symmetry and separation of variables encyclopedia of mathematics and its applications

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Symmetry And Separation Of Variables

Author : Willard Miller
ISBN : 0521177391
Genre : Mathematics
File Size : 64. 4 MB
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Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner. Some group-theoretic twists in the ancient method of separation of variables that can be used to provide a foundation for much of special function theory are shown. In particular, it is shown explicitly that all special functions that arise via separation of variables in the equations of mathematical physics can be studied using group theory.

Special Functions

Author : R.A. Askey
ISBN : 1402003196
Genre : Mathematics
File Size : 54. 74 MB
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'This book will become useful and important, not just as a handy place to locate a reference, but for the many thought-provoking ideas generously provided by the authors.' Foundations of Physics, 16:9 (1986)

Quantum Group Symmetry And Q Tensor Algebras

Author : L. C. Biedenharn
ISBN : 9789810223311
Genre : Science
File Size : 89. 13 MB
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Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction. Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail. This book is a good reference for graduate students in physics and mathematics.

More Progresses In Analysis

Author :
ISBN : 9789814469685
Genre :
File Size : 22. 34 MB
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Mathematical Tools For Physicists

Author : Michael Grinfeld
ISBN : 9783527684274
Genre : Science
File Size : 67. 24 MB
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The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Mathieu Functions And Spheroidal Functions And Their Mathematical Foundations

Author : J. Meixner
ISBN : 9783540384113
Genre : Mathematics
File Size : 42. 23 MB
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Il Nuovo Cimento Della Societa Italiana Di Fisica A

Author :
ISBN : UCAL:B4395046
Genre :
File Size : 39. 81 MB
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Il Nuovo Cimento Della Societ Italiana Di Fisica

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ISBN : CHI:33388942
Genre : Physics
File Size : 37. 80 MB
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Nuclei Particles And Field

Author :
ISBN : UCSD:31822017903691
Genre : Physics
File Size : 81. 66 MB
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Seminar On Stochastic Analysis Random Fields And Applications

Author : Robert C. Dalang
ISBN : STANFORD:36105024331766
Genre : Mathematics
File Size : 80. 16 MB
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