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It is well known that computer algebra systems have revolutionized teaching and the learning processes in mathematics, science, and - gineering, allowing students to computationally investigate complicated problems to ?nd exact or approximate analytic solutions, numeric so- tions, and illustrative two- and three-dimensional graphics. Since the 1960s there has existed individual packages for solving s- ci?c analytic, numerical, graphical and other problems. The need to solve all those problems with the aid of a single system, has led to the idea of construction of a modern general purpose computer algebra s- tem. The ?rst two papers describing analytic calculations realized on a computer were published in 1953 [7]. In the early 1970s, systems of - alytic computations (SAC),or computer algebra systems (CAS), began to appear. Computer algebra systems are computational interactive programs that facilitate symbolic mathematics and can handle other type of pr- lems. The ?rst popular systems were Reduce, Derive, and Macsyma, which are still commercially available. Macsyma was one of the ?rst and most mature systems. It was developed at the Massachusetts - stitute of Technology (MIT), but practically its evolution has stopped since thesummer of 1999. Afree software version of Macsyma, Maxima, is actively being maintained. To the present day, there have been developed more than a hundred computer algebra systems [7], [18]. Among these we can ?nd Axiom, Derive, Maxima, Maple, Mathematica, Matlab, MuMATH, MuPAD, Reduce, etc. All these systems can be subdivided into specialized and general-purpose computer algebra systems ([7], [18], [2]).

Mathematical control systems --- Computer science --- Computer. Automation --- informatica --- wiskunde --- informaticaonderzoek

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Mathematical control systems --- Computer science --- Computer. Automation --- informatica --- wiskunde --- informaticaonderzoek

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This book presents a selected collection of contributions on a focused treatment of important elements of Computational Intelligence. Unlike traditional comp- ing, Computational Intelligence (CI) is tolerant of imprecise information, partial truthanduncertainty.TheprinciplecomponentsofCIthatcurrentlyhavefrequent applicationinEngineeringandManufacturingare:NeuralNetworks(NN),fuzzy logic(FL)andSupportVectorMachines(SVM).InCI,NNandSVMareconcerned withlearning,whileFLwithimprecisionandreasoning. ? This volume mainly covers a key element of Computational Intelligence learning. All the contributions in this volume have a direct relevance to neural ? networklearning fromneuralcomputingfundamentalstoadvancednetworkssuch asMultilayerPerceptrons(MLP),RadialBasisFunctionNetworks(RBF),andtheir relations with fuzzy set and support vector machines theory. The book also d- cussesdifferentapplicationsinEngineeringandManufacturing.Theseareamong applicationswhereCIhaveexcellentpotentialsforuse. Bothnoviceandexpertreadersshouldfindthisbookausefulreferenceinthefield ofComputationalIntelligence.Theeditorsandtheauthorshopetohavecontributed tothefieldbypavingthewayforlearningparadigmstosolvereal-worldproblems D.Andina xi ACKNOWLEDGEMENTS This document has been produced with the financial assistance of the European Community,ALFAprojectII-0026-FA.Theviewsexpressedhereinarethoseof theAuthorsandcanthereforeinnowaybetakentoreflecttheofficialopinionof theEuropeanCommunity. TheeditorswishtothankDrA.AfifyofCardiffUniversityandMrA.Jevticof theTechnicalUniversityofMadridfortheirsupportandhelpfulcommentsduring therevisionofthistext. The editors also wish to thank Nagib Callaos, President of the International Institute of Informatics and Systemics, IIIS, for his permission and freedom to reproduceinChapters2and4ofthisbookcontentsfromthebookbyD.Andina and F.Ballesteros (Eds), Recent Advances in Neural Networks  Ed. IIIS press, ILL,USA(2000). xiii CHAPTER 1 SOFTCOMPUTINGANDITSAPPLICATIONS INENGINEERINGANDMANUFACTURE D.T.PHAM,P.T.N.PHAM,M.S.PACKIANATHER,A.A.AFIFY ManufacturingEngineeringCentre,CardiffUniversity,CardiffCF243AA,UnitedKingdom INTRODUCTION Softcomputingisarecenttermforacomputingparadigmthathasbeeninexistence foralmostfiftyyears.Thischapterreviewsfivesoftcomputingtools.Theyare: knowledge-based systems, fuzzy logic, inductive learning, neural networks and genetic algorithms. All of these tools have found many practical applications. Examples of applications in engineering and manufacture will be given in the chapter. 1. KNOWLEDGE-BASEDSYSTEMS Knowledge-basedsystems,orexpertsystems,arecomputerprogramsembodying knowledge about a narrow domain for solving problems related to that domain.

Mathematical statistics --- Electronics --- Electrical engineering --- Computer science --- Computer. Automation --- patroonherkenning --- factoranalyse --- informatica --- elektronica --- informaticaonderzoek --- elektrische circuits

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Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems. Furthermore, solution algorithms for single- and multi-processor computing environments, enabling methods that span from multi-contact to multi-scale approaches are discussed together with numerical experiments related to soil mechanics using discontinuous deformation analysis.

Classical mechanics. Field theory --- Fluid mechanics --- Computer science --- Computer. Automation --- informatica --- algoritmen --- informaticaonderzoek --- mechanica --- numerieke analyse

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The articles in this volume summarize the research results obtained in the former SFB 359 "Reactive Flow, Diffusion and Transport" which has been supported by the DFG over the period 1993-2004. The main subjects are physical-chemical processes sharing the difficulty of interacting diffusion, transport and reaction which cannot be considered separately. Typical examples are the chemical processes in flow reactors and in the catalytic combustion at surfaces. Further examples are models of star formation including diffusive mass transport, energy radiation and dust formation and the polluting transport in soil and waters. For these complex processes mathematical models are established and numerically simulated. The modeling uses multiscale techniques for nonlinear differential equations while for the numerical simulation and optimization goal-oriented mesh and model adaptivity, multigrid techniques and advanced Newton-type methods are developed combined with parallelization. This modeling and simulation is accompanied by experiments.

Chemistry --- Computer science --- Computer. Automation --- chemie --- informatica --- algoritmen --- informaticaonderzoek --- numerieke analyse