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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.
An Investigation of the Laws of Thought
by George BooleGeorge Boole was on of the greatest mathematicians of the 19th century, and one of the most influential thinkers of all time. Not only did he make important contributions to differential equations and calculus of finite differences, he also was the discoverer of invariants, and the founder of modern symbolic logic. According to Bertrand Russell, "Pure mathematics was discovered by George Boole in his work published in 1854."This work is the first extensive statement of the modern view that mathematics is a pure deductive science that can be applied to various situations. Boole first showed how classical logic could be treated with algebraic terminology and operations, and then proceeded to a general symbolic method of logical interference; he also attempted to devise a calculus of probabilities which could be applied to situations hitherto considered beyond investigation.The enormous range of this work can be seen from chapter headings: Nature and Design of This Work; Signs and Their Laws; Derivation of Laws; Division of Propositions; Principles of Symbolical Reasoning; Interpretation; Elimination; Reduction; Methods of Abbreviation; Conditions of a Perfect Method; Secondary Propositions; Methods in Secondary Propositions; Clarke and Spinoza; Analysis, Aristotelian Logic; Theory of Probabilities; General Method in Probabilities; Elementary Illustrations; Statistical Conditions; Problems on Causes; Probability of Judgments; Constitution of the Intellect. This last chapter, Constitution of the Intellect, is a very significant analysis of the psychology of discovery and scientific method.
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 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
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 [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 Pearson EducationNIMAC-sourced textbook
Investigations in Number, Data, and Space Student Math Handbook
by Terc Firm Pearson Scott ForesmanNIMAC-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 Dale SeymourNIMAC-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.
Investing in Your Future
by National Association of Investors CorporationThis practical and accessible guide explains the benefits of long-term investment, illustrates how to evaluate mutual funds and corporations, and walks through the stock selection guide developed by BetterInvesting. The worksheets and career advice suggest the book could also be used in community college courses. The second edition devotes an entire chapter to stock selection. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)