New Analytic And Geometric Methods In Inverse Problems
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New Analytic And Geometric Methods In Inverse Problems
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Author : Kenrick Bingham
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
New Analytic And Geometric Methods In Inverse Problems written by Kenrick Bingham 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 2013-04-17 with Mathematics categories.
In inverse problems, the aim is to obtain, via a mathematical model, information on quantities that are not directly observable but rather depend on other observable quantities. Inverse problems are encountered in such diverse areas of application as medical imaging, remote sensing, material testing, geosciences and financing. It has become evident that new ideas coming from differential geometry and modern analysis are needed to tackle even some of the most classical inverse problems. This book contains a collection of presentations, written by leading specialists, aiming to give the reader up-to-date tools for understanding the current developments in the field.
Geometric Methods In Inverse Problems And Pde Control
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Author : Chrisopher B Croke
language : en
Publisher:
Release Date : 2004-02-26
Geometric Methods In Inverse Problems And Pde Control written by Chrisopher B Croke and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-26 with categories.
Applications Of Analytic And Geometric Methods To Nonlinear Differential Equations
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Author : P.A. Clarkson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Analytic And Geometric Methods To Nonlinear Differential Equations written by P.A. Clarkson 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 2012-12-06 with Science categories.
In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.
Geometric Methods In Inverse Problems And Pde Control
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Author : Chrisopher B. Croke
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Methods In Inverse Problems And Pde Control written by Chrisopher B. Croke 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 2012-12-06 with Mathematics categories.
This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title. We would like to thank Christopher B. Croke (University of Penn sylva nia), Irena Lasiecka (University of Virginia), Gunther Uhlmann (University of Washington), and Michael S. Vogelius (Rutgers University) for their ex cellent work as organizers of the two-week summer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a selected number of articles based on lectures delivered at the IMA 2001 Summer Program on "Geometric Methods in Inverse Problems and PDE Control. " The focus of this program was some common techniques used in the study of inverse coefficient problems and control problems for partial differential equations, with particular emphasis on their strong relation to fundamental problems of geometry. Inverse coef ficient problems for partial differential equations arise in many application areas, for instance in medical imaging, nondestructive testing, and geophys ical prospecting. Control problems involving partial differential equations may arise from the need to optimize a given performance criterion, e. g. , to dampen out undesirable vibrations of a structure , or more generally, to obtain a prescribed behaviour of the dynamics.
Geometric Inverse Problems
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Author : Gabriel P. Paternain
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-31
Geometric Inverse Problems written by Gabriel P. Paternain 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 2022-12-31 with Mathematics categories.
Cutting-edge mathematical tools are used in this treatment of recent developments in geometric inverse problems.
Quaternion And Clifford Fourier Transforms And Wavelets
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Author : Eckhard Hitzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-24
Quaternion And Clifford Fourier Transforms And Wavelets written by Eckhard Hitzer 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 2013-06-24 with Mathematics categories.
Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.
Free Boundary Problems In Fluid Dynamics
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Author : Albert Ai
language : en
Publisher: Springer Nature
Release Date :
Free Boundary Problems In Fluid Dynamics written by Albert Ai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Journal Of Nonlinear Mathematical Physics Vol 14
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Author :
language : en
Publisher: atlantis press
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Journal Of Nonlinear Mathematical Physics Vol 14 written by and has been published by atlantis press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Inverse Problems And Applications
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Author : Gunther Uhlmann
language : en
Publisher: Cambridge University Press
Release Date : 2013
Inverse Problems And Applications 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 2013 with Mathematics categories.
Inverse problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a variety of medical and other imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the Earth's interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modeling in the life sciences among others. The expository survey essays in this book describe recent developments in inverse problems and imaging, including hybrid or couple-physics methods arising in medical imaging, Calderon's problem and electrical impedance tomography, inverse problems arising in global seismology and oil exploration, inverse spectral problems, and the study of asymptotically hyperbolic spaces. It is suitable for graduate students and researchers interested in inverse problems and their applications.
Inverse Problems
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Author : Alexander G. Ramm
language : en
Publisher: Springer
Release Date : 2004-12-16
Inverse Problems written by Alexander G. Ramm and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-16 with Computers categories.
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.