The authors continue construction of the theory of nonstationary diffusiophoresis of large non-volatile solid spherical particle in a viscous gas medium. The solution of diffusion problem is carried out. This problem is divided into stationary and strictly nonstationary parts. Final formula for determining stationary diffusiophoresis velocity component of the particle was obtained. For determining nonstationary diffusiophoresis velocity component of this particle corresponding formula in the space of Laplace images was obtained. Dependence of nonstationary diffusiophoresis velocity component of the particle from strictly nonstationary concentration gradient at large and small values of time was obtained using theorems about limiting values from operational calculus.

The theory of nonstationary evaporation of spherical aerosol fixed drop is constructed paying attention to accounting of the surface tension coefficient of drop agent. Detailed analysis of limiting formulas obtained from the formula of rate of drop radius change, which is valid for all values of time, was carried out.

The formula of the density of the matter flow in the non-stationary gas-liked system of many particles with regard for the non-potential term is considered. The analytical formulae of the components of the curl of the density of the matter flow are obtained. The analysis and graphical presentation of the obtained formulae are performed.

In the paper an investigation of the regions E and F of the Earth ionosphere is carried out. Since the well-known model of the standard atmosphere becomes unsatisfactory when altitudes are higher than 150 km, a new model of the upper ionosphere is proposed. In it strong electric fields in the Earth atmosphere are taken into account and described by means of the Yang-Mills nonlinear generalization with SU (2) symmetry of the Maxwell equations. It is shown that the proposed nonlinear model is in good agreement with experimental data for the ionospheric regions E and F.

In the paper modeling of the Earth atmosphere at the altitudes ranged from 1000 to 2000 km is carried out, in which strong electric fields are taken into account and considered within the framework of the Yang-Mills theory with SU (2) symmetry. The application of this method to the ionospheric layers E and F in the region of altitudes ranged from 90 to 1000 km showed good agreement with empirical data. At the same time the standard model of the Earth atmosphere at the altitudes higher than 150 km gives substantial deviations from empirical data, increasing with height.

Tudied the inverse problem on determination of the inhomogeneous member of the evolutionary equation with the operator, generating integrated semigroup. Considered a model point-to-point inverse problem, we obtained the formulas that determine the solution of this problem.

In this paper the inverse problems for the parabolic equations for Cauchy problems and for the first and the second bounded problems are considered . Additional information for the direct problems (overdetermination) is given in the fixed points for any specific f time. The existence and uniqueness theorems for linear equations of parabolic type are formulated. For nonlinear equations of parabolic type the uniqueness theorems are formulated.

Asymptotically exact constants in the estimates of the order of approximation of continuous periodic functions by operators of convolution type through the second modulus of continuity are found. This result is used to construct estimates of approximation of functions by the sums of Riesz.

We study finite-time singularities in the linear advection–diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow at a 180◦ contact angle. Using apriori energy estimates, we derive conditions on variable speed that guarantee that a sufficiently smooth solution of the linear advection–diffusion equation blows up in a finite time. Using the class of self-similar solutions to the linear advection–diffusion equation, we find the blow-up rate of singularity formation. This blow-up rate does not agree with previous numerical simulations of the model problem.

The problem of the representation of continuous functions of Fourier series operators is considered with triangular matrices like The theorem, which generalizes Theorem K.V.Ermakov on the uniform convergence of these operators under certain restrictive conditions on the elements of the matrix is proved.

This article examines trends in mobile learning programming. Also it describes a course "Programming for Windows Phone for students". On the example of this course author examine the main aspects and features of the teaching of mobile programming. Announced major themes and brief content of the course, the aim of which is the training of the development of applications on the mobile platform Windows Phone 7, using technologies such as Microsoft Silverlight and XNA game platform. This course was developed by the author of the article on the grant of Microsoft Corporation. Special attention is paid to the perspectives of this course in system of profile education of school students.

The article dealt with the issues of choice and use of alternative office suites for training in office applications on a computer and IT lessons. The greatest attention is paid to use the lessons of informatics and IT business applications based on cloud computing, cloud service on an example of Zoho. Provides an overview of the functionality of the applications included in the Zoho Office Suite and designed to work with documents. The problems of using these applications in different sections of the school year of computer science and IT, as well as addresses of their methodological features used.

The concept of a training set of physics to elementary school with the requirements of education. Special attention is paid to the introduction of the activity approach to teaching physics, experimental studies, the application of the basic forms of expression of scientific knowledge and methods of knowledge specific to mechanics, thermodynamics and molecular physics, electrodynamics, quantum physics, atomic physics and nuclear physics.

In this paper complex approach for solving performance problem in computing based on parallel technologies is considered. Demonstrated applying modern tools for parallelization, errors and “bottlenecks” catching in the problem of modeling internal gravity waves in closed basins. Parallel algorithm of trapping coefficient computing is designed and implemented. The algorithm performance is estimated.