Renato Spigler - Böcker

'Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point all".' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non* The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Hea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

This text presents the state-of-the-art in applied and industrial mathematics, updating the earlier Kluwer publication "Applied and Industrial Mathematics, Venice-1, 1989". The current work includes a selection of main invited papers as well as conference contributions from a number of leading scientists working in the areas of applied mathematics, industrial mathematics applied analysis, numerical mathematics, mathematical physics and applied probability.

Lax and Nirenberg are two of the most distinguished mathematicians of our times. Their work on partial differential equations (PDEs) over the last half-century has dramatically advanced the subject and has profoundly influenced the course of mathematics. A huge part of the development in PDEs during this period has either been through their work, motivated by it or achieved by their postdocs and students. A large number of mathematicians honored these two exceptional scientists in a week-long conference in Venice (June 1996) on the occasion of their 70th birthdays. This volume contains the proceedings of the conference, which focused on the modern theory of nonlinear PDEs and their applications. Among the topics treated are turbulence, kinetic models of a rarefied gas, vortex filaments, dispersive waves, singular limits and blow-up of solutions, conservation laws, Hamiltonian systems, and others.The conference served as a forum for the dissemination of new scientific ideas and discoveries and enhanced scientific communication by bringing together such a large number of scientists working in related fields. The event allowed the international mathematics community to honor two of its outstanding members.

In this volume, I have collected several papers which were presented at the international conference called "Venice-2/Symposium on Applied and In­ dustrial Mathematics". Such a conference was held in Venice, Italy, between June 11 and 16,1998, and was intended as the follow-up of the very successful similar event (called "Venice-1/Symposium on Applied and Industrial Math­ ematics"), that was also organized in Venice in October 1989. The Venice-1 conference ended up with a Kluwer volume like this one. I am grateful to Kluwer for having accepted to publish the present volume, the aim of which is to update somehow the state-of-the-art in the field of Ap­ plied Mathematics as well as in that of the nowadays rather more developed area of Industrial Mathematics. The most of the invited (key-note) speakers contributed to this volume with a paper related to their talk. There are, in addition·, a few significant contributed papers, selected on the basis of their quality and relevance to the present-time research activities. The topics considered in the conference range from rather general sub­ jects in applied and numerical analysis, to more specialized subjects such as polymers and disordered media, granular flow, semiconductor mathematics, superconductors, elasticity, tomography and other inverse problems, financial modeling, photographic sciences, etc. The papers collected in this volume provide a selection of them. It is clear from the previous list that some attention has been paid to relatively new and emerging fields.

'Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point all".' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non* The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Hea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Industrial mathematics is evolving into an important branch of mathematics. Mathematicians, in Italy in particular, are becoming increasingly aware of this new trend and are engaged in bridging the gap between highly specialized mathematical research and the emerging demand for innovation from industry. In this respect, the contributions in this volume provide both R&D workers in industry with a general view of existing skills, and academics with state-of-the-art applications of mathematics to real-world problems, which may also be incorporated in advanced courses.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences