In the work, taking into account the state of the issue in the field of applying multilayer heat-shielding and wear-resistant coatings, directions of research are substantiated. The objectives of the development are: improvement of powder materials containing zirconium dioxide partially stabilized with yttrium oxide for plasma deposition of heat-shielding coa-tings; improvement of powder materials containing oxide ceramics and nickel-based alloys for plasma deposition of wear-resistant coatings; development of technological parameters of plasma spraying and subsequent processing by the effects of compression plasma on the coating; analysis of the quality of protective coatings obtained using the optimal technology by studying their structure and physical and mechanical properties. The ZrO₂ – 7 % Y₂O₃ particles contain the predominant tetragonal Y_0.15Zr_0.85O_0.93 phase, monoclinic and cubic ZrO₂ phases, and the Al₂O₃–TiO₂–Ni–Cr–Al–Y–Ta composition contains the Cr_1.12Ni_2.88 phase of the nickel-based solid solution, the a-Al₂O₃, g-Al₂O₃ phases, and the orthorhombic phase of titanium oxide TiO₂ that contribute to its wear resistance. subsequent optimization of technological parameters for the process of plasma spraying of multilayer heat-shielding and wear-resistant coatings. Technological parameters for the process of plasma spraying of multi-layer heat-shielding and wear-resistant coatings are investigated with subsequent optimization. The optimization criteria were the utilization factor of the sprayed powder material and the structure of the coatings. The influence of the spraying distance on the values of operational characteristics of the formed plasma coatings on Al₂O₃–TiO₂–Ni–Cr–Al–Y–Ta has been studied. The obtained results of controlling the phase composition of coatings by varying the chemical composition of powder materials are presented. In the process of deposition, the differences in the phase composition of the formed material are the more significant, the more inhomogeneous the distribution of elements in the initial powder material. Tests have been carried out for cyclic testing in an oven at a maximum temperature within 1300 °C of heat-shielding coatings to determine their heat resistance. They proved the influence of the phase composition of the formed coatings on their ability to withstand high-temperature oxidation.

Using the MOGA genetic algorithm built into the DesignXplorer module of the ANSYS Workbench program, optimization of laser processing of 12Х18Н9Т-steel  by annular beams has been performed. The calculation of temperature fields has been carried out taking into account the dependence of the thermophysical properties of the material on temperature 

by the finite element method in the ANSYS Workbench program. A regression model has been obtained for processing 12Х18Н9Т-steel  by annular laser beams using a face-centered variant of the central compositional plan of the experiment. The power density and duration of laser radiation pulses, the outer and inner diameters of the laser beam in the processing plane were used as variable factors. The penetration depths of the material and the maximum temperatures in the laser processing zone were used as responses. The influence of processing parameters on the penetration depths of the material in the laser impact zone and the maximum temperature values has been evaluated. It has been established that the depth of penetration of the material and the maximum temperatures are most affected by the power density of laser radiation. Optimization of laser processing of 12Х18Н9Т-steel  by annular beams was carried out by setting the limiting values of the maximum tempe-rature in the processing zone for three variants of the minimum penetration depth. The parameters obtained as a result of optimization using the MOGA algorithm and the parameters obtained as a result of finite element modeling are compared. The maximum relative error of the results when determining the maximum temperatures did not exceed 1 % and when determining the maximum penetration depths did not exceed 6 %.

Mathematical modeling of  the processing of balls by the method of free lapping using a tool in the form of a hollow thin-walled cylinder (tool bushings) has been performed. An analytical expression has been obtained for calculating the cutting  

paths, which, according to the formula of F. Preston, are proportional to the amount of material removal from the workpiece being processed. The calculation of the cutting paths in the diametrical sections of the ball during its rotation by a total angle of 4000 radians was carried out. The calculation is performed for various values of such adjustment parameters of the base machine as the amplitude of the reciprocating rotational movement of the device with tool bushings fixed in it, the distance between the symmetry axes of the tool bushings and the axis of rotation of the device, the speed of rotation of the input link of the actuator mechanism of the base machine and a faceplate fixed on its spindle and serving to communicate relative rotation to the ball blanks. In this case, the section with the greatest divergence of cutting paths was considered and the relative value of these paths was determined, which is proportional to the accuracy of processing. Studies have been carried out that have made it possible to identify at least three locations of tool bushings, in which the minimum value of the relative cutting paths on the machined ball surface is achieved, i. e. maximum accuracy of processing, which makes it possible in practice to combine the operations of preliminary, main and final grinding of the parts under consideration. It is shown that the degree of correlation between experimental and theoretical results is at the level of 80–85 %, and the polishing performance according to the proposed scheme increases by about 30 % in comparison with the classical scheme for performing this operation.

Cardiovascular diseases, and in particular, coronary heart disease are the most common cause of death worldwide. Finding the most effective method of treatment seems to be an advanced task. Stenting is a minimally invasive effective way to solve this problem. Immediately with the advent of endoprostheses (stents), there was a problem of repeated vasoconstriction (restenosis) due to neointimal hyperplasia (excessive build-up of the inner shell of the vessel), the causes of which are the release of metal ions from the stent material, damage to the artery wall during implantation, allergic reactions. Initially, they tried to find a solution by searching for the optimal design and material of the stent, as evidenced by the release of more than five hundred models of intravascular endoprostheses differing in design, material, geometric shape, profile, overall dimensions and other parameters. Currently, the most effective way to solve the problems of biocompatibility of stent materials is the formation of coatings on the surface of stents. It is possible to distinguish a number of different intravascular endoprostheses with modifiable coatings: secreting medicinal substances, with biodegradable coatings, with bioactive coatings. The paper presents the results of the analysis of the literature sources of the most advanced research in the field of surface modification of intravascular endoprostheses, which allowed to justify the choice of titanium oxynitride coating as recommended for further optimization and application due to high corrosion resistance, biocompatibility with cells, tissues and fluids of the human body, a good level of adhesion. At the same time there are a number of limiting factors associated with obtaining such coatings while maintaining all structural and technological requirements. 

The main canals of reclamation systems, along with the best economic performance, must also meet the requirements for connecting the conductive network in the vertical plane and the technology for the construction of the channel. 

Although the channels of the hydraulically most advantageous profile are the most economical un terms of excavation volume, often turn out to be too deep and of small width along the bottom, which does not meet the specified requirements.  All these factors can be taken into account by slightly reducing the water flow velocity u (compared to the velocity in the channel with the most hydraulically advantageous cross section u_h.a.), which leads to a significant decrease in the channel depth and, accordingly, an increase in the width of the channel along the bottom.  Such a decrease in velocity is economically justified (without a significant increase in the cross-sectional area) in the region of the most hydraulically advantageous sections, where the curve of the function h = f(u) sharply increases and asymptotically approaches the ordinate with the maximum possible velocity u_h.a. This area can be approximately characterized by the values of the velocity u = (0.95–1.0)u_h.a. For the convenience of calculation, the formula obtained earlier by the author for the channel depth of the hydraulically most advantageous profile has been converted to a simpler form. An analytical method is proposed for calculating the optimal parameters of the channel section, located in the area of the most hydraulically advantageous sections, which is characterized by the optimization coefficient K_opt = u/u_h.a, varying within K_opt. = 0.95–1.0. In this area, the cross section of the channel differs slightly from  the most hydraulically advantageous profile, and, at the same time, satisfies the requirements for conjugation of the conductive network in the vertical plane and the conditions of work. The proposed calculation method is less laborious and is applicable in a wide range of changes pertaining to exponent y in the formula of N. N. Pavlovsky to determine the Chezy’s coefficient. The calculation according to the proposed method is performed based on the use of dependencies to determine the characteristics of the most hydraulically advantageous section and the formulas of channel hydraulics (with a slight gradual decrease in the water flow rate u). Formulas are obtained for determining the depth and width of the channel along the bottom at various values of velocity.

The homogeneity of the structure of the boired pile shaft has been studied based on the results of four-channel inter-well ultrasonic (US) monitoring.  The actual lengthy of the piles has been determined with the detection of defragmentation of the pile shaft, the compressive defects have been determined, and continuity defects have been identified based on a joint analysis of data from the method of interwell ultrasonic monitoring. The use of four channels allows to control separately the peripheral and central areas of the pile in six directions. The data of the seismoacoustic method coincided with the parameters of ultrasonic monitoring in terms of identifying zones of concrete heterogeneity, reducing the pile cross section, etc. 

For all of the listed piles, data are not registered by the named test methods indicating defragmentation of the pile shaft – the presence of sections in the cross sections of which there is no concrete at all.  These test methods for all piles confirmed the compliance of their actual length with the design values. A significant defect in the continuity of the concrete of the 40op pile, according to the data of ultrasonic monitoring and seismoacoustic method, was registered in the interval of marks – (17.5–18) m, manifesting itself a sa decrease in the propagation velocity of the ultrasonic pulse from 25 to 50 % in two sounding directions, inclu-ding diametrical. This defect can be interpreted as a decrease in the effective section of the pile to 25–50 % of the average value. Defective sections of piles were found in their upper part at depth marks from 0 to –1.5 m, counting from the end surface of the head. At the same time, differences in the physical and mechanical parameters of concrete at these marks were also observed within the cross section of piles [1–5].

The paper considers a mixed problem with boundary conditions of the second kind for a one-dimensional wave equation. The solution to this problem is written in integral form using the Green’s function. For practical use, this solution is of little use, since, firstly, the Green’s function is a trigonometric series and, therefore, its calculation presents certain difficulties, secondly, it is necessary to calculate approximately the five integrals with the Green’s function included in the solution of the problem, and, thirdly, it is extremely difficult to estimate the error of the approximate calculation of the solution.  In this work, these difficulties are overcome, namely, simple expression for the Green’s function  is found in terms of a periodic piecewise linear function, the integrals included in the approximate solution are calculated using periodic piecewise linear, piecewise quadratic and piecewise cubic functions, and, finally,  a  simple and efficient estimate of the approximation error is obtained. The error estimate is linear in the grid steps of the problem and uniform in the spatial variable at any fixed point in time.  Thus, an approximate solution of the problem with an arbitrarily small error is effectively expressed in terms of elementary functions.   An example of solving the problem by the proposed method is given, and graphs of the exact and approximate solutions are plotted.

The paper considers modeling the emergence and growth of possible fractal structures and defects on the inner surface of the chambers of thermal power units, which allow control and regulation of the development of such stochastic dynamic processes. We are talking about the use of modeling procedures for the given analysis, which are quite universal in the framework of certain approaches. A general qualitative consideration of the modeling of processes such as the deposition of materials on a solid surface of various complex configurations, and the occurrence of its fracturing and defects of fractal types, is given. In the first part, we consider an analogy between the processes of the emergence and growth of fractal structures and chamber defects with laser processes of controlled deposition of substances on the surface of a solid body and the growth of its fracturing. A number of models have been developed for the emergence and growth of fractal inhomogeneities of various types and configurations on a solid surface with identification of the possibility of their preliminary monitoring at the initial stage of their appearance. At the same time, both various surfaces in the form of coatings and the formation of fracturing and cluster zones of inhomogeneities and defects have been analyzed. The emphasis in the course of research has been made both on the analysis of their regulated structure, and also on the dynamics of the growth of fracturing and cluster zones of heterogeneities and defects in a certain direction. At the initial stage, the indicated process of formation of fractures and cluster zones of inhomogeneities and defects in space was monitored with different scaling: nano- and microscales. This study has been carried out within the framework of an analogy under the following conditions: firstly, given control over the cha-racteristics of similar objects in the corresponding laser experiment; secondly, the presence of a real possibility of ensuring their formation on the inner surfaces of the chambers in contact with the working substance; thirdly, the possibility of such structures influencing on the efficiency of various types of thermal power units in the context of achieving the desired direction and/or undesirability of changing the indicators and characteristics of units taking into account the laws of technical thermodynamics.

The traditional pectin production technology is highly energy-intensive and environmentally unsafe. One of the possible ways to improve the technological process of pectin production is to dry directly the petine hydrolyzate before it is precipitated with ethyl alcohol. The most effective method of drying pectin hydrolyzate is drying in a vibrofluidized layer of an inert material, which provides high productivity in terms of evaporated moisture per unit volume of the chamber and the quality of the resulting dry product. This paper proposes a method for optimizing the drying process of pectin hydrolyzatein the apparatus of a vibrofluidized layer of an inert material, which makes it possible to determine the values of regime parameters at which the drying process proceeds with minimal costs for thermal and electrical energy. The technique is based on the experimentally obtained relationship between the specific productivity of the drying unit and the following operating parameters of the drying process: the air velocity in the drying chamber, the initial air temperature, the specific load related to the area of the gas distribution grid, the initial concentration for dry substances. On the basis of this experimental dependence, the criteria for assessing the reduced costs for heat and electric energy are formalized. A complex criterion for optimizing the drying process in a vibrofluidized bed is formulated, the minimization of which makes it possible to increase the efficiency of the drying process. Restrictions on the ranges of variation of the operating parameters of the drying process are formulated  as well. The posed problem of optimization of the drying process in a vibrofluidized  bed is solved numerically using the method of sequential quadratic programming and recommendations are formulated on the values of operating parameters for conducting the process in the optimal mode.

he demand for electric vehicles and plug-in hybrids, supported by green technologies and the IT-sector, is making significant changes in the structural transformation of the economy. The coverage of energy and raw materials markets bythe reduction in the consumption of petroleum products does not allow us to assert confidently that tax losses will be compensated by revenues from the increase in electricity consumption, including from the transport infrastructure. This is partly due to different levels of taxation of electricity and oil products. Removing obstacles hindering the development of electric vehicles through fiscal policy is an important prerogative of the state. On the part of the state, timely measures are needed regarding the revision of taxes and tax rates in support of the development of mechanisms for the introduction of environmentally friendly electric transport, plug-in hybrids, adaptive expansion of infrastructure for vehicle categories M, MG, N, NG, as well as minimizing losses from tax maneuvers of foreign trade relations. Investors are more likely to respond to positive market signals, where in many cases government regulation has a significant impact on the sustainable and economically safe formation of the investment climate. The development of electric transport narrows the fleet of cars on internal combustion engines, or on a fossil energy source. The fall in demand for oil products will hold back the replenishment of the budget revenue savings by reducing tax revenues on fuel. In order to avoid loss of economic benefits with the renewal of the car fleet  with electric vehicles, the paper examines the mechanism for  adapting the motor vehicle service to modern challenges of the global economy.

The paper deals with the actual problem of achieving sustainable development, through ensuring the sustainability of certain sectors of the national economy, in particular the road sector. The concept of “sustainable development” has been revealed and the steps to achieve it in the Republic of Belarus today have been assessed. In addition, an attempt has been made to substantiate the impact of the sustainability of the road sector, as an integral and connecting part of economic entities on the sustainable development of countries and regions. The influence of the road sector on the elements of sustainable development is considered and its further prospects are assessed. For this, it is proposed to consider the impact of road construction at various structural levels: mega-, meso-, macro- and micro-level, which affect all aspects of the road economy, such as design, construction, maintenance and repair, production of building materials and products. The possibility of implementing the concept of nega-resources in the road sector is considered. Nega-resources are understood as such potential resources that are formed as a result of improving the processes of handling the final product by rationalizing its consumption, as well as with initial resources by optimizing individual stages of the production and logistics cycles. A market for nega-resources could be created following the example of the existing market for emissions allowances under the Kyoto Protocol and the Paris Climate Agreement. The road sector today has many promising technologies, the use of which generates a larger amount of nega-resources. So taking into account nega-resources in the life cycle of transport facilities, as well as creating a system of material incentives based on nega-resources, will ensure the sustainability of road construction, and at the same time the sustainable development of the country and the region as a whole.