Generalization of the Dependent Function in Extenics For Nested Sets with Common Endpoints to 2D-Space, 3D-Space, and Generally To N-D-Space

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Dr. Florentin Smarandache
Dr. Florentin Smarandache
1 University of New Mexico

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Generalization of the Dependent Function in Extenics  For Nested Sets with Common Endpoints to 2D-Space, 3D-Space, and Generally To N-D-Space Banner
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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.

4 Cites in Articles

References

  1. Wen Cai (1983). Extension Set and Non-Compatible Problems [J].
  2. Yang Chunyan,Cai Wen (2007). Extension Engineering.
  3. F Smarandache (2012). Generalizations of the Distance and Dependent Function in Extenics to 2D, 3D, and n-D.
  4. F Smarandache,V Vlădăreanu (2012). Applications of Extenics to 2D-Space and 3D-Space.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

. 2012. \u201cGeneralization of the Dependent Function in Extenics For Nested Sets with Common Endpoints to 2D-Space, 3D-Space, and Generally To N-D-Space\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 12 (GJSFR Volume 12 Issue F10): .

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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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v1.2

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September 3, 2012

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English

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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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Generalization of the Dependent Function in Extenics For Nested Sets with Common Endpoints to 2D-Space, 3D-Space, and Generally To N-D-Space

Dr. Florentin Smarandache
Dr. Florentin Smarandache University of New Mexico

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