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Well Posed Ill Posed And Intermediate Problems With Applications
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Book Synopsis Well-posed, Ill-posed, and Intermediate Problems with Applications by : Petrov Yuri P.
Download or read book Well-posed, Ill-posed, and Intermediate Problems with Applications written by Petrov Yuri P. and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operator Theory and Ill-Posed Problems by : Mikhail M. Lavrent'ev
Download or read book Operator Theory and Ill-Posed Problems written by Mikhail M. Lavrent'ev and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Continuum Theory and Modeling of Thermoelectric Elements by : Christophe Goupil
Download or read book Continuum Theory and Modeling of Thermoelectric Elements written by Christophe Goupil and published by John Wiley & Sons. This book was released on 2016-02-23 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Inverse Problems with Applications in Science and Engineering by : Daniel Lesnic
Download or read book Inverse Problems with Applications in Science and Engineering written by Daniel Lesnic and published by CRC Press. This book was released on 2021-11-10 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Numerical Methods for the Solution of Ill-Posed Problems by : A.N. Tikhonov
Download or read book Numerical Methods for the Solution of Ill-Posed Problems written by A.N. Tikhonov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a FORTRAN program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.
Book Synopsis Complex Systems: Spanning Control and Computational Cybernetics: Applications by : Peng Shi
Download or read book Complex Systems: Spanning Control and Computational Cybernetics: Applications written by Peng Shi and published by Springer Nature. This book was released on 2022-09-18 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Inverse Problems in Partial Differential Equations by : David L. Colton
Download or read book Inverse Problems in Partial Differential Equations written by David L. Colton and published by SIAM. This book was released on 1990-01-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters by : Nitta, Tohru
Download or read book Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters written by Nitta, Tohru and published by IGI Global. This book was released on 2009-02-28 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book covers the current state-of-the-art theories and applications of neural networks with high-dimensional parameters"--Provided by publisher.
Book Synopsis Wspc Reference On Organic Electronics, The: Organic Semiconductors (In 2 Volumes) by : Marder Seth R
Download or read book Wspc Reference On Organic Electronics, The: Organic Semiconductors (In 2 Volumes) written by Marder Seth R and published by World Scientific. This book was released on 2016-06-24 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Inverses and Applications by : M. Zuhair Nashed
Download or read book Generalized Inverses and Applications written by M. Zuhair Nashed and published by Elsevier. This book was released on 2014-05-10 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Mathematics and Advanced Applications by : Miloslav Feistauer
Download or read book Numerical Mathematics and Advanced Applications written by Miloslav Feistauer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings collect the major part of the lectures given at ENU MATH2003, the European Conference on Numerical Mathematics and Ad vanced Applications, held in Prague, Czech Republic, from 18 August to 22 August, 2003. The importance of numerical and computational mathematics and sci entific computing is permanently growing. There is an increasing number of different research areas, where numerical simulation is necessary. Let us men tion fluid dynamics, continuum mechanics, electromagnetism, phase transi tion, cosmology, medicine, economics, finance, etc. The success of applications of numerical methods is conditioned by changing its basic instruments and looking for new appropriate techniques adapted to new problems as well as new computer architectures. The ENUMATH conferences were established in order to provide a fo rum for discussion of current topics of numerical mathematics. They seek to convene leading experts and young scientists with special emphasis on con tributions from Europe. Recent results and new trends are discussed in the analysis of numerical algorithms as well as in their applications to challenging scientific and industrial problems. The first ENUMATH conference was organized in Paris in 1995, then the series continued by the conferences in Heidelberg 1997, Jyvaskyla 1999 and Ischia Porto 2001. It was a great pleasure and honour for the Czech numerical community that it was decided at Ischia Porto to organize the ENUMATH2003 in Prague. It was the first time when this conference crossed the former Iron Courtain and was organized in a postsocialist country.
Book Synopsis Inverse and Ill-Posed Problems by : Heinz W. Engl
Download or read book Inverse and Ill-Posed Problems written by Heinz W. Engl and published by Elsevier. This book was released on 2014-05-10 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advanced Data Mining and Applications by : Xue Li
Download or read book Advanced Data Mining and Applications written by Xue Li and published by Springer Science & Business Media. This book was released on 2005-07-12 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Conference on Advanced Data Mining and Applications, ADMA 2005, held in Wuhan, China in July 2005. The conference was focused on sophisticated techniques and tools that can handle new fields of data mining, e.g. spatial data mining, biomedical data mining, and mining on high-speed and time-variant data streams; an expansion of data mining to new applications is also strived for. The 25 revised full papers and 75 revised short papers presented were carefully peer-reviewed and selected from over 600 submissions. The papers are organized in topical sections on association rules, classification, clustering, novel algorithms, text mining, multimedia mining, sequential data mining and time series mining, web mining, biomedical mining, advanced applications, security and privacy issues, spatial data mining, and streaming data mining.
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Inverse Problems in Diffusion Processes by : Heinz W. Engl
Download or read book Inverse Problems in Diffusion Processes written by Heinz W. Engl and published by SIAM. This book was released on 1995-01-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of expository papers encompasses both the theoretical and physical application side of inverse problems in diffusion processes.
Book Synopsis Advanced Methods of Joint Inversion and Fusion of Multiphysics Data by : Michael S. Zhdanov
Download or read book Advanced Methods of Joint Inversion and Fusion of Multiphysics Data written by Michael S. Zhdanov and published by Springer Nature. This book was released on 2024-01-29 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Different physical or geophysical methods provide information about distinctive physical properties of the objects, e.g., rock formations and mineralization. In many cases, this information is mutually complementary, which makes it natural for consideration in a joint inversion of the multiphysics data. Inversion of the observed data for a particular experiment is subject to considerable uncertainty and ambiguity. One productive approach to reducing uncertainty is to invert several types of data jointly. Nonuniqueness can also be reduced by incorporating additional information derived from available a priori knowledge about the target to reduce the search space for the solution. This additional information can be incorporated in the form of a joint inversion of multiphysics data. Generally established joint inversion methods, however, are inadequate for incorporating typical physical or geological complexity. For example, analytic, empirical, or statistical correlations between different physical properties may exist for only part of the model, and their specific form may be unknown. Features or structures that are present in the data of one physical method may not be present in the data generated by another physical method or may not be equally resolvable. This book presents and illustrates several advanced, new approaches to joint inversion and data fusion, which do not require a priori knowledge of specific empirical or statistical relationships between the different model parameters or their attributes. These approaches include the following novel methods, among others: 1) the Gramian method, which enforces the correlation between different parameters; 2) joint total variation functional or joint focusing stabilizers, e.g., minimum support and minimum gradient support constraints; 3) data fusion employing a joint minimum entropy stabilizer, which yields the simplest multiphysics solution that fits the multi-modal data. In addition, the book describes the principles of using artificial intelligence (AI) in solving multiphysics inverse problems. The book also presents in detail both the mathematical principles of these advanced approaches to joint inversion of multiphysics data and successful case histories of regional-scale and deposit-scale geophysical studies to illustrate their indicated advantages.
Book Synopsis Applications of Item Response Theory To Practical Testing Problems by : F. M. Lord
Download or read book Applications of Item Response Theory To Practical Testing Problems written by F. M. Lord and published by Routledge. This book was released on 2012-11-12 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in 1980, Applications of Item Response Theory To Practical Testing Problems is a valuable contribution to the field of Education.
