Gallier, J., University of Pennsylvania, Philadelphia, PA, USA
Geometric Methods and Applications
2000. Approx. 610 pp. 77 figs.
0-387-95044-3
As an introduction to fundamental geometric concepts and tools needed for solving problems of a
geometric nature using a computer, this book fills the gap between standard geometry books, which are
primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not
cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective,
computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many
of the practical applications of geometry. Some of these include computer vision, efficient communication,
error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text
covers most of the geometric background needed for conducting research in computer graphics, geometric
modeling, computer vision, and robotics and as such will be of interest to a wide audience including
computer scientists, mathematicians, and engineers.
Contents: Preface.- Introduction.- Basics of Affine Geometry.- Properties of Convex Sets, A Glimpse.-
Embedding an Affine Space in a Vector Space.- Basics of Projective Geometry.- Basics of Euclidean
Geometry.- The Cartan-DieudonnETheorem.- Quaternions and Rotations.- Dirichlet-Voronoi Diagrams.-
Basics of Hermitian Geometry.- Spectral Theorems.- Singular Value Decomposition (SVD) and Polar Form.-
Applications of Euclidean Geometry.- Basics of Classical Lie Groups.- Basics of the Differential Geometry of
Curves.- Basics of the Differential Geometry of Surfaces.- Appendix.- Bibliography.- Index.
Series: Texts in Applied Mathematics.VOL. 38
Bang-Jensen, J., University of Odense, Denmark
Gutin, G., Brunel University, Uxbridge, UK
Digraphs
Theory, Algorithms and Applications
2000. Approx. 670 pp.
1-85233-268-9
The study of directed graphs has developed enormously over recent decades, yet no book covers more
than a tiny fraction of the results from more than 3000 research articles on the topic. Digraphs is the first
book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical
aspects, including detailed proofs of many important results, the authors present a number of algorithms
and applications. The applications of digraphs and their generalizations include among other things recent
developments in the Travelling Salesman Problem, genetics and network connectivity. More than 700
exercises and 180 figures will help readers to study the topic while open problems and conjectures will
inspire further research.
This book will be essential reading and reference for all graduate students, researchers and professionals in
mathematics, operational research, computer science and other areas who are interested in graph theory and
its applications.
Contents: Basic Terminology, Notation and Results.- Distances.- Flows in Networks.- Classes of Digraphs.-
Hamiltonicity and Related Problems.- Hamiltonian Refinements.- Global Connectivity.- Orientations of
Graphs.- Disjoint Paths and Trees.- Cycle Structure of Digraphs.- Generalizations of Digraphs.- Additional
Topics.- References.- Symbol Index, Author Index, Subject Index.
Series: Springer Monographs in Mathematics.
Edited by Francis Blanchard
Alejandro Maass
and Arnaldo Nogueira
Topics in Symbolic Dynamics and Applications
This book is devoted to recent developments in symbolic dynamics, and it comprises eight chapters. The first two are concerned with the study of symbolic sequences of 'Low complexity' the following two introduce 'High complexity'systems. Chapter five presents results on asymptotic laws for the random times of occurrence of rare events. Chapter six deals with diophantine problems and combinatorial Ramsey theory. Chapter seven looks at the dynamics of symbolic systems arising from numeration systems, and finally chapter eight gives a complete description of the symbolic dynamics of Lorenz maps.
1. Sequences of low complexity: automatic and sturmian sequences V. BerthE 2. Substitution subshifts and Bratteli diagrams B. Host; 3. Algebraic aspects of symbolic dynamics M. Boyle; 4. Dynamics of Zd actions on Markov subgroups B. Kitchens; 5. Asymptotic laws for symbolic dynamical systems Z. Coelho; 6. Ergodic theory and diophantine problems V. Bergelson; 7. Number representation and finite automata C. Frougny; 8. A note on the topological classification of Lorenz maps on the interval R. Labarca.
London Mathematical Society Lecture Note Series, 279
0 521 79660 1 Paperback
June 2000
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