Kenneth Falconer

Fractal Geometry: Mathematical Foundations and Applications, 2nd Edition

ISBN: 0-470-84861-8
Hardcover
328 pages
October 2003
ISBN: 0-470-84862-6
Paperback
328 pages
October 2003

Description

Table of Contents
Since its original publication in 1990, Kenneth Falconer’s Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition.
・ Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals.

・ Each topic is carefully explained and illustrated by examples and figures.

・ Includes all necessary mathematical background material.

・ Includes notes and references to enable the reader to pursue individual topics.

・ Features a wide selection of exercises, enabling the reader to develop their understanding of the theory.

・ Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers.

Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences.

Oliver Stein

Bi-level Strategies in Semi-infinite Programming

July 2003, ISBN 1-4020-7567-7, Hardbound

Book Series: NONCONVEX OPTIMIZATION AND ITS APPLICATIONS : Volume 71

This is the first book that exploits the bi-level structure of semi-infinite programming systematically. It highlights topological and structural aspects of general semi-infinite programming, formulates powerful optimality conditions, which take this structure into account, and gives a conceptually new bi-level solution method. The results are motivated and illustrated by a number of problems from engineering and economics that give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, robust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming.

Audience: The book is suitable for graduate students and researchers in the fields of optimization and operations research.

Valery A. Gaiko

Global Bifurcation Theory and Hilbert's Sixteenth Problem

August 2003, ISBN 1-4020-7571-5, Hardbound

Book Series: MATHEMATICS AND ITS APPLICATIONS : Volume 562

This volume is devoted to the qualitative investigation of two-dimensional polynomial dynamical systems and is aimed at solving Hilbert's Sixteenth Problem on the maximum number and relative position of limit cycles. The author presents a global bifurcation theory of such systems and suggests a new global approach to the study of limit cycle bifurcations.

The obtained results can be applied to higher-dimensional dynamical systems and can be used for the global qualitative analysis of various mathematical models in mechanics, radioelectronics, in ecology and medicine.

Audience: The book would be of interest to specialists in the field of qualitative theory of differential equations and bifurcation theory of dynamical systems. It would also be useful to senior level undergraduate students, postgraduate students, and specialists working in related fields of mathematics and applications.

Fred W. Steutel / Technische Universiteit Eindhoven, The Netherlands
Klaas van Harn / Vrije Universiteit, Amsterdam, The Netherlands

Infinite Divisibility of Probability Distributions on the Real Line

Series
Pure and Applied Mathematics series.Volume: 259

Textbook | Print Published: 09/01/2003
Hard Cover
550 pages | Illustrated
Print ISBN: 0-8247-0724-9

Description

Includes a separate section featuring approximately 100 examples.

Fundamental to theoretical probability and valuable in such applications as financial, insurance, and biological modeling and deconvolution problems in mathematical physics, infinite divisibility has proven to be a very profitable area of research. Reassessing classical theory and presenting new developments, Infinite Divisibility of Probability Distributions on the Real Line is a definitive, example-filled text focused on divisibility with respect to convolution and addition of independent random variables.

Table of Contents

Introduction and Overview
Infinitely Divisible Distributions on the Nonnegative Integers
Infinitely Divisible Distributions on the Nonnegative Reals
Infinitely Divisible Distributions on the Real Line
Self-Decomposability and Stability
Infinite Divisibility and Mixtures
Infinite Divisibility in Stochastic Processes
Appendix A: Prerequisites from Probability and Analysis
Appendix B: A List of Well-Known Distributions
Notations and Conventions
Bibliography
Author Index
Subject Index.

Edited by: Sanford Bolton / Charles Bon

Pharmaceutical Statistics,
Practical and Clinical Applications: Fourth Edition, Revised and Expanded

Series
Drugs and The Pharmaceutical Sciences series.Volume: 135

Book | Print Published: 10/01/2003
Hard Cover
650 pages | Illustrated
Print ISBN: 0-8247-4695-3

Description

Includes a disk with special programs to aid in problem analysis. Presents fresh material on concept conformity and release targets. Describes linear regression and correlation, the analysis of variance, and crossover designs.

Table of Contents

Basic Definitions and Concepts
Data graphics
Introduction to Probability: The Binomial and Normal Probability Distributions
Choosing Samples
Statistical Inference: Estimation and Hypothesis Testing
Sample Size and Power
Linear Regression and Correlation
Analysis of Variance
Factorial Designs
Transformations and Outliers
Experimental Design in Clinical Trials
Quality Control
Validation
Computer-Intensive Methods
Nonparametric Methods
Optimization Techniques and Screening Designs
Appendix I: Some Properties of the Variance
Appendix II: Comparison of Slopes and Testing of Linearity: Determination of Relative Potency
Appendix III: Multiple Regression
Appendix IV: Tables
Appendix V: Outlier Tests and Chemical Assays
Appendix VI: Should a Single Unexplained Failing Assay Be Reason to Reject a Batch
Answers to Exercises
Index.

Vijay Srinivasan
IBM Corp., White Plains, New York, U.S.A.

Theory of Dimensioning
An Introduction to Parametering Geometric Models

Series
Mechanical Engineering series. Volume: 163

Textbook | Print Published: 10/01/2003
Hard Cover
350 pages | Illustrated
Print ISBN: 0-8247-4624-4

Description

Presents a theory of dimensioning synthesized from several areas of geometry, starting from the works of Euclid and culminating in some recent results in classification of continuous symmetry groups. Features numerous examples and illustrations for better understanding of concepts.

Table of Contents

Congruence
Dimensioning Elementary Curves
Conics
Free-form Curves
Space Curves
Dimensioning Elementary Surfaces
Quadrics
Free-form Surfaces
Swept Surfaces
Dimensioning Relative Positions of Elementary Objects
Distances and Angles
Some Cases Involving Points
Relative Positioning Two Lines
Relative Positioning Line and Plane
Relative Positioning Two Planes
Cases Involving Oriented Lines and Oriented Planes
Cases Involving Helices
Symmetry
Groups
Symmetry Groups
Connected Lie Subgroups of the Rigid Motion Group
Classification of Continuous Symmetry Groups
Classification of Tuples of Sets
Classification of Lower Order Kinematic Pairs
General Theory of Dimensioning Relative Positions
Tuple Congruence
Number of Dimensions for Relative Positions
More on Relative Positioning Spherical, Cylindrical, Planar, and Helical Classes
Adding the Revolute Class
Adding the Prismatic Class
Adding the General Class
Dimensional Constraints
Basic Geometric Constraints
Rigidity Theory
Inducing Hierarchy in Simultaneity
Dimensioning Solids
Dimensioning a Solid Polyhedron
Dimensioning Procedurally Defined Solids
Dimensioning Features
Appendices
A1. Matrices
A2. Groups
A3. Graphs
A4. Solids
Bibliography