Stellar pulsations provide a complex system in stars. This complexity is studied by analyzing the non-sinusoidal, semi-regular, or irregular light curves. This unique volume summarizes the application of recent theoretical results obtained from stellar pulsation studies. In addition, the latest developments in hydrodynamic simulations are discussed. A historical sketch of the study of beat Cepheids, first known for their variable amplitudes, is given as an introduction to the book. This introduction clearly demonstrates how complicated the study of variable stars can be, and therefore challenges and invites the reader to study the entire book.

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.

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.

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.

This book surveys our understanding of stars which change in brightness because they pulsate. Pulsating variable stars are keys to distance scales inside and beyond the Milky Way galaxy. They test our understanding not only of stellar pulsation theory but also of stellar structure and evolution theory. Moreover, pulsating stars are important probes of the formation and evolution of our own and neighboring galaxies. Our understanding of pulsating stars has greatly increased in recent years as large-scale surveys of pulsating stars in the Milky Way and other Local Group galaxies have provided a wealth of new observations and as space-based instruments have studied particular pulsating stars in unprecedented detail.

Supernovae, hypernovae and gamma-ray bursts are among the most energetic explosions in the universe. The light from these outbursts is, for a brief time, comparable to billions of stars and can outshine the host galaxy within which the explosions reside. Most of the heavy elements in the universe are formed within these energetic explosions. Surprisingly enough, the collapse of massive stars is the primary source of not just one, but all three of these explosions. As all of these explosions arise from stellar collapse, to understand one requires an understanding of the others. Stellar Collapse marks the first book to combine discussions of all three phenomena, focusing on the similarities and differences between them. Designed for graduate students and scientists newly entering this field, this book provides a review not only of these explosions, but the detailed physical models used to explain them from the numerical techniques used to model neutrino transport and gamma-ray transport to the detailed nuclear physics behind the evolution of the collapse to the observations that have led to these three classes of explosions.

The Pacific Rim Conferences for the first decade from the mid 1980's to the mid 1990's were primary concerned with binary stars research. The Conference expanded to all areas of Stellar Astrophysics for the last two meetings in Hong Kong; at Hong Kong University of Science and Technology in 1997 and at the Hong Kong University in 1999. At the conclusion of the very successful Pacific Rim Conference on Stellar Astrophysics held in Hong Kong University, members of the Sci entific Organizing Committee began planning for the next conference. We approached Professor Tan Lu of Nanjing University and Professor Tipei Li of the Institute of High Energy Physics about hosting a con ference in China. The city of Xi'an in Shaanxi province and a city in Yunnan province, were considered to be the most likely locations. It be came crucial to find the right person to serve as Chair (or Co-chairs) for the Local Organizing Committee. Initially, Professor Lu was the logical choice but he declined for personal reasons. Professor Li was invited to lead a new department of Astrophysics at Tsinghua University so he could not take on the additional load of chairing the LOC. Professor Gang Zhao of Beijing Astronomical Observatory was approached to take on the task but he also declined. This has been a busy time for Chinese astronomers. The SOC decided to have the conference dedicated to honor Dr. Helmut A.