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Image synthesis
503
Book Reviews
W. Mlak, Hilbert Spaces and Operator US$149, UIE81, ISBN 0-7923-1042-X.
Theory. Kluwer,
Dordrecht,
1991. 290 pp., Dfl.235,
The theory of Hilbert spaces is a rapidly developing part of functional analysis and has found many applications in mathematics and theoretical physics. This volume gives a comprehensive presentation of the basic notions and methods of this important theory, with the emphasis being on clear exposition. This is not, however, a volume presenting a standard introduction to Hilbert space and operators. A far greater emphasis is placed on algebraic lattices and integral representations. The volume begins by describing the underlying notion of the algebraic lattice which presents the theory of (representations) of Hilbert spaces. The spectral theory of operators on Hilbert spaces is then treated via representations of function algebras and semi-spectral measures. The discussion of theorems and problems is accompanied by much explanation, and the author provides numerous examples and exercises. It is assumed that the reader is familiar with elementary measure theory and the fundamentals of set theory and general topology. However, no prior knowledge of functional analysis is assumed.
WFN R. Delanghe, F. Sommen and V. Soucek, Clifford Algebra Function Theory for the Dirac Operator). Kluwer, Dordrecht, UIWO2, ISBN 0-7923-0229-X.
and Spinor-Valued Functions ,(A 1992. 485 pp., Dfl.295, US$176,
This volume describes the substantial developments in Clifford analysis which have taken place during the last decade, and, in particular, the role of the spin group in the study of null solutions of real and complexified Dirac and Laplace operators. The book has six main chapters. The first two (Chapters 0 and I) present classical results on real and complex Clifford algebras and show how lower-dimensional real Clifford algebras are well-suited for describing basic geometric notions in Euclidean space. Chapters II and III illustrate how Clifford analysis extends and refines the computational tools available in complex analysis in the plane or harmonic analysis in space. In Chapter IV the concept of monogenic differential forms is generalized to the case of spin-manifolds. Chapter V deals with analysis on homogeneous spaces, and shows how Clifford analysis may be connected with the Penrose transform. The volume concludes with some appendices which present basic results relating to the algebraic and analytic structures discussed. These are made accessible for computational purposes by means of computer algebra programmes written in REDUCE and are contained on an accompanying floppy disk.
WFA) M. Bret, Image Synthesis. O-7923-1488-3.
Kluwer, Dordrecht,
1991. 289 pp., Dfl.180,
US$99,
UK&61, ISBN
This English edition is a translation of “Images de Synthbe. Mkthodes et Algorithmes pour la originally published by Editions Bordas in 1988. The book
Rkalisation d’lmages Numbiques”
504
Book Reuiews
gives a complete overview of the techniques of image synthesis by computer. The different stages of the creation of a numerical image are explained in detail, and they are accompanied by descriptions of the most modern methods. Thus the geometrical models that are described go from those with plane polygonal faces, via surfaces of all types, to systems of particles. Visualization is treated in complete detail, and due attention is given to all the various roads that lead to a realistic image; simple projections on the basis of wire-frame models, the elimination of hidden parts, and finally the modelling of light and its effects. The volume will be of interest to all those interested in computer graphics, from the scientist in this field, and to the computer scientist involved in computer graphics research.
K. Truemper, Matroid Decomposition. ISBN O-1270-1225-7.
Academic
Press, Boston,
MA, 1992. 398 PP., US$39.95,
Matroids were first defined in 1935 as an abstract generalization of graphs and matrices. A large collection of applicable matroid theorems exists. This book does not assume any prior knowledge of matroid theory. It is confined to that part of the theory dealing with decomposition and composition of matroids. Chapter 1 is an introduction. Chapter 2 contains basic definitions concerning graphs and matrices. In Chapter 3 the binary matroids are defined and a number of results, such as the operations of deletion and contraction and their properties, are established. Chapters 4-6 contain fundamental matroid constructions, tools and theorems. The techniques and results of Chapters 4-6 are put to use in Chapters 7 and 8. In Chapter 7 the splitter theorem is proven and in Chapter 8 fundamental notions and theorems about matroid decomposition and composition are determined. The second half of the book begins with Chapter 9 in which fundamental facts are found about total unimodularity. In Chapters lo-13 the authors establish a number of decomposition and composition results about the class of regular matroids and about other, closely related matroid classes. Chapters 9-13 provide polynomial testing algorithms, representative applications, and, except for the almost regular case, characterizations in terms of excluded minors.
WFA) N.R. Wallach, O-1273-2961-7.
Real Reductive
Groups II. Academic
Press, Boston,
MA, 1992. US$75,
ISBN
This volume is the second book in the series Real Reductive Groups and is intended to be read as a continuation of the first volume. Indeed, the chapters are numbered as a continuation of the first. In volume II the emphasis is on the more analytic aspects of the theory. The chapters are as follows: Chapter 10: Intertwining Operators. Chapter 11: Completions of Admissible Modules.
Book Reviews
W. Mlak, Hilbert Spaces and Operator US$149, UIE81, ISBN 0-7923-1042-X.
Theory. Kluwer,
Dordrecht,
1991. 290 pp., Dfl.235,
The theory of Hilbert spaces is a rapidly developing part of functional analysis and has found many applications in mathematics and theoretical physics. This volume gives a comprehensive presentation of the basic notions and methods of this important theory, with the emphasis being on clear exposition. This is not, however, a volume presenting a standard introduction to Hilbert space and operators. A far greater emphasis is placed on algebraic lattices and integral representations. The volume begins by describing the underlying notion of the algebraic lattice which presents the theory of (representations) of Hilbert spaces. The spectral theory of operators on Hilbert spaces is then treated via representations of function algebras and semi-spectral measures. The discussion of theorems and problems is accompanied by much explanation, and the author provides numerous examples and exercises. It is assumed that the reader is familiar with elementary measure theory and the fundamentals of set theory and general topology. However, no prior knowledge of functional analysis is assumed.
WFN R. Delanghe, F. Sommen and V. Soucek, Clifford Algebra Function Theory for the Dirac Operator). Kluwer, Dordrecht, UIWO2, ISBN 0-7923-0229-X.
and Spinor-Valued Functions ,(A 1992. 485 pp., Dfl.295, US$176,
This volume describes the substantial developments in Clifford analysis which have taken place during the last decade, and, in particular, the role of the spin group in the study of null solutions of real and complexified Dirac and Laplace operators. The book has six main chapters. The first two (Chapters 0 and I) present classical results on real and complex Clifford algebras and show how lower-dimensional real Clifford algebras are well-suited for describing basic geometric notions in Euclidean space. Chapters II and III illustrate how Clifford analysis extends and refines the computational tools available in complex analysis in the plane or harmonic analysis in space. In Chapter IV the concept of monogenic differential forms is generalized to the case of spin-manifolds. Chapter V deals with analysis on homogeneous spaces, and shows how Clifford analysis may be connected with the Penrose transform. The volume concludes with some appendices which present basic results relating to the algebraic and analytic structures discussed. These are made accessible for computational purposes by means of computer algebra programmes written in REDUCE and are contained on an accompanying floppy disk.
WFA) M. Bret, Image Synthesis. O-7923-1488-3.
Kluwer, Dordrecht,
1991. 289 pp., Dfl.180,
US$99,
UK&61, ISBN
This English edition is a translation of “Images de Synthbe. Mkthodes et Algorithmes pour la originally published by Editions Bordas in 1988. The book
Rkalisation d’lmages Numbiques”
504
Book Reuiews
gives a complete overview of the techniques of image synthesis by computer. The different stages of the creation of a numerical image are explained in detail, and they are accompanied by descriptions of the most modern methods. Thus the geometrical models that are described go from those with plane polygonal faces, via surfaces of all types, to systems of particles. Visualization is treated in complete detail, and due attention is given to all the various roads that lead to a realistic image; simple projections on the basis of wire-frame models, the elimination of hidden parts, and finally the modelling of light and its effects. The volume will be of interest to all those interested in computer graphics, from the scientist in this field, and to the computer scientist involved in computer graphics research.
K. Truemper, Matroid Decomposition. ISBN O-1270-1225-7.
Academic
Press, Boston,
MA, 1992. 398 PP., US$39.95,
Matroids were first defined in 1935 as an abstract generalization of graphs and matrices. A large collection of applicable matroid theorems exists. This book does not assume any prior knowledge of matroid theory. It is confined to that part of the theory dealing with decomposition and composition of matroids. Chapter 1 is an introduction. Chapter 2 contains basic definitions concerning graphs and matrices. In Chapter 3 the binary matroids are defined and a number of results, such as the operations of deletion and contraction and their properties, are established. Chapters 4-6 contain fundamental matroid constructions, tools and theorems. The techniques and results of Chapters 4-6 are put to use in Chapters 7 and 8. In Chapter 7 the splitter theorem is proven and in Chapter 8 fundamental notions and theorems about matroid decomposition and composition are determined. The second half of the book begins with Chapter 9 in which fundamental facts are found about total unimodularity. In Chapters lo-13 the authors establish a number of decomposition and composition results about the class of regular matroids and about other, closely related matroid classes. Chapters 9-13 provide polynomial testing algorithms, representative applications, and, except for the almost regular case, characterizations in terms of excluded minors.
WFA) N.R. Wallach, O-1273-2961-7.
Real Reductive
Groups II. Academic
Press, Boston,
MA, 1992. US$75,
ISBN
This volume is the second book in the series Real Reductive Groups and is intended to be read as a continuation of the first volume. Indeed, the chapters are numbered as a continuation of the first. In volume II the emphasis is on the more analytic aspects of the theory. The chapters are as follows: Chapter 10: Intertwining Operators. Chapter 11: Completions of Admissible Modules.