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1000 tulosta hakusanalla Vector Hasting

Vector Variational Inequalities and Vector Optimization

Vector Variational Inequalities and Vector Optimization

Qamrul Hasan Ansari; Elisabeth Kobis; Jen-Chih Yao

Springer International Publishing AG
2017
sidottu
This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.
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Vector Network Analyzer (VNA) Measurements and Uncertainty Assessment

Vector Network Analyzer (VNA) Measurements and Uncertainty Assessment

Nosherwan Shoaib

Springer International Publishing AG
2018
nidottu
This book describes vector network analyzer measurements and uncertainty assessments, particularly in waveguide test-set environments, in order to establish their compatibility to the International System of Units (SI) for accurate and reliable characterization of communication networks. It proposes a fully analytical approach to measurement uncertainty evaluation, while also highlighting the interaction and the linear propagation of different uncertainty sources to compute the final uncertainties associated with the measurements. The book subsequently discusses the dimensional characterization of waveguide standards and the quality of the vector network analyzer (VNA) calibration techniques. The book concludes with an in-depth description of the novel verification artefacts used to assess the performance of the VNAs. It offers a comprehensive reference guide for beginners to experts, in both academia and industry, whose work involves the field of network analysis, instrumentation and measurements.
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Vector Variational Inequalities and Vector Optimization

Vector Variational Inequalities and Vector Optimization

Qamrul Hasan Ansari; Elisabeth Köbis; Jen-Chih Yao

Springer International Publishing AG
2018
nidottu
This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.
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Vector Fields on Manifolds

Vector Fields on Manifolds

Michael Francis Atiyah

Springer-Verlag
1970
nidottu
This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist­ ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens­ ions of Hopf's theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle).
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Vector Optimization

Vector Optimization

Guang-ya Chen; Xuexiang Huang; Xiaogi Yang

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2005
nidottu
Vector optimization model has found many important applications in decision making problems such as those in economics theory, management science, and engineering design (since the introduction of the Pareto optimal solu­ tion in 1896). Typical examples of vector optimization model include maxi­ mization/minimization of the objective pairs (time, cost), (benefit, cost), and (mean, variance) etc. Many practical equilibrium problems can be formulated as variational in­ equality problems, rather than optimization problems, unless further assump­ tions are imposed. The vector variational inequality was introduced by Gi- nessi (1980). Extensive research on its relations with vector optimization, the existence of a solution and duality theory has been pursued. The fundamental idea of the Ekeland's variational principle is to assign an optimization problem a slightly perturbed one having a unique solution which is at the same time an approximate solution of the original problem. This principle has been an important tool for nonlinear analysis and optimization theory. Along with the development of vector optimization and set-valued optimization, the vector variational principle introduced by Nemeth (1980) has been an interesting topic in the last decade. Fan Ky's minimax theorems and minimax inequalities for real-valued func­ tions have played a key role in optimization theory, game theory and math­ ematical economics. An extension was proposed to vector payoffs was intro­ duced by Blackwell (1955).
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Vector and Parallel Processing - VECPAR 2000

Vector and Parallel Processing - VECPAR 2000

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2001
nidottu
This book is the ?nal outcome of VECPAR 2000 – 4th International Meeting on Vector and Parallel Processing. VECPAR constitutes a series of conferences, which have been organized by the Faculty of Engineering of the University of Porto since 1993, with the main objective of disseminating new knowledge on parallel computing. Readership of This Book The book is aimed at an audience of researchers and graduate students in a broad range of scienti?c areas, including not only computer science, but also applied mathematics and numerical analysis, physics, and engineering. Book Plan From a total of 66 papers selected on the basis of extended abstracts for p- sentation at the conference, a subset of 34 papers were chosen during a second review process leading to their inclusion in the book, together with the invited talks. The book contains a total of 40 papers organized into 6 chapters, where each may appeal to people in di?erent but still related scienti?c areas. All ch- ters, with the exception of Chapter 6, are initiated by a short text, providing a quick overview of the organization and papers in the chapter. The 13 papers in Chapter 1 cover the aspects related to the use of multiple processors. Operating systems, languages and software tools for scheduling, and code transformation are the topics included in this chapter, initiated by the talk on computing over the Internet, entitled Grid Computing,byIan Foster.
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Vector Bundles on Curves - New Directions

Vector Bundles on Curves - New Directions

Shrawan Kumar; Gérard Laumon; Ulrich Stuhler

Springer-Verlag Berlin and Heidelberg GmbH Co. K
1997
nidottu
The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. It deals with: 1. The relation between conformal blocks and generalised theta functions (Lectures by S. Kumar) 2. Drinfeld Shtukas (Lectures by G. Laumon) 3. Drinfeld modules and Elliptic Sheaves (Lectures by U. Stuhler) The latter topics are useful in connection with Langlands programme for function fields. The contents of the book would give a comprehensive introduction of these topics to graduate students and researchers.
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Vector and Parallel Processing - VECPAR'96

Vector and Parallel Processing - VECPAR'96

Springer-Verlag Berlin and Heidelberg GmbH Co. K
1997
nidottu
This book constitutes a carefully arranged selection of revised full papers chosen from the presentations given at the Second International Conference on Vector and Parallel Processing - Systems and Applications, VECPAR'96, held in Porto, Portugal, in September 1996.Besides 10 invited papers by internationally leading experts, 17 papers were accepted from the submitted conference papers for inclusion in this documentation following a second round of refereeing. A broad spectrum of topics and applications for which parallelism contributes to progress is covered, among them parallel linear algebra, computational fluid dynamics, data parallelism, implementational issues, optimization, finite element computations, simulation, and visualisation.
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Vector and Parallel Processing - VECPAR'98

Vector and Parallel Processing - VECPAR'98

Springer-Verlag Berlin and Heidelberg GmbH Co. K
1999
nidottu
This book stands as the visible mark of VECPAR'98 - 3rd International Meeting on Vector and Parallel Processing, which was held in Porto (Portugal) from 21 to 23 June 1998. VECPAR'98 was the third of the VECPAR series of conferences initiatedin1993and organisedby FEUP, the FacultyofEngineering of the University of Porto. The conference programme comprised a total of 6 invited talks, 66 c- tributedpapers and18posters. Thecontributed papers andposters were selected from 120 extended abstracts originating from 27 countries. Outline of the book The book, with 7 chapters, contains 41 contributed papers and 6 invited talks. The 41 papers included in these proceedings result from the reviewing of all papers presented at the conference. Each of the ?rst 6 chapters includes 1 of the 6 invited talks of the conference, and related papers. Chapters 1, 2, 4, 5 and 7 are initiated by an introductory text providing the reader with a guide to the chapter contents. Chapter 1 is on numerical algebra.It begins with an introductory text by - cente Hern'andez, followedby the invited talk by Gene Golub, entitled Some - usual Eigenvalue Problems.The remaining11contributed articles in thischapter deal either with large scale eigenvalue problems or with linear system problems. Computational?uiddynamicsandcrashandstructural analysiswere brought under the same chapter and that is Chapter 2, which contains the invited talk byTimothyBarth, entitledParallel Domain Decomposition Pre-conditioning for Computational Fluid Dynamics, plus 8 contributed papers. Timothy Barth also authors the introductory text to the chapter.
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Vector Calculus

Vector Calculus

Paul C. Matthews

Springer-Verlag Berlin and Heidelberg GmbH Co. K
1998
nidottu
Vector calculus is the fundamental language of mathematical physics. It pro­ vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top­ ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro­ gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un­ derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.
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Vector fields on Singular Varieties

Vector fields on Singular Varieties

Jean-Paul Brasselet; José Seade; Tatsuo Suwa

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2009
nidottu
Vector?eldsonmanifoldsplaymajorrolesinmathematicsandothersciences. In particular, the Poincar' e-Hopf index theorem and its geometric count- part,the Gauss-Bonnettheorem, giveriseto the theoryof Chernclasses,key invariants of manifolds in geometry and topology. One has often to face problems where the underlying space is no more a manifold but a singular variety. Thus it is natural to ask what is the "good" notionofindexofavector?eld,andofChernclasses,ifthespaceacquiress- gularities.Thequestionwasexploredbyseveralauthorswithvariousanswers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph. Marseille Jean-Paul Brasselet Cuernavaca Jos' e Seade Tokyo Tatsuo Suwa September 2009 v Acknowledgements Parts of this monograph were written while the authors were staying at various institutions, such as Hokkaido University and Niigata University in Japan, CIRM, Universit' e de la Mediterran' ee and IML at Marseille, France, the Instituto de Matem' aticas of UNAM at Cuernavaca, Mexico, ICTP at Trieste, Italia, IMPA at Rio de Janeiro, and USP at S" ao Carlos in Brasil, to name a few, and we would like to thank them for their generous hospitality and support. Thanks are also due to people who helped us in many ways, in particular our co-authors of results quoted in the book: Marcelo Aguilar, Wolfgang Ebeling, Xavier G' omez-Mont, Sabir Gusein-Zade, LeDung " Tran ' g, Daniel Lehmann, David Massey, A.J. Parameswaran, Marcio Soares, Mihai Tibar, Alberto Verjovsky,andmanyother colleagueswho helped usin variousways.
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Vector Control of Three-Phase AC Machines

Vector Control of Three-Phase AC Machines

Nguyen Phung Quang; Jörg-Andreas Dittrich

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2010
nidottu
The book deals with the problem area of the vector control of the three-phase AC machines like that one of the induction motor with squirrel-cage rotor (IMSR), the permanentmagnet excited synchronous motor (PMSM) and that one of the doubly fed induction machine (DFIM) from the view of the practical development. It is primarily about the use of the IMSR as well as the PMSM in the electrical drive systems, at which the method of the field-oriented control has been successful in the practice, and about the use of the grid voltage oriented controlled DFIM in the wind power plants. After a summary of the basic structure of a field-oriented controlled three-phase AC drive, the main points of the design and of the application are explained. The detailed description of the design rules forms the main emphasis of the book. The description is expanded and made understandable by numerous formulae, pictures and diagrams. Using the basic equations, first the continuous and then the discrete machine models of the IMSR as well as of the PMSM are derived. The vectorial two-dimensional current controllers, which are designed with help of the discrete models, are treated in detail in connection with other essential problems like system boundary condition and control variable limitation. Several alternative controller configurations are introduced. The voltage vector modulation, the field orientation and the coordinate transformations are treated also from the view of the practical handling. The problems like the parameter identification, parameter adaptation and the management of machine states, which are normally regarded as abstract, are so represented that the book reader does not receive only attempts but also comprehensible solutions for his system. The practical style in the description of the design rules of the drive systems are also continued consistently for the wind power systems using the DFIM. The represented control concept is provenpractically and can be regarded as pioneering for new developments. The introduced control structures of the three machine types have led to a relatively mature stage of development in the practice. Some disadvantages have nevertheless remained at these linear control concepts, which have to be cleared only with nonlinear controllers. Going out from the structural nonlinearity of the machines, the suitable nonlinear models are derived. After that, nonlinear controllers are designed on the basis of the method of the "exact linearization" which proves to be the most suitable in comparison with other methods like "backstepping-based or passivity-based designs".
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Vector Optimization

Vector Optimization

Johannes Jahn

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2010
sidottu
Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning.This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.
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Vector Optimization with Infimum and Supremum

Vector Optimization with Infimum and Supremum

Andreas Löhne

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2011
sidottu
The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.
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Vector Optimization with Infimum and Supremum

Vector Optimization with Infimum and Supremum

Andreas Löhne

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2013
nidottu
The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.
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