This textbook presents the mathematics that is foundational to multimedia applications. Featuring a rigorous survey of selected results from algebra and analysis, the work examines tools used to create application software for multimedia signal processing and communication.

Replete with exercises, sample programs in Standard C, and numerous illustrations, Mathematics for Multimedia is an ideal textbook for upper undergraduate and beginning graduate students in computer science and mathematics who seek an innovative approach to contemporary mathematics with practical applications. The work may also serve as an invaluable reference for multimedia applications developers and all those interested in the mathematics underlying multimedia design and implementation.

This book is on the iterative learning control (ILC) with focus on the design and implementation. We approach the ILC design based on the frequency domain analysis and address the ILC implementation based on the sampled data methods. This is the first book of ILC from frequency domain and sampled data methodologies. The frequency domain design methods offer ILC users insights to the convergence performance which is of practical benefits. This book presents a comprehensive framework with various methodologies to ensure the learnable bandwidth in the ILC system to be set with a balance between learning performance and learning stability. The sampled data implementation ensures effective execution of ILC in practical dynamic systems. The presented sampled data ILC methods also ensure the balance of performance and stability of learning process. Furthermore, the presented theories and methodologies are tested with an ILC controlled robotic system. The experimental results show that the machines can work in much higher accuracy than a feedback control alone can offer. With the proposed ILC algorithms, it is possible that machines can work to their hardware design limits set by sensors and actuators. The target audience for this book includes scientists, engineers and practitioners involved in any systems with repetitive operations.

This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.

Featuring original research from well-known experts in the field of sliding mode control, this book presents new design schemes for a useful and practical optimal control with very few impractical assumptions. The results presented allow optimal control theory to grow in its applicability to real-world systems. On the cutting-edge of optimal control research, this book is an excellent resource for both graduate students and researchers in engineering, mathematics, and optimal control.

This book focuses on the nonlinear behaviour of thin-wall shells (single- and multilayered with delamination areas) under various uniform and non-uniform loadings.
The dependence of critical (buckling) load upon load variability is revealed to be highly non-monotonous, showing minima when load variability is close to the eigenmode variabilities of solution branching points of the respective nonlinear boundary problem.
A novel numerical approach is employed to analyze branching points and to build primary, secondary, and tertiary bifurcation paths of the nonlinear boundary problem for the case of uniform loading. The load levels of singular points belonging to the paths are considered to be critical load estimates for the case of non-uniform loadings.

It is the aim of INDICES to document recent explorations in the various fields of philosophical logic and formal linguistics and their applications in other disciplines. The main emphasis of this series is on self-contained monographs covering particular areas of recent research and surveys of methods, problems, and results in all fields of inquiry where recourse to logical analysis and logical methods has been fruitful. INDICES will contain monographs dealing with the central areas of philosophical logic (extensional and intensional systems, indexical logics, non-classical logics, philosophy of logic, etc.) as well as studies in which these systems are applied to specific issues in philosophy, in the formal semantics of natural languages, the foundations of linguistic theory, in computational linguistics, and in theoretical computer science. Constructive type theory was first presented in 1970, by the Swedish logician Per Martin-Lof. It has become one of the main approaches used in the foundations of mathematics and computer science. But it has remained relatively unknown among linguists and philosophers, although it provides a considerable extension of the concepts and techniques of logic. The book first gives an introduction to type theory from the point of view of linguistics and the philosophy of language. Type theory is then applied in the areas of quantification, anaphora, temporal reference, and the structure of text and discourse. By virtue of the type-theoretical concepts of proof object and context, various phenomena of dependence and progression in language can be discussed in precise terms, and several well-known problems can be solved. A categorial grammar is presented togenerate formally a fragment of English, together with an example of a computer implementation.

Focuses on acquiring spatial models of physical environments through mobile robots

The robotic mapping problem is commonly referred to as SLAM (simultaneous localization and mapping).

3D maps are necessary to avoid collisions with complex obstacles and to self-localize in six degrees of freedom (x-, y-, z-position, roll, yaw and pitch angle)

New solutions to the 6D SLAM problem for 3D laser scans are proposed and a wide variety of applications are presented

This book represents the results of cross-fertilization between OR/MS and CS/AI. It is this interface of OR/CS that makes possible advances that could not have been achieved in isolation. Taken collectively, these articles are indicative of the state-of-the-art in the interface between OR/MS and CS/AI and of the high caliber of research being conducted by members of the INFORMS Computing Society.

This thesis tackles fundamental questions concerning the discharge of a pre-Pyrenean karst aquifer system and an Antarctic glacier system, utilizing a system engineering methodology and data-driven approach. It presents for the first time a simplified and effective linear transfer function for karst aquifers. The author provides detailed wavelet spectrum results, which reveal certain non-linearities in drought periods. In addition, structures based on Hammerstein-Wiener blocks have yielded a nonlinear model that is substantially more efficient than its linear counterparts. Another pioneering finding is the use of wavelet coherence between glacier discharge and air temperature to estimate SEC (Seasonal Effective Core) boundaries. The yearly SEC is essential to obtaining a model based on Hammerstein-Wiener structures, which offers considerably higher efficiency. Moreover, two different types of glacier dynamics have been discovered (over damped and overshoot), depending on the annual cycle and the SEC average temperature.

This book explores the life and scientific legacy of Manfred Schroeder through personal reflections, scientific essays and Schroeder s own memoirs. Reflecting the wide range of Schroeder s activities, the first part of the book contains thirteen articles written by his colleagues and former students. Topics discussed include his early, pioneering contributions to the understanding of statistical room acoustics and to the measurement of reverberation time; his introduction of digital signal processing methods into acoustics; his use of ray tracing methods to study sound decay in rooms and his achievements in echo and feedback suppression and in noise reduction. Other chapters cover his seminal research in speech processing including the use of predictive coding to reduce audio bandwidth which led to various code-excited linear prediction schemes, today used extensively for speech coding. Several chapters discuss Schroeder s work in low-peak factor signals, number theory, and maximum-length sequences with key applications in hearing research, diffraction gratings, artificial reverberators and de-correlation techniques for enhancing subjective envelopment in surround sound. In style, the articles range from truly scientific to conversationally personal. In all contributions, the relationship between the current research presented and Manfred Schroeder s own fields of interest is, in general, evident. The second part of the book consists of Schroeder s own memoirs, written over the final decade of his life. These recollections shed light on many aspects not only of Schroeder s life but also on that of many of his colleagues, friends and contemporaries. They portray political, social and scientific events over a period that extends from pre-war to the present. These memoirs, written in an inimitable and witty style, are full of information, entertaining and fun to read, providing key insight into the life and work of one of the greatest acousticians of the 20th century."

This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2018 International Symposium, which was held at the University Hassan II, Morocco, from October 29th to November 2nd, 2018. The topics covered include applications of mathematical modeling in hepatitis B, HIV and Chikungunya infections; tumor cell dynamics; inflammatory processes; chemotherapeutic drug effects; and population dynamics. Also discussing the application of techniques like the generalized stochastic Milevsky-Promislov model, numerical simulations and convergence of discrete and continuous models, it is an invaluable resource on interdisciplinary research in mathematical biology for students, researchers, and professionals. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. The 2018 edition of BIOMAT International Symposium received contributions by authors from seventeen countries: Algeria, Brazil, Cameroon, Canada, Chad, Colombia, France, Germany, Hungary, Italy, Mali, Morocco, Nigeria, Poland, Portugal, Russia, and Senegal. Selected papers presented at the 2017 edition of this Symposium were also published by Springer, in the volume "Trends in Biomathematics: Modeling, Optimization and Computational Problems" (978-3-319-91091-8).

One of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions. Applications of renewal processes play a key role in actuarial and financial mathematics as well as in engineering, operations research and other fields of applied mathematics. On the other hand, regular variation of functions is a property that features prominently in many fields of mathematics. The structure of the book reflects the historical development of the authors' research work and approach - first some applications are discussed, after which a basic theory is created, and finally further applications are provided. The authors present a generalized and unified approach to the asymptotic behavior of renewal processes, involving cases of dependent inter-arrival times. This method works for other important functionals as well, such as first and last exit times or sojourn times (also under dependencies), and it can be used to solve several other problems. For example, various applications in function analysis concerning Abelian and Tauberian theorems can be studied as well as those in studies of the asymptotic behavior of solutions of stochastic differential equations. The classes of functions that are investigated and used in a probabilistic context extend the well-known Karamata theory of regularly varying functions and thus are also of interest in the theory of functions. The book provides a rigorous treatment of the subject and may serve as an introduction to the field. It is aimed at researchers and students working in probability, the theory of stochastic processes, operations research, mathematical statistics, the theory of functions, analytic number theory and complex analysis, as well as economists with a mathematical background. Readers should have completed introductory courses in analysis and probability theory.

The revised edition of this advanced textbook provides the reader with a solid grounding in the formalism of classical mechanics, underlying a number of powerful mathematical methods that are widely used in modern theoretical and mathematical physics. It reviews the fundamentals of Lagrangian and Hamiltonian mechanics, and goes on to cover related topics such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. New material for the revised edition includes additional sections on the Euler-Lagrange equation, the Cartan two-form in Lagrangian theory, and Newtonian equations of motion in context of general relativity. Also new for this edition is the inclusion of problem sets and solutions to aid in the understanding of the material presented. The mathematical constructions involved are explicitly described and explained, so the book is a good starting point for the student new to this field. Where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for more advanced students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.

This thesis provides an introduction to the physics of the Standard Model and beyond, and to the methods used to analyse Large Hadron Collider (LHC) data. The 'hierarchy problem', astrophysical data and experiments on neutrinos indicate that new physics can be expected at the now accessible TeV scale. This work investigates extensions of the Standard Model with gravitons and gravitinos (in the context of supergravity). The production of these particles in association with jets is studied as one of the most promising avenues for researching new physics at the LHC. Advanced simulation techniques and tools, such as algorithms allowing the computation of Feynman graphs and helicity amplitudes are first developed and then employed.

Manifolds fall naturally into two classes depending on whether they can be fitted with a distance measuring function or not. The former, metrisable manifolds, and especially compact manifolds, have been intensively studied by topologists for over a century, whereas the latter, non-metrisable manifolds, are much more abundant but have a more modest history, having become of increasing interest only over the past 40 years or so. The first book on this topic, this book ranges from criteria for metrisability, dynamics on non-metrisable manifolds, Nyikos's Bagpipe Theorem and whether perfectly normal manifolds are metrisable to structures on manifolds, especially the abundance of exotic differential structures and the dearth of foliations on the long plane. A rigid foliation of the Euclidean plane is described. This book is intended for graduate students and mathematicians who are curious about manifolds beyond the metrisability wall, and especially the use of Set Theory as a tool.

In the present work, the target station of the accelerator-driven neutron source HBS is optimized in comprehensive parameter studies using the Monto-Carlo method. The dependence of the most important performance characteristics of such a system on the external parameters is investigated neglecting technical and mechanical limitations. In this way, qualitative and quantitative statements for all possible configurations and envisaged applications can be derived and should be considered in the detailed planning of such facilities. For this purpose, different scenarios are considered that place completely different requirements on the design of the target station. The central statements derived in this thesis can be transferred to any framework conditions, such as different accelerator energies, so that these results can be used in the development of other neutron sources, which together with the HBS form a European network and provide a prosperous community in neutron science.

Many large mathematical models, not only models arising and used in environmental studies, are described by systems of partial differential equations. The discretization of the spatial derivatives in such models leads to the solution of very large systems of ordinary differential equations. These systems contain many millions of equations and have to be handled over large time intervals by applying many time-steps (up to several hundred thousand time-steps). Furthermore, many scenarios are as a rule to be run. This explains the fact that the computational tasks in this situation are enormous. Therefore, it is necessary to select fast numerical methods; to develop parallel codes and, what is most important when the problems solved are very large to organize the computational process in a proper way.
The last item (which is very often underestimated but, let us re-iterate, which is very important) is the major topic of this book. In fact, the proper organization of the computational process can be viewed as a preparation of templates which can be used with different numerical methods and different parallel devices. The development of such templates is described in the book. It is also demonstrated that many comprehensive environmental studies can successfully be carried out when the computations are correctly organized. Thus, this book will help the reader to understand better that, while (a) it is very important to select fast numerical methods as well as (b) it is very important to develop parallel codes, this will not be sufficient when the problems solved are really very large. In the latter case, it is also crucial to exploit better the computer architecture by organizing properly the computational process.
- Use of templates in connection with the treatment of very large models
- Performance of comprehensive environmental studies
- Obtaining reliable and robust information about pollution levels
- Studying the impact of future climatic changes on high pollution levels
- Investigating trends related to critical levels of pollution

This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed.< The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available.

This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.

The volumes in this authoritative series present a multidisciplinary approach to modeling and simulation of flows in the cardiovascular and ventilatory systems, especially multiscale modeling and coupled simulations. Volume 5 is devoted to cells, tissues, and organs of the cardiovascular and ventilatory systems with an emphasis on mechanotransduction-based regulation of flow. The blood vessel wall is a living tissue that quickly reacts to loads applied on it by the flowing blood. In any segment of a blood vessel, the endothelial and smooth muscle cells can sense unusual time variations in small-magnitude wall shear stress and large-amplitude wall stretch generated by abnormal hemodynamic stresses. These cells respond with a short-time scale (from seconds to hours) to adapt the vessel caliber. Since such adaptive cell activities can be described using mathematical models, a key objective of this volume is to identify the mesoscopic agents and nanoscopic mediators required to derive adequate mathematical models. The resulting biomathematical models and corresponding simulation software can be incorporated into platforms developed in virtual physiology for improved understanding and training.

During the 21st century business environments have become more complex and dynamic than ever before. Companies operate in a world of change influenced by globalisation, volatile markets, legal changes and technical progress. As a result, they have to handle growing volumes of data and therefore require fast storage, reliable data access, intelligent retrieval of information and automated decision-making mechanisms, all provided at the highest level of service quality. Successful enterprises are aware of these challenges and efficiently respond to the dynamic environment in which their business operates. Business Intelligence (BI) and Performance Management (PM) offer solutions to these challenges and provide techniques to enable effective business change. The important aspects of both topics are discussed within this state-of-the-art volume. It covers the strategic support, business applications, methodologies and technologies from the field, and explores the benefits, issues and challenges of each. Issues are analysed from many different perspectives, ranging from strategic management to data technologies, and the different subjects are complimented and illustrated by numerous examples of industrial applications. Contributions are authored by leading academics and practitioners representing various universities, research centres and companies worldwide. Their experience covers multiple disciplines and industries, including finance, construction, logistics, and public services, amongst others. Business Intelligence and Performance Management is a valuable source of reference for graduates approaching MSc or PhD programs and for professionals in industry researching in the fields of BI and PM for industrial application.

shift and dramatic improvementfrom the yearly data of the 1970s. For several years now, disaggregated methods (i. e., single-case comparisons) have been used to test theories (Davenport and Eads 2001; Rasler 1996; Francisco 1993, 1995, 1996). The single area of Snyder's(Snyder 1978)demandsthat has faltered is in linking levels of analysis in the eld of protest and repression. James DeNardo's (DeNardo 1985) and Lichbach's (Lichbach 1996) formal models have for the most part not beentestedempirically, norhaveRonaldWintrobe's(Wintrobe1998)modelsofd- tators' strategic behavior. The dif culty stems from the disjuncture between game theory or micro models and macro, aggregate data. Green and Shapiro (Green and Shapiro 1994) took an extreme position on this problem: little empirical evidence from rational choice and game theory exists. To the extent that empirical evidence comprises our understanding of politics, rational choice and game theory have - guably contributed as much or more than any other approach. Think of interest group theory before Olson's The Logic of Collective Action, of electoral theory before Cox's (Cox 1997) Making Votes Count, or of coalition theory before Riker's (Riker 1963) The Theory of Political Coalitions. There are few social scientists who would not judge these books as great for economics and political science. Cox's book alone has won every major book prize appropriate in political science. On the normative side, too few political scientists researching democratization are aware of the theory of social choice. Its ndings challenge the foundations of democratic theory (Riker 1982).

This book focuses on the finite element method in fluid flows. It is targeted at researchers, from those just starting out up to practitioners with some experience. Part I is devoted to the beginners who are already familiar with elementary calculus. Precise concepts of the finite element method remitted in the field of analysis of fluid flow are stated, starting with spring structures, which are most suitable to show the concepts of superposition/assembling. Pipeline system and potential flow sections show the linear problem. The advection-diffusion section presents the time-dependent problem; mixed interpolation is explained using creeping flows, and elementary computer programs by FORTRAN are included. Part II provides information on recent computational methods and their applications to practical problems. Theories of Streamline-Upwind/Petrov-Galerkin (SUPG) formulation, characteristic formulation, and Arbitrary Lagrangian-Eulerian (ALE) formulation and others are presented with practical results solved by those methods.

ThisbookcontainstheproceedingsoftheFourthInternationalConference onComputationalFluidDynamics(ICCFD4),heldinGent,Belgiumfrom July10through16,2006. TheICCFDconferenceseriesisanoutcomeofthe mergeroftwoimportantstreamsofconferencesinComputationalFluid- namics:InternationalConferenceonNumericalMethodsinFluidDynamics, ICNMFD(since1996)andInternationalSymposiumonComputationalFluid Dynamics,ISCFD(since1985). In1998itwasdecidedtojointhetwoand ICCFD emerged as a biannual meeting, held in Kyoto in 2000, Sydney in 2002, Toronto in 2004 and Gent in 2006. Thus, the ICCFD series became theleadinginternationalconferenceseriesforscientists,mathematiciansand engineersinterestedinthecomputationof?uid?ow. The4theditionoftheconferencehasattracted200participantsfromall overtheworld;270abstractswerereceived,ofwhich135wereselectedina carefulpeerreviewprocessbytheexecutivecommittee(C. H. Bruneau,J. -J. Chattot,D. Kwak,N. Satofuka,D. W. Zingg,E. DickandH. Deconinck)for oralpresentationandafurther21forposterpresentation. Thepaperscontainedintheseproceedingsprovideanexcellentsnapshot of the ?eld of Computational Fluid Dynamics as of 2006. Invited keynote lecturesbyrenownedresearchersareincluded,withcontributionsinthe?eld ofdiscretizationschemes,high-endcomputingandengineeringchallenges,and two-phase?ow. Thesekeynotecontributionsarecomplementedby137regular papersonthemostdiverseaspectsofCFD: -Innovativealgorithmdevelopmentfor?owsimulation,optimisationandc- trol:higher-ordermethods(DG,FV,FEandRDmethods),iterativemethods andmultigrid,solutionadaptivemeshtechniques,errorestimationandc- trol,parallelalgorithms. -Innovativemodelingof?owphysicsintheareaofcompressibleandinc- pressible ?ows: hypersonic and reacting ?ows, two-phase ?ows, turbulence (LES,DES,DNS,andtransition),vortexdynamics,boundarylayerstability, multi-scalephysics,magnetohydrodynamics. Preface VII -advancedapplicationsusingtheabovementionedinnovativetechnology,and multidisciplinaryapplicationsincludingaero-elasticityandaero-acoustics. ThanksareduetooursponsorsNASA,theFWOResearchFoundation FlandersandtheEuropeanUnionthroughtheEUA4XMarieCurieproject. Inparticular,thegenerousgrantfromNASAisakeyfactorinthesuccessof thisconferenceseriesandthepublicationoftheseProceedings. Wealsowouldliketothankthesta?andPhDstudentsofthevonKarman InstituteandtheDepartmentof?ow,heatandcombustionmechanicsofthe University of Gent, for the help they provided toward the success of this conference. Sint-Genesius-Rode,Belgium HermanDeconinck vonKarmanInstituteforFluidDynamics Ghent,Belgium ErikDick GhentUniversity September2006 ConferenceChair Contents PartIInvitedSpeakers Twonewtechniquesforgeneratingexactlyincompressible approximatevelocities BernardoCockburn...3 RoleofHigh-EndComputinginMeetingNASA'sScience andEngineeringChallenges RupakBiswas,EugeneL. Tu,WilliamR. VanDalsem...14 RecentAdvancesofMulti-phaseFlowComputationwiththe AdaptiveSoroban-gridCubicInterpolatedPropagation(CIP) Method TakashiYabe,YouichiOgata,KenjiTakizawa...29 PartIISchemes OntheComputationofSteady-StateCompressibleFlows UsingaDGMethod HongLuo,JosephD. Baum,RainaldL..ohner...47 Space-TimeDiscontinuousGalerkinMethodforLarge AmplitudeNonlinearWaterWaves YanXu,JaapJ. W. vanderVegt...53 AdiscontinuousGalerkinmethodwithHancock-typetime integrationforhyperbolicsystemswithsti?relaxationsource terms YoshifumiSuzuki,BramvanLeer...59 Contents IX VeryHighOrder,Non-OscillatoryFluctuationDistribution Schemes M. E. Hubbard,N. Z. Mebrate...65 High-orderresidualdistribution:discontinuitycapturing crosswinddissipationanddi?usion N. Villedieu-Ligout,M. Ricchiuto,H. Deconinck...7 1 High-OrderFluctuation-SplittingSchemesforAdvection- Di?usionEquations HiroakiNishikawaandPhilipRoe...77 ConstructionofHigherOrderResidualDistributionSchemes R'emiAbgrallandC'edricTav'e...83 Stableandconvergentresidualdistributionforti- dependentconservationlaws MarioRicchiuto,R'emiAbgrall...89 AnALEFormulationoftheMultidimensionalResidual DistributionSchemeforComputationsonMovingMeshes Jir'?Dobes,HermanDeconinck...95 SolutionofthesteadyEulerequationsusingFluctuation Splittingschemesonquadrilateralelements D. T. Rubino,P. DePalma,G. Pascazio,M. Napolitano ...101 AResidual-BasedCompactSchemeforAll-SpeedFlowson UnstructuredGrids ChristopheCorre,AlbertoBeccantini,ThibaudKloczko ...107 VorticityPreservingSchemeforUnsteadyCompressible Flows FabriceFalissard,AlainLerat,JacquesSid'es ...113 ExtensionoftheSDMethodtoViscousFlowonUnstructured Grids Z. J. Wang,YuzhiSun,C. Liang,Yen,Liu...119 StrictlyStableHighOrderDi?erenceMethodsforthe CompressibleEulerandNavier-StokesEquations BernhardMul ..ler...125 UniformFlowPreservingPropertyofHighOrderUpwind FiniteDi?erenceSchemesonGeneralizedCoordinateSystem TakuNonomura,NobuyukiIizuka,KozoFujii...1 31 X Contents ImplementationofanEnhancedFluxFormulationfor UnsteadyNavier-StokesSolutions G. Xia,S. Sardeshmukh,V. Sankaran,C. L. Merkle...137 ComputationofEigenspacesofHyperbolicSystems S. K. Godunov,O. B. Feodoritova,V. T. Zhukov...143 AProposedCuretotheCarbunclePhenomenon FarzadIsmail,PhilipL. Roe,HiroakiNishikawa ...149 TheHighOrderWLSQRSchemeanditsApplicationsin Turbomachinery Jivr'?Furst ...

Extra dimensions ? beyond space and time ? are the best methods for unifying gravity with particle physics. The basic extension is to five dimensions (5D), as in the induced-matter and membrane theory. This descriptive text gives an up-to-date account of the classical and quantum consequences of 5D physics. It includes topics that range from Einstein's original theory of relativity to modern views on matter. The book is mathematically precise and focuses on new ideas which appeal to readers. Examples of new ideas are: The big-bang universe, which is curved by matter in 4D, may be viewed as a smooth and empty world in 5D; the uncertainty of quantum interactions in spacetime may be regarded as the consequence of deterministic laws in higher dimensions. This book will interest people who think about the ?meaning of things?.