Bøger i International Series of Numerical Mathematics serien

The subjects covered treat bifurcation problems, ranging from theoretical investigations to numerical results, with emphasis placed upon applications. Different kinds of bifurcations are treated: Hopf bifurcation, bifurcation from continuous spec trum, complex bifurcation, and bifurcation near tori.

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.

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.

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.

The Third International Symposium on Hultivariate Approximation Theory was held at the Oberwolfach !1athematical Research Insti­ tute, Black Forest, February 8-12, 1982. The preceding conferen­ ces on this topic were held in 1976* and 1979**. The conference brought together 50 mathematicians from 14 coun­ tries. These Proceedings form arecord of most of the papers pre­ sented at the Symposium. The topics treated cover different problems on multivariate approximation theory such as new results concerning approxima­ tion by polynomials in Sobolev spaces, biorthogonal systems and orthogonal series of functions in several variables, multivariate spline functions, group theoretic and functional analytic methods, positive linear operators, error estimates for approximation procedures and cubature formulae, Boolean methods in multivari­ ate interpolation and the numerical application of summation procedures. Special emphasis was posed on the application of multivariate approximation in various fields of science. One mathematician was sorely missed at the Symposium. Professor Arthur Sard who had actively taken part in the earlier conferen­ ces passed away in August of 1980. Since he was a friend of many of the participants, the editors wish to dedicate these Procee­ dings to the memory of this distinguished mathematician. Abrief appreciation of his life and mathematical work appears as well *"Constructive Theory of Functions of Several Variables". Edited by w. Schempp and Karl Zeller. Lecture Notes in 1-1athematics, Vol.

Brannigan, M. A Multivariate Adaptive Data Fitting Algorithm 30 Brass, H. Zur numerischen Berechnung konjugierter Funktionen 43 Bultheel, A.

This monograph contains a collection of 16 papers that were presented at the confer ence "Free Boundary Problems: Numerical 7reatment and Optimal Control", held at the Mathematisches Forschungsinstitut Oberwolfach, West Germany, July 9-15, 1989.

The publication of Oberwolfach conference books was initiated by Birkhauser Publishers in 1964 with the proceedings of the conference 'On Approximation Theory', conducted by P.

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.

Particular examples of problems on which substantial progress has been made are the control and stabilization of mechatronic structures, the control of growth of thin films and crystals, the control of Laser and semi-conductor devices, and shape optimization problems for turbomachine blades, shells, smart materials and microdiffractive optics.

The international symposium held in October 1984 at the Uni versity of Mannheim was the first with the special aim to expose the connection of the Theory of Delay Eauations and Approximation Theory with the emphasis on constructive methods and applications.

This volume contains the proceedings of a conference held in Wiirzburg, August 20-24, 1990. How trends vary may be seen by comparing these proceedings with previous ones, in particular with the conference held in Dortmund 1986 (proceedings published in ISNM 79).

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

Jim Douglas, Jr.' These proceedings reflect some of the thoughts expressed at the Oberwolfach Con ference on Porous Media held June 21-27, 1992, organized by Jim Douglas, Jr., Ulrich Hornung, and Cornelius J, van Duijn.

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.

22 papers on control of nonlinear partial differential equations highlight the area from a broad variety of viewpoints. A significant part of the volume is devoted to applications in engineering, continuum mechanics and population biology.

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".

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.

This book introduces general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators.

In November 2001 the Mathematical Research Center at Oberwolfach, Germany, hosted the third Conference on Mathematical Models and Numerical Simulation in Electronic Industry. It brought together researchers in mathematics, electrical engineering and scientists working in industry.The contributions to this volume try to bridge the gap between basic and applied mathematics, research in electrical engineering and the needs of industry.

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.

The International Meetings on Approximation Theory attempt to keep track in particular of fun damental advances in the theory of function approximation, for example by (or thogonal) polynomials, (weighted) interpolation, multivariate quasi-interpolation, splines, radial basis functions and several others.

Chapter IV contains papers on harmonic analysis in connection with approximation and, finally, Chapter V is devoted to approximation by splines, algebraic polynomials, rational functions, and to Pade approximation.

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.

While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have become a major tool in numerical analysis of partial differential equations.

Methods for the Solution of Fredholm Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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.

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;

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.

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.