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060927s2005 nju ob 001 0 eng d |
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|a 9812565361
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|a 9789812565365
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|a 9812703152
|q (electronic bk.)
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|a 9789812703156
|q (electronic bk.)
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|a 1281899143
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|a 9781281899149
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|a COCUF
|b eng
|e pn
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|a QA274.45
|b .R348 2005eb
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| 100 |
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|a Ramm, A. G.
|q (Alexander G.)
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| 245 |
1 |
0 |
|a Random fields estimation /
|c Alexander G. Ramm.
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| 260 |
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|a Hackensack, NJ :
|b World Scientific,
|c ©2005.
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| 300 |
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|a 1 online resource (xiii, 373 pages)
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| 500 |
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|a Based partly on the author's earlier book: Random fields estimation theory. Harlow, Essex, England : Longman Scientific & Technical ; New York : Wiley, 1990.
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| 504 |
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|a Includes bibliographical references (pages 363-369) and index.
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| 505 |
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|a Cover -- Preface -- Contents -- 1. Introduction -- 2. Formulation of Basic Results -- 2.1 Statement of the problem -- 2.2 Formulation of the results (multidimensional case) -- 2.2.1 Basic results -- 2.2.2 Generalizations -- 2.3 Formulation of the results (one-dimensional case) -- 2.3.1 Basic results for the scalar equation -- 2.3.2 Vector equations -- 2.4 Examples of kernels of class R and solutions to the basic equation -- 2.5 Formula for the error of the optimal estimate -- 3. Numerical Solution of the Basic Integral Equation in Distributions -- 3.1 Basic ideas -- 3.2 Theoretical approaches -- 3.3 Multidimensional equation -- 3.4 Numerical solution based on the approximation of the kernel -- 3.5 Asymptotic behavior of the optimal filter as the white noise component goes to zero -- 3.6 A general approach -- 4. Proofs -- 4.1 Proof of Theorem 2.1 -- 4.2 Proof of Theorem 2.2 -- 4.3 Proof of Theorems 2.4 and 2.5 -- 4.4 Another approach -- 5. Singular Perturbation Theory for a Class of Fredholm Integral Equations Arising in Random Fields Estimation Theory -- 5.1 Introduction -- 5.2 Auxiliary results -- 5.3 Asymptotics in the case n = 1 -- 5.4 Examples of asymptotical solutions: case n = 1 -- 5.5 Asymptotics in the case n> 1 -- 5.6 Examples of asymptotical solutions: case n> 1 -- 6. Estimation and Scattering Theory -- 6.1 The direct scattering problem -- 6.1.1 The direct scattering problem -- 6.1.2 Properties of the scattering solution -- 6.1.3 Properties of the scattering amplitude -- 6.1.4 Analyticity in k of the scattering solution -- 6.1.5 High-frequency behavior of the scattering solutions -- 6.1.6 Fundamental relation between u+ and u- -- 6.1.7 Formula for det S (k) and state the Levinson Theorem -- 6.1.8 Completeness properties of the scattering solutions -- 6.2 Inverse scattering problems -- 6.2.1 Inverse scattering problems -- 6.2.2 Uniqueness theorem for the inverse scattering problem -- 6.2.3 Necessary conditions for a function to be a scatterng amplitude -- 6.2.4 A Marchenko equation (M equation) -- 6.2.5 Characterization of the scattering data in the 3D inverse scattering probtem -- 6.2.6 The Born inversion -- 6.3 Estimation theory and inverse scattering in R3 -- 7. Applications -- 7.1 What is the optimal size of the domain on which the data are to be collected? -- 7.2 Discrimination of random fields against noisy background -- 7.3 Quasioptimal estimates of derivatives of random functions -- 7.3.1 Introduction -- 7.3.2 Estimates of the derivatives -- 7.3.3 Derivatives of random functions -- 7.3.4 Finding critical points -- 7.3.5 Derivatives of random fields -- 7.4 Stable summation of orthogonal series and integrals with randomly perturbed coefficients -- 7.4.1 Introduction -- 7.4.2 Stable summation of series -- 7.4.3 Method of multipliers -- 7.5 Resolution ability of linear systems -- 7.5.1 Introduction -- 7.5.2 Resolution ability of linear systems -- 7.5.3 Optimization of resolution ability -- 7.5.4 A general definition of resolution ability -- 7.6 Ill-posed problems and estimation theory -- 7.6.1 Introduction -- 7.6.2 Stable solution of ill-posed problems -- 7.6.3 Equations with random noise -- 7.7 A remark on nonlinear (polynomial) estimates -- 8. Auxiliary Results -- 8.1 Sobolev spaces and distributions -- 8.1.1 A general imbedding theorem -- 8.1.2 Sobolev space.
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| 650 |
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|a Random fields.
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| 650 |
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|a Estimation theory.
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| 650 |
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7 |
|a MATHEMATICS
|x Probability & Statistics
|x General.
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| 650 |
|
7 |
|a Estimation theory.
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| 700 |
1 |
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|a Ramm, A. G.
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| 856 |
4 |
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|u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=174689
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|b 5a04673f6c5ad14ac1ef062e
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