The relevance of scientific work lies in the need to improve existing software designed to analyze the compliance of the results of software testing ofthe stated requirements. For the implementation of this goal, neural networks can be used by quality control specialists to make decisions aboutsoftware quality, or project managers as an expert system, for one of the quality indicators for the customer. The article deals with software testingwhich is a process of validation and verification of compliance of the software application or business program with the technical requirements thatguided its design and development, and work as expected, and identifies important errors or deficiencies classified by the severity of the program to befixed. Existing systems do not provide for or have only partial integration of systems of work with the analysis of requirements, which should ensurethe formation of expert assessment and provide an opportunity to justify the quality of the software product. Thus, a data processing model based on afuzzy neural network was proposed. An approach to allow determining the compliance of the developed software with functional and non-functionalrequirements was proposed, taking into account how successfully or unsuccessfully implemented this or that requirement. The ultimate goal ofscientific work is the development of algorithmic software analysis of compliance of software testing results to stated requirements for support in thedecisions taken. The following tasks are solved in scientific work: analysis of advantages and disadvantages of using existing systems when workingwith requirements; definition of general structure and classification of testing and requirements; characteristic main features of the use of neuralnetworks; designing architecture, the module of research of conformity of results of testing software to the stated requirements.

Relevance of the research work is the analysis of the main features of 3D modeling for further implementation in e-commerce. Namely, the features ofcreating a human body 3D model with the ability to edit personal settings of individual parts of the body, as well as a basic set of clothes to provide amore realistic representation of the model. The features of the 3D model in general were considered in this article. The mathematical analysis of the 3Dgraphics rendering on the 2D monitor and the possibilities of control and editing of such models have been presented. The developed software productallows the user to create an anatomical three-dimensional model of the human body and then adjust it to his needs. The user can apply on createdmodel variety of settings, namely more than 15 different views, with a full package of changes. It is possible to change the size, color of hair,eyebrows, eyes, face, body, legs. Also, the user is able to select the levels of skeletal frame views and additionally can select different backgrounds toprovide a more realistic representation of the model in space. Additional functionality was implemented for more flexible configuration of the model’sface. The user can pre-determine points to select directions or sizes of different parts of the face using settings, displayed on the mouse or touchpadcontrol. After adjustments, the user is able to manage the clothes that he had saved in the shopping cart from the online store, from which he laterproceeded to the online fitting. After the fitting the user can test the creation of animations in 360 degrees of free movement. Finally, the user can go tothe store to pay for the items he left in the shopping cart. Developed software allows improving main metrics of the on-line stores, which has a positiveimpact on increasing the growth of earnings.

Currently, the question of state, formation and development of the information source interaction system, the scientific interaction and users' requestsin certain fields of activity remains relevant under the conditions of the development of the use of Internet services. Recommendation systems are oneof the types of artificial intelligence technologies for predicting parameters and capabilities.Due to the rapid increase in data on the Internet, it is becoming more difficult to find something really useful. And the recommendations offered by theservice itself may not always correspond to the user's preferences. The relevance of the topic is to develop a personal recommendation system forsearching books, which will not only reduce time and amount of unnecessary information, but also meet the user's preferences based on the analysis oftheir assessments and be able to provide the necessary information at the right time. All this makes resources based on referral mechanisms attractiveto the user. Such a system of recommendations will be of interest to producers and sellers of books, because it is an opportunity to provide personalrecommendations to customers according to their preferences.The paper considers algorithms for providing recommender systems (collaborative and content filtering systems) and their disadvantages.Combinations of these algorithms using a hybrid algorithm are also described. It is proposed to use a method that combines several hybrids in onesystem and consists of two elements: switching and feature strengthening. This made it possible to avoid problems arising from the use of each of thealgorithms separately.A literature web application was developed using Python using the Django and Bootstrap frameworks, as well as SQLite databases, and a system ofrecommendations was implemented to provide the most accurate suggestion. During the testing of the developed software, the work of the literatureservice was checked, which calculates personal recommendations for users using the method of hybrid filtering. The recommendation system wastested successfully and showed high efficiency.

Applications architecture is the baseline of any organizational activity, which main goal is to provide the executional environment for businessprocesses in order to deliver products or services to satisfy customer needs and generate revenue. Nowadays, large software engineering projectsalways begin with the architecture design phase, despite the waterfall or agile methodology is used by a software development team. Applicationsarchitecture design is the most important and, at the same time, error-prone stage of the whole software engineering project. It is well-known thatdesign shortcomings made on the design phase may increase drastically to testing and maintenance phases. Further costs to defects fixing may behundred times higher in the later project stages in compare to the design stage on which applications architecture is defined. Common system designsolutions, which were proven on practice and used in many projects, are known as architectural patterns. Software architecture patterns are consideredas building block for system implementation. The most popular and efficient way to share architectural patterns are graphical models that used as anyother blueprints of engineering solutions. Applications architecture models are built to represent system design, whereas, such models are alreadybased on certain patterns as the industry best practices. Hence, in this paper we consider a relevant problem of applications architecture modelsanalysis, which relevance is defined by those fact that designed blueprints of information systems and other software solutions should be carefullychecked for all presumable inefficiencies in order to avoid extra efforts and related costs for defects fixing in the later project stages. It is proposed touse ArchiMate enterprise architecture modeling language, since it can be used not only to represent applications architecture, but is connection tobusiness and technology layers. In order to evaluate applications architecture models, respective ArchiMate metamodel is considered and representedas labeled directed graph, and coupling software metric is selected for analysis. Sample calculations are demonstrated, obtained results are discussed,conclusion and future work directions are formulated.

An approach to the mathematical description of the criterion for the effectiveness of a new object of research – virtual promotion is presented in thepaper. The emergence of this new object of research is connected, on the one hand, with the classical theory of marketing, and on the other withmodern Internet technologies. Marketing is based on the 4P principle: product, price, location and promotion. Promotion is a component of thisprinciple. But in modern conditions, this phenomenon is changing under the influence of the Internet. Now this 4P component is becoming a fullyvirtual instrument. The traditional scheme of promotion functioning is as follows. A message is created to a potential buyer and the delivery channel ofthis message undergoes a change. It is based on the principle: money – goods – money. While the new sales scheme is described by the scheme: weattract a client, make money on a client, we spend money. In the new scheme, we deal with product knowledge in the form of the so-called semanticcore of web content. Knowledge describes for a potential client how a given product can cover his need for something. Using the logistic principles ofthe transfer of goods, this semantic core is loaded into the specified Internet nodes. That is, virtual promotion is formed as two channels: logistics andmarketing. The first one performs three operations: concentration, formatting and distribution of semantic cores on the Internet. The second managesthis process, forming a virtual promotion map. This map is a graph of Internet nodes. It is required to define such a tree of Internet nodes so that virtualpromotion has maximum efficiency. The paper analyzes modern metrics related to the processes of search engine optimization on the Internet.Unfortunately, these metrics evaluate only statistically after the fact of visiting a web resource or the budget of the Internet site in which theadvertising message about the product was placed. Therefore, based on the conversion metric, a criterion for the effectiveness of virtual promotion wasproposed in the work, which takes into account both the attractiveness of the semantic core and the attractiveness of the Internet site where thesemantic core will be located. The criterion reflects the income that we receive depending on the attractiveness of the semantic kernel and the Internetsite.

The article presents the results of research and calculations on the formation of a radial electron beam by a magnetron gun with a secondary emission cathode in the electron energy range 35...65 keV and measuring its parameters during transportation in the total decreasing magnetic field of thesolenoid and the stray field of permanent magnets. The beam was transported in a system consisting of copper rings with an inner diameter of 66 mm,located at a distance of 85 mm from the exit of the magnetron gun. The dependence of the beam current on the amplitude and gradient of the fielddecay has been studied. The studies carried out have shown the possibility of stable formation of a radial electron beam with an energy of tens of keVin the decreasing magnetic field of the solenoid. By optimizing the distribution of the magnetic field (created by the solenoid and ring magnets) and itsdecay gradient, it is possible to achieve an increase in the incident of electrons on one ring (up to ~72% of the beam current). On the basis of themathematical model of the movement of the electron flow, a software tool has been synthesized that makes it possible to obtain and interpret thecharacteristics of the resulting flows. The obtained numerical dependences are in satisfactory agreement with the experimental results for a magneticfield with a large decay gradient. Various configurations of the magnetic field are considered. Solutions to the direct problem of modeling electrontrajectories for given initial conditions and parameters are obtained. Various configurations of the magnetic field are considered. It is shown that forthe selected initial conditions for the electron beam and the distributions of the longitudinal magnetic field along the axis of the gun and the transportchannel, the electron flux falls on a vertical section, the length of which is on the order of a millimeter. Thus, by changing the amplitude anddistribution of the magnetic field, it is possible to control the current in the radial direction along the length of the pipe, and, therefore, the place of theelectron irradiation.

The subject of the research is the processes of constructing explanations based on causal relationships between states or actions of an intellectualsystem. An explanation is knowledge about the sequence of causes and effects that determine the process and result of an intelligent informationsystem. The aim of the work is to develop a counterfactual temporal model of cause-and-effect relationships as part of an explanation of the process offunctioning of an intelligent system in order to ensure the identification of causal dependencies based on the analysis of the logs of the behavior ofsuch a system. To achieve the stated goals, the following tasks are solved: determination of the temporal properties of the counterfactual description ofcause-and-effect relationships between actions or states of an intelligent information system; development of a temporal model of causal connections,taking into account both the facts of occurrence of events in the intellectual system, and the possibility of occurrence of events that do not affect theformation of the current decision. Conclusions. The structuring of the temporal properties of causal links for pairs of events that occur sequentially intime or have intermediate events is performed. Such relationships are represented by alternative causal relationships using the temporal operators"Next" and "Future", which allows realizing a counterfactual approach to the representation of causality. A counterfactual temporal model of causalrelationships is proposed, which determines deterministic causal relationships for pairs of consecutive events and pairs of events between which thereare other events, which determines the transitivity property of such dependencies and, accordingly, creates conditions for describing the sequence ofcauses and effects as part of the explanation in intelligent system with a given degree of detail The model provides the ability to determine cause-andeffect relationships, between which there are intermediate events that do not affect the final result of the intelligent information system.

The problem and the main stages of choosing a rational configuration of a four-level logistics network that is resistant to the impact of emergencies forstrategic planning are considered. The problem under consideration belongs to the class of multicriteria optimization problems. Criteria related to thefinancial costs of building and operating a logistics distribution channel, as well as criteria related to the level of quality of customer service, arecontradictory. To solve the problem of stability of the logistics system configuration to emergencies, such as failure of intermediate warehouses,failure of transport arteries, etc., a strategic management information system was developed by integrating existing software components at the level ofenterprise software applications. The integration of the system was based on a service-oriented architecture, as all its components are heterogeneous innature. This approach allows you to reuse existing program code. To determine a sustainable configuration option, two criteria are used, which areconsidered equivalent: the level of costs for the maintenance of the logistics channel and the level of service quality in the event of differentemergencies. Since the probability of emergencies is unknown, the minimax criterion is used to minimize the risk when choosing a rationalconfiguration of the logistics network. For this purpose, losses from emergencies are calculated according to all criteria, and there is a variant of thelogistics network configuration that will be the least risky. That is, we will not be able to get a worse result than the one we rely on. The results of thestudy are presented in the form of a configuration variant of the logistics distribution system, which can be used in the future to determine businessoptions.

Mathematical models of the epidemic have been developed and researched to predict the development of the COVID-19 coronavirus epidemic on thebasis of information technology for optimizing complex dynamic systems. Mathematical models of epidemics SIR, SIRS, SEIR, SIS, MSEIR in theform of nonlinear systems of differential equations are considered and the analysis of use of mathematical models for research of development ofepidemic of coronavirus epidemic COVID-19 is carried out. Based on the statistics of the COVID-19 coronavirus epidemic in the Kharkiv region, theinitial values of the parameters of the models of the last wave of the epidemic were calculated. Using these models, the program of the first-degreesystem method from the module of information technology integration methods for solving nonlinear systems of differential equations simulated thedevelopment of the last wave of the epidemic. Simulation shows that the number of healthy people will decrease and the number of infected peoplewill increase. In 12 months, the number of infected people will reach its maximum and then begin to decline. The information technology ofoptimization of dynamic systems is used to identify the parameters of the COVID-19 epidemic models on the basis of statistical data on diseases in theKharkiv region. Using the obtained models, the development of the last wave of the COVID-19 epidemic in Kharkiv region was predicted. Theprocesses of epidemic development according to the SIR-model with weakening immunity are given, with the values of the model parameters obtainedas a result of identification. Approximately 13 months after the outbreak of the epidemic, the number of infected people will reach its maximum andthen begin to decline. In 10 months, the entire population of Kharkiv region will be infected. These results will allow us to predict possible options forthe development of the epidemic of coronavirus COVID-19 in the Kharkiv region for the timely implementation of adequate anti-epidemic measures.

The article considers the study of methods for numerical solution of systems of differential equations using neural networks. To achieve this goal, thefollowing interdependent tasks were solved: an overview of industries that need to solve systems of differential equations, as well as implemented amethod of solving systems of differential equations using neural networks. It is shown that different types of systems of differential equations can besolved by a single method, which requires only the problem of loss function for optimization, which is directly created from differential equations anddoes not require solving equations for the highest derivative. The solution of differential equations’ system using a multilayer neural networks is thefunctions given in analytical form, which can be differentiated or integrated analytically. In the course of this work, an improved form of constructionof a test solution of systems of differential equations was found, which satisfies the initial conditions for construction, but has less impact on thesolution error at a distance from the initial conditions compared to the form of such solution. The way has also been found to modify the calculation ofthe loss function for cases when the solution process stops at the local minimum, which will be caused by the high dependence of the subsequentvalues of the functions on the accuracy of finding the previous values. Among the results, it can be noted that the solution of differential equations’system using artificial neural networks may be more accurate than classical numerical methods for solving differential equations, but usually takesmuch longer to achieve similar results on small problems. The main advantage of using neural networks to solve differential equations` system is thatthe solution is in analytical form and can be found not only for individual values of parameters of equations, but also for all values of parameters in alimited range of values.