Robert Aumann's career in game theory has spanned over research - from his doctoral dissertation in 1956 to papers as recent as January 1995. Threaded through all of Aumann's work (symbolized in his thesis on knots) is the study of relationships between different ideas, between different phenomena, and between ideas and phenomena. When you look closely at one scientific idea, writes Aumann, you find it hitched to all others. It is these hitches that I have tried to study.

H-infinity engineering continues to establish itself as a discipline of applied mathematics. As such, this extensively illustrated monograph makes a significant application of H-infinity theory to electronic amplifier design, demonstrating how recent developments in H-infinity engineering equip amplifier designers with new tools and avenues for research. The presentation, at the interface of applied mathematics and engineering, emphasizes how to (1) compute the best possible performance available from any matching circuits; (2) benchmark existing matching solutions; and (3) generalize results to multiple amplifiers. As the monograph develops, many research directions are pointed out for both disciplines. The physical meaning of a mathematical problem is made explicit for the mathematician, while circuit problems are presented in the H-infinity framework for the engineer. A final chapter organizes these research topics into a collection of open problems ranging from electrical engineering, numerical implementations, and generalizations to H-infinity theory.

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.

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The book discusses the complete proof of the Brown-Douglas-Fillmore theorem along with a number of its applications.

This book, first published in 1987, brings together from a variety of sources analysis on the major issues involved in the collection of scientific journals. Working from the premise that scientists tend to know much more about their subject than about their journals, it examines the rationale for journal choices, journals and tenure, journals and budgeting, and the elements of a good journal. It shows librarians how to penetrate the internal structure of some imposing technical literatures in a way that can help them make responsible collection management decisions that even their science clientele will respect.

The book stresses particularly Noll's method of axiomatization of physical theories, his axiomatics of continuum mechanics, thermodynamics of materials, special relativity theory, his discovery of the neo-classical space-time of mechanics, his theories of inhomogeneities in simple bodies, fit regions, contact interactions, annihilators of linear differential operators, and finite-dimensional spaces.