The paper provides a brief overview of publications on the application of mathematical modeling methods in the study of the patterns of functioning of hydroelectric power plants (HPPs). In particular, the following are considered: mathematical models of the total minimum water consumption for a cascade hydropower system in China; a mathematical model of hydropower plants; a mathematical model of two small hydroelectric power plants operating in tandem; accurate modeling of hydraulic transient characteristics in a complex drainage system. The task of filling in the gaps in the data concerning the operation of hydroelectric power plants is formulated. The approach to its solution is proposed to be based on the use of the method described in previous publications by one of the authors and based on the use of regression analysis apparatus. The specific task of filling in data gaps for a hydroelectric unit of one of the Siberian hydroelectric power plants has been solved. The following factors are used: active and reactive power of the electric generator, voltage, current and temperature of the stator iron, rotor current, air cooler hot air temperature.

Keywords: hydroelectric power plant, electric generator, data gaps, predictive analytics, regression model, adequacy criteria

One of the most important points in increasing the conversion component of a web resource is identifying the most attractive places for the site user. To identify these locations, a site user activity data visualization tool was created that provides a visual representation of each user action on a site page.

Keywords: heat map, site, oculograph, fixation, priority area

In the work, based on the previously constructed multifactor dynamic regression model of water level in the Iya River (Eastern Siberia), the authors forecast this indicator for June 2023 in three options: pessimistic, optimistic and neutral (base). A comparison of the forecasting results with the actual value of the water level confirmed the high adequacy of the model and good prospects for its future successful use to solve a wide range of applied and practical problems.

Keywords: regression model, river water level, lag time, seasonal variable, forecast, adequacy, criteria

The article considers the solution of the urgent problem of calculating the size of the effective focal spot of a microfocus X-ray tube using computer modeling methods. The principle of operation of the calculation method used by the authors is to compare interference images obtained using tested microfocus X-ray tubes with simulated interference patterns formed using the developed software by numerically solving the wave equation. It should be noted that modeling a one-dimensional interference pattern using fast Fourier transform requires a significant amount of RAM and takes considerable time even when using modern computer equipment. The paper presents the results of modeling phase contrast profiles for two types of test objects – nylon fishing line and aluminum wire. The considered method for determining the size of the focal spot is characterized by good sensitivity and allows efficient and high-precision calculations for all types of microfocus X-ray tubes.

Keywords: computer modeling, X-ray tube, microfocus source, focal spot, non-destructive testing

The public education project ""Dream School"", implemented in support of the federal school overhaul program, attracts students of architectural and design schools in the regions, which will allow them to simultaneously acquire applied competencies in the learning process. During the development of the design project, the need for specialists to conduct a preliminary design analysis was revealed, since one of the five schools did not meet the standards in terms of their spatial planning parameters. It is proposed to carry out the reconstruction of this educational institution. The premises of the dining room and the assembly hall are transferred to the annex block.

Keywords: school design project, school renovation, school recreation, public education project "Dream School", school reconstruction

This paper analyzes the performance of solving the classification problem using various open-source artificial intelligence and machine learning libraries in the field of marketing and customer relationship management; based on the results of experiments, the best library is selected for the purpose of introducing artificial intelligence into domestic CRM systems based on numerical performance indicators.

Keywords: artificial intelligence, machine learning, big data, classification, marketing, customer relationship management, import substitution, open source

In the paper, parametric equations of right conoidal surfaces with an orthogonal coordinate system with different guiding curves are obtained for the first time. Parametric equations for conoids with guide curves sine, cosine and parabola are presented. In the MathCad system, the constructions of right conoids with selected guide curves with various initial geometric parameters are visually performed and presented in the paper for the possibility of expanding their use in architectural design, construction and other industries.

Keywords: conoid, orthogonal coordinate system, sine, cosine, parabola, parametric equation, MathCad system

The article discusses identification methods in industry and equipment presented on the Russian market for marking and identification of objects. The purpose of the article is to analyze the equipment and installations available on the Russian market for marking and identification of straight-seam steel pipes in production. A comparison of methods based on a scoring system for marking and identification of straight-seam steel pipes in production is presented. Barcode marking technologies using labels, laser marking and RFID tags are presented and considered as identification methods.

Keywords: barcoding, laser marking, RFID tag, straight-seam steel pipe, thermal label printer, automated identification system

An approach to solving the problem of justifying a project for the development of a complex system, taking into account the possibility of realizing the values of its characteristics and the presence of restrictions on their values is proposed . The general goal is formulated in terms of the theory of fuzzy sets and the theory of possibilities. Based on the global development goal of a complex system, local goals and objectives are determined. The problem of taking into account factors influencing the achievement of a global goal is considered. Achieving the general goal is associated with taking into account restrictions on the values of system indicators, as well as the need to determine their optimal values. Unlike existing models, the proposed approach allows us to consider a more general relationship between the elements of the system and take into account the fuzzy nature of the implementation of the parameters. To solve this problem, an effective decomposition method has been developed.

Keywords: diversification of management, production diversification, financial and economic purposes of a diversification, technological purposes of ensuring flexibility of production

The integration of blockchain technology with the Internet of Things (IoT) offers transformative potential for various sectors. This article delves into 16 distinct methods of integrating blockchain with IoT, emphasizing that there isn't a one-size-fits-all solution. Each method has its unique advantages and potential drawbacks, necessitating careful consideration based on specific IoT system requirements. For instance, integrating with public blockchains like Bitcoin and Ethereum offers transparency and decentralization but faces scalability issues. Sidechains introduce flexibility but might pose security risks. Blockchain platforms like Hyperledger Fabric expedite development but can lead to vendor lock-in. The diversity of these methods underscores the importance of a well-thought-out approach tailored to the specific needs of the IoT system in question. As technology evolves, we anticipate more innovative approaches to emerge, emphasizing the continuous need for research, experimentation, and collaboration to fully harness the potential of IoT and blockchain integration.

Keywords: blockchain , IOT , BIoT, smart contracts, IoT security

Assessment of the technical condition (hereinafter TC) of technical systems is a prerequisite for a modern strategy for their operation. The study of new methods and algorithms that provide express assessments of the condition of technical devices and reduce the subjective component in these assessments is an urgent and in demand task. The paper presents a constructive approach to assessing the TC indicators of complex technical systems based on a modified method of analyzing hierarchies and the TC index (hereinafter referred to as ITS) of equipment, which is determined on the basis of weights and ITS of the main components of the equipment in question. The ITS of the main nodes is calculated based on the comparative characteristics of the operating parameters of the equipment during its operation, and the weights of the nodes are determined based on the methods of the matrix of paired comparisons (Saaty method) and the degree of importance of the line (DIL - Degree Importance Line method). The testing of the methodology and algorithms in this study was carried out on the basis of statistical data from a NASA turbojet engine (hereinafter referred to as turbofan engine), published in 2008.

Keywords: technical condition, technical condition index, complex technical system, maintenance and repair, hierarchy analysis method, DIL method, constructive method for assessing technical condition, algorithm for express assessment of technical condition

The article contains the methodology and results of theoretical and experimental studies of the stress-strain state of a conical radial-beam dome with triangular shell elements. The results obtained by various methods are analyzed and compared. The triangular membrane panel is part of the radial beam dome structure and consists of a support frame and a steel membrane in the shape of a triangle. The shape of the triangle forming the membrane panel can be different and depends on the number of ribs in the radial beam dome. The supporting contour is a compressed-bending element of the dome and is made, as a rule, from a rolled steel profile with a channel section. The membrane is made of thin steel sheet and attached to the upper flange of the channel with self-tapping screws or spot welding. To assess the strength and deformability of a steel membrane sheet, its operation under the action of a uniformly distributed snow load, an unevenly distributed snow load and a concentrated installation load was considered. Several options for nonlinear static calculations in various computer systems are shown.

Keywords: building structures, wooden structures, membrane panel, stress-strain state, radial beam dome, dome, membrane, design, experimental study

The article explores the problem of creating aircraft flight models in the Simulink environment. The reference systems in which transformations are carried out are considered. The equations of motion used in the simplest converters are given. The initial conditions for the equations are determined: the speed of the body, the angular orientation of the body's pitch position, the angle between the velocity vector and the body, the speed of rotation of the body, the initial position, the mass and inertia of the body, the source of gravity, the acceleration due to gravity, the curb and total mass of the body, speed of air flow, inertia of an empty and full body, flight trajectory, etc. An analysis of converters of aerodynamic forces and moments into the trajectory of motion as part of an aerospace package in the Simulink environment was carried out. Recommendations are given for their use for various modeling purposes. The results of modeling a simple converter with three degrees of freedom are presented.

Keywords: modeling, MatLab, Simulink, equations of motion, aerodynamic torque, flight path, coordinate transformations, reference system, degrees of freedom

The article discusses the issues of identifying and ranking threats at an important government facility. The classification of threats by type is described. The article discusses the concepts of “design-based threats” and “the most dangerous variant of the violator’s actions” and their differences. An example of ranking threats and reducing their number to reduce the dimensionality of the vulnerability analysis problem is considered. An important government object is considered as an object in the example. Experts are tasked with ranking threats according to the level of potential losses for an important government facility if they are realized. In practice, the implementation of an accepted design threat may lead to lower potential losses than the most dangerous option for violators and, as a result, to lower requirements for the effectiveness of the physical protection system.

Keywords: comprehensive security, methods, models, security forces, intruders, important government facilities, clashes between security forces and attacks, ranking of threats

A method for recording holograms using digital cameras with high spatial resolution is considered. To register holograms obtained in optical setups with an inclined reference beam, a high resolution of registration systems is required. To do this, it is necessary to use media with a resolution of 2000-4000 lines per mm. The use of photographic plates requires a fairly long exposure and development time, which is usually done separately from the optical setup. In the case of holographic interferometry systems, it is necessary to provide for mounting the hologram back into the optical setup with sufficiently high accuracy. Therefore, digital holography methods have been developed to record holograms on photomatrices with limited resolution. These methods are based on the use of optical schemes at small angles (less than 5 degrees) between interfering beams. Recently, sensors with a single element size of 1.33 µm and 0.56 µm have appeared. This resolution makes it possible to return to registration schemes with angles between interfering beams of 30-60 degrees. This allows us to hope for the revival of holographic methods and methods of holographic interferometry at the modern level without the use of intermediate recording media.

Keywords: digital holography, high spatial resolution photo matrix, tilted reference beam holography, Fourier transform