Springer Nature (Germany)

"This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as will students of mathematics."--BOOK JACKET.

1: Principles of Bootstrap Methodology.- 2: Principles of Edgeworth Expansion.- 3: An Edgeworth View of the Bootstrap.- 4: Bootstrap Curve Estimation.- 5: Details of Mathematical Rigour.- Appendix I: Number and Sizes of Atoms of Nonparametric Bootstrap Distribution.- Appendix II: Monte Carlo Simulation.- II.1 Introduction.- II.2 Uniform Resampling.- II.3 Linear Approximation.- II.4 Centring Method.- II.5 Balanced Resampling.- II.6 Antithetic Resampling.- II.7 Importance Resampling.- II.7.1 Introduction.- II.7.2 Concept of Importance Resampling.- II.7.3 Importance Resampling for Approximating Bias, Variance, Skewness, etc..- II.7.4 Importance Resampling for a Distribution Function.- II.8 Quantile Estimation.- Appendix III: Confidence Pictures.- Appendix IV: A Non-Standard Example: Quantite Error Estimation.- IV. 1 Introduction.- IV.2 Definition of the Mean Squared Error Estimate.- IV.3 Convergence Rate of the Mean Squared Error Estimate.- IV.4 Edgeworth Expansions for the Studentized Bootstrap Quantile Estimate.- Appendix V: A Non-Edgeworth View of the Bootstrap.- References.- Author Index.

Preface to the Second Edition Preface to the First Edition List of Figures Prerequisites by Chapter Standard Notation Introduction: Closed Linear Groups Lie Algebras and Lie Groups Complex Semisimple Lie Algebras Universal Enveloping Algebra Compact Lie Groups Finite-Dimensional Representations Structure Theory of Semisimple Groups Advanced Structure Theory Integration Induced Representations and Branching Theorems Prehomogeneous Vector Spaces Appendices Hints for Solutions of Problems Historical Notes References Index of Notation Index

The regulation of the serine-threonine kinase Akt by lipid products of phosphoinositide 3-kinase (PI 3-kinase) was investigated. Akt activity was found to correlate with the amount of phosphatidylinositol-3,4-bisphosphate (PtdIns-3,4-P2) in vivo, and synthetic PtdIns-3,4-P2 activated Akt both in vitro and in vivo. Binding of PtdIns-3,4-P2 occurred within the Akt pleckstrin homology (PH) domain and facilitated dimerization of Akt. Akt mutated in the PH domain was not activated by PI 3-kinase in vivo or by PtdIns-3, 4-P2 in vitro, and it was impaired in binding to PtdIns-3,4-P2. Examination of the binding to other phosphoinositides revealed that they bound to the Akt PH domain with much lower affinity than did PtdIns-3,4-P2 and failed to increase Akt activity. Thus, Akt is apparently regulated by the direct interaction of PtdIns-3,4-P2 with the Akt PH domain.

The appearance of this book is quite timely as it provides a much needed state-of-the-art exposition on fault detection and diagnosis, a topic of much interest to industrialists. The material included is well organized with logical and clearly identified parts; the list of references is quite comprehensive and will be of interest to readers who wish to explore a particular subject in depth. The presentation of the subject material is clear and concise, and the contents are appropriate to postgraduate engineering students, researchers and industrialists alike. The end-of-chapter homework problems are a welcome feature as they provide opportunities for learners to reinforce what they learn by applying theory to problems, many of which are taken from realistic situations. However, it is felt that the book would be more useful, especially to practitioners of fault detection and diagnosis, if a short chapter on background statistical techniques were provided. Joe Au

ABSTRACT Trading losses associated with information asymmetries can be mitigated by designing securities which split the cash flows of underlying assets. These securities, which can arise endogenously, have values that do not depend on the information known only to informed agents. Bank debt (deposits) is an example of this type of liquid security which protect relatively uninformed agents, and we provide a rationale for deposit insurance in this content. High‐grade corporate debt and government bonds are other examples, implying that a money market mutual fund‐based payments system may be an alternative to one based on insured bank deposits.

Large Eddy Simulation (LES) is an approach to compute turbulent flows based on resolving the unsteady large-scale motion of the fluid while the impact of the small-scale turbulence on the large scales is accounted for by a sub-grid scale model. This model distinguishes LES from any other method and reduces the computational demands compared with a Direct Numerical Simulation. On the other hand, the cost typically is still at least an order of magnitude larger than for steady Reynolds-averaged computations. The LES approach is attractive when statistical turbulence models fail, when insight into the vortical dynamics or unsteady forces on a body is desired, or when additional features are involved such as large-scale mixing, particle transport, sound generation etc. In recent years the rapid increase of computer power has made LES accessible to a broader scientific community, and this is reflected in an abundance of papers on the method and its applications. Still, however, some fundamental aspects of LES are not conclusively settled, a fact residing in the intricate coupling between mathematical, physical, numerical and algorithmic issues. In this situation it is of great importance to gain an overview of the available approaches and techniques. Pierre Sagaut, in the style of a French encyclopedist, gives a very complete and exhaustive treatment of the different kinds of sub-grid scale models which have been developed so far. After discussing the separation into resolved and unresolved scales and its application to the Navier-Stokes equations, more than 140 pages are directly devoted to the description of sub-grid scale models. They are classified according to different criteria, which helps the reader to find his or her way through the arsenal of reasonings. The theoretical framework for which these models have mostly been developed is isotropic turbulence. The required notions from classical turbulence theory are summarized together with notions from EDQNM theory in two concise and helpful appendices. Further sections deal with numerical and implementational issues, boundary conditions and validation practice. A final section assembles a few key applications, cumulating in a condensed list of some general experiences gained so far. The book very wisely concentrates on issues particular to LES, which to a large extent is sub-grid scale modelling. Classical issues of CFD, such as numerical discretization schemes, solution procedures etc, or post-processing are not addressed. Limiting himself to incompressible, non-reactive flows, the author succeeds in describing the fundamental issues in great detail, thus laying the foundations for the understanding of more complex situations. The presentation is essentially theoretical and the reader should have some prior knowledge of turbulence theory and Fourier transforms. The text itself is well written and generally very clear. A pedagogical effort is made in several places, e.g. when an overview over a group of models is given before these are described in detail. A few typing errors and technical details should be amended in a second edition, though, such as the statement that a filter which is not a projector is invertible (p 12), but this is not detrimental to the quality of the text. Overall the book is a very relevant contribution to the field of LES and I read it with pleasure and benefit. It constitutes a worthy reference book for scientists and engineers interested in or practising LES and may serve as a textbook for a postgraduate course on the subject. Jochen Fröhlich

Introduction to Survival Analysis.- Kaplan-Meier Survival Curves and the Log-Rank Test.- The Cox Proportional Hazards Model and Its Characteristics.- Evaluating the Proportional Hazards Assumption.- The Stratified Cox Procedure.- Extension of the Cox Proportional Hazards Model for Time-Dependent Variables.- Parametric Survival Models.- Recurrent Events Survival Analysis.- Competing Risks Survival Analysis.

Based on the author's lectures at the University of Bonn in 1983-84, this book introduces classical scattering theory and the time-dependent theory of linear equations in mathematical physics. Topics include proof of the existence of wave operators, some special equations of mathematical physics, exterior boundary value problems, radiation conditions, and limiting absorption principles. 1986 edition.

The story of Shuji Nakamura and the blue laser diode is remarkable. It is clear from this book that he enjoys this fact and wishes his readers to become familiar with his success. Nakamura was a little known researcher at a small but successful Japanese company, Nichia Chemical, on Shikoku, one of Japan's four main islands. One of their successful lines was phosphors for fluorescent lights. In 1989, Nakamura was given a few million dollars by the company's Chairman Nobuo Ogawa. Nakamura chose to research into blue light emitters using gallium nitride, a material that had been studied by Pankove at RCA some 20 years earlier and largely written off by the conventional semiconductor industry. In spite of many factors against progress, this second edition of The Blue Laser Diode testifies to the success of this gamble. The book is subtitled `The complete story'. This is an unlikely epithet for the book because there is still a long way to go. The book is written with a mixture of academic integrity and commercial trumpet blowing. There is too often a lack of detail and logical order. There is inadequate discussion of the case for and against other materials such as ZnSe. One feels that the commercial pressure not to give away all the answers about gallium nitride has triumphed over the wish for scientific disclosure to enable results to be repeated. The book clearly reports the two most significant difficulties faced by gallium nitride. First, it appeared from Pankove's work that it would not to be easy to find an appropriate p-type dopant that could make suitable p-n junctions. Two chapters consider this problem, starting with low energy electron beam irradiation and then in the second chapter considering thermal annealing in nitrogen. The writing and detail suggest that it is still a technology rather than science (or, perhaps more unkindly, cook-book recipes of time and temperature). The second important difficulty is that gallium nitride has too many dislocations for long-life laser action. Growth on sapphire with appropriate buffer layers is described as an initial step in reducing the dislocations. Later in the book, it is recognized that In x Ga 1- x N offers greater versatility, and this is considered in more detail along with InGaN/AlGaN double heterostructures. Regrettably it is not easy though to dig out from this book all the details of lattice matching that are required and how successful lattice matching has been in removing dislocations and increasing lifetime. Clearly the general trend of longer lifetimes means that there has been useful success. Blue laser diodes are now claimed to be commercially available with lifetimes measured in thousands of hours while blue light emitting diodes, with their lower current densities, are said to have lifetimes measurable in years. The book has a little for everyone. Applications are noted briefly as well as blow-by-blow accounts of the manufacturing technology of double heterostructure, multi-quantum well lasers and progress to room temperature operation. Applications range from the mundane traffic light, through full colour displays to 15-20 Gbyte optically read data storage discs. Interestingly it is the mundane applications that may have the biggest financial impact. A statistic that appears on the Internet is that if all the traffic signals in Japan could be switched to suitable LEDs then one could save the construction of at least one nuclear power plant. Although Nakamura is an admirer of Pankove's work, the writing and scientific style does not match that of Pankove. Nevertheless the book records a thorough solid achievement and as such there should be a similar solid basis for many readers in materials science and laser technology wishing to read this book. The book regrettably gives no indication why Nakamura has left Nichia for a Professorship at Santa Barbara after such magnificent early support by Nichia. Nor does the book explain why Nakamura's co-author Gerhard Fasol is undercutting the joint venture by selling for $15 over the web a 28 page summary about blue laser diodes using gallium nitride. However, if price is no consideration, there is also advertised on the web a 222 page report SC-23 from Strategies Unlimited entitled `Gallium Nitride 2000 - Technology Status, Applications, and Market Forecast' for a modest $3950. Clearly the present book cannot be `the complete story'. That will run for quite a time yet. John Carroll

This paper studies whether removing barriers to trade induces efficiency gains for producers. Like almost all empirical work which relies on a production function to recover productivity measures, I do not observe physical output at the firm level. Therefore, it is imperative to control for unobserved prices and demand shocks. I develop an empirical model that combines a demand system with a production function to generate estimates of productivity. I rely on my framework to identify the productivity effects from reduced trade protection in the Belgian textile market. This trade liberalization provides me with observed demand shifters that are used to separate out the associated price, scale, and productivity effects. Using a matched plant–product level data set and detailed quota data, I find that correcting for unobserved prices leads to substantially lower productivity gains. More specifically, abolishing all quota protections increases firm-level productivity by only 2 percent as opposed to 8 percent when relying on standard measures of productivity. My results beg for a serious reevaluation of a long list of empirical studies that document productivity responses to major industry shocks and, in particular, to opening up to trade. My findings imply the need to study the impact of changes in the operating environment on productivity together with market power and prices in one integrated framework. The suggested method and identification strategy are quite general and can be applied whenever it is important to distinguish between revenue productivity and physical productivity.

An algorithm is described for obtaining an optimal approximation, using triangulation, of a three-dimensional surface defined by randomly distributed points along contour lines. The combinatorial problem of finding the best arrangement of triangles is treated by assuming an adequate objective function. The optimal triangulation is found using classical methods of graph theory. An illustrative example gives the procedure for triangulation of contour lines of a human head for use in radiation therapy planning.

Many engineers, working in the field of automotive control systems and mechatronics, as well as lecturing at technical universities, will welcome this book. It gives a broad insight view of the latest automotive technologies in use which have been adopted over a long period of time from research activities at universities and in industry. About twenty years ago the microcomputer started to revolutionize the possibility of introducing intelligence in systems, for example in the form of advanced control algorithms. By chance, this incredible evolution coincided with increasing environmental demands to reduce pollution and oil consumption and to contribute one of the major tools to meet those demands. This may have been one of the reasons why the automotive industry was rather early in introducing the new technique. However, it would have been interesting if the book had given a short historic review. In fact the authors do not rule out that the modern four-stroke engine in a car may work as an air-cleaning filter, and after going through the part describing the lambda-control together with the catalytic conversion, it is hard to argue against it, at least when the vehicle is running at constant speed. Reading this book you realize that the times are long gone when you could use a screwdriver and feeler gauge to adjust the ignition of your car engine. The subtitle of the book is engine, driveline and vehicle and the book is also divided in that logical order. In the first part, after describing the thermodynamic cycles of different engine types, spark ignited and diesel, the basic engine operations are presented and the reader is given a theoretical insight into what can be done to enhance the performance of the engine. If you have forgotten the basic laws of thermodynamics there is an appendix to recapitulate (however, there is no explanation of the word stoichiometric in case you are not familiar with that). You will also find information on the efficiency of different fuels as well as the efficiency of engines derived from crankshaft motions and thermodynamics. The next chapter describes how the derived models of engine management are used for advanced engine control. The chapter also presents simulation results as well as measurement results. What is especially interesting to read about is how effectively the catalytic conversion works together with lambda-control at stoichiometric combustion of the spark-ignited engine. This is thoroughly explained in the text but a curious reader will not get any information about problems or if there are ongoing activities with emission reduction concerning its competitor, the diesel engine. It is understandable that the book concentrates on the most popular automotive engines but an interested reader might miss that there is nothing in the book that covers the state-of-the-art spark-ignited two-stroke engine. The second part of the book covers the driveline, that is, the parts that transfer the torque of the engine to the wheels. The initial chapters cover the derivation of general models of driveline, basically by applying Newton's second law of motion. Those models are then applied to the modern truck for simulation of the dynamical behaviour. After validation, the appropriate simulation model is used in designing a control system for a transmission that does not need a clutch for shifting gears. Consequently, this part of the book is very interesting since, most likely, one of the authors has worked in close cooperation with the Swedish truck manufacturer Scania. He describes the development behind this unique and patented transmission system. The third and last part of the book deals with the vehicle itself. Initially, geometrical vehicle models of different complexity, the two-track and single-track, are described. They are used to derive the forces acting on the wheels due to road friction and road profile, as well as the driver's input, such as steering and braking. The book claims to have 291 illustrations. The third part of the book, however, could have benefited from more illustrations, for example, the classical geometrical terms such as caster, camber, toe-in and out, etc. As in the previous driveline part of the book, the models are validated and applied on an observer design. The models of the torque balance and the wheel-road contact are then used to design an ABS control system. This is also a very interesting state-of-the-art part since one of the authors is well acquainted with the Bosch ABS system. A guess is that the next updated publication of the book will also cover active suspension. Finally, the authors describe different approaches to enhance the vehicle model with using a driver model. Simpler PID-controllers as well as more advanced controllers to describe human behaviour are covered. In summary this is a really interesting book, well worth reading and studying. It covers the whole chain of the main parts of a modern vehicle. The book excites the reader and gives a broad insight into modern automotive control, as well as general control theory. All advanced control techniques seem to be in use in modern vehicle design, for example, adaptive control, linear quadratic design with loop-recovery, fuzzy estimators, Kalman filters, non-linear observer design, etc. The book is brimming over with important information of different kinds. However, it is a pity that the book does not have an alphabetic index. Carl During

The book Plasma Kinetics in Atmospheric Gases is a worthwhile contribution to the basic phenomena in nitrogen, oxygen and other atmospheric gases. It contains basic introductory chapters on relaxation in translational, rotational (short) and vibrational (extensive) distribution and on the physics of electron excitation and electron distribution functions. In the latter, electron beam excitation (i.e. high electron energies) are included. In the following chapters, much detail follows on spectroscopic constants of various molecules, molecular fragments and ions, on transport coefficients such as diffusion coefficients, relaxation times and rates. The transfer between translational energies and rotational and vibrational energies are treated in this context. Many (electron) excitation rates, electronic lifetimes and rates for chemical reactions for molecules, fragments and ions are given. The background part of the book is completed with an introductory chapter on wall reactions and accommodation coefficients. In this way an enormous wealth of data for nitrogen-, oxygen- and hydrogen-containing molecules can be found in this book. The book continues with the discussion of discharge physics in pure nitrogen and oxygen, and in mixtures. Some examples are given of applications, of which cleaning of atmospheric gases is, in my view, one of the most important. The many processes which play a role in the ionosphere are another important example of the application of the basic material for nitrogen, oxygen and other molecules. The kinetics which play a role in re-entry problems, and which have a limiting effect on the heat flux, are another example of the application of the plasma chemistry of nitrogen and oxygen gases. In this context fits also a short treatment of acoustic and shock waves, with which the book closes. The structure of the book is that of separate chapters which are in a logical order and follow naturally from the preceding ones. The chapters are separate in the sense that there are not many cross-references between them and all contain their own reference lists. Most of the reference lists (but not all) are extensive and contain recent references. A particular value of the book is the coverage of Russian references. However, I missed in several chapters some references as, for example, a recent book by Ricard on a related subject and other publications of, for example, French and Japanese groups which work on N 2 and O 2 discharges. This means also that some rates are given without mention of the discussion on them. Nevertheless, in my view this is a very useful book and I will use it extensively. The physics and chemistry of nitrogen- and oxygen-containing plasmas present a great challenge, and much is still unknown and not fully understood, in particular also in combination with surface processes. In this research the book will prove to be a valuable contribution. Professor D C Schram Department of Physics, Eindhoven University of Technology, 5600 MB Eindhoven

Various theories have been proposed to explain increases in muscle extensibility observed after intermittent stretching. Most of these theories advocate a mechanical increase in length of the stretched muscle. More recently, a sensory theory has been proposed suggesting instead that increases in muscle extensibility are due to a modification of sensation only. Studies that evaluated the biomechanical effect of stretching showed that muscle length does increase during stretch application due to the viscoelastic properties of muscle. However, this length increase is transient, its magnitude and duration being dependent upon the duration and type of stretching applied. Most of these studies suggest that increases in muscle extensibility observed after a single stretching session and after short-term (3- to 8-week) stretching programs are due to modified sensation. The biomechanical effects of long-term (>8 weeks) and chronic stretching programs have not yet been evaluated. The purposes of this article are to review each of these proposed theories and to discuss the implications for research and clinical practice.

This book is the second edition of a textbook published in 1996 by McGraw Hill and originates from a graduate level course given by the authors at the University of Naples. The topics include kinematics, statics and dynamics of robot manipulators together with trajectory planning and active control. There are only minor additions the first edition, which are mainly the use of quaternion to describe the orientation of the end effector and a short description of a closed chain architecture for a manipulator (parallelogram arm). The book is largely devoted to serial manipulators, with special developments about active control including adaptative control, robust controls and stability analysis. Another strength of this book is the great number of problems proposed at the end of each chapter, together with a list of references related to it. The fundamental features covered by the text are illustrated on simple examples of serial manipulators (two-link planar arm, parallelogram arm) including analytical results and numerical tests. The book has nine chapters followed by three appendices. The first appendix is devoted to linear algebra, the second recalls some fundamental aspects of rigid body mechanics and the third gives some basic principles of feedback control of linear systems. Chapter one is an introduction to the study of robot manipulators, giving an interesting classification of their architectures, the corresponding workspace and describes the tasks for which they are used. After some standard examples of industrial manipulators, bibliographical reference texts are proposed, including textbooks on modelling and control of robots, general books on robotics, specialized texts, scientific robotic reviews and some international conferences on robotics. Chapters two, three and four are devoted to mechanical modelling of robot manipulators. The fundamental basics of kinematics are given in chapter two, including the representation of finite rotations by Euler angles or unit quaternions, homogeneous transformations, Denavit-Hartenberg parameters and workspace. The direct and inverse kinematical problems are solved in analytical form for some typical manipulator structures. The differential kinematics of robots are presented in chapter three, with an introduction to the geometric and analytic Jacobian matrices, kinematic singularities and redundancy. The inverse kinematic problem is presented, with special attention to the case of redundant robots where the solution is obtained by a linear optimization problem leading to the introduction of the pseudo-inverse Jacobian matrix and to the solution of several objectives such as avoidance of collision with an obstacle or moving away from singularities. Several inverse kinematics algorithms are given wih an interesting application to a three-link planar arm. Finally, a property of kineto-statics duality is deduced from the principle of virtual work applied to an equilibrium configuration of the robot. Chapter four is a standard presentation of the derivation of the dynamical model by Lagrange formulation and then by the Newton-Euler method. In the Lagrange formulation method, the linearity with respect to inertial parameters is shown and a detailed formulation of the dynamical model is obtained for a two-link Cartesian arm, a two-link planar arm and a parallelogram arm. The problem of dynamic parameter identification is also briefly presented from a numerical point of view. The recursive algorithm constructed from the Newton-Euler formulation is presented and illustrated by considering a two-link planar arm. Finally, the operational space dynamic model is introduced. In chapter five, paths and trajectory planning in joints and in operational spaces are presented; several classical methods of interpolation are described. Chapter six is an extensive study of active control of manipulators. Several methods are presented, involving classical independent joint control, non-linear centralized control, robust control and adaptative control. Both joint-space control and operational-space control are studied together with stability analysis by using Liapounoff functions. An interesting application to the two-link planar arm already used shows the comparison between various control schemes. Chapter seven deals with interaction control of serial manipulators with the working environment. Several strategies involving compliance control, impedance control, force control and hybrid control are presented. Chapter eight describes the actuators and the sensors used in robotics. Several types of servomotors (electric and hydraulic) are presented, together with the model giving their input/output relationship. Several kinds of sensors are also described including encoders, tachometers, force and vision sensors. The last chapter gives a short presentation of the functional architecture of a robot's control system, including characteristics of the programing environment and the hardware architecture. In conclusion, the book provides a good insight about simulation and control of robot manipulators, with a detailed study of the various control strategies and several interesting and pedagogical applications. This book is an excellent review of the standard knowledge needed not only for graduate students but also for researchers interested in robot manipulators. M Pascal

Computer algebra is an alternative and complement to numerical mathematics. Its importance is steadily increasing. This volume is the first systematic and complete treatment of computer algebra. It presents the basic problems of computer algebra and the best algorithms now known for their solution with their mathematical foundations, and complete references to the original literature. The volume follows a top-down structure proceeding from very high-level problems which will be well-motivated for most readers to problems whose solution is needed for solving the problems at the higher level. The volume is written as a supplementary text for a traditional algebra course or for a general algorithms course. It also provides the basis for an independent computer algebra course.

The dynamics of modern economic systems since the Industrial Revolution show that permanent changes in the absolute levels of some basic magnitudes (such as gross national product, total consumption, total investments, total employment, etc.) are inherently associated with changes in their composition ; that is, with structural change . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This monograph is intended to be a reasonably self -contained and fairly complete exposition of rigorous results in abstract kinetic theory. Throughout, abstract kinetic equations refer to (an abstract formulation of) equations which describe transport of particles, momentum, energy, or, indeed, any transportable physical quantity. These include the equations of traditional (neutron) transport theory, radiative transfer, and rarefied gas dynamics, as well as a plethora of additional applications in various areas of physics, chemistry, biology and engineering. The mathematical problems addressed within the monograph deal with existence and uniqueness of solutions of initial-boundary value problems, as well as questions of positivity, continuity, growth, stability, explicit representation of solutions, and equivalence of various formulations of the transport equations under consideration. The reader is assumed to have a certain familiarity with elementary aspects of functional analysis, especially basic semigroup theory, and an effort is made to outline any more specialized topics as they are introduced. Over the past several years there has been substantial progress in developing an abstract mathematical framework for treating linear transport problems. The benefits of such an abstract theory are twofold: (i) a mathematically rigorous basis has been established for a variety of problems which were traditionally treated by somewhat heuristic distribution theory methods; and (ii) the results obtained are applicable to a great variety of disparate kinetic processes. Thus, numerous different systems of integrodifferential equations which model a variety of kinetic processes are themselves modelled by an abstract operator equation on a Hilbert (or Banach) space.

Das Buch führt anhand konkreter Vorgehensweisen in die Diskussion und Praxis der Triangulation ein. Es zeichnet Ursprung und Geschichte des Konzepts sowie kritische Diskussionen nach. Triangulation so