Classification of Simplex Sections Defined by a Hyperplane

Authors

  • Shodiyev Oybek Narzullayevich National University of the Republic of Uzbekistan named after Mirzo Ulugbek

Keywords:

Simplex, section of simplex, convex independence

Abstract

In a number of applied problems [6]-[8] the points of the simplex are considered as states of some biological (physical, economic, etc.) system. The transition from one state to another is specified by an evolutionary operator, which can be a differential equation (with or without memory) or a difference equation. Depending on the parameters, the evolution of the system can occur only on some hyperplane intersecting the simplex [1]. In this case, the problem of determining the type of the resulting polyhedron arises.

References

A. D. Alexandrov, Convex Polyhedra, State Publishing House of Technical Theoret. lit., M., 1950.

M. Berger, Geomeria, part 1,2., Mir, M., 1974.

H. S. M. Coxeter, Introduction to Geometry, N.Y.. 1969.

N. V. Efimov, Higher Geometry, Nauka, M., 1971.

B. A. Rosenfeld, Multidimensional Spaces, Nauka, M., 1966.

J. Murray, Mathematical Biology, Springer, M., 2011.

R. Diestel, Graph Theory, Springer, N.Y., 2000.

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Published

2024-10-07

How to Cite

Narzullayevich, S. O. (2024). Classification of Simplex Sections Defined by a Hyperplane. American Journal of Education and Evaluation Studies, 1(7), 25–29. Retrieved from https://semantjournals.org/index.php/AJEES/article/view/233

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