Frontiers And Prospects Of Contemporary Applied Mathematics

This collection of articles covers the hottest topics in contemporary applied mathematics. Multiscale modeling, material computing, symplectic methods, parallel computing, mathematical biology, applied differential equations and engineering computing problems are all included. The book contains the latest results of many leading scientists and provides a window on new trends in research in the field.

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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.

This invaluable volume is a collection of articles in memory of Jacques-Louis Lions, a leading mathematician and the founder of the Contemporary French Applied Mathematics School. The contributions have been written by his friends, colleagues and students, including C Bardos, A Bensoussan, S S Chern, P G Ciarlet, R Glowinski, Gu Chaohao, B Malgrange, G Marchuk, O Pironneau, W Strauss, R Temam, etc. The book concerns many important results in analysis, geometry, numerical methods, fluid mechanics, control theory, etc. Contents:Stable and Unstable Ideal Plane Flows (C Bardos et al.)Sensitivity of Darcy's Law to Discontinuities (C Bernardi & O Pironneau)Reiterated Homogenization of Degenerate Nonlinear Elliptic Equations (J Byström et al.)On the Connection in Finsler Space (S S Chern)On the Classification of Initial Data for Nonlinear Wave Equations (C Gu)Local Exact Boundary Controllability for a Class of Quasilinear Hyperbolic Systems (T Li & B Rao)On Nonlinear Differential Galois Theory (B Malgrange)Quadrilateral Mesh (P Ming & Z Shi)On the Hyperbolic Obstacle Problem of First Order (J F Rodrigues)and other articles Readership: Graduate students and researchers in applied mathematics, numerical analysis and applied science. Keywords:Partial Differential Equation;Differential Geometry;Numerical Method;Control Theory;Fluid Dynamics;Jacques-Louis LionsKey Features:Most of the articles are by well-known mathematiciansResults presented are important to analysis and numerical methodsContains an introduction to Jacques-Louis Lions

This book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a state-of-the-art in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective. The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also presented. Applications range for the reconstruction of noisy or blurred images, pattern and face recognition, to nonlinear approximation in strongly anisotropic contexts, and to the classification tools based on multifractal analysis.

This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

This book provides a systematic introduction to the fundamental methods and techniques and the frontiers of ? along with many new ideas and results on ? infectious disease modeling, parameter estimation and transmission dynamics. It provides complementary approaches, from deterministic to statistical to network modeling; and it seeks viewpoints of the same issues from different angles, from mathematical modeling to statistical analysis to computer simulations and finally to concrete applications.