Recent book reviews

Five recent book reviews

Measure Theory and Integration

Author(s): 
M. E. Taylor
Publisher: 
American Mathematical Society, Providence: Graduate Studies in Mathematics, vol. 76
Year: 
2006
ISBN: 
0-8218-4180-7
Price (tentative): 
USD 59
MSC main category: 
28 Measure and integration
Review: 

This book starts with chapters on classical notions of integration and measure theory (the Riemann integral, the Lebesgue measure, the Carathéodory process, product measures, abstract integration, Lp-spaces, Radon and Hausdorff measures, the Vitali, Besicovitch and Rademacher theorems and maximal functions). The next chapters explore connections between measure theory and probability theory (ergodic theory, laws of large numbers, the central limit theorem, the Wiener measure, Brownian motion and martingales). The book has several appendices on topological notions, diffeomorphisms, the Whitney extension theorem, the Marcinkiewicz interpolation theorem, Sard's theorem, integration of differential forms and the Gauss-Green formula. Each chapter ends with many exercises of varying difficulty, which give further applications and extensions of the theory. The book ends with a bibliography, a list of standard symbols and a subject index. The book is very understandable, requiring only a basic knowledge of analysis. It can be warmly recommended to a broad spectrum of readers, to graduate students as well as young researchers.

Reviewer: 
jl

Models for Intensive Longitudinal Data

Author(s): 
T. A. Walls, J.L. Schafer, Eds.
Publisher: 
Oxford University Press, Oxford
Year: 
2006
ISBN: 
978-0-19-517344-4
Price (tentative): 
GBP 38,99
MSC main category: 
62 Statistics
Review: 

Classical longitudinal analysis is mainly focused on examples to some ten occasions. New technologies lead to longitudinal databases with a considerably higher intensity and a substantially larger volume of data, for which the new term ‘intensive longitudinal data’ (ILD) is used. The number of occasions in ILD may be hundreds or thousands. However, the main difference between ILD and other models pertain to the scientific motivations for collecting ILD, the nature of hypotheses about them and the complex features of the data. The main themes in ILD modeling are: (i) the complexity and variety of individual trajectories, (ii) the role of time as a covariate, (iii) effects found in the covariance structure, (iv) relationships that change over time, (v) interest in autodependence and regulatory mechanisms.

The book is a collection of eleven papers (arranged as chapters) written by different authors. The introductory chapters focus on multilevel models and on marginal modelling through generalized estimating equations. Later chapters describe methodological tools from item response theory, functional data analysis, time series, state-space modeling, stochastic differential equations, engineering control systems, and models of point processes. Theory is illustrated on real data drawn from psychology, studies of smoking and alcohol use, brain imaging and traffic engineering. Some authors have supplied programs and source code examples. They are available at a website accompanying the book. By the way, the formula on page 118, line 6, should read sm=c22m-1+c22m. The remark on page 130 that the order p of an autoregressive process is often determined heuristically should be complemented by another remark that the order p is also often determined using AIC, BIC and similar criteria. This collection contains many interesting models and practical examples. The volume can be attractive reading for statisticians working in biostatistics and behavioural and social sciences.

Reviewer: 
ja

Agency and the Semantic Web

Author(s): 
C. Walton
Publisher: 
Oxford University Press, Oxford
Year: 
2006
ISBN: 
0-19-929248-5
Price (tentative): 
GBP 29,95
MSC main category: 
68 Computer science
Review: 

The growing complexity and dynamics of the Web have enforced the development and use of ever more intelligent and powerful tools able to look for knowledge rather than simply information on the Web. One intended technique to solve this issue is the Semantic Web. The main aim of this book is to show that a fruitful contribution to the implementation of the Semantic Web can be the application of results of the long existing research of autonomous intelligent agents. The agents must be able to work in the framework of the successful software engineering concept of the Web and Web services. It implies the agents must be able to use related XML–based languages. The book describes ontologies as the central concept of the Semantic Web and discusses the basic properties of the languages for the specification of ontologies as a knowledge description tool on the Web (the RDF and OWL family of web ontology languages).

Several chapters are devoted to various concepts of intelligent agents and their behaviour (reactive agents and several models of planning agents and of deductive and reasoning agents). The remaining chapters (Reasoning on the Web, Agent Communication and Semantic Web service) are devoted to methods that can be used in the implementation of agents as Web services. A majority of chapters contain exercises, which are often supported by sources available on the Web, and suggested reading lists. The book covers a broad collection of topics on agency and on software engineering of the Web. The book presents more than ten languages and several logics. The explanation is intuitive using instructive examples. It usually presents only the main ideas and attitudes. Almost no practical experience with discussed visions, concepts and tools is mentioned.

Reviewer: 
jkral

Introduction to Asymptotic Methods

Author(s): 
J. Awrejcewicz, V.A. Krysko
Publisher: 
Chapman & Hall/CRC, Boca Raton
Year: 
2006
ISBN: 
1-58488-677-3
Price (tentative): 
USD 89,95
MSC main category: 
34 Ordinary differential equations
Other MSC categories: 
70-01
Review: 

This book surveys various mathematical approaches to perturbation theory and illustrates their applicability on a number of simple, physically motivated examples and exercises expressed in terms of differential equations. These methods simplify the original formulation, still giving under certain conditions the essential characteristics of analysed processes. The topics covered include: (i) tools to study regular and singular perturbations, (ii) renormalization, characteristics and multiple scale methods for one-dimensional time-dependent nonlinear waves, (iii) the Padé approximation and its application in mechanics, (iv) oscillators with negative Duffing type stiffness, and (v) differential equations with discontinuous nonlinearities. The importance of understanding the physical concepts behind the model under consideration is emphasized throughout the book.

Reviewer: 
jmal

Multi-dimensional Hyperbolic Partial Differential Equations - First-order Systems and Applications

Author(s): 
S. Benzoni-Gavage, D. Serre
Publisher: 
Oxford University Press, Oxford: Oxford Mathematical Monographs
Year: 
2006
ISBN: 
0-19-921123-X
Price (tentative): 
GBP 60
MSC main category: 
35 Partial differential equations
Review: 

This carefully written and well-thought-out book presents a comprehensive view on mathematical theory concerning multi-dimensional hyperbolic partial differential equations. The main body of the book consists of four parts. The first part deals with the theory of linear Cauchy problems that involve both constant and variable coefficients, the latter illustrating the power of pseudo-differential and para-differential calculus (presented separately in the appendix). The second part is devoted to linear initial boundary value problems, proceeding from simpler to more complicated systems (symmetric, constant coefficients, variable coefficients). The third part is devoted to the theory of nonlinear problems, focusing on the notion of a smooth solution and a piecewise smooth solution suitable for analysis of shock waves (as is carefully proved). The last part investigates problems in gas dynamics and it includes a discussion of appropriate boundary conditions and shock-wave analysis. The text is completed with an extensive bibliography including classical and recent papers both in partial differential equation analysis and applications (mainly in gas dynamics).

Reviewer: 
jmal