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 : 26. 93 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 Group Theoretical Aspects And Applications

Author : R.A. Askey
ISBN : 1402003196
Genre : Mathematics
File Size : 42. 68 MB
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Approach your problems from It isn't that they can't see the right end and begin with the solution. the answers. Then one day, It is that they can't see the perhaps you will find the problem. final question. G.K. Chesterton. The Scandal 'The Hermit Clad in Crane of Father Brown 'The Point of Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging SUbdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Stochastic Models Information Theory And Lie Groups Volume 1

Author : Gregory S. Chirikjian
ISBN : 9780817648039
Genre : Mathematics
File Size : 45. 70 MB
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This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

More Progresses In Analysis

Author :
ISBN : 9789814469685
Genre :
File Size : 50. 55 MB
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Quantum Group Symmetry And Q Tensor Algebras

Author : L. C. Biedenharn
ISBN : 9789810223311
Genre : Science
File Size : 26. 77 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.

Mathematical Tools For Physicists

Author : Michael Grinfeld
ISBN : 9783527684274
Genre : Science
File Size : 56. 5 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.

Nouvelles Math Matiques Internationales

Author :
ISBN : UCSD:31822020224010
Genre : Mathematics
File Size : 62. 92 MB
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Angular Momentum In Quantum Physics

Author : L. C. Biedenharn
ISBN : MINN:319510004835498
Genre : Angular momentum
File Size : 68. 53 MB
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Il Nuovo Cimento Della Societa Italiana Di Fisica A

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ISBN : UCAL:B4395046
Genre :
File Size : 77. 37 MB
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Il Nuovo Cimento Della Societ Italiana Di Fisica

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ISBN : CHI:33388942
Genre : Physics
File Size : 29. 97 MB
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