Vol 19, No 6 (2013)

In the article a new method for the solution of inverse problems generated by perturbations of self-adjoint operators on their spectral characteristics is developed. The method was tested on inverse problems for Sturm-Liouville problems. The results of numerous calculations showed the computational efficiency of the method.

In this work necessary and sufficient conditions for uniqueness of a solution to the first boundary problem for Lavrentiev-Bitsadze equation in rectangular domain are established. The solution to the problem is constructed as a sum of series with respect of eigenfunctions of a corresponding one-dimensional Stour-m-Liouviele problem. The stability is shown.

The activity presents an efficient description of symmetric closed classes of discrete functions preserving every unary predicate.

In the work a method of numerical finding of eigen values of class of non linear problems on eigen values arising from the problem of defining stress-edly-deformed state near the apex of crack in the materials with exponential determining equations in conditions of compound deforming in full range of mixed forms of deformation from normal fracture up to simple shear is suggested. With the help of suggested approach new eigen values of the problem, different from the known eigen value, that corresponds to the classical solution of Hutchison-Rice-Rosengren are obtained.

The paper a theoretical model and migration of methane bubbles in the hydrate formation conditions in the upward flow of water in a vertical channel is suggested and built. We obtain critical values of mass flow rates of gas and water, providing the necessary conditions for the full transition to the reactor, the gas in the gas hydrate. It is found out that at migration of gas bubbles in the reactor, two possible modes of the process of hydrate depending on the initial mass flow rate of water: gas bubbles or completely converted into hydrated state as separate inclusions or partially, forming bubbles with a hydrated shell. Analysis of influence of size of gas bubbles on the process of hydrate formation).

Non-stationary axisymmetric problem for a thin circular bimorphous plate under the action on the end surfaces of electric potential, which is an arbitrary function of time is viewed. On the basis of the theory of Tymoshenko by method of finite integral transformation a new closed solution for the viewed electricity and elastic system of stepped variable rigidity and thickness is built. The obtained calculated correlations allow to explore the frequency characteristics and stress-deformed state of bimorphous elements.

A mathematical model of motion of centre of mass of space vehicle is suggested and methods of processing of parameters based on the usage of Kalman filter and combined wavelet filter are also suggested. The results of numerical experiments of defining parameters are presented.

In this article the analytical characteristics of method of analysis of ephedrine and verapamyle with application of thin-layer chromatography and densitometry is considered. Detection limit of ephedrine and verapamyle is 10,0 /tg/ml in a sample. The possibility of ephedrine and verapamyle quantitative determination in model samples in the range of 10,0-250,0 /tg/ml concentration is indicated.

The effect of low concentrations of peptide compounds of hemolymph of wax moth larvae on the kinetic characteristics of alkaline phosphatase of E.coli is studied. Activating effect of one of the components of chromatographic fractions of hemolymph on the rate of phosphatase reaction after 2-4 minutes after the addition of substrate is disclosed. It is assumed that peptide compounds in small doses can have a regulatory effect on the activity of enzymes of E.coli.

In the article the inhibitory effects on respiratory parameters during electrical or chemical stimulation of the magnus raphe nucleus are induced mainly by the participation of GABA. To elucidate the involvement of GABA