Joachim Rosenthal - Böcker

Mark Alber, Bei Hu and Joachim Rosenthal ...vii Part I Some Remarks on Applied Mathematics Roger Brockett ...1 Mathematics is a Profession Christopher 1. Byrnes ...4 Comments on Applied Mathematics Avner Friedman ...9 Towards an Applied Mathematics for Computer Science Jeremy Gunawardena ...11 Infomercial for Applied Mathematics Darryl Holm ...15 On Research in Mathematical Economics M. Ali Khan ...21 Applied Mathematics in the Computer and Communications Industry Brian Marcus ...25 'frends in Applied Mathematics Jerrold E. Marsden ...28 Applied Mathematics as an Interdisciplinary Subject Clyde F. Martin ...31 vi Contents Panel Discussion on Future Directions in Applied Mathe- matics Laurence R. Taylor ...38 Part II Feedback Stabilization of Relative Equilibria for Mechanical Systems with Symmetry A. M. Bloch, J. E. Marsden and G. Sanchez ...43 Oscillatory Descent for Function Minimization R. Brockett ...65 On the Well-Posedness of the Rational Covariance Extension Problem C. l. Byrnes, H. J. Landau and A. Lindquist ...83 Singular Limits in Fluid Mechanics P. Constantin ...109 Singularities and Defects in Patterns Far from Threshold N. M. Ercolani ...137 Mathematical Modeling and Simulation for Applications of Fluid Flow in Porous Media R. E. Ewing ...161 On Loeb Measure Spaces and their Significance for N on- Cooperative Game Theory M. A. Khan and Y. Sun ...183 Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms J. E. Marsden and J. M. Wendlandt ...219 Preface The applied sciences are faced with increasingly complex problems which call for sophisticated mathematical models.

Mathematical systems theory is a vibrant research area in its own right. The theory has an impact in numerous applications areas including aeronautics, biological systems, chemical engineering, communication systems, financial engineering and robotics to name just a few. This volume contains survey and research articles by some of the leading researchers in mathematical systems theory. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists. The articles contained in this volume are from those presented as plenary lectures, invited one hour lectures and minisymposia at the 15th International Symposium on the Mathematical Theory of Networks and Systems held at the University of Notre Dame, August 12-16, 2002.

Coding theory, system theory, and symbolic dynamics have much in common. Among the central themes in each of these subjects are the construction of state space representations, understanding of fundamental structural properties of sequence spaces, construction of input/output systems, and understanding the special role played by algebraic structure. A major new theme in this area of research is that of codes and systems based on graphical models.This volume contains survey and research articles from leading researchers at the interface of these subjects.