2016 Issue №4

Covariant derivatives of tangent tensor and pseudotensor are considered. Parallel displacements of tangent tensor and pseudotensor are described.

The article is focused on various generalizations of the Deuring Reduction Theorem. Our research proves that the most appropriate theorem for further elaboration is the one that relates the decomposition of pK into prime ideals with the decomposition of A[p] into indecomposable BT1-group schemes up to isomorphism. The article investigates basic problems of the theorem's further generalization and some ways of solving them as well as formulates tasks for further work in this direction.

Voss and Green's normalizations of the main structural subbundles of hyperband distribution of H -distribution of affine space are constructed internally invariantly.

The smooth surface in affine space is considered. With the derivation formulas and equations of the structure of an affine space constructed three pairs Akivis-Laptev on the surface. It is shown that the surface of an affine space is a holonomic smooth manifold.

A detailed analysis of sinusoidal waves in two-layer liquid is made. The dispersion relations for short and long waves are studied. The success was helped significantly by a technique created by us.

Interim results of the creation of the climate control system are presented. The algorithmic base of functioning of system is created. The control system of heating is realized.

We consider a new way of solving the problem of the sinusoidal wave on the surface of a homogeneous perfect fluid. Its feature is used instead of the potential speed of the original characteristics of wave motion: horizontal and vertical components of the velocity and pressure. It is noted that it will generalize the problem under consideration in the event of a multi-layer liquid. The results, including the dispersion relation, fully consistent with the known. Specially considered long-wave approximation.