Bøger i NATO Science Series C serien

Proceedings of the NATO Advanced Study Institute, Capri, Italy, September 7-18, 1981

Proceedings of the NATO Advanced Study Institute, Glasgow, U.K., September 6-18, 1981

Proceedings of the NATO Advanced Study Institute on Chemistry of Ions in the Gas Phase, Vimeiro, Portugal, September 16-17, 1982

Proceedings of the NATO Advanced Study Institute, Bombannes, France, September 16-27, 1985

Proceedings of the NATO Advanced Study Institute, Alvor, Algarve, Portugal, March 17-27, 1987

Proceedings of the NATO Advanced Research Workshop, Lerici, Italy, June 15-19, 1987

Proceedings of the NATO Advanced Study Institute on New Developments in Polarized Spectroscopy of Ordered Systems, Rimini, Italy, October 11-23, 1987

Proceedings of the NATO Advanced Research Workshop, Bowness-on-Windermere, UK, September 7-11, 1987

Proceedings of the NATO Advanced Study Institute, Erice, Italy, May 20-30, 1986

Proceedings of the NATO Advanced Research Workshop, Leuven, Belgium, September 18-22, 1989

Proceedings of the NATO Advanced Study Institute, Versailles, France, September 2-13, 1975

Proceedings of the NATO Advanced Study Institute, Acquafredda di Maratea, Italy, June 3-15, 1979

Proceedings of the NATO Advanced Study Institute, Corinthia, Attica, and the Cycladic Islands, Greece, June 3-16, 1985

Proceedings of the NATO Advanced Study Institute, Victoria, B.C., Canada, August 17-30, 1986

Proceedings of the NATO Advanced Study Institute on Modelling the Ocean General Circulation and Geochemical Tracer Transport, Les Houches, France, February 15-26, 1988

Proceedings of the NATO Advanced Research Workshop on The Long-Range Atmospheric Transport of Natural and Contaminant Substances from Continent to Ocean and Continent to Continent, St. Georges, Bermuda, January 10-17, 1988

Proceedings of the NATO Advanced Study Institute, Dundee, U.K., August 14-September 3, 1988

Proceedings of the NATO Advanced Study Institute on Partially Integrable Nonlinear Evolution Equations and Their Physical Applications, Les Houches, France, March 21-30, 1989

Proceedings of the NATO Advanced Study Institute, Riva dei Tessali, Italy, June 17-28, 1989

Proceedings of the NATO Advanced Research Workshop, Les Arcs, France, July 5-9, 1989

Proceedings of the NATO Advanced Study Institute, Kusadasi, Turkey, September 11-22, 1989

Proceedings of the NATO Advanced Research Workshop on Geohydrological Management of Sea Level and Mitigation of Drought, Fuerteventura, Canary Islands, Spain, March 1-7, 1989

Proceedings of the NATO Advanced Study Institute and Seminaire de mathematiques superieures, Montreal, Canada, July 3-21, 1989

Proceedings of the NATO Advanced Research Workshop, Richmond, VA, U.S.A., October 8-12, 1991

This proceedings is composed of the papers resulting from the NATO work-shop "e;Perspectives in Ring Theory"e; and the work-shop "e;Geometry and Invariant The- ory of Representations of Quivers"e; . Three reports on problem sessions have been induced in the part corresponding to the work-shop where they belonged. One more report on a problem session, the "e;lost"e; problem session, will be published elsewhere eventually. vii Acknowledgement The meeting became possible by the financial support of the Scientific Affairs Division of NATO. The people at this division have been very helpful in the orga- nization of the meeting, in particular we commemorate Dr. Mario di Lullo, who died unexpectedly last year, but who has been very helpful with the organization of earlier meetings in Ring Theory. For additional financial support we thank the national foundation for scientific research (NFWO), the rector of the University of Antwerp, UIA, and the Belgian Ministry of Education. We also gladly acknowledge support from the Belgian Friends of the Hebrew University and the chairman Prof. P. Van Remoortere who honored Prof. S. Amitsur for his continuous contributions to the mathematical activities at the University of Antwerp. I thank the authors who contributed their paper(s) to this proceedings and the lecturers for their undisposable contributions towards the success of the work-shop. Finally I thank Danielle for allowing me to spoil another holiday period in favor of a congress.

The near Infra-Red emission of the Interstellar Medium is a very puzzling subject. In the brightest regions, where spectroscopic observa- tions are possible from the ground, several bands (3.3 - 3.4 - 6.2 - 7.7 - 8.6 - 11.3 ~m) have been observed since 1973. The absence of satisfying explanation was so obvious that they were called "e;Unidenti- fied IR Emission Bands"e;. The puzzle still increased when were known the first results of the general IR sky survey made by the satellite IRAS. On a large scale, the near IR emission of the Interstellar medium was expected to be very small but it was observed to be about one third of the total IR emission for our own galaxy ..* The situation has moved in 1984 when it was suggested that a class of stable organic molecules, the Polycyclic Aromatic Hydrocarbons (PAH's) could be at the origin of this near IR emission. Initially based on the required refractory character of particules that should be heated to high temperature without subliming, this hypothesis leads to a sugges- tive spectroscopic similarity with the observed astronomical bands. This hypothesis is attractive and it has many implications, for ins- tance, the PAHs would be the most abundant organic molecules in the universe. However, many points have to be clarified and the different consequences of this suggestion should be explored.

This volume corresponds to the invited lectures and advanced research papers presented at the NATD Advanced Study Institute on Nonlinear Stochastic Problems with emphasis on Identification, Signal Processing, Control and Nonlinear Filtering held in Algarve (Portugal), on May 1982. The book is a blend of theoretical issues, algorithmic implementation aspects, and application examples. In many areas of science and engineering, there are problems which are intrinsically nonlinear 3nd stochastic in nature. Clear examples arise in identification and mOdeling, signal processing, nonlinear filtering, stochastic and adaptive conLrol. The meeting was organized because it was felt that there is a need for discussion of the methods and philosophy underlying these different areas, and in order to communicate those approaches that have proven to be effective. As the computational technology progresses, more general approaches to a number of problems which have been treated previously by linearization and perturbation methods become feasible and rewarding.

Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.

This volume consists of the proceedings of the NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics, which was held at Hanstholm, Denmark. These proceedings include the main invited talks and contributed papers given during the workshop. The aim of these lectures was to present a selection of results of the latest research in the field. In addition to covering topics in approximation by solutions of partial differential equations and quadrature formulae, this volume is also concerned with related areas, such as Gaussian quadratures, the Pompelu problem, rational approximation to the Fresnel integral, boundary correspondence of univalent harmonic mappings, the application of the Hilbert transform in two dimensional aerodynamics, finely open sets in the limit set of a finitely generated Kleinian group, scattering theory, harmonic and maximal measures for rational functions and the solution of the classical Dirichlet problem. In addition, this volume includes some problems in potential theory which were presented in the Problem Session at Hanstholm.

It has been said that `String theorists talk to string theorists and everyone else wonders what they are saying'. This book will be a great help to those researchers who are challenged by modern quantum field theory. Quantum field theory experienced a renaissance in the late 1960s. Here, participants in the Les Houches sessions of 1970/75, now key players in quantum field theory and its many impacts, assess developments in their field of interest and provide guidance to young researchers challenged by these developments, but overwhelmed by their complexities. The book is not a textbook on string theory, rather it is a complement to Polchinski's book on string theory. It is a survey of current problems which have their origin in quantum field theory.