Scientific Works of Vinnytsia National Technical University

DEPENDENCE OF THE SAWDUST DENSITY ON THE SIZE OF ITS PARTICLES AND HYDRAULIC PRESS COMPACTION PRESSURE

Oleh Bereziuk — 2026-02-05

In the process of timber processing large volume of waste products is formed, they constitute more than 17 % of energy potential of biomass in Ukraine. This enables to obtain annually while their usage energy effect equivalent to burning more than 1.5 mil. tons of coal. The paper contains the results of the determination of regression dependence of the sawdust density on the size of its particles and pressure, performed by the hydraulic press by means of rotatable central compositional planning of the experiment, using Wilson-Box method of the second order. Adequate regression dependence of the sawdust density on the size of its particles and hydraulic press compaction pressure is obtained. Adequacy of regression model was verified according to Fisher criterion and significance of the regression coefficient – by the Student`s criterion. The suggested mathematical model can be used for modeling the compaction process and for compaction drive design. It is established that according to Fisher criterion the hypothesis regarding the adequacy of the obtained regression model can be considered correct with 95 % validity. Correlation factor was 0.95829, this proves the sufficient validity of the obtained results. Using the Student`s criterion it was established that among the studied factors the hydraulic pressure exercises the greatest impact on sawdust density and the least impact – average size of sawdust particles. Response surface of the efficiency function – sawdust density in the plane of impact parameters is constructed, it enables to demonstrate the above-mentioned dependence.

COMPUTER SIMULATION OF THERMODYNAMIC PROCESSES FOR EDUCATIONAL PURPOSES

Volodymyr Bondarev — 2026-02-05

The paper describes simulation model of the ideal gas, constructed according to the laws of mechanics, applied to numerous simple objects. Objects of the study are perfectly elastic balls, having certain mass and size. Balls collide with each other and with the walls of the vessel elastically, i. e., without energy losses for plastic deformation. Calculation of the collisions follows from the laws of conservation of energy and momentum, this is necessary condition of model physicality.

Balls move in the discrete time, i. e., their coordinates and pulses change by jumps, that is actually numerical solution of differential equations of motion. Relation between the discrete time and real is determined by the frequency of the program mover and is within 10 to 100 cycles per second. Frequency of mover operation depends on the power of the processor and on the complexity of the investigated model. Gas model is 2D, this reduces the number of the necessary calculations to the acceptable value and enables to use model for creation of the interactive study guide.

On the base of the model the computer program is developed, it enables to simulate the laboratory installations and carry out the experiments. Installations consist of vessels, vessels with the pistons, heating and measuring devices. Experiments may cover wide spectrum of the phenomena, such as diffusion, Brownian motion, various kinds of heat capacity of gas, division of particles velocity, conversion of the thermal energy into mechanical, different thermodynamic cycles, etc.

Although computer simulation is not viable substitute of physical experiments, it is flexible and able to reproduce far more experiments than any school or institute laboratory. Computer model promotes the development of the experimental skills of the students and makes educational process more interesting and efficient.

STUDY OF THE METHODS OF TOURIST TRAVELS FORMATION

Oleksandr Dolganenko — 2026-02-05

Objective of the paper is the analysis of the methods of decision-making in the sphere of tourist travels planning. Aim of tourist travels is to get bright impressions and the correct choice of the site of the travel, well-planned route will certainly improve the impressions of the tourist trip. Goal of the given study is to improve the efficiency of users support while choosing the direction of the tourist travel and planning the sequence of the sites to visit by means of development the quality software in this field. For the development of the corresponding software it is suggested to use the combined decision-taking methods, which take into account individual features and advantages of the users. Methods, suitable for the solution of the given task were considered, these methods included linear additive convolution with normalizing factors and weight coefficients, combinatorics, travelling salesman problem. The improved algorithm of selection and planning of the tourist trips, which uses the combination of these methods for obtaining the best solution for the user was proposed. Experimental study of the suggested algorithm was carried out, the study enabled to verify its efficiency at all the stages. Experimental study was performed at various types of the input data and took into account different wishes and advantages of the users. For the formation of the datasets of the experiments different sources of data about cities, countries and tourist attractions were analyzed and compared. Algorithm was realized and integrated in the mobile application for Android with the possibility of expansion, the methodology of pure architecture was applied. The suggested solution can be integrated in other system of tourist sphere. By the results of the research the following conclusion can be made: the suggested improved algorithm and software solution, developed on its base, allows to take into consideration the advantages of the users and improve the experience of tourist travels planning.

BOOSTING METHOD OF HETEROSKEDASTIC MODELS FOR THE PREDICTION OF THE SAHARA DUST CONCENTRATION IN THE ATMOSPERIC AIR OF UKRAINE

Volodymyr Kopniak — 2026-02-05

The paper presents new method of heteroskedastic models boosting and its applied usage on the example of the Sahara dust concentration in the atmospheric air of Ukraine. Recently the increased frequency of fine dust transfer from the Sahara Desert across the Mediterranean sea on the territory of Europe, in particular – in Ukraine, is observed. This phenomenon complicates the prediction of atmospheric air quality as a result of destruction of the stable regularities of pollution, as new factors are added, they need special models for adequate description. Special meteorological mode of the Sahara Desert dust spread enables to assume that the dispersion of the remains of ARIMA model may be random process and for its description it is expedient to use heteroskedastic models, such as GARCH. However, the conventional GARCH-models are efficient only if one dominating random process is available. If several such processes are added, conventional models loose their efficiency.

In the given study the application of boosting approach for the construction of the assembly models is suggested, these models, unlike the available, comprise the cooperation of the decision trees and heteroskedastic models for modeling complex heteroskedastic processes. The suggested method, as it is accepted for the boosting models, is based on the iterative process of models selection, where the next model takes into account the errors of the previous model. For the verification of the efficiency of the method the data of civil monitoring of atmospheric air EcoCity were used, in particular, data regarding Vinnytsia region by PM1 index, which indicate the periods, when the concentration of the Sahara fine dust in the atmospheric air of the region reached especially abnormal values.

It was proved that the process of the Saharan dust spreading in Vinnytsia region is heteroskedastic. SARIMAX models and typical GARCH-models using Python-libraries statsmodels and arch are constructed. It is revealed that the model ARIMA demonstrates far better results as compared with classic
GARCH-models with different parameters, this shows insufficient efficiency of these GARCH-models. The suggested method of boosting heteroskedastic models allows to reach far greater accuracy than all these models in the whole range of values, except the value of the largest anomaly, this value is impossible to foresee. Thus, the forecasting method, developed in this research is an efficient approach for the solution of complex forecasting problems, the example of which is forecasting of the atmospheric air quality during the Sahara dust spreading in Ukraine.

HYBRID MULTIFACTOR AUTHENTICATION OF PEER-TO-PEER NETWORK NODES

Mykhailo Krentsin — 2026-02-05

Method of hybrid multifactor authentication of nodes in the peer-to-peer network is developed. Method includes the authentication both of initial nodes and secondary nodes (connected to the available network). Each node must first perform authentication by the server, as a result of the authentication it obtains the token of access to the server, communication taken (necessary for performing communication with the node), and service token (for the exchange of the service data with other nodes). Further the node must be authenticated by other node. For this purpose predefined identifiers, zero knowledge proof method and network of trust are. Knowing identifier of another user the node can be authenticated after passing verification by zero knowledge proof method in three stages. First it is verified that the node possesses the knowledge of the server address. Further the validity of token is verified by means of verification of the date of issuing a token (in this process, server, which provides date of issue by identifier participates). The last step is verification is if the node can correctly code certain data. For this purpose, pseudo-random sequence of numbers is generated, it must be coded by the server and node. Only server and node know the encryption key (in case of server authentication key is generated for each node). If all verification stages are successful, then the nodes exchange identification data and, thus, become mutually authenticated. By means of the network of trust, if two nodes are not mutually authenticated but are authenticated by the third node, then they can directly exchange identification data without passing the verification process by means of zero knowledge proof. The suggested method is directed to the increase of the security level of peer-to-peer networks. Important aspect is the possibility to cut off potentially harmful nodes before their actual connection to the network.

ANALYSIS OF THE TECHNOLOGIES OF WEB-APPLICATIONS PENETRATION TESTING

Leonid Kupershtain — 2026-02-05

The paper analyzes the technology of penetration testing, used for detecting the vulnerabilities in
web-applications. White box, grey box and black box methods are considered, each of these methods has its unique approaches and advantages in revealing the vulnerabilities . Standards OSSTMM, NIST, OWASP, PTES and ISAAF are considered in detailed, each of these standards provides its methodologies and recommendations for penetration test. For instance, OSSTMM, is international technology, which suggests the division into three main classes of safety and describes in details the procedures of preparation for testing. NIST is focused on planning, execution and post-operation, underlying the importance of collecting information at planning stage. OWASP stresses the need of the safety testing at each stage of the software development, PTES gives practical recommendations regarding each of seven stages of the penetration test. ISAAF suggests a three-phase approach, including planning, testing and formation of the report. Besides, the paper studies the frameworks Mitre ATT&CK, CIS Controls and Cyber Kill Chain, which help the organizations understand and counteract the cyberattacks. Mitre ATT&CK is known for its wide coverage of attacks and deep analysis of the tactics and methods of the attacks. CIS Controls is concentrated on specific security controls, which can be directly applied for systems protection, and Cyber Kill Chain provides structural approach to the analysis and prevention of cyber attacks. The paper also contains recommendations, regarding the implementation and usage of modern penetration testing techniques for the improvement of the information systems security. Results of the research can be useful for cybersecurity specialists and developers of web-applications, they will help understand better and implement the efficient methods of cybersecurity.

COMPUTER PROGRAM FOR AUTOMATIC DESIGN OF THE DIAMETRICAL ULTRASONIC FLOWMETERS

Vitaliy Roman — 2026-02-05

Paper highlights another stage of global scientific-practical objective of the authors – development of computer system of automatic design of ultrasonic flowmeters of all available types. For the base of the current stage authors used previously developed computer program for automatic design of multi-channel chord ultrasonic flowmeters Auto Design USM, to which two new functional possibilities are added –calculation of hydrodynamic error of the diametrical single channel single beam ultrasonic flowmeters and calculation of the correction factor on the profile of the flow, which must eliminate this error of flow measuring. To reveal the essence of the added functional possibilities the authors in the given paper theoretically substantiate the emerging of the hydrodynamic error in the diametrical single channel single beam ultrasonic flowmeters
(it may achieve more than 30 % for laminar and 8 % for turbulent modes of measured flow motion) and available methods of obtaining the correction factor on the profile of the flow ( known empirically obtained analytical dependences or using certain theoretical profile of the flow rate and its numerical integration). As a result of the research carried out the authors of the paper improved the computer program Auto Design USM, this enables the user to apply it in console form for automatic design of the diametrical single channel single beam ultrasonic flowmeters. At the input such program requests the user the value of Reynolds number (indicates the rate of the flow), at the output it allows to obtain the value of Nikuradze number, correction factor on the profile of the flow by four empirical analytical dependences and value of the hydrodynamic error of the diametral ultrasonic flowmeter. The paper formulates the conclusions where further stages of the work on the given subject for achieving the global scientific-practical objective, aimed at the development of the system of automatic design of ultrasonic flowmeters are outlined.

CHARACTERISTIC FEATURES OF AUTOMATED PARKING SYSTEMS IMPLEMENTATION IN LARGE CITIES

Igor Polishchuk — 2026-02-05

Paper considers main problems, dealing with the motor vehicles parking in large cities and organization of the correct urban planning, the analysis of the available automatic parking is carried out, disadvantages of their implementation are characterized. Most efficient systems of automation which need large budget investments for their realization, are determined.

Various approaches, aimed at achieving the compromise between high cost for the parking space at automatic parking and level of comfort and time saving they provide, are considered. Possible variants of loyalty programs application for increasing the demand for automatic parking usage are presented. Approaches for studying the demand and optimization of losses while designing the automatic parking, using module structures in the process of construction are noted.

Variants of creation and usage of common parking, with the possibility of parking spaces transfer between the users are described. Architecture of the automatic parking system, based on creation of the services for the collection, storage and processing of the information in the cloud environment is suggested in the paper. The system provides the application of the data lakes for storing of large volumes of the raw information from the smart sensors indicating available free parking spaces and videocams for monitoring the transport vehicles at the parking. Data processing is performed by the specialized cloud services, which have the possibility of scalability, depending on the number of system users. Processed data are used for the forecasting of parking load, situational awareness of the drivers by means of mobile application as well as for the assistance in planning the route to free parking space with the help of drone assistants. Architecture of the system of automatic parking enables to construct modern infrastructure of parking in large cities, improve general comfort of private transport vehicles usage. Accumulated data, stored in cloud storages, can be used for further modeling and analysis of the demand for automatic parking.

DYNAMICS OF TICK-BORNE ENCEPHALITIS MORBIDITY IN VINNYTSIA

Oleh Bereziuk — 2026-02-05

One of the most widely spread diseases is tick-borne encephalitis. Most frequently the growth of tick-borne encephalitis cases are connected with the intense activity of these parasites in the period from April to September. Tick-borne encephalitis is spread in all the countries of the world and the morbidity level is within the 300 to 500 cases per hundred thousand population.

The object of the study in the given research is tick-borne encephalitis incidence in Vinnytsia, this disease is one of the most common viral disease. Determination of the regression dependence, describing the dynamics of tick-borne encephalitis incidence of the population in Vinnytsia is relevant scientific-engineering problem. Objective of the research is determination of the regression dependence, which describes the dynamics of the tick-borne encephalitis incidence of the population in Vinnytsia, this dependence can be used for the prediction of the incidence rate of the disease. In the course of the study method of regression analysis of the results of single-factor experiments and other paired dependences with the selection of the rational type of function from sixteen most widely used variants by the criterion of maximum value of the correlation factor was used. Regression was carried out on the base of linearized transformations which enable to reduce non-linear dependence to linear one. Determination of the coefficients of regression equations was performed, applying the method of least squares by means of the developed computer program "RegAnaliz", protected by the Certificate of the State registration of the rights to the copyright object. Adequate regression power dependence, describing the dynamics of the tick-borne encephalitis incidence of the population in Vinnytsia was obtained, the dependence can be used for the prediction of the incidence rate of the disease. Graphic interpretation of the dependence, describing the dynamics of tick-borne encephalitis incidence of the population in Vinnytsia was constructed, it enables to illustrate this dependence and show the sufficient convergence of the theoretical results with actual ones.

BASES OF BIPYRAMID

Anzhelika Motailo — 2026-02-05

Research is devoted to the study of functions interpolation, applying the method of finite elements in the area of quadrilateral b bipyramid. Main task of the study is to obtain general formula of finite-element basis of bipyramid and analysis of approximation properties of basis functions on this polyhedron.

In the given study bipyramid is considered as a finite element, obtained from the regular octahedron as a result of linear deformations of its semi-axes. Depending on the number of directions of deformation bipyramid may have one/two/three moving nodes. Such method of bipyramid formation is the result of adaptation of gratings of tetrahedrally-octahedral structure to the boundaries of areas, which have complex geometric form.

The paper contains general formulas for the bases of bipyramid with six and seven interpolation nodes, which are parametric functions of three variables. Values of parameters correspond to the elongation compression factors of the semi-axes of bipyramid and weight coefficient for six-node basis functions.

For the functions of bipyramid bases with seven and six interpolation nodes geometric properties of functions which are associated with the vertices of a polyhedron, are studied. The given functions are presented by the surfaces of zero level. Dependence of the type of surface on the value of parameters of bases functions of bipyramid is determined.

Approximation properties of seven node base of bipyramid functions are investigated in the paper. Quality criterion of approximation minimal trace of the stiffness matrix on a polyhedron is chosen. Critical values of elongation /compression parameters of bipyramid semi-axes which deliver minimum functionality to the trace of the stiffness matrix of bipyramid with seven nodes of interpolation are found. Additionally interval assessments for the parameters of seven node base function of bipyramid are obtained, they determine the boundaries of finite element deviation in the form of bipyramid from regular octahedron.

Perspective of further studies is mathematical substantiation of bipyramids application in the method of finite elements, determination of quality indices of bipyramid, used in the systems of finite-element analysis for asymmetric 3D-elements, obtaining of cubature formulas.