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Mathematics --- Mathématiques --- Periodicals --- Périodiques --- Mathématiques --- Mathématique. --- Mathématique appliquée. --- 31.80 applications of mathematics --- Earth Sciences --- Mathematical Sciences --- Geophysics --- Applied Mathematics
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Mathematics --- Mathematics. --- Mathematical Theory --- Math --- Science --- interdisciplinary applications of mathematics and computation --- data mining --- applied mathematics --- mathematical modelling --- numerical analysis --- Mathematical statistics --- Computer. Automation
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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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Computer. Automation --- Mathematics --- Mathématiques --- Periodicals --- Data processing --- Périodiques --- Informatique --- Electronic data processing --- Mathématiques --- 31.80 applications of mathematics --- Périodiques. --- #TS:TCPW --- #TS:WDEP --- 681.3 --- Computer science --- Environmental Sciences --- Ecosystems & Ecology --- Mathematical Sciences --- Applied Mathematics --- Environmental Sciences. --- Ecosystems & Ecology. --- Electronic data processing. --- 31.80 applications of mathematics. --- Data processing. --- ADP (Data processing) --- Automatic data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Industries --- Automation --- 681.3* / / / / / / / / / / / / / / / / / / / / / / / / / / / / --- Periodicals.
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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 continuous-time 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 single-server flow networks coverage*application to specific models of manufacturing systems and queuing networks*select collection of open problems for the subject*self-contained 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 up-to-date 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 book---Part III---employs 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 user-friendly 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 real-life 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. MATLAB-software satisfies the need of user-friendliness. [....] 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 --- Numerical analysis - Textbooks --- Analyse numérique. --- Manuels d'enseignement
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This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are useful in statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Chapters 3-7 contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results. In addition to improving the presentation, the new edition makes Chapter 1 a self-contained chapter for probability theory with emphasis in statistics. Added topics include useful moment inequalities, more discussions of moment generating and characteristic functions, conditional independence, Markov chains, martingales, Edgeworth and Cornish-Fisher expansions, and proofs to many key theorems such as the dominated convergence theorem, monotone convergence theorem, uniqueness theorem, continuity theorem, law of large numbers, and central limit theorem. A new section in Chapter 5 introduces semiparametric models, and a number of new exercises were added to each chapter.
Mathematical statistics. --- Mathematical statistics --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- 519.2 --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Statistical methods --- Statistics . --- Applied mathematics. --- Engineering mathematics. --- Statistical Theory and Methods. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Acqui 2006
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This book is concerned with the general theory of optimal estimation of - rameters in systems subject to random e?ects and with the application of this theory. The focus is on choice of families of estimating functions, rather than the estimators derived therefrom, and on optimization within these families. Only assumptions about means and covariances are required for an initial d- cussion. Nevertheless, the theory that is developed mimics that of maximum likelihood, at least to the ?rst order of asymptotics. The term quasi-likelihood has often had a narrow interpretation, asso- ated with its application to generalized linear model type contexts, while that of optimal estimating functions has embraced a broader concept. There is, however, no essential distinction between the underlying ideas and the term quasi-likelihood has herein been adopted as the general label. This emphasizes its role in extension of likelihood based theory. The idea throughout involves ?nding quasi-scores from families of estimating functions. Then, the qua- likelihood estimator is derived from the quasi-score by equating to zero and solving, just as the maximum likelihood estimator is derived from the like- hood score.
Parameter estimation --- Parameter estimation. --- Mathematical statistics --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Estimation d'un paramètre --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Applications of Mathematics. --- Estimation theory --- Stochastic systems --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics
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Exponential families of stochastic processes are parametric stochastic p- cess models for which the likelihood function exists at all ?nite times and has an exponential representation where the dimension of the canonical statistic is ?nite and independent of time. This de?nition not only covers manypracticallyimportantstochasticprocessmodels,italsogivesrisetoa rather rich theory. This book aims at showing both aspects of exponential families of stochastic processes. Exponential families of stochastic processes are tractable from an a- lytical as well as a probabilistic point of view. Therefore, and because the theory covers many important models, they form a good starting point for an investigation of the statistics of stochastic processes and cast interesting light on basic inference problems for stochastic processes. Exponential models play a central role in classical statistical theory for independent observations, where it has often turned out to be informative and advantageous to view statistical problems from the general perspective of exponential families rather than studying individually speci?c expon- tial families of probability distributions. The same is true of stochastic process models. Thus several published results on the statistics of parti- lar process models can be presented in a uni?ed way within the framework of exponential families of stochastic processes.
Exponential families (Statistics). --- Stochastic processes. --- Mathematical statistics --- Exponential families (Statistics) --- Processus stochastiques --- Familles exponentielles (Statistique) --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Distribution (Probability theory. --- Engineering --- Engineering analysis --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Risk --- Families, Exponential (Statistics) --- Distribution (Probability theory) --- Random processes --- Probabilities
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