Let [Formula: see text] be a free Burnside group of a sufficiently large odd exponent n with a basis [Formula: see text] of cardinality at least 2. We prove that every normal automorphism of [Formula: see text] is inner. We also prove that a free Burnside group of large odd exponent n can be normally embedded into group of exponent n only as a direct factor.
We consider a large-scale directed graph G = (V, E) whose edges are endowed with a family of characteristics. A subset of vertices of the graph, V ⊂ V , is selected and some additional conditions are imposed on these vertices. An algorithm for reducing the optimization problem on the graph G to an optimization problem on the graph G = (V , E ) of a lower dimension is developed. The main steps of the solution and some methods for constructing an approximate solution to the problem on the transformed graph G are presented.
To develop a long-term strategy for managing the fire risks level at the sites of supervision in the Russian Federation regions, we collected, analyzed and summarized statistical data on fires occurring. Based on the obtained results, it proposed to take management decisions aimed at minimizing fire risks in the Russian Federation. The article presents the results of a comprehensive study of fire risks.
In this study, special attention paid to identifying the influence of social factors among the causes of fires occurring in Russia. Based on the panel data analysis for the regions of Russia, a quantitative dependence of the probability of fires occurrence at economic and administrative objects of supervision obtained. An assessment of the risk of death for a year because of such fires carried out. A comparative analysis of the values of the regional socio-economic factors corresponding indicators for the previous year carried out. A comparison of the results obtained with the rapid response time to fires rescue units of EMERCOM of Russia.
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