Описание: In mathematical modeling of processes one often encounters optimization problems involving more than one objective function, so that Multiobjective
Optimization (or Vector Optimization) has received new impetus. The growing interest in multiobjective problems, both from the theoretical point of view and as it concerns applications to
real problems, asks for a general scheme which embraces several existing developments and stimulates new ones. In this book the authors provide the newest results and applications
of this quickly growing field.
This book will be of interest to graduate students in mathematics, economics, and engineering, as well as researchers in pure and applied
mathematics, economics, engineering, geography, and town planning. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient
background for this book.
Описание: The mathematical theory of contact mechanics is a growing field in engineering and scientific computing. This book is intended as a unified and readily accessible source for mathematicians, applied mathematicians, mechanicians, engineers and scientists, as well as advanced students. The first part describes models of the processes involved like friction, heat generation and thermal effects, wear, adhesion and damage. The second part presents many mathematical models of practical interest and demonstrates the close interaction and cross-fertilization between contact mechanics and the theory of variational inequalities. The last part reviews further results, gives many references to current research and discusses open problems and future developments. The book can be read by mechanical engineers interested in applications. In addition, some theorems and their proofs are given as examples for the mathematical tools used in the models.
Автор: SmГdl VГЎclav, Quinn Anthony Название: The Variational Bayes Method in Signal Processing ISBN: 3540288198 ISBN-13(EAN): 9783540288190 Издательство: Springer Рейтинг: Цена: 13107 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is the first book-length treatment of the Variational Bayes (VB) approximation in signal processing. It has been written as a self-contained, self-learning guide for academic and industrial research groups in signal processing, data analysis, machine learning, identification and control. It reviews the VB distributional approximation, showing that tractable algorithms for parametric model identification can be generated in off-line and on-line contexts. Many of the principles are first illustrated via easy-to-follow scalar decomposition problems. In later chapters, successful applications are found in factor analysis for medical image sequences, mixture model identification and speech reconstruction. Results with simulated and real data are presented in detail. The unique development of an eight-step "VB method", which can be followed in all cases, enables the reader to develop a VB inference algorithm from the ground up, for their own particular signal or image model.
Описание: There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.
Описание: This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.
Описание: This text covers the fundamental concepts of energy principles and variational methods and their function in the formulation and solution of problems of mechanics. It has been completely revised and updated to meet the increased application of these methods.
Описание: Over the years, nonlinear analysis has been broadly and rapidly developed. Lectures presented in the International Conference on Variational Methods at the Chern Institute of Mathematics in Tianjin of May 2009 reflect this development from different angles. This volume contains articles based on these lectures.
Автор: Scherzer, Otmar Grasmair, Markus Grossauer, Harald Название: Variational methods in imaging preliminary entry 650 ISBN: 0387309314 ISBN-13(EAN): 9780387309316 Издательство: Springer Рейтинг: Цена: 7479 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Deals with the study of variational methods in imaging. This title covers a treatment of the approach from an inverse problems point of view. It includes numerical examples that accompany the theory. It is suitable for graduate students, researchers in applied mathematics, and researchers in the area of imaging science.
Описание: The book provides a comprehensive exposition of modern topics in nonlinear analysis with applications to various boundary value problems with discontinuous nonlinearities and nonsmooth constraints. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. In addition to the existence of solutions, a major part of the book is devoted to the study of different qualitative properties such as multiplicity, location, extremality, and stability. The treatment relies on variational methods, monotonicity principles, topological arguments and optimization techniques. The book is based on the authors' original results obtained in the last decade. A great deal of the material is published for the first time in this book and is organized in a unifying way. The book is self-contained. The abstract results are illustrated through various examples and applications.
Описание: This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time. Audience: The book is suitable for researchers, and for doctoral and post-doctoral courses.
Описание: This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time.
Описание: The study of shape optimization problems encompasses a wide spectrum of academic research with numerous applications to the real world. In this work these problems are treated from both the classical and modern perspectives and target a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems.* Presents foundational introduction to shape optimization theory* Studies certain classical problems: the isoperimetric problem and the Newton problem involving the best aerodynamical shape, and optimization problems over classes of convex domains* Treats optimal control problems under a general scheme, giving a topological framework, a survey of "gamma"-convergence, and problems governed by ODE* Examines shape optimization problems with Dirichlet and Neumann conditions on the free boundary, along with the existence of classical solutions* Studies optimization problems for obstacles and eigenvalues of elliptic operators* Poses several open problems for further research* Substantial bibliography and indexDriven by good examples and illustrations and requiring only a standard knowledge in the calculus of variations, differential equations, and functional analysis, the book can serve as a text for a graduate course in computational methods of optimal design and optimization, as well as an excellent reference for applied mathematicians addressing functional shape optimization problems.
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