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Based on the most significant features of the angular velocity dynamic measurements selected by the authors, the main phases of measuring information transformation were established, which allowed to obtain new mathematical models in the form of transformation function, equations for estimating quantization errors, analytical dependences for measuring range that are initial for modeling physical processes occurring in such digital measuring channels with microprocessor control. The process of converting an analog quantity into a binary code is analytically described, an equation for estimating the absolute and relative quantization error is obtained and a measurement range is established, which provides a normalized value of relative quantization error for angular velocity measuring channels with encoder. For the first time, the equation of sampling error was obtained, and it was proved that the limiting factor of the angular velocity measurements upper limit is not only the normalized value of quantization error, as previously thought, but also the value of sampling frequency fD. Therefore, to expand the measurement range (by increasing the upper limit of measurement), it is proposed not only to increase the speed of analog-to-digital conversion hardware, but also to reduce the execution time of software drivers for transmitting measurement information to RAM of microprocessor system. For this purpose, the analytical dependences of estimating the upper limit of measurement based on the value of the sampling step for different modes of measurement information transmission are obtained. The practical implementation of the software mode measurement information transmission is characterized by a minimum of hardware costs and maximum execution time of the software driver, which explains its low speed, and therefore provides a minimum value of the upper limit measurement. In the interrupt mode, the upper limit value of the angular velocity measurement is higher than in the program mode due to the reduction of the software driver’s execution time (tFl = 0). The maximum value of the angular velocity measurements upper limit can be achieved using the measurement information transmission in the mode of direct access to memory (DMA) by providing maximum speed in this mode (tFl = 0, tDR = 0). In addition, the application of the results obtained in the work allows at the design stage (during physical and mathematical modeling) to assess the basic metrological characteristics of the measuring channel, aimed at reducing the development time and debugging of hardware, software, and standardization of their metrological characteristics.

The paper analyzes the main areas of application of mathematical methods in medical diagnostics, formulates principles of diagnostics based on fuzzy logic; developed mathematical models and algorithms that formalize the process of making diagnostic decisions based on fuzzy logic with quantitative and qualitative parameters of the patient's condition; developed mathematical models of membership function. Mathematical models and algorithms have been developed that formalize the process of making diagnostic decisions based on fuzzy logic with quantitative and qualitative parameters of the patient's condition; developed mathematical models of membership functions, formalizing the representation of quantitative and qualitative parameters of the patient's condition in the form of fuzzy sets, used in models and algorithms for diagnosis and finding a diagnosis of assessing the intensity of reactive postoperative edema in patients of all study groups. An expert system was implemented for solving the problems of medical diagnosis based on fuzzy logic when assessing the intensity of reactive swelling of soft tissues, which develops in the postoperative period in patients of all study groups against the background of diabetes. The paper analyzes the main areas of application of mathematical methods in medical diagnostics, formulates the principles of diagnostics based on fuzzy logic.

In the present work, an exergy analysis was done of two-circuit flat solar collector with thermosiphon circulation. The article presents a mathematical model of energy and exergic analysis of flat solar collectors, as well as calculations of solar radiation efficiency, temperature, flow rate of the fluid, exergy rates and exergy loss rates are done. The significance of the results achieved is high, since experimental studies can detect inefficient components of the solar heating system. The exergetic efficiency of a dual-circuit flat solar collector with a thermosiphon circulation describes irreversibility of the process according to thermodynamic parameters. This is caused by a large the degree of overheating achieved at the end of the processes of compression and evaporation, which leads to large differences in heat exchange temperature based on the heat pump cycle. The exergy efficiency value for the entire system is 70. Maximum values energy efficiency and exergy at noon, 32.5% and 2.23%, respectively. The efficiency of exergy is 4%, and the highest the loss of exergy is the difference between the absorber plates and the sun, accounting for 52.86% of the total exergy rate.

A solution for the problems of the finger spelling alphabet of gesture language modelling and recognition based on cross-platform technologies is proposed. Modelling and recognition performance can be flexible and adjusted, based on the hardware it operates or based on the availability of an internet connection. The proposed approach tunes the complexity of the 3D hand model based on the CPU type, amount of available memory and internet connection speed. Sign recognition is also performed using cross-platform technologies and the tradeoff in model size and performance can be adjusted. the methods of convolutional neural networks are used as tools for gestures of alphabet recognition. For the gesture recognition experiment, a dataset of 50,000 images was collected, with 50 different hands recorded, with almost 1,000 images per each person. The experimental researches demonstrated the effectiveness of proposed approaches.

Wind power is one of the three main renewable energy sources, along with solar and hydropower, which are widely used to produce electricity worldwide. As an energy resource, wind is widespread and can provide electricity to much of the world, but it is both intermittent and unpredictable, making it difficult to rely on wind power alone. However, when used in combination with other types of production or in combination with energy storage, wind can make a valuable contribution to the global energy balance. Over the past few decades, wind power has emerged in a number of countries as a separate energy sector that has successfully competed with conventional energy. Attention is paid to wind power plants (WT) as part of distribution and transmission networks. In this regard, an urgent scientific and technical task is the efficient use of wind potential, which is not only to improve aerodynamic characteristics WT, but also to increase productivity WT as a whole. This article presents the type of wind turbines, among the possible applications and very promising is the wind turbine Bolotov (WRTB), which by its technical characteristics surpasses the traditional propeller and other installations using wind energy in the production of electrical energy. The increase (WEUF - wind energy utilization factor) in all modes of operation WT by improving various methods of automatic control is relevant, and the proposed work is devoted to this issue.

The paper investigates the optimal control system of diesel automotive engineering with application of complex criteria, depending on fuel consumption rate and travel time, with adjustable coefficients of physical process mathematical model, considering influence of disturbing effects factors. This control principle allows saving fuel consumption rate, reducing transport influence on environment, and also reducing the importance of human factor for motor transport control.

This article analyzes work of metallurgical shop as a complex control object. It also includes description of copper complex and synthesizes three-level structure of control system. Technical and economical indexes and also control object are defined in this article.