1984
DOI: 10.1070/im1984v023n01abeh001458
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Special Cases of the Theory of Multiple Trigonometric Sums

Abstract: The finite difference method is extended. through the use of the electrical analogue, to enable calculation of temperature distribution and heat flow in composite materials made from anisotropic materials. The standard finite difference equations have been modified on a node-by-node basis to take account of anisotropy by local re-orientation of the grid. The temperature distribution and heat tlow have been derived tor a composite material made trom two materials with anisotropic thermal conductivity. The effec… Show more

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Cited by 12 publications
(20 citation statements)
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“…Let x 2 and y 2 be any one of the O(X 2 ) permissible choices counted by 2 (X; h). By hypothesis, one has F (x 2 , y 2 ; h) = 0.…”
Section: R(n; H)mentioning
confidence: 99%
“…Let x 2 and y 2 be any one of the O(X 2 ) permissible choices counted by 2 (X; h). By hypothesis, one has F (x 2 , y 2 ; h) = 0.…”
Section: R(n; H)mentioning
confidence: 99%
“…More general systems of Diophantine equations and associated trigonometric sums are treated in [2]. The Vinogradov method [28], when applied to bounding a more general sum N < n < 2 N e pn; pn a 1 n .…”
Section: Introductionmentioning
confidence: 99%
“…It follows from the more precise and general Theorem 1 of Ch. VI in Arhipov, Karatsuba and Chubarikov (1987; cf. a paper 1982 of the same authors).…”
Section: Lattice Pointsmentioning
confidence: 98%