The article is devoted to one of the key issues of the theory of international relations and geopolitical science – the definition of the power of the state. At the same time, the state is considered as the main (structure-forming) element of the global geopolitical space. Starting from the fact of the real inequality of states in the system of international relations and ran-king them by weight and influence in world affairs, the author analyzes two main approaches to assessing the strength of the state: attributive and behavioral. The article distinguishes between the concepts of "the potential of the country" and «the power of the state»; justifies the need to use a more precise than the generally accepted concept – «the total power of the state» (TPS). The subject of special attention is the question of the possibility of measu-ring the TPS, in connection with which the factors that determine it are analyzed in detail. In this connection, the "tangible" (measurable) and «intangible» (immutable) factors of TPS are distinguished and their interrelation is considered. Based on these considerations, the author offers his own «formula» of the TPS.

Keywords: global geopolitical space, the state, ranking of states, the potential of the country, the power of the state, the total power of the state (TPS), components of the TPS, the measure-ment of power (as a problem), «tangible» (measurable) and «intangible»

The open labor market has contributed to the emergence of new forms of employment for workers due to the recognition of remote work as one of the forms of organization of production and labor, including in the organization of construction production. With the massive penetration of digital technologies into the business models of modern companies, employers are increasingly turning to freelancers. This transition was associated with the development of the Internet, the emergence of online platforms and cloud data storages that connect customers and contractors and allow the employee to carry out labor activities regardless of the territorial location. Such transformations have formed a new socio-economic model, called "gignomics". Today, gigonomics is developing at a rapid pace throughout the world, as this model is attractive to both workers and employers.

Keywords: gigonomics, remote work, remote work, organization of construction industry, digital transformation, digitalization, non-standard forms of employment

The article presents the results of a study of the mechanism of occurrence of cracks in the material of heated cylindrical porous powder blanks being deposited. The type of cracks is classified and the role of the boundaries between the "particles" of powder on the surface of a porous workpiece as stress concentrators contributing to the formation of cracks during its deformation is noted.

Keywords: dynamic hot pressing, heating temperature, powder billet, pore, crack, sintering temperature, plasticity

The article analyzes the influence of the roughness and thermal conductivity of the processed steel on the choice of gas laser cutting parameters. The authors describe the possibilities and advantages of using gas laser cutting in production. The article presents the results of an experimental study of samples made of St3 steel of various thicknesses. An analysis of the data obtained showed that with an increase in the gas laser cutting speed, the roughness parameter increases, and the laser power has practically no effect on the roughness value. The authors also attempt to take into account the influence of the thermal conductivity of the processed material on the choice of laser cutting characteristics. It was found that in order to ensure a minimum roughness for steels with higher thermal conductivity, increased power and cutting speed should be used.

Keywords: gas laser cutting, roughness, thermal conductivity, parameters, mathematical models, experimental study

The operating conditions of polycrystalline dielectrics in external mechanical and electric fields make it relevant to study the properties of such materials and their resistance to extreme loads, which depends on the processes of polarization reversal and the dynamics of the domain structure. Based on the model of motion of domain walls and the rheological model, equations are obtained for the dependence of polarization on the applied mechanical, electrical, or simultaneous electromechanical load. It is shown that the nonlinearity of the current in the ferroelectric ceramic is due to the dependence of the coefficients of the model on the through conduction current and the current associated with the emission of charges from traps. The physical meaning of the coefficients makes it possible to use their well-known dependences on the electric field and external mechanical stresses both in the range of the linear piezoelectric effect and in the region of external loads, when linearity ceases to exist. The obtained coefficients make it possible to pass from polarization (macroscopic parameter) to domain walls (mesoscopic scale). The parameters of the model depend on the change in the domain structure and its interaction with defects; therefore, the current relaxation time in the ferroceramic is described by changing the corresponding times for 180°-domains and non-180°-domains. The model considers two polarization components: elastic and irreversible. Changes in polarization after the external action of the electric field can be explained by the movement of domain and interphase boundaries. When a critical mechanical load is applied, the domain boundaries are detached from the defects and the crack grows abruptly, and as a result, destruction occurs. The relaxation motion of domain walls with constant friction leads to the growth of cracks due to the creation of mechanical stresses. The chosen rheological model and approach, taking into account the mechanisms of motion of domain walls, will make it possible to describe the rate of polarization change using the behavior of defects (dislocations, domain walls). The model will allow from a unified point of view to describe the experimental patterns of the behavior of currents under electromechanical action.

Keywords: ferroelectric ceramics, computer simulation, rheological model, polarization current, polarization current density, domain wall, 1800-domains, not 1800-domains, mechanical load, electrical load, relaxation time

This article explores the use of machine learning algorithms to identify anomalies in a solar heating system. The developed solar heating system consists of several parts to simplify the process of description and modeling. The author propose a new neural network architecture based on ordinary differential equations. The idea is to apply the new architecture to practical problems of accident forecasting (the problem of extrapolation of time series) and classification (classification of accidents based on historical data). The developed machine learning algorithms, artificial intelligence methods, and the theory of differential equations - these areas allow us to build a model for predicting system failure. Database management theory (relational databases) - these systems allow you to establish optimal storage of large time series.

Keywords: flat solar collector, solar heating system, machine learning, algorithm

The analysis of the frequency-controlled drive currently used on the technological equipment of the Volgogradneftemash enterprise is presented. Taking into account the peculiarities of the pumping and ventilation equipment installed at the enterprise, the principles of regulation are determined and the influence of a frequency-controlled drive on the quality of electrical energy is evaluated. The negative influence of the frequency-controlled drive of ventilation and pumping equipment on individual indicators of electricity quality was noted. In order to reduce this influence, an energy-saving device has been proposed for installation. The issues of the possibility of using an energy-saving device at the facility are considered, as well as an analysis of its efficiency during operation from the point of view of improving the quality of electricity in the internal power supply system of the Volgogradneftemash open Joint stock company is carried out. The use of the device is an effective solution, since it leads to high energy efficiency of technological equipment by reducing current surge, suppression of higher harmonics and electromechanical interference.

Keywords: electric drive, ventilation system, frequency-controlled drive, quality of electrical energy, energy saving device

The article analyzes the elements of recursion and methods of its optimization, gives a name to the elements of the structure of recursion, an analysis is carried out, a pseudocode is shown. The relevance of using a recurrent approach when conducting inspection activities in order to ensure transport security is revealed. Algorithms of actions of transport security units based on recursion are specified.

Keywords: recursion, transport security, inspection, memoization, segmentation, transport security zone

The task of building a decision-making system within the framework of automated systems of accident-free control of technological processes based on prediction models is considered. The decision-making system includes emergency forecasting system, integral criterion of accident-free control, preventive maintenance system, automated process control system. The aim of the work is to develop a compositive model for predicting emergencies of chemical water cleaning process. MATLAB software package and visual programming environment MICROSOFT VISUAL STUDIO were selected as a toolkit for predicting emergency situations of the technological process. The prediction model is a composition of thermodynamic, linguistic and neural network components. An example of compositive model for forecasting emergency situations of chemical water cleaning process is considered. Computational experimental research of the model is presented. It is concluded that the components of the prediction model complement each other, and an objective assessment of the state of the chemical water cleaning process should be carried out on the basis of the prediction of all three models.

Keywords: forecasting, emergency situation, technological process, accident-free control, decision-making system, automated system, compositive model, integral criterion, chemical water cleaning, computational experiment, real-time mode

The support in the bottom-hole zone of the trunk is a system of rings made of monolithic concrete having a different hardening period, which increases from the face up the trunk and is determined by the duration of the tunneling cycle. The strength and deformation parameters of the concrete support depend on the age of the concrete. Thus, to determine the strength of concrete in the early stages of concrete hardening, various empirical dependencies are used that link the strength of concrete at the design age with the strength at the required age. Based on a series of calculations performed by the finite element method, it was found that the change in the penetration rate does not significantly affect the relationship between stresses and deformations when static equilibrium is reached in the ""support – array"" system, which occurs at a high penetration rate at a greater distance from the bottom of the trunk. At the same time, intensive loading of the support at an early age can disrupt the process of natural hardening of concrete, lead to a violation of its structure, the development of fracturing, which will entail a decrease in the bearing capacity and water resistance of the support, a decrease in its durability.

Keywords: shaft, sinking, support, concrete, stress, deformation, strength, bearing capacity

To improve the quality of bearing rings, modern production strives to apply new modern methods for detecting defects based on the causes of their occurrence, as well as to introduce quality control systems by creating specialized software. An accurate assessment of the dynamic properties of bearings is very important for machines and helps to avoid serious mechanical damage. As part of the experiments, the main control methods were considered and the most effective one was established - eddy current control, which has a number of advantages compared to others. To prevent the occurrence of defective products in the control system, the fractal dimension method was considered and a neural network was built to solve the tasks of diagnosing.

Keywords: defect diagnosis, bearings, neural networks, automated control, fractal dimension, SVD filtering, Matlab software, monitoring system.

The article presents the results of a study of an automated system of commercial accounting of energy resources. The open architecture of the top-level software of the automated information and measurement system of commercial electricity metering, based on WEB technologies, has been developed and tested, which will allow further research and scientific activities in the field of mathematical and software processing of data on electricity consumption. A module of planning and management of enterprise resources has been developed for the implementation of AIIS KUE in the MCD based on the developed diagram of use cases.

Keywords: WEB technology, automated information and measurement system, electricity, energy consumption, automatic control

The paper considers the problem of personnel training. The first part describes a mathematical model that describes staff training through scheduling theory. The second part of the article describes a numerical solution using MS Excel and provides several examples of scheduling, the results obtained show how it is necessary to schedule classes to minimize teacher downtime. At the end of the work, practical conclusions and shortcomings of the model are described. This model allows you to reduce the time for scheduling teachers, thereby reducing the possible costs of the enterprise.

Keywords: theory of schedules, discrete mathematics, optimization, training, mathematical modeling, linear programming

The paper presents the results of numerical experiments on solving systems of linear algebraic equations (SLAE) with discharged matrices by the LU decomposition method, the Jacobi method, the Gauss-Seidel method, the modified Gauss-Seidel method and the modified Jacobi method with a relaxation parameter ω. In the course of numerical experiments on the solution of (SLAE) with test discharged matrices of various dimensions using the MATLAB package, it was found that the best results in the time of solving the problem were obtained by the modified Gauss-Seidel method with a relaxation parameter ω = 0.5 or a given accuracy of solutions ε= 10^-6. In the future, this method was used to calculate the integral characteristics of the functioning of distributed information processing systems for various practical applications.average system response time to user requests).

Keywords: distributed information processing system, a system of linear algebraic, equations, sparse matrix, LU decomposition, Jacobi method, Gauss-Seidel method, relaxation parameter

The concept of the Virtual DOM technology in the library for creating web user interfaces React.js is considered. A comparative analysis of approaches to the construction of modern user interfaces is carried out. The technological implementation of the internal mechanisms and algorithms of the Virtual DOM concept in React.js is considered. Describes current trends in the development of web applications.

Keywords: data processing, data visualization, web applications, user interfaces, algorithms, software development, data updating, client-server applications, web development trends

Electroretinography is a hightly informative method for diagnosing heterogeneous diseases associated with disorders of the vascular structures. This article describes the biomedical ophthalmic signal of an electroretinogram using wavelet analysis. The spectral characteristics of the signal, the time-frequency picture of the wavelet scalogram are estimated, and approaches to the automation of signal analysis using the available Python libraries are described. The description of the formation of wavelet scalograms of signals using the cwt function of the PyWT library has been formalized. The Gaussian wavelet of the 8th order is chosen as the basic function of the wavelet transform. In order to automate the analysis of wavelet scalograms, the sequence of determining the connectivity of segments using the connectedComponents function from the library of computer vision algorithms, image processing, and general-purpose numerical algorithms with open source OpenCV is described.

Keywords: electrophysiology, epr, electroretinogram, erg, wavelet analysis, decision support system, connected components, Otsu method, retinal dystrophy

The problem of optimal control synthesis is formulated and the matrix and vector components in the Riccati system are taken into account. Bellman's dynamic programming method was used to determine the patterns. A specific mathematical model of the oscillatory process is considered and its properties are numerically investigated. Examples of linear and quasi-linear problems are given and the minimum possible value of the quality criterion is determined. The corresponding graphical dependencies are constructed and with the help of optimal control tools, the state of the object is transferred from one point to another. Based on the use of the Zubov power series method, optimal control is revealed. Numerical calculations are carried out and Riccati functions are obtained in a nonlinear system with concentrated parameters.

Keywords: synthesis tasks, optimal control, matrix and vector components, Ricatti system, oscillatory process, quality criteria

In this paper, we study the process of heat conduction in a flat wall with an internal heat source under boundary conditions of the first kind. Various numerical and analytical methods are used to solve heat transfer problems. Each method has a number of advantages and disadvantages. The paper proposes to use the numerical method of finite differences. The original differential equation, as well as the boundary conditions, are approximated using a finite difference scheme. The essence of the method is to apply a spatiotemporal grid to the computational domain. For each grid node, a difference relation is written (the original differential equation with boundary conditions is replaced by the corresponding expressions obtained using the difference scheme). Solving this scheme, we obtain the temperature values ​​in the plate for each step in time and coordinate. On the basis of the solution obtained, graphical dependences of temperature on time and coordinates are constructed, and their analysis is carried out.

Keywords: finite difference method, thermal conductivity, plate, internal heat source, boundary conditions of the first kind

In this work, an automatic control controller for a two-circuit solar installation with thermosiphon circulation based on the STM32 platform has been developed. The system operates using six sensors (temperature sensor, water flow sensor, pressure sensor, coolant temperature sensor in the heater tank, coolant temperature sensor in the heat exchanger and outdoor temperature sensor.

Keywords: flat solar collector, heat pump, two-circuit solar installation with thermosiphon circulation, automation system, SCADA, solar heat supply system, PLC, control system

The implementation of market mechanisms in the transport and logistics system of the railway industry contributes to the development of competitive relations between market participants and stimulates the search for new ways to gain a competitive advantage. Technological outsourcing of industrial enterprises can strengthen the position of operator companies in the market and increase the efficiency of organizing the movement of car traffic on the railway network by redistributing responsibilities in the supply chain. Possible options for organizing interaction between operator companies and industrial enterprises and a model for organizing technological outsourcing are considered. The general structure is represented schematically in a graph formulation by bipartite graphs with various types of one-to-one, one-to-many relationships. Optimization mathematical models of the logistics of such interaction with different levels of generalization in nonlinear and combinatorial formulations are presented, adequately reflecting the practice of using technological outsourcing.

Keywords: Transport and logistics systems, technological outsourcing, operator activity, one-to-one, one-to-many interaction mechanism, linear integer programming

The article analyzes the current state of the postal services market, including the dynamics of the turnover of the postal services market in Russia, as well as an assessment of the development of postal items. The existing route network for the delivery of mail to Russian Post JSC is considered and the design location of the main objects of the sorting center in Rostov-on-Don - an automated sorting center in the immediate vicinity of the Platov airport is presented, an estimate of the costs of the current and project route networks.

Keywords: transport and logistics technologies, express delivery, postal services, postal operator, route network, logistics postal center, automated sorting center, comparison, costs