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ON THE DERIVATION OF SOLUTIONS DUE TO A POINT SOURCE FROM LINE SOURCE RESPONSES

Stephen A. Thau, Yih−Hsing Pao

Abstract

Abstract : A sequence of linear, mathematical operations are derived which transform the generalized function representing a concentrated line source into the generalized function representing an axi-symmetric point source. Geometrically, the transformation consists of superposing the derivatives of the Hilbert transforms of line sources in all azimuths through a given point, to produce a concentrated source at that point. Thus, for linear systems the response due to a point source can be deduced from that due to line sources by the same operations. Conditions for which the transformation becomes useful and various alternate forms of the transformation, with examples, are also given. (Author)

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Key concepts: Transformation (genetics), Line source, Point source, Line (geometry), Point (geometry), Function (biology), Mathematics, Sequence (biology)