Five recent book reviews

Publisher:

Chapman & Hall/CRC

Year:

2007

ISBN:

978-1-58488-589-4

Price (tentative):

USD 79.95

MSC main category:

62 Statistics

Review:

This is the fourth edition of the book “Randomization Tests” containing a large number of innovative applications of randomization tests in experimental design, significance testing, computing facilities and other fields. The book focuses more on design than on test statistics. This volume can serve as a practical source book for researchers but, at the same time, it puts emphasis on randomization tests rationale. In comparing with the third edition, this volume gives a more didactical approach in the exposition and it contains many new examples making the book more accessible as a textbook for students in applied statistics. The book contains 15 chapters on topics including statistical tests that do not require random sampling, randomized experiments, between-subject and factorial designs, repeated-measures and randomized, block design and multivariate design, trend tests, tests of quantitative laws, tests of direction and magnitude of effect.

Reviewer:

lkl

Publisher:

American Mathematical Society

Year:

2006

ISBN:

978-0-8218-4145-7

Price (tentative):

USD 99

MSC main category:

60 Probability theory and stochastic processes

Review:

This book is focused on recent results on large deviation for a general class of Markov processes obtained mostly by the authors. It is not intended for beginners and inexperienced readers and a very good mathematical background and a preliminary knowledge of Markov processes and stochastic analysis is an advantage when reading the book. The volume itself is divided into five parts. The book starts with an introduction and overview with many motivating examples and it ends with an extensive appendix containing useful results on operators, semigroups and mass transport theory. The core of the book is in the remaining three sections. Large deviations in general are treated in section 1. The exponential tightness and necessary and sufficient conditions for it are given in an analogous way as for classical tightness of measures. The rate function is introduced and the problem of identifying the rate function is studied. Section 2 gives an overview of the classical semigroup approach to large deviations of Markov processes and an alternative approach using viscosity solutions. The proofs of large deviation results need verification of a comparison principle. Since it is typically the most difficult step, a chapter in section 3 is devoted to this problem. In the rest of section 3, the comparison principle is discussed for different stochastic processes, in particular for nearly deterministic processes with almost negligible perturbation, for stochastic processes in a random environment, for occupation measures of Markov processes and, finally, for solutions of stochastic equations in infinite dimensions. Large deviations have many applications in probability and statistics, hence the book may be recommended to researchers in the field of stochastic processes and their applications or to specialists in statistics of stochastic processes.

Reviewer:

dhl

Publisher:

CNRS Editions

Year:

2007

ISBN:

978-2-271-06013-3

Price (tentative):

EUR 60

MSC main category:

01 History and biography

Review:

This book contains d’Alembert’s mathematical texts on pure mathematics written between 1740 and 1752, when he was one of the most important members of the Academy of Sciences in Paris. The book is the fourth volume of the first series of the critical edition of d’Alembert’s collected papers prepared by a group of mathematicians, historians of sciences and philosophers (directed by Christian Gilain, a specialist in the history of mathematical analysis and a professor at Université Pierre et Marie Curie, Paris). The book starts with a comprehensive introduction, where d’Alembert’s mathematical ideas, works and results are presented and their role in the development of mathematics is analysed. The next part contains three texts with the title “Recherches sur le calcul intégral” (1745, 1746, 1747) containing d’Alembert’s fundamental contributions to integral calculus (e.g. integration of algebraic functions of a real variable, integration of rational and irrational functions, the Riccati equation and its solution, the d’Alembert equation and its singular solutions, rectification of ellipse and hyperbola, methods for solution of some systems of differential equations) together with many notes and remarks. The paper “Observation sur quelques mémoires imprimés dans le volume de l’Academie 1749” (1752) contains d’Alembert’s theory of complex numbers and his contributions to the fundamental theorem of algebra, which were inspired by Euler’s works. The fifth text “Sur les logarithmes des quantités négatives” (1752) shows d’Alembert’s concept of the logarithm of negative, and complex, numbers. The sixth of d’Alembert’s published articles “Additions aux recherches sur le calcul intégral” (1752) contains some corrections and an extension of his text on integral calculus from 1747. At the end of the book, there are three appendices containing some proofs of the fundamental theorem of algebra inspired by d’Alembert’s works, a large list of references, indexes and a list of illustrations. The book can be recommended to a wide audience; it is suitable for mathematicians, historians of mathematics and science, students and teachers.

Reviewer:

mbec

Publisher:

Chapman & Hall/CRC

Year:

2007

ISBN:

978-1-58488-606-8

Price (tentative):

USD 152.96

MSC main category:

49 Calculus of variations and optimal control

Review:

This book contains 24 selected papers presented at the conference “Free and moving boundary analysis, simulation and control” held in Houston, Texas, in 2004. It includes a discussion of various concepts of how to treat moving domains and moving boundary conditions in systems described by partial differential equations (e.g. the concept of fictitious domains introduced by R. Glowinski, the concept of arbitrary Euler-Lagrange representations and a level set technique for moving geometry). Many papers in the volume also discuss various applications to other fields (algebraic problems in biomathematics, dynamical control of geometry, problems arising from continuum mechanics, stabilization of structures, three-dimensional electromagnetism, inverse problems and numerical simulation of suspensions and liquids).

Reviewer:

vs

Publisher:

Cambridge University Press

Year:

2007

ISBN:

978-0-521-70564-6

Price (tentative):

GBP 40

MSC main category:

00 General

Review:

This book has a special character. A continuation of the outstanding quality and tradition of Russian mathematical schools at home in new conditions is not at all automatic. The book offers the second volume of papers written by young mathematicians in Russia on their recent achievements. The first volume concentrated on geometry and number theory, while the second volume contains contributions in the field of algebraic geometry, topology and combinatorics. The papers form revised and expanded versions of research articles generally having the character of survey papers. The topics vary a lot; the papers are written by A. E. Guterman (matrices over semi-rings), I. V. Kazachkov (algebraic geometry over Lie algebras), A. V. Malyutin (the Markov destabilization of braids), D. V. Osipov (higher-dimensional local fields and higher adelic theory), T. E. Panov (equivariant topology of torus actions), A.M. Raigorodskii (the Borsuk partition problem), A. B. Skopenkov (embedding and knotting of manifolds) and V. V. Ten (Maxvellian and Boltzmann distributions).

Reviewer:

vs