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 mat

On the occasion that the Officers' Meeting and the Board Meeting ofICIAM (International Council for Industrial and Applied Mathematics)was held in Shanghai from May 26 to May 27, 2006, many famous in-dustrial and applied mathematicians gathered in Shanghai from differentcountries. The Shanghai Forum on Industrial and Applied Mathemat-ics was organized from May 25 to May 26, 2006 at Shanghai ScienceHall for the purpose of inviting some of them to present their recentresults and discuss recent trends in industrial and applied mathematics.Sixteen invited lectures have been given for this activity. This volumecollects the material covered by most of these lectures. It will be veryuseful for graduate students and researchers in industrial and appliedmathematics.

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
……

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.