Bücher der Reihe The IMA Volumes in Mathematics and its Applications

Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research.

This three-week summer program considered the symmetries preserving various natural geometric structures. The articles in the first part are expository but all contain significant new material. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.

The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. A unique feature is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science.

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions.

Contains refereed papers submitted by international experts who participated in the Atmospheric Modeling workshop March 15 -19, 2000 at the Institute for Mathematics and Its Applications (IMA) at the University of Minnesota. These papers cover a range of mathematics and modeling topics presented in the workshop.

This IMA Volume in Mathematics and its Applications ALGORITHMS FOR PARALLEL PROCESSING is based on the proceedings of a workshop that was an integral part of the 1996-97 IMA program on "MATHEMATICS IN HIGH-PERFORMANCE COMPUTING.

This IMA Volume in Mathematics and its Applications DIAGNOSIS AND PREDICTION is one of the series based on the proceedings of a very successful 1997 IMA Summer Program on "Statistics in the Health Sciences. " I would like to thank Seymour Geisser of University of Minnesota, School of Statistics for his excellent work as organizer of the meeting and for editing the proceedings. I am grateful to Donald A. Berry, Duke Uni­ versity (Statistics); Patricia Grambsch, University of Minnesota (Biostatis­ tics); Joel Greenhouse, Carnegie Mellon University (Statistics); Nicholas Lange, Harvard Medical School (Brain Imaging Center, McLean Hospital); Barry Margolin, University of North Carolina-Chapel Hill (Biostatistics); Sandy Weisberg, University of Minnesota (Statistics); Scott Zeger, Johns Hopkins University (Biostatistics); and Marvin Zelen, Harvard School of Public Health (Biostatistics) for organizing the six weeks summer program. I also take this opportunity to thank the National Science Foundation (NSF) and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr. , Professor and Director v PREFACE This volume contains refereed papers submitted by participants of the third week of a six week workshop on Statistics in the Health Sciences held by the Institute of Mathematics and its Applications in Minneapolis, Minnesota during July of 1997. This week was devoted to the closely related topics of Diagnosis and Prediction.

This IMA Volume in Mathematics and its Applications TOPOLOGY AND GEOMETRY IN POLYMER SCIENCE is based on the proceedings of a very successful one-week workshop with the same title.

The 1995-1996 program at the Institute for Mathematics and its Applications was devoted to mathematical methods in material science, and was attended by materials scientists, physicists, geologists, chemists engineers, and mathematicians.

This IMA Volume in Mathematics and its Applications DIRECTIONS IN ROBUST STATISTICS AND DIAGNOSTICS is based on the proceedings of the first four weeks of the six week IMA 1989 summer program "Robustness, Diagnostics, Computing and Graphics in Statistics".

This IMA Volume in Mathematics and its Applications SHOCK INDUCED TRANSITIONS AND PHASE STRUCTURES IN GENERAL MEDIA is based on the proceedings of a workshop that was an integral part of the 1990-91 IMA program on "Phase Transitions and Free Boundaries."

This IMA Volume in Mathematics and its Applications LINEAR ALGEBRA, MARKOV CHAINS, AND QUEUEING MODELS is based on the proceedings of a workshop which was an integral part of the 1991-92 IMA program on "Applied Linear Algebra".

This IMA Volume in Mathematics and its Applications COMBINATORIAL AND GRAPH-THEORETICAL PROBLEMS IN LINEAR ALGEBRA is based on the proceedings of a workshop that was an integral part of the 1991-92 IMA program on "Applied Linear Algebra."

This IMA Volume in Mathematics and its Applications VARIATIONAL AND FREE BOUNDARY PROBLEMS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries.

Robust control originates with the need to cope with systems with modeling uncertainty. There have been several mathematical techniques developed for robust control system analysis. The articles in this volume cover all of the major research directions in the field.

The articles in this volume focus on control theory of systems governed by nonlinear linear partial differential equations, identification and optimal design of such systems, and modelling of advanced materials.

This IMA Volume in Mathematics and its Applications NONSMOOTH ANALYSIS AND GEOMETRIC METHODS IN DETERMINISTIC OPTIMAL CONTROL is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory.

Environmental protection has become a universal issue with world-wide support. Unfortunately, scientists, mathematicians, and engineers immersed in developing and applying environmental models, computational methods, statistical techniques and computational hardware advance with separate and often discordant paces.

This IMA Volume in Mathematics and its Applications Homogenization and Effective Moduli of Materials and Media represents the proceedings of a workshop which was an integral part of the 19R4-R5 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS.

This IMA Volume in Mathematics and its Applications Coding Theory and Design Theory Part I: Coding Theory is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS.

This IMA Volume in Mathematics and its Applications TWO PHASE FLOWS AND WAVES is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES.

This IMA Volume in Mathematics and its Applications SOLITONS IN PHYSICS, MATHEMATICS, AND NONLINEAR OPTICS is based on the proceedings of two workshops which were an integral part of the 1988-89 IMA program on NONLINEAR WAVES.

This IMA Volume in Mathematics and its Applications NONLINEAR EVOLUTION EQUATIONS THAT CHANGE TYPE is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES.

This IMA Volume in Mathematics and its Applications COMPUTER AIDED PROOFS IN ANALYSIS is based on the proceedings of an IMA Participating Institutions (PI) Conference held at the University of Cincinnati in April 1989.

If P( t, x, Dt,x) is a strictly hyperbolic operator or system then the singular support of f gives an upper bound for the singular support of u (Courant-Lax, Lax, Ludwig), namely singsupp u C the union of forward rays passing through the singular support of f.

This IMA Volume in Mathematics and its Applications ON THE EVOLUTION OF PHASE BOUNDARIES is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries".