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Author: Karl W. Breitung
Publisher: Springer
ISBN: 3540490337
Category : Technology & Engineering
Languages : en
Pages : 157
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Book Description
This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.
Author: Karl W. Breitung
Publisher: Springer
ISBN: 3540490337
Category : Technology & Engineering
Languages : en
Pages : 157
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Book Description
This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.
Author: Karl Wilhelm Breitung
Publisher: Springer Verlag
ISBN: 9780387586175
Category : Mathematics
Languages : en
Pages : 146
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Book Description
This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.
Author: R. Wong
Publisher: Academic Press
ISBN: 1483220710
Category : Mathematics
Languages : en
Pages : 561
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Book Description
Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.
Author: P. Thoft-Christensen
Publisher: Springer Science & Business Media
ISBN: 3642838286
Category : Technology & Engineering
Languages : en
Pages : 432
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Book Description
The present book contains 30 papers presented at the 2nd Working Conference on Reliability and Optimization of Structural Systems. The purpose of the Working Group was - to promote modern structural system optimization and reliability theory, - to advance international cooperation in the field of structural system optimization and reliability theory, - to stimulate research, development and application of structural system optimization and reliability theory, - to further the dissemination and exchange of information on reliability and optimization of structural system optimization and reliability theory, - to encourage education in structural system optimization and reliability theory.
Author: Nico M. Temme
Publisher: World Scientific Publishing Company
ISBN: 9789814612159
Category : Differential equations
Languages : en
Pages : 0
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Book Description
This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.
Author: Robert E. Melchers
Publisher: John Wiley & Sons
ISBN: 1119265991
Category : Technology & Engineering
Languages : en
Pages : 530
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Book Description
Structural Reliability Analysis and Prediction, Third Edition is a textbook which addresses the important issue of predicting the safety of structures at the design stage and also the safety of existing, perhaps deteriorating structures. Attention is focused on the development and definition of limit states such as serviceability and ultimate strength, the definition of failure and the various models which might be used to describe strength and loading. This book emphasises concepts and applications, built up from basic principles and avoids undue mathematical rigour. It presents an accessible and unified account of the theory and techniques for the analysis of the reliability of engineering structures using probability theory. This new edition has been updated to cover new developments and applications and a new chapter is included which covers structural optimization in the context of reliability analysis. New examples and end of chapter problems are also now included.
Author: Carlos Guedes Soares
Publisher: Springer Science & Business Media
ISBN: 940115614X
Category : Technology & Engineering
Languages : en
Pages : 411
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Book Description
This book contains contributions from various authors on different important topics related with probabilistic methods used for the design of structures. Initially several of the papers were prepared for advanced courses on structural reliability or on probabilistic methods for structural design. These courses have been held in different countries and have been given by different groups of lecturers. They were aimed at engineers and researchers who already had some exposure to structural reliability methods and thus they presented overviews of the work in the various topics. The book includes a selection of those contributions, which can be of support for future courses or for engineers and researchers that want to have an update on specific topics. It is considered a complement to the existing textbooks on structural reliability, which normally ensure the coverage of the basic topics but then are not extensive enough to cover some more specialised aspects. In addition to the contributions drawn from those lectures there are several papers that have been prepared specifically for this book, aiming at complementing the others in providing an overall account of the recent advances in the field. It is with sadness that in the meanwhile we have seen the disappearance of two of the contributors to the book and, in fact two of the early contributors to this field.
Author: Daniel Straub
Publisher: CRC Press
ISBN: 0203841417
Category : Technology & Engineering
Languages : en
Pages : 259
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Book Description
This volume contains 28 papers by renowned international experts on the latest advances in structural reliability methods and applications, engineering risk analysis and decision making, new optimization techniques and various applications in civil engineering. Moreover, several contributions focus on the assessment and optimization of existing str
Author: A Baratta
Publisher: World Scientific
ISBN: 9814546569
Category :
Languages : en
Pages : 651
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Book Description
Structural control offers opportunities to design new structures and to retrofit existing structures by the application of counter-forces, smart materials, frictional devices, etc., instead of just increasing the strength of the structure at greater cost.The Association for the Control of Structures (ACS) is promoting in Europe the development of this new technology in architectural design and infrastructure renewal and rehabilitation. The First European Conference on Structural Control was organized as one of the major initiatives toward this objective.
Author: Carlos A. Berenstein
Publisher: Springer Science & Business Media
ISBN: 9783540642077
Category : Mathematics
Languages : en
Pages : 178
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Book Description
This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.
