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