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The international conference on which the book is based brought together many of the world's leading experts, with particular effort on the interaction between established scientists and emerging young promising researchers, as well as on the interaction of pure and applied mathematics. All material has been rigorously refereed. The contributions contain much material developed after the conference, continuing research and incorporating additional new results and improvements. In addition, some up-to-date surveys are included.Among the recent advances treated are new developments in- moving boundary problems- asymptotics in non-linear Volterra equations- Poincaré inequality on stratified sets- behaviour of granular matter- stochastic aspects of the Hamilton-Jacobi-Bellmann equation- very general Paley-Wiener results applied to both classical and generalized functions- Ornstein-Uhlenbeck operators- semigroup approach in economics (pricing theory)- convolution-evolution equation in aeroelasticity