Werner Krabs's Books

Dynamical Systems

Stability, Controllability and Chaotic Behavior

By: Werner Krabs

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Dynamical Systems

Stability, Controllability and Chaotic Behavior

By: Werner Krabs

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.

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245

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Springer Science & Business Media

Published Date

ISBN 10

3642137229

ISBN 13

9783642137228

Modelling, Analysis and Optimization of Biosystems

By: Werner Krabs

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Modelling, Analysis and Optimization of Biosystems

By: Werner Krabs

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. This book presents several of these models and shows applications of them to different biological and medical problems. The book shows that operations research expertise is necessary in respect to modeling, analysis and optimization of biosystems.

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210

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Springer Science & Business Media

Published Date

ISBN 10

3540714537

ISBN 13

9783540714538

Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games

By: Werner Krabs

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Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games

By: Werner Krabs

Focuses on the analysis, optimization and controllability of time-discrete dynamical systems and games under the aspect of stability, controllability and (for games) cooperative and non-cooperative treatment. The investigation of stability is based on Lyapunov's method which is generalized to non-autonomous systems. Optimization and controllability of dynamical systems is treated, among others, with the aid of mapping theorems such as implicit function theorem and inverse mapping theorem. Dynamical games are treated as cooperative and non-cooperative games and are used in order to deal with the problem of carbon dioxide reduction under economic aspects. The theoretical results are demonstrated by various applications.

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198

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Springer Science & Business Media

Published Date

ISBN 10

3642189733

ISBN 13

9783642189739

Numerical Methods of Approximation Theory, Vol.6 \ Numerische Methoden der Approximationstheorie, Band 6

Workshop on Numerical Methods of Approximation Theory Oberwolfach, January 18–24, 1981 \ Tagung über Numerische Methoden der Approximationstheorie Oberwolfach, 18.–24.Januar 1981

By: Collatz,Meinardus,Werner

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Numerical Methods of Approximation Theory, Vol.6 \ Numerische Methoden der Approximationstheorie, Band 6

Workshop on Numerical Methods of Approximation Theory Oberwolfach, January 18–24, 1981 \ Tagung über Numerische Methoden der Approximationstheorie Oberwolfach, 18.–24.Januar 1981

By: Collatz,Meinardus,Werner

Der Band enthalt Manuskripte zu Vortragen, die auf einer von den Herausgebern geleiteten Tagung tiber "Numerische Methoden der Approximationstheorie" am Mathematischen Forschungsinstitut Ober wolfach in der Zeit vom 18.-24. Januar 1981 gehalten wurden. Das Spektrum der Vortrage reichte von der klassischen Approximations theorie tiber mehrdimensionale Approximationsverfahren bis hin zu praxisbezogenen Fragestellungen. Zu den zuerst genannten Gebieten gehorten z. B. die Verfeinerung von Fehlerabschatzungen bei der Polynominterpolation, Fragen zur Eindeutigkeit, Charakterisierung optimaler Interpolationsprozesse und Algorithmen zur rationalen Interpolation. Bei den weiteren genannten Gebieten spiegel ten zahlreiche Vortrage das steigende Interesse an der mehrdimensio nalen Interpolation, insbesondere mit verschiedenen Arten von Splines wider. Hier standen u. a. Probleme der Parameterschatzung in der Medizin und Flugtechnik, Fragen der Approximationstheorie bei der Konstruktion von Plottern und stabile Algorithmen beim Arbeiten mit mehrdimensionalen B-Splines im Mittelpunkt des Interesses. Die Tagung lieferte einen reprasentativen Ueberblick tiber die aktuellen Trends in der Approximationstheorie. Zum guten Erfolg der Tagung trug wie immer die hervorragende Be treuung durch die Mitarbeiter und Angestellten des Instituts so-' wie das verstandnisvolle Entgegenkommen des Institutsdirektors, Herrn Professor Dr. Barner, bei. Un serer besonderer Dank gilt dem Birkhauser Verlag ftir die wie stets sehr gute Ausstattung. Helmut Werner Lothar Collatz Gtinther Meinardus Hamburg Mannheim Bonn 7 INDEX Blatt, H.-P. Strenge Eindeutigkeitskonstanten und Fehlerabschatzungen bei linearer Tschebyscheff-Approximation 9 Bohmer, K. Polynom- und Spline-Interpolation (Ein Farbfilm) 26 Brannigan, M.A Multivariate Adaptive Data Fitting Algorithm 30 Brass, H. Zur numerischen Berechnung konjugierter Funktionen 43 Bultheel, A

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Page Count

267

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Birkhäuser

Published Date

ISBN 10

3034871864

ISBN 13

9783034871860

Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory

Vortragsauszüge der Tagung über numerische Methoden der Approximationstheorie vom 25. bis 31. Mai 1975 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald)

By: Meinardus,Collatz,Werner

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Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory

Vortragsauszüge der Tagung über numerische Methoden der Approximationstheorie vom 25. bis 31. Mai 1975 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald)

By: Meinardus,Collatz,Werner

Der vorliegende Band stellt Vortragsmanuskripte einer am Mathematischen Forschungsinstitut, Oberwolfach, in der Zeit vom 25. bis 31. Mai 1975 veran stalteten Tagung zusammen, die unter der Leitung der Unterzeichner stand. Die letzten dieser Tagungen über numerische Methoden der Approximations theorie fanden 1971 und 1973 statt - der Schwerpunkt lag bei Fragen der Numerik von Algorithmen zur Darstellung von Funktionen -, ließen aber bereits ein wachsendes Interesse an Anwendungen erkennen. Die diesjährige Tagung war gekennzeichnet durch die Behandlung praktischer AufgabensteI lungen sowie durch die Einbeziehung der Anwendungen aus Nachbargebie ten bzw. die Verwendung der Methoden dieser Gebiete in der Approxima tionstheorie, insbesondere wurde auch auf die Beziehungen von Optimierung und Kontrolltheorie zu speziellen approximationstheoretischen Aufgaben eingegangen. Der starke Einfluß auf die numerischen Methoden zur Behand lung von Differentialgleichungen wurde etwa bei der Methode der finiten Elemente oder bei Kollokationsaufgaben deutlich. So ist zu hoffen, daß auch diese Tagung dazu beigetragen hat, Theorie und Anwendungen wieder stärker zu verbinden. Die spezifische Atmosphäre des Forschungsinstituts stimulierte einen intensi ven, durch die breite internationale Streuung der Tagungsteilnehmer verstärk ten, fruchtbaren Gedankenaustausch. Zum Erfolg der Tagung trug - wie immer - die hervorragende Betreuung durch die Mitarbeiter und Angestellten des Forschungsinstituts und das verständnisvolle Entgegenkommen von Herrn Kollege Barner bei. Unser besonderer Dank gilt ferner dem Birkhäuser Verlag für die sehr gute Ausstattung des Buches. L. COLLATZ, G. MEINARDUS, H. WERNER Inhaltsverzeichnis ANSELONE, P.M., LEE, J.W. : Double Approximation Methods for the Solution of Fredholm Integral Equations ...

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326

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Birkhäuser

Published Date

ISBN 10

3034876920

ISBN 13

9783034876926

Unique Solutions for Strategic Games

Equilibrium Selection Based on Resistance Avoidance

By: Werner Güth,Brigitte Kalkofen

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Unique Solutions for Strategic Games

Equilibrium Selection Based on Resistance Avoidance

By: Werner Güth,Brigitte Kalkofen

This book develops a general solution concept for strategic games which resolves strategic uncertainty completely. The concept is described by a mathematically formulated solution procedure and illustrated by applying it to many interesting examples. A long nontechnical introduction tries to survey and to discuss the more technical parts of the book. The book and especially the introduction provide firm and consistent guidance for scholars of game theory. There are many open problems which could inspire further research efforts.

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211

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Springer Science & Business Media

Published Date

ISBN 10

3642483674

ISBN 13

9783642483677

Optimization

Theory and Algorithms

By: Jean-Bapiste Hiriart-Urruty,Werner Oettli,Josef Stoer

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Optimization

Theory and Algorithms

By: Jean-Bapiste Hiriart-Urruty,Werner Oettli,Josef Stoer

This book is concerned with tangent cones, duality formulas, a generalized concept of conjugation, and the notion of maxi-minimizing sequence for a saddle-point problem, and deals more with algorithms in optimization. It focuses on the multiple exchange algorithm in convex programming.

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272

Publisher

CRC Press

Published Date

ISBN 10

1000110516

ISBN 13

9781000110517

Sequential Binary Investment Decisions

A Bayesian Approach

By: Werner Jammernegg

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Sequential Binary Investment Decisions

A Bayesian Approach

By: Werner Jammernegg

This book describes some models from the theory of investment which are mainly characterized by three features. Firstly, the decision-maker acts in a dynamic environment. Secondly, the distributions of the random variables are only incompletely known at the beginning of the planning process. This is termed as decision-making under conditions of uncer tainty. Thirdly, in large parts of the work we restrict the analysis to binary decision models. In a binary model, the decision-maker must choose one of two actions. For example, one decision means to undertake the invest ·ment project in a planning period, whereas the other decision prescribes to postpone the project for at least one more period. The analysis of dynamic decision models under conditions of uncertainty is not a very common approach in economics. In this framework the op timal decisions are only obtained by the extensive use of methods from operations research and from statistics. It is the intention to narrow some of the existing gaps in the fields of investment and portfolio analysis in this respect. This is done by combining techniques that have been devel oped in investment theory and portfolio selection, in stochastic dynamic programming, and in Bayesian statistics. The latter field indicates the use of Bayes' theorem for the revision of the probability distributions of the random variables over time.

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Page Count

167

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Springer Science & Business Media

Published Date

ISBN 10

364246646X

ISBN 13

9783642466465

Dynamical Systems

Stability, Controllability and Chaotic Behavior

By: Werner Krabs

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Dynamical Systems

Stability, Controllability and Chaotic Behavior

By: Werner Krabs

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245

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Springer Science & Business Media

Published Date

ISBN 10

3642137229

ISBN 13

9783642137228

Modelling, Analysis and Optimization of Biosystems

By: Werner Krabs

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Modelling, Analysis and Optimization of Biosystems

By: Werner Krabs

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Page Count

210

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Springer Science & Business Media

Published Date

ISBN 10

3540714537

ISBN 13

9783540714538

On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes

By: Werner Krabs

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On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes

By: Werner Krabs

The main concern of this book is the application of infinite moment theory to the problem of controllability of one-di- mensional vibrating systems (like strings and beams) and heating processes. Distributed as well as boundary control is considered. In the case of vibrating systems trigonometric moment pro- blems are to be investigated which is done on the basis of an abstract moment theory in Hilbert spaces. Equivalently, alsothe theory of linear operator equations on Hilbert spa- ces ( 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 to be dealt with which is done on the basis of an ab- stract moment theory in Banach spaces. Time-minimal control- lability is also treated with the aid of the theory of line- aroperator equations on Banach spaces. Some advanced knowledge in functional analyis and on partial differential equations is preassumed for a fluent reader of the book, but parts of it are also readable with basic ma- thematical knowledge (for instance, the finite-dimensional part of the introduction).

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177

Publisher

Springer

Published Date

ISBN 10

3662164450

ISBN 13

9783662164457

Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games

By: Werner Krabs

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Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games

By: Werner Krabs

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198

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Springer Science & Business Media

Published Date

ISBN 10

3642189733

ISBN 13

9783642189739

Dynamical Systems

Stability, Controllability and Chaotic Behavior

By: Werner Krabs

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Dynamical Systems

Stability, Controllability and Chaotic Behavior

By: Werner Krabs

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Page Count

238

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Springer

Published Date

ISBN 10

3642137237

ISBN 13

9783642137235

Modelling, Analysis and Optimization of Biosystems

By: Werner Krabs

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Modelling, Analysis and Optimization of Biosystems

By: Werner Krabs

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Page Count

203

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Springer

Published Date

ISBN 10

3540836578

ISBN 13

9783540836575

Book's by Werner Krabs

Dynamical Systems

Dynamical Systems

Modelling, Analysis and Optimization of Biosystems

Modelling, Analysis and Optimization of Biosystems

Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games

Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games

Numerical Methods of Approximation Theory, Vol.6 \ Numerische Methoden der Approximationstheorie, Band 6

Numerical Methods of Approximation Theory, Vol.6 \ Numerische Methoden der Approximationstheorie, Band 6

Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory

Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory

Unique Solutions for Strategic Games

Unique Solutions for Strategic Games

Optimization

Optimization

Sequential Binary Investment Decisions

Sequential Binary Investment Decisions

Dynamical Systems

Dynamical Systems

Modelling, Analysis and Optimization of Biosystems

Modelling, Analysis and Optimization of Biosystems

On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes

On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes

Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games

Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games

Dynamical Systems

Dynamical Systems

Modelling, Analysis and Optimization of Biosystems

Modelling, Analysis and Optimization of Biosystems

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