Embedding of phenomenologically symmetric geometries of two sets of the rank $(N,2)$ into phenomenologically symmetric geometries of two sets of the rank~$(N+1,2)$
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 3, pp. 312-323
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In this paper, we propose a new method of classification of metric functions of phenomenologically symmetric geometries of two sets. It is called the method of embedding, the essence of which is to find the metric functions of phenomenologically symmetric geometries of two high-rank sets for the given phenomenologically symmetric geometry of two sets having rank less by 1. By the previously known metric function of phenomenologically symmetric geometry of two sets of the rank $(2,2)$ the metric function of phenomenologically symmetric geometry of two sets of the rank $(3,2)$ is found, by the phenomenologically symmetric geometry of two sets of the rank $(3,2)$ we find phenomenologically symmetric geometry of two sets of the rank $(4,2)$. Then it is proved that embedding of phenomenologically symmetric geometry of two sets of the rank $(4,2)$ into the phenomenologically symmetric geometry of two sets of the rank $(5,2)$ is absent. To solve the problem we generate special functional equations which are reduced to well-known differential equations.
Keywords:
phenomenologically symmetric geometry of two sets, metric function, differential equation.
@article{VUU_2016_26_3_a1,
author = {V. A. Kyrov},
title = {Embedding of phenomenologically symmetric geometries of two sets of the rank $(N,2)$ into phenomenologically symmetric geometries of two sets of the rank~$(N+1,2)$},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {312--323},
publisher = {mathdoc},
volume = {26},
number = {3},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2016_26_3_a1/}
}
TY - JOUR AU - V. A. Kyrov TI - Embedding of phenomenologically symmetric geometries of two sets of the rank $(N,2)$ into phenomenologically symmetric geometries of two sets of the rank~$(N+1,2)$ JO - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki PY - 2016 SP - 312 EP - 323 VL - 26 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VUU_2016_26_3_a1/ LA - ru ID - VUU_2016_26_3_a1 ER -
%0 Journal Article %A V. A. Kyrov %T Embedding of phenomenologically symmetric geometries of two sets of the rank $(N,2)$ into phenomenologically symmetric geometries of two sets of the rank~$(N+1,2)$ %J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki %D 2016 %P 312-323 %V 26 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/VUU_2016_26_3_a1/ %G ru %F VUU_2016_26_3_a1
V. A. Kyrov. Embedding of phenomenologically symmetric geometries of two sets of the rank $(N,2)$ into phenomenologically symmetric geometries of two sets of the rank~$(N+1,2)$. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 3, pp. 312-323. http://geodesic.mathdoc.fr/item/VUU_2016_26_3_a1/