S. Kobayashi – författare

This volume Macromolecular Engineering: Recent Advances has been developed based on the 1 st International Conference on "Advanced Polymers Via Macromolecular Engineering" (APME '95), June 24-29, 1995 at the Vassar College campus, Poughkeepsie, New York. In APME '95, 100 oral and over 50 poster presentations are to be delivered from scientists around the globe. The scientific program covers recent advances in macromolecu­ lar engineering. It is our vision that the knowledge of the past and the promise of the future are blended together in APME '95 to enrich and stimulate the scientists, which will bring about the progress of macromolecular engineering. Scientists from over 30 countries will be joining together to share this vision. Although over 150 papers are to be presented in APME '95 conference, we could not include all the papers in this book for a variety of reasons, most importantly the authors willingness to contribute to this volume in time to meet the deadline. However, the 24 comprehensive chapters included in this volume are a true reflection of some of the important themes of macromolecular engineering that are part of the APME '95 conference. We believe macromolecular engineering is the key to developing new polymeric materials and, to this end, it is hoped this volume will aid in this introspection.

This volume attests to the vitality of differential geometry as it probes deeper into its internal structure and explores ever widening connections with other subjects in mathematics and physics. To most of us Professor S. S. Chern is modern differential geometry, and we, his students, are grateful to him for leading us to this fertile landscape. The aims of the symposium were to review recent developments in geometry and to expose and explore new areas of research. It was our way of honoring Professor Chern upon the occasion of his official retirement as Professor of Mathematics at the University of California. This book is a record of the scientific events of the symposium and reflects Professor Chern''s wide interest and influence. The conference also reflected Professor Chern''s personality. It was a serious occasion, active yet relaxed, mixed with gentleness and good humor. We wish him good health, a long life, happiness, and a continuation of his extraordinarily deep and original contributions to mathematics. I. M. Singer Contents Real and Complex Geometry in Four Dimensions M. F. ATIYAH. . . . . . . . . . . . . Equivariant Morse Theory and the Yang-Mills Equation on Riemann Surfaces RAOUL BaTT .. 11 Isometric Families of Kahler Structures EUGENIO CALABI. . 23 Two Applications of Algebraic Geometry to Entire Holomorphic Mappings MARK GREEN AND PHILLIP GRIFFITHS. • . . . • . . 41 The Canonical Map for Certain Hilbert Modular Surfaces F. HIRZEBRUCH . . . . . • . . . . . . . . . 75 Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in EN NICOLAAS H. KUIPER .

This volume attests to the vitality of differential geometry as it probes deeper into its internal structure and explores ever widening connections with other subjects in mathematics and physics. To most of us Professor S. S. Chern is modern differential geometry, and we, his students, are grateful to him for leading us to this fertile landscape. The aims of the symposium were to review recent developments in geometry and to expose and explore new areas of research. It was our way of honoring Professor Chern upon the occasion of his official retirement as Professor of Mathematics at the University of California. This book is a record of the scientific events of the symposium and reflects Professor Chern's wide interest and influence. The conference also reflected Professor Chern's personality. It was a serious occasion, active yet relaxed, mixed with gentleness and good humor. We wish him good health, a long life, happiness, and a continuation of his extraordinarily deep and original contributions to mathematics. I. M. Singer Contents Real and Complex Geometry in Four Dimensions M. F. ATIYAH. . . . . . . . . . . . . Equivariant Morse Theory and the Yang-Mills Equation on Riemann Surfaces RAOUL BaTT .. 11 Isometric Families of Kahler Structures EUGENIO CALABI. . 23 Two Applications of Algebraic Geometry to Entire Holomorphic Mappings MARK GREEN AND PHILLIP GRIFFITHS. • . . . • . . 41 The Canonical Map for Certain Hilbert Modular Surfaces F. HIRZEBRUCH . . . . . • . . . . . . . . . 75 Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in EN NICOLAAS H. KUIPER .

This volume Macromolecular Engineering: Recent Advances has been developed based on the 1 st International Conference on "Advanced Polymers Via Macromolecular Engineering" (APME ''95), June 24-29, 1995 at the Vassar College campus, Poughkeepsie, New York. In APME ''95, 100 oral and over 50 poster presentations are to be delivered from scientists around the globe. The scientific program covers recent advances in macromolecu­ lar engineering. It is our vision that the knowledge of the past and the promise of the future are blended together in APME ''95 to enrich and stimulate the scientists, which will bring about the progress of macromolecular engineering. Scientists from over 30 countries will be joining together to share this vision. Although over 150 papers are to be presented in APME ''95 conference, we could not include all the papers in this book for a variety of reasons, most importantly the authors willingness to contribute to this volume in time to meet the deadline. However, the 24 comprehensive chapters included in this volume are a true reflection of some of the important themes of macromolecular engineering that are part of the APME ''95 conference. We believe macromolecular engineering is the key to developing new polymeric materials and, to this end, it is hoped this volume will aid in this introspection.

The Boundary Element Methods (BEM) has become one of the most efficient tools for solving various kinds of problems in engineering science. The International Association for Boundary Element Methods (IABEM) was established in order to promote and facilitate the exchange of scientific ideas related to the theory and applications of boundary element methods. The aim of this symposium is to provide a forum for researchers in boundary element methods and boundary-integral formulations in general to present contemporary concepts and techniques leading to the advancement of capabilities and understanding of this com­ putational methodology. The topics covered in this symposium include mathematical and computational aspects, applications to solid mechanics, fluid mechanics, acoustics, electromagnetics, heat transfer, optimization, control, inverse problems and other interdisciplinary problems. Papers deal­ ing with the coupling of the boundary element method with other computational methods are also included. The editors hope that this volume presents some innovative techniques and useful knowl­ edge for the development of the boundary element methods. February, 1992 S. Kobayashi N. Nishimura Contents Abe, K.

The Boundary Element Methods (BEM) has become one of the most efficient tools for solving various kinds of problems in engineering science. The International Association for Boundary Element Methods (IABEM) was established in order to promote and facilitate the exchange of scientific ideas related to the theory and applications of boundary element methods. The aim of this symposium is to provide a forum for researchers in boundary element methods and boundary-integral formulations in general to present contemporary concepts and techniques leading to the advancement of capabilities and understanding of this com­ putational methodology. The topics covered in this symposium include mathematical and computational aspects, applications to solid mechanics, fluid mechanics, acoustics, electromagnetics, heat transfer, optimization, control, inverse problems and other interdisciplinary problems. Papers deal­ ing with the coupling of the boundary element method with other computational methods are also included. The editors hope that this volume presents some innovative techniques and useful knowl­ edge for the development of the boundary element methods. February, 1992 S. Kobayashi N. Nishimura Contents Abe, K.