The article presents an attempt to describe mathematically the effect of the semantic kernel of a web resource on the Internet. In accordance with the theory of marketing, the product that we want to sell on the network is characterized by the following basic properties: price, time and place. In other words, a potential buyer wants to receive a given product in the right place at a given time. To satisfy this need, it is necessary to use the classic component of marketing, product promotion. However, this component is now becoming a fully virtual instrument. This tool functions in a hypertext, video and image environment. Therefore, the user analyzes the meaning of these elements in order to get the desired product. The results of web projects carried out in this area indicate the emergence of a new phenomenon, which reflects the main meaning of virtual promotion – this is the semantic core. The core is a short annotation of the main properties of the product, its location and time of appearance. Therefore, the purpose of this article is both a presentation of a new object of research and a mathematical description. It is assumed that the semantic core is formed on the basis of natural language terms. In other words, the semantic core is a set of keywords that are grouped by meaning. We propose to use data mining approaches for clustering to group terms. The classic clustering method at the moment is k-means. The article presents a model of the semantic core based on this method. This method and its distance function are considered as the second stage of web content processing. At the first stage, web content is converted into a semantic web. However, the k-means technique has significant drawbacks when modeling the semantic core. Therefore, in the development of this idea, the work shows an alternative way to modeling the kernel. As an alternative approach, the construction of clusters based on the concept of maximum flow is considered. This approach has the significant advantage that the type of links in the semantic network overlaps with the type of distance function in this method. As a result, on a real web project, the effect of the connection between the semantic core model and the level of new users of the web resource was demonstrated over the past five years. Keywords: semantic kernel, keyword, k-means, max flow.

A two-mode cylindrical magnetic field is considered, the potential of which has a minimum. The object of this work is the study of the parameters of an electron beam when it moves in a solenoid field with the longitudinal trap formed by the magnetic field, and the construction of the computational model of the motion of an electron beam. The problem is posed of the stability of the motion of electrons in such solenoid magnetic field. The possibility of obtaining oscillatory modes of particle motion has been studied. It was found that for oscillations of particles with an energy of tens of kiloelectronvolts in the potential well in a well, the field with the amplitude of tens of thousands of Oersteds is required. For the solenoid magnetic field of the solenoid, the formation of electron beam with an energy of 55 keV in the longitudinal and radial directions during its transportation is studied. A section of a magnetron gun was used as the physical object. One possible direction is to combine the two matched magnetic systems of the gun to create the potential magnetic field well. It is shown that, for the chosen conditions, the motion of electrons can be associated with the model of three-dimensional oscillations. In this work, on the basis of the Hamiltonian formalism of the motion of electrons in a magnetic field and an algorithm for numerically finding solutions to the differential equations of dynamics, a software tool is constructed that allows one to obtain arrays of values of particle trajectories in the volume. The use of the software made it possible to simulate the main dependences of the motion of the electron beam in a given two-mode solenoid magnetic field. The results of numerical simulation of electron trajectories in the gradient magnetic field with the point secondary emission cathode located in the middle of the system are presented. The formation of the beam with energy of 55 keV in the radial and longitudinal directions during its transportation in a solenoid magnetic field with a large gradient is considered. For significant time intervals, the possibility of three-dimensional oscillations is shown and the operating modes of the magnetic system are obtained, in which the particle undergoes stable three-dimensional oscillations. The influence of the initial conditions during emission on the occurrence of the reciprocating oscillatory effect has been studied. It is shown that for a given electron energy and fixed magnetic field, the parameter that determines the reflection of a particle, is the polar angle of entry relative to the axis of the cylindrical magnetic field. The dependence of the formation of the final distribution of particles on the amplitude and gradient of the magnetic field along the axis of the system is investigated. The results of numerical simulation on the motion of the electron flow are presented. The characteristics of the resulting electron beam are considered on the basis of a model of electron flow motion. The obtained simulation results show that it is possible to establish the phenomenon of oscillatory-return longitudinal motion under experimental conditions. Keywords: electron beam, magnetron gun, three-dimensional oscillations, electron dynamics, gradient magnetic field, mathematical modeling.

The existing publications that investigate vehicle course stability optimization were analyzed. A mathematical model, which describes the disturbed movement of a car with a tank, was compiled. This model allows to consider the liquid free surface oscillations and determine their effect on the car course stability during constant motion or emergency braking. There was described the main information regarding the car that was used to perform mathematical calculations. An algorithm was developed for deriving the characteristic equation for a complex system of differential equations describing dynamic changes in the movement parameters of a car, oscillations of partial layers of liquid in a tank and the operation of an electromagnetic drive of the control valve and an electronic PID controller for a two-circuit system for ensuring course stability. Based on the developed mathematical model, the influence of forced oscillations of the fluid on the stability area of the system built in the plane of variable parameters of the controller is investigated. It is shown that low-frequency oscillations of the free surface of a liquid lead to a significant reduction in the stability area, which indicates the need to consider such oscillations when solving problems of analysis and synthesis of this system. It was found that for a car with a tank, where low-frequency transverse oscillations of the liquid occur, which are accompanied by a redistribution of mass and disturb the movement, an increase of the speed unambiguously leads to a deterioration in directional stability. That enables exclusion of speed from the number of variable parameters and significantly simplify the problem being solved. The calculations for cases with different loading levels were performed. It was found out that the level of liquid in the tank, considering its relationship with the speed, has an ambiguous effect on the car course stability, and it is unacceptable to limit the research calculations to the case with 50 % load. Instead of this, it is necessary to find a line that bends from above the stability boundaries that correspond to many liquid levels. Keywords: fluid vibrations; exchange rate stability system; area of stability; tank; PID-controller; parameters.

The task to research the enterprises when locating them in the new areas is posed and solved. The relevance of the problem is related to both moral and physical aging of production systems, which leads to the need for their modernization and reengineering. For the development of the enterprise, new areas are required to accommodate modern technological equipment. Due to the diversification of the company's activities and the appearance of new orders, it is advisable to place modern production lines with a high degree of automation in new areas. The requirements for the organization of new industries, taking into account the concept of Industry 4.0, have led to the creation of enterprises in the form of virtual industries focused on the creation of new innovative products. The aim of the work is to develop models for the rational location of virtual production in the new areas in conditions of limited enterprise capabilities. Due to the complexity of the problem being solved, the study is carried out in three stages: optimization of location on the earth's surface; creation of the communication infrastructure for virtual production; simulation of the virtual enterprise production cycle. The efficient location of virtual production is carried out using both local and multicriteria optimization. In order to create the communication infrastructure of the virtual enterprise the selection of the optimal route for highway laying is carried out. Simulation of the production cycle is carried out considering time delays and queues when performing technological operations. The new scientific result is the solution of the problem of virtual production system locating on the earth's surface, taking into account the proposed indicators and restrictions, which include the cost of land plots renting (acquiring), as well as the costs associated with earth and construction works. Mathematical methods were used: integer optimization, simulation modeling, agent-based modeling. Keywords: virtual enterprise, optimization of technological objects location, communication infrastructure of the enterprise, simulation modeling, agent-based modeling.

The subject of the research is automatic control system modeling features for tensioning of stands roughing group, which takes into account changes in the rolling speed at exit of the previous stand and entrance to the next stand. Control systems for high-speed rolling on section mills are the most critical systems, since the trouble-free operation of rolling mill largely depends on their work. Rolling speed control is understood to mean tension regulation in the roughing group of stands and stabilization of the rolling loop in the finishing groups. The influence of such technological factors as uneven heating of blanks, change in the crimping mode in stands, etc. leads to the appearance of tension or back-up forces, deviation of rolled loop from the specified values. Tension rolling, in contrast to loop rolling, is a stable rolling mode. However, (at significant values of tension in the rolled products) such a rolling mode leads to different thicknesses of the finished product. The loop rolling mode is an unstable mode and is impossible without automatic control systems. Both in the tension rolling mode and in the free rolling mode with a loop, it is necessary to study automatic control systems in order to determine the possibilities of compensating for disturbing influences and obtaining rolled products of the given accuracy. Therefore, the main task of the automatic control system is to maintain the rolling mode with the lowest possible tension. To achieve this goal, direct control of the tension of the rolled strip with modern technical means is rather difficult, and the operation of tension control systems is based on indirect methods of measuring it, and the study of the system efficiency is reduced to modeling the process itself. The developed model consists of three stands and two inter-stand spaces, since it takes into account changes in rolling speed at the exit of previous stand and the entrance to the next stand. It is due to this that adequate simulation results are obtained that are close to the real rolling process. Keywords: automation, rolls, stand, inter-stand spacing, modeling, loop tension, rolling mill, roughing group.

Currently, the volume of news data streams is growing that contributes to increasing interest in systems that allow automating the big data streams processing. Based on intelligent data processing tools, the semantic similarity identification of text information will make it possible to select common information spaces of news. The article analyzes up-to-date statistical metrics for identifying coherent fragments, in particular, from news texts displaying the agenda, identifies the main advantages and disadvantages as well. The information technology is proposed for identifying the common information space of relevant news in the data stream for a certain period of time. The technology includes the logical-linguistic and distributive-statistical models for identifying collocations. The MI distributional semantic model is applied at the stage of potential collocation extraction. At the same time, regular expressions developed in accordance with the grammar of the English language make it possible to identify grammatically correct constructions. The advantage of the developed logical-linguistic model formalizing the semantic-grammatical characteristics of collocations, based on the use of algebraicpredicate operations and a semantic equivalence predicate, is that both the grammatical structure of the language and the meaning of words (collocates) are analyzed. The WordNet thesaurus is used to determine the synonymy relationship between the main and dependent collocation components. Based on the investigated corpus of news texts from the CNN and BBC services, the effectiveness of the developed technology is assessed. The analysis shows that the precision coefficient is 0.96. The use of the proposed technology could improve the quality of news streams processing. The solution to the problem of automatic identification of semantic similarity can be used to identify texts of the same domain, relevant information, extract facts and eliminate semantic ambiguity, etc. Keywords: data stream, agenda, logical-linguistic model, distribution-statistical model, collocation, semantic similarity, WordNet, news text corpus, precision.

The actual problem of synthesizing the optimal control law for the intermittent heating mode of office buildings is considered, which consists in the programmed reduction of the room temperature during off-hours. The analysis of information sources showed the absence of sufficiently justified methods for solving the problem of optimizing the thermal processes of buildings, which provide comfortable conditions for the functioning of personnel, on the one hand, and save costs for buildings maintenance, on the other hand. The statement of the building thermal state optimal control problem is formulated, which contains a mathematical model of the process, a control goal, constraints on control actions and an integral quadratic quality criterion, including deviations of the room temperature from a given program and heat consumption. The limitation on the control action is taken into account by the method of penalty functions. As a mathematical model of the optimized thermal process, a two-dimensional controlled system of differential equations with constant coefficients is applied. The values of these coefficients are determined on the basis of building similarity criteria, which allows solving the optimization problem in a dimensionless form. The model includes a control action - the supplied heat flux, and a disturbing action - the ambient temperature, changing according to a given harmonious law. The numerical solution of the optimal control problem is implemented by the Chernous'ko method of successive approximations. A description of the user interface is given, as well as examples of the implementation of the thermal state optimal control. The proposed software allows on the stage of designing the heating system to obtain express assessments of various thermal modes of the building, and can also be used as computer support for automated individual heating points. Keywords: intermittent heating mode, optimal control, mathematical model, control quality criterion, control constraints, penalty function, successive approximations, program interface, automated individual heating point.

This article is devoted to the issues of assessing the effectiveness of information systems for enterprises engaged in retail trade in consumer goods. This article describes the tasks that the retail FMCG trade, as well as the functions of the retail trade, solve. The features of the subject area were considered, which will form the basis for the formation of scales for assessing the effectiveness of information systems. The priorities, tasks, and features of the business model of enterprises engaged in retail trade in consumer goods, depending on the market segment they occupy. Various types of corporate information systems that can be used in retail trade are considered. The analysis of the subject area made it possible not only to determine important metrics for assessing the effectiveness of information systems but also to determine the priority of the requirements for the availability of certain functionality in the information system from each business segment, large, medium and small. Also, the existing standards in the subject areas of software development and enterprise organization were considered. This article proposes a methodology for evaluating information systems for enterprises engaged in consumer goods retail trade that belong to different market segments. The proposed methodology is based on the approach of multi-criteria expert assessment. An example of linguistic variables for one of the questions of the questionnaire for experts is given. The order of operation of the expert system is also presented in the form of an activity diagram. The developed expert information system can be monetized by providing referral links to the products of companies supplying information systems for retail. In the future, it is planned to add the ability for qualified experts to select combination of metrics for assessment, as well as change the assessment scale to increase accuracy. Keywords: information system, retail trade, consumer goods, performance assessment, expert assessments.

The paper provides information on the need to pass the “Unified entrance exam” in a foreign (English) language by students who have received a bachelor’s degree and wish to continue their studies to obtain a master’s degree. It is determined that when working with undergraduate students, it is advisable, firstly, to determine the percentage of graduates whose passing EVE is unlikely, and secondly, to intensify work with such graduates to increase this probability. The task was set to create a model for predicting the results of the unified entrance exam in a foreign language by bachelor’s graduates of higher education institutions upon entering the master’s program. A number of factors that affect the EVE score are proposed, namely: competitive score at enrollment (indicator of the student’s basic level), rating (assessment) based on the results of the first year of study (exam in the compulsory subject “Foreign Language”), choice “Foreign language” in the 2-3rd year (maximum of all or “0”, if the student did not choose), the rating of additional classes “Foreign language” in the 4th year, the average rating for the penultimate session (indicator “current” student’s attitude to the educational process), the fact of having additional points (an indicator of the student’s interest in other activities than learning), the average rating of a bachelor’s degree (an indicator of the general student’s attitude to the educational process). The available data concerning students of two years of the department of intelligent decision-making systems of the Donbas State Engineering Academy are given. A method of artificial neural networks with a two-layer perceptron architecture with ten neurons in each hidden layer, a sigmoid activation function, and an error backpropagation algorithm for network training is proposed. Calculations were performed in the Deductor Studio Lite environment, their results were analyzed. It is noted that the proposed approach to forecasting can be applied when working with undergraduate students, to determine the percentage of graduates whose EVI is unlikely to pass, and to intensify work with such graduates to increase this probability. Keywords: educational and qualification level, the only entrance exam, forecasting, artificial neural network, perceptron, sigmoid, network training.

The paper deals with the problems of increasing the efficiency of software development, in particular, the issue of reducing the time for developing programs and using automated synthesis of programs, which will avoid the revision of the original product. The software should be tested along with other system components in all combinations that may occur. Testing is time-consuming because hidden bugs are revealed through unexpected interactions between software components. With structural analysis, data flow diagrams are not the end result, they are a developer tool. First, diagrams are built, and then mechanisms are developed to ensure the required system behavior. A graphical approach to solving the problem of automation of software development is being developed, based on the involvement of visual forms of program presentation. For any program object, you can select a finite number of states in which it is at each moment of time. The program progress is associated with the transition of an object from one state to another. The graph replaces the textual form of the description of the program algorithm, while the visual representation of the algorithm is realized. The specification of data structures, as well as the setting of intermodular interfaces according to data, is separated from the description of the structure of the algorithm and controls. Basic modules and data types are used. Basic modules are local calculable functions, on the basis of which all other technology objects are generated. Data types describe the syntactic and semantic aspects of constructing data used in base functions. Algorithms for finding routes on directed graphs are considered. When defining routes from the root vertex to the final ones, the properties of the algebra of three-valued logic were used. Based on the considered approach, as well as taking into account its shortcomings, a method for classifying data types was proposed, based on the implementation of a partial enumeration of the routes of the graph of program links and a method for designing software based on it, taking into account minimizing the time and cost of the project. Keywords: software, computer engineering, information systems, components, partial enumeration of graph routes, development costs.