It was founded the general expression for longitudinal component of magnetic susceptibility tensor of fractal easy-axis ferromagnetic with dimension , where .

Stated the method of tritium planigrafy (TP). A comparison with other methods. A comprehensive approach to the study of the spatial structure of proteins, based on the joint use of the experimental method and the TP software package for the interpretation of experimental data and prediction of protein structure. Some results of this approach to a wide range of tasks such as building three-dimensional structure of biomolecules and its comparison with the crystal (if known), the definition of the orientation of the molecule and its degree of immersion, when it is at the interface, and others.

The velocity of propagation and the coefficient of absorption of ultrasound, at frequency 2.7 MHz, in emulsions of liquid crystal (LC) N96 in water has been studied using samples with sizes of droplets in the range from 200 to 5000 nm (sample I) and from 200 to 1500 нм (sample II). The possibility of an acoustic study of characteristics of phase transition from nematic to isotropic phase and critical dynamics of LC in droplets of both microns and submicrons sizes is shown using analyze of ultrasound characteristics of LC emulsions.

Multilayered periodic structures are widely applied in devices of various frequency ranges and comparative are in detail investigated in the field of a transparency of environments. In this work dispersive characteristics of two-componental structure with an evanescent layer of the strengthening environment are received. It is established, that introduction of environment with strengthening allows to receive structures with constant on frequency in factor of strengthening.

We report the mesomorphic and physic-chemical properties of some liquid crystalline cyanoethyl esters. The influence of the molecular structure of these compounds on their properties is discussed.

In this paper the topological relational systems for a modeling different subject fields are introduced. The formalization procedure for the determination of the type of an object in the subject field indication space is taken.

In this paper the necessary and sufficient conditions for the wide class locally invariant affine connected manifolds are found. The cases of locally invariance of an affine connected space with respect to reductive and symmetric spaces are considered.

The category equivalence of models and universal algebras is proved. The construction may be used of the construction of the algorithms of processing of intelligent relation data bases.

In article the first and second two-dimensional boundary problems for the diffusion equation in the isotropic environment with coefficient (of diffusion) depending on concentration are considered. Construction of the numerical solution of such problems is interfaced to great difficulties. The technique based on discretization of initial problems on time variable and iterative process of construction for each considered moment of time of approximate solutions of auxiliary linear problems is used. The approximate solutions of auxiliary problems are under construction the method of basic potentials. With the help of this technique are constructed approximate solutions of considered nonlinear problems. The general view of these approximate solutions is reduced. On concrete examples convergence of approximate solutions of the problems to the exact is shown.

This paper proposes a method of averaging for compressible and incompressible Newtonian fluid dynamics equations. This method derives new set of equations for averaged and fluctuating variables with the closed chain of equations for the given averaging scale. This scale is not related with the mesh size, hence the computational procedure is much cheaper than the LES method. Numerical method for the derived equations is proposed. The work is supported by RFFI grants 08-07-00074а and 09-07-00078а.

The paper considers a lattice Boltzmann method stabilization when Reynolds number goes to infinity, i.e. infinitely small viscosity. Stream and collide algorithm is considered and every fractural step is analyzed for stability. As the result of the analysis, the local limiter of the particle probability distribution function evolution is introduced for entropy deviation. The limiter is equivalent to the classic CFD TVD limiters. A set of initial-boundary value problems is solved on D2Q9 lattice to verify the method and its stability properties. The work is supported by RFFI grants 08-07-00074а and 09-07-00078а

The task in this work is and is forecasting in MDX economic area with the use of analytical mathematical models built on multidimensional statistical data. Set of models forms a knowledge base to generate full Combinatorial set of forecasting scripts. Each script realizes iterative procedure of definition regular stable forecast point. There are the appraisals of the amount of the script depending on the dimension of economic space. In theory it’s disclosed that MDX prediction is a NP task with the nondeterministic algorithm. In practice it`s revealed that time of serial solution of the task forecasting exponentially depends on the dimensions of space. Parallel decision task of forecasting is fulfilled polynomials that is confirmed experimentally for different types of forecasting, for example, population of Germany, GDP and other settings MDX economic space of its statistics.