Vol 17, No 5 (2011)

In this paper a hyperbolic equation with non-classical boundary conditions
for a hyperbolic equation is studied. This problem can be viewed as the gener
alization of the problem about the oscillation of the string if it ends experience
the resistance of medium. The unique solvability of the problem is proved. The
prove of solvability is based on the received a priory estimates in Sobolev space.

In this article, we consider a nonlocal problem for hyperbolic equation with integral conditions of the first kind. The main goal of this article is to show the method which allows to reduce posed problem to the problem with integral condition of the second kind. Existence and uniqueness of generalized solution is proved.

Linear operators satisfying some conditions are considered. The given operators are a particular kind of class operators (by P.P. Korovkin). For the estimate derivation the interpolation method is used, described in the works by Yu.G. Abakumov and O.N. Shestakova

The paper is devoted to two new results concerning varieties of Leibniz alge
bras. In case of prime characteristic p we construct an example of a non-nilpo
tent variety of Leibniz algebras with Engel condition. In case of field of character
istic zero we obtain a new result concerning the space of multilinear components
of the variety of left-nilpotent Leibniz algebra of class three.

In the frameworks of classical molecular dynamics method the coefficients of
diffusion and viscosity of fullerenes in fluid (benzol) depending on the tempera
ture of nanosuspension have been calculated.The effective potential of fullerene
molecule interaction used in calculations is obtained under the assumption of
additivity of fullerene and fluid molecules interaction, where fullerene is consid
ered as a solid particle.

The influence of dipole-dipole interaction on the entanglement between two
atoms with different initial W-like states in Tavis Cummings model with
degenerate two-photon transitions has been investigated. The results show that
the dipole-dipole interaction leads to the stabilization of atomic entanglement.

Derivatives of D-galactose and D-glucose substituted for the primary hydrox
yl group, which contain an aglycone azolylmethylphenyl fragments (for imida
zole, 1,2,4-triazole, benzimidazole and benzotriazole) has been synthesized. To
protect the secondary hydroxyl groups of monosaccharides acetyl and isopropy
lidene groups were used.

The results of study of the derivatives of 1,4-hydroquinone as inhibitors of
microbiological corrosion and hydrogen absorption of mild steel in a water-salt
media supporting the development of sulphate reducing bacteria (SRB) and
close by its composition to the sea water containing biogenic hydrogen sulphide.
Content of H2S, bacterial titre in the corrosive meas well as its pH, Eh and
potential of steel '; were determined together with the quantity of hydrogen
absorbed by surface layers of steel. Protective efficiency of the best studied
species from corrosion reaches 65...84 %, as for their action against hydrogen
absorption by steel specimen 60...72 %. The decrease of the number of SRB
cells due to the action of the derivatives of 1,4-hydroquinone was found to be
48...84 %, while the suppression degree 29...57 % (at the concentration of
5 mMol/L).
Key words:

The estimate of perspectiveness of 20 species of North-American trees and
bushes of the family of Rosaceae which are cultivated in the arboretum of
Mountain-Taiga station of FEB RAS. Higher indicators (96–97 points) have
Amelanchier spicata, A. alnifolia, Aronia melanocarpa, Physocarpus opulifolia,
P. monogynus, P. capitatus, Prunus americana, Rubus odoratus, Rubus occiden
talis. Quite perspective (82–90 points) are Cerasus besseyi, Crataegus flabellate,
C. macracantha, C. rotundifolia, C. submollis, Padus pensylvanica, P. serotina,
P virginiana, Rosa nutcana, Sorbus americana. Less perspective (67 points) and
demanding further study is Rosa Palnstris.

According to the data received in 2003–2004 years results of morphology and
reproduction characteristics of Bentophilus Stellatus from Ulyanovsk stretch of
Kuibyshev Reservoir are given, size-age structure, qualitative and quantitative
food composition are considered.