Generalization of the Dependent Function in Extenics For Nested Sets with Common Endpoints to 2D-Space, 3D-Space, and Generally To N-D-Space
extend, nested, geometrical, Critical
Abstract
In this paper we extend Prof. Yang Chunyan and Prof. Cai Wen's dependent function of a point P with respect to two nested sets X 0 ⊂ X, for the case the sets X 0 and X have common ending points, from 1Dspace to n-D-space. We give several examples in 2Dand 3D-spaces. When computing the dependent function value k(.) of the optimal point O, we take its maximum possible value. Formulas for computing k(O), and the geometrical determination the Critical Zone are also given.
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References
Wen Cai (1983) Extension Set and Non-Compatible Problems [J]. (1), 83-97.
Yang Chunyan, Cai Wen (2007) Extension Engineering.
F Smarandache (2012) Generalizations of the Distance and Dependent Function in Extenics to 2D, 3D, and n-D.
F Smarandache, V Vlădăreanu (2012) Applications of Extenics to 2D-Space and 3D-Space.
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2012-09-03
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