Invariant Imbedding and Inverse Problems


Book Description

This volume on invariant imbedding and inverse problems is based on a conference held in Alberquerque, New Mexico, in April 1990.




Handbook of Analytic Computational Methods in Applied Mathematics


Book Description

Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The f







Inverse Problems in Quantum Scattering Theory


Book Description

The normal business of physicists may be schematically thought of as predic ting the motions of particles on the basis of known forces, or the propagation of radiation on the basis of a known constitution of matter. The inverse problem is to conclude what the forces or constitutions are on the basis of the observed motion. A large part of our sensory contact with the world around us depends on an intuitive solution of such an inverse problem: We infer the shape, size, and surface texture of external objects from their scattering and absorption of light as detected by our eyes. When we use scattering experiments to learn the size or shape of particles, or the forces they exert upon each other, the nature of the problem is similar, if more refined. The kinematics, the equations of motion, are usually assumed to be known. It is the forces that are sought, and how they vary from point to point. As with so many other physical ideas, the first one we know of to have touched upon the kind of inverse problem discussed in this book was Lord Rayleigh (1877). In the course of describing the vibrations of strings of variable density he briefly discusses the possibility of inferring the density distribution from the frequencies of vibration. This passage may be regarded as a precursor of the mathematical study of the inverse spectral problem some seventy years later.




Factorization of Boundary Value Problems Using the Invariant Embedding Method


Book Description

Factorization Method for Boundary Value Problems by Invariant Embedding presents a new theory for linear elliptic boundary value problems. The authors provide a transformation of the problem in two initial value problems that are uncoupled, enabling you to solve these successively. This method appears similar to the Gauss block factorization of the matrix, obtained in finite dimension after discretization of the problem. This proposed method is comparable to the computation of optimal feedbacks for linear quadratic control problems. - Develops the invariant embedding technique for boundary value problems - Makes a link between control theory, boundary value problems and the Gauss factorization - Presents a new theory for successively solving linear elliptic boundary value problems - Includes a transformation in two initial value problems that are uncoupled




Electrical Impedance Tomography


Book Description

In recent years, there has been steady progress in the research of electrical impedance tomography (EIT), leading to important developments. These developments have excited interest in practitioners and researchers from a broad range of disciplines, including mathematicians devoted to uniqueness proofs and inverse problems, physicists dealing with bioimpedance, electronic engineerers involved in developing and extending its applications, and clinicians wishing to take advantage of this powerful new imaging method. With contributions from leading international researchers, Electrical Impedance Tomography: Methods, History and Applications provides an up-to-date review of the progress of EIT, the present state of knowledge, and a look at future advances and applications. Divided into four parts, the book presents an interdisciplinary approach. The first part discusses reconstruction algorithms while the second part describes the aspects of EIT instrumentation, including frequencies and electrodes. The third part features various EIT studies, such as breast cancer screening and artificial ventilation in intensive care units. The final part surveys new developments in magnetic induction tomography and magnetic resonance EIT (MREIT) as well as offers insight into three of the most productive and longstanding EIT research groups. The book also includes two nontechnical appendices that provide a brief and simple introduction to bioimpedance and the methods of EIT. Written in a style accessible to all related backgrounds, this reference will be helpful in establishing new methods and experiments of EIT, hopefully leading to radical breakthroughs in mainstream clinical practice.




Computational Techniques And Applications: Ctac 97 - Proceedings Of The Eight Biennial Conference


Book Description

This proceedings volume contains three invited papers and 93 contributed papers. The topics covered range from studies of theoretical aspects of computational methods to simulation of industrial processes, with an emphasis on the efficient use of computers to solve practical problems. Developers and users of computational techniques who wish to keep up with recent developments in the application of modern computational technology to problems in science and engineering will have much interest in this volume.




Tomography, Impedance Imaging, and Integral Geometry


Book Description

One of the most exciting features of tomography is the strong relationship between high-level pure mathematics (such as harmonic analysis, partial differential equations, microlocal analysis, and group theory) and applications to medical imaging, impedance imaging, radiotherapy, and industrial nondestructive evaluation. This book contains the refereed proceedings of the AMS-SIAM Summer Seminar on Tomography, Impedance Imaging, and Integral Geometry, held at Mount Holyoke College in June 1993. A number of common themes are found among the papers. Group theory is fundamental both to tomographic sampling theorems and to pure Radon transforms. Microlocal and Fourier analysis are important for research in all three fields. Differential equations and integral geometric techniques are useful in impedance imaging. In short, a common body of mathematics can be used to solve dramatically different problems in pure and applied mathematics. Radon transforms can be used to model impedance imaging problems. These proceedings include exciting results in all three fields represented at the conference.







Review of Progress in Quantitative Nondestructive Evaluation


Book Description

These Proceedings, consisting of Parts A and B, contain the edited versions of most of the papers presented at the annual Review of Progress in Quantitative Nondestructive Evaluation held at Bowdoin College, Brunswick, Maine on July 28 to August 2, 1996. The Review was organized by the Center for NDE at Iowa State University, in cooperation with the American Society of Nondestructive Testing, the Ames Laboratory of the USDOE, the Federal Aviation Administration, the National Institute of Standardsand Technology, and the National Science Foundation Industry!University Cooperative Research Centers pro gram. This year's Review of Progress in QNDE was attended by approximately 400 participants from the U.S. and many foreign countries who presented over 350 papers. As usual, the meetingwas divided into 36 sessions, with as many as four sessions running concurrently. The Review covered all phases of NDE research and development from fundamental investigations to engineering applications or inspection systems, and it included many important methods of inspection techniques from acoustics to x-rays. In the last eight to ten years, the Review has stabilized at about its current size, which most participants seem to agree is large enough to permit a full-scale overview of the latest developments, but still small enough to retain the collegial atmosphere which has marked the Review since its inception.