Bücher der Reihe The IBM Research Symposia Series

The applications of liquid crystals have developed dramatically in the past ten years. The first commercial application (1940's) of liquid crystals was the preparation of a light polarizer. The third major application of liquid crystals dealt with commercial displays. Liquid crystals using color displays will become commercially practical.

The papers collected in this volume were presented at the International Symposium on Methods and Materials in Microelectronic Technology. The progress of semiconductor and microelectronic technology has become so rapid and the field so sophisticated that it is imperative to exchange the latest insight gained as frequently as it can be accomplished.

During the past few years, there has been dramatic progress in theoretical and computational studies of large molecules and local ized states in solids.

70, 4044 (1979)] succeeded in finding the predicted near infrared absorption of the cis triplet acetylene (no corresponding absorp tion for the trans form was found, which is in agreement with theory), and the resolved structure of the spectrum confirmed the predicted geometries conclusively.

The role played by surface phenomena in the overall behavior of a material has been a subject for speculation for a long time, but only during the last decade or so have experimental and theor etical tools been developed which make it possible to investigate surface structure and related surface phenomena uniquely.

This book contains papers on sparse matrices and their appli cations which were presented at a Symposium held at the IBM Thomas J. This is a very active field of research since efficient techniques for handling sparse matrix calculations are an important aspect of problem solving.

Furthermore, time was allowed after the conference to permit the papers to be written with the conference in retrospect, and five "prepared discussion" papers written by attendees of the conference but not on the original program are included.

During the past 20 years, solid state physics has become one of the major branches of physics. -5 The combination of solid state physics and comp~tation may be termed computational solid state physics. They can be found in the traditional physics journals and review series, such as The Physical Review and Solid State Physics;

(1) Determining lower bounds on the number of operations or steps required for computational solutions of specific problems such as matrix and polynomial calculations, sorting and other combinatorial problems, iterative com putations, solving equations, and computer resource allocation.

During the years since the first conference in this series was held at Thousand Oaks, California, in 1970, ion implantation has been an expanding and exciting research area.

The papers in these proceedings were presented at an Inter national Symposium on Stiff Differential Systems, which was held at the Hotel Quellenhof, Wildbad, Federal Republic of Germany, October 4-6, 1973.

The applications of liquid crystals have developed dramatically in the past ten years. The first commercial application (1940's) of liquid crystals was the preparation of a light polarizer. The third major application of liquid crystals dealt with commercial displays. Liquid crystals using color displays will become commercially practical.