Vol 19, No 9.1 (2013)

A new numerical method for solving inverse spectral problems generated by perturbed self-adjoint operators from their spectral characteristics is developed. The method was tested on the problems for perturbed Sturm - Liouville operator. The results of numerous calculations have shown its computational efficiency. The simple algebraic formulas for finding the eigenvalues of discrete operators was found. At that the calculation of eigenvalues of perturbed self-adjoint operator can start from any number, no matter known the eigenvalues from previous numbers or not.

The scheme of definition of an error of numerical method of calculation of limit of maximal mean for periodic function is offered. The example of calculation of limit of maximal mean is considered.

Certain general conditions of integrability in elementary functions for the systems on the tangent bundle of two-dimensional sphere are studied. At that an interesting example of three-dimensional phase pattern of pendulum-like system which describes the motion of spherical pendulum, placed in an over-run medium flow. Sufficient conditions of existence of the first integrals expressed through the finite combination of elementary functions, for multi-parametric third order systems are presented.

In the article questions, connected with the notion of topological projectiv-ity are viewed. It is shown that this type of projectivity can be represented as a partial case of certain general-categorical scheme, based on a notion of framed category. Apart from that topologically free 'classical', as well as quantum normed modules are described. Analogous results were obtained for topo-logical injectivity.

Results of researchers on dynamics modeling of the systems containing different physical elements are proposed. The construction method of the physical systems dynamics equations, providing constraints stabilization, is discussed. The problem of corresponding constraints reactions or determination of control actions is reduced to the construction of the system of differential equations, assuming that the partial integrals are given. The conditions of asymptotic stability and exponential stability an integral manifold's corresponding constraint equations are defined.

The algorithm of calculation of sequence of states of queueing system with heterogeneous equipment and separate storage devices on the basis of preset sequence of input signals and initial state with the help of finite Mealy automatons is presented.

The influence of dipole-dipole interaction on dynamics of three- and four-particle GHZ states for two Д-type superconducting flux cubits interacting with one or two different electronic LC cavities via two-photon processes has been investigated. The results show that dipole-dipole interaction does not lead to the disappearance of the effect of entanglement sudden death and does not change the maximum degree of entanglement.

An increase in the production of peptide compounds in human erythrocytes incubated by them in conditions of hyperglycemia (10 mmol/L) compared with normoglycemia (5 mmol/L) is found. At that the spectrum of peptide compounds changes, since a change of their action on the activity of cathepsin D leukocytes: in normoglycemia allocated erythrocytes peptides increase the activity of cathepsin D with calcium deficiency in the environment, and in conditions of hyperglycemia, on the contrary inhibit the enzyme in the presence of calcium ions.

The preliminary results of after-flight laboratory and field studies fulfilled with the higher plants seeds exposed for 30 days on the board of spacecraft "BION-M" № 1 are presented in the article.

The analysis of deviation in parameters of erythrocytic system state in condition of 1,1-di(azolil-1)imins administration has established the expressed ability of these substances to stimulate erythropoiesis.

The paper presents a model for the calculation of morphofunctional erythrocyte properties. The model represents the erythrocyte as a homogeneous elastic body with elastic depending on the distance to the center of symmetry of the erythrocyte. The data for modeling were taken from the experimental study, which were used by atomic force microscopy (measuring the elasticity of the membrane of erythrocytes and morphology) and the Coulter method. In the developed model, the elasticity of the membrane to change depending on the distance to the center within 1-1,6 kPa. The calculation of the elastic properties is made by two methods - finite element analysis and optimization methods. In the model the dependence of erythrocyte morphology on the membrane pressure was obtained. Pressure difference across the erythrocyte membrane varied in the range of 0,5-2 kPa.

The article is devoted to the problem of development by methods of approximate solution of rigid integral and differential problem on the example of modeling of isoelectric focusing (IEF) in the so-called "anomalous" regimes. Two new methods of asymptotic solution of problem with large parameter are represented: the geometric tangent method, based on approximation of solution by the system of broken lines with known geometric parameters.