Burkard, R., University of Graz, Austria /Deuflhard, P., Konrad-Zuse-Zentrum, Berlin, Germany
Jameson, A., University of Stanford, CA, USA/ Strang, G., M IT, Cambridge, MA, USA
Lions, J.-L., College de France, Paris, France /Capasso, V., University of Milan, Italy
Engl, H., Johannes Kepler Universitat Linz, Austria /Periaux, J., Dassault Aviation, Saint Cloud, France
(Eds.)

Computational Mathematics Driven by Industrial Problems

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo
(C.I.M.E.) held in Martina, Franca, Italy, June 21-27, 1999

2000. VI, 418 pp.
3-540-67782-8

These lecture notes by very authoritative scientists survey recent advances of mathematics driven by
industrial application showing not only how mathematics is applied to industry but also how mathematics
has drawn benefit from interaction with real-word problems.
The famous David Report underlines that innovative high technology depends crucially for its
development on innovation in mathematics. The speakers include three recent presidents of ECMI, one of
ECCOMAS (in Europe) and the president of SIAM.

Keywords: Computational mathematics, inverse problems, optimization, control, stochastics . Mathemtics
Subject Classification : 65-XX, 49-XX

Contents: R.E. Burkhard, Trees and Paths: Graph Optimisation Problems with Industrial Applications. V.
Capasso, Mathematical Models for Polymer Crystallization Processes. P. Deuflhard, Differential Equations
in Technology and Medicine: Computational Concepts, Adaptive Algorithms, and Virtual Labs. H.W. Engl,
Inverse Problems and Their Regularization. A. Jameson and L. Matinelli, Aerodynamic Shape Optimization
Techniques Based on Control Theory. J.L. Lions, Complexity in Industrial Problems - Some Remarks. K.
Laevksy, B.J. van der Linden, R.M.M. Mattheij, Flow and Heat Transfer in Pressing of Glass Products. J.-W.
He, M. Chevalier, R. Glowinski, R. Metcalfe, A. Nordlander, J. Periaux, Drag Reduction by Active Control for
Flow Past Cylinders. G. Strang, Signal Processing for Everyone.

Series: Lecture Notes in Mathematics.VOL. 1739

Nikolaev, I.,
The Fields Institute for Research in Mathematical Sciences, Toronto, Ont., Canada

Foliations on Surfaces

2000. XXII, 450 pp. 123 figs.
3-540-67524-8

Foliations is one of the major concepts of modern geometry and topology meaning a partition of topological
space into a disjoint sum of leaves. This book is devoted to geometry and topology of surface foliations
and their links to ergodic theory, dynamical systems, complex analysis, differential and noncommutative
geometry. This comprehensive book addresses graduate students and researchers and will serve as a
reference book for experts in the field.

Keywords: Foliations, Riemann Surfaces, Geodesics, Teichm・ler Space, Noncommutative Geometry MSC
Classification ( 1991 ): Primary : 57R, 58F Secondary : 05C, 28F, 30E, 34C, 46L

Contents: Foliations on 2-Manifolds.- General Theory.- Local Theory. Morse-Smale Foliations. Foliations
Without Holonomy. Invariants of Foliations. Curves on Surfaces. Non-compact Surfaces.- Applications.-
Ergodic Theory. Homeomorphisms of the Unit Circle. Diffeomorphisms of Surfaces. C*-Algebras. Quadratic
Differentials. Flat Structures. Principal Curvature Lines. Differential Equations. Positive Differential 2-forms.
Control Theory (by B. Piccoli).- Appendix.- Riemann Surfaces.

Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in
Mathematics.VOL. 41

Lombardi, E., Institut Non Lineaire de Nice, Valbonne, France

Oscillatory Integrals and Phenomena Beyond all Algebraic Orders
with Applications to Homoclinic Orbits in Reversible Systems

MSC (2000): 34C23, 34C37

2000. XV, 413 pp.
3-540-67785-2

During the last two decades, in several branches of science (water waves, crystal growth, travelling waves
in one dimensional lattices, splitting of separatrices,...) different problems appeared in which the key point is
the computation of exponentially small terms. This self-contained monograph gives new and rigorous
mathematical tools which enable a systematic study of such problems. Starting with elementary illuminating
examples, the book contains (i) new asymptotical tools for obtaining exponentially small equivalents of
oscillatory integrals involving solutions of nonlinear differential equations; (ii) implementation of these
tools for solving old open problems of bifurcation theory such as existence of homoclinic connections near
resonances in reversible systems.

Keywords: Oscillatory integrals, exponential equivalents, homoclinic connections, reversible systems

Contents: Introduction. I: Toolbox for oscillatory integrals. Expotential tools for evaluating oscillatory
integrals.- II: Toolbox for reversible sytems studied near resonances. Resonances of reversible vector fields.
Analytic description of periodic orbits bifurcating from a pair of simple purely imaginary eigenvalues.
Constructive Floquet Theory for Periodic Matrices near a constant one. Inversion of affine equations
around reversible homoclinic connections.- III: Applications to homoclinic orbits near resonances in
reversible systems. The 02+iw resonance. The 02+iw resonance in infinite dimensions. Application to water
waves. The (iw0)2iw1 resonance.

Series: Lecture Notes in Mathematics.VOL. 1741

John von Newmann
With a foreword by Paul M. Churchland and Patricia S. Churchland

THE COMPUTER AND THE BRAIN,
SECOND EDITION

2000 Physical Science
112 pp. 5 x 7 3/4
Paper ISBN 0-300-08473-0

This book represents the views of one of the greatest mathematicians of the twentieth century on the analogies between computing machines and the living human brain. John von Neumann concludes that the brain operates in part digitally, in part analogically, but uses a peculiar statistical language unlike that employed in the operation of man-made computers. This edition includes a new foreword by two eminent figures in the fields of philosophy, neuroscience, and consciousness.

"This innocent-looking little book lies at the eye of a hurricane. It represents a locus of clarity and calm at the center of a vast vortex of powerful arguments and competing research programs.
And it is all the more singular for having been written . . . at the very beginning of the recent explosion in electronic computer technology."--Paul and Patricia Churchland, from the foreword

From reviews of the first edition:

"Highly original and intensely stimulating."--S. Ulam, Scientific American

"An outstanding example of J. von Neumann's insight, brilliance and clarity." --Mathematical Reviews

At the time of his death in February 1957, John von Neumann, renowned for his theory of games and his work at the Electronic Computer Project at the Institute for Advanced Study, was serving as a member of the Atomic Energy Commission. Paul M. and Patricia S. Churchland are professors of philosophy at the
University of California, San Diego.