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A compilation of original articles by Bayesian experts, this volume presents perspectives on recent developments on nonparametric and semiparametric methods in Bayesian statistics. The articles discuss how to conceptualize and develop Bayesian models using rich classes of nonparametric and semiparametric methods, how to use modern computational tools to summarize inferences, and how to apply these methodologies through the analysis of case studies.
Bayesian statistical decision theory  Nonparametric statistics  Bayesian statistical decision theory.  Nonparametric statistics.  Mathematical statistics  Applied mathematics.  Engineering mathematics.  Applications of Mathematics.  Engineering  Engineering analysis  Mathematical analysis  Mathematics
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Mathematical analysis  Engineering mathematics  517  519.6  Engineering  Engineering analysis  Analysis  Computational mathematics. Numerical analysis. Computer programming  Mathematics  Engineering mathematics.  519.6 Computational mathematics. Numerical analysis. Computer programming  517 Analysis
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Engineering mathematics  Mathematics  Industrial applications  Mathematical Sciences  Applied Mathematics  Mathematics.  Industrial applications.  Math  Engineering  Engineering analysis  Science  Mathematical analysis  Operations research  Operations research.  Operational analysis  Operational research  Industrial engineering  Management science  Research  System theory  wiskunde  mathematics  Toegepaste wiskunde
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Engineering mathematics  Probabilities  519.21  Probability  Statistical inference  Combinations  Mathematics  Chance  Least squares  Mathematical statistics  Risk  Engineering  Engineering analysis  Mathematical analysis  519.21 Probability theory. Stochastic processes  Probability theory. Stochastic processes  Stochastic processes
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In September 1997, the Working Week on Resolution of Singularities was held at Obergurgl in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up part I of this volume. They are complemented in part II by fifteen selected contributions on specific topics and resolution theories. The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems.
Differential geometry. Global analysis  512.76  Singularities (Mathematics)  Geometry, Algebraic  Birational geometry. Mappings etc.  512.76 Birational geometry. Mappings etc.  Birational geometry. Mappings etc  Géométrie algébrique  Singularités (mathématiques)  Algebraic geometry.  Topology.  Applied mathematics.  Engineering mathematics.  Algebraic Geometry.  Applications of Mathematics.  Engineering  Engineering analysis  Mathematical analysis  Analysis situs  Position analysis  Rubbersheet geometry  Geometry  Polyhedra  Set theory  Algebras, Linear  Algebraic geometry  Mathematics
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Interactive Particle Systems is a branch of Probability Theory with close connections to Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T. Liggett, Interacting Particle System, ISBN 354096069) that treated the subject as it was at that time. The present book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. In so doing, many of the most useful techniques in the field are explained and developed, so that they can be applied to other models and in other contexts. Extensive Notes and References sections discuss other work on these and related models. Readers are expected to be familiar with analysis and probability at the graduate level, but it is not assumed that they have mastered the material in the 1985 book. This book is intended for graduate students and researchers in Probability Theory, and in related areas of Mathematics, Biology and Physics.
Statistical physics  Processus stochastiques  Stochastic processes  Stochastische processen  Probabilities.  Mathematical physics.  Applied mathematics.  Engineering mathematics.  Probability Theory and Stochastic Processes.  Theoretical, Mathematical and Computational Physics.  Mathematical and Computational Engineering.  Engineering  Engineering analysis  Mathematical analysis  Physical mathematics  Physics  Probability  Statistical inference  Combinations  Mathematics  Chance  Least squares  Mathematical statistics  Risk
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Hybrid dynamical systems, both continuous and discrete dynamics and variables, have attracted considerable interest recently. This emerging area is found at the interface of control theory and computer engineering, focusing on the analogue and digital aspects of systems and devices. They are essential for advances in modern digital controller technology. "Qualitative Theory of Hybrid Dynamical Systems" provides a thorough development and systematic presentation of the foundations and framework for hybrid dynamical systems. The presentation offers an accessible, but precise, development of the mathematical models, conditions for existence of limit cycles, and criteria of their stability. The book largely concentrates on the case of discretely controlled continuoustime systems and their relevance for modeling aspects of flexible manufacturing systems and dynamically routed queuing networks. Features and topics: *differential automata*development and use of the concept "cyclic linear differential automata" (CLDA)*switched singleserver flow networks coverage*application to specific models of manufacturing systems and queuing networks*select collection of open problems for the subject*selfcontained presentation of topics, with the necessary background This new book is an excellent resource for the study and analysis of hybrid dynamical systems used in systems and control engineering. Researchers, postgraduates and professionals in control engineering and computer engineering will find the book an uptodate development of the relevant new concepts and tools.
Ordinary differential equations  Electronic controllers  Digital control systems  Analog electronic systems  Applied mathematics.  Engineering mathematics.  System theory.  Control engineering.  Robotics.  Mechatronics.  Applications of Mathematics.  Systems Theory, Control.  Control, Robotics, Mechatronics.  Mechanical engineering  Microelectronics  Microelectromechanical systems  Automation  Machine theory  Control engineering  Control equipment  Control theory  Engineering instruments  Programmable controllers  Systems, Theory of  Systems science  Science  Engineering  Engineering analysis  Mathematical analysis  Philosophy  Mathematics
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This monograph, unique in the literature, is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Among the lensing topics discussed are multiple quasars, giant luminous arcs, Einstein rings, the detection of dark matter and planets with lensing, time delays and the age of the universe (Hubble’s constant), microlensing of stars and quasars. The main part of the bookPart IIIemploys the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation and solve certain key lensing problems. Results are published here for the first time. Mathematical topics discussed: Morse theory, Whitney singularity theory, Thom catastrophe theory, Mather stability theory, Arnold singularity theory, and the Euler characteristic via projectivized rotation numbers. These tools are applied to the study of stable lens systems, local and global geometry of caustics, caustic metamorphoses, multiple lens images, lensed image magnification, magnification cross sections, and lensing by singular and nonsingular deflectors. Examples, illustrations, bibliography and index make this a suitable text for an undergraduate/graduate course, seminar, or independent these project on gravitational lensing. The book is also an excellent reference text for professional mathematicians, mathematical physicists, astrophysicists, and physicists.
Differential geometry. Global analysis  Physics.  Applied mathematics.  Engineering mathematics.  Differential geometry.  Astrophysics.  Mathematical Methods in Physics.  Applications of Mathematics.  Differential Geometry.  Astrophysics and Astroparticles.  Astronomical physics  Astronomy  Cosmic physics  Physics  Differential geometry  Engineering  Engineering analysis  Mathematical analysis  Natural philosophy  Philosophy, Natural  Physical sciences  Dynamics  Mathematics
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Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performance on examples and counterexamples which outline their pros and cons. This is done using the MATLABTM software environment which is userfriendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLABTM computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of reallife problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in engineering, mathematics, physics and computer sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields. In this second edition, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been added. From the reviews of the first edition: "This is an excellent and modern textbook in numerical mathematics! It is primarily addressed to undergraduate students in mathematics, physics, computer science and engineering. But you will need a weekly 4 hour lecture for 3 terms lecture to teach all topics treated in this book! Well known methods as well as very new algorithms are given. The methods and their performances are demonstrated by illustrative examples and computer examples. Exercises shall help the reader to understand the theory and to apply it. MATLABsoftware satisfies the need of userfriendliness. [....] In the reviewers opinion, the presented book is the best textbook in numerical mathematics edited in the last ten years." Zentralblatt für Mathematik 2001, 991.38387.
Numerical analysis  519.61  519.61 Numerical methods of algebra  Numerical methods of algebra  Mathematical analysis  Mathematical Sciences  Applied Mathematics  Mathematics.  Applied mathematics.  Engineering mathematics.  Numerical analysis.  Applications of Mathematics.  Mathematics, general.  Numerical Analysis.  Appl.Mathematics/Computational Methods of Engineering.  wiskunde  Mathematics  Mathematical and Computational Engineering.  Engineering  Engineering analysis  Math  Science
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From the reviews: "...Here we have a book which we can wholeheartedly suggest. The mathematics is sound and pared to essentials; the examples are an impressive, wellchosen selection from the biomathematics literature, and the problem sets provide both useful exercises and some fine introductions to the art of modeling... Batschelet has written an introduction to biomathematics which is notable for its clarity  not only a clarity of presentation, but also a clarity of purpose, backed by a sure grasp of the field..." #Bulletin of Mathematical Biology#1 "For research workers in the biomedical field who feel a need for freshening up their knowledge in mathematics, but so far have always been frustrated by either too formal or too boring textbooks, there is now exactly what they would like to have: an easy to read introduction. This book is highly motivating for practical workers because only those mathematical techniques are offered for which there is an application in the life sciences. The reader will find it stimulating that each tool described is immediately exemplified by problems from latest publications." #Int. Zeitschrift für klinische Pharmakologie, Therapie und Toxikologie#2.
Astrophysics.  Heliosphere (Ionosphere)  Research.  Orbiting solar observatories.  Physics.  Sun  Corona  Research.  Biology  Health & Biological Sciences  Biology  General  Biomathematics.  Mathematics  Engineering.  Life sciences.  Applied mathematics.  Engineering mathematics.  Appl.Mathematics/Computational Methods of Engineering.  Mathematical and Computational Biology.  Life Sciences, general.  Biomathematics. Biometry. Biostatistics  Mathematical and Computational Engineering.  Biosciences  Sciences, Life  Science  Engineering  Engineering analysis  Mathematical analysis
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