Magnetic black universes and wormholes with a phantom scalar

We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic fields which describe traversable wormholes (with flat and AdS asymptotics) and regular black holes, in particular, black universes. A black universe is a nonsingular black hole where, beyond the horizon, instead of a singularity, there is an expanding, asymptotically isotropic universe. The scalar field in these solutions is phantom (i.e., its kinetic energy is negative), minimally coupled to gravity and has a nonzero self-interaction potential. The configurations obtained are quite diverse and contain different numbers of Killing horizons, from zero to four. This substantially widens the list of known structures of regular black hole configurations. Such models can be of interest both as descriptions of local objects (black holes and wormholes) and as a basis for building nonsingular cosmological scenarios.Comment: 13 pages, 6 figure

Estimates for solutions in a predator-prey model describing plankton-fish interaction

In the paper we consider a system of differential equations with two delays describing plankton--fish interaction. We study stability of the equilibrium point corresponding to the presence of phytoplankton and zooplankton in the system and the absence of fish. In the case of asymptotic stability, we indicate conditions for the initial data under which solutions stabilize to this equilibrium point and establish estimates for solutions characterizing the stabilization rate at infinity. The results are obtained using Lyapunov-Krasovskii functional. The obtained theoretical results can be used for numerical study of behavior of solutions to the considered model

The value of estimating component in the content of the concept «relations» in modern english

The article discusses specific features of realization of a segment, aimed at expressing the category of evaluation in the field of material and ideal life of society on the basis of the concept of «relation(s)».В статье рассматривается специфика объективации сегмента, направленного на актуализацию категории оценочности в области материально-идеальной жизнедеятельности социума на основе концепта «relation(s)»

750 Natalia the economic and legal analysis of the terms of international delivery contracts involving Russian suppliers

Purpose: The article presents an economic and legal analysis of the terms of contracts for international delivery of goods involving Russian suppliers. Design/Methodology/Approach: The authors analysed the international norms of regulating relations for the goods’ delivery involving the foreign element. Terms of the goods delivery are investigated according to the national legislation of the Russian Federation. Findings: As a result, it is necessary to use an economic and legal approach when developing contract terms for the goods’ delivery to take into account norms of international law, the national legislation of the supplier country and in accordance with the calculations of the contract price and payment terms. Practical Implications: The proposed method is in accordance with the international legal framework and it can be adopted by the Russian Federation easily. Originality/Value: There is no such an approach eligible to modernize the existing system in the country.peer-reviewe