This interdisciplinary meeting has brought together a group of astrophysicists with hands-on experience in the numerical computation of astrophysical fluid dynamics, in particular nonlinear stellar pulsations, and a group of applied mathematicians who are actively engaged with the development of novel and improved numerical methods. The goal of the workshop has been for the astrophysicists to discuss in detail the numerical problems encountered in the modelling of stellar pulsations and for the mathematicians to present a survey of recent developments in numerical techniques. This astrophysical-mathematical intercourse will help the astrophysicists in the future development of more reliable and efficient codes, on the one hand, and it has introduced the mathematicians to an unfamiliar area which is a tough testing ground for their techniques. Since the difficulties encountered are common to other fluid dynamics problems, and are in fact perhaps more severe, fluid dynamicists in other research areas may fmd the results of this workshop of interest as well. Much of our theoretical understanding of the intricate and interesting behavior of variable stars rests on our ability to perform accurate numerical hydrodynamical computations of stellar models. Extensive calculations of nonlinear radial stellar pulsations with the use of increasingly powerful computers are showing more and more clearly that the numerical codes in current use have serious deficiencies.

The nonlinear theory of oscillating systems brings new aspects into the study of variable stars. Beyond the comparison of linear periods and the estimate of stability, the appearance and disappearance of possible modes can be studied in detail. While nonlinearity in stellar pulsations is not a very complicated concept, it generally requires extensive and sometimes so phisticated numerical studies. Therefore, the development of appropriate computational tools is required for applications of nonlinear theory to real phenomena in variable stars. Taking trends in variable star studies into consideration, the International Astronomical Union organized a colloquium for the nonlinear phenomena of variable stars at Mito, Japan in 1992. The colloquium served to give an overview of the new frontiers of variable star studies and to encourage further development of this field. The colloquium covered the fundamental theory, interesting observational facts, and the numerical modeling. The publication of the proceedings was somewhat delayed since one of the editors, M. T., was overwhelmed by administrative work. We are sorry that the excellent reviews of Drs. H. :Mori, M. Sano, and K. Makishima cannot be found in the proceedings. We also miss the summary given by Dr. W. W. Dziembowski. Throughout the editing procedure Dr. Y. Tanaka of Ibaraki University kindly helped us. Because of the unfortunate delay of the publication~ the significance of several papers may be affected. Even so, we believe that the papers are useful to variable star researchers because of their scientific importance.

How can the interior of the Sun, white dwarfs and other stars be studied by stellar seismology? What can Doppler imaging tell us about high-degree pulsations? What impact are CCD and infrared observations having on extending the Cepheid and RR Lyrae distance scale? And how are other classes of pulsators providing independent checks of the distance scale? These and many other critical questions are answered in this timely review of the dramatic advances made in pulsating star research in the last decade. This survey collects together more than thirty comprehensive reviews and over one hundred summaries of research papers from the 139th IAU Colloquium, held in Victoria, British Columbia. Together these cover all aspects of recent developments in the field of variable star research and preview some of the exciting advances anticipated for the next decade. This volume provides an essential review for graduate students and researchers.

This fascinating book reviews the progress made in Mercury studies since the flybys by Mariner 10 in 1974-75. Thus far, it is the only book on Mercury which balances a wide range of Earth-based observations, made under difficult conditions, with the only available space-based data. The text is based on continued research using the Mariner 10 archive, on observations from Earth, and on increasingly realistic models of this mysterious planet’s interior evolution.

IAU Transactions are published as a volume corresponding to each General Assembly. Volume A is produced prior to the Assembly and contains Reports on Astronomy, prepared by each Commission President. The intention is to summarize the astronomical results that have affected the work of the Commission since the production of the previous Reports up to a time which is about one year prior to the General Assembly. Volume B is produced after the Assembly and contains accounts of Commission Meetings which were held, together with other material. The reports included in the present volume range from outline summaries to lengthy compilations and references. Most reports are in English.

Contributors examine the physics of wind origin and physical phenomena in winds, including heliospheric shocks, magnetohydrodynamic turbulence, and kinetic phenomena--and their interactions with surrounding media. Contributions range from studies of the interstellar cloud surrounding the solar system to solar wind interaction with comets.

Mathematics is a universal language. Differential equations, mathematical modeling, numerical methods and computation form the underlying infrastructure of engineering and the sciences. In this context mathematical modeling is a very powerful tool for studying engineering problems, natural systems and human society. This interdisciplinary book cont

This book provides a survey of the basic ideas of the cellular automaton (CA) modelling environment, emphasising the relevance of this framework to astrophysical applications. It contains introductory level lectures on lattice gases, and on CA turbulence, diffusion-reaction processes, percolation and self-organised criticality. Further, it gives a variety of astrophysical applications, including stellar oscillations, galactic evolution, distribution of luminous matter in the universe, etc.

Editing the proceedings of a scientific meeting is not an easy task. Sometimes people who give an excellent talk do not send the manuscript by the deadline. However, this time, thanks to the punctuality of all the participants, we have this excellent volume for the workshop on mass losing pulsating stars and their circumstellar matter prepared in time. Almost all of the oral presentations including the summary are collected in this volume. We regret that we cannot put in this volume a few posters that we failed to receive before the editorial work. The workshop was planned as a small meeting with less than fifty attendants because the city of Sendai was far from the most of the active institutions. However, the number of submitted papers exceeded the SOC's expectation; many interesting contributions had to be scheduled in the poster session. Still, the oral sessions were so tight that many participants might have felt frustrated for the shortage of discussions. The organizers of the workshop have to apologize to the attendants for the inconvenience caused from such a happy underestimate about the size of the workshop.

'Fractal geometry addressesitselfto questions that many people have been asking themselves. It con cerns an aspect of Nature that almost everybody had been conscious of, but could not address in a formal fashion. ' 'Fractal geometry seems to be the proper language to describe the complezity of many very compli cated shapes around us. ' (Mandelbrot, 1990a) 'I believe that fractals respond to a profound un easiness in man. ' (Mandelbrot, 1990b) The catchword fractal, ever since it was coined by Mandelbrot (1975) to refer to a class of abstract mathematical objects that were already known at the turn ofthe 19th century, has found an unprecedented resonance both inside and outside the scientific community. Fractal concepts, far more than the concepts of catastrophe theory introduced a few years earlier, are currently being applied not only in the physical sciences, but also in biology and medicine (Goldberger and West 1987). In the mid-eighties, Kadanoff (1986) asked the question: 'Why all the fuss about /ractals'! '. He offered a twofold answer: in the first place, it is 'because of the practical, technological importance of fractal objects'. Indeed he emphasised the relevance of these structures for materials scientists and oil drilling engineers, in search of structures with novel properties, or models for the flow of oil through the soil. His second answer was: 'Because of the intellectual interest of fractals '.