Statistical solution and Liouville type theorem for coupled Schrödinger-Boussinesq equations on infinite lattices

<p style='text-indent:20px;'>In this article, we are concerned with statistical solutions for the nonautonomous coupled Schrödinger-Boussinesq equations on infinite lattices. Firstly, we verify the existence of a pullback-<inline-formula><tex-math id="M1">\begin{document}$ {\mathcal{D}} $\end{document}</tex-math></inline-formula> attractor and establish the existence of a unique family of invariant Borel probability measures carried by the pullback-<inline-formula><tex-math id="M2">\begin{document}$ {\mathcal{D}} $\end{document}</tex-math></inline-formula> attractor for this lattice system. Then, it will be shown that the family of invariant Borel probability measures is a statistical solution and satisfies a Liouville type theorem. Finally, we illustrate that the invariant property of the statistical solution is indeed a particular case of the Liouville type theorem.</p>

CHOICE OF LOCOMOTIVE PARK MAINTENANCE STRATEGY WHEN INTRODUCING THE SERVICE

In operation, sometimes there are situations of uncertainty in assessing the technical condition of locomotive equipment and at the same time choosing the optimal strategy for its maintenance, including the possibility of using the service. Application of the concept of service gives the chance to stimulate work of all divisions of locomotive economy, to save all kinds of resources for operation of locomotives. According to this, the article substantiates the choice of strategy for maintaining the locomotive fleet using the provisions of the theory of statistical solutions. Game theory approaches were used to theoretically substantiate the transition to a service for decision-making in conflict situations and to determine the optimal strategy of behavior of each of the participants in this situation. Approaches to the choice of strategy for the maintenance of the locomotive fleet during the introduction of the service on the basis of the provisions of the theory of strategic games on the criterion of maximum efficiency were considered. It is shown on examples of the decision of some problems of a choice of maintenance strategy of locomotives for various industrial situations. It is concluded that a mixed strategy describes different situations best and allows to made rational decisions. It is also noted that the most effective approach to concretize the algorithm of actions is the complex application of the theory of strategic decisions, the theory of fuzzy sets, the theory of pattern recognition.

Use of social media and their desires to be liked by women who do sports

The desire to admire has varied with the introduction of social media networks into our lives. This diversity is among the subjects worth researching, especially among women who do sports. The study aims to examine the desire to be liked and the level of use of social media networks in terms of various variables. For this purpose, the "personal information form" developed by the researchers and the "desire to like" scale developed by Kaşıkara and Doğan (2017) were applied to 120 women with an average age of 30.65. The Chi-square test was applied for the statistical solutions of the study. As a result of the analysis, a difference was found between demographic characteristics, but no similarity was found in terms of scale scores.

Equivalence between invariant measures and statistical solutions for the 2D non-autonomous magneto-micropolar fluid equations

In this article, we aim to investigate the regularity of statistical solution for the 2D non-autonomous magneto-micropolar fluid equations as well as the relationship between invariant measures and statistical solutions. Firstly, to get the regularity of the statistical solution, we prove the existence and regularity of the pullback attractor for the equations. Then we prove the statistical solution possesses some regularity properties by using regularity of the pullback attractor. Finally, we prove the statistical solution is actual an invariant measure for the equations.