The paper shows the analytical relations for calculation in the linear approximation by measurement errors assessment of geographical coordinates and correlation matrix of points on the Earth's surface when using a combination of differential-ranging and dynamical methods. There is said that the use of dynamical and differential-ranging methods reduces the number of spacecraft to 2 when implementing high positioning accuracy inherent to RDM and simplifies the maintenance of configuration groups.

The article proposes revised method of solving the contact problem for ring layer, taking into account frictional forces in the contact zone. The law of changes radial contact pressures is presented in the form of infinite series containing two groups of unknown constants. To determine unknown constants there was obtained the system of two functional equations.

On the basis of the equations of the theory of elastic-plastic deformation of materials, which have a special characteristic of additional isotropic hardening at disproportionate (complex) cyclic loading, there was retrieved an applied variant of the theory of elastoplastic processes and the kinetic equation of damage accumulation. The basic experiment and method of identification of the material functions are formulated, which final the variant of theory.

The article offers the trigonometric probability distribution, and the method of sequences of numbers generating distributed on trigonometric law. Economic variables have a pronounced cyclicity so the distribution can be very useful in the analysis, research, planning, forecasting and modeling of the economic variables, objects and processes.

The paper presents an option of the weighted regression, called the method of scaling, moreover, this method allows to get the regression equations for functions that on the domain of existence have a break point. This method also allows to receive the regression equations describing the transient processes near the break points and extends the tools of mathematical statistics, widen the range of their application, improve the accuracy and efficiency of the obtained results.

The article proposes a statistical theory of inelasticity of endochronic type, which takes into account initial microstresses and initial microdeformations, that are contained in the material. The theory main relations are formulated. The examples of the two-and one-element models were taken to provide calculations of hypothetical material uniaxial loading, which demonstrate the approach by assuming a uniform distribution of initial microdeformations. There is emphasized that in the process of loading the structural elements of the model can generate deformation of different signs that expands the boundaries of applicability of the theory.

The article displays the generalized equation of the relativistic quantum mechanics from Clifford algebras structure equations. It is shown that the equation relates to the two particles one of which is massless. Hence, the resulting equation is considered as belonging to leptons of one generation.

The similarity parameters in the problem of flutter of a cylindrical shell were studied. As a mathematical theory of shells there was adopted a technical theory in mixed form. For a manometric pressure either formula of piston theory or formula of linearized potential flow theory is accepted. Physical conditions of modeling were derived from the equation of similarity parameters of the model and full-scale processes.

The analysis of the current state of research on the free and forced nonlinear oscillations of three-layer and multilayer thin elastic plates and shells under periodic influences was made. There were discussed some various approaches to the solution of nonlinear dynamic equations of laminated plates and shells, which are applied to this class of problems. There was also analyzed the impact of physical, mechanical, geometrical parameters, the packet structure of layers, forms of plates, boundary conditions on the nature of non-linear oscillations and form of amplitude-frequency characteristics of laminated plates and shells, as well as the available experimental results.

A known method of calculating the velocity of movement of constrained freeform solids under gravity is extended to cases of monomodal motion of gas bubbles and liquid droplets of arbitrary shape.

The flutter of a rectangular plate with variable thickness, placed in the supersonic gas flow, was analyzed with application of the linear piston theory. A solution for optimization of the plate thickness’ distribution was proposed for the case of some additional constraints. The critical velocity of the flow under different values of operation factors was obtained with tetramerous approximation using Galerkin method. Comparison of results was made.

The results of application the axisymmetric rigid-plastic membrane finite element model to the study of forming a thin contour fixed metal plate under hydrostatic pressure are outlined. A comparison with the known numerical solutions and experimental data is provided.

The article considers the interaction of nanoparticle chains. With the help of specialized software experimental data were obtained allowing to solve the quasistatic problem with certain input parameters in nanotribology. During the research, it was found that the change in the number of atoms in a chain directly affects the acceleration of force oscillations. Furthermore, it was shown that during the increase of time of force action by the moving the chain a, represented by a sinusoidal function, the amplitude of the displacement increases.

The paper presents the results of experimental studies of the effective thermal conductivity of gas, water and oil-filled limestone samples under high pressures up to 400 MPa and temperatures in the range of 273-523 K. It is shown that the pressure leads to a nonlinear increase of the effective thermal conductivity of limestone and affects the nature of its temperature dependence.

In this article the author investigates the question of energy dissipation during its transmission to the object or vice versa, from working object. Existing hypotheses of energy dissipation are considered and the results of their application are evaluated in terms of actual observable processes and phenomena. Dissipative function is conveniently represented as a positive-definite quadratic form of generalized velocities.

The article examines the prediction of the residual life on the results of diagnosis of full-scale constructions with continuous monitoring of their technical condition.

The paper outlines the results of application of an axisymmetric rigid-plastic momentless finite element model in investigation of the process of forming round steel plate by a spherical punch which radius is significantly smaller than the radius of the plate. The breaking of molded shell is predicted by computational model by strain localization. Numerical simulation results were compared with experimental data.

In the paper the authors present a calculation of the characteristics of an airlift unit based on the methods of computational fluid dynamics (CFD). As a result of numerical simulation of unit operation its characteristics were received as well as the scalar distribution field of the gas phase. The basic methodologies for calculating airlift units such as Geyer method, a method developed in Donetsk National Technical University (DonNTU) and cfd-method are considered. A comparative analysis of the accuracy of these methods was conducted. It was shown that the results of calculations based on computational fluid dynamics and results obtained by the method of DonNTU are consistent with each other.