A. Weinstein – författare

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering

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 .