This article is cited in 5 papers

MATHEMATICS

On an invariant of surface mapping as applied to metallic mesh tailoring

M. S. Bukhtyak, A. V. Solomina

Tomsk State University, Tomsk, Russian Federation

Abstract: As in previous publications, the authors establish a goal to study tailoring of a metallic mesh to form an axially symmetric parabolic reflector. The tailoring is identified with a one-to-one mapping of a plane onto a part of a paraboloid of revolution. This representation of tailoring has a strong but inevitable idealization. The issue of a comparison criterion for two tailoring schemes is deemed important. In general terms this refers to a criterion of mapping a surface to surface. The mapping defect criterion proposed by the authors is not perfect — like any other criterion. In any case, it makes it possible to answer the question: in what sense one mapping is preferable to another. The article gives examples of the criterion’s application.

Keywords: parabolic reflector, metallic mesh, mapping of surfaces, defect of surface-to-surface mapping, approximation.

UDC: 519.711.3, 514.181.22

Received: 22.10.2015

DOI: 10.17223/19988621/39/2

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