X system Ib-TEX. I wish to thank her for the beautiful work and the numerous discussions on the contents of this book. I am indebted to Peter Fassler, Neu-Technikum Buchs, Switzerland, for drafting the figures, to my students Kurt Rothermann and Stefan Strahl for computer enhancing and labeling the graphics, to Pascal Felder and Markus Wittwer for a simulation program that generated the figures in the stochastics sections. My thanks go to my new colleague at work, Daniel Neuenschwander, for the inspiring discussions related to the section in stochastics and for reading the manuscript to it. I am also grateful to Dacfey Dzung for reading the whole manuscript. Thanks go especially to Professor \Valter Gander of ETH, Zurich, who at the finishing stage and as an expert of 'JEXgenerously invested numerous hours to assist us in solving software as well as hardware problems; thanks go also to Martin Muller, Ingenieurschule Biel, who made the final layout of this book on the NeXT computer. Thanks are also due to Helmut Kopka of the Max Planck Institute, for solving software problems, and to Professor Burchard Kaup of the Uni versity of Fribourg, Switzerland for adding some useful software; also to Birkhauser Boston Inc. for the pleasant co-operation. Finally, let me be reminiscent of Professor E. Stiefel (deceased 1978) with whom I had many interesting discussions and true co-operation when writing the book in German.

It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems. This analysis was especially fruitful in application to the basic equations of mechanics and physics because the invariance principles are already involved in their derivation. It is in no way a coincidence that the equations of hydrodynamics served as the first object for applying the new ideas and methods of group analysis which were developed by 1. V. Ovsyannikov and his school. The authors rank themselves as disciples of the school. The present monograph deals mainly with group-theoretic classification of the equations of hydrodynamics in the presence of planar and rotational symmetry and also with construction of exact solutions and their physical interpretation. It is worth noting that the concept of exact solution to a differential equation is not defined rigorously; different authors understand it in different ways. The concept of exact solution expands along with the progress of mathematics (solu tions in elementary functions, in quadratures, and in special functions; solutions in the form of convergent series with effectively computable terms; solutions whose searching reduces to integrating ordinary differential equations; etc. ). We consider it justifiable to enrich the set of exact solutions with rank one and rank two in variant and partially invariant solutions to the equations of hydrodynamics.

Group Theoretical Methods in Physics: Proceedings of the Fifth International Colloquium provides information pertinent to the fundamental aspects of group theoretical methods in physics. This book provides a variety of topics, including nuclear collective motion, complex Riemannian geometry, quantum mechanics, and relativistic symmetry. Organized into six parts encompassing 64 chapters, this book begins with an overview of the theories of nuclear quadrupole dynamics. This text then examines the conventional approach in the determination of superstructures. Other chapters consider the Hamiltonian formalism and how it is applied to the KdV equation and to a slight variant of the KdV equation. This book discusses as well the significant differential equations of mathematical physics that are integrable Hamiltonian systems, including the equations governing self-induced transparency and the motion of particles under an inverse square potential. The final chapter deals with the decomposition of the tensor product of two irreducible representations of the symmetric group into a direct sum of irreducible representations. This book is a valuable resource for physicists.

In this volume the author gives an introduction to the theory of group representations and their applications in image science. The main feature of the presentation is a systematic treatment of the invariance principle in image processing and pattern recognition with the help of group theoretical methods. The invariance properties of a problem often largely define the solution to the problem. Invariance principles are well known in theoretical physics but their use in image processing is only a few years old. The reader will find that group theory provides a unifying framework for many problems in image science. The volume is based on graduate-level lectures given by the author, and the book is intended for students and researchers interested in theoretical aspects of computer vision.

An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet.

Chemists are used to the operational definition of symmetry, which crystallographers introduced long before the advent of quantum mechanics. The ball-and-stick models of molecules naturally exhibit the symmetrical properties of macroscopic objects. However, the practitioner of quantum chemistry and molecular modeling is not concerned with balls and sticks, but with subatomic particles: nuclei and electrons. This textbook introduces the subtle metaphors which relate our macroscopic understanding of symmetry to the molecular world. It gradually explains how bodily rotations and reflections, which leave all inter-particle distances unaltered, affect the study of molecular phenomena that depend only on these internal distances. It helps readers to acquire the skills to make use of the mathematical tools of group theory for whatever chemical problems they are confronted with in the course of their own research.

This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.