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The Fifth International Conference on General Inequalities was held from May 4 to May 10, 1986, at the Mathematisches Forschungsinstitut Oberwolfach (Black Forest, Germany). The organizing committee consisted of W.N. Everitt (Birmingham), L. Losonczi (Debrecen) and W. Walter (Karlsruhe). Dr. A. Kovacec served efficiently an'd enthusiastically as secretary to the con­ ference. The meeting was attended by 50 participants from 16 countries. In his opening address, W. Walter had to report on the death of five colleagues who had been active in the area of inequali­ ties and who had served the mathematical community: P.R. Beesack, G. Polya, D.K. Ross, R. Bellman, G. Szegö. He made special mention of G. Polya, who had been the last surviving author of the book InequaZities (Cambridge University Press, 1934), who died at the age of 97 years and whose many and manifold contributions to mathematics will be recorded elsewhere, in due course. Inequalities continue to play an important and significant role in nearly all areas of mathematics. The interests of the participants to this conference reflected the many different fields in which both classical and modern inequalities continue to influence developments in mathematics. In addition to the established fields, the lectures clearly indicated the importance of inequalities in functional analysis, eigenvalue theory, con­ vexi ty., number theory, approximation theory, probability theory, mathematical prograrnrning and economics.

New trends in free boundary problems and new mathematical tools together with broadening areas of applications have led to attempts at presenting the state of art of the field in a unified way.

The book is an outgrowth of the international conference "Centennial Hurwitz on Stability Theory" which was held to honor Adolf Hurwitz, whose arti cle on the location of roots of a polynomial was published one hundred years ago.

The present volume contains manuscripts of lectures or topics related to the lectures which were given at the conference on "Inverse Problems" at the mathematical Research Institute at Oberwolfach.

Consisting of 16 refereed original contributions, this volume presents a diversified collection of recent results in control of distributed parameter systems. Topics addressed include - optimal control in fluid mechanics - numerical methods for optimal control of partial differential equations - modeling and control of shells - level set methods - mesh adaptation for parameter estimation problems - shape optimization Advanced graduate students and researchers will find the book an excellent guide to the forefront of control and estimation of distributed parameter systems.

A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.

Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary".

Herbert Hornlein, Klaus Schittkowski The finite element method (FEM) has been used successfully for many years to simulate and analyse mechanical structural problems. They proceed from the design model as defined for structural analysis, to perform an internal adaption of design pa rameters based on formal mathematical methods.

This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures.

The fields of boundary integral equations and of inequality problems, or more gen erally, of nonsmooth mechanics, have seen, in a remarkably short time, a considerable development in mathematics and in theoretical and applied mechanics.

A description of the latest and most appropriate mathematical and numerical methods for optimizing soil venting. This book will be of interest to applied mathematicians, geophysicists, geoecologists, soil physicists, and environmental engineers.

The 12th conference on "Variational Calculus, Optimal Control and Applications" took place September 23-27, 1996, in Trassenheide on the Baltic Sea island of Use dom. The conferences were founded, and led ten times, by Professor Bittner (Greifswald) and Professor KlCitzler (Leipzig), who both celebrated their 65th birthdays in 1996.

Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear;

Inequalities continue to play an essential role in mathematics. Since the seminal work Inequalities (1934) of Hardy, Littlewood and P6lya mathematicians have laboured to extend and sharpen the earlier classical inequalities.

The Taylor-Couette system is one of the most studied examples of fluid flow exhibiting the spontaneous formation of dynamical structures. In this book, the variety of time independent solutions with periodic spatial structure is numerically investigated by solution of the Navier-Stokes equations.

The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in this book can be considered as further developments of the results presented in the highly respected books of the Russian mathematician A. A. Samarskii. It is shown that the new Samarskii-like techniques open the horizon for the numerical treatment of more complicated problems.The book contains exercises and the corresponding solutions enabling the use as a course text or for self-study. Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving boundary value ODEs.

The finite difference and finite element methods are powerful tools for the approximate solution of differential equations governing diverse physical phenomena, and there is extensive literature on these discre tization methods.

It is probably more efficient to present such material after a strong grasp of (at least) linear algebra and calculus has already been attained -but at this stage those not specializing in numerical mathematics are often interested in getting more deeply into their chosen field than in developing skills for later use.

It is probably more efficient to present such material after a reasonable competence in (at least) linear algebra and calculus has already been attained - but at this stage those not specializ ing in numerical mathematics are often interested in getting more deeply into their chosen field than in developing skills for later use.

The present Volume contains the contributions to the fourth meeting on Unilateral Problems in Structural Analysis, held at Capri on June 14 to 16,1989.

Arguably, many industrial optimization problems are of the multiobjective type.

Numerically oriented articles study finite difference, finite volume, and finite ele ment schemes, adaptive, multiresolution, and artificial dissipation methods.

Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed.This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems.Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.

This book contains the refereed papers which were presented at the interna tional conference on "Multivariate Approximation and Splines" held in Mannheim, Germany, on September 7-10,1996.

O I 1 -1 durch die GauB-Quadraturformel Q I n n L w 0 f (x 0) ¿ i=1 1 1 Sei Rn : = I - Q das Fehlerfunktional. n Izl1, Fur eine im Kreis Kr I Kr : = {z E a: holomorphe Funktion f, f(z) = L i=O sei f i i ¿ = x . ( 1. 1) : = sup{ I a 0 I r i E:JN und R (qo) * O}, qo (x) o 1 n 1 1 In Xr := {f: f holomorph in Kr und Iflr < oo} ist I . I eine Seminorm. Das Fehlerfunktional Rn ist in r (X I· I r) stetig I und fUr II Rn II I r, gilt die Identitat 00 (1 . 2) L i=O Dieser Zugang zu ableitungsfreien Abschatzungen des Fehlerterms (1 ¿ 3) geht auf Hammerlin [4] zurUck. 15 Erftillt die Gewichtsfunktion w eine der Bedingungen w (t ) w(t ) 1 2 ;;; (1. 4. a) w (-t ) w (-t ) 1 2 beziehungsweise w (t ) w(t ) 1 2 (1. 4. b) ~ w (-t ) w (-t ) 1 2 so gilt mit P (x) (X-X ) ¿. ¿ (X-X ) ftir die Fehlernorm 1 n n r 1 Pn(x) (1. 5. a) --,-. . - J w (x) dx Pn(r) -1 r-x beziehungsweise r 1 P (x) (1. 5. b) ( ) J w(x) ~ dx .

The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.

These Proceedings include 42 of the 49 invited conference papers, three papers sub mitted subsequently, and a report devoted to new and unsolved problems based on two special problem sessions and as augmented by later communications from the participants.

Numerical simulation and modelling of electric circuits and semiconductor devices are of primal interest in today's high technology industries. They include contributions on special topics of current interest in circuit and device simulation, as well as contributions that present an overview of the field.

The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. An appreciation of his li fe and contributions was presented verbally by Georges Alexits, while the written version bears the signa tures of both Alexits and Marc Zamansky.