In the last decade it has become increasingly evident that strong correla tions between electrons are an essential and unifying factor in such diverse phenomena within solid state physics as high-temperature superconductivity, colossal magnetoresistance, the quantum Hall effect, heavy-fermion metals and Coulomb blockade in single-electron transistors. A new paradigmofnon FermiLiquidbehaviourisalsoemergingand, inanumberofsystems, replacing the Fermi liquid, which has been the cornerstone ofthe physics of metals and superconductors for the pastdecades. In spite of major achievements, the...

Many satellites have recently been launched or are in preparation, which operate in the microwave to IR ranges, the main objective being to observe the earth's atmosphere or interstellar clouds. Analysis of the data they supply requires extensive laboratory work because we still only have sufficiently accurate data (line positions, intensities, and profiles) for only a few species. Furthermore, the observer community is making increasing calls for laboratory data, as new development open up new observational possibilities (such as submillimeter observation). Research on these subjects...

Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions.
The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters.
The articles collected here can be grouped under...

A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY...

For many years, the physics of strongly correlated systems was considered a theorists' playground, right at the border with pure mathematics, where physicists from the real world' did not venture. The time has come, however, when healthy physics cannot exist without these techniques and results.
Lectures on selected topics in the theory of strongly correlated systems are here presented by the leading experts in the field. Topics covered include a use of the form factor approach in low-dimensional systems, applications of quantum field theory to disorder, and dynamical mean field theory....

In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect...

Terahertz technology has moved on from being a useful but expensive circuit technique, applied largely in astronomy and space science, to become a subject in its own right, with important applications - terahertz imaging in particular. Indeed, the driving force in terahertz technology is currently imaging and spectroscopy. We now have the means to obtain images and chemical information in this frequency band. The images reproduced in this volume are striking and, not surprisingly, the clinical and analytical uses are the subject of intense activity. There is still, however, no complete range...

Over the last three decades representation theory of groups, Lie algebras and associative algebras has undergone a rapid development through the powerful tool of almost split sequences and the Auslander-Reiten quiver. Further insight into the homology of finite groups has illuminated their representation theory. The study of Hopf algebras and non-commutative geometry is another new branch of representation theory which pushes the classical theory further. All this can only be seen in connection with an understanding of the structure of special classes of rings. The aim of this book is to...

The Advanced Study Institute brought together researchers in the main areas of special functions and applications to present recent developments in the theory, review the accomplishments of past decades, and chart directions for future research. Some of the topics covered are orthogonal polynomials and special functions in one and several variables, asymptotic, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painleve classification."

The main scope of this Cargese NATO Advanced Study Institute (June 5-17 2000) was to bring together a number of international experts, covering a large spectrum of the various Physical Aspects of Fracture. As a matter of fact, lecturers as well as participants were coming from various scientific communities: mechanics, physics, materials science, with the common objective of progressing towards a multi-scale description of fracture. This volume includes papers on most materials of practical interest: from concrete to ceramics through metallic alloys, glasses, polymers and composite materials....