Special iterative methods of solving the Fredholm singular perturbed functional equations are offered. The current approximation is defined completely from resolvability of the equation for the next approximation in the case when the similar equation has a nontrivial solution. Estimations of convergence velocity have been obtained.

mamiy2010_1.pdf

(158 Kb)

It is proved that if the cubic differential system of the second order has at least one singular point it cannot have more than five straight-line isoclines parallel to each other. The problem on existence of other straight-line isoclines is considered provided the system has the maxi-mum number of straight-line isoclines parallel to each other.

ushkho2010_1.pdf

(199 Kb)

Physics

A definition of a class of the semiclassical approximation solutions is made for the Fokker-Planck equation with variable coefficients and nonlocal nonlinearity. The evolution of m-order moments of a solution of this class is described by Einstein-Ehrenfest dynamic system of (k, m)-type, representing the evolutionary, relative to time t, system of integro-differential equations. The examples of systems of (1,1) and (2,1) types for the Fokker-Planck equation with an operator, quadratic relative to space variables and derivatives are considered.

lyamkin2010_1.pdf

(273 Kb)

We present a simple and effective method for computation of electronic excitation spectra of molecules. The method is formulated within the density-functional theory, making use of Petersilka-Gossmann-Gross equation for linear density response.

koval2010_1.pdf

(2 Mb)

The paper describes theoretically, in the Stokes approximation, the stationary motion of the large evaporating aerosol spherical particle, which is under powerful electromagnetic radiation in binary gas mixture. The motion is considered assuming that the average temperature of the particle surface differs insignificantly from the temperature of gaseous medium. As a result of solution of gas-dynamic equations, the analytical expressions for the force and velocity of photophoresis were obtained taking into account the effect of medium motion.

malay1_2010_1.pdf

(280 Kb)

The solution of the Navier-Stokes equation in a spheroidal coordinate system with a power kind of dependence of dynamic viscosity factor upon temperature has been obtained.

malay2_2010_1.pdf

(290 Kb)

Nanodimensional heterosystems are investigated on the basis of ferromagnetic semiconductors. In them, feasibility of obtaining the condensed condition from lowermost by energy triplet excitons is considered. Key parameters at which bose-condensation of excitons is possible are calculated.

golovnev1_2010_1.pdf

(213 Kb)

In the work, the problem about resonant tunneling of carriers of a current through ferromagnetic barriers is considered. The interaction of electron and magnon on the resonant centre, leading to formation of spin polaron and to degradation of power dependence of a tunnel transparency is considered by a method of tunnel Hamiltonian.

golovnev2_2010_1.pdf

(203 Kb)

Natural Sciences

A system structurally functional scheme of geographical systems is developed on the basis of functionally mutually conditioned empirically objective system-structural units, promoting the integrated approach to researches of geospace. The authors create the digital model of geographical systems providing interdisciplinary researches, application of modern numerical methods for the solution of key problems of geography - workings out of algorithms of procedures of the spatial-time analysis by structural levels of geographical systems and definition of the spatial-time organization of processes of their development.

varshanina2010_1.pdf

(221 Kb)

Technical Sciences

The paper examines briefly the problem on appointments in the general organization. Results of application of the system-cognitive analysis and its toolkit – “Eidoses” system – are used to solve generalization of a problem on the appointments not found in the literature previously. This provides automatic forecasting the degree of utility of cargoes for different backpacks making use of cargo features by solving the problem of recognition, with application of the model basing on precedents database.

lutsenko2010_1.pdf

(201 Kb)