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The Republic of Belarus uses traditional and modern systems of fare payment for public passenger transport. In the traditional system, paper tickets are used as proof of payment; such a system is common in all settlements of the country. Electronic tickets generated in mobile applications of various electronic systems, on physical media – contactless smart cards, as well as records of relevant transactions from bank card accounts are used in modern fare systems to confirm payment for a transport service. Both single trips and multiple travel tickets can be recorded in the form of an electronic ticket or an electronic entry on the contactless smart cards. The paper proposes measures aimed at increasing the level of payback of public passenger transport, analyzes the volume of passenger traffic for 2016–2020, the decisions of local authorities in force in the cities of Belarus that establish regulatory and cost indicators for fares in public passenger transport. The comparison of modern fare payment systems implemented in cities is carried out. TapXphone and T-PAY systems are recommended for distribution on public passenger transport in Belarusian cities on the basis of the comparison of the positive аnd negative aspects of the functioning of electronic fare collection systems from the position of a passenger and a carrier.

The paper presents the technology of multi-component briquetting of solid fuel (MSF-fuel) developed by the authors, which makes it possible to reduce economic losses from the non-use of combustible waste from industrial and municipal human activities. The issues of energy and resource saving, rational use of natural and secondary resources in accordance with the National Strategy for Sustainable Development of the Republic for the period up to 2035 are considered in the paper. The concept, structure and principles of the circular economy are analyzed. The paper provides characteristics of the main areas of use and processing of waste that have not found application in traditional technologies and energy. Some aspects of the conducted research on the production of multicomponent solid fuels are presented in the paper. The technology of briquetting wet mixtures with the addition of various binders, including combustible waste, is described, taking into ac-count the factors that affect the performance of the briquetting plant and the density of the fuel. Various ratios of the components of briquetting fuel have been analyzed and the compositions are determined, at which the best production, consumer and environmental indicators are analyzed. The paper studies the energy and physicochemical characteristics of the produced multicomponent fuel. Algorithms for selecting fuel components have been developed. The results obtained can be used to solve problems of rational use of combustible industrial waste by producing a multicomponent solid fuel that meets the established energy and environmental requirements.

The proposed paper is a continuation of the author's theoretical work presented earlier in the development of the theory and methodology for calculating flexible orthotropic reinforced concrete plates on an elastic foundation, taking into account the physical nonlinearity of the plate material. The paper presents numerical results of elastic and nonlinear calculations of an isolated rectangular orthotropic plate on an elastic foundation, modeled by an elastic homogeneous isotropic layer rigidly connected to a non-deformable foundation under the action of an external static load, taking into account the own weight of the reinforced concrete plate. The change in its stiffness at the time of cracking and further active opening of cracks has been taken into account in the calculation of the structure under study. The nonlinear calculation of the studied structure takes into account the change in its rigidity at the time of cracking and further active crack opening. The calculation of a flexible orthotropic plate on an elastic foundation in a nonlinear formulation is performed iteratively by the method of B. N. Zhemochkin. A mixed method of structural mechanics has been used to determine the coefficients of canonical equations and free terms. At the first iteration, the reinforced concrete plate is calculated as linearly elastic, homogeneous, and orthotropic; at the subsequent ones – as linearly elastic, inhomogeneous, and orthotropic at each Zhemochkin site. Camber plates with a clamped normal in the primary system of mixed method due to the action of a concentrated force are determined by the Ritz method when the deflections were represented as a power polynomial in a new original expression that has been proposed for the first time in the Part 1 of the paper. The solution algorithm has been implemented using the Wolfram Mathematica 11.3 computer program. Numerical and graphical results of elastic and non-linear calculations of sediment concrete road plate, contact stresses and bending moment diagrams on the plate are presented in the paper.

The paper considers an issue of international logistics development in Belarus under world coronavirus COVID-19 pandemic. As a result of analytical reviewing of the up-to-date scientific literature on the problem under study, the expediency is stated for highlighting the logistics of international road freight transportation as an independent area of theoretical research and practical activity. Further development of international road freight transportation logistics in the Republic of Belarus requires a complex economic analysis of the present state and dynamics of the international road freight transportation market, which is the main purpose of the present publication. The paper contains the results of the analysis of the market for international and transit freight road transportation. Separately the paper points out the dynamics of transit goods transportation segment in this market in response to the reorientation of international freight flows. Interconnection is shown between the volume indices of international road freight transit through the territory of Belarus and the dynamics of goods import to the Russian Federation from the EU countries. For the first time a proposal is given to use the methodological tools of systemmatrix diagnostic analysis for investigation of the macroeconomic development process of international road freight transit logistics. The author’s set of initial parameters for the analysis has been formed, and its results are presented on the basis of the data of the State statistical reporting form for 2019–2020. A suggestion is given for joint usage of system-matrix diagnostic tools in combination with author’s methodology for assessing the effectiveness of transit (international) freight transportation while evaluating the competitiveness of economic entities in the industry. The most typical trends of the market development in the short term are stated, taking into account the more complicated market conditions.

Previously, the author obtained an analytical solution for determining the vertical displacements of the homogeneous isotropic quarter-space face, which is affected by a vertical concentrated force. This expression gave an exact solution for determining the vertical displacements of a quarter-space face made of incompressible material and an approximate solution for a Poisson ratio different from 0.5. Later, in the published paper by S. V. Bosakov and P. D. Skachek “Action of Concentrated Force on 1/8 of Homogeneous Isotropic Space”, it was shown that by combining solutions for determining the vertical displacements of a quarter-space and a half-space from the action of concentrated forces, one can find vertical displacements for one-eighth face of a homogeneous isotropic space. The resulting expressions allow solving contact problems for non-classical domains in the form of a quarter of a space and one eighth of a space. Below, the author obtains the first approximation for displacements of a quarter-space face from the action of a vertical concentrated force. In this paper, the author gives the first approximation for determining the vertical displacements of a quarter-space face from the action of a vertical concentrated force, widely using the special approximation method developed in the works of V. M. Alexandrov and allowing to calculate successfully improper integrals. The constructed graphs show good results when determining displacements with a Poisson’s ratio different from 0.5 and equal to 0.5. It should be noted that the approach indicated in the paper by S. V. Bosakov and P. D. Skachek can be successfully used in determining all displacements of the faces of one-eighth face of a homogeneous isotropic sharpened forces tangent to the edge of a quarter-space and this will allow to solve contact problems taking into account friction forces in the contact zone of the beam or plate.

Internet marketing in the industrial market has a number of features and differs from that in the consumer market. The first is characterized by specialized and personalized approaches, as well as it must take into account the long cycle of the transaction, and the presence of a large number of decision makers. Marketers at industrial enterprises must have a range of knowledge about the market and industry trends, possess information about the organization of procurement processes and the operation of distribution channels, and be able to build a communication process with a certain type of customer. The paper presents methods for online promotion of industrial products and a study of the features of choosing of internet marketing tools for industrial enterprises. The main idea of the paper is to highlight the expert component for such enterprises as the main tool for communication with customers. To solve this problem, the internet marketing tools of an industrial enterprise has been considered and the expert component in its content strategy has been shown, approaches to the systematization of internet marketing tools have been studied. In the course of the study, general scientific methods have been used: analysis, synthesis, generalization. The result of the research is a model of product promotion in the logic of the industrial consumer's journey, which is based on the connection of the consumer's journey map with internet marketing tools.

An analysis of the probability and conditions for the occurrence of soil liquefaction at the base and in the vicinity of hydraulic structures is presented in the paper. As a rule, hydraulic structures are erected in the valleys of watercourses, the structure of the soil in which contributes to the occurrence of liquefaction processes. These soils are fine-grained, non-cohesive, usually consisting of fine- and medium-grained or silty sands, sandy loams, interspersed with layers of loams. Massifs under pressure hydraulic structures are quite water-saturated. Soil liquefaction occurs as a result of the destruction of structural bonds between particles in water-saturated dispersed soils under the action of stresses of various types. An external dynamic or static load applied to a water-saturated massif composed of weak, finely dispersed soils can lead to a complete or partial loss of soil bearing capacity and its transition to a fluid state. The magnitude of soil resistance to shear is determined by the degree of its water saturation; at a moisture content of about 20 %, the angle of repose of sandy soils is significantly reduced. The restoration of the strength properties of soils is prevented by the pore water pressure, the process of compaction (consolidation) of the soil mass occurs after the water is squeezed out of the pores, the flow time of which depends on the filtration properties of the massif. Liquefaction of soils leads to a disruption in the normal functioning of a hydraulic structure, the creation of emergency situations. The paper provides examples of accidents at hydraulic structures in Russia caused by liquefaction phenomena. It is noted that the main directions of protecting the structures of hydraulic structures from dangerous liquefaction are to prevent the possibility of liquefaction and the reduction of its harmful effects. In this regard, several methods are considered – compaction and strengthening of soils at the base of structures; filtering surcharge device using geotextiles and geogrids; creation of an effective drainage system.

The paper studies the issue of improving the evenness of the prefabricated concrete pavement by changing the design of the slabs from which it is assembled. Irregularities of the prefabricated pavement mainly occur at the junction of the plates and are called “keyboard” effect. The reason for the unevenness is the vertical movement of the ends of the plates relative to each other when the car passes. In order to correct this situation, the authors propose to arrange transverse ribs of rectangular cross section at the ends of the plates. Such ribs will create a reliable support at the edges of the slab, which will reduce the vertical movement of its ends. To determine the effectiveness of the use of transverse ribs, a concrete slab with dimensions of 3´6 m has been examined in the paper. The transverse rib in cross section had the shape of a rectangle with sides 20´10 cm. In order to compare the test results, a concrete slab of the same dimensions, but without transverse ribs, has been studied. Deformations and stresses of the slab under load have been determined by the finite element method using the Lira software package. Calculations have shown the effectiveness of the slabs with transverse ribs mounted on its edges. The vertical displacements of the ends of the slabs with ribs are two times less than those of the slabs without ribs, and the stresses are 2.4 times less. It is obvious that the use of concrete slabs with transverse ribs at the ends will reduce the unevenness of the prefabricated coating at the points of their mating.

The main directions of the concept of national strategies for sustainable development are considered, taking into account the problems of energy and resource saving, as well as the need for the rational use of natural and secondary resources in many countries of the world community in order to transition to a “green” economy. An assessment of the energy potential of combustible waste that has not found technological application is given as one of the priority areas in the field of nontraditional energy. The paper presents aspects of research into obtaining and production of multicomponent solid fuels. A technology is described for briquetting wet mixtures with the addition of various binders, including various combustible wastes, in order to obtain solid fuel. The features of the fuel frame formation are given, taking into account the factors affecting the performance of the briquetting plant, as well as achieving the optimal density of the briquette. A qualitative assessment was made with respect to various ratios of the components of briquetted fuel, at which the best production and consumer indicators are achieved. The features of the preparation of materials and the technological equipment used as part of the preparation and briquetting line are considered. The practical aspects of the production, drying, use of briquetted solid fuels are outlined in the paper. The paper presents studies of the energy and physico-chemical characteristics of multicomponent fuel compositions using various research laboratory equipment and methods. The proposed algorithm for solving the problem makes it possible to rationally use substandard combustible production waste to obtain multicomponent solid fuel, while energy and environmental aspects are taken into consideration at the production stage.

The development of research in the field of creating a mobile monitoring system for diagnosing the technical condition of mining equipment in terms of mechanical vibration parameters is one of the most science-intensive areas. The paper presents the results of investigations on the possibility of isolating the mechanical vibrations of the handles with a natural frequency of 5 Hz, which occur with a greater or lesser amplitude in almost all registered spectra, arising from breakages of cutters on the cutting discs of double-flow drives of the executive body of a mining machine. Therefore, it can be used for operational mobile monitoring of breakages in the cutters of the executive bodies of mining machines. An analysis of vibrations has confirmed the fact that they are transmitted to almost all non-rotating parts of the combine, where they can be registered, which allows them to be used for mobile automated monitoring of cutter breakages on cutting discs. On the example of the combine “Universal-600” it has been found that the most convenient when registering these vibrations from the standpoint of the absence of the need to introduce a signal transmission module from the rotating parts of the combine into the measuring path can be considered the placement of a vibration sensor on the body of the input gearbox of the executive body drive with its orientation in the direction combine movements, where oscillations with a frequency of 5 Hz are prevalent and it is quite simple to isolate them from the low-frequency range using standardized low-frequency one-third octave filters. The paper proposes a technique for creating a system for automated mobile monitoring of cutter breakages based on the parameters of mechanical vibrations of cutting discs with natural frequency.

By usage of the technical and economic calculation method developed by the authors for installations with recuperative-type heat exchangers, the operational modes of the centralized supply and exhaust system of organized ventilation, in which the supplying air is heated by the solar radiation heat and the heat of the air removed from the premises, have been investigated in the paper. The paper presents results of the thermal and economic efficiency assessment of such ventilation system for multi-storey buildings. A comparison of the thermal energy consumption for the needs of heating and ventilation through the use of the proposed ventilation system has been made for two variants of buildings – with the thermal protection level of enclosing structures that meets modern regulatory requirements (buildings with heat consumption up to 130 kW×h/(m2×year)), and for a building similar in terms of planning structure, but with enclosing structures, the insulation level of which corresponds to buildings built before 1993 (buildings with heat consumption up to 260 kW×h/(m2×year)). The temperature conditions have been determined under which it becomes necessary to turn on the operation of devices for additional (peak) heating of the supply air, when the thermal potential of solar radiation and secondary energy resources is insufficient to provide the calculated temperature of the supply air. For the ventilation system under consideration, it has been established that the thermal resistance of the building envelope influences the indicators of the thermodynamic and economic efficiency of the proposed solution. The climatic conditions under which the utilization of the exhaust air heat in the proposed ventilation system is technically justified and economically expedient have been determined. The results of the research

The paper considers the influence of the parameters of the plasma spraying process on the technological characteristics of multilayer coatings based on nickel-chromium, nickel-chromium-aluminum-yttrium materials, oxide ceramics, intended for operation at high temperature and additional dynamic loads. The design of plasma coatings during their application (with subsequent high-energy processing) under such conditions requires a comprehensive solution – both the use of high-quality powder ingredients and the optimization of technological parameters. The plasma process of applying powder materials has been improved to obtain the maximum values of their utilization factors. The technological characteristics that affect the properties of plasma coatings are optimized, namely: the flow rates of the plasma-forming and materials-transporting gases, the flow rate of supplied powder materials, the current and voltage of the electric arc of the plasma torch, the distance from the plasma torch nozzle exit to the substrate. The paper presents the results of studies of the structure of coatings, performed using scanning electron microscopy. Their analysis has made it possible to form general regularities obtained by the action of radiation of compression plasma flows on coatings formed by air plasma. The considered structures are created using the processes of melting, compaction and high-speed cooling of plasma coatings. The main optimization indicators are the maximum local compaction and spillage of the obtained compositions with the absence of defects and destruction from the impact of compression plasma flows. The main effect during the action of radiation of a compression plasma flow on previously formed coatings is thermal. It contributes heating of the near-surface layer. When the coating is exposed to radiation of compression plasma flows, a remelted layer of oxides with a thickness of about 12–15 µm is created, smoothing the relief of the formed surface and creating a network of cracks on the surface, diverging into the depth of the coating. The liquid-phase processes occurring in the molten phase of the near-surface layers after exposure to compression plasma radiation change the structure of the layers and contribute to the modification of their mechanical properties. By smoothing the surface, increasing the density of the surface crystallized layer and minimizing macro-defects – pores or macrocracks – the mechanical characteristics of the coatings increase.

To analyze the synchronization of machine-building production processes, a statistical approach is used on the correctness of the choice of parameters. The accuracy of the parameters is achieved by modeling. This method allows checking how correctly the parameters are selected and whether they ensure uninterrupted operation of production. Statistical analysis of parameters gives information on failures in a particular production unit, on violations of the synchronization of production processes, technological processes. With the help of statistical characteristics, it is possible to evaluate production as a whole. Statistical multidimensional analysis of complex production data allows to analyze the work of individual units, production blocks. The cluster analysis has been carried out by the method of K-medium production process with minimization of the total error probability. A geometric interpretation of the results of cluster analysis of production processes is given in the paper. The influence of factors on the work of production has been determined in the paper. The index factorial method with a different comparison base and different weights has been applied. The hypothesis about the adequacy of the model of production processes has been tested. A statistical analysis of the complex data of the production process has been carried out in the search for optimal solutions in the case of uncertainty and in conditions of risk using the following methods: Bayes, Laplace and Germeyer using the simplex method. The network methods of decision-making have been used in the paper. Statistical methods with the help of mathematical modeling have substantiated the optimal sizes of both individual parts and volumes of local warehouses, so that there were no delays in the transfer of production processes, disruptions in work, downtime of working equipment. In this case, the criterion for the optimality of production volumes can be the minimum of total losses from idle time of individual units and production blocks to the possibility of disruption of the synchronous process modes due to lack of equipment (arising production pockets) or due to long-used outdated units.

The paper considers options for reducing environmental losses in Polotsk and Novopolotsk through the development of trolleybus and tram systems – various types of urban electric transport. In order to reduce the costs of creating transport (including charging) infrastructure, as well as operating costs, the effectiveness of such systems has been determined when using not only classic types of transport, but also hybrid buses, electric buses, duo-buses. Approaches and methods have been developed to improve the quality of passenger service without deteriorating the environmental situation – this will become possible thanks to the development of tram and trolleybus traffic in Polotsk and Novopolotsk. Variants of scenarios for the use of various types of urban eclectic transport in the cities under study are presented, which will reduce investment in vehicles and the cost of creating an operational base at the expense of existing production facilities, for example, a tram fleet. In addition, this will make it possible to create and organize a unique agglomeration rail passenger system, which can become one of the ways to develop the tourist potential of Polotsk and Novopolotsk. The proposals outlined in the paper are aimed at improving the environmental situation in these cities by reducing the volume of emissions of harmful substances by buses, especially on the central streets.

The regional cluster of renewable energy sources (RES) is an industrial cluster and has the characteristics of the energy industry. Therefore, it needs its own mechanism and structure of formation to ensure integrated development. The paper examines the structure of the regional RES cluster for Vietnam and proposes an apparatus for managing it. Taking into account the experience of other countries, the formation of the structure of the regional RES cluster for the conditions of Vietnam has been substantiated in order to ensure the socio-economic development of the country and its energy system,built and analyzed in accordance with the actual conditions for the use of renewable energy sources in Vietnam and includes five components: profile and non-profile members of the cluster, suppliers, consumers, competitors. A diagram describing the structure of the cluster is illustrated in detail, the roles of the participants are presented. The organizational and management structures of the regional cluster, which correspond to the specific conditions of Vietnam are considered in the paper. The management structure of the Vietnam regional cluster consists of a senior steering committee, facilitator, project manager and working groups. The responsibilities of the participants in the organizational structure are formulated in such a way as to reflect their role in the work of the regional renewable energy cluster. The structure of a regional RES cluster is able to show the relationship between participants inside and outside of the cluster. The organizational structure of the regional cluster and the strategy for its development are the foundations for building a policy in the field of renewable energy sources in the country.

The paper proposes a method for determining a vehicle stopping distance based on a braking rate and a coefficient of using an adhesion force by an automated control system for regulating a braking force on the example of a multi-axle vehicle. The aim of the study is to calculate parameters of the braking efficiency of a multi-axle wheeled vehicle equipped with an automated braking force control system based on the adhesion between a tire and a supporting surface. A peculiarity of the considered method is the use of the calculated braking coefficient of the vehicle and the coefficient of use of adhesion forces during the operation of automated system for regulating the braking force. The presence of new mathematical relationships between the position of the coordinate of the vehicle’s gravity center, realized by the clutches of its wheels, and the braking coefficient of the vehicle makes it possible to simulate the change in the deceleration of a wheeled vehicle in various braking modes of its motion. The terms describing the interaction of an elastic tire with a supporting surface in the braking mode of a wheeled vehicle have been substantiated. Equations are written that permit to calculate: a position of the coordinate of gravity center of a multi-axle wheeled vehicle relative to its front and rear axles; a braking coefficient value of a multi-axle wheeled vehicle based on the coordinates of the position of its gravity center, clutches that are realized between its tires and a supporting surface; load distribution between the respective front and rear axles of the vehicle. To calculate the stopping distance of a wheeled vehicle, it is proposed to take a coefficient value of use of the adhesion force equal to 0.83, regardless of the change in weather and climatic conditions in which the vehicle is operated (a calculation error under an accepted assumption is not more than 5 %). In a graphical form, a design diagram of the coordinate position of a gravity center of a multi-axle wheeled vehicle is presented, which gives a general idea about the redistribution of masses between front and rear axles of the vehicle. Scientific publications on the change in the value of the realized adhesion between the tire and the supporting surface in the braking mode of the automobile wheel under various factors have been analyzed in the paper. The proposed concept for determining parameters of the braking efficiency of a multi-axle wheeled vehicle clarifies some provisions in the theory of vehicle motion, in particular, it allows to apply the calculated method for determining the deceleration of a vehicle in the problem of increasing vertical loads on the axles of a multi-axle wheeled vehicle in the braking mode. The given method for calculating coefficients of weight distribution between adjacent front or rear axles of a multi-axle wheeled vehicle increases an accuracy of determining the amount of deceleration of the vehicle by the calculation method.

The paper presents the main hypotheses of frost destruction of cement concrete. The influence of cyclic temperature changes and the effect of static and dynamic (shock) loads on concrete on changes in the structure and strength of concreteis considered. The paper provides results of comparative tests of frost resistance of concrete containing a porous additive and a plasticizer, which contribute to an increase in the density and impermeability of its structure. It has been shown experimentally that the introduction of air-entraining additives with an additional effect of hydrophobization is productive from the standpoint of ensuring frost resistance of concrete of relatively low classes (up to C30/37), compressive strength up to 50 MPa and water absorption by mass more than 4.0 %. It is advisable to increase the frost resistance of concrete with greater impermeability and strength by increasing these indicators, in particular, due to the maximum decrease in the initial water content and high-quality compaction. This conclusion is experimentally confirmed by the data presented in the paper, since the “mechanism” of frost destruction of cement concrete is multifactorial, and the growth of its density (impermeability) and strength provide a higher ability to resist “force” effects associated with repeated alternating deformations of concrete, as well as the action of external loads, accumulation of fatigue phenomena, hydrodynamics of liquid filtration under the influence of changing temperature fields, etc. A comparative assessment of concrete frost resistance has been carried out using standardized and patented techniques containing a porous (air-entraining) additive, as well as plasticizing and mineral additives of amorphous micro-silica, introduced into concrete in order to increase its density, impermeability and strength and on this basis – increasing frost resistance. Experimental data are presented, reflecting the relationship and patterns of decrease in frost resistance of concrete subjected to the simultaneous action of static (for compression – different levels from the corresponding indicator of concrete strength) and shock, concentratedly applied dynamic loads. The regularity of the relationship between the accelerated frost destruction of concrete and the action of mechanical loads that cause cracking in its structure has been confirmed.

Vibromonitoring is the most methodologically developed and technically equipped with recording tools and data processing approach. However, in the sources of scientific and technical information about mining it is presented much less than other monitoring methods. One of the promising ways to solve this problem, in particular monitoring the breakage of cutting disc cutters of an executive body, is to use parameters of natural oscillations of the parts of gearboxes that occur during impulse loading due to such breakages. It should be noted that in the technically complex equipment of the mining industry, in particular in mining machines, there are many sources of vibration, the vibtaions of which are superimposed on each other. And it is not always possible to isolate and identify the required informative signal with the source. With this in mind the paper presents a research methodology on the possibility of monitoring the breakage of the executive body cutters on the example of the continuous miner “Universal 600” according to the parameters of natural vibrations of the executive body cutting discs arising from the breakage of the cutters. The place of registration of these vibrations is determined – the gearbox handles, on the output shafts of which cutting discs are placed. The frequency of such vibrations is set equal to ~5 Hz. The possibility of using the AGAT-M vibration analyzer with M/AC102-1A vibration sensors as a means of further research has been substantiated in the paper. The paper considers an option of placing vibration sensors on non-rotating gear housings of the executive body drive. An algorithm for recording vibration parameters has been developed, which makes it possible to separate its sources.

The paper describes a technique for modelling and optimization of ring-shaped compound ultrasonic waveguides consisting of two sequentially joined segments of different materials by means of finite elements method. The possibility of using such waveguides for amplifying vibrations in amplitude has been justified in the paper. The advantage of the developed technique consists in possibility of its realization by means of standard engineering software, particularly COMSOL Multiphysics. The correctness and efficiency of the technique is proved by comparing the numerical data with the simulation results by means of transfer matrix method using equations of vibration of Euler – Bernoulli and Timoshenko type. It is shown that in compound ring-shaped waveguides two kinds of vibration modes are possible – variable-sign and constant-sign, moreover only constant-sign modes are of practical interest for amplification of vibration amplitude. Recommendations for selection of optimal geometric parameters of the waveguides are given, particularly it is shown that for ensuring maximum vibration amplification factor it is necessary to choose central angles of the waveguide segments with account for calculated dependence between amplification factor and angle, characterized by presence of several local maxima of the amplification factor. It is noted that the high accuracy of the existing semi-analytical methods for calculating and designing ring-shaped waveguides is achieved using methods based on the application of Timoshenko-type equations of vibration.

Results of a study of an actual scientific and technical problem of determining the road safety level on road sections are presented in the paper. The aim of the study is to develop an express method for assessing road safety based on improving the method of the final accident rate by reducing the partial accident rate with the required accuracy of determining the safety level on public roads. The formalization of the relationship between the parameters of road traffic conditions has been carried out to study the level of safety on highways. Latent factors of the parameters of traffic conditions have been obtained on the basis of reduction of their aggregate by the method of principal components, taking into account the relationship of partial accident rates. This condition has allowed to develop analytical models for determining road safety for implementation in the practice of conducting a road safety audit. A method for identifying hazardous areas on highways has been proposed in the paper. It includes 11 parameters of road conditions out of 18 partial accident rates proposed in the prototype and regulatory documents of Ukraine. The adequacy of the model is determined by deviation values of the obtained data according to the prototype model from the values of the relative accident rate, which were 3.22 and 18.61, respectively. The proposed model reduces the deviation value by six times and affects the accuracy of determining the safety level. Experimental studies have been conducted on 79 km of highways (on 385 sectors with constant values of traffic conditions parameters). The results of a comparative analysis of the safety level for the prototype model and the developed model have been identical and shown a decrease in time and labor costs by 1.6 times without loss of accuracy. Thus, the developed methodology is recommended to be applied for determining the potential danger of road sections during an express analysis of the road safety or when conducting a safety audit at various stages of the road life cycle.

The paper is devoted to the development of methodological foundations for the application of virtual reality technologies (VR-technologies) at various stages of car design and their promotion on the market, in particular, when performing design, prototyping, development of educational and advertising products. The paper analyzes the main areas of application of virtual reality technologies in industrial design in mechanical engineering. An overview of the parameters of the specialized software Unreal Engine 4 and the HTC Vive hardware set used to create and demonstrate virtual projects is performed. System requirements for computer software and hardware for creating virtual projects have been formed. A generalization of our own experience of using virtual reality technologies in the design of an electric vehicle with a frame-panel structure is carried out. The technique of using virtual reality tools in order to create virtual projects for demonstration of design solutions and functionality of mechanical engineering products is described. The issues of choosing software and hardware, their characteristics are considered, as well as a description of the stages of creating a virtual project is given. The process of developing a virtual project is divided into the stages of preparing and transforming a three-dimensional computer model of the demonstrated product into its virtual digital prototype, creating a virtual environment for it, assigning materials and textures with the necessary properties to the environment and the object, setting lighting, navigation parameters and animated actions, optimizing the display of shadows and finalizing the project. The main results of approbation of the developed methodology are presented on the example of creating virtual projects for demonstrating an electric vehicle: in an urban virtual environment and in a virtual pavilion.

. It is known that at present, methods of thermal spraying are widely used to restore and strengthen various worn-out machine parts. As a rule, metal coatings applied by thermal spraying have lower strength characteristics than solid materials. It is believed that the strength of coatings is proportional to their adhesive and cohesive strength. The value of adhesive and cohesive strength depends on various factors, including the nature of the materials and the technology of coating. An important factor characterizing the possibility of using metal coatings in various industries is the strength of adhesion of coatings to the base metal. The paper presents the determination of the adhesive and cohesive strength of coatings from different materials, applied by the method of hypersonic metallization. The results of testing the strength of metal coatings made of ER316LSi-grade wire, nichrome (Cr20Ni80) and molybdenum wire are given in the paper. Based on the results of metallographic studies, the proportion of the participation of cohesive and adhesive components in the strength of coatings has been determined, and some features of coating destruction have been described. It has been found that the participation of the cohesive and adhesive components of the coating strength differs depending on the material used. The cohesive component prevails in the strength of coatings made of high-alloy wire of the ER316LSi-grade, at which destruction mainly occurs along the coating-base boundary. For nichrome coatings and especially for coatings made of molybdenum, the cohesive component is predominant, in which the destruction of the coating occurs not along the coating-base boundary, but between the coating layers.

Today, there are several methods for predicting the durability of reinforced concrete structures. In most cases, one of the dominant destruction processes is taken into account – either carbonization or chloride penetration. Experimental results and field observations show that this is an unrealistic approach. Therefore, it is necessary to develop a method for determining the durability of concrete under combined impacts, i. e. with the penetration of chlorides into it and mechanical load. The paper describes in detail an experimental method for studying the effect of mechanical load on the penetration of chlorides into the pore space of cement-based materials. A test method is presented that makes it possible to determine realistic diffusion coefficients of chloride ions in concrete under compressive or tensile stress. As a result of the experiments carried out, it has been determined that the combination of mechanical loads and environmental influences can be much more significant than just environmental influence without the influence of mechanical loading. In fact, the service life of reinforced concrete structures depends on many possible combinations of mechanical loads and environmental influences, including freeze-thaw cycles. Thus, cracks formed during freeze-thaw cycling should be taken into account in tests of combined environmental and mechanical stress in order to better understand and systematically describe the effect of such exposure on the durability of concrete. For reliable prediction of the service life of reinforced concrete structures, it is also necessary to take into account the influence of the applied cyclic stress.

The paper considers the technological scheme of the hydraulic elevator installation, according to which water from a pressure tank is supplied by a working pump to the well through two parallel pipelines: a hydraulic monitor with a washing nozzle for destroying a sand plug and a supply pipeline that is connected to the working nozzle of a hydraulic elevator containing suction and supply pipelines for taking slurry and cleaning single- and double-column water wells from sand plugs The methodology for calculation and selection of parameters of technological equipment of the installation is given. Based on the compiled equations of fluid motion along the supply pipeline with an active nozzle and the hydraulic monitoring pipeline with a scouring nozzle, expressions have been obtained for constructing the pressure characteristics of these pipelines. A graphic-analytical method is proposed for determining water flow rates in them by constructing the characteristics of a working pump and pipelines and finding the coordinates of the operating point. By varying the parameters of the pipelines and the characteristics of the working pump, without changing the parameters of the jet pump-hydraulic elevator, the values of the useful lifting height of the hydraulic elevator were calculated, which has made it possible to select two options for the technological equipment of the hydraulic elevator installation (for polypropylene and steel pipes) for removing sand plugs from water wells with a maximum depth of 50 and 75 m.

In modern practice of diagnosing complex technical devices, along with developing built-in diagnostic systems, a wide niche is still occupied by troubleshooting based on logical patterns. Logical algorithms for troubleshooting are the basis for diagnostic maps of car power plants. They do not always have an optimal structure in terms of achieving the lowest cost and time indicators of the diagnostic process. Thus, the problem of structural optimization of logical diagnostic algorithms is relevant, as well as the formation of a simple and understandable standardized procedure for optimizing diagnostic algorithms. The paper substantiates the criterion for evaluating the effectiveness of a diagnostic algorithm and the structure of the initial data for calculating the criterion. Variants of visual formalization of a diagnostic map are proposed in order to increase visibility and carry out further actions to optimize its structure, as well as options for formalizing visual information in digital form for its processing by computing means. The procedure for optimizing the structure in the JavaScript programming language has been developed and implemented. The reverse transition from a digital form to graphic one is described, which will immediately introduce the results into the practice of car service organizations. An analysis of a sample of 22 diagnostic maps has shown that the proposed optimization method will reduce the average cost of diagnostics up to 17 %.

The increase in the thermal protection level of the existing buildings enclosing structures, due to the need to comply with the current norms of building heat engineering requirements, leads to increasing in the part of heat losses in the thermal balance of a building due to infiltration and exhaust ventilation operation. After exhaustion of the possibilities for the implementation of technical measures to reduce energy costs by changing in volumetric planning solutions and insulating building envelopes further decreasing heat consumption level should be associated with the use of the secondary and renewable resources potential. The paper presents the results of assessing the technical and economic feasibility of using the exhaust air thermal potential for heating the supply air in the forced supply-and-exhaust ventilation system of a building taking as a low-capacity unit as an example. For a counterflow air-to-air recuperative type heat utilizer finned with ribbed heat pipes in the form of a plurality of continuous sheets, the influence of changes in the physical properties of the exhaust air during the phase transition of the water vapor contained in it into a liquid state on the heat exchanger-utilizer performance and characteristics of its efficiency has been established. The conditions of heat exchange are determined (without condensate, with condensate in the part of the heat exchanger-utilizer, with condensate in the entire heat exchanger-utilizer and with the risk of icing) in the supply air temperature range from (–26) to (+8) °C for three variants of its operation with a balance of the nominal amount of exhaust and supply air and with two variants of imbalance. Variants with imbalances have been investigated in order to find possible combinations of supply and exhaust air temperatures, at which there would be no phase transition of water vapor in the exhaust air flow to the liquid state in the entire volume of the heat utilizer, which would eliminate the need for measures to collect and remove condensate and preventing it from freezing.

To represent local displacement fields in the problem of the steady-state growth of a crack, which contains a plate of incompressible material, the strain intensity formula is used in the form of a polynomial of the second degree. The case of plane deformation for an elastoplastic material is considered. The solution is obtained by the method of asymptotic expansions. Numerical analysis is carried out for the first term of the expansion. The aim of the work is the process of obtaining analytical solutions to applied problems of the theory of plasticity: finding the components of stress and strain tensors. The paper considers a variant of the method of asymptotic expansions and its application for the problem of the distribution of the stress-strain state in an elastoplastic specimen with a crack. The method of asymptotic expansions has some advantages over the numerical approach in studying the stress-strain state in the vicinity of a crack. It allows to establish exact quantitative relationships between the radial component, the angle, and the components of the stress and strain tensor. Another advantage of this method is the possibility of compiling the mechanical characteristics of an object at the design stage. A system of differential equations has been developed that contains V0 and its derivatives up to the third order. An example of stress distribution in the vicinity of a crack tip in a steel sample, obtained in a computer system by a numerical method, is given. The deformation diagram has been constructed for the material steel 40. The research results can be used to construct stress and strain fields in the vicinity of a crack, as well as to predict the further direction of crack development.

The paper considers a rectangular orthotropic insulated slab on an elastic foundation, modeled by an elastic homogeneous isotropic layer rigidly connected to a non-deformable foundation. Elastic and nonlinear calculations of this plate opening. The calculation of a flexible orthotropic slab on an elastic foundation in a nonlinear formulation is carried out iteratively by the method of B. N. Zhemochkin. To determine the coefficients of the canonical equations and free terms, a mixed method of structural mechanics was used. The deflections of a slab with a pinched normal in the main system of the mixed method due to the action of a concentrated force are determined by the Ritz method when the deflections are represented as a power polynomial in a new original expression, which is proposed by the author for the first time in the studies. This expression satisfies not only the boundary conditions of the pinched slab in terms of displacements, but also the biharmonic equation. In nonlinear calculations, when finding the variable (secant) stiffness for the Zhemochkin section, at each iteration, the “stiffness – curvature” dependence is used for each of the X and Y directions, approximated by a nonlinear function, the nature of the dependence of which graphically indicates the nonlinear-elastic operation of the orthotropic plate and its deformation taking into account crack formation and crack opening. The algorithm for the above solution is implemented using the Wolfram Mathematica 11.3 computer program.

Developing and implementing innovative goods, new product groups, services and technologies in all spheres of society in terms of «economic» global digitalization requires advanced training of existing personnel, as well as the emergence of new specialties and professions. In this aspect, it is necessary to forecast the need for personnel in new specialties and specializations, as well as to study the possibilities for advanced training and retraining of existing specialists. The experience of the Comprehensive Forecast of Scientific and Technological Progress (CF STP) of the Republic of Belarus for 2021–2025 and for the period up to 2040 is analyzed in terms of staffing for innovative development. The required human resources potential has been assessed by the method of an expert survey in the process of forming the CF STP. Forecasting the need for personnel in the CF STP had a number of limitations. These limitations could be partially eliminated when developing the next CF STP and other forecasts of the need for personnel in the innovation economy. The paper considers possible directions for improving the forecasting of the provision of the economy with personnel for innovative development. It is advisable to assess the availability of personnel in the economy, taking into account the study of the ratio of supply and demand for them in quantitative and qualitative aspects. Algorithms are proposed for assessing: the needs of the national economy in personnel for innovative development; availability of personnel for innovative development and their competencies in organizations of the real sector of the economy; opportunities of the education system for training personnel for innovative development. The improvement of the methodology for forecasting the availability of personnel will allow to identify the most promising areas of training personnel with the necessary competencies and qualifications capable of developing and implementing technological innovations for the further development of the Republic of Belarus.

The description of a plane traveling electromagnetic wave existing in the physical literature by identical solutions of wave equations for the strengths of electric and magnetic fields is physically incorrect, since such solutions contradict the physical meaning of Maxwell’s equations and violate the energy conservation law. The paper gives a physically correct description of electromagnetic waves in the framework of Maxwell’s theory. New solutions of Maxwell’s wave equations for traveling electromagnetic wave are proposed, in which the strength of its electric and magnetic components change in time with shifts of a quarter of the period and a quarter of the wavelength along coordinate. The solutions describe a traveling electromagnetic wave, in which the energy of the electrical component is sequentially converted into the energy of the magnetic component and vice versa; the total energy density of the lossless wave remains constant in space at any time; the mutual orientation of the intensity vectors of the electric, magnetic fields and phase velocity changes from a left-handed three to a right-handed three every quarter of the wavelength; the energy flux density of the traveling wave is described by the Umov vector. It is shown that the formation of a standing electromagnetic wave does not require the loss of half a wave of one of the components of the wave reflected at the interface between the media. In a standing wave, the total energy density remains constant in time, but it is a function of coordinates: there are points in space where the total energy density of the wave at any time is zero – these are nodes, and there are points where it has a maximum value – these are antinodes. Due to the inhomogeneity of the distribution of the total energy density of the wave in space, a standing electromagnetic wave cannot be considered as a harmonic oscillator, but a lossless traveling electromagnetic wave can.

. Many important questions in the theory of elasticity lead to a variational problem associated with a biharmonic equation and to the corresponding boundary value problems for such an equation. The paper considers the main boundary value problem for the biharmonic equation in the unit circle. This problem leads, for example, to the study of plate deflections in the case of kinematic boundary conditions, when the displacements and their derivatives depend on the circular coordinate. The exact solution of the considered boundary value problem is known. The desired biharmonic function can be represented explicitly in the unit circle by means of the Poisson integral. An approximate solution of this problem is sometimes foundusing difference schemes. To do this, a grid with cells of small diameter is thrown onto the circle, and at each grid node all partial derivatives of the problem are replaced by their finite-difference relations. As a result, a system of linear algebraic equations arises for unknown approximate values of the biharmonic function, from which they are uniquely found. The disadvantage of this method is that the above system is not always easy to solve. In addition, we get the solution not at any point of the circle, but only at the nodes of the grid. For real calculations and numerical analysis of solutions to applied problems, the authors have constructed its unified analytical approximate representation on the basis of the known exact solution of the boundary value problem while using logarithms. The approximate formula has a simple form and can be easily implemented numerically. Uniform error estimates make it possible to perform calculations with a given accuracy. All coefficients of the quadrature formula for the Poisson integral are non-negative, which greatly simplifies the study of the approximate solution. An analysis of the quadrature sum for stability is carried out. An example of solving a boundary value problem is considered.

The present paper describes experiments and research outcomes concerning the construction of cement concrete pavements in South Kazakhstan, taking into account significant climate changes. The study has identified potential problems in the construction of cement concrete pavements in the region, where there was no experience of their construction until the mid-2000s. In order to develop an optimal solution, the technical factors that characterize the process of arranging these coatings using sliding molds are analyzed and quantitatively normalized. These factors include the optimal amount of mortar for curing concrete, the optimal joint cutting time, the interval and effective width of expansion joints to prevent the formation of cracks in concrete at an early age. The effectiveness of the use of polyethylene film to prevent the formation of contraction cracks and maintain the required mode of hardening of the cement concrete pavement is shown. The main cause of damage to the expansion joints along the length of the day coverage of coatings in the conditions of South Kazakhstan has been established. Recommendations have been developed for the installation of cement-concrete pavement and expansion joints during the construction of roads in this region. The accumulated data on climatic factors and methods of work with the use of polyethylene film have made it possible to create an optimal method for the construction of cement concrete pavements, which will improve the quality of roads in South Kazakhstan.

In modern mechanical engineering, along with reducing the metal consumption of structures, the main task is to increase the reliability and durability of parts, assemblies of mechanisms. This problem never loses its relevance due to the ever-increasing requirements for manufacture of products, with the need to save scarce expensive metals and alloys and, as a result, replace them with economically more profitable options. One of the most promising, from the point of view of ecology, ways to replace metals, is to use in the construction of plastic assemblies, in particular polylactic acid (PLA). PLA is a biodegradable thermoplastic used in 3D-printing. The paper presents results of an experimental study on the rupture of samples obtained by 3D-printing from PLA under various technological operating modes of 3D-printer. The following parameters have been chosen as variable parameters: the form of filling samples (triangle, hexagon (honeycomb), line, edge), nozzle temperature (190–205 °С), sample filling factor (from 10 up to 40 %). Tensile testing of the samples have been carried out on a hydraulic tensile machine with a measuring software package in the Kason WDW-5 set. When performing tests, the conditional yield strength was considered the main out put indicator. The analysis of experimental data has shown a significant effect of the investigated technological parameters on the conventional yield point, which varied from 16.5 to 22.42 MPa. The most rational forms and sample filling factor, as well as the temperature of nozzle when printing with PLA, have been determined.

The paper identifies promising directions in the economic development of the road sector, ensuring the rational use of investments and improving the processes of construction, reconstruction and repair of roads based on the logisticsapproach, as well as contributing to the organization of safe and economically profitable transportation of goods and passengers necessary for the sustainable economic development of the country and increasing its transit potential. The set of basic logistics principles is supplemented with applied ones, the application of which will allow to manage the cycle of economic activity in the road sector as a whole. Describing the features of the logistics approach in the field under study, it has been established that the hierarchy of the construction of logistics systems is due to the use of various schemes of control actions, depending on the specifics of the functioning flows of each level. The management of the macro-logistic road management system is based on the need to increase the competitiveness of road transport services by improving the maintenance of transport flows, which is dependent on the level of development of the road infrastructure and the construction of a system for changing its state. The foundation of micro-logistic systems is formed by the resource flows of road construction production, perceived in a systemic unity. The main idea of the logistics approach to the economic development of the road economy is manifested through rational planning (macro-level) and implementation (micro-level) of measures for the development and operation of roads. The requirements of users are the basis for the choice of directions for improving their condition, which links the organization of work on road facilities with the strategy for the development of the transport and logistics system of the country. Organization of transportation of goods and passengers by road is consistent with the processes of road works, which together makes them optimal for each of the areas and the formed system as a whole. The logistics approach provides the necessary connecting framework in the management of intersectoral flow processes for the provision of road transport services and road activities, as well as intra-industry – between road services as part of the logistics system.

The aim of this work is to carry out molecular dynamics simulation of the uniaxial stretching of a cooled Al/Cu composition. The LAMMPS software package has been used for calculations, which includes the classic molecular dynamics code with an emphasis on modeling materials. The Ovito program has been used for visualization, which has a large number of functions, so that the user can thoroughly investigate the results obtained. When describing the interatomic interaction in the Al/Cu nanocomposite, we used the potential of the embedded EAM atom. The choice of potential is due to the fact that it adequately describes and reproduces the properties of a wide class of materials, including metals, semiconductors and alloys. The simulation has been carried out in two stages. At the first stage, a sample consisting of two crystallites of aluminum and copper in the form of parallelepipeds, connected along one of the joint boundaries, was placed in the computational domain and cooled at constant pressure. Cooling was carried out to stabilize the nanosystem. At the second stage, corresponding to the deformation, the temperature and pressure were changed in accordance with the ongoing physical processes. The algorithm of the thermostat and the Nose – Hoover barostat has been used to control the temperature and pressure at the initial stage of cooling. The paper demonstrates the nature of the distribution of longitudinal stresses over the entire volume of the crystal in the process of stretching. When the sample reached the elastic limit, the nucleation of crystal lattice defects and their distribution over the crystal in the form of shifts and rotations of atoms in crystal planes were observed. Areas of plastic deformation origin have been determined. The maximum destruction of the material occurred along the interface. The parameters of the Al/Cu composition (deformation, temperature, mechanical stress) have been dynamically investigated using molecular dynamics simulation. Comparison of the characteristics of the sample in the deformation process has been carried. Under loading conditions, a variety of processes are implemented in the material, including generation of defects, elastic and plastic deformation, generation of damage, and mechanical mixing.

The paper examines two methods of choosing the initial reference point for exergy of the moist air flow. The first method is characterized by a zero exergy value at the current temperature and humidity of the outdoor air, which are variable both in daily and annual periods. Another is characterized by constant values of parameters of moist indoor air (its temperature and humidity in the room). A comparative study has shown the advantages of the second method: greater stability of values in air processing processes and their convenient presentation on exergy chart. However, it should be noted that this method provides a non-standard technical representation in which the entire energy flow is reduced to zero. The climatic information (temperature and humidity of the outside air) for numerical-analytical experiment has been used from official open sources. The city where the air conditioning system was supposedly installed is Stavropol. The research has been carried out in the summer and cold periods of the year. It is assumed that there are not installed any large heat sources in the room and the main heat sources appeared depending on the period of the year. Additionally, the air conditioning system was equipped with a recirculation line from the serviced room with a mechanical ventilator. The recirculated air entered the mixing chamber in the air conditioning unit which is reducing the consumption of heat energy in the cold season. There are the processes of air conditioning on the Ramzin's h–d-diagram for warm and cold operational modes of air conditioning unit, the air conditioning system under consideration.

The production of concretes with a hard hardening rate is not feasible without the use of modifying additives. The development of the chemical industry has led to the emergence of a large number of additives with different properties. Some increase the frost and corrosion resistance, the strength of building materials, while others affect the setting of concrete and the water-cement ratio. Of greatest interest is the joint work of the additives in the composition of the cement stone. The paper analyzes and determines the effect of various combinations of chemical additives (sodium carbonate Na2CO3, sodium chloride NaCl and sodium nitrate NaNO3) on the structure formation and properties of cement stone as part of a complex additive using the simplex-lattice experiment planning method. In the course of the research, to obtain cement stone, Portland cement M500 D0 has been used with the addition of Na2CO3, NaCl and NaNO3 in the established proportions. As a result of tests, it has been found that the following proportions of the components in the composition of the complex additive are optimal: NaNO3 – 12–38 %; NaCl – 34–54 %; Na2CO3 – 26–42 %. With the introduction of this complex into the composition of the concrete mixture, positive dynamics have been observed in neutralizing the corrosion effect on reinforcement in concrete, as well as an accelerated set of concrete hardness. The results obtained can be used at specialized enterprises of the chemical industry, as well as in further research in the development of modifying additives.

The efficiency of the functioning of urban passenger transport routes has been studied in the paper. It has been established that the functioning of urban passenger transport routes takes place in a non-isolated environment, which affects the system from the moment of its formation and can lead to discrepancy between the calculated and actual efficiency of the system. As a result of the fucntioning indicator analysis of the passenger transportation route, it has been revealed that the environment of the route functioning affects the efficiency in a complex manner. Consequently, the mutual influence of one factor on others should be taken into account. Performance evaluation should be carried out for the entire route system, and not within the separately considered subsystem. As a result of the analysis of such key indicators as income, fuel costs, lubricants, maintenance and repair, discrepancies have been found between the planned values of indicators and actual data. It is determined that the distribution function of the random variables of these indicators is described by a normal law. At the final stage of the study, regularities in the influence of the road transport enterprise parameters on the probability of investment return have been obtained. The proposed integrated approach to determining the efficiency of urban passenger transport routes is based not only on the established, but also on the stochastic parameters that occur during the functioning of these routes. An algorithm has been developed for determining the efficiency of urban route passenger traffic, which takes into account the interrelation of income and expenses, modern ideas about the patterns of change in the prpbability of development of optimistic, pessimistic and intermediate scenarios for improvement of route efficiency events. The algorithm is based on formalized dependences of the change in time of the probabilities of income and expenses which are taken into account in the operation process of urban passenger transport routes with their various parameters.

The paper discusses problems of assessing the impact of mass attraction centers on the adjacent street and road network in the process of their functioning, expansion or conversion. The choice of criteria for assessing the organization of traffic flow, given in the Russian and foreign literature, has been substantiated, in particular, it is proposed to use v/c ratio for adjacent junction and corresponding level of traffic service (LOS). The main models for estimating capacity of signalized intersections are presented. The procedures of forming a mathematical model for estimating the load factor of signalized intersections is shown. The concepts of lane group capacity, total lost time per cycle, phase coefficients, saturation flow rate, and coefficients taking into account the decrease in the ideal saturation flow rate are explained. A mathematical model for estimating transport demand is presented, which allows to calculate the intensity of traffic flow to and from the center of mass attraction on the basis of the total traffic flow of correspondence, share of visitors in individual transport, average filling of individual transport, and coefficient of daily irregularity upon arrival and departure of visitors on an individual transport. An integrated mathematical model of loaf factor is proposed which includes parameters for estimating transport demand for centers of mass embarrassment and parameters that determine the signalized intersections capacity. The uniqueness of the integrated model is that it simultaneously involves parameters reflecting the demand and capacity of loading intersection. Recommendations are made on assessing the level of traffic service flows and the v/s ratio, based on the data of transport demand and capacity, adjacent to the centers of mass attraction of the road network. The presented method of estimating the LOS based on the capacity of the signalized intersections allows us to estimate the influence degree of mass attraction centers on the adjacent urban road network.

The problem of determining the spectral characteristic of a controlled sample under conditions of limited a priori information using regularization methods is considered in the paper. A change in the state of the surface of optical elements significantly increases the light scattering, so it is necessary regularly to take into account the amount of scattered light in the light flux reflected from the surface and the measured and comparative samples. The conversion of the light flux into the electrical signal of the photodetector can also occur non-linearly. This requires the development of such measurement method that considers both the scattered light and various non-linearities of the measuring circuit. It is known that the mathematical model of measurement is described by the Fredholm integral equation of the first kind, its solution under the accepted assumptions is recommended to be sought in the form of a matrix equation using a recurring procedure. With regard to the fact that the estimation of the initial data errors in the equation is associated with certain difficulties, in the case under consideration, it is advisable to determine the regularization parameter based on the method of quasi-optimality. A characteristic disadvantage of the known analytical and experimental methods for determining the hardware function of a spectral device is that they do not take into account its change during operation. Since the actual hardware function of the device usually differs from the Gaussian curve, the use of hardware functions in the form of analytical dependencies does not always give the desired result, and for experimental methods, special equipment with a quasi-monochromatic radiation source is required. An algorithm for restoring the hardware function of a spectral device based on regular methods for solving ill-posed problems is proposed. The estimation of the matrix operator of the hardware function is proposed to be obtained on the basis of explicit least squares estimation algorithms. The expediency of choosing a value of the regularization parameter that minimizes the accepted characteristic of the accuracy of the solution is indicated.

Abstract. Currently the Republic of Belarus is solving the problem of processing a by-product – phosphogypsum, formed in the process of phosphorric acid production. The issue of utilization of phosphogypsum is becoming more and more relevant, and there are several reasons for this: transportation of phosphogypsum to dumps and its storage require large capital investments and operating costs; when creating phosphogypsum dumps, it is necessary to alienate large areas, sometimes even cultivated land; storage of this material in dumps, even with the neutralization of soluble impurities and with the observance of dump operational rules causes irreparable harm to the environment. There are known studies of scientists on the use of phosphogypsum for road construction as a binder for strengthening soils, foundations and repair work. The paper presents the results of experiments on obtaining road-building materials from this waste without converting it into a binder. Based on the research, a technology for the preparation of asphalt concrete mixtures with the use of mineral powder in the form of phosphogypsum dihydrate has been developed.

The aim of the work is to develop a technology for the restoration of damaged sections of sewer collectors using clinker bricks. A significant part of such collectors in the Ukraine has completely exhausted their depreciation resource. For their construction, concrete and reinforced concrete were used, which are subject to destruction as a result of the influence of many factors and, above all, microbiological corrosion. Therefore, the selection of the optimal repair technology using corrosion-resistant clinker brick is relevant. The paper considers the problems of repair and reconstruction of worn-out collectors. Technical and technological solutions of an open method for their recovery using pneumatic formwork and corrosionresistant clinker brick are presented. The design of the collector lining structure has been carried out using the finite element method. To justify the feasibility of using the proposed technology, two options for restoring a worn-out collector have been considered: the “pipe-in-pipe” method and method developed by the authors using clinker bricks. The second option in terms of the cost of materials is almost four times more economical and more expedient than the first one (where polymer materials are used). The advantage of restoring circular sewer collectors by means of laying clinker bricks lies in the durability and resistance of this material (taking into account the anticorrosive composition of concrete) to the aggressive effects of the sewer environment. It should be noted that the application of the developed restoration technology is the most appropriate in conditions of sparse building or outside the city due to the significant volume of earthworks.

The paper considers the optimization problem of hinged reinforced concrete rectangular smooth and ribbed slabs. The static calculation of the slabs has been performed while using the finite element method. The model is built from rectangular finite elements containing four nodes each and having twelve degrees of freedom. The load is presented in the form of nodal vertical forces. To take into account the nonlinearity of the deformation of reinforced concrete, the finite elements are taken as inhomogeneous multilayer plates. The modulus of elasticity changed according to the hyperbolic dependence. The determination of the stress-strain state has been carried out by the iterative method. For optimization, a method has been used to reduce resources for strength, stiffness, and crack opening with gradient descent along the boundary of the allowable area. The cost of the material spent on the manufacture of the slab and the volume of concrete are taken as objective functions. Restrictions on strength, stiffness and width of cracks are set. By scanning, the boundaries of the admissible search area for the optimal solution are set; the boundary of this region has a curvilinear outline. According to the results of the calculation, the trajectories of the search for optimal solution are obtained. Examples are given and optimal solutions are found for various starting points. It has been established that for the accepted conditions of the problem, the extreme points are located near the boundaries of the admissible region. The speed of gradient descent and the location of the starting points do not significantly affect the results. Due to the fact that the objective function can have several minima, a method is proposed to search for a global minimum by preliminary scanning and analysis of extrema values. It is confirmed that the applied method ensures the stability of the optimal solution.