Gutierrez,C.

The Monge-Ampere Equation and Related Topics.

Apr. 2001 152 pp.
3-7643-4177-7


The classical Monge-Ampere equation has been the center of considerable interest in recent years because of its role in several areas of applied mathematics. This text reflects these developments, stressing the geometric aspects of the theory as well as its applications to optimization in particular. The exposition is self-contained, with complete proofs given for all theorems. Key features of the book include open problems, examples, illustrations, comprehensive bibliographical references, and an index. A concise and useful book for graduate students and researchers in nonlinear equations.

Kubrusly,C.

Elements of Operator Theory.

Feb. 2001 552 pp.
3-7643-4174-2

Written in a user-friendly, motivating style, this book presents the fundamental topics of operator theory in a systematic fashion, i. e., set theory, algebraic structures, topological structures, Banach spaces, Hilbert Spaces, culminating with the Spectral Theorem. Aimed at a new generation of researchers and graduate students in the field, the exposition is concept-driven and as much as possible avoids the formula-computational approach. Each chapter is self-contained with required background material included. The text contains 500 rigorous proofs, many of them new, specially tailored to the presentation. More than 100 examples and, in several cases, interesting counterexamples that demonstrate the frontiers of an important theorem are presented, and over 300 problems, many with hints, are introduced. Both the problems and examples underscore further auxiliary results and extensions of the main theory. In this non-traditional framework, the reader is challenged and has a chance to prove the principal theorems anew.

Picardello,M.(ed.)

Harminic Analysis and Integral Geometry.

2000 206 pp.
1-58488-183-6

Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lectures and coordinated courses on specific research topics within this fast growing subject. Harmonic Analysis and Integral Geometry presents important recent advances in the fields of Radon transforms, integral geometry, and harmonic analysis on Lie groups and symmetric spaces. Several articles are devoted to the new theory of Radon transforms on trees. With its related presentations addressing recent developments in various aspects of these intriguing areas of study, Harmonic Analysis and Integral Geometry becomes an important addition not only to the Research Notes in Mathematics series, but to the general mathematics literature.

Sprent,P./Smeeton,N.

Applied Nonparametric Statistical Methods, 3rd ed.

2000 480 pp.
1-58488-145-3

This new edition follows the basic easy-to-digest pattern that was so well received by users of the earlier editions. The authors substantially update and expand Applied Nonparametric Statistical Methods to reflect changing attitudes towards applied statistics, new developments, and the impact of more widely available and better statistical software. The book takes into account computing developments since the publication of the popular Second Edition, rearranging the material in a more logical order, and introducing new topics. It emphasizes better use of significance tests and focuses greater attention on medical and dental applications. Applied Nonparametric Statistical Methods: Third Edition explains the rationale of procedures with a minimum of mathematical detail, making it an excellent up-to-date reference for professionals who do their own statistical analyses. New in the Third Edition: o Expanded coverage of topics - such as ethical considerations and calculation of power and of sample sizes needed o Refers to a wide variety of statistical packages - such as StatXact, Minitab, Testimate, S-plus, Stata, and SPSS o Includes sections on the analysis of angular data, the use of capture-recapture methods, the measurement of agreement between observers, runs tests, and regression diagnostics.

Bagchi,B.K.

Supersymmetry in Quantum and Classical Mechanics.

(Pitman Monographs & Surveys in Pure & Applied Mathematics,vol.116)
2000 222 pp.
1-58488-197-6

Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research. In recent years, progress in this field has been dramatic and the literature continues to grow. Until now, no book has offered an overview of the subject with enough detail to allow readers to become rapidly familiar with its key ideas and methods. Supersymmetry in Classical and Quantum Mechanics offers that overview and summarizes the major developments of the last 15 years. It provides both an up-to-date review of the literature and a detailed exposition of the underlying SCQM principles. For those just beginning in the field, the author presents step-by-step details of most of the computations. For more experienced readers, the treatment includes systematic analyses of more advanced topics, such as quasi- and conditional solvability and the role of supersymmetry in nonlinear systems.

Lele,S./Richtsmeier,J.

An Invariant Approach to the Statistical Analysis of Shapes.

2000 200pp
0-8493-0319-2

Natural scientists perceive and classify organisms primarily on the basis of their appearance and structure- their form , defined as that characteristic remaining invariant after translation, rotation, and possibly reflection of the object. The quantitative study of form and form change comprises the field of morphometrics. For morphometrics to succeed, it needs techniques that not only satisfy mathematical and statistical rigor but also attend to the scientific issues. An Invariant Approach to the Statistical Analysis of Shapes results from a long and fruitful collaboration between a mathematical statistician and a biologist. Together they have developed a methodology that addresses the importance of scientific relevance, biological variability, and invariance of the statistical and scientific inferences with respect to the arbitrary choice of the coordinate system. They present the history and foundations of morphometrics, discuss the various kinds of data used in the analysis of form, and provide justification for choosing landmark coordinates as a preferred data type. They describe the statistical models used to represent intra-population variability of landmark data and show that arbitrary translation, rotation, and reflection of the objects introduce infinitely many nuisance parameters. The most fundamental part of morphometrics-comparison of forms-receives in-depth treatment, as does the study of growth and growth patterns, classification, clustering, and asymmetry. Morphometrics has only recently begun to consider the invariance principle and its implications for the study of biological form.

Mhaskar,H./Pai,D.

Fundamentals of Approximation Theory.

2000 544 pp.
0-8493-0939-5

The subject of approximation theory plays an increasingly important role in applications to many branches of applied sciences and engineering. Written in the span of almost a decade, Fundamentals of Approximation Theory serves as both an introductory text as well as an advanced review of the field. The first five chapters give the reader the core information to begin research in this domain. The next three chapters devote attention to special topics, exposing the reader to complex analytic methods and techniques of functional analysis. The authors emphasize the connections between different branches of analysis with approximation theory - between the 'classical' and the 'abstract.' They also include noteworthy features such as K-functionals, Hermite-Birkhoff interpolation, Lagrange-Hermite-Fejev-type interpolation, and complex methods in the treatment of Fourier series.