Invariance Theory
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Invariance Theory
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Author : Peter B. Gilkey
language : en
Publisher: CRC Press
Release Date : 1994-12-22
Invariance Theory written by Peter B. Gilkey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-22 with Mathematics categories.
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.
Multiplicative Invariant Theory
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Author : Martin Lorenz
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-08
Multiplicative Invariant Theory written by Martin Lorenz 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 2005-12-08 with Mathematics categories.
Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far.. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori. Throughout the text, numerous explicit examples of multiplicative invariant algebras and fields are presented, including the complete list of all multiplicative invariant algebras for lattices of rank 2. The book is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and, mostly, invariant theory.
Modular Invariant Theory
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Author : H.E.A. Eddy Campbell
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-12
Modular Invariant Theory written by H.E.A. Eddy Campbell 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 2011-01-12 with Mathematics categories.
This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.
Computational Invariant Theory
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Author : Harm Derksen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Computational Invariant Theory written by Harm Derksen 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 2013-04-17 with Mathematics categories.
Invariant theory is a subject with a long tradition and an astounding abil ity to rejuvenate itself whenever it reappears on the mathematical stage. Throughout the history of invariant theory, two features of it have always been at the center of attention: computation and applications. This book is about the computational aspects of invariant theory. We present algorithms for calculating the invariant ring of a group that is linearly reductive or fi nite, including the modular case. These algorithms form the central pillars around which the book is built. To prepare the ground for the algorithms, we present Grabner basis methods and some general theory of invariants. Moreover, the algorithms and their behavior depend heavily on structural properties of the invariant ring to be computed. Large parts of the book are devoted to studying such properties. Finally, most of the applications of in variant theory depend on the ability to calculate invariant rings. The last chapter of this book provides a sample of applications inside and outside of mathematics.
Invariance Theory Of Automatic Control Systems
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Author : Isukapalli Gopala Sarma
language : en
Publisher:
Release Date : 1964
Invariance Theory Of Automatic Control Systems written by Isukapalli Gopala Sarma and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Automatic control categories.
Classical Invariant Theory
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Author : Peter J. Olver
language : en
Publisher: Cambridge University Press
Release Date : 1999-01-13
Classical Invariant Theory written by Peter J. Olver and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-13 with Mathematics categories.
The book is a self-contained introduction to the results and methods in classical invariant theory.
Conformal Invariance And Applications To Statistical Mechanics
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Author : C Itzykson
language : en
Publisher: World Scientific
Release Date : 1998-09-29
Conformal Invariance And Applications To Statistical Mechanics written by C Itzykson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-29 with categories.
This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions.
Economic Theory And Sustainable Development
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Author : Vincent Martinet
language : en
Publisher: Routledge
Release Date : 2012
Economic Theory And Sustainable Development written by Vincent Martinet and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Business & Economics categories.
This work examines the different ways in which the concepts of sustainability and sustainable development are interpreted in economics. As well as the oft-studied neoclassical take on matters, the author develops new approaches that are less reliant on utilitarianism and discounting.
Algebraic Combinatorics And Computer Science
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Author : H. Crapo
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-01-01
Algebraic Combinatorics And Computer Science written by H. Crapo 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 2001-01-01 with Mathematics categories.
This book, dedicated to the memory of Gian-Carlo Rota, is the result of a collaborative effort by his friends, students and admirers. Rota was one of the great thinkers of our times, innovator in both mathematics and phenomenology. I feel moved, yet touched by a sense of sadness, in presenting this volume of work, despite the fear that I may be unworthy of the task that befalls me. Rota, both the scientist and the man, was marked by a generosity that knew no bounds. His ideas opened wide the horizons of fields of research, permitting an astonishing number of students from all over the globe to become enthusiastically involved. The contagious energy with which he demonstrated his tremendous mental capacity always proved fresh and inspiring. Beyond his renown as gifted scientist, what was particularly striking in Gian-Carlo Rota was his ability to appreciate the diverse intellectual capacities of those before him and to adapt his communications accordingly. This human sense, complemented by his acute appreciation of the importance of the individual, acted as a catalyst in bringing forth the very best in each one of his students. Whosoever was fortunate enough to enjoy Gian-Carlo Rota's longstanding friendship was most enriched by the experience, both mathematically and philosophically, and had occasion to appreciate son cote de bon vivant. The book opens with a heartfelt piece by Henry Crapo in which he meticulously pieces together what Gian-Carlo Rota's untimely demise has bequeathed to science.
Mathematical Principles Of Human Conceptual Behavior
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Author : Ronaldo Vigo
language : en
Publisher: Psychology Press
Release Date : 2014-10-03
Mathematical Principles Of Human Conceptual Behavior written by Ronaldo Vigo and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-03 with Psychology categories.
The ability to learn concepts lies at the very core of human cognition, enabling us to efficiently classify, organize, identify, and store complex information. In view of the basic role that concepts play in our everyday physical and mental lives, the fields of cognitive science and psychology face three long standing challenges: discovering the laws that govern concept learning and categorization behavior in organisms, showing how they inform other areas of cognitive research, and describing them with the mathematical systematicity and precision found in the physical sciences. In light of these theoretical and methodological shortcomings, this volume will introduce a set of general mathematical principles for predicting and explaining conceptual behavior. The author’s theory is based on seven fundamental constructs of universal science: invariance, complexity, information, similarity, dissimilarity, pattern, and representation. These constructs are joined by a novel mathematical framework that does not depend on probability theory, and derives key results from conceptual behavior research with other key areas of cognitive research such as pattern perception, similarity assessment, and contextual choice. The result is a unique and systematic unifying foundation for cognitive science in the tradition of classical physics.