The paper analyzes three key indicators of economic growth and life quality from the National Development Goals of the Russian Federation. The following equivalents of these indicators were identified to form regions into clusters and highlight the main trends in their development: the growth rate of gross regional product (GRP), life expectancy, and poverty level. We studied the nationwide data based on the indicators, analyzed the distribution of regions, and carried out a cluster analysis according to 2017-2019 data. Our results suggest expanding the list of the Russian Federation subjects that require additional support in their development. More than one-third of the regions of the Russian Federation have been developing at a rate of less than one percent per year in the last three years. Considering the consequences of the pandemic, it can lead to serious problems in achieving the declared growth rates. Plans to increase life expectancy have already been adjusted. Considering the little-studied consequences of coronavirus infection, additional measures in the medical field will be required. The level of poverty of the population also demonstrates a significant degree of differentiation of the Russian Federation regions.

The paper presents a numerical and analytical investigation of the stability of a cantilevered pipeline transporting an incompressible fluid flow at a constant speed compressed by tracking force at the free end. To solve the problem, a dynamic approach based on the analysis of the behavior of the system’s own characteristics is used. In contrast to the classical research approaches, which are based on the representation of the solution of the problem using a finite number of basic functions, an algorithm that does not require such a restriction is proposed.

The paper presents the results of a research of the stability of a rigid homogeneous rotor with a symmetrical relative to the middle arrangement of radial EMB, supported in the vertical direction by an axial EMB. In the first part of the work, the researches were held using a proportional-differential regulator in the system. In the second part of the work was considered the impact of the control function parameters in the cases of instantaneous generation of the displacement signal and with delay.

This study deals with the analysis of the factors that determine life expectancy in Russia at the macro level. Among the available statistical indicators, those were selected that can be considered as a macroeconomic alternative to the basic microeconomic determinants affecting the life expectancy of an individual. As a result of the regression analysis, significant indicators were identified, which included the marriage rate, the unemployment rate, the number of students, the number of hospital beds, the gross regional product, budget expenditures on health care, and the region’s subtropical climate. A cluster analysis of the regions was also carried out for these indicators, with the exception of the last one, and it was shown that the regions are distributed into 5 clusters. The cluster, which includes Moscow and St. Petersburg, where there is a high life expectancy due to the metropolitan area of these regions and good medicine, is singled out separately. The regions of the North Caucasus are also characterized by high life expectancy, but here it is due to completely different reasons: religious and climatic features. The Tyumen, Magadan, Sakhalin regions and the Chukotka Autonomous Okrug are united into a separate cluster. These regions are characterized by the highest GRP, but low life expectancy and the lowest number of students.