By G. P. Astrakhantsev (auth.), V. M. Babich (eds.)

The papers comprising this assortment are at once or not directly with regards to a huge department of mathematical physics - the mathematical idea of wave propagation and diffraction. The paper via V. M. Babich is worried with the applying of the parabolic-equation process (of Academician V. A. Fok and M. A, Leontovich) to the matter of the asymptotic habit of eigenfunc tions centred in a local of a closed geodesie in a Riemannian area. The options utilized in this paper were föund important in fixing convinced difficulties within the thought of open resonators. the subject of G. P. Astrakhantsev's paper is identical to that of the paper via V. M. Babich. right here additionally the parabolic-equation procedure is used to discover the asymptotic resolution of the pliancy equations which describes Love waves focused in an area of a few floor ray. The paper of T. F. Pankratova is anxious with discovering the asymptotic habit of th~ eigenfunc tions of the Laplace operator from the precise resolution for the outside of a triaxial ellipsoid and the re gion external to it. the 1st 3 papers of B. G. Nikolaev are a bit except the principal subject of the col lection; they deal with the essential transforms with recognize to linked Legendre services of first type and their functions. Examples of such functions are using this remodel for the answer of indispensable equations with symmetrie kernels and for the answer of yes difficulties within the idea of electric prospecting.

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______. 10- 3 3 2 Fig. 7 We use graphs to show the results of computing the intensity of the field (I rl~ 0, t -1) for a fixed value of 0.. The program written can be used to compute the function lu~ ( S, Cl) 1. , 't.. Iu,. - con~t); the parameters of the problem are shown on the figures. The qualitative picture of the variation of the field in a neighborhood of a limiting ray for the sphere is in agreement with the results obtained for the planar case in [8]. In that paper the diffraction of a spherical wave by a planar boundary between two media with n< f is studied, and the coefficient of reflection of the spherical wave is computed for various values of the parameters of the problem.

Buldyrev for his eonstant interest in this work and for diseussion of the results. 0. 5-4. We replaee the Air~ functions W (T) and ~ (T) appearing in the integrand of the integral for as follow§: GM (Y) by functions of W (1) U t (I) where We then represent GM (~) as a sum of two integrals The integrals over the line segments (2Te-}li~ 0) and (O,2T+ e'i l can be redueed to integrals over the intervals (2T_, 0) and (0,2T+ I of the realline. If we then use the relations [9] (11) . (TI RQ G/,4(n and and 11'(T) , are real Airy functions, and carry out the eorresponding eomputations, then for Im GM(r!

4 Fig. 2 Fig. 6 INTERFERENCE WAVES FOR DIFFRACTION BY CYLINDER AND SPHERE is interseeted along the are I U2; (rl I dd 35 (Fig. 5). Figure 9 shows the results of eomputing the field intensity (dashed lines) along the line tt (Fig. 5) parallel to the plane T T. For eomparison, Fig. = coMt. It is evident that in the region ~< 0 the field intensity eomputed along the line tt exeeeds that along the are cici (in the region > 0). r For the ease of a eylinder, the field in a neighborhood of a limiting ray ean be studied in a similar manner.