Vol 9, No 4-4 (2015)

This article proposed analytical method of solving of the contact problem for an elastic coating of a cylindrical hole in a solid body when it interacts with a solid cylinder. The law of contact pres- sure changing is presented in the form of an infinite series with an infinite number of unknown con- stants. As a result, the authors found the relationship between the resultant load acting on the solid cylinder, and the contact area and contact pressure distribution law.

In this paper a study of mathematical models of motion of coupled space objects. The authors developed a method of determining of basic characteristics of the couple and the parameters of itsmotion when pointing the spacecraft of space cable systems for meeting with other spacecraft.

The article contains a summary of three basic and two weighted linear multiple regression tech- niques in matrix form, together with the method of least squares of Gauss constitute a new tool re- gression analysis. The article contains a matrix formula that can be used to obtain equations of line- ar multiple regression and the basic weighted least-squares method to obtain regression equations without constant term and the method of obtaining the regression equations of general form. The article provides an example of use of matrix methods to obtain the coefficients of regression equa- tion of the general form, ie equation of equal performance.

The paper proposed a new approximate method of obtaining of non-linear regression equation - parabolic optimization. There is an example of its application to obtain a nonlinear equation that can not be obtained by known methods. As a statistical criterion for evaluation of the quality of the re- sulting equation standard deviation is used.

Block-matrix model of treelike actuator of walking robot is developed by considering external links imposed. This paper proposes an algorithm of formation of the mathematical model based on the use of matrices (4x4) and graph theory. The authors showed efficiency of its use for walking robots (by example of a bipedal walking robot).

In this paper, the authors derived generalized formula for calculating of the ratio of the rate of constrained precipitation to the rate of free precipitation for monodisperse particles of arbitrary shape based on analysis of known empirical relationships and semi-empirical method of calculation.

In this paper, the system with two non-linearities, one of which is the multiplicative, constructed Lyapunov function containing 5 variable parameters. There is indicated possible application of this function to locate the region of asymptotic stability of the zero solution and optimization of thetransition process.

In this article are considered some problems of oscillations of complex systems of underground pipelines under seismic loading. The resulting system of equations is solved by the finite difference of the second order of accuracy. The program is based on a computer algorithm implementation on oriented language Borland Delphi 7. Results of the solution are given in the form of graphs.

In this study, the authors investigated the possibility of using of red bauxite slurry (waste of alu- minum production) as adsorbent of ions of heavy metals from aqueous solutions. It was studied the dependence of adsorption of zinc cations and the pH of the nickel and the initial concentration ofaqueous solutions.