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 2009; 530 pp; hardcover ISBN-10: 3-03719-056-6 ISBN-13: 978-3-03719-056-2 List Price: US$148 Member Price: US$118.40 Order Code: EMSICIAM/2007 The International Council for Industrial and Applied Mathematics (ICIAM) is the worldwide organization of societies which are dedicated primarily or significantly to applied and/or industrial mathematics. The ICIAM Congresses, held every 4 years, are run under the auspices of the Council with the aim to advance the applications of mathematics in all parts of the world. The Sixth ICIAM Congress was held in Zürich, Switzerland, July 16-20, 2007, and was attended by more than 3000 scientists from 47 countries. This volume collects the invited lectures of this Congress, the appreciations of the ICIAM Prize winners' achievements, and the Euler Lecture celebrating the 300th anniversary of Euler. The authors of these papers are leading researchers in their fields, rigorously selected by a distinguished international program committee. The book presents an overview of contemporary applications of mathematics, new perspectives, and open problems. Topics embrace analysis of and numerical methods for: linear and nonlinear partial differential equations multiscale modeling nonlinear problems involving integral operators controllability and observability asymptotic solutions of Hamilton-Jacobi equations contact problems in solid mechanics topology optimization of structures dissipation inequalities in systems theory greedy algorithms sampling in function space order-value optimization parabolic partial differential equations and deterministic games Moreover, particular applications involve risk in financial markets, radar imaging, brain dynamics, and complex geometric optics applied to acoustics and electromagnetics. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in applied and/or industrial mathematics. Table of Contents Invited Lectures G. Allaire, F. Jouve, and N. Van Goethem -- A level set method for the numerical simulation of damage evolution C. Ebenbauer, T. Raff, and F. Allgöwer -- Dissipation inequalities in systems theory: An introduction and recent results L. Caffarelli -- Some nonlinear problems involving non-local diffusions C. Canuto -- High-order methods for PDEs: Recent advances and new perspectives M. Cheney -- Radar imaging A. Cohen -- Adaptive approximations by greedy algorithms Weinan E -- Multiscale analysis of density functional theory M. Fortin, C. Robitaille, A. Fortin, and A. Rezgui -- Frictional contact in solid mechanics R. Glowinski -- Numerical methods for fully nonlinear elliptic equations H. Ishii -- Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics B. Keyfitz -- Hyperbolic conservation laws. Past and future R. Kohn and S. Serfaty -- Second-order PDE and deterministic games T. Li -- Controllability and observability: From ODEs to quasilinear hyperbolic systems J. Martínez -- Order-value optimization and new applications C. Schütte, F. Noe, E. Meerbach, P. Metzner, and C. Hartmann -- Conformation dynamics A. Beskos and A. Stuart -- MCMC methods for sampling function space I. Tsuda -- Chaotic itinerancy reality in the dynamic brain--episodic memory formation G. Uhlmann -- Visibility and invisibility J. Xu -- Optimal algorithms for discretized partial differential equations Euler Special Lecture W. Gautschi -- Leonhard Euler: His life, the man, and his works