Bücher der Reihe NATO Science Series C

Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated direction exist. The clue is to ask the right question. Classical geometry is a typical example in which the factorization of a motion into reflections or, more generally, of a collineation into central collineations, supplies valuable information on the geometric and algebraic structure. This mode of investigation has gained momentum since the end of last century. The tradition of geometric-algebraic interplay brought forward two branches of research which are documented in Parts I and II of these Proceedings. Part II deals with the theory of reflection geometry which culminated in Bachmann's work where the geometric information is encoded in properties of the group of motions expressed by relations in the generating involutions. This approach is the backbone of the classification of motion groups for the classical unitary and orthogonal planes. The axioms in this char- acterization are natural and plausible. They provoke the study of consequences of subsets of axioms which also yield natural geometries whose exploration is rewarding. Bachmann's central axiom is the three reflection theorem, showing that the number of reflections needed to express a motion is of great importance.

Pulsating and eccentric binary stars play a fundamentally important role in deciphering the mass distribution within stars. The present volume reviews the fundamental concepts of both radial and nonradial oscillations in the stars, including the Sun. Helio- and astroseismological results are reviewed, from the basics to the most recent developments. A new theory is presented, which seems to explain the mechanism of the light and radial velocity variations of recently discovered Ap stars. This textbook covers almost all kinds of variable stars of widely different characteristics. It will serve as a reference text for a very long time to come, not only for specialists but also for undergraduate students of physics and astronomy.

A few years ago, a real break-through happened in observational astronomy: the un­ derstanding of the effect of atmospheric turbulence on the structure of stellar images, and of ways to overcome this dramatic degradation. This opened a route to diffraction-limited observations with large telescopes in the optical domain. Soon, the first applications of this new technique led to some outstanding astrophysical results, both at visible and infrared wavelengths. Yet, the potential of interferometric observations is not fully foreseeable as the first long-baseline arrays of large optical telescopes are being built or cOIIllnissioned right now. In this respect a comparison with the evolution of radio-astronomy is tempting. From a situation where, in spite of the construction of giant antennas, low angular resolution was prevailing, the introduction of long baseline and very long baseline interferometry and the rapid mastering of sophisticated image reconstruction techniques, have brought on a nearly routine basis high dynamic range images with milliarcseconds resolution. This, of course, has completely changed our views of the radio sky.

The 1980 Maratea NATO Advanced Study Institute (= ASI) followed the lines of the 1976 Liege NATO ASI. Indeed, the interest of boundary problems for linear evolution partial differential equations and systems is more and more acute because of the outstanding position of those problems in the mathematical description of the physical world, namely through sciences such as fluid dynamics, elastodynamics, electro­ dynamics, electromagnetism, plasma physics and so on. In those problems the question of the propagation of singularities of the solution has boomed these last years. Placed in its definitive mathematical frame in 1970 by L. Hormander, this branch -of the theory recorded a tremendous impetus in the last decade and is now eagerly studied by the most prominent research workers in the field of partial differential equations. It describes the wave phenomena connected with the solution of boundary problems with very general boundaries, by replacing the (generailly impossible) computation of a precise solution by a convenient asymptotic approximation. For instance, it allows the description of progressive waves in a medium with obstacles of various shapes, meeting classical phenomena as reflexion, refraction, transmission, and even more complicated ones, called supersonic waves, head waves, creeping waves, ¿¿¿¿¿¿ The !'tudy of singularities uses involved new mathematical concepts (such as distributions, wave front sets, asymptotic developments, pseudo-differential operators, Fourier integral operators, microfunctions, ¿¿¿ ) but emerges as the most sensible application to physical problems. A complete exposition of the present state of this theory seemed to be still lacking.

The Supramolecular Compounds refer to organised multi-molecular assemblies and associated phenomena. The stability and the properties of these compounds strongly involve structural three-dimensional (3D) information. The crystal itself can be considered as a giant supermolecule. Thus, a thorough understanding of crystal structures and crystal growth provides a unique information on the intermolecular interactions. Indeed, each crystal reflects in a particular way the recognition properties of molecules. More so, modern crystallography allows to study in detail two­ or three-component crystalline solids in which the recognition processes can be seen from the structural standpoint. Crystallography of smaller and smaller single crystals, faster and faster experiments, time-resolved x-ray crystallography, are extremely potent source of physico-chemical information. The present Advanced Study Institute (A.S.I.) - which was planned five years ago as the 22nd Course of the International School of Crystallography (director: T. L. BLUNDELL), 1-11 June 1995, E. Majorana Centre, Erice, Italy - is probably the first international meeting specifically devoted to the Crystallography of Supramolecular Compounds. The presence of crystallographers, chemists and physicists enhanced the coherence of the typical sequence: Conception and Design - Synthesis - Structure and Visualisation - Properties. The interactive and interdisciplinary character of this research is central to the development of general structural models for a large spectrum of compounds: ionophores, cryptates, fullerenes, calixarenes, cyclodextrins, cyclotriveratrylenes, pillar type compounds, zeolites, hydrates, solvates and others.

by K. Lambeck, R. Sabadini and E. B08Chi Viscosity is one of the important material properties of the Earth, controlling tectonic and dynamic processes such as mantle convection, isostasy, and glacial rebound. Yet it remains a poorly resolved parameter and basic questions such as whether the planet's response to loading is linear or non-linear, or what are its depth and lateral variations remain uncertain. Part of the answer to such questions lies in laboratory observations of the rheology of terrestrial materials. But the extrapolation of such measurements from the laboratory environment to the geological environment is a hazardous and vexing undertaking, for neither the time scales nor the strain rates characterizing the geological processes can be reproduced in the laboratory. General rules for this extrapolation are that if deformation is observed in the laboratory at a particular temperature, deformation in geological environments will occur at a much reduced temperature, and that if at laboratory strain rates a particular deformation mechanism dominates over all others, the relative importance of possible mechanisms may be quite different at the geologically encountered strain rates. Hence experimental results are little more than guidelines as to how the Earth may respond to forces on long time scales.

This volume contains refereed papers and extended abstracts of papers presented at the NATO Advanced Research Workshop entitled 'Numerical Integration: Recent Developments, Software and Applications', held at Dalhousie University, Halifax, Canada, August 11-15, 1986. The Workshop was attended by thirty-six scientists from eleven NATO countries. Thirteen invited lectures and twenty-two contributed lectures were presented, of which twenty-five appear in full in this volume, together with extended abstracts of the remaining ten. It is more than ten years since the last workshop of this nature was held, in Los Alamos in 1975. Many developments have occurred in quadrature in the intervening years, and it seemed an opportune time to bring together again researchers in this area. The development of QUADPACK by Piessens, de Doncker, Uberhuber and Kahaner has changed the focus of research in the area of one dimensional quadrature from the construction of new rules to an emphasis on reliable robust software. There has been a dramatic growth in interest in the testing and evaluation of software, stimulated by the work of Lyness and Kaganove, Einarsson, and Piessens. The earlier research of Patterson into Kronrod extensions of Gauss rules, followed by the work of Monegato, and Piessens and Branders, has greatly increased interest in Gauss-based formulas for one-dimensional integration.

This was the fourth postgraduate summer school on remote sensing to be held in Dundee. These summer schools were originated by, and continue to remain in, the programme of EARSel (European Association of Remote Sensing Laboratories) Working Group 3 on Education and Training in Remote Sensing. The first of these summer schools was held in 1980 on "e;Remote Sensing in Meteorology, Oceanography and Hydrology"e;. This was followed in 1982 by a more specialised summer school on "e;Remote Sensing Applications in Marine Science and Technology"e; which built on the foundation laid in 1980 and then concentrated on the marine applications of remote sensing techniques. The present summer school was another follow-up of the original 1980 summer school but this time concentrating on the atmospheric rather than the marine applications of remote sensing techniques. The 1984 summer school had not specifically involved atmospheric and marine applications but had been involved with the use of remote sensing in the field of civil engineering. This year's summer school was extremely successful. First of all, this was due to our sponsors, for without their very significant material contributions there would have been no summer school. These sponsors included the Scientific Affairs Division of NATO, together with the European Association of Remote Sensing Laboratories, the Council of Europe, the European Space Agency, the German Aerospace Establishment (DFVLR) and the Natural Environment Research Council.

For the first time in human history, developments in many branches of science provide us with an opportunity of formula- ting a comprehensive picture of the universe from its beginning to the present time. It is an awesome reflection that the carbon in our bodies is the very carbon which was generated during the birth of a star. There is a perceptible continuum through the billions of years which can be revealed by the study of chemistry. Studies in nucleosynthesis have related the origin of the elements to the life history of the stars. The chemical elements we find on earth, HYdrogen, Carbon, Oxygen, and Nitrogen, were created in astronomical processes that took place in the past, and these elements are not spread throughout space in the form of stars and galaxies. Radioastronomers have discovered a vast array of organic molecules in the interstellar medium which have a bearing on prebiological chemical processes. Many of the molecules found so far contain the four elements, C, N, 0, H. Except for the chem- ically unreactive He, these four elements are the most abundant in the galaxy. The origin of polyatomic interstellar molecules is an unresolved problem. While we can explain the formation of some diatomic molecules as due to two atom collisions, it is much more difficult to form polyatomic molecules by collisions between diatomic molecules and atoms. There may be other produc- tion mechanisms at work such as reactions taking place on the surface of interstellar dust grains.

Proceedings of the NATO Advanced Study Institute, Trieste, Italy, July 10-August 1, 1980