The method of equivalence and its applications CBMS-NSF regional conference series in applied mathematics Geometry, Differential Invariants Transformations (Mathematics) Transformation Mathematik (DE-588)4060637-5 gnd Differentialgeometrie (DE-588)4012248-7 gnd Invariante (DE-588)4128781-2 gnd |
| subject_GND | (DE-588)4060637-5 (DE-588)4012248-7 (DE-588)4128781-2 |
| title | The method of equivalence and its applications |
| title_alt | Equivalence and its applications |
| title_auth | The method of equivalence and its applications |
| title_exact_search | The method of equivalence and its applications |
| title_full | The method of equivalence and its applications Robert B. Gardner |
| title_fullStr | The method of equivalence and its applications Robert B. Gardner |
| title_full_unstemmed | The method of equivalence and its applications Robert B. Gardner |
| title_short | The method of equivalence and its applications |
| title_sort | the method of equivalence and its applications |
| topic | Geometry, Differential Invariants Transformations (Mathematics) Transformation Mathematik (DE-588)4060637-5 gnd Differentialgeometrie (DE-588)4012248-7 gnd Invariante (DE-588)4128781-2 gnd |
| topic_facet | Geometry, Differential Invariants Transformations (Mathematics) Transformation Mathematik Differentialgeometrie Invariante |
| url | https://doi.org/10.1137/1.9781611970135 |
| volume_link | (DE-604)BV046682627 |
| work_keys_str_mv | AT gardnerrobertb themethodofequivalenceanditsapplications AT gardnerrobertb equivalenceanditsapplications |