Werner Krabs - Böcker

Mathematisch prazise fuhrt dieses Lehrbuch in die Grundlagen der Spieltheorie und deren dynamische Behandlung ein. Dabei werden zugleich die wichtigen Anwendungsmoglichkeiten dieser Theorie z.B. in den Wirtschaftswissenschaften aufgezeigt und anhand von Beispielen erlautert. Beginnend mit der Arbeit von John von Neumann uber die Theorie der Gesellschaftsspiele fuhrt Sie dieses Buch bis zu den modernen Konzepten der dynamischen Behandlung von Spielen

In neuerer Zeit sind so viele Lehrbücher über Approximationstheorie erschienen, daß man nach der Berechtigung eines weiteren Buches fragen mag. Die Motivie­ rung ergab sich aus der Tatsache, daß sowohl in der Zeitschriftenliteratur über Approximationstheorie als auch in den meisten Lehrbüchern relativ wenig auf die Anwendungen eingegangen wird. Es scheint in der heutigen Zeit eine gewisse Diskrepanz zu bestehen zwischen manchen viel von Mathematikern bearbeiteten Gebieten und den Gebieten, deren mathematische Untersuchung von seiten der Anwendungen aus dringend erwünscht wäre. Die in physikalischen und technischen Fragestellungen auftretenden Approximationsprobleme sind, im Zug der fort­ schreitenden Entwicklung, so vielseitig und oft andersartig als in der bisher ge­ wöhnlich betrachteten Theorie und dabei zugleich häufig mathematisch sehr interessant und tiefliegend, so daß sich hier ein außerordentlich reiches Betäti­ gungsfeld für die mathematische Forschung ergibt. Sehr oft sind wir von Studen­ ten, Diplomanden, Doktoranden nach Themen aus der Approximationstheorie gefragt worden, die zugleich praktische Bedeutung haben, und da hierüber viel­ fach nicht genügend bekannt zu sein scheint, versucht dieses Büchlein, die Lücke zwischen Theorie und Anwendungen ein wenig aufzufüllen. Da bei den Anwen­ dungen von den verschiedenen Approximationsarten die Tschebyscheffsche Approximation, kurz T. A. , die anderen Typen an Bedeutung weit zu übertreffen scheint, befaßt sich das Buch vorwiegend mit der T. A. , und zwar sowohl mit der Theorie als auch mit den Anwendungen. Der Brücke zwischen bei den dienen auch verschiedene Übungsaufgaben am Schluß des Buches.

In vector optimization one investigates optimization problems in an abstract setting which have a not necessarily real-valued objective function. This scientific discipline is closely related to multi-objective optimization and multi-criteria decision making. This book contains refereed contributions to the "International Conference on Vector Optimization" held at the Technical University of Darmstadt from August 4-7, 1986. This meeting was an interdisciplinary forum devoted to new results in the theory, to applications as well as to the solution of vector optimization problems which are relevant in practice. Because of the great variety of topics covered by the contributions, the 25 articles of this volume are organized in different sections: Historical retrospect, mathematical theory, goal setting and decision making, engineering applications, and related topics. The papers of the invited State-of-the-Art Tutorials given by Professors J.M. Borwein, H. Eschenauer, W. Stadler and P.L. Yu are also included.

J. P. La Salle has developed in [20] a stability theory for systems of difference equations (see also [8]) which we introduce in the first chapter within the framework of metric spaces. The stability theory for such systems can also be found in [13] in a slightly modified form. We start with autonomous systems in the first section of chapter 1. After theoretical preparations we examine the localization of limit sets with the aid of Lyapunov Functions. Applying these Lyapunov Functions we can develop a stability theory for autonomous systems. If we linearize a non-linear system at a fixed point we are able to develop a stability theory for fixed points which makes use of the Frechet derivative at the fixed point. The next subsection deals with general linear systems for which we intro­ duce a new concept of stability and asymptotic stability that we adopt from [18]. Applications to various fields illustrate these results. We start with the classical predator-prey-model as being developed and investigated by Volterra which is based on a 2 x 2-system of first order differential equations for the densities of the prey and predator population, respectively. This model has also been investigated in [13] with respect to stability of its equilibrium via a Lyapunov function. Here we consider the discrete version of the model.

The purpose of the Conference on Optimal Control of Partial Differential Equations was to bring together leading experts in this field and to exchange ideas and information about recent advances in control theory connected with partial differential equations. The papers collected in these Proceedings are mainly research papers in which new results are presented. Out of a broad spectrum of topics the problem of exact controllability played a central role, and also shape control was given some special attention. Nonlinear problems were mainly treated under the aspect of optimality whereas identification problems and also numerical aspects were considered only treated marginally.

The main concern of this book is the application of infinite moment theory to the problem of controllability of one-dimensional vibrating systems (like strings and beams) and heating processes. Distributed control and boundary control are considered. In the case of vibrating systems, trigonometric moment problems are investigated on the basis of abstract moment theory in Hilbert spaces. Additionally, the theory of linear operator equations on Hilbert spaces (partly with unbounded operators) is applied to the problem of controllability and time-minimal controllability. In the case of heating processes, exponential moment problems are dealt with on the basis of abstract moment theory in Banach spaces. Time-minimal controllability is also treated with the aid of the theory of linear operator equations on Banach spaces. Some advanced knowledge in functional analysis and on partial differential equations is required for a full reading of the book, but parts of it are also readable with basic mathematical knowledge.

A collection of 10 lectures on modern methods of optimization. Each lecture describes the development of a current optimization topic in detail. The text is intended to be useful to newcomers to optimization and to those wishing to expand their familiarity beyond their own area. This book is based upon the work done at a Summer School held at the University of Bayreuth in 1990.

Mathematical models in biology and medicine cannot be based on natural laws as it is the case with physics and chemistry. In general, several mathematical models can be designed in order to describe a biological or medical process and there is no unique criterion which model gives the best description.

Mathematical models in biology and medicine cannot be based on natural laws as it is the case with physics and chemistry. In general, several mathematical models can be designed in order to describe a biological or medical process and there is no unique criterion which model gives the best description.

At the end of the nineteenth century Lyapunov and Poincaré developed the so called qualitative theory of differential equations and introduced geometric- topological considerations which have led to the concept of dynamical systems. In its present abstract form this concept goes back to G.D. Birkhoff. This is also the starting point of Chapter 1 of this book in which uncontrolled and controlled time-continuous and time-discrete systems are investigated. Controlled dynamical systems could be considered as dynamical systems in the strong sense, if the controls were incorporated into the state space. We, however, adapt the conventional treatment of controlled systems as in control theory. We are mainly interested in the question of controllability of dynamical systems into equilibrium states. In the non-autonomous time-discrete case we also consider the problem of stabilization. We conclude with chaotic behavior of autonomous time discrete systems and actual real-world applications.