C. Musili, University of Hyderabad, India

Algebraic Geometry for Beginners

Description

This volume offers a nearly self-contained introduction to some of the basic concepts of algebraic geometry. Prerequisites have been kept to a minimum in order to examine the following areas and some of their standard applications: Be'zout's Theorem, the Fundamental Theorem of Projective Geometry, and Zariski's Main Theorem. The exposition is modern, but in the language of "varieties", rather than that of "schemes", making it more accessible to the non-expert. There is extensive coverage of plane curves, including elliptic curves and complex tori, moduli questions, and applications to cryptology.

Contents
Commutative algebra
Affine varieties
Projective varieties
Non-singular varieties
Plane curves
Zariski's main theorem
Bibliography
Index
Glossary

Details:

Publisher: Hindustan Book Agency
Distributor: American Mathematical Society
Number: 7
Publication Year: 2001
ISBN: 81-85931-27-5
Paging: 335 pp.
Binding: Hardcover

Mohammad-Djafari, A., Laboratoire des Signaux et Systemes, Gif-sur-Yvette, France (Ed.)

Bayesian Inference and Maximum Entropy Methods in Science and Engineering : 20th International Workshop, Gif-sur-Yvette, France, 8-13 July 2000

2001. Approx. 660 pp. Hardcover
0-7354-0004-0

Bayesian inference and maximum entropy methods are central points of new scientific inference in mathematical physics and in all inverse problems in engineering and all probabilistic data analysis. This volume contains peer-reviewed selection of the papers presented at this international workshop.
Topics included are: axiomatics and concepts, bayesian parameter estimation, algorithms for bayesian computation, deconvolution and source separation, quantum tomography, tomographic imaging and image processing, as well as bayesian inference in applications.

Keywords: Inference methods ; complex systems ; probability theory ; approximations

Series: AIP Conference Proceedings.VOL. 568

Giangiacomo Gerla
Dept. of Mathematics and Computer Sciences, University of Salerno, Italy

Fuzzy Logic
Mathematical Tools for Approximate Reasoning

TRENDS IN LOGIC Volume 11

The theme of this book is fuzzy logic in a narrow sense, a promising new chapter of fuzzy logic. The basic ideas of formal logic were formulated by Lotfi Zadeh in 1975. The aim of this logic is to investigate the wonderful human capacity of reasoning with vague notions by attempting to formalize the `approximate reasoning' we use in everyday life. A peculiarity of this book is to propose a general framework based on three mathematical tools: the theory of fuzzy closure operators, an extension principle for crisp logics and the theory of recursively enumerable fuzzy subsets. This book is unique in that it treats fuzzy logics which are not truth-functional in nature (as an example, the logic of the necessities, probabilistic logics and similarity-based logics). The book is addressed to people interested in artificial intelligence, fuzzy control, formal logic, and philosophy. It can be used in special post-graduate university studies and in advanced courses. The book is completely self-contained.

Contents
Preface. 1. Abstract logic in a lattice. 2. Abstract fuzzy logic. 3. Extending an abstract crisp logic. 4. Approximate reasoning. 5. Logic as management of constraints on the truth values. 6. Canonical extension of a crisp Hilbert logic. 7. Graded consequence relations. 8. Truth-functional logic and fuzzy logic. 9. Probabilistic fuzzy logics. 10. Fuzzy control and approximate reasoning. 11. Effectiveness in fuzzy logic. References. Index. List of symbols.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6941-6
April 2001, 288 pp.

James C. Robinson / University of Warwick, Coventry, UK
Paul A. Glendinning / UMIST, Manchester, UK

From Finite to Infinite Dimensional Dynamical Systems
Proceedings of the NATO Advanced Study Institute, Cambridge, UK, 21 August-1 September 1995

NATO SCIENCE SERIES: II: Mathematics, Physics and Chemistry Volume 19

The central theme of this book is how ideas familiar from finite dimensional dynamical systems may be used in the study of infinite dimensional dynamical systems, such as partial differential equations.

After an introduction to the study of partial differential equations from the perspective of dynamical systems, some of the ideas are applied to the equations of fluid dynamics and the application of low-dimensional models of turbulence. A discussion of chaos in lattice dynamical systems (for which the spatial dimension is discrete) is followed by the use of such models in biology.

The book provides an introduction to a range of new techniques and applications in dynamics and will interest any graduate student starting work in the area, as well as more experienced scientists and mathematicians keen to extend their knowledge.
Contents


Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6975-0
Paperback, ISBN 0-7923-6976-9
April 2001, 228 pp.

Saburou Saitoh/Dept. of Mathematics, Gunma University
Nakao Hayashi/Dept. of Applied Mathematics, Science University of Tokyo
Masahiro Yamamoto/Dept. of Mathematical Sciences, University of Tokyo

Analytic Extension Formulas and their Applications

INTERNATIONAL SOCIETY FOR ANALYSIS, APPLICATIONS AND COMPUTATION Volume 9

Analytic Extension is a mysteriously beautiful property of analytic functions. With this point of view in mind the related survey papers were gathered from various fields in analysis such as integral transforms, reproducing kernels, operator inequalities, Cauchy transform, partial differential equations, inverse problems, Riemann surfaces, Euler-Maclaurin summation formulas, several complex variables, scattering theory, sampling theory, and analytic number theory, to name a few.

Audience: Researchers and graduate students in complex analysis, partial differential equations, analytic number theory, operator theory and inverse problems.

Contents and Contributors

Preface. 1. Extending holomorphic functions from subvarieties; K. Adachi. 2. Representations of analytic functions on typical domains in terms of local values and truncation error estimates; K. Amano, et al. 3. Uniqueness in determining damping coefficients in hyperbolic equations; A.L. Bukhgeim, et al. 4. Analytic continuation of Cauchy and exponential transforms; B. Gustafsson, M. Putinar. 5. Analytic function spaces and their applications to nonlinear evolution equations; N. Hayashi. 6. A sampling principle associated with Saitoh's fundamental theory of linear transformations; J.R. Higgins. 7. The enclosure method and its applications; M. Ikehata. 8. On analytic properties of a multiple L-function; H. Ishikawa. 9. Multi-dimensional inverse scattering theory; H. Isozaki. 10. Holomorphic spaces related to orthogonal polynomials and analytic continuation of functions; D. Karp. 11. Extension and division on complex manifolds; T. Ohsawa. 12. Analytic extension formulas, integral transforms and reproducing kernels; S. Saitoh. 13. Analytic continuation beyond the ideal boundary; M. Shiba. 14. Justification of a formal derivation of the Euler-Maclaurin summation formula; M. Sugihara. 15. Extension of Lo"wner-Heinz inequality via analytic continuation; M. Uchiyama. 16. The Calogero-Moser model, the Calogero model and analytic extension; S. Watanabe.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6950-5
April 2001, 296 pp.