Research
Extention Transformation Used in I Ching
In this paper we show how to using the extension transformation in I Ching in order to transforming a hexagram to another one. Each binary hexagram (and similarly the previous trigram) has a degree of Yang and a degree of Yin. As in neutrosophic logic and set, for each hexagram <H> there is corresponding an opposite hexagram <antiH>, while in between them all other hexagrams are neutralities denoted by <neutH>; a neutrality has a degree of <H> and a degree of <antiH>. A generalization of the trigram (which has three stacked horizontal lines) and hexagram (which has six stacked horizontal lines) to n-gram (which has n stacked horizontal lines) is provided. Instead of stacked horizontal lines one can consider stacked vertical lines - without changing the composition of the trigram/hexagram/n-gram. Afterwards, circular representations of the hexagrams and of the n-grams are given.
Generalization of the Dependent Function in Extenics For Nested Sets with Common Endpoints to 2D-Space, 3D-Space, and Generally To N-D-Space
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 X0 ⊂ X, for the case the sets X0 and X have common ending points, from 1D - space to n-D-space. We give several examples in 2D- and 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.
