Korte, Bernhard, Vygen, Jens

Combinatorial Optimization, 3rd ed.
Theory and Algorithms

Series: Algorithms and Combinatorics, Vol. 21
2006, XVI, 597 p., Hardcover
ISBN: 3-540-25684-9

About this textbook

This comprehensive textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. Since the complete book contains enough material for at least four semesters (4 hours a week), one usually selects material in a suitable way. The book contains complete but concise proofs, also for many deep results, some of which did not appear in a book before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization. This third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new sections and further material on various topics. New exercises and updates in the bibliography were added.

Table of contents

Preface.- Introduction.- Graphs.- Linear Programming.- Linear Programming Algorithms.- Integer Programming.- Spanning Trees and Arborescences.- Shortest Paths.- Network Flows.- Minimum Cost Flows.- Maximum Matchings.- Weighted Matching.- b-Matchings and T-Joins.- Matroids.- Generalizations of Matroids.- NP-Completeness.- Approximation Algorithms.- The Knapsack Problem.- Bin Packing.- Multicommodity Flows and Edge-Disjoint Paths.- Network Design Problems.- The Traveling Salesman Problem.- Facility Location.- Notation Index.- Author Index.- Subject Index.

Dager, Rene, Zuazua, Enrique

Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures

Series: Mathematiques et Applications, Vol. 50

2006, IX, 221 p. with blank pages: X, 8, 102, 182, 196, 204, 212, 220., Softcover
ISBN: 3-540-27239-9

About this book

This volume presents a detailed study of partial differential equations on planar graphs modeling networked flexible mechanical structures. Special emphasis is laid on the understanding of wave propagation phenomena, through the analysis of the problems of observability and controllability from small regions of the graph or its boundary. Some of these results are extended to the heat, beam and Schrodinger equations on planar graphs. Designed as a self-contained introductory course on control and observation of networks, the volume contains also some advanced topics and new techniques which may be of interest for researchers in this area. It also includes a list of open problems and topics for future research.

Table of contents

Li, Zhong; Halang, Wolfgang A.; Chen, Guanrong (Eds.)

Integration of Fuzzy Logic and Chaos Theory

Series: Studies in Fuzziness and Soft Computing, Vol. 187
2005, Approx. 250 p., Hardcover
ISBN: 3-540-26899-5

About this book

This book attempts to present some current research progress and results on the interplay of fuzzy logic and chaos theory. More specifically, this book includes a collections of some state-of-the-art surveys, tutorials, and application examples written by some experts working in the interdisciplinary fields overlapping fuzzy logic and chaos theory. The content of the book covers fuzzy definition of chaos, fuzzy modeling and control of chaotic systems using both Mamdani and Takagi-Sugeno models, fuzzy model identification using genetic algorithms and neural network schemes, bifurcation phenomena and self-referencing in fuzzy systems, complex fuzzy systems and their collective behaviours, as well as some applications of combining fuzzy logic and chaotic dynamics, such as fuzzy-chaos hybrid controllers for nonlinear dynamic systems, and fuzzy-model-based chaotic cryptosystems. This book can serve as a handy reference for researchers working in the interdisciplines related, among others, to both fuzzy logic and chaos theory.

Table of contents

Beyond the Li-Yorke definition of chaos.- Chaotic dynamics with fuzzy systems.- Fuzzy modeling and control of chaotic systems.- Fuzzy model identification using a hybrid mGA scheme with application to chaotic system modeling.- Fuzzy control of chaos.- Chaos control using fuzzy controllers.- Digital fuzzy set-point regulated chaotic systems: An intelligent digital redesign approach.- Anti-control of chaos for Takagi-Sugeno fuzzy systems.- Fuzzy chaos synchronization via sampled driving signals.- Bifurcation phenomena in elementary Takagi-Sugeno fuzzy systems.- Self-reference, chaos, and fuzzy logic.- Chaotic behaviour in recurrent Takagi-Sugeno models.- A theory of fuzzy chaos for simulation and control of nonlinear systems.- Complex fuzzy systems and their collective behaviour.- Real-time identification and forecasting of chaotic time series using hybrid systems of computational intelligence.- Fuzzy-chaos hybrid controllers for nonlinear dynamic systems.- Fuzzy model-based chaotic cryptosystems.- Evolution of complexity.- Problem solving via fuzziness-based coding of continuous constraints yielding synergetic and chaos-dependent origination structures.- Some applications of fuzzy dynamic models with chaotic properties.

Gurariy, Vladimir I., Lusky, Wolfgang

Geometry of Muntz Spaces and Related Questions

Series: Lecture Notes in Mathematics, Vol. 1870
2005, XIII, 182 p., Softcover
ISBN: 3-540-28800-7

About this book

Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality.

Table of contents

Preface.- Part I Subspaces and Sequences in Banach Spaces: Disposition of Subspaces.- Sequences in Normed Spaces.- Isomorphism, Isometries and Embeddings.- Spaces of Universal Disposition.- Bounded Approximation Properties.- Part II On the Geometry of Muntz Sequences: Coefficient Estimates and the Muntz Theorem.- Classification and Elementary Properties of Muntz Sequences.- More on the Geometry of Muntz Sequences and Muntz Polynomials.- Operators of Finite Rank and Bases in Muntz Spaces.- Projection Types and the Isomorphism Problem for Muntz Spaces.- The Classes [M], A, P, and Pe.- Finite Dimensional Muntz Limiting Spaces in C.- References.- Index.

Ausloos, Marcel; Dirickx, Michel (Eds.)

The Logistic Map and the Route to Chaos

From The Beginnings to Modern Applications
This title is included in the Springer Complexity program
Series: Understanding Complex Systems
2006, Approx. 400 p., Hardcover
ISBN: 3-540-28366-8

About this book

Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paragdigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramification of the developments initiated by Verhulst over a century ago.

Table of contents

Chaotic Growth With The Logistic Model of P.F.Verhulst.- Pierre-Francoiss Verhultst`s Final Triumph.- Limits to Sucess. The Iron Law of Verhulst.- Recurrent Generation of Verhulst Chaos Maps .- Coherence in Complex Networks of Oscillators. Agglomeraton /Aggregation and Chaotic Behaviour.- Logistic Population Growth and Beyond.- Extinction Dynamics in Lotka-Volterra Ecosystems on Evolving Networks.- A Chaos and Fractal Dynamic Approach to Fracture Mechanics.- Singular Dynamics at The Edge of Chaos.- Exact Law of Live Nature.- Manifestation of Chaos in Real Complex Systems: Case of Parkinson`s Disease.- Monte Carlo Simulatons of Ageing and Speciation.- Influence of Information Flow in the Formation of Economic Cycles.- Logistic Function in Large Financial Crashes.- Growth of Random Sequences.- Quantum Chaos Versus Classical Chaos.- Using Riemannian Geometry for Prediction Chaos in Restricted Three-Body Problem.- Order and Chaos in Some Hamiltonian Systems of Interest in Plasma Physics.- Non-Linear Dynamics and Fractal Avalanches in Pile of Rice.- Agent Based Approaches to Income Distributions and the Impact of Memory.

Jakimovski, Amnon, Sharma, Ambikeshwar, Szabados, Jozsef

Walsh Equiconvergence of Complex Interpolating Polynomials

Series: Springer Monographs in Mathematics
2006, Approx. 295 p., Hardcover
ISBN: 1-4020-4174-8

About this book

This book is a collection of the various old and new results, centered around the following simple and beautiful observation of J.L. Walsh - If a function is analytic in a finite disc, and not in a larger disc, then the difference between the Lagrange interpolant of the function, at the roots of unity, and the partial sums of the Taylor series, about the origin, tends to zero in a larger disc than the radius of convergence of the Taylor series, while each of these operators converges only in the original disc.

This book will be particularly useful for researchers in approximation and interpolation theory.

Table of contents

Dedication. Preface. Lagrange Interpolation and Walsh Equiconvergence.- Hermite and Hermite-Birkhoff Interpolation and Walsh Equiconvergence.- A generalization of the Taylor Series to Rational Functions and Walsh Equiconvergence.- Sharpness Results.- Converse Results.- Pade Approximation and Walsh Equiconvergence for Meromorphic Functions with v-Poles.- Quantitative Results in the Equiconvergence of Approximation of Meromorphic Functions.- Equiconvergence for Functions Analytic in an Ellipse.- Walsh Equiconvergence Theorems for the Faber Series.- Equiconvergence on Lemniscates.- Walsh Equiconvergence and Summability.- References.