Inverse Problems In The Mathematical Sciences
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Inverse Problems In The Mathematical Sciences
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Author : Charles W. Groetsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-14
Inverse Problems In The Mathematical Sciences written by Charles W. Groetsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-14 with Technology & Engineering categories.
Classical applied mathematics is dominated by the Laplacian paradigm of known causes evolving continuously into uniquely determined effects. The classical direct problem is then to find the unique effect of a given cause by using the appropriate law of evolution. It is therefore no surprise that traditional teaching in mathema tics and the natural sciences emphasizes the point of view that problems have a solution, this solution is unique, and the solution is insensitive to small changes in the problem. Such problems are called well-posed and they typically arise from the so-called direct problems of natural science. The demands of science and technology have recently brought to the fore many problems that are inverse to the classical direct problems, that is, problems which may be interpreted as finding the cause of a given effect or finding the law of evolution given the cause and effect. Included among such problems are many questions of remote sensing or indirect measurement such as the determination of internal characteristics of an inaccessible region from measurements on its boundary, the determination of system parameters from input output measurements, and the reconstruction of past events from measurements of the present state. Inverse problems of this type are often ill-posed in the sense that distinct causes can account for the same effect and small changes in a perceived effect can correspond to very large changes in a given cause. Very frequently such inverse problems are modeled by integral equations of the first kind.
Inside Out
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Author : Gunther Uhlmann
language : en
Publisher: Cambridge University Press
Release Date : 2003-11-10
Inside Out written by Gunther Uhlmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-10 with Mathematics categories.
In this book, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics.
Inverse Problems And Spectral Theory
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Author : Hiroshi Isozaki
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Inverse Problems And Spectral Theory written by Hiroshi Isozaki and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This volume grew out of a workshop on spectral theory of differential operators and inverse problems held at the Research Institute for Mathematical Sciences (Kyoto University). The gathering of nearly 100 participants at the conference suggests the increasing interest in this field of research. The focus of the book is on spectral theory for differential operators and related inverse problems. It includes selected topics from the following areas: electromagnetism, elasticity, the Schrodinger equation, differential geometry, and numerical analysis. The material is suitable for graduate students and researchers interested in inverse problems and their applications.
The Mathematical Sciences In 2025
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Author : National Research Council
language : en
Publisher: National Academies Press
Release Date : 2013-05-13
The Mathematical Sciences In 2025 written by National Research Council and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-13 with Mathematics categories.
The mathematical sciences are part of nearly all aspects of everyday life-the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. The Mathematical Sciences in 2025 examines the current state of the mathematical sciences and explores the changes needed for the discipline to be in a strong position and able to maximize its contribution to the nation in 2025. It finds the vitality of the discipline excellent and that it contributes in expanding ways to most areas of science and engineering, as well as to the nation as a whole, and recommends that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematical sciences, the report emphasizes that universities and the government need to continue to invest in the full spectrum of the mathematical sciences in order for the whole enterprise to continue to flourish long-term.
Handbook Of Mathematical Methods In Imaging
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Author : Otmar Scherzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-23
Handbook Of Mathematical Methods In Imaging written by Otmar Scherzer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-23 with Mathematics categories.
The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Perspectives In Mathematical Sciences
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Author : Yisong Yang
language : en
Publisher: World Scientific
Release Date : 2010
Perspectives In Mathematical Sciences written by Yisong Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
1. Periodic boundary problems for analytic function including automorphic functions / Haitao Cai and Jian-Ke Lu -- 2. Subharmonic bifurcations and chaos for a model of micro-cantilever in MEMS / Yushu Chen, Liangqiang Zhou and Fangqi Chen -- 3. Canonical sample spaces for random dynamical systems / Jinqiao Duan, Xingye Kan and Bjorn Schmalfuss -- 4. Epidemic propagation dynamics on complex networks / Xinchu Fu ... [et al.] -- 5. Inverse problems for equations of parabolic type / Zhibin Han, Yongzhong Huang and Ming Jian -- 6. The existence and asymptotic properties of nontrivial solutions of nonlinear (2 - q)-Laplacian type problems with linking geometric structure / Gongbao Li and Zhaofen Shen -- 7. Chaotic dynamics for the two-component Bose-Einstein condensate system / Jibin Li -- 8. Recent developments and perspectives in nonlinear dynamics / Zengrong Liu -- 9. Mathematical aspects of the cold plasma model / Thomas H. Otway -- 10. Gravitating Yang-Mills fields in all dimensions / Eugen Radu and D. H. Tchrakian -- 11. Hamiltonian constraint and Mandelstam identities over extended knot families [symbol] and [symbol] in extended loop gravity / Dan Shao, Liang Shao and Changgui Shao -- 12. Lattice Boltzmann simulation of nonlinear Schrödinger equation with variable coefficients / Baochang Shi -- 13. Exponential stability of nonlocal time-delayed burgers equation / Yanbin Tang -- 14. Bifurcation analysis of the Swift-Hohenberg equation with quintic nonlinearity and Neumann boundary condition / Qingkun Xiao and Hongjun Gao -- 15. A new GL method for mathematical and physical problems / Ganquan Xie and Jianhua Li -- 16. Harmonically representing topological classes / Yisong Yang.
An Introduction To The Mathematical Theory Of Inverse Problems
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Author : Andreas Kirsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-24
An Introduction To The Mathematical Theory Of Inverse Problems written by Andreas Kirsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-24 with Mathematics categories.
This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces the reader to the inverse problem of electrical impedance tomography.
Statistical And Computational Inverse Problems
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Author : Jari Kaipio
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Statistical And Computational Inverse Problems written by Jari Kaipio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering.
Mathematical Methods In Interdisciplinary Sciences
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Author : Snehashish Chakraverty
language : en
Publisher: John Wiley & Sons
Release Date : 2020-06-02
Mathematical Methods In Interdisciplinary Sciences written by Snehashish Chakraverty and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-02 with Mathematics categories.
Brings mathematics to bear on your real-world, scientific problems Mathematical Methods in Interdisciplinary Sciences provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics. The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include: Structural static and vibration problems Heat conduction and diffusion problems Fluid dynamics problems The book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.
Mathematics Of Computation 1943 1993 A Half Century Of Computational Mathematics
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Author : Walter Gautschi
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Mathematics Of Computation 1943 1993 A Half Century Of Computational Mathematics written by Walter Gautschi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Proceedings of an International Conference held in Vancouver, B.C., August 1993, to commemorate the 50th anniversary of the founding of the journal Mathematics of Computation. It consisted of a Symposium on Numerical Analysis and a Minisymposium of Computational Number Theory. This proceedings contains 14 invited papers, including two not presented at the conference--an historical essay on integer factorization, and a paper on componentwise perturbation bounds in linear algebra. The invited papers present surveys on the various subdisciplines covered by Mathematics of Computation, in a historical perspective and in a language accessible to a wide audience. The 46 contributed papers address contemporary specialized work. Annotation copyright by Book News, Inc., Portland, OR