This volume collects the material covered by most of these lectures. It will be very useful for graduate students and researchers in industrial and applied mathematics.The purpose of inviting some of them to present their recent results and discuss recent trends in industrial and applied mathematics.Sixteen invited lectures have been given for this activity.

The Shanghai Forum on Industrial and Applied Mathematics was organized in May 2006 on the occasion that many famous industrial and applied mathematicians gathered in Shanghai from different countries to participate in the Officers' Meeting and the Board Meeting of the ICIAM (International Council for Industrial and Applied Mathematics). This volume collects the material covered by the majority of the lectures of which reflects panoramically recent results and trends in industrial and applied mathematics. This book will be very useful for graduate students and researchers in industrial and applied mathematics.

Preface

Samir Adly, Daniel Goeleven, Michel Thera: A Continuation Method

for a Class of Periodic Evolution Variational Inequalities

GStz Alefeld: Complementarity Problems: An Overview on

Existing Verification Procedures

Fernando Antoneli, Ana Paula S. Diets, Martin Golubitsky, Yunjiao

Wang: Synchrony in Lattice Differential Equations

Alam Damlamian: The Periodic Unfolding Method for Quasi-convex

Functionals

Iain S. Duff. Sparse System Solution and the HSL Library

Heinz W. Engl, Gerald Goekler, Andrea Schatz, Helmut Zeisel:

Modelling and Numerics for the Transient Simulation of

the Blast Furnace Process

Loredana Faienza, Antonio Fasano, Mario Primicerio:

Gelification of Hydrocarbons: A Model Problem

Nguyen Van Huu, Vuong Quan Hoang:. On the Martingale

Representation Theorem and on Approximate

Hedging a Contingent Claim in the Minimum

Deviation Square Criterion

Roll Jeltsch, Manuel Torrilhon: Flexible Stability Domains for

Explicit Runge-Kutta Methods

Taketorno Mitsui, Yoshihiro Saito: MS-Stability Analysis for

Numerical Solutions of Stochastic Differential Equations--Beyond Single-step Single Dim——

R. D. Russell, J. F. Williams, X. Xu: A Comparison of

Direct Discretization of 4th Order Problems

Versus System Reduction

Ya-xiang Yuan: Subspace Techniques for Nonlinear Optimization