The problems of modern technology for processing lenses for optical devices are noted. Among these problems, the temperature deformation in the process of blocking with adhesive resin has the greatest effect on the quality of parts. It is substantiated that this problem can be solved using a technology that allows simultaneously processing both surfaces 

of the lens blank when it is fixed to the non-working surface using a photopolymer resin that hardens under the influence of ultraviolet radiation. A scheme of a device for implementing the proposed technology for processing parts with executive spherical surfaces, in particular lenses, with their vertical orientation in the processing zone, which improves the distribution of the abrasive suspension during shaping and thereby increases the intensity of stock removal, is proposed in the paper. Mathematical modeling of the nature of the processing of spherical surfaces of parts of optical devices under the conditions of a power circuit has been performed and a formula has been obtained for calculating the friction paths in the zone of contact between the tool and the surface to be machined. The use of this expression makes it possible to identify the optimal modes of lens shaping, which provide satisfactory quality and the level of intensity of stock removal.

Modern imaging devices make it possible to solve a complex of technical applied problems that require the synthesis and analysis of computer processing methods using threshold binarization, image classification, clustering, and the use of machine  learning to determine  areas of interest.  Thus,  segmentation  algorithms are widely  used for processing  medical  images. Computer technologies are used for the functioning of the intellectual environment, which allows to analyze the state of human health. The development of microelectronics makes it possible to increase the complexity of the applied image processing algorithms used to solve applied engineering problems. The issues of segmentation, pattern recognition, description and presentation of details, morphological analysis of images obtained by industrial equipment are widely discussed in the literature. For example, theories of optical signal processing taking into account interference, issues of image perception and analysis are presented in detail in domestic and foreign literature. The paper describes the  developed algorithm for localizing a car license plate, implemented in the Wolfram Mathematica system. First, the region of interest is determined, isolated from the rest of the image for its subsequent processing. An image representation is implemented using an affine transformation. Further segmentation of the characters on the license plate allows the characters to be identified. In the Mathematica system, a program code for the car license plate localization  algorithm  for its further recognition  has been  developed. The solution to the problem was obtained using the step-by-step application of the built-in and user-defined functions of the Wolfram Mathematica system. The algorithm has been tested on a representative sample of images. The average error did not exceed 10 %, which is in line with modern industrial image processing algorithms. The resulting car license plate identification algorithm can be used in digital devices to automatically determine and further image processing.

The paper reflects the problems of 3D-concreting technology, which is developing quite intensively in modern conditions of construction production. The most important condition for its practical implementation is the development of concrete mixture compositions that provide the necessary rheological (technological) properties for  formation of products, 

elements of building structures or the structure as a whole, as well as providing the required pace of work and physical and mechanical characteristics and properties of the hardened concrete. At the initial stage of research carried out in the Research and Testing Laboratory of Concrete and Building Materials of the Belarusian National Technical University a number of concrete mixtures compositions were developed that are designed and provide the necessary conditions for the implementation of 3D-concreting of  self-supporting and  load-bearing structural elements respectively, in the manufacture of  products of  small architectural forms and  the erection (arrangement) of building structures for various purposes. A methodology has been developed and implemented for the selection of a rational granulometric composition of  aggregate,  type, properties and amount of  binder, chemical and mineral additives, together providing the required technological properties of concrete mixtures after they have been mixed with water. Original methods for assessing the rheological properties of water-soluble concrete mixtures and their changes over time,  leading to an increase in the plastic strength of molded concrete, as well as a method for calculating the rate of concrete work depending on the properties of the concrete mixtures used, are proposed and experimentally substantiated. As a result, prerequisites have been created for further expansion of a number of  compositions of dry concrete mixes  taking into account their purpose for 3D-concreting, and for  developing  methods and evaluating  the physical and mechanical characteristics and properties of hardened concrete, taking into consideration the purpose of manufactured products and erected (arranged) building structures.

The calculation of building structures begins with the determination of loads and effects. The correctness of determining the values of loads and impacts, and in particular their calculated values, largely determines the reliability of structural forms, their durability and economic efficiency. The paper considers the regulatory documents for determining snow, wind and crane loads, as well as loads due to their own weight of load-bearing and enclosing structures. In most cases, changing  the values of snow loads in the direction of their increase is labor- and material-intensive, since after this, it is required to examine all the supporting structures that perceive snow loads,  recalculation them, and quite often, strengthen 

them. It is proposed to review snow loads no more than once every 20–25 years. Wind speed increases with height increases. This is confirmed by statistical data obtained at many weather stations located in the Republic of Belarus and foreign countries. Failure to take into account the change in wind pressure along the height leads to significant increase in the efforts from the wind load by 2-3 times. The increase in the efforts from the wind load, as well as from the snow load, entails the need for a mass survey of buildings and structures and, as a rule, expensive work to strengthen the supporting structures. Determination of loads from overhead cranes in the current regulatory documents is completely focused on the characteristics of European hoisting mechanisms, which largely does not correspond to the characteristics of cranes used in the Republic of Belarus. It is proposed to determine crane loads according to SP [Sanitary Regulations] CYbG20.133330.2011 “Loads and impacts” (updated edition of SNiP [Construction Standards and Regulations] 2.01.07–85*). When determining the design loads from the own mass of structural forms, the reliability factor for loads is used. The values of these coefficients in the current regulatory documents are unreasonably high, especially for metal structures.

Concrete is the most commonly used building material worldwide. One of its main disadvantages is the fragility of fracture and low crack resistance. The use of dispersed reinforcement of concrete composites is a promising direction in solving this type of problem. Dispersed fibers, evenly distributed over the entire volume of the material, create a spatial frame and contribute to the inhibition of developing cracks under the action of destructive forces. In order to increase the fracture toughness of concrete, dispersed fiber reinforcement is increasingly used in practice. The beginning of crack nucleation occurs at the nanoscale in the cement matrix. Thus, the use of nano-reinforcement with dispersed nanofibers can have a positive effect on the crack resistance of the cement composite. It is proposed to consider carbon nanotubes as such nanofibers. The presence of carbon nanofibers changes the microstructure and nanostructure of cement modified with carbon nanotubes. The result of the processes occurring in capillaries and cracks are deformations in the intergranular matrix, the free flow of which is prevented by rigid clinker grains and nanocarbon tubes, which creates a certain stress intensity at the tips of the separation cracks. The working hypothesis is confirmed that the required fracture toughness of structural concrete is provided by multi-level reinforcement: at the level of the crystalline aggregate of cement stone – carbon nanotubes, and at the level of fine-grained concrete – various macro-sized fibers (steel, polymer). Reinforcement of a crystalline joint with carbon nanotubes leads to an increase in the fracture toughness of the matrix (cement stone) by 20 %, compressive strength by 12 %, and tensile strength in bending by 20 %. When reinforcing at the level of fine-grained concrete, we obtain a composite – nanofibre-reinforced concrete with fracture toughness.

Prefabricated construction is one of the most intensively developing areas of research in the field of construction and building technology in the world. The results of the scientometric analysis prefabricated construction are presents in this paper. The purpose of the scientometric analysis was to study the directions and effectiveness of research, to determine the leading countries, organizations, scientific journals, to define the level of prefabricated construction in the Republic of Belarus in the context of economically developed countries. The scientometric analysis was carried out in the analytical system SciVal with the use visualization tools, quantitative and qualitative scientometric metrics. Growth of the number of publications in the field of prefabricated construction and indicators of analyzed scientometrics metrics confirms the fact that prefabricated construction attracts more and more researchers all over the world and is a promising direction of scientific research. Determined that design and informational modeling, organization of construction and precast structures production, delivery of structures to the construction site and their assembly, including reliability, efficiency, environmental friendliness of prefabricated construction are main topics in the field of prefabricated construction. At the same time, topics in the field of research of technologies and organization production of reinforced concrete elements in plant, production management are given less attention, which requires further research in these areas. The results of the scientometric analysis allow us to identify trends, determine priority areas for further research and their connection with other fields of science, and can be a scientific basis for identifying data gaps in current research in the field of prefabricated construction.

A comprehensive analysis of the multilayer wall panel has been performed. The heat-insulating layer,   the thickness of which affects both the dimensions of the enclosing structure and the heat-shielding efficiency of the wall panel, has been studied,. Reducing the thickness of the thermal insulation layer is an important issue, since the production of three-layer panels is expensive in energy and material terms. The features of using a different number of screens to reduce the size of the thermal insulation layer are presented. An example of the possibility of  a maximum reduction in the size of the heat-insulating layer, when the thickness of the interlayer d_in cannot be less than 3–5 mm is given. It is shown that the total thickness of the thermal insulation layer will be 0.057 m in the presence of the maximum possible number of screens – 12. For these conditions, the temperatures in the enclosure planes are calculated, according to the values of which the values of the maximum partial pressures E and partial pressures of water vapor e are determined (for the variants of perforated е¢ and non-perforated е¢¢ screens). According to the obtained values the dependences E, е¢, е¢¢ on the temperature in the planes of the fence are constructed. The calculations carried out and a general assessment of the heat and humidity regime in the enclosing structures were confirmed with the help of the compiled program and the calculation of the necessary parameters е and t in the layers of the structure. It has been established that various shielding materials can be used to exclude condensation zones during the operation of enclosing structures.

In the measuring elements of the current of microprocessor protection, the controlled values are usually the effective values of the fundamental harmonic of the currents. They are determined by the orthogonal components of the input signals, which are formed by digital Fourier filters. Due to the inertia of these filters, the time for obtaining reliable effective values is one or more periods of the input current, which mainly determines the speed of the measuring element. When the frequency of the input signal deviates from the nominal value, its effective values become oscillatory. As a result of this, unstable functioning of the specified organ may occur at current values that are close to the operation and return areas. To increase the speed of the measuring body, it is proposed to determine the effective value of the current by multiplying its value obtained using the orthogonal Fourier components by a correction factor. To ensure the stable functioning of the current organ, it is recommended to filter the effective current value using a digital moving average filter. Evaluation of the effectiveness of the proposed solutions has been carried out by the method of computational experiment using the
dynamic simulation environment MATLAB-Simulink. The proposed solutions provide an increase in the speed of the current measuring organs and their stable operation when the frequency deviates from the nominal. As a result of the research, it has been found that the proposed digital current measuring organ in comparison with an organ based on the Fourier algorithm has a speed of 1.4-2 times greater. In addition, it functions stably both under the condition when the tripping current is less than the fault current, and in the case when the indicated currents are comparable when the frequency deviates from the nominal by ±2 Hz. The proposed digital measuring body can be used in many microprocessor-based current protection of electric installations.

The paper presents the results of a study in the field of assessing the level of development of the logistics infrastructure of the regions. The analysis of existing approaches and methods for assessing the logistics infrastructure revealed that most of them take into account mainly the transport component of the logistics infrastructure, and the financial and information components are represented by indicators of foreign direct investment in human capital and the cost of logistics facilities. At the same time, the assessment of some indicators is carried out by researchers mainly with the help of expert methods. To assess the level of development of the logistics infrastructure of the regions of the Republic of Belarus for the purpose of their comparative analysis and study of the dynamics, a methodology has been developed for assessing the logistics infrastructure of the regions. In order to eliminate the identified features of existing approaches to the assessment of the logistics infrastructure, the methodology presented by the authors used indicators that describe the development of both the transport and storage, information and financial components of the logistics infrastructure using economic and mathematical methods for processing and evaluating data. After selecting indicators and collecting data on them, an assessment was made of the correspondence of the distribution of indicator values in the sample to the normal distribution law using the Kolmogorov – Smirnov criterion with a check for multicollinearity. Further, all indicators were transferred to one measurement scale and the internal consistency of the indicators was checked using the a-Cronbach coefficient. To test the developed methodology, a comparison was made of the logistics infrastructure of the regions of the Republic of Belarus and an assessment of its dynamics based on data for 2015, 2018 and 2021, using factor analysis. Calculations for all stages of the developed methodology were carried out using the IBM SPSS Statistics 20 program.

A significant reserve for ensuring the socio-economic development of the Republic of Belarus is the rational use of the entrepreneurial potential of business entities as an important component of the economic policy of the state. The paper analyzes the main theoretical approaches to the definition of entrepreneurial activity. The versatility of approaches creates difficulties in formulating a universal term due to the change in the content of this category in the process of development of economic science. The paper proposes the author's definition of entrepreneurial activity, taking into account the modern features of its development. The value added indicator has been introduced into the concept, which will allow taking into account a part of the cost of goods (works, services) incremented by the organization, as well as assessing the efficiency of the regional economy. The development of integration processes and the fragmentation of production activities increase the number of participants in the production chain from different countries that create intermediate imports, which include the added value segmented by them. Consequently, the country's gain from foreign trade, its export and technological potential will be largely determined by the added value it creates. This kind of assessment becomes the most demanded in the analysis of trade indicators of business entities, including their foreign trade. The main criteria for classifying enterprises as large, medium and small have been analyzed in the paper. In different countries, quantitative criteria are not the same, the initial criterion is the number of employees. The difficulty in determining the criteria lies in the fact that they cannot be equivalent for all sectors of the economy and for individual countries, since there is a dependence on established practice and the goals of state policy in relation to small and medium-sized businesses. An accurate description of business entities in terms of size will make it possible to identify their features, patterns of development, advantages and disadvantages. An additional quantitative criterion for referring to business entities in the Republic of Belarus is proposed – gross revenue.

Directions for improving the business models of industrial enterprises in the Republic of Belarus in the context of digitalization have been developed. Studies of the theoretical foundations of business models transformation have been carried out in the industry. To achieve this goal, tasks such as identifying the specifics of the digital transformation of an industrial enterprise, studying the prerequisites for the transformation of business models of industrial enterprises in the Republic of Belarus in the context of digitalization, developing and essentially characterizing areas for improving the business models of industrial enterprises in the Republic of Belarus in the context of digitalization. The materials used are the works of domestic and foreign scientists-economists, data from research reports performed by the authors, and national statistical data. The systematic and institutional approaches, analysis and synthesis have been applied. A methodological approach has been developed to transform the business model under the influence of digitalization as to the process of irreversible qualitative changes in the mechanism of reproduction of the use value of the economic system, due to the introduction of digital technologies and tools in production and business processes, in systems of interaction with other participants in the value chain and consumers, as well as in the goods or services themselves. This made it possible to explore the possibilities of transforming business models under the influence of digitalization of the interaction of an enterprise with other participants in the value chain (network) and the state; interaction between the enterprise and the consumer; improvement of internal production and business processes, including creation of digital services. Technical-technological and organizational-economic relations at an industrial enterprise are considered as factors in the digitalization of its business model. As prerequisites for the transformation of business models of industrial enterprises in the Republic of Belarus in the context of digitalization, the following were identified: an increase in the access of industrial enterprises to computing power, high-speed data transfer, and cloud technologies;  a positive dynamics of indicators of digitalization of the Belarusian economy and society, digitalization of the sphere of public administration and interactions “state-business” and “state-population”. All this, as a result of the study, made it possible to develop directions for improving the business models of industrial enterprises in the Republic of Belarus in the context of digitalization.