The article describes the initial boundary value problem with vacuum boundary conditions on resistive diffusion in a conducting sphere. The formal solution for a case of axially symmetric magnetic fields, where azimuth element is identically zero, is developed.

An effective semi-analytical method for the integrated optimization of the routing matrix and node speeds for non-Markov queuing networks is proposed. As the objective function, the average time spent on the application through the network is used. The method combines a fast accurate calculation of the objective function gradient in the space of variable transition probabilities and an accelerated analytic-simulation calculation of the objective function gradient in the space of variable nodes speeds.
Methods of integrated optimization of transport networks are developed. They are based on their approximation by non-Markov networks of queuing with multi-linear nodes (roads), the speed of which decreases with increasing load. The proposed methods are oriented to different modes of transport load. Examples of the application of the proposed methods are given. It is demonstrated that the greatest effect in combating blockings is provided by the integrated optimization of transport networks oriented to the regime of high transport load.

The article deals with the methodological aspects of the statistical analysis of incomplete time series and interpretation of the results obtained by the example of the analysis of the integral aerosol backscattering coefficient of the stratospheric aerosol.

The article describes the development of physical and mathematical models allowing considering the effect of multiphase fuel (liquid hydrocarbon + solid combustible material) on the conditions of ignition and modes of combustion propagation in polydisperse nonhomogeneous mixtures. In this case, the combustion of different droplet fractions occurs in different modes: the volatile fraction evaporates and burns in the gas-phase mode, and the solid fuel fraction is reactive with the oxidizer in the heterogeneous mode. The effect of the presence of a solid fraction in droplets reacting in a heterogeneous mode on the evaporation rate of the volatile fuel component is studied. The effect of tightness on the evaporation rate of each drop due to the presence of other drops is taken into account. The results of computational modeling of flame propagation during ignition of the polydisperse mixture of liquid hydrocarbon fuel droplets with solid fine carbon particles are presented.

The concrete is in a state of triaxial compression when the concrete column in a steel cage is operated under load. The concrete is under the reactive lateral pressure from the tube, therefore strength of concrete increases. However, the steel casing in concrete-filled steel tube structures of this type occurs to be not loaded enough, since it is not loaded in the longitudinal direction. In this regard, it is most expedient to use a composite casing instead of a steel one. It is proposed to use a composite cage, which has high strength properties in the transverse direction and insignificant properties in the longitudinal direction.
The article describes the deduced formula for the three-dimensional model of a composite cage material in a stress-strain state. The paper presents the formula for reactive lateral compression from a composite cage to a concrete. The analytical solution to the problem of compressing a concrete column in a composite cage taking into account the nonlinear behavior of concrete is obtained. The increases in the loadbearing capacity of the concrete column in steel and composite basalt-plastic cages are compared.
It brings us to the conclusion that the use of composite cage in concrete-filled steel tube structures is a promising direction for further research and that it is necessary to use fibers having higher deformation characteristics.

The paper discusses some aspects of hydraulic fracturing crack numerical modeling. In particular, methods for modeling fracture growth in a non-uniformly stressed medium are suggested, and results of test simulations aimed at parametric studies are presented. The method for mathematical modeling of arbitrary oriented flat cracks interaction in 3D space is also developed.

The article considers the model of particle diffuse reflection from the anisotropic medium.
The author resolved an issue of finding a particle reflection probability from the medium. Mathematical simulation of this task is given, mathematical solutions of finding a particle reflection probability from the nonuniform medium are provided. The mathematical description of the designated tasks allows solving more complex problems of random walks in the continuous anisotropic medium. Pure scattering is also considered and the corresponding formulas are obtained.

The relevance of the research is caused by the complexity and importance of tracking prob-lem of the dynamic interaction of individuals in groups (study groups, work collectives, social net-works). In the course of joint activity, representatives of various groups interact and relate to each other (managerial, psychological, behavioral, communicative, etc.) The result of mutual influence is the transition of individuals from one group to another. These transitions change the quantitative structure of groups. Force of mutual influence of individuals depends on the quantitative structure of group, coefficients and time of influence. The similar complexity problem arises at the research of groups of intelligent agents in agent-based systems. The article describes the development of the mathematical model of numerical structure change in groups based on the differential equations system. The general and partial (special cases) solutions for this system are obtained. Actual numer-ical examples are given for an illustration of the received theoretical results. The solution to these examples is demonstrated in MS Excel. Results of the article can be useful not only in the social and economic sphere but also in numerous applications of artificial intelligence technologies.

The article presents some results of three-dimensional numerical simulations of processes in chemically reacting hydrogen-air mixture of ideal gases after reflecting and focusing of a shock wave against a wedge. Depending on the intensity of the shock wave, several different scenarios of emerging processes are obtained, and the conditions for detonation onset are determined. Comparisons of numerical simulations results with experimental data are also presented.

The chaotic dynamics of the distribution functions of f(x) parameters of human movements have been repeatedly proved before. Considering the problem of homogeneity of the obtained samples, it can be assumed that the obtained samples (having a chaotic dynamics of behavior) can be heterogeneous. The paper demonstrates the low efficiency of the thermodynamics of the non-equilibrium systems by I. R. Prigogine in the evaluation of the homogeneity samples. At the same time, it is proved that high efficiency and objectivity of the methods as a part of the chaos and self-organization theory in establishing the homogeneity or heterogeneity of the resulting samples. Thus, as a result of the study, it can be concluded that the methods and approaches in the framework of the chaos and self-organization theory have a unique mathematical apparatus that can not only establish a change in the homeostasis of the subject but also objectively evaluate the resulting samples for homogeneity.

The qualification of a process control operator is one of the most important factors of safe production. Professional operator training courses give the opportunity to improve the operating efficiency, productivity, and skills using special simulators that imitate technological processes with the help of special hardware and software. Such simulators have high cost and do not take into account all factors of human-machine interaction.
The proposed simulator concept involves the development of a complex simulator for training a team of control operators (for example, operators of a multi-stage oil refining process). Simulations should be performed with a visual simulation of the production by mnemonic diagrams, providing operators with the necessary information, as well as supporting them in decisions making using indicators, audio signals and information messages. Time parameters of operators’ interaction and criteria of quality control are assumed to be estimated to analyze the quality of operators’ teamwork.

The article considers the problem of mathematical modeling of catalytic cracking. The model is a system of homogeneous differential equations of the first order with constant coefficients. An approach to algorithm presentation of the numerical solution of a system of differential equations in the problems of modeling the refining process is proposed.

The article describes the method of studying the stratification of gases with a scanning laser ray. An approach to measuring the concentration of gas is proposed. The method involves the angular deviation of a laser ray in a stratified flow through the change in the transverse gradient concentration and the angle of inclination of the stratification boundary in an open oil reservoir. The de-pendence of the angular deviation of the laser ray on the rate of the oil spill is found. Control meas-urements of the concentration distribution of hydrocarbon gases are carried out.

The task of calculating the resonant frequencies is relevant in the design of printed circuit assemblies structures of onboard electronic devices. Analysis of the amplitude-frequency characteristics based on the estimated values of the resonant frequencies and their subsequent analysis is indicative of the technical condition of the object of study.
All geometrical dimensions of the structural elements of the electronic device and the location of the electronic components on the printed circuit board have to meet the tolerances specified in the design documentation. It is impossible to maintain an exact technology during production, therefore all parameters may have tolerance limits.
Any changes in the parameters of the printed circuit assembly within the tolerance leads to a variation of the resonant frequencies relative to the idealized value, therefore forming the tolerance intervals of the resonant frequencies.

The paper describes the methods for calculating the diversities of the printed circuit resonant frequencies: experimental, the worst case method, the method of moments and the Monte Carlo method. The analysis of the features of each method is made. It is proposed to use the Monte Carlo method, as having the greatest accuracy and ease of implementation, taking into account the computational capabilities of modern electronic computers.
A block diagram of the Monte Carlo method application is proposed, the mathematical apparatus is presented. The process of integrating software systems for calculating the diversities of the resonant frequencies of a printed circuit assembly is described.

Currently, in various branches, such as space and automotive industry, computer vision algorithms are widely applied. In different tasks of computer vision, it may be necessary to determine the order of the objects in space. At first glance, this task may seem insignificant, but the quality of the images strongly depends on shooting conditions. There is a set of solutions for finding the order of objects on images. At the same time, most of the solutions are not very useful for working with human-made objects. One of the special cases of this task is the ordering objects according to a flat table. The main problems in solving this task are photographs with perspective distortions and small displacements of objects relative to each other. The article presents the results of the research conducted in this area. Heuristic and neural network approaches to the solution are considered. The neural network method showed the most sufficient results. The authors named the design of described neural network as neurotabulator.

The authors analyze modern approaches to the development of a decision support system for forest firefighting in the territory of KhMAO – Ugra. This system will allow modeling not only the process of fires behavior but also to predict the probability of their occurrence, as well as to assess the material, environmental and social-organizational consequences of potential fires. It is established that in general a forest fire extinguishing process control can be considered as management of complex organizational system which consists of collecting information, making a decision, and also an implementation of this decision. These steps are repeated in a cycle, and each next step evaluates the quality of the management process in the previous step.

The paper presents a tensor model of the enterprise's integrated data storage. Problem analysis of databases integration represented in different formats is conducted. Tensor models of databases currently known are considered. The principle of constructing a tensor model of an integrated relational database in the form of a multidimensional matrix is proposed, where the relation is considered as an invariant. A testing example of the proposed model for building an integrated relational database is described. A method for storing multidimensional and two-dimensional matrices in the relational database is proposed, where the SQL query is used for the multiplication of a multi-dimensional matrix by a two-dimensional matrix.
A comparative analysis of the speed for the proposed method and the method based on the analysis of system tables is carried out using test sets of random data.
The usage of the tensor representation of the information system's databases allows obtaining a compact mathematical description, and the binary coding of the relational model entities allows simplifying the programmatic access to the integrated data storage. Experimentally confirmed that the sample contains more than 15 000 records, the tensor representation of the data storage allows shortening the time of execution from 25 % to 11 500 %.

In the early 2010s, in the Department of Educational Informatics of System Research Insti-tute, Russian Academy of Sciences, by the state order of the Russian Academy of Sciences, non-textual educational programming system PiktoMir was developed. The system was intended to sup-port basic courses of programming for preschoolers and primary school pupils [1–3]. This freely distributed and multi-platform system can be downloaded to tablets, laptops and other computers with Android, iOS, Microsoft for offline use and can also run using the web interface on any computer devices with Internet access.
PiktoMir allows performing not only the individual but also team (joint) programming tasks. Each team member individually works on his part of the program on his computer during a team task, which makes it possible to objectively evaluate the contribution of each team member to the overall collective result. Cooperative programming can be used both in the regular programming course and for conducting team competitions.

A process of collecting urban-traffic density statistics is connected to a range of complications. Municipal authorities do not always gather such statistics. Due to various reasons, access to street cameras is not always possible. The authors describe the development of mobile application intended to track citizens’ automotive movement geolocations and possibilities to use the collected data for analysis of urban traffic density.

The paper presents the most common construction principles for the dispatch control of the unified energy system of the Russian Federation. The approaches used in the implementation of technological tasks are described. Models of software products used to provide dispatch control, work planning and forecasting, as well as the provision of system services in the energy system of the Russian Federation, are introduced. Examples of the use of artificial neural networks are given. The specificity of information entering the dispatching centers and the difficulties that arise in the process of increasing its quantity is described. The principles of the verification of telemetry parameters and the order of their implementation established in the “System Operator of the United Power System” of the Russian Federation are noted. The concepts of software development for the verification of telemetry parameters are detailed. Algorithms and methods for preparing input data for further adaptation of the attributes of parameters affecting the final decision about truth or falsehood are presented. The principles for the further use of adapted data in calculations based on neural net-works with feedback are described. The implementation code for the simple neural network in the Python language is given. The results of experiments on two data samples are provided.

Surgut State University became a member of the CDIO initiative in 2017. The Department of Automation and Computer Systems is the first in the University that began implementation of educational programs according to the CDIO standards. The Department provides two education programs: “Control in engineering systems” and “Software engineering”. Research and analysis of the CDIO initiative’s organizational principles caused changes in the implementation strategy of education programs. The more efficient improvement of education programs will be possible after the first stu-dents’ graduation and the survey of the stakeholders about the learning outcomes of the graduates.

Modern medicine has risen to a previously unattainable level over the past decade. Simultaneously one of the main directions in the Internet of things is the development of medicine and public health. Within the health care system, the issue of monitoring patients, tracking their location and health status (monitoring of temperature, pressure, palpitation and other physical parameters) is especially topical. Due to the development of the Internet of things, the digital transformation in health care is expanding at a high rate. The authors focus on the creation of a special web application for distant high-risk group patient’s heart-rate tracking with a fitness bracelet (fitness tracker). Based on the existing two main approaches for creating web applications the authors determine the effectiveness of bracelet’s use in the health care system for distant high-risk group patients. The results showed that the described method of creating native hybrid applications is the fastest way, perfectly suitable for rapid prototyping and initial launch of the project, however, for a more serious and heavily loaded application, it is worth choosing React Native. Conclusions. This study demonstrates the implementation of IoT and IoMT based on a web application. The application of any approach in public health services should be based on the questions posed to the developer and the medical institution.

The process of digital transformation affects all spheres of life in modern society. All areas of human activity are now subject to digitalization in one form or another: economics, ecology, sci-entific activities, etc. Although some technologies, together with their accompanying competencies, become outdated, new technologies are emerging that require effective methods for recognizing elements of the environment, tracking the movements of controlled objects in interaction, including augmented reality. At the same time, neural networks are becoming increasingly popular for solving problems of recognizing objects in static images, as well as in video streams. The data markup for further deep learning is an integral part of any project that involves the use of a neural network of computer vision technologies. For training neural networks the task of classifying images or finding objects requires a huge amount of marked data. The more classes of objects, the more data is required for training. Naturally, time-consuming manual marking has a number of drawbacks: the long marking time itself and possible errors due to the routine of the task. The article discusses various approaches for automating the task of marking images for deep learning, which can be used to integrate image recognition technologies and create an augmented reality, with possible implementation on personal computers and mobile devices.

The development of an intelligent information system combining a situational approach and methods of statistical control over processes is proposed. The main goal is to identify and prevent the threat of emergency shutdowns in the boiler room. The initial data is filtered, then control charts are constructed, which determine the limits of the stable state of operation of the boiler rooms. The system promptly signals any deviations during the process of heat generating. The rules of Shewhart control charts form the basis for classification of emergency situations and are entered into the system’s knowledge base, where each class corresponds to one of the possible basic solutions.

An interactive method of collecting, analyzing and processing expert opinions to select the most significant factors for diagnosing obliterating atherosclerosis of lower limbs is developed. This technique allows minimizing the feature space by taking into account the maximum and minimum possible expert evaluations. A novelty is the consideration of the limited capabilities of a person’sonline expert survey, decision-making support system in medicine, expert evalu-ation, expert analysis, consistency of experts. memory in selection tasks. The interactive method is designed to collect expert opinions, according to data divided into semantic groups consisting of no more than nine parameters, in order to identify a specific number of parameters of a feature space in a weakly formalized subject area.