On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing

Consider the Klein-Gordon equation (KGE) in $\R^n$, $n\ge 2$, with constant or variable coefficients. We study the distribution $\mu_t$ of the random solution at time $t\in\R$. We assume that the initial probability measure $\mu_0$ has zero mean, a translation-invariant covariance, and a finite mean energy density. We also asume that $\mu_0$ satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. The main result is the convergence of $\mu_t$ to a Gaussian probability measure as $t\to\infty$ which gives a Central Limit Theorem for the KGE. The proof for the case of constant coefficients is based on an analysis of long time asymptotics of the solution in the Fourier representation and Bernstein's `room-corridor' argument. The case of variable coefficients is treated by using an `averaged' version of the scattering theory for infinite energy solutions, based on Vainberg's results on local energy decay.Comment: 30 page

Peculiar Motions in the Region of the Ursa Major Supercluster of Galaxies

We have investigated the peculiar motions of clusters of galaxies in the Ursa Major (UMa) supercluster and its neighborhood. Based on SDSS (Sloan Digital Sky Survey) data, we have compiled a sample of early-type galaxies and used their fundamental plane to determine the cluster distances and peculiar velocities. The samples of early-type galaxies in the central regions (within R_200) of 12 UMa clusters of galaxies, in three main subsystems of the supercluster -- the filamentary structures connecting the clusters, and in nine clusters from the nearest UMa neighborhood have similar parameters. The fairly high overdensity (3 by the galaxy number and 15 by the cluster number) suggests that the supercluster as a whole is gravitationally bound, while no significant peculiar motions have been found: the peculiar velocities do not exceed the measurement errors by more than a factor of 1.5-2. The mean random peculiar velocities of clusters and the systematic deviations from the overall Hubble expansion in the supercluster are consistent with theoretical estimates. For the possible approach of the three UMa subsystems to be confirmed, the measurement accuracy must be increased by a factor of 2-3.Comment: 21 pages, 4 tables, 7 figure

The level of training of dental surgeons for the diagnosis and prevention of complications of dental implantation (case study)

Modern dental implants can most adequately compensate the lost teeth and the functions of a full dentition. The method of dental implantation is still fraught with a high risk of complications in each of its stages. A particularly acute problem for the early diagnosis and prevention of complications of dental implants. Unprofessional actions of a dentist, poor knowledge of the anatomy of the maxillofacial region, neglecting the necessity of full X-rays are able to neutralize any result achieved by using the most advanced technologies and materials. The article analyzes the data obtained from the survey 295 dentists on dental implants with different work experience in the field of medicine and dentistry - from 5 to 20 years. The findings of the study data indicate inadequate training of doctors, significant gaps in academic and specialized knowledge of the majority of the doctors surveyed, which gives rise to the need for correction of both academic and postgraduate education curriculu

CONSIDERATION OF THE DYNAMICS OF INDUSTRIAL PRODUCTION IN THE EVALUATION OF ENERGY SAVING POTENTIAL AT THE LEVEL OF INDIVIDUAL COUNTRIES AND REGIONS

An approach to the allocation of economic and macroeconomic factors, affecting the final energy consumption, taking into account the seasonal unevenness of industrial production and the inertia of changes in the production of final products relative to the consumption of energy required for their production, has been considered in the article. In addition, factors have been reviewed not only at the end of the value chain on the basis of gas-consuming industries, but also taking into account the indicators of the raw material sector of the economy, which determines the beginning of the value chain

The Structure of Clusters with Bimodal Distributions of Galaxy Radial Velocities. I. A1035

The structure of the A1035 cluster of galaxies (10h32m +40d13', cz ~ 22000 km/s), which exhibits a bimodal distribution of galaxy radial velocities (\Delta V\approx 3000 km/s), is analyzed using three methods of determining the relative distances to clusters from early-type galaxies: the Kormendy relation corrected for the dependence of residuals on galaxy magnitude, the photometric plane, and the fundamental plane. We use the data obtained with the 1-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences and SDSS (DR5) data to show that A1035 consists of two gravitationally unbound independent clusters. These clusters with the velocity dispersions of 566 km/s and 610 km/s and masses within R_200 equal to 2.7 10^14 and 3.5 10^14 M_sun, respectively, obey the Hubble law.Comment: 13 pages, 3 tables, 6 figure

Christian values in spiritual and moral upbringing of students

© 2018, Ecozone, OAIMDD. All rights reserved. The issue of spiritual and moral upbringing of student-age youth is quite topical for the contemporary Science and practice. The article substantiates the necessity of spiritual and moral upbringing of the young generation on the basis of Christian values, and highlights as well as the gained experience in the implementation of the Christian values into education system of higher educational institutions. The purpose of the present study is to establish psychological patterns and mechanisms of spiritual and moral upbringing of the student‟s personality through inclusion and acceptance of Christian values. The objective of the research involves the solution of the following tasks: carrying out psychological, theoretical and methodological analysis of the problem on spiritual and moral upbringing of the personality; providing a system of psychological and pedagogical practices designed to promote spiritual and moral upbringing of the student‟s personality; and developing and testing a training program of spiritual formation of the student‟ personality. The authors have proposed the formation mechanisms of spiritual values of the student‟s personality, and developed psychological training program to form spirituality in the student‟s personality