Ikeda, K., Tohoku University, Sendai, Japan; Murota, K., University of Kyoto, Japan

Imperfect Bifurcation in Structures and Materials
Engineering Use of Group-theoretic Bifurcation Theory

2002. Approx. 425 pp. 194 figs. Hardcover
0-387-95409-0

This book provides modern investigation into the bifurcation phenomena of physical and structural problems. Systematic methods --based on asymptotic, stochastic, and group-theoretic standpoints-- are used to examine experimental and computational data from numerous examples (soil, sand, kaolin, concrete, domes, etc.). Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory. For mathematicians, static bifurcation theory for finite dimensional systems, as well as its implications for practical problems, is illuminated by the numerous examples.

Keywords: Bifurcation phenomena, Static bifurcation theory, Group-theoretic bifurcation theory, Bifurcation theory

Contents: Introduction to Bifurcation Behavior.- Critical Point and Local Behavior.- Imperfection Sensitivity Laws.- Critical Initial Imperfections (I).- Stochasticity of Initial Imperfections (I).- Experimentally-observed Bifurcation Diagrams.- Group-theoretic Bifurcation Theory.- Bifurcation Behavior of Dn-equivariant Systems.- Critical Initial Imperfections (II).- Stochasticity of Initial Imperfections (II).- Description of Bifurcation Behaviors.- Bifurcation of Cylindrical Sand Specimens.- Echelon-mode Formation.- Bifurcation of Steel Specimens.- Miscellaneous Aspects of Bifurcation Phenomena.- References.- Index.

Series: Applied Mathematical Sciences. VOL. 149

Skorokhod, A.V., Michigan State University, East Lansing, MI, USA;
Hoppensteadt, F.C., Arizona State University, Tempe, AZ, USA;
Salehi, H.D., Michigan State University, East Lansing, MI, USA

Random Perturbation Methods with Applications
in Science and Engineering

2002. Approx. 500 pp. 31 figs. Hardcover
0-387-95427-9

This book covers the impact of noise on models that are widely used in science and engineering applications. It applies perturbed methods which assume noise changes on a faster time or space scale than the system being studied. The book is written in two parts. The first part presents a careful development of mathematical methods needed to study random perturbations of dynamical systems. The second part presents non-random problems in a variety of important applications. Such problems are reformulated to account for both external and system random noise. Finally, the results from Part I are applied to analyze, simulate, and visualize the same problems now perturbed by noise. Applications from mechanical, electrical, and biological problems are discussed. In addition, numerous computer simulations and examples are included. Researchers and graduate students in mathematics and engineering will find this book useful.

Keywords: Dynamical systems, Random dynamical systems, Probability theory, Stochastic processes, Random pertubation method, Random pertubation, Pertubation

Contents: Introduction.- Ergodic Theorems.- Convergence Properties of Stochastic Processes.- Averaging.- Normal Deviation.- Diffusion Approximation.- Stability.- Markov Chains with Random Transition Probabilities.- Randomly Perturbed Mechanical Systems.- Dynamical Systems on a Torus.- The Phase Locked Loop.- Models in Population Biology.- Genetics.- Appendices.- Index.

Series: Applied Mathematical Sciences. VOL. 150

Toutenburg, H., University of Munich, Germany

Statistical Analysis of Designed Experiments, 2nd ed.

2002. Approx. 530 pp. Hardcover
0-387-98789-4

The book is unique in the sense that it starts off with relatively simple statistical concepts and ideas found in most introductory statistical textbooks and afterwards, it proceeds to cover more and more materials useful for undergraduates and graduate students in statistics and biostatistics.

Contents: Introduction.- Comparison of Two Samples.- The Linear Regression Model.- Single-Factor Experiments with Fixed and Random Effects.- More Restrictive Designs.- Multifactor Experiments.- Repeated Measures Model.- Cross-Over Design.- Statistical Analysis of Incomplete Data.- Models for Categorical Response.

Series: Springer Texts in Statistics.

Bluman, G., The University of British Columbia, Vancouver, BC, Canada;
Anco, S., The University of British Columbia, Vancouver, BC, Canada

Symmetry and Integration Methods for Differential Equations, 2nd ed.

2002. Approx. 425 pp. 17 figs. Hardcover
0-387-98654-5

This book provides a comprehensive treatment of symmetry methods and dimensional analysis. The authors discuss aspects of Lie groups of point transformations, contact symmetries, and higher order symmetries that are essential for solving differential equations. Emphasis is given to an algorithmic, computational approach to finding integrating factors and first integrals. Numerous examples including ordinary differential equations arising in applied mathematics are used for illustration and exercise sets are included throughout the text.
This book is designed for advanced undergraduate or beginning graduate students of mathematics and physics, as well as researchers in mathematics, physics, and engineering.

Keywords: Differential Equations, Lie Groups, Symmetry Methods

Contents: Preface.- Introduction.- Dimensional Analysis, Modelling, and Invariance.- Lie Groups of Transformations and Infinitesimal Transformations.- Ordinary Differential Equations.- Partial Differential Equations.- Noether's Theorem and Lie-B cklund Symmetries.- Construction of Mappings Relating Differential Equations.- Potential Symmetries.- References.- Author Index.- Subject Index.

Series: Applied Mathematical Sciences. VOL. 81