Landa, P.S., Moscow State University, Moscow, Russia
Regular and Chaotic Oscillations
2001. Approx. 400 pp. Hardcover
3-540-41001-5
In this book the modern theory of both regular and chaotic nonlinear oscillations is set out,
primarily, as applied to mechanical problems. The material is presented in a nontraditional manner
with emphasis on the new results of the theory obtained partially by the author, who is one of the
leading experts in the area. Among the up-to-date topics are synchronization and chaotization of
self-oscillatory systems and the influence of weak random vibrations on the modification of
characteristics and behavior of nonlinear systems. One of the purposes of the book is to enable
readers to gain a thorough understanding of this theory and to show that it can be very useful in
engineering investigations. The primary audience for this book is researchers working with different
oscillatory processes and students interested in a thorough study of the general laws and
applications of the theory of nonlinear oscillations.
Keywords: Mechanics
Contents: Introduction.- The main analytical methods of studies of nonlinear oscillations in
near-conservative systems.- General properties of autonomous dynamical systems.- Examples of
natural oscillations in systems with one degree of freedom.- Natural oscillations in systems with
many degrees of freedom. Normal oscillations.- Self-oscillatory systems with one degree of
freedom.- Self-oscillatory systems with one and a half degrees of freedom.- Examples of
self-oscillatory systems with two and more degrees of freedom.- Synchronization and chaotization
of self-oscillatory systems by an external harmonic force.- Interaction of two self-oscillatory
systems. Synchronization and chaotization of self-oscillations.- Interaction of three and more
self-oscillatory systems.- Oscillations of nonlinear systems excited by external periodic forces.-
Parametrical excitation of oscillations.- Changes in the dynamical behavior of nonlinear systems
induced by high-frequency vibration or by noise.
Foundations of Engineering Mechanics.Series:
Salinas, S., University of Sao Paolo, Brazil
Introduction to Statistical Physics
2001. Approx. 425 pp. 67 figs. Hardcover
0-387-95119-9
Intended for beginning graduate students or advanced undergraduates, this text covers the
statistical basis of equilibrium thermodynamics, both classical and quantum, including examples
from solid-state physics. It also treats some topics of more recent interest such as phase
transitions and non-equilibrium phenomena. The approach to equilibrium statistical mechanics is
based on the Gibbs microcanonical ensemble. The presentation introduces modern ideas, such as
the thermodynamic limit and the equivalence of ensembles, and uses simple models (ideal gas,
Einstein solid, ideal paramagnet) to make the mathematical ideas clear. Frequently used
mathematical methods are reviewed in an appendix. The book begins with a review of statistical
methods and classical thermodynamics, making it suitable for students from a variety of
backgrounds. Classical thermodynamics is treated in the in the context of the classical ideal gas
and the canonical and grand canonical ensembles. The discussion of quantum statistical
mechanics includes Bose and Fermi gases. the Bose-Einstein condensation, phonons and
magnons. Phase transitions are first treated classically (using the van der Waals and Curie-Weiss
phenomenological models as examples), and then quantum mechanically (the Ising model, scaling
theory and renormalization). The book concludes with two chapters on nonequilibrium phenomena:
one using Boltzmann's approach, the other based on stochastic models. Exercises at the end of
each chapter are an integral part of the course, clarifying and extending topics discussed in the
text. Hints and solutions can be found on the author's web site.
Contents: (1) Introduction to statistical methods.- (2) Statistical description of a physical system.-
(3) Overview of classical thermodynamics.- (4) Microcanonical ensemble.- (5) Canonical ensemble.-
(6) The classical gas in the canonical formalism.- (7) The grand canonical and pressure
ensembles.- (8) The ideal quantum gas.- (9) The ideal Fermi gas.- (10) Free bosons: Bose-Einstein
condensations; Gas of photons.- (11) Phonons and magnons.- (12) Phase transitions and critical
phenomena: classical theories.- (13) The Ising model.- (14) Scaling theories and the
renormalization group.- (15) Non-equilibrium phenomena. I. Kinetic methods.- (16) Non-equilibrium
phenomena. II. Stochastic methods.
Graduate Texts in Contemporary Physics.Series:
Wieczorek, M., SQS Software Quality Systems AG, Koln, Germany
Meyerhoff, D., SQS Software Quality Systems AG, Koln, Germany
(Eds.)Software Quality
State of the Art in Management, Testing, and Tools
2001. XIV, 287 pp. 99 figs. 17 tabs. Softcover
3-540-41441-X
This book compiles current trends in software quality management and testing. Selected
practitioners, experts and researchers contribute articles that provide both overviews over important topics as well as practical experience and insights from software development projects in industry.
The topics include knowledge management QA and testing in the areas of webAbased applications
and railway/safety critical systems, cost effectiveness of quality management systems, test
process improvement, testing of non-functional requirements and test tool trends.
Keywords: Software testing, certification, E-business, embedded systems, software quality
management, knowledge management, safety critical systems, software development methods,
WWW, Internet .
Contents: Preface.- List of Contributors.- Software Quality Management.- Pradigms of Software
Quality Management and Software Development.- Process Oriented Software Quality
Management.- Knowledge and Quality Management.- Cost Benefit Models for Quality Assurance.-
Certification and Testing.- Testing Functional and Non-Functional Requirements.- Testing Web and
E-Business Applications.- Certification and Testing of Embedded and Safety-Critical Systems.-
Tools.
Deutsch, F.R., Pennsylvania State University, University Park, PA, USA
Best Approximation in Inner Product Spaces
2001. Approx. 350 pp. 25 figs. Hardcover
0-387-95156-3
This is the first systematic study of best approximation theory in inner product spaces and, in
particular, in Hilbert space. Geometric considerations play a prominent role in developing and
understanding the theory. The only prerequisites for reading the book is some knowledge of
advanced calculus and linear algebra. Throughout the book, examples and applications have been
interspersed with the theory. Each chapter concludes with numerous exercises and a section in
which the author puts the results of that chapter into a historical perspective. The book is based on
lecture notes for a graduate course on best approximation which the author has taught for over 25
years.
Keywords: MSC : 46-XX, 41-XX
Contents: Inner Product Spaces.- Best Approximation.- Existence and Uniqueness of Best
Approximations.- Characterization of Best Approximations.- The Metric Projection.- Bounded Linear Functionals and Best Approximation from Hyperplanes and Half-spaces.- Error of Approximation.- Generalized Solutions of Linear Equations.- The Method of Alternating Projections.- Constrained Interpolation from a Convex Set.- Interpolation and Approximation.- Convexity of Chebyshev Sets.
CMS Books in Mathematics.VOL. 7
Postnikov, M.M., MIRAN, Moscow, Russia
Geometry VI
Riemannian Geometry
2001. XVI, 504 pp. Hardcover
3-540-41108-9
This book treats that part of Riemannian geometry related to more classical topics in a very
original, clear and solid style. Before going to Riemannian geometry, the author presents a more
general theory of manifolds with a linear connection. Having in mind different generalizations of
Riemannian manifolds, it is clearly stressed which notions and theorems belong to Riemannian
geometry and which of them are of a more general nature. Much attention is paid to transformation groups of smooth manifolds. Throughout the book, different aspects of symmetric spaces are treated. The author successfully combines the co-ordinate and invariant approaches to differential geometry, which give the reader tools for practical calculations as well as a theoretical understanding of the subject. The book contains a very useful large Appendix on foundations of differentiable manifolds and basic structures on them which makes it self-contained and practically independent from other sources.
Keywords: Riemannian geometry, connections, symmetric spaces, Lie groups
Contents: Preface.- 1. Affine Connections.- 2. Covariant Differentiation. Curvature.- 3. Affine
Mappings. Submanifolds.- 4. Structural Equations. Local Symmetries.- 5. Symmetric Spaces.- 6.
Connections on Lie Groups.- 7.- 8. Affine Fields and Related Topics.- 9. Cartan Theorem.- 10.
Palais and Kobayashi Theorems.- 11. Lagrangians in Riemannian Spaces.- 12. Metric Properties of
Geodesics.- 13. Harmonic Functionals and Related Topics.- 14. Minimal Surfaces.- 15. Curvature in
Riemannian Space.- 16. Gaussian Curvature.- 17. Some Special Tensors.- 18. Surfaces with
Conformal Structure.- 19. Mappings and Submanifolds I.- 20. Submanifolds II.- 21. Fundamental
Forms of a Hypersurface.- 22. Spaces of Constant Curvature.- 23. Space Forms.- 24.
Four-Dimensional Manifolds.- 25. Metrics on a Lie Group I.- 26. Metrics on a Lie Group II.- 27.
Jacobi Theory.- 28./29. Some Additional Theorems I and II.- Addendum (Chaps.30-36).
For complete Contents see our catalogue at
http://www.springer.de/math/
Encyclopaedia of Mathematical Sciences.VOL. 91