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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2016, Volume 26, Issue 3, Pages 312–323 (Mi vuu541)  

This article is cited in 5 scientific papers (total in 5 papers)

MATHEMATICS

Embedding of phenomenologically symmetric geometries of two sets of the rank $(N,2)$ into phenomenologically symmetric geometries of two sets of the rank $(N+1,2)$

V. A. Kyrov

Mathematics, Associate Professor, Gorno-Altaisk State University, ul. Lenkina, 1, Gorno-Altaisk, 649000, Russia

Abstract: 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.

DOI: https://doi.org/10.20537/vm160302

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Bibliographic databases:

UDC: 517.912+514.1
MSC: 39A05, 39B05
Received: 21.06.2016

Citation: 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 $(N+1,2)$”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:3 (2016), 312–323

Citation in format AMSBIB
\Bibitem{Kyr16}
\by V.~A.~Kyrov
\paper Embedding of phenomenologically symmetric geometries of two sets of the rank $(N,2)$ into phenomenologically symmetric geometries of two sets of the rank~$(N+1,2)$
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2016
\vol 26
\issue 3
\pages 312--323
\mathnet{http://mi.mathnet.ru/vuu541}
\crossref{https://doi.org/10.20537/vm160302}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3558444}
\elib{http://elibrary.ru/item.asp?id=26726579}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Kyrov, “Vlozhenie fenomenologicheski simmetrichnykh geometrii dvukh mnozhestv ranga $(N,M)$ v fenomenologicheski simmetrichnye geometrii dvukh mnozhestv ranga $(N+1,M)$”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:1 (2017), 42–53  mathnet  crossref  elib
    2. V. A. Kyrov, G. G. Mikhailichenko, “Analiticheskii metod vlozheniya evklidovoi i psevdoevklidovoi geometrii”, Tr. IMM UrO RAN, 23, no. 2, 2017, 167–181  mathnet  crossref  elib
    3. V. A. Kyrov, G. G. Mikhailichenko, “Vlozhenie additivnoi dvumetricheskoi fenomenologicheski simmetrichnoi geometrii dvukh mnozhestv ranga $(2,2)$ v dvumetricheskie fenomenologicheski simmetrichnye geometrii dvukh mnozhestv ranga $(3,2)$”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:3 (2018), 305–327  mathnet  crossref  elib
    4. V. A. Kyrov, “Analiticheskii metod vlozheniya mnogomernykh psevdoevklidovykh geometrii”, Sib. elektron. matem. izv., 15 (2018), 741–758  mathnet  crossref
    5. V. A. Kyrov, “Analiticheskoe vlozhenie nekotorykh dvumernykh geometrii maksimalnoi podvizhnosti”, Sib. elektron. matem. izv., 16 (2019), 916–937  mathnet  crossref
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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