Bücher veröffentlicht von Springer Netherlands

On the occasion of the sixtieth birthday of Andre Lichnerowicz a number of his friends, many of whom have been his students or coworkers, decided to celebrate this event by preparing a jubilee volume of contributed articles in the two main fields of research marked by Lichnerowicz's work, namely differential geometry and mathematical physics. Limitations of space and time did not enable us to include papers from all Lichnerowicz's friends nor from all his former students. It was equally impossible to reflect in a single book the great variety of subjects tackled by Lichnerowicz. In spite of these limitations, we hope that this book reflects some of the present trends of fields in which he worked, and some of the subjects to which he contributed in his long - and not yet finished - career. This career was very much marked by the influence of his masters, Elie Cartan who introduced him to research in mathematics, mainly in geometry and its relations with mathematical physics, and Georges Darmois who developed his interest for mechanics and physics, especially the theory of relativity and electromagnetism. This par- ticular combination, and his personal talent, made of him a natural scientific heir and continuator of the French mathematical physics school in the tradition of Henri Poincare. Some of his works would even be best qualified by a new field name, that of physical ma- thematics: branches of pure mathematics entirely motivated by physics.

In the last five years or so there has been an important renaissance in the area of (mathematical) modeling, identification and (stochastic) control. It was the purpose of the Advanced Study Institute of which the present volume constitutes the proceedings to review recent developments in this area with par- ticular emphasis on identification and filtering and to do so in such a manner that the material is accessible to a wide variety of both embryo scientists and the various breeds of established researchers to whom identification, filtering, etc. are important (such as control engineers, time series analysts, econometricians, probabilists, mathematical geologists, and various kinds of pure and applied mathematicians; all of these were represented at the ASI). For these proceedings we have taken particular care to see to it that the material presented will be understandable for a quite diverse audience. To that end we have added a fifth tutorial section (besides the four presented at the meeting) and have also included an extensive introduction which explains in detail the main problem areas and themes of these proceedings and which outlines how the various contributions fit together to form a coherent, integrated whole. The prerequisites needed to understand the material in this volume are modest and most graduate students in e. g. mathematical systems theory, applied mathematics, econo- metrics or control engineering will qualify.

I am pleased to participate in this Summer School and look forward to sharing some ideas with you over the next few days. At the outset I would like to describe the approach I will take in 1 presenting the material. I aim to present the material in a non- rigorous way and hopefully in an intuitive manner. At the same time I will draw attention to some of the major technical problems. It is pitched at someone who is unfamiliar with the area. The results presented here are unfamiliar to actuaries and insurance mathematicians although they are well known in some other fields. During the next few minutes I will make some preliminary comments. The purpose of these comments is to place the lectures in perspective and motivate the upcoming material. After this I will outline briefly the topics to be covered during the rest of this lecture and in the lectures that will follow. One of the central themes of these lectures is RISK-SHARING. Risk-sharing is a common response to uncertainty. Such uncertainty can arise from natural phenomena or social causes. One particular form of risk-sharing is the insurance mechanism. I will be dealing with models which have a natural application in the insurance area but they have been applied in other areas as well. In fact some of the paradigms to be discussed have the capacity to provide a unified treatment of problems in diverse fields.

The role of energy in the modern world goes beyond mere technology and economics to influence welfare, environment, life quality and, broadly, civilisation. Since the industrial revolution, energy conversion technology has been at the forefront of innovation required to satisfy the needs of mankind. This technology more than others has always been very dependent on the performance of the materials used; especially over the last two decades during which efficiency and environmental concerns have become challenging objectives. In this context the European Commission has developed significant collaborative programmes in Europe within the COST framework, to enhance the state of the art in this technology. The Li~ge Conferences pursue the mission to report on the achievements of these programmes in the light of progress made elsewhere. The first four conferences in this series were held in 1978, 1982, 1986 and 1990, and provided the opportunity to present and review the work of the EuropeanMaterials Collaborative Programmes COST-50 (gas turbines), COST-505 (steam turbines) and COST- 501 (energy conversion from fossil fuels). The proceedings of these conferences were published by Applied Science Publishers (1978) and by D. ReideIlKluwer Publishing Company (1982, 1986 and 1990). While the first two Conferences have dealt essentially with high temperature alloys for gas turbines (COST 50), the third and fourth Conferences held in 1986 and 1990 were concerned with a broader range of topics, including the work of the third round of COST-50 (1972-1983), that of COST-50l, which was initiated in 1981 and COST 505 (1983-1990).