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Elementary feedback stabilization of the linear reaction-convection-diffusion equation and the wave equation
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ISBN: 9783642046131 9783642046124 3642046126 Year: 2010 Publisher: New York: Springer,

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Mathematical control theory of applied partial differential equations is built on linear andnonlinearfunctionalanalysisand manyexistencetheoremsin controlt- ory result from applications of theorems in functional analysis. This makes control theoryinaccessibleto studentswhodo nothave a backgroundin functionalanalysis. Many advanced control theory books on in?nite-dimensionalsystems were wr- ten, using functional analysis and semigroup theory, and control theory was p- sented in an abstract setting. This motivates me to write this text for control theory classes in the way to present control theory by concrete examples and try to m- imize the use of functional analysis. Functional analysis is not assumed and any analysis included here is elementary, using calculus such as integration by parts. The material presented in this text is just a simpli?cation of the material from the existing advanced control books. Thus this text is accessible to senior undergra- ate studentsand?rst-yeargraduatestudentsin appliedmathematics,who havetaken linear algebra and ordinary and partial differential equations. Elementary functional analysis is presented in Chapter 2. This material is - quired to present the control theory of partial differential equations. Since many control conceptsand theories for partial differentialequations are transplanted from ?nite-dimensionalcontrol systems, a brief introduction to feedback control of these systemsispresentedinChapter3.Thetopicscoveredinthischapterincludecontr- lability, observability,stabilizability, pole placement, and quadratic optimal control.


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Mechanics : from Newton's laws to deterministic chaos
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ISBN: 9783642053702 9783642053696 Year: 2010 Publisher: Berlin : Springer,

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This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present fifth edition is updated and revised with more explanations, additional examples and sections on Noether's theorem. Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics. The book contains more than 120 problems with complete solutions, as well as some practical examples which make moderate use of personal computers. This will be appreciated in particular by students using this textbook to accompany lectures on mechanics. The book ends with some historical notes on scientists who made important contributions to the development of mechanics.


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Discrete, continuous, and hybrid Petri Nets
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ISBN: 9783642106699 9783642106682 3642106684 Year: 2010 Publisher: Berlin: Springer,

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This monograph presents a well written and clearly organized introduction in the standard methods of discrete, continuous and hybrid Petri Nets. Starting from the basics of Petri nets the book imparts an accurate understanding of continuous and hybrid Petri Nets. Preserving the consistency of basic concepts throughout the text it introduces a unified framework for all the models presented. The book is a scientific monograph as well as a didactic tutorial which is easy to understand due to many exercises with solutions, detailed figures and several case studies. It demonstrates that Petri nets are a deep, practical and alive field important for researchers, engineers and graduate students in engineering and computer science. Improvements and additions in this second edition have widely benefited from teaching, student questions, and various discussions with colleagues interested or involved in the topic.


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Image Fusion : Theories, Techniques and Applications
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ISBN: 9783642112164 9783642112157 Year: 2010 Publisher: Berlin Heidelberg Springer Berlin Heidelberg

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This textbook provides a comprehensive introduction to the theories, techniques and applications of image fusion. It is aimed at advanced undergraduate and first-year graduate students in electrical engineering and computer science. It should also be useful to practicing engineers who wish to learn the concepts of image fusion and use them in real-life applications. The book is intended to be self-contained. No previous knowledge of image fusion is assumed, although some familiarity with elementary image processing and the basic tools of linear algebra is recommended. The book may also be used as a supplementary text for a course on advanced image processing. Apart from two preliminary chapters, the book is divided into three parts. Part I deals with the conceptual theories and ideas which underlie image fusion. Particular emphasis is given to the concept of a common representational framework and includes detailed discussions on the techniques of image registration, radiometric calibration and semantic equivalence. Part II deals with a wide range of techniques and algorithms which are in common use in image fusion. Among the topics considered are: sub-space transformations, multi-resolution analysis, wavelets, ensemble learning, bagging, boosting, color spaces, image thresholding, Markov random fields, image similarity measures and the expectation-maximization algorithm. Together Parts I and II form an integrated and comprehensive overview of image fusion. Part III deals with applications. In it several real-life examples of image fusion are examined in detail, including panchromatic sharpening, ensemble color image segmentation and the Simultaneous Truth and Performance algorithm of Warfield et al. The book is accompanied by a webpage from which supplementary material may be obtained. This includes support for course instructors and links to relevant matlab code.


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Handbook of geomathematics.
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ISBN: 364201545X 9786613569448 1280391529 3642015468 3642015476 Year: 2010 Publisher: Berlin : Springer,

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During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.


Book
Oligopoly : old ends, new means
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ISBN: 364215963X 9786612994982 3642159648 1282994980 Year: 2010 Publisher: Heidelberg ; New York : Springer,

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The book focuses classical oligopoly theory as developed in 1840-1940. By the end of this period oligopoly came under the spell of game theory in its probabilistic equilibrium format. Work by Cournot, von Stackelberg, Palander, and Hotelling, causal and dynamic in essence, but ignored, is reconsidered in the light of modern dynamics using topology and numerics. As particular features, von Stackelberg leadership is included in the dynamic Cournot model, the Hotelling problem is solved with elastic demand, thus skipping the absurd idea of quadratic transportation costs. Further, it is shown that the celebrated destabilisation of Cournot equilibrium under increased competition is due to mistakenly assuming constant returns, and that the whole idea of rational expectations is untenable in dynamic oligopoly. Early original ideas in oligopoly theory, such as coexistence and multiplicity of attractors are focused again after many undeserved decades of oblivion.


Book
Groups and Symmetries : From Finite Groups to Lie Groups
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ISBN: 9780387788661 9780387788654 Year: 2010 Publisher: New York NY Springer New York

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Unlike many other texts, this book deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume. Key Topics: ¢ Brisk review of the basic definitions of group theory, with examples ¢ Representation theory of finite groups: character theory ¢ Representations of compact groups using the Haar measure ¢ Lie algebras and linear Lie groups ¢ Detailed study of SO(3) and SU(2), and their representations ¢ Spherical harmonics ¢ Representations of SU(3), roots and weights, with quark theory as a consequence of the mathematical properties of this symmetry group This book is illustrated with portraits and a few historical remarks. With only linear algebra and calculus as prerequisites, Groups and Symmetries: From Finite Groups to Lie Groups is accessible to advanced undergraduates in mathematics and physics, and will still be of interest to beginning graduate students. Exercises for each chapter and a collection of problems with complete solutions make this an ideal text for the classroom and for independent study.


Book
Mathematics for Multimedia
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ISBN: 9780817648800 9780817648794 Year: 2010 Publisher: Boston Birkhäuser Boston

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This concise 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. Key features include: * Over 100 exercises with complete solutions; * Useful algorithms presented in pseudocode and Standard C to help readers with programming, experimentation, and the solution of exercises; * Numerous illustrations based on data from real studies; * Suggestions for further reading at the end of each chapter; * A companion website maintained by the author providing computer programs described in the book as well as additional references and data files, such as images and sounds, to enhance the reader's understanding of key topics; * A supplementary manual containing several hundred exercises, solutions, and sample programs not included in the book available to instructors upon request; * Minimal prerequisites only an undergraduate-level knowledge of mathematics, not including statistics, is required. Mathematics for Multimedia is an ideal textbook for upper undergraduate and beginning graduate students in pure and applied mathematics, engineering, and computer science seeking an innovative approach to contemporary mathematics with practical applications. The work may also serve as a useful reference for multimedia applications developers and other researchers and practitioners interested in the mathematics underlying multimedia software design and implementation.


Book
Matematica Numerica Esercizi, Laboratori e Progetti
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ISBN: 8847016398 9786613695246 8847016401 1280784857 Year: 2010 Publisher: Milano : Springer Milan : Imprint: Springer,

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La Matematica Numerica è una disciplina che si sviluppa in simbiosi con il calcolatore. Questo testo propone, oltre a richiami degli argomenti fondamentali, sia Esercizi teorici da risolvere "con carta e penna'', atti a far comprendere meglio al lettore la teoria, sia Laboratori, in cui per un dato problema si debbono scegliere gli algoritmi più adatti, realizzare un programma in linguaggio Matlab per la loro implementazione, infine rappresentare, interpretare ed analizzare alla luce della teoria i risultati numerici. Per ogni Esercizio ed ogni Laboratorio si presenta una risoluzione dettagliata, completata da una ampia discussione critica. Il testo contiene infine alcuni Progetti, riguardanti il primo gli algoritmi di page ranking dei moderni motori di ricerca, il secondo la determinazione del campo elettrico fra due conduttori, il terzo alcuni sistemi dinamici oscillanti di grande rilevanza in applicazioni elettroniche e biologiche.


Book
Real Analysis and Applications : Theory in Practice
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ISBN: 1441900055 0387980970 9786613568960 1280391049 0387980989 Year: 2010 Publisher: New York, NY : Springer New York : Imprint: Springer,

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This new approach to real analysis stresses the use of the subject in applications, showing how the principles and theory of real analysis can be applied in various settings. Applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and physics, Fourier series and approximation, wavelets, and convexity and optimization. Each chapter has many useful exercises. The treatment of the basic theory covers the real numbers, functions, and calculus, while emphasizing the role of normed vector spaces, and particularly of Rn. The applied chapters are mostly independent, giving the reader a choice of topics. This book is appropriate for students with a prior knowledge of both calculus and linear algebra who want a careful development of both analysis and its use in applications. Review of the previous version of this book, Real Analysis with Real Applications: "A well balanced book! The first solid analysis course, with proofs, is central in the offerings of any math.-dept.; ---and yet, the new books that hit the market don't always hit the mark: the balance between theory and applications, ---between technical proofs and intuitive ideas, ---between classical and modern subjects, and between real life exercises vs. the ones that drill a new concept. The Davidson-Donsig book is outstanding, and it does hit the mark." Palle E. T. Jorgenson, Review from Amazon.com Kenneth R. Davidson is University Professor of Mathematics at the University of Waterloo. Allan P. Donsig is Associate Professor of Mathematics at the University of Nebraska-Lincoln.

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