Описание: The behaviour of systems occurring in real life is often modelled by partial differential equations. This book investigates how a user or observer can influence the behaviour of such systems mathematically and computationally. A thorough mathematical analysis of controllability problems is combined with a detailed investigation of methods used to solve them numerically, these methods being validated by the results of numerical experiments. In Part I of the book the authors discuss the mathematics and numerics relating to the controllability of systems modelled by linear and non-linear diffusion equations; Part II is dedicated to the controllability of vibrating systems, typical ones being those modelled by linear wave equations; finally, Part III covers flow control for systems governed by the Navier-Stokes equations modelling incompressible viscous flow. The book is accessible to graduate students in applied and computational mathematics, engineering and physics; it will also be of use to more advanced practitioners.
Описание: This book presents the authorвЂ™s new method of two-stage maximization of a likelihood function, which helps to solve a series of non-solving before the well-posed and ill-posed problems of pseudosolution computing systems of linear algebraic equations (or, in statistical terminology, parametersвЂ™ estimators of functional relationships) and linear integral equations in the presence of deterministic and random errors in the initial data. This book presents, for the first time, a solution of the problem of reciprocal influence of passive errors of regressors and of active errors of predictors by computing point estimators of functional relationships.
Описание: Filling a longstanding need in the physical sciences, Bayesian Inference offers the first basic introduction for advanced undergraduates and graduates in the physical sciences. This text and reference generalizes Gaussian error intervals to situations in which the data follow distributions other than Gaussian. This usually occurs in frontier science because the observed parameter is barely above the background or the histogram of multiparametric data contains many empty bins. In this case, the determination of the validity of a theory cannot be based on the chi-squared-criterion. In addition to the solutions of practical problems, this approach provides an epistemic insight: the logic of quantum mechanics is obtained as the logic of unbiased inference from counting data. Requiring no knowledge of quantum mechanics, the text is written on introductory level, with many examples and exercises, for physicists planning to, or working in, fields such as medical physics, nuclear physics, quantum mechanics, and chaos.
Описание: This book presents a detailed and contemporary account of the classical theory of convergence of semigroups and its more recent development treating the case where the limit semigroup, in contrast to the approximating semigroups, acts merely on a subspace of the original Banach space (this is the case, for example, with singular perturbations). The author demonstrates the far-reaching applications of this theory using real examples from various branches of pure and applied mathematics, with a particular emphasis on mathematical biology. The book may serve as a useful reference, containing a significant number of new results ranging from the analysis of fish populations to signaling pathways in living cells. It comprises many short chapters, which allows readers to pick and choose those topics most relevant to them, and it contains 160 end-of-chapter exercises so that readers can test their understanding of the material as they go along.
Автор: Abdon Atangana Название: Derivative with a New Parameter ISBN: 0081006446 ISBN-13(EAN): 9780081006443 Издательство: Elsevier Science Рейтинг: Цена: 8012 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Derivative with a New Parameter: Theory, Methods and Applications discusses the first application of the local derivative that was done by Newton for general physics, and later for other areas of the sciences. . The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes on to introduce the new parameters for the local derivative, including its definition and properties. Additional topics define beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, including their properties, and then go on to describe the method for partial differential with the beta derivatives. . Subsequent sections give examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases. The book gives an introduction to the newly-established local derivative with new parameters, along with their integral transforms and applications, also including great examples on how it can be used in epidemiology and groundwater studies.
Описание: The nature and the human creations are full of complex phenomena, which sometimes can be observed but rarely follow our hypotheses. The best we can do is to build a parametric model and try to adjust (identify) the unknown parameters based on the available observations. The authors discuss problems relevant to materials and structures like inverse analysis in structures, crack, material parameter and damage identification, modal analysis and thermographic methods. The solution methods vary from classical optimization to neural networks and genetic algorithms. Since all the authors are engineers, well-known in the academic and industrial world, the emphasis is posed on methods which really work. In fact, the chapters provide state-of-the-art information supplemented by selected examples and numerous references to modern publications, so that the reader can directly proceed with the study of his own problems.
Описание: Fixed-Point Algorithms for Inverse Problems in Science and Engineering presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.
Описание: Provides a solid mathematical framework for a structured approach to strongly stabilizable systems through integration of fundamental theory, physical applications, and numerical results. The author includes a mathematical framework for studying PDE models of large flexible structures.
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