Asymptotic Theory of Wave Propagation
Asymptotic Theory of Wave Propagation
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In our eReader you can find the full English version of the book. Read Asymptotic Theory of Wave Propagation Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Asymptotic Theory of Wave Propagation
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, q. (ll) The last equation also determines the values of t\ . (K) = ri . [h(K), k] = tj . (h) in terms of the matrix Q . It can be shown that if the numbers tj, . . . , ri are distinct, equations (9 -11) determine the eigenvectors r uniquely except for a unitary factor expfia. ] (a. Real). Such a unitary factor has no effect on the value of (8). If the t) . Are not distinct the eigenvectors are uniquely determined by (9-11) except for a imitary -51- (^-5) transformation (of the form r = / a. .... R'^, where (a. . ) is a unitary matrix) which again leaves the value of (8) unchanged. Since (9), (10), (11) are identical to (3-2. 3, ^, H) we may, for the case of constant coefficients, identify the eigenvectors of chapter 3 and chapter k. For this reason we have used the same notation in both chapters.
Our asymptotic solution (8) of the problem (U. 1. 1, 2, ^4-) is the main result of this chapter. It was derived under conditions (1-6) which are listed in appendix G. For real source functions f, (8) can be simplified provided we assi^me that the matrices A and E are real (condition 9), while E (w) and aj£)(co) are even functions (condition 10).
What to read after Asymptotic Theory of Wave Propagation?
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To quickly assess the difficulty of the text, read a short excerpt:
, q. (ll) The last equation also determines the values of t\ . (K) = ri . [h(K), k] = tj . (h) in terms of the matrix Q . It can be shown that if the numbers tj, . . . , ri are distinct, equations (9 -11) determine the eigenvectors r uniquely except for a unitary factor expfia. ] (a. Real). Such a unitary factor has no effect on the value of (8). If the t) . Are not distinct the eigenvectors are uniquely determined by (9-11) except for a imitary -51- (^-5) transformation (of the form r = / a. .... R'^, where (a. . ) is a unitary matrix) which again leaves the value of (8) unchanged. Since (9), (10), (11) are identical to (3-2. 3, ^, H) we may, for the case of constant coefficients, identify the eigenvectors of chapter 3 and chapter k. For this reason we have used the same notation in both chapters.
Our asymptotic solution (8) of the problem (U. 1. 1, 2, ^4-) is the main result of this chapter. It was derived under conditions (1-6) which are listed in appendix G. For real source functions f, (8) can be simplified provided we assi^me that the matrices A and E are real (condition 9), while E (w) and aj£)(co) are even functions (condition 10).
What to read after Asymptotic Theory of Wave Propagation?
You can find similar books in the "Read Also" column, or choose other free books by Robert M Lewis to read onlineMoreLess
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