The article studies possibilities for analyzing geopolitical processes within the framework of situational analysis methodology using cognitive modeling. Situational analysis description is given, and scenario for developing events is presented where two stages are distinguished: a preparatory stage (a pre-scenario stage) which is essential for performing descriptive and explanatory functions of predictive research, and a scenario stage intended for substantive and formal research as well as for description of predicted processes, construction of system models and preparation of all significant information for scenario synthesis. Furthermore, a method for applying situational analysis is proposed to be used within the framework of the cognitive modeling toolkit of a “future scenario” option and its analysis with account of new “main” factors, relationships, feedbacks and dynamics of their alterations. When forming a scenario for a specific geopolitical situation within the framework of cognitive modeling, this method can be presented by causal (functional) and logical-semantic relation between the elements/agents of actions and counteractions. By interpreting the logical-semantic as structural, and the causal as dynamic, we obtain a structural-dynamic systemic description of geopolitical confrontation using the language of cognitive graphs, i.e. presenting a graphical expression of causal relationships between the concepts (factors) that characterize a particular geopolitical process. Thus, within the framework of a scenario stage the following procedures are conducted: analyzing the initial geopolitical situation, namely: determining key factors that build up the scheme of internal connections and external relationships, and their structuring; defining factors that make an impact; determining impact directions and force (positive and negative effect); choosing basic stereotypes or generalized models of interactions that correspond to the initial situation; constructing cognitive models of the current state of a situation; studying trends for the situation’s development and its dynamics analysis; transferring a scenario onto a practical basis.

Keywords: geopolitical processes, situational analysis, cognitive modeling, methodology for constructing predictive scenarios

The article considers the issues of imitation modeling of fibrous material mixing processes using Markov processes. The correct combination and redistribution of components in a two-component mixture significantly affects their physical properties, and the developed model makes it possible to optimize this process. The authors propose an algorithm for modeling transitions between mixture states based on Markov processes.

Keywords: modeling, imitation, mixture, mixing, fibrous materials

The article discusses a mathematical model of the production application distribution process on an aggregator platform. A formal approach based on a finite state machine and Petri nets is proposed to describe the states of orders, their transitions and constraints. A comprehensive model has been developed that takes into account the criteria for selecting a contractor, selecting equipment, and analyzing the production process, taking into account time, cost, and resource availability. The presented approaches ensure accuracy and efficiency in order management on digital production platforms.

Keywords: mathematical modeling, finite state machine, Petri net, digital production, service aggregator, choice of contractor

Using numerical simulation, we carried out studies on the effect of the length of a porous heat exchanger on the deposition of dust particles. The heat exchanger models with lengths of 5, 10, 20 and 30 mm were the subject of the studies. At the boundaries of the computational domain, we set the air velocity at 0.1, 1, and 5 m/s and the diameter of dust particles from 10-7 to 10-4 m. Research results have shown that with increasing length of the porous heat exchanger, the efficiency of dust particle deposition increases. This can lead to a decrease in the thermal and hydraulic characteristics of the heat exchanger.

Keywords: porous media, heat exchanger, numerical simulation, calculation, deposition of dust particles, heat exchanger length, air flow velocity, particle diameter, air cooling, microelectronics

This work is devoted to the research and development of an automated control system for the technological process of leading of long sleeves. Long sleeves are an important and promising direction for the development of industrial and metallurgical industries. Now there is a wide variety of designs and sizes of sleeves. However, there are four main methods of their manufacture: mandrel, half-mandrel, without mandrel and on flexible mandrels. The article presents an analysis of the advantages and disadvantages of each of them. Mastering and improving the technology of manufacturing sleeves on flexible mandrels is the main way to increase the volume and speed of sleeve production. The results of mathematical modeling of the automated system are presented. The simulation was performed using the ViSim software tool. The control object is a lead melting bath. The temperature of lead is accepted as an adjustable technological parameter. The method of passive experiment was used to build an automated control system.

Keywords: automated control system, technological process, long sleeve, lead, temperature, mathematical modeling, control object, transfer function, control parameters

TThe modeling of the process of distribution of profile oil pipes in a well by means of a cone punch is considered and the determination of the force necessary for its pushing is carried out on this basis. The normal force for one protrusion of the pipe profile was found. The change in the deformation resistance and profile geometry during distribution is taken into account. The optimal taper angle is determined and the geometric parameters of the punch are selected, including the largest and smallest diameters and its length. A numerical example of calculation based on the obtained formulas is given, which shows the technical feasibility of the process.

Keywords: distribution, oil profile pipes, protrusion force, equilibrium equation, deformation resistance, tool geometry, numerical example

This article discusses the problems of constructing convolutional neural networks for determining road objects. The general relevance and formulation of the problem of determining road objects is presented. The rationale for the use of artificial neural networks for determining road objects has been formed. The Retinanet network architecture is used as the main architecture of an artificial neural network for determining road objects. The general concept of this architecture and the main subnets are visualized. Error functions for the main subnets of the Retina net network are described. The design description of algorithms for constructing data annotation for training an artificial neural network, as well as algorithms for constructing the neural network architecture of classification, regression and feature pyramid is given. The dynamics of changes in the general error function when determining road objects is determined. The result of training an artificial neural network is presented.

Keywords: convolutional neural networks, classification, regression, convolutional neural networks, deep learning, big data, mathematical modeling, computer science, RetinaNet architecture

The lack of water resources determines the problem of their rationing. Existing water consumption standards provide for a wide range of daily consumption values. This does not take into account possible measures to save water, provided for by the concept of buildings with a zero balance of water consumption. In addition, the technical specifications for the design of water supply systems include, for economic reasons, the smallest possible number of residents. The actual occupancy may exceed the planned one by several times, which requires further investment of additional funds already in the reconstruction of the newly built network. The objective of the study is to develop an analytical model of water consumption, the analysis of which allows us to evaluate the dynamics of changes in the specific water consumption with a variable population.

Keywords: specific water consumption, indifference curves, resource replacement rates, marginal water consumption

In this article discusses the problems of determining traffic signs for driving a motor vehicle using an artificial neural network apparatus. The relevance of research at this point in time is described, as well as the advantages of using neural networks in determining traffic signs. The input data for determining traffic signs for convolutional neural networks are presented. The architecture of the convolutional neural classification network is formed, in particular, the sequence of layers of the image classification network is considered. A mathematical description of the modeling of the error function and the stochastic gradient descent method is given. A mathematical model of the learning process of an artificial neural network, as well as activation functions: linear functions and sigmoids is presented. An algorithm for forming an artificial neural network model is proposed. The learning process of this function is visualized on the graph. The result of the training is presented.

Keywords: artificial neural networks, classification, convolutional neural networks, deep learning, big data, mathematical modeling, informatics

This article discusses the importance of timely defect detecting of automated electronic car control systems for prevention of serious failures. Also the first stage of mathematic modeling mechanism is presented, it includes construction models of the dependence of the number of failures by time with various methods of diagnosting the technical condition of the car.

Keywords: diagnosting, modeling, technical service of the car, failure, automated system, electronic control unit, engine

Mathematical modeling and optimization of the process of controlling the sulfate regime when the apatite load changes on the phosphoric acid extractor is considered. It is shown that the preservation of the "sulfuric acid/apatite" ratio with a sharp change in the apatite consumption leads to a violation of the technological regulations for SO3. The algorithm of correction of this ratio in the transition mode is developed, which minimizes the probability of violation of the regulatory indicators. A variant of implementing the optimal apatite load correction procedure using stand-alone scenarios is proposed. The results were confirmed during the simulation.

Keywords: algorithm, mathematical model, stabilization of the sulfate regime, extraction phosphoric acid, change in the load on the extractor, phosphorus yield coefficient from apatite, optimization, autonomous scripts

Blasting operations are often the only way to prepare the material for the recess for laying roads and railways in the rocks. Explosive loosening is also used to extract stone as a building material. Field testing is costly and often dangerous. Therefore, it is necessary to first conduct a series of experiments on the model and find out the conditions for ensuring good quality loosening of rocks. In order for the results of model tests to be transferred to nature, a similarity between model and specimen is required. The approximate similarity is achieved by the equality of the similarity criteria for the model and specimen. The characteristic similarity criteria are obtained by analyzing the physical quantities inherent in a mechanical system using the theory of dimension and similarity. The received criteria are presented in the classical form. These are the criteria of Strouhal, Froude, Cauchy and Newton.

Keywords: explosive loosening, rock material, deceleration interval, similarity criterion, modeling, rock density, model, specimen, expansion height, dimensionality, physical quantity

A mathematical model of the surface of deformation zones as a set of flat cross-section described on the basis of spline functions for profiling pipes in rollers with subsequent calibration is proposed.

Keywords: Mathematical model, deformation zone surface, flat cross-section, spline functions, рipe profiling

Cementation studies focus almost exclusively on the movement of carbon, described through the diffusion equations, often with constant coefficients and without regard to temperature. This approach does not allow, to take into account the further diffusion of carbon into the workpiece in a lower temperature range at the stage preceding quenching. The paper describes the modeling of the diffusion saturation of steel by carbon in the cementation process, taking into account the influence of temperature on the example of a numerical solution of the gear cementation problem using the COMSOL Multiphysics program. It was shown that the finite element mathematical calculation of the process of saturation of austenite with carbon during cementation gives good agreement with experimental data, and finite element analysis methods can be used for multivariate calculation of the carbon content in austenite after diffusion saturation

Keywords: carbon diffusion, carburization, COMSOL Multiphysics, numerical modeling, carbon distribution, carburization, Fick diffusion law, mass transfer, heat transfer, gear, finite element method

The issues of improving the quality of products produced by predicting the resulting geometric characteristics of the shape of the pipes to be profiled and their accuracy are considered. An objective mathematical model was created that adequately describes the real process. The computational experiment was performed using software packages that allow implementing the ANSIS and DEFORM finite element method. The dependencies of the studied shape parameters on the outer diameter of the workpiece are established. The presented dependencies and the proposed guidelines for the conduct of the process are of practical use and are useful to developers and consumers of process equipment for predicting the results of profiling

Keywords: Pipe profiling, deformation, stress, mathematical model, finite element method, accuracy, quality