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

The papers comprising this assortment are without delay or ultimately concerning an incredible department of mathematical physics - the mathematical conception of wave propagation and diffraction. The paper by way of V. M. Babich is anxious with the applying of the parabolic-equation strategy (of Academician V. A. Fok and M. A, Leontovich) to the matter of the asymptotic habit of eigenfunc­ tions focused in an area of a closed geodesie in a Riemannian house. The thoughts utilized in this paper were föund priceless in fixing yes difficulties within the concept of open resonators. the subject of G. P. Astrakhantsev's paper is identical to that of the paper by way of V. M. Babich. the following additionally the parabolic-equation strategy is used to discover the asymptotic answer of the pliancy equations which describes Love waves focused in an area of a few floor ray. The paper of T. F. Pankratova is worried with discovering the asymptotic habit of th~ eigenfunc­ tions of the Laplace operator from the precise resolution for the skin of a triaxial ellipsoid and the re­ gion external to it. the 1st 3 papers of B. G. Nikolaev are just a little except the significant topic of the col­ lection; they deal with the quintessential transforms with appreciate to linked Legendre features of first variety and their functions. Examples of such purposes are using this remodel for the answer of indispensable equations with symmetrie kernels and for the answer of convinced difficulties within the conception of electric prospecting.