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Books > Science & Mathematics > Mathematics > Geometry > General

Asymptotic Cyclic Cohomology (Paperback, 1996 ed.): Michael Puschnigg Asymptotic Cyclic Cohomology (Paperback, 1996 ed.)
Michael Puschnigg
R1,816 Discovery Miles 18 160 Ships in 18 - 22 working days

The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on noncommutative geometry. Asymptotic cyclic cohomology faithfully reflects the basic properties and features of operator K-theory. It thus becomes a natural target for a Chern character. The central result of the book is a general Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. Besides this, the book contains numerous examples and calculations of asymptotic cyclic cohomology groups.

Fractals and Fractional Calculus in Continuum Mechanics (Paperback, 1997 ed.): Alberto Carpinteri, Francesco Mainardi Fractals and Fractional Calculus in Continuum Mechanics (Paperback, 1997 ed.)
Alberto Carpinteri, Francesco Mainardi
R3,363 Discovery Miles 33 630 Ships in 18 - 22 working days

The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.

Geometric Methods in Degree Theory for Equivariant Maps (Paperback, 1996 ed.): Alexander M. Kushkuley, Zalman I. Balanov Geometric Methods in Degree Theory for Equivariant Maps (Paperback, 1996 ed.)
Alexander M. Kushkuley, Zalman I. Balanov
R1,072 Discovery Miles 10 720 Ships in 18 - 22 working days

The book introduces conceptually simple geometric ideas based on the existence of fundamental domains for metric G- spaces. A list of the problems discussed includes Borsuk-Ulam type theorems for degrees of equivariant maps in finite and infinite dimensional cases, extensions of equivariant maps and equivariant homotopy classification, genus and G-category, elliptic boundary value problem, equivalence of p-group representations.
The new results and geometric clarification of several known theorems presented here will make it interesting and useful for specialists in equivariant topology and its applications to non-linear analysis and representation theory.

Applied Computational Geometry. Towards Geometric Engineering - FCRC '96 Workshop, WACG '96, Philadelphia, PA, May 27... Applied Computational Geometry. Towards Geometric Engineering - FCRC '96 Workshop, WACG '96, Philadelphia, PA, May 27 - 28, 1996, Selected Papers (Paperback, 1996 ed.)
Ming C. Lin, Dinesh Manocha
R1,465 Discovery Miles 14 650 Ships in 18 - 22 working days

This anthology is based on the First ACM Workshop on Applied Computational Geometry, WACG '96, held in Philadelphia, PA, USA, in May 1996, as part of the FCRC Conference.
Today, CG is in transition and applied computational geometry has established itself as a fertile meeting ground for theorists from core computational geometry and practitioners from the potential application areas to exchange their ideas and identify issues of common interest. The book presents 11 invited contributions and state-of-the-art reports by leading experts together with 12 refereed full papers selected from 32 submissions. It points the way towards geometrical engineering and addresses researchers and professionals sharing an interest in geometric algorithms and techniques and their use in computational sciences and engineering.

Strange Phenomena in Convex and Discrete Geometry (Paperback, Softcover reprint of the original 1st ed. 1996): Chuanming Zong Strange Phenomena in Convex and Discrete Geometry (Paperback, Softcover reprint of the original 1st ed. 1996)
Chuanming Zong
R1,374 Discovery Miles 13 740 Ships in 18 - 22 working days

Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult - such as the sphere-packing problem (what is the densest possible arrangement of spheres in an n-dimensional space?) and the Borsuk problem (is it possible to partition any bounded set in an n-dimensional space into n+1 subsets, each of which is strictly smaller in "extent" than the full set?) - in terms that a layman can understand; and one can reasonably make conjectures about their solutions with little training in mathematics.

Homotopy Theory: Proceedings of the Durham Symposium 1985 (Paperback): E. Rees, J.D.S. Jones Homotopy Theory: Proceedings of the Durham Symposium 1985 (Paperback)
E. Rees, J.D.S. Jones
R1,150 Discovery Miles 11 500 Ships in 10 - 15 working days

This 1987 volume presents a collection of papers given at the 1985 Durham Symposium on homotopy theory. They survey recent developments in the subject including localisation and periodicity, computational complexity, and the algebraic K-theory of spaces.

Geometric Quantization (Paperback, 2nd Revised edition): N.M.J. Woodhouse Geometric Quantization (Paperback, 2nd Revised edition)
N.M.J. Woodhouse
R4,830 Discovery Miles 48 300 Ships in 18 - 22 working days

This is a new in paperback version of a very successful monograph first published in 1980. The book presents a survey of the geometric quantization theory of Konstant and Souriau. For this new paperback edition the text has been extensively rewritten and brought up-to-date, with the addition of many new examples, and an expansion of the material on field theory.

Lie Groupoids and Lie Algebroids in Differential Geometry (Paperback): K. Mackenzie Lie Groupoids and Lie Algebroids in Differential Geometry (Paperback)
K. Mackenzie
R2,403 Discovery Miles 24 030 Ships in 18 - 22 working days

This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of Lie algebroid: in principal bundle terms this is the Atiyah sequence. The author's viewpoint is that certain deep problems in connection theory are best addressed by groupoid and Lie algebroid methods. After preliminary chapters on topological groupoids, the author gives the first unified and detailed account of the theory of Lie groupoids and Lie algebroids. He then applies this theory to the cohomology of Lie algebroids, re-interpreting connection theory in cohomological terms, and giving criteria for the existence of (not necessarily Riemannian) connections with prescribed curvature form. This material, presented in the last two chapters, is work of the author published here for the first time. This book will be of interest to differential geometers working in general connection theory and to researchers in theoretical physics and other fields who make use of connection theory.

Algebraic and Differential Topology of Robust Stability (Hardcover, New): Edmond A. Jonckheere Algebraic and Differential Topology of Robust Stability (Hardcover, New)
Edmond A. Jonckheere
R3,464 Discovery Miles 34 640 Ships in 10 - 15 working days

In this book, two seemingly unrelated fields -- algebraic topology and robust control -- are brought together. The book develops algebraic/differential topology from an application-oriented point of view. The book takes the reader on a path starting from a well-motivated robust stability problem, showing the relevance of the simplicial approximation theorem and how it can be efficiently implemented using computational geometry. The simplicial approximation theorem serves as a primer to more serious topological issues such as the obstruction to extending the Nyquist map, K-theory of robust stabilization, and eventually the differential topology of the Nyquist map, culminating in the explanation of the lack of continuity of the stability margin relative to rounding errors. The book is suitable for graduate students in engineering and/or applied mathematics, academic researchers and governmental laboratories.

Discrete Geometry for Computer Imagery - 6th International Workshop, DGCI'96, Lyon, France, November 13 - 15, 1996,... Discrete Geometry for Computer Imagery - 6th International Workshop, DGCI'96, Lyon, France, November 13 - 15, 1996, Proceedings (Paperback, 1996 ed.)
Serge Miguet, Annick Montanvert, Stephane Ubeda
R1,534 Discovery Miles 15 340 Ships in 18 - 22 working days

This book constitutes the refereed proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery, DGCI'96, held in Lyon, France, in November 1996.
Computer imaging essentially depends on discrete models for coding, processing, recognition, representation, etc. The volume presents 24 revised full papers selected from 41 submissions together with 3 invited contributions and a tutorial paper, which bridges the gap between theory and practice. The issues addressed are topology, geometry, shape representation, 3D surfaces and volumes, models for discrete space, image transformation and generation.

Nonstandard Analysis in Practice (Paperback, Softcover reprint of the original 1st ed. 1995): Francine Diener, Marc Diener Nonstandard Analysis in Practice (Paperback, Softcover reprint of the original 1st ed. 1995)
Francine Diener, Marc Diener
R1,478 Discovery Miles 14 780 Ships in 18 - 22 working days

This book introduces the graduate mathematician and researcher to the effective use of nonstandard analysis (NSA). It provides a tutorial introduction to this modern theory of infinitesimals, followed by nine examples of applications, including complex analysis, stochastic differential equations, differential geometry, topology, probability, integration, and asymptotics. It ends with remarks on teaching with infinitesimals.

Cellular Spaces, Null Spaces and Homotopy Localization (Paperback, 1996 ed.): Emmanuel D Farjoun Cellular Spaces, Null Spaces and Homotopy Localization (Paperback, 1996 ed.)
Emmanuel D Farjoun
R1,338 Discovery Miles 13 380 Ships in 18 - 22 working days

In this monograph we give an exposition of some recent development in homotopy theory. It relates to advances in periodicity in homotopy localization and in cellular spaces. The notion of homotopy localization is treated quite generally and encompasses all the known idempotent homotopy functors. It is applied to K-theory localizations, to Morava-theories, to Hopkins-Smith theory of types. The method of homotopy colimits is used heavily. It is written with an advanced graduate student in topology and research homotopy theorist in mind.

A General Topology Workbook (Paperback, 1996 ed.): Iain T. Adamson A General Topology Workbook (Paperback, 1996 ed.)
Iain T. Adamson
R1,421 Discovery Miles 14 210 Ships in 18 - 22 working days

This book has been called a Workbook to make it clear from the start that it is not a conventional textbook. Conventional textbooks proceed by giving in each section or chapter first the definitions of the terms to be used, the concepts they are to work with, then some theorems involving these terms (complete with proofs) and finally some examples and exercises to test the readers' understanding of the definitions and the theorems. Readers of this book will indeed find all the conventional constituents--definitions, theorems, proofs, examples and exercises but not in the conventional arrangement. In the first part of the book will be found a quick review of the basic definitions of general topology interspersed with a large num ber of exercises, some of which are also described as theorems. (The use of the word Theorem is not intended as an indication of difficulty but of importance and usefulness. ) The exercises are deliberately not "graded"-after all the problems we meet in mathematical "real life" do not come in order of difficulty; some of them are very simple illustrative examples; others are in the nature of tutorial problems for a conven tional course, while others are quite difficult results. No solutions of the exercises, no proofs of the theorems are included in the first part of the book-this is a Workbook and readers are invited to try their hand at solving the problems and proving the theorems for themselves."

Spatial Representation and Motion Planning (Paperback, 1995 ed.): Angel P. Del Pobil, Miquel A. Serna Spatial Representation and Motion Planning (Paperback, 1995 ed.)
Angel P. Del Pobil, Miquel A. Serna
R1,474 Discovery Miles 14 740 Ships in 18 - 22 working days

This book is devoted to the development of adequate spatial representations for robot motion planning. Drawing upon advanced heuristic techniques from AI and computational geometry, the authors introduce a general model for spatial representation of physical objects. This model is then applied to two key problems in intelligent robotics: collision detection and motion planning. In addition, the application to actual robot arms is kept always in mind, instead of dealing with simplified models.
This monograph is built upon Angel del Pobil's PhD thesis which was selected as the winner of the 1992 Award of the Spanish Royal Academy of Doctors.

From Newton to Mandelbrot - A Primer in Theoretical Physics with Fractals for the Personal Computer (Paperback, 2nd, enlarged... From Newton to Mandelbrot - A Primer in Theoretical Physics with Fractals for the Personal Computer (Paperback, 2nd, enlarged ed. 1996)
Dietrich Stauffer, H. Eugene Stanley
R1,400 Discovery Miles 14 000 Ships in 18 - 22 working days

From Newton to Mandelbrot takes the student on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, and, the most modern and exciting of all, the physics of fractals. The treatment is confined to the essentials of each area, and short computer programs, numerous problems, and beautiful color illustrations round off this unusual textbook. Ideally suited for a one-year course in theoretical physics it will also prove useful in preparing and revising for exams. This edition is corrected and includes a new appendix on elementary particle physics, answers to all short questions, and a diskette where a selection of executable programs exploring the fractal concept can be found.

Modern Geometry with Applications (Paperback, 1st ed. 1994. Corr. 3rd printing 1997): George A. Jennings Modern Geometry with Applications (Paperback, 1st ed. 1994. Corr. 3rd printing 1997)
George A. Jennings
R1,669 Discovery Miles 16 690 Ships in 18 - 22 working days

This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.

Translation Planes - Foundations and Construction Principles (Paperback, 1995 ed.): Norbert Knarr Translation Planes - Foundations and Construction Principles (Paperback, 1995 ed.)
Norbert Knarr
R1,061 Discovery Miles 10 610 Ships in 18 - 22 working days

The book discusses various construction principles for translation planes and spreads from a general and unifying point of view and relates them to the theory of kinematic spaces. The book is intended for people working in the field of incidence geometry and can be read by everyone who knows the basic facts about projective and affine planes.
The methods developed work especially well for topological spreads of real and complex vector spaces. In particular, a complete classification of all semifield spreads of finite dimensional complex vector spaces is obtained.

Excursions into Combinatorial Geometry (Paperback, 1997 ed.): Vladimir Boltyanski, Horst Martini, P.S. Soltan Excursions into Combinatorial Geometry (Paperback, 1997 ed.)
Vladimir Boltyanski, Horst Martini, P.S. Soltan
R2,025 Discovery Miles 20 250 Ships in 18 - 22 working days

Geometry undoubtedly plays a central role in modern mathematics. And it is not only a physiological fact that 80 % of the information obtained by a human is absorbed through the eyes. It is easier to grasp mathematical con- cepts and ideas visually than merely to read written symbols and formulae. Without a clear geometric perception of an analytical mathematical problem our intuitive understanding is restricted, while a geometric interpretation points us towards ways of investigation. Minkowski's convexity theory (including support functions, mixed volu- mes, finite-dimensional normed spaces etc.) was considered by several mathe- maticians to be an excellent and elegant, but useless mathematical device. Nearly a century later, geometric convexity became one of the major tools of modern applied mathematics. Researchers in functional analysis, mathe- matical economics, optimization, game theory and many other branches of our field try to gain a clear geometric idea, before they start to work with formulae, integrals, inequalities and so on. For examples in this direction, we refer to [MalJ and [B-M 2J. Combinatorial geometry emerged this century. Its major lines of investi- gation, results and methods were developed in the last decades, based on seminal contributions by O. Helly, K. Borsuk, P. Erdos, H. Hadwiger, L. Fe- jes T6th, V. Klee, B. Griinbaum and many other excellent mathematicians.

Finite Element Methods in Mechanics (Paperback): Noboru Kikuchi Finite Element Methods in Mechanics (Paperback)
Noboru Kikuchi
R1,321 Discovery Miles 13 210 Ships in 10 - 15 working days

This is a textbook written for mechanical engineering students at first-year graduate level. As such, it emphasizes the development of finite element methods used in applied mechanics. The book starts with fundamental formulations of heat conduction and linear elasticity and derives the weak form (i.e. the principle of virtual work in elasticity) from a boundary value problem that represents the mechanical behaviour of solids and fluids. Finite element approximations are then derived from this weak form. The book contains many useful exercises and the author appropriately provides the student with computer programs in both BASIC and FORTRAN for solving them. Furthermore, a workbook is available with additional computer listings, and also an accompanying disc that contains the BASIC programs for use on IBM-PC microcomputers and their compatibles. Thus the usefulness and versatility of this text is enhanced by the student's ability to practise problem solving on accessible microcomputers.

Geometric Modelling - Dagstuhl 1993 (Paperback, Softcover reprint of the original 1st ed. 1995): R. Albrecht Geometric Modelling - Dagstuhl 1993 (Paperback, Softcover reprint of the original 1st ed. 1995)
R. Albrecht; Edited by H. Hagen, G. Farin, Hartmut Noltemeier
R1,450 Discovery Miles 14 500 Ships in 18 - 22 working days

Experts from university and industry are presenting new technologies for solving industrial problems and giving many important and practicable impulses for new research. Topics explored include NURBS, product engineering, object oriented modelling, solid modelling, surface interrogation, feature modelling, variational design, scattered data algorithms, geometry processing, blending methods, smoothing and fairing algorithms, spline conversion. This collection of 24 articles gives a state-of-the-art survey of the relevant problems and issues in geometric modelling.

Modern Analysis and Topology (Paperback, 1995 ed.): Norman R. Howes Modern Analysis and Topology (Paperback, 1995 ed.)
Norman R. Howes
R1,574 Discovery Miles 15 740 Ships in 18 - 22 working days

The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. The reader should have taken an advanced calculus course and an introductory topology course. It is intended that a subset of the book could be used for an upper-level undergraduate course whereas much of the full text would be suitable for a one-year graduate class. An attempt has been made to document the history of all the central ideas and references and historical notes are embedded in the text. These can lead the interested reader to the foundational sources where these ideas emerged.

Topology and Combinatorics of 3-Manifolds (Paperback, 1995 ed.): Klaus Johannson Topology and Combinatorics of 3-Manifolds (Paperback, 1995 ed.)
Klaus Johannson
R1,926 Discovery Miles 19 260 Ships in 18 - 22 working days

This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds

Graph Drawing - Symposium on Graph Drawing, GD'95; Passau, Germany, September 20-22, 1995. Proceedings (Paperback, 1996... Graph Drawing - Symposium on Graph Drawing, GD'95; Passau, Germany, September 20-22, 1995. Proceedings (Paperback, 1996 ed.)
Franz Brandenburg
R1,630 Discovery Miles 16 300 Ships in 18 - 22 working days

This book constitutes the refereed proceedings of the international Symposium on Graph Drawing, GD '95, held in Passau, Germany, in September 1995.
The 40 full papers and 12 system demonstrations were selected from a total of 88 submissions and include, in their revised versions presented here, the improvements suggested during the meeting. This book also contains a report on the graph-drawing contest held in conjunction with GD '95. Graph drawing is concerned with the problem of visualizing structural information, particularly by constructing geometric representations of abstract graphs and networks. The importance of this area for industrial applications is testified by the large number of people with industrial affiliations, submitting papers and participating in the meeting.

Results and Problems in Combinatorial Geometry (Paperback): Vladimir G. Boltjansky, Israel Gohberg Results and Problems in Combinatorial Geometry (Paperback)
Vladimir G. Boltjansky, Israel Gohberg; Translated by B. Bollobas, A. Harris
R1,119 Discovery Miles 11 190 Ships in 10 - 15 working days

In this short book, the authors discuss three types of problems from combinatorial geometry: Borsuk's partition problem, covering convex bodies by smaller homothetic bodies, and the illumination problem. They show how closely related these problems are to each other. The presentation is elementary, with no more than high-school mathematics and an interest in geometry required to follow the arguments. Most of the discussion is restricted to two- and three-dimensional Euclidean space, though sometimes more general results and problems are given. Thus even the mathematically unsophisticated reader can grasp some of the results of a branch of twentieth-century mathematics that has applications in such disciplines as mathematical programming, operations research and theoretical computer science. At the end of the book the authors have collected together a set of unsolved and partially solved problems that a sixth-form student should be able to understand and even attempt to solve.

Syzygies (Paperback): E.Graham Evans, Phillip Griffith Syzygies (Paperback)
E.Graham Evans, Phillip Griffith
R1,211 Discovery Miles 12 110 Ships in 18 - 22 working days

The aim of this book, which was originally published in 1985, is to cover from first principles the theory of Syzygies, building up from a discussion of the basic commutative algebra to such results as the authors' proof of the Syzygy Theorem. In the last three chapters applications of the theory to commutative algebra and algebraic geometry are given.

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