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Two models of machine learning are proposed for the automatic prediction of political views held by Russian users of the Vkontakte social network based on a microapproach to data analysis. The results are tested on various scientific and applied fields. One of them is monitoring of public opinion: based on testing a sample of 22 million digital fingerprints of adult user accounts, two estimates were made reflecting the political preferences of the users on the eve of the presidential election in 2018. When these estimates were used to develop a retrospective forecast of the elections, the average absolute errors were 12% and 19.4%, respectively; moreover, the first estimate was correct in ranking the first three candidates. In addition, an approach is presented to calibrate the parameters of mathematical models simulating the dynamics in opinions, namely, the quantities that determine the opinions held by users themselves. This approach is based on the estimates generated by the constructed algorithms. [ABSTRACT FROM AUTHOR]

On the basis of the special theory of relativity and a solution of the Schwarzschild equations of general relativity, a generalized equation of Friedmann-Einstein-de Sitter type has been obtained for the expanding Universe. As a result of our work on the boundary value problem for this equation, we have found the eigenvalue of the resulting eigenvalue problem, linking the density of the Universe in the comoving coordinates, the Hubble constant, and the gravitational constant. We have calculated a value for the density of matter in the Universe which is in agreement with the observational data. We have shown that the missing dark energy is the relativistic kinematic and potential energy of the expanding Universe. [ABSTRACT FROM AUTHOR]

The statement and solution of the problem of the expansion of the Universe in nonstationary spherically-symmetric coordinates in the Schwarzschild metric are considered without pressure taken into account. The observational data of astronomers investigating the rates of recession of distant stars are explained on the basis of the obtained solutions. [ABSTRACT FROM AUTHOR]

On the basis of the special relativity theory (SRT), the mean density of matter in the Universe is calculated with the relativistic kinetic energy of receding galaxies taken into account. Within the framework of the general relativity theory (GRT), we estimate the influence on the mean density of the effect of gravitation. A contradiction between the hypothesis of dark energy and conclusions following from SRT and GRT is noted. [ABSTRACT FROM AUTHOR]

The algorithm and results of numerical calculations of a detached turbulent gas flow by directly solving the Navier-Stokes equations are presented. It has been shown that the turbulent energy dissipated in a detached flow by heat conduction is of the same order of magnitude as that dissipated due to viscosity. It has been revealed that the actual turbulence dissipation begins in turbulent structures whose size is much greater than the internal (Kolmogorov) scale. [ABSTRACT FROM AUTHOR]