Ganzha, V.G., Technische Universitat Munchen, Germany
Mayr, E.W., Technische Universitat Munchen, Germany
Vorozhtsov, E.V., Russian Academy of Sciences, Novosibirsk, Russia
(Eds.)
Computer Algebra in Scientific Computing CASC 2000
Proceedings of the Third Workshop on Computer Algebra in Scientific Computing,
Samarkand, October 5-9, 2000
2000. XI, 439 pp.
3-540-41040-6
The book covers various topics of computer algebra methods, algorithms and software applied to scientific
computing. One of the important topics of the book is the application of computer algebra methods for the
development of new efficient analytic and numerical solvers, both for ordinary and partial differential
equations. A specific feature of the book is a detailed analysis of the advanced software systems like
Mathematica, Maple etc. from the viewpoint of their applicability for the solution of scientific computing
problems. The book will be useful for researchers and engineers who apply the advanced computer algebra
methods for the solution of their tasks.
Keywords: computer algebra, scientific computing
Pressley, A., King's College, London, UK
Elementary Differential Geometry
2000. X, 334 pp. 185 figs.
1-85233-152-6
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about
them are natural and easily understood. Differential geometry is concerned with the precise mathematical
formulation of some of these questions, and with trying to answer them using calculus techniques. It is a
subject that contains some of the most beautiful and profound results in mathematics, yet many of them are
accessible to higher level undergraduates.
Elementary Differential Geometry presents the main results in the differential geometry of curves and
surfaces while keeping the prerequisites to an absolute minimum. Nothing more than first courses in linear
algebra and multivariate calculus are required, and the most direct and straightforward approach is used at
all times. Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces
discussed there.
Contents: 1. Curves in the Plane and in Space.- 2. How much does a Curve Curve?- 3. Global Properties of
Curves.- 4. Surfaces in Three Dimensions.- 5. The First Fundamental Form.- 6. Curvature of Surfaces.- 7.
Gaussian Curvature and the Gauss Map.- 8. Geodesics.- 9. Minimal Surfaces.- 10. Gauss's Theorema
Egregium.- 11. The Gauss-Bonnet Theorem.- Solutions.- Index.
Series: Springer Undergraduate Mathematics Series.
Jones, C.K.R.T., Brown University, Providence, RI, USA
Khibnik, A., United Technologies Research Center, East Hartford, CT, USA
(Eds.)
Multiple-Time-Scale Dynamical Systems
2000. Approx. 290 pp. 76 figs.
0-387-95126-1
Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical
reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers
that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed
geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in
higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations
implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and
jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role
in the development of these techniques and one paper is directed specifically at applying geometric
singular perturbation theory to reveal the synchrony in networks of neural oscillators.
Contents: Homoclinic orbits to invariant Tori in Hamiltonian systems.- Geometric singular perturbation
theory beyond normal hyperbolicity.- A primer on the exchange lemma for fast-slow systems.- Geometric
analysis of the singularly perturbed planar fold.- Multiple time scales and canards in a chemical oscillator.-
A geometric method for periodic orbits in singularly-perturbed systems.- The phenomenon of delayed
bifurcation and its analyses.- Synchrony in networks of neuronal oscillators.- Metastable dynamics and
asymptotics in multi-dimensional domains.
Series: The IMA Volumes in Mathematics and its Applications.VOL. 122
Moallem, M., University of Western Ontario, London, Ont., Canada
Patel, R.V., University of Western Ontario, London, Ont., Canada
Khorasani, K., Concordia University, Montreal, Que., Canada
Flexible-link Robot Manipulators
Control Techniques and Structural Design
2000. XI, 159 pp. 40 figs.
1-85233-333-2
This monograph is concerned with the development and implementation of nonlinear mathematical
techniques for feedback control and shape design of robot manipulators whose links have considerable
structural flexibility. Several nonlinear control and observation techniques are studied and implemented by
simulations and experiments in a laboratory setup. These techniques include integral manifolds in singular
perturbation theory, nonlinear input-output decoupling, nonlinear observers and sliding control.
The study of dynamic properties and control techniques for flexible-link manipulators can also be a
framework for designing the mechanical shape and material of these systems such that improved properties
can be achieved in order to facilitate the control problem. Therefore, structural shape optimization is
considered as a means of improving the dynamic behaviour of flexible-link manipulators.
Contents: Introduction.- Tracking Control by Integral Manifolds.- Decoupling Control.- Observer-based
Decoupling Control.- Inverse Dynamics Sliding Control.- Optimum Structure Design for Control.-
Concluding Remarks.- Stability Proofs.- Kinematic Description.- Dynamic Models.
Series: Lecture Notes in Control and Information Sciences.VOL. 257
Milman, V.D., University of Tel Aviv, Israel
Schechtman, G., Weizmann Institute of Science, Rehovot, Israel
(Eds.)
Geometric Aspects of Functional Analysis
Israel Seminar (GAFA) 1996-2000
2000. VIII, 289 pp.
3-540-41070-8
This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only
reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the
recent new trends in Banach Space Theory and related topics. These include the tighter connection with
convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric,
and the treatment of bodies which have only very weak convex-like structure. Another topic represented
here is the use of new probabilistic tools; in particular transportation of measure methods and new
inequalities emerging from PoincarElike inequalities.
Keywords: local theory of Banach spaces, asymptotic geometric analysis, convexity . Mathematics Subject
Classification : 46-06, 52-06, 60-06
Contents: M. Anttila, The Transportation Cost for the Cube.-J. Arias-de-Reyna, R. Villa, The Uniform
Concentration of Measure Phenomenon in l p^n.- G. Schechtman, An Editorial Comment on the Preceding
Paper.- K. Ball, A Remark on the Slicing Problem.- S.G. Bobkov, Remarks on the Growth of L^p-norms of
Polynomials.- J. Bourgain, Positive Lyapounov Exponents for Most Energies.- J. Bourgain, S. Jitomirskaya,
Anderson Localization for the Band Model.- A.A. Giannopoulos, V.D. Milman, M. Rudelson, Convex
Bodies with Minimal Mean Width.- O. Guion, A.E. Litvak, Euclidean Projections of a p-convex Body.- B.
Klartag, Remarks on Minkowski Symmetrizations.- A. Koldobsky, M. Lifshits, Average Volume of Sections
of Star Bodies.- R. Latala, K. Oleszkiewicz, Between Sobolev and PoincarE A.E. Litvak, N.
Tomczak-Jaegermann, Random Aspects of High-dimensional Convex Bodies.- V.D. Milman, S.J. Szarek, A
Geometric Lemma and Duality of Entropy Numbers.- V.D. Milman, N. Tomczak-Jaegermann, Stabilized
Asymptotic Structures and Envelopes in Banach Spaces.- G. Paouris, On the Isotropic Constant of
Non-symmetric Convex Bodies.- G. Schechtman, J. Zinn, Concentration on the l p^n Ball.- S.J. Szarek, D.
Voiculescu, Shannon's Entropy Power Inequality via Restricted Minkowski Sums.- R. Wagner, Notes on an
Inequality by Pisier for Functions on the Discrete Cube.- A. Zvavitch, More on Embedding Subspaces of L
p into l^N p<p<1. , 0<p<1.- Seminar Talks (with related Workshop and Conference Talks)
Series: Lecture Notes in Mathematics.VOL. 1745
Degtyarev, A., Bilkent University, Ankara, Turkey
Itenberg, I., Institut de Recherche Mathematiques de Rennes (CNRS), France
Kharlamov, V., Universite Louis Pasteur et IRMA (CNRS), Strasbourg, France
Real Enriques Surfaces
2000. XV, 259 pp.
3-540-41088-0
This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up
to deformation. Simple explicit topological invariants are elaborated for identifying the deformation classes
of real Enriques surfaces. Some of theses are new and can be applied to other classes of surfaces or
higher-dimensional varieties. Intended for researchers and graduate students in real algebraic geometry it
may also interest others who want to become familiar with the field and its techniques. The study relies on
topology of involutions, arithmetics of integral quadratic forms, algebraic geometry of surfaces, and the
hyperkahler structure of K3-surfaces. A comprehensive summary of the necessary results and techniques
from each of these fields is included. Some results are developed further, e.g., a detailed study of lattices
with a pair of commuting involutions and a certain class of rational complex surfaces.
Keywords: Enriques surfaces, real algebraic surfaces, deformation of surfaces, hyperkahler structure,
topology of real algebraic varieties . Mathematics Subject Classification : 14P25, 14J28, 14J15, 15J50, 14J80,
57S17, 58D27
Contents: Part I. Tools.- Topology of involutions.- Integral lattices and quadratic forms.- Algebraic
surfaces.- Real surfaces: the topological aspects. Part II. Enriques surfaces.- Deformation classes.-
Topology of real Enriques surfaces.- Moduli of real Enriques surfaces.- Deformation types: the hyperbolic
and parabolic cases.- Deformation types: the elliptic and parabolic cases.- Appendix A: Beginner's manual
on the moduli of real curves and surfaces.- Appendix B: Horikawa models.- Appendix C: Determination of
real Enriques surfaces.- Appendix D: A few by-products.
Series: Lecture Notes in Mathematics.VOL. 1746