This volume contains the fourteen papers presented at the NATO-sponsored Ad vanced Research Workshop on the 'Status and Future Developments in the Study of Transport Properties' held in Porto Carras, Halkidiki, Greece from May 29 to May 31, 1991. The Workshop was organised to provide a forum for the discussion among prac titioners of the state-of-the-art in the treatment of the macroscopic, non-equilibrium properties of gases. The macroscopic quantities considered all arise as a result of the pairwise interactions of molecules in states perturbed from an equilibrium, Maxwellian distribution....

This volume contains edited versions of 11 contributions given by main speakers at the NATO Advanced Study Institute on lReal and Complex Dynamical Systems in Hiller0d, Denmark, June 20th - July 2nd, 1993. The vision of the institute was to illustrate the interplay between two important fields of Mathematics: Real Dynamical Systems and Complex Dynamical Systems. The interaction between these two fields has been growing over the years. Problems in Real Dynamical Systems have recently been solved using complex tools in the real or by extension to the complex. In return, problems in Complex...

Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of Seiberg-Witten theory, which has revolutionised the subjects since its introduction in late 1994.
Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of...

THEOREM: Rotational symmetries of order greater than six, and also five-fold rotational symmetry, are impossible for a periodic pattern in the plane or in three-dimensional space. The discovery of quasicrystals shattered this fundamental 'law', not by showing it to be logically false but by showing that periodicity was not synonymous with long-range order, if by 'long-range order' we mean whatever order is necessary for a crystal to produce a diffraction pat- tern with sharp bright spots. It suggested that we may not know what 'long-range order' means, nor what a 'crystal' is, nor how...

Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras.
Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures...

The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of...

An up-to-date summary of our understanding of the dynamics and thermodynamics of moist atmospheric convection, with a strong focus on recent developments in the field. The book also reviews ways in which moist convection may be parameterised in large-scale numerical models - a field in which there is still some controversy - and discusses the implications of convection for large-scale flow.
Audience: The book is aimed at the graduate level and research meteorologists as well as scientists in other disciplines who need to know more about moist convection and its representation...

An overview of the most successful algorithms and techniques for solving large, sparse systems of equations and some algorithms and strategies for solving optimization problems. The most important topics dealt with concern iterative methods, especially Krylov methods, ordering techniques, and some iterative optimization tools.
The book is a compendium of theoretical and numerical methods for solving large algebraic systems, special emphasis being placed on convergence and numerical behaviour as affected by rounding errors, accuracy in computing solutions for ill-conditioned matrices,...

A NATO Advanced Research Workshop entitled New Methods for the Study of Molecular Aggregates was held at Tbe Lodge at Kananaskis Village, Alberta, Canada from 16 -20 June 1996. In fact the meeting was entirely concerned with the problem of analyzing biomolecular complexes, so the title of these proceedings has been altered to give a more precise description of the content. Tbe workshop was hosted by the time-of-flight group of the Department of Physics at the University of Manitoba, and was attended by 64 participants from around the world. ' venty-one invited talks were given and 27 papers...

The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and...