Well-posed, Ill-posed, and Intermediate Problems with Applications

Well-posed, Ill-posed, and Intermediate Problems with Applications PDF

Author: Petrov Yuri P.

Publisher: Walter de Gruyter

Published: 2011-12-22

Total Pages: 245

ISBN-13: 3110195305

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This book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples.

Operator Theory and Ill-Posed Problems

Operator Theory and Ill-Posed Problems PDF

Author: Mikhail M. Lavrent'ev

Publisher: Walter de Gruyter

Published: 2011-12-22

Total Pages: 697

ISBN-13: 3110960729

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This book consists of three major parts. The first two parts deal with general mathematical concepts and certain areas of operator theory. The third part is devoted to ill-posed problems. It can be read independently of the first two parts and presents a good example of applying the methods of calculus and functional analysis. The first part "Basic Concepts" briefly introduces the language of set theory and concepts of abstract, linear and multilinear algebra. Also introduced are the language of topology and fundamental concepts of calculus: the limit, the differential, and the integral. A special section is devoted to analysis on manifolds. The second part "Operators" describes the most important function spaces and operator classes for both linear and nonlinear operators. Different kinds of generalized functions and their transformations are considered. Elements of the theory of linear operators are presented. Spectral theory is given a special focus. The third part "Ill-Posed Problems" is devoted to problems of mathematical physics, integral and operator equations, evolution equations and problems of integral geometry. It also deals with problems of analytic continuation. Detailed coverage of the subjects and numerous examples and exercises make it possible to use the book as a textbook on some areas of calculus and functional analysis. It can also be used as a reference textbook because of the extensive scope and detailed references with comments.

Continuum Theory and Modeling of Thermoelectric Elements

Continuum Theory and Modeling of Thermoelectric Elements PDF

Author: Christophe Goupil

Publisher: John Wiley & Sons

Published: 2016-02-23

Total Pages: 362

ISBN-13: 3527413375

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Sound knowledge of the latest research results in the thermodynamics and design of thermoelectric devices, providing a solid foundation for thermoelectric element and module design in the technical development process and thus serving as an indispensable tool for any application development. The text is aimed mainly at the project developer in the field of thermoelectric technology, both in academia and industry, as well as at graduate and advanced undergraduate students. Some core sections address the specialist in the field of thermoelectric energy conversion, providing detailed discussion of key points with regard to optimization. The international team of authors with experience in thermoelectrics research represents such institutes as EnsiCaen Universite de Paris, JPL, CalTech, and the German Aerospace Center.

Inverse Problems with Applications in Science and Engineering

Inverse Problems with Applications in Science and Engineering PDF

Author: Daniel Lesnic

Publisher: CRC Press

Published: 2021-11-10

Total Pages: 360

ISBN-13: 0429683251

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Driven by the advancement of industrial mathematics and the need for impact case studies, Inverse Problems with Applications in Science and Engineering thoroughly examines the state-of-the-art of some representative classes of inverse and ill-posed problems for partial differential equations (PDEs). The natural practical applications of this examination arise in heat transfer, electrostatics, porous media, acoustics, fluid and solid mechanics – all of which are addressed in this text. Features: Covers all types of PDEs — namely, elliptic (Laplace’s, Helmholtz, modified Helmholtz, biharmonic and Stokes), parabolic (heat, convection, reaction and diffusion) and hyperbolic (wave) Excellent reference for post-graduates and researchers in mathematics, engineering and any other scientific discipline that deals with inverse problems Contains both theory and numerical algorithms for solving all types of inverse and ill-posed problems

Inverse and Ill-Posed Problems

Inverse and Ill-Posed Problems PDF

Author: Heinz W. Engl

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 585

ISBN-13: 1483272656

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Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June 1986. The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for integral and operator equations of the first kind. Other papers deal with applications in tomography, inverse scattering, detection of radiation sources, optics, partial differential equations, and parameter estimation problems. One paper discusses three topics on ill-posed problems, namely, the imposition of specified types of discontinuities on solutions of ill-posed problems, the use of generalized cross validation as a data based termination rule for iterative methods, and also a parameter estimation problem in reservoir modeling. Another paper investigates a statistical method to determine the truncation level in Eigen function expansions and for Fredholm equations of the first kind where the data contains some errors. Another paper examines the use of singular function expansions in the inversion of severely ill-posed problems arising in confocal scanning microscopy, particle sizing, and velocimetry. The collection can benefit many mathematicians, students, and professor of calculus, statistics, and advanced mathematics.

Complex Systems: Spanning Control and Computational Cybernetics: Applications

Complex Systems: Spanning Control and Computational Cybernetics: Applications PDF

Author: Peng Shi

Publisher: Springer Nature

Published: 2022-09-18

Total Pages: 551

ISBN-13: 3031009789

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This book, dedicated to Professor Georgi M. Dimirovski on his anniversary, contains new research directions, challenges, and many relevant applications related to many aspects within the broadly perceived areas of systems and control, including signal analysis and intelligent systems. The project comprises two volumes with papers written by well known and very active researchers and practitioners. The first volume is focused on more foundational aspects related to general issues in systems science and mathematical systems, various problems in control and automation, and the use of computational and artificial intelligence in the context of systems modeling and control. The second volume is concerned with a presentation of relevant applications, notably in robotics, computer networks, telecommunication, fault detection/diagnosis, as well as in biology and medicine, and economic, financial, and social systems too.

Wspc Reference On Organic Electronics, The: Organic Semiconductors (In 2 Volumes)

Wspc Reference On Organic Electronics, The: Organic Semiconductors (In 2 Volumes) PDF

Author: Seth R Marder

Publisher: World Scientific

Published: 2016-06-24

Total Pages: 896

ISBN-13: 9814699241

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This 2-volume set provides the reader with a basic understanding of the foundational concepts pertaining to the design, synthesis, and applications of conjugated organic materials used as organic semiconductors, in areas including organic photovoltaic devices, light-emitting diodes, field-effect transistors, spintronics, actuation, bioelectronics, thermoelectrics, and nonlinear optics.While there are many monographs in these various areas, the emphasis here is both on the fundamental chemistry and physics concepts underlying the field of organic semiconductors and on how these concepts drive a broad range of applications. This makes the volumes ideal introductory textbooks in the subject. They will thus offer great value to both junior and senior scientists working in areas ranging from organic chemistry to condensed matter physics and materials science and engineering.Number of Illustrations and Tables: 168 b/w illus., 242 colour illus., 13 tables.

Generalized Inverses and Applications

Generalized Inverses and Applications PDF

Author: M. Zuhair Nashed

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 1069

ISBN-13: 1483270297

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Generalized Inverses and Applications, contains the proceedings of an Advanced Seminar on Generalized Inverses and Applications held at the University of Wisconsin-Madison on October 8-10, 1973 under the auspices of the university's Mathematics Research Center. The seminar provided a forum for discussing the basic theory of generalized inverses and their applications to analysis and operator equations. Numerical analysis and approximation methods are considered, along with applications to statistics and econometrics, optimization, system theory, and operations research. Comprised of 14 chapters, this book begins by describing a unified approach to generalized inverses of linear operators, with particular reference to algebraic, topological, extremal, and proximinal properties. The reader is then introduced to the algebraic aspects of the generalized inverse of a rectangular matrix; the Fredholm pseudoinverse; and perturbations and approximations for generalized inverses and linear operator equations. Subsequent chapters deal with various applications of generalized inverses, including programming, games, and networks, as well as estimation and aggregation in econometrics. This monograph will be of interest to mathematicians and students of mathematics.

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