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Symmetry. --- Aesthetics --- Proportion

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This monograph is a synthesis of the theory of the pairwise coupling of the angular momenta of arbitrarily many independent systems to the total angular momentum in which the universal role of doubly stochastic matrices and their quantum-mechanical probabilistic interpretation is a major theme. A uniform viewpoint is presented based on the structure of binary trees. This includes a systematic method for the evaluation of all 3n-j coefficients and their relationship to cubic graphs. A number of topical subjects that emerge naturally are also developed, such as the algebra of permutation matrice

Symmetry (Physics) --- Combinatorial analysis.

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Symmetrie Von Molek Len: Eine Einf Hrung in Die Anwendung Von Symmetriebetrachtungen in Der Chemie

Molecular theory. --- Symmetry (Physics) --- Group theory.

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Symmetry (Physics) --- Special relativity (Physics) --- Space and time. --- Relativity (Physics)

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Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference.

Difference equations. --- Symmetry (Mathematics) --- Integrals. --- Calculus, Integral --- Invariance (Mathematics) --- Group theory --- Automorphisms --- Calculus of differences --- Differences, Calculus of --- Equations, Difference