Non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary

We have discussed non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary. By photogravitational we mean that both primaries are radiating. We normalised the Hamiltonian using Lie transform as in Coppola and Rand (1989). We transformed the system into Birkhoff's normal form. Lie transforms reduce the system to an equivalent simpler system which is immediately solvable. Applying Arnold's theorem, we have found non-linear stability criteria. We conclude that $L_6$ is stable. We plotted graphs for $(\omega_1, D_2).$ They are rectangular hyperbola.Comment: Accepted for publication in Astrophysics & Space Scienc

The project method in teaching future mathematics teachers

This paper deals with the problem of using the project method in teaching future mathematics teachers. The authors showed that one of such technologies is project training, which involves joint learning and cognitive activity of students, having a common goal, agreed ways of working. This paper notes also the need to use project technology, which consists in developing the ability of future teachers to have an analytical, creative thinking; self-acquisition of missing math knowledge from various sources; thinking, based on knowledge of mathematical facts, the laws of science; and ability to work in a team, performing various social role

MODERNIZATION OF STATIONARY FISHING GEAR AS A FACTOR IN INCREASING THE EFFICIENCY OF FISHING IN THE SHALLOW WATERS OF THE NORTH CASPIAN

In the last 15-20 years of the twentieth century in the Volga-Caspian region, the fishing has changed dramatically fishing conditions that have led to considerable changes of the fisheries in this region. Venterny fishing in the region has a high selectivity of fishing gear and the quality of fish caught. To improve fishing Venter is currently at the Department of Industrial Fisheries ASTU developed new designs. This significantly increases the catchability of fish venternymi plants