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Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Pham Loi VuInverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. This book is intended for a wide community working with ISPs and their applications. There is an especially strong traditional community in mathematical physics. In this monograph, the problems are presented step-by-step, and detailed proofs are given for considered problems to make the topics more accessible for students who are approaching them for the first time. New to the Second Edition All new chapter dealing with the Bäcklund transformations between a common solution of both linear equations in the Lax pair and the solution of the associated IBVP for NLEEs on the half-line Updated references and concluding remarks Features Solving the direct and ISP, then solving the associated initial value problem (IVP) or initial-boundary value problem (IBVP) for NLEEs are carried out step-by-step. The unknown boundary values are calculated with the help of the Lax (generalized) equations, then the time-dependent scattering data (SD) are expressed in terms of preassigned initial and boundary conditions. Thereby, the potential functions are recovered uniquely in terms of the given initial and calculated boundary conditions. The unique solvability of the ISP is proved and the SD of the scattering problem is described completely. The considered ISPs are well-solved. The ISPs are set up appropriately for constructing the Bӓckhund transformations (BTs) for solutions of associated IBVPs or IVPs for NLEEs. The procedure for finding a BT for the IBVP for NLEEs on the half-line differs from the one used for obtaining a BT for non-linear differential equations defined in the whole space. The interrelations between the ISPs and the constructed BTs are established to become new powerful unified transformations (UTs) for solving IBVPs or IVPs for NLEEs, that can be used in different areas of physics and mechanics. The application of the UTs is consistent and efficiently embedded in the scheme of the associated ISP.
Inverse Spectral Problems for Linear Differential Operators and Their Applications (Analytical Methods and Special Functions)
by V A YurkoAims to construct the inverse problem theory for ordinary non-self-adjoint differential operators of arbitary order on the half-line and on a finite interval. The book consists of two parts: in the first part the author presents a general inverse problem of recovering differential equations with integrable coefficients when the behaviour of the spe
Inverse Spectral and Scattering Theory: An Introduction (SpringerBriefs in Mathematical Physics #38)
by Hiroshi IsozakiThe aim of this book is to provide basic knowledge of the inverse problems arising in various areas in mathematics, physics, engineering, and medical science. These practical problems boil down to the mathematical question in which one tries to recover the operator (coefficients) or the domain (manifolds) from spectral data. The characteristic properties of the operators in question are often reduced to those of Schrödinger operators. We start from the 1-dimensional theory to observe the main features of inverse spectral problems and then proceed to multi-dimensions. The first milestone is the Borg–Levinson theorem in the inverse Dirichlet problem in a bounded domain elucidating basic motivation of the inverse problem as well as the difference between 1-dimension and multi-dimension. The main theme is the inverse scattering, in which the spectral data is Heisenberg’s S-matrix defined through the observation of the asymptotic behavior at infinity of solutions. Significant progress has been made in the past 30 years by using the Faddeev–Green function or the complex geometrical optics solution by Sylvester and Uhlmann, which made it possible to reconstruct the potential from the S-matrix of one fixed energy. One can also prove the equivalence of the knowledge of S-matrix and that of the Dirichlet-to-Neumann map for boundary value problems in bounded domains. We apply this idea also to the Dirac equation, the Maxwell equation, and discrete Schrödinger operators on perturbed lattices. Our final topic is the boundary control method introduced by Belishev and Kurylev, which is for the moment the only systematic method for the reconstruction of the Riemannian metric from the boundary observation, which we apply to the inverse scattering on non-compact manifolds. We stress that this book focuses on the lucid exposition of these problems and mathematical backgrounds by explaining the basic knowledge of functional analysis and spectral theory, omitting the technical details in order to make the book accessible to graduate students as an introduction to partial differential equations (PDEs) and functional analysis.
Invertibility and Singularity for Bounded Linear Operators
by Robin HarteThis introduction to functional analysis focuses on the types of singularity that prevent an operator from being invertible. The presentation is based on the open mapping theorem, Hahn-Banach theorem, dual space construction, enlargement of normed space, and Liouville's theorem. Suitable for advanced undergraduate and graduate courses in functional analysis, this volume is also a valuable resource for researchers in Fredholm theory, Banach algebras, and multiparameter spectral theory. The treatment develops the theory of open and almost open operators between incomplete spaces. It builds the enlargement of a normed space and of a bounded operator and sets up an elementary algebraic framework for Fredholm theory. The approach extends from the definition of a normed space to the fringe of modern multiparameter spectral theory and concludes with a discussion of the varieties of joint spectrum. This edition contains a brief new Prologue by author Robin Harte as well as his lengthy new Epilogue, "Residual Quotients and the Taylor Spectrum."Dover republication of the edition published by Marcel Dekker, Inc., New York, 1988.
Investigations 3 in Number, Data, and Space, Student Activity Book [Grade 2]
by Scott ForesmanNIMAC-sourced textbook
Investigations 3 in Number, Data, and Space, Student Activity Book [Grade 3]
by Scott ForesmanNIMAC-sourced textbook
Investigations 3 in Number, Data, and Space, Student Activity Book [Grade K]
by Scott ForesmanNIMAC-sourced textbook
Investigations in Number Data and Space (2nd edition)
by Pearson Scott ForesmanA student activity book for factors, multiples, arrays, shape of the data, Multiple Towers and Division Stories, Size, Shape, and Symmetry, Landmarks and Large Numbers, Fraction Cards and Decimal Squares, Moving Between Solids and Silhouettes, Penny Jars and Plant Growth.
Investigations in Number, Data, and Space Student Activity Book
by Economopoulos RussellNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Activity Book
by Economopoulos RussellNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Activity Book
by Pearson Scott ForesmanNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Activity Book
by Pearson Scott ForesmanNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Activity Book
by Pearson Scott Foresman. TercNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Activity Book [Grade 2]
by Scott ForesmanNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Activity Book [Grade 3]
by Pearson EducationTextbook.
Investigations in Number, Data, and Space Student Math Handbook
by Dale SeymourNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Math Handbook
by Economopoulos RussellNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Math Handbook
by Economopoulos RussellNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Math Handbook
by Pearson EducationNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Math Handbook
by Pearson Scott Foresman Terc FirmNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Math Handbook [Grade 5]
by Pearson Scott ForesmanTextbook.
Investing in China and Chinese Investment Abroad
by Xiuping Zhang Bruce P. CorrieThe book provides a study of the investment environment for international enterprises in China and overseas investment by Chinese enterprises. Applying statistical methods and up-to-date data analysis, it examines every aspect of the investment environment in China. The author’s ideas are further illustrated with 39 figures and diagrams. Its 18 chapters discuss topics ranging from history, the current situation and problems of foreign investment in China, to China’s policies for attracting foreign investment, the top 500 global companies in China, urban competitive analysis and multinational corporations in Beijing. It also analyzes Chinese investment in foreign countries. It is a valuable investment guide, and is also a useful reference resource for academic research and teaching related to international business and the Chinese economy.