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## Archive of Issues

Russia Gorno-Altaisk
Year
2016
Volume
26
Issue
3
Pages
312-323
 Section Mathematics Title Embedding of phenomenologically symmetric geometries of two sets of the rank $(N,2)$ into phenomenologically symmetric geometries of two sets of the rank $(N+1,2)$ Author(-s) Kyrov V.A.a Affiliations Gorno-Altaisk State Universitya 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 UDC 517.912, 514.1 MSC 39A05, 39B05 DOI 10.20537/vm160302 Received 21 June 2016 Language Russian Citation Kyrov V.A. 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. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 3, pp. 312-323. References Kulakov Yu.I. The one principle underlying classical physics, Soviet Physics Doklady, 1971, vol. 15, no. 7, pp. 666-668. Mikhailichenko G.G. Two-dimensional geometry, Soviet Mathematics. Doklady, 1981, vol. 24, no. 2, pp. 346-348. Mikhailichenko G.G. The solution of functional equations in the theory of physical structures, Soviet Mathematics. Doklady, 1972, vol. 13, no. 5, pp. 1377-1380. Mikhailichenko G.G. Matematicheskii apparat teorii fizicheskikh struktur (The mathematical apparatus of the theory of physical structures), Gorno-Altaisk: Gorno-Altaisk State University, 1997, 144 p. Kyrov V.A. Functional equations in pseudo-Euclidean geometry, Sib. Zh. Ind. Mat., 2010, vol. 13, no. 4, pp. 38-51 (in Russian). Kyrov V.A. Functional equations in symplectic geometry, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2010, vol. 16, no. 2, pp. 149-153 (in Russian). Kyrov V.A. On some class of functional-differential equation, Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2012, vol. 26, no. 1, pp. 31-38 (in Russian). DOI: 10.14498/vsgtu986 Mikhailichenko G.G. Gruppovaya simmetriya fizicheskikh struktur (The group symmetry of physical structures), Barnaul: Barnaul State Pedagogical University, 2003, 204 p. Kulakov Yu.I. Elementy teorii fizicheskikh struktur (Elements of the theory of physical structures), Novosibirsk: Novosibirsk State University, 1968, 226 p. Elsgolts L.E. Differentsial'nye uravneniya i variatsionnoe ischislenie (Differential equations and the calculus of variations), Moscow: Nauka, 1969, 424 p. Full text