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Proceedings ArticleDOI

An extension of Wiener-Hopf method: ordinary differential equations associated with diffraction problems

01 Jan 1999-pp 176-182
TL;DR: In this paper, a functional equation of Wiener-Hopf type with analytical restrictions on unknown functions is derived for plane wave scattering on a strip or on a set of strips located in a plane.
Abstract: The problem of plane wave scattering on a strip or on a set of strips located in a plane is under consideration. A functional equation of Wiener-Hopf type with analytical restrictions on unknown functions is derived. It is shown that the solution of the problem (the spectrum of the scattered field) is a solution of an ordinary differential equation (ODE). The coefficients of the ODE are known up to several constants. The restrictions enabling one to determine the constants are discussed. Thus, the problem of diffraction by strips is reduced to the problem of finding the constants and solving the ODE, but not the integral equation.
Citations
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Proceedings ArticleDOI
01 Jan 2000
TL;DR: In this paper, the authors studied the diffraction series (Schwarzschild's series) to solve the problem of diffraction at a slit with ideal boundary conditions and derived the representation obtained by Williams (1982) and the differential equations for the unknown functions.
Abstract: We study the diffraction series (Schwarzschild's series) to solve the problem of diffraction at a slit with ideal boundary conditions. Using this series we derive the representation obtained by Williams (1982) and the differential equations for the unknown functions.

4 citations

Journal ArticleDOI
TL;DR: In this article, a diffraction series (Schwarzschild's series) that solves the problem on diffraction by a slit with ideal boundary conditions is considered, the representation obtained earlier by M. Williams is derived, and differential equations for unknown functions are obtained.
Abstract: A diffraction series (Schwarzschild's series) that solves the problem on diffraction by a slit with ideal boundary conditions is considered. Using this series, the representation obtained earlier by M. Williams is derived, and differential equations for unknown functions are obtained. Bibliography: 9 titles.

3 citations


Cites background or methods or result from "An extension of Wiener-Hopf method:..."

  • ...where the prime corresponds to differentiation with respect to k. The coefficients X and Y can be represented in the form (see [ 5 ])...

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  • ...On the other hand, representation (3.21) does not follow from [ 5 ]....

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  • ...• A comparison with the results from [3] and [ 5 ] was carried out....

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  • ...The approach developed in [ 5 ] can be applied to such problems, but the calculations are extremely difficult because of a great number of unknown parameters and monodromy restrictions....

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  • ...Unfortunately, in [3] and [ 5 ] the solutions are represented in rather different forms, and it is not easy to compare them or transform one into another....

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Journal ArticleDOI
TL;DR: In this paper, a three-tier methodology of analytical identification has been provided, which unlike the known approaches is based on aggregated models, which can be used to identify the technical condition of a power-plant boiler.

2 citations

References
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Reference BookDOI
TL;DR: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool as discussed by the authors, and it can be found in many libraries.
Abstract: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.

4,083 citations