Naukovi notatky

OPTIMAL CONSTRUCTION OF MATHEMATICAL TABLES AND DETERMINANTS OF MATRICES IN THE LATEX SYSTEM

H.M. Hubal — 2025-02-12

In this article, optimal construction of mathematical tables and determinants of matrices in the LaTeX system is carried
out. New macros are created that construct mathematical tables in which the values of the first row are automatically filled and
conditional printing of the values of the second row is carried out; write the inputted matrices into memory and output the
written matrices; generate matrix determinants by excluding a given row and a given column.

STUDY OF MECHANICAL PROPERTIES AND STRUCTURE OF BIOMPOSITS FILLED WITH CHOPPED STALKS OF CEREALS CROPS

O. Sadova — 2025-02-12

The article examines the compressive strength of biocomposite materials based on a glutinous matrix, which was
prepared with different ratios of components. Chopped stalks of grain crops are used as a filler for biocomposite materials. The
compressive strength of biocomposites was studied depending on the degree of drying of the composition. Additional heat
treatment of biocomposites was carried out in order to increase the mechanical properties of biocomposites. The impact strength
of biocomposites is determined depending on the content of the filler, the degree of drying of the composition, the pressing
pressure of the composition and the additional heat treatment of biocomposites. Analysis of the structure with the detection of
functional groups of biocomposites was investigated by IR spectroscopy.

RESEARCH ON AUGMENTED REALITY TECHNOLOGIES IN TECHNICAL SCIENCES: PRACTICAL APPLICATION

Y. Maksymiuk — 2025-02-12

The relevance of the study is determined by the need to optimize technical processes through augmented reality (AR)
technologies, which enhance productivity, accuracy, and efficiency. The aim is to evaluate the impact of AR on technical
processes and develop recommendations for its integration. Methods include literature analysis, modeling of economic effects,
and applied calculations. The results demonstrate that AR reduces task completion time, lowers costs, and improves product
quality. The conclusions emphasize the need for standardization, personnel training, and pilot projects to ensure effective AR
integration.

TRANSFORMATION OF FREQUENCY DISPERSION IN ELECTRICAL PARAMETERS OF LIVER TISSUE DURING MEASUREMENT WITH INVASIVE ELECTRODES BASED ON DISTANCE BETWEEN ELECTRODES

T.V. Pryjmak — 2025-02-12

This study investigates the spectra of electrical impedance in biological tissues (pig liver samples) depending on
experimental conditions. Nyquist plots were obtained using a two-electrodeconfiguration with invasive electrodes by using
different distances between them. Optimalequivalent electrical circuit models of the studied systems were obtained and
processed, and thecomponents of their parameters were calculated. Changes in the frequency dispersion of electrical parameters
were demonstrated. The study concludes on the interdependence of the electric field intensity, the frequencies which were used,
location of the electrodes in the sample, and the ability of impedance spectroscopy to differentiate the state of biological tissue
damage based on its electrical properties.

ОБҐРУНТУВАННЯ ПАРАМЕТРІВ ВІБРАЦІЙНОГО КОНВЕЄРА ДЛЯ ЗАВАНТАЖЕННЯ АВТОМАТИЗОВАНОГО ОБЛАДНАННЯ СИПКИМИ ПРОДУКТАМИ

O.V. Gavrylchenko — 2025-02-12

The paper considers a vibrating conveyor with an elliptical trajectory of vibrations of the conveying surface for loading
automated equipment with bulk products. A dynamic model of the conveyor with three working masses, which are assigned
different transportation speeds, is developed.

MANUFACTURE OF FILAMENTS FOR 3D PRINTING FROM ABS PLASTIC REINFORCED WITH BASALT FIBERS

K.S. Shevchuk — 2025-02-12

This article discusses the process of manufacturing filament for 3D printing from ABS plastic reinforced with basalt
fibers. ABS was extruded from 10wt.% basalt fibers, which made it possible to obtain a composite material for FDM printing
technology. The analysis showed a uniform distribution of fibers in the matrix. Problems related to the fragility of the filament
and its poor adhesion to the platform during printing have been identified. The parameters of the 3D printer for printing
complex shape parts were optimized.

TiO2-BASED NANOCOMPOSITES FOR PHOTOCATALYTIC DEGRADATION OF ORGANIC DYES

L.I. Nykyruy — 2025-02-12

This review focuses on nanocomposite photocatalysts as effective materials for the removal of organic dyes from water
(including Congo Red, Methylene Blue, Methyl Orange, Rhodamine B and others). Nanocomposite photocatalysts are
structured porous materials capable of floating on the water surface and absorbing sunlight to activate chemical reactions. The
review outlines the principles of photocatalyst action in processes such as the degradation of organic compounds, prevention of
biological contamination, and self-cleaning of water surfaces. This review emphasizes the importance of further research and
development of nanocomposite photocatalysts to enhance their efficiency and expand their application in water purification.

JUSTIFICATION OF THE PARAMETERS OF A VIBRATING CONVEYOR WITH INDEPENDENT OSCILLATIONS FOR THE TRANSPORTATION OF PRODUCTS AND MATERIALS

O.V. Gavrylchenko — 2025-03-03

The paper considers a vibrating conveyor with independent normal and longitudinal vibrations of the conveying tray, provides calculations of the elastic system, which ensure stable operation of the conveyor and high transportation speed, as well as the results of experimental studies of the dependence of the transportation speed of products made of different materials on the parameters of independent vibrations.

OPTIMIZATION OF THE COLD ISOSTATIC PRESSING PROCESS OF MAGNESIUM POWDERS AND ITS ALLOYS

V. Sheremet — 2025-03-03

The regularities of the formation processes of magnesium powder alloys using the cold isostatic pressing (CIP) method followed by sintering have been investigated. The study was conducted at various pressing pressures (100–400 MPa) using CIP and uniaxial pressing methods for comparison. The results indicate that CIP provides higher uniformity of compaction due to isotropic compression, in contrast to uniaxial pressing, which suffers from anisotropy and uneven compaction. The mechanisms of mechanical and chemical contact formation between particles in magnesium-based alloys, particularly Mg-20wt.%WE43-10wt.%ZK61, were identified. It was shown that the activation of magnesium slip systems under isotropic compression leads to material flow and densification. It was established that during CIP, diffusion processes of mass transfer are accelerated due to an increase in the contact area between particles, contributing to the formation of a denser microstructure after sintering.

INFLUENCE OF THE INTERNAL STRUCTURE AND DIMENSIONS OF TYPICAL NOZZLES ON THE CUTTING PRESSURE FIELD OF THE ASSISTANT GAS IN GAS LASER CUTTING

V.I. Osypenko — 2025-03-03

This paper presents the developed equipment and methodology for studying the aerodynamic interaction between the assist gas jet and the surface of a workpiece. This interaction forms cutting pressure, which plays an important role in gas laser cutting technologies. Air and nitrogen were used as the assist gases. The results of a systematic set of experimental studies of the regularities of the influence of the internal structure and geometric dimensions of nozzles, gauge pressure inside the nozzle, the gap size between the nozzle tip and the workpiece on the formation of the jet geometry, and the cutting pressure in an arbitrary jet cross section are presented. The obtained data can serve as the basis for the efficient design of gas laser cutting processes for maximum productivity by accurately predicting the cutting pressure that the gas jet of the selected nozzle will create under specific technological conditions.

SEARCH OF THE RATIONAL PROFILE OF THE CUTTING EDGE OF THE KNIFE OF THE CUTTER OF PLASTIC VISCOUS MATERIALS

V.I. Osypenko — 2025-03-03

The article is dedicated to the study of the plastically sticky stuff cutting process and search of the profile for a cutting edge to comply with all the technical demands and supply efficacy and reduction of energy while cutting process. The dependence on a working and a constructive angle of the knife sharpening while sliding is calculated. There was calculated the appropriate profile of the cutting edge of the knife that supplies the reduce of the working angle of sharpening to constructive one. This provides the reducing strength of materials and energy consumption.

DEVELOPMENT OF METHODS FOR ANOMALY DETECTION IN WEB APPLICATIONS USING DATA MINING TECHNIQUES

V. Yakovets — 2025-03-03

The article addresses the issue of automated anomaly detection in web applications amid increasing system complexity and data volumes. Three algorithms were developed and experimentally validated to enhance the accuracy and speed of anomaly detection. It was established that the time correlation module demonstrates the highest accuracy, the adaptive threshold monitoring ensures rapid response, and hybrid clustering offers balanced performance. Key implementation challenges, including computational complexity and the need for model adaptation, were identified. Recommendations for integrating the algorithms into monitoring systems were proposed, and prospects for developing optimized methods and exploring new types of threats were outlined.

MANAGEMENTAND QUALITYCONTROL IN PRODUCTION IN THEMANUFACTUREOF HOUSING TYPE PARTS

V.M. Franchuk — 2025-03-03

The paper presents an analysis of existing quality management and controlsystems in the production of housing-type parts. The UCF 208 type housing wastaken as a sample for analysis, and its manufacturing process was examined, including potential errors at each stage. The most effective techniques that can assist solve these issues were identified, specifically SPC, LIMS, ZQS methods, as well as the use of computer vision and AI-based inspection systems. The proposed approaches improve the manufacturing process by preventing defects in the production of housing-type parts.

DEVELOPMENT OF MODERN INDIVIDUAL SAFETY SYSTEMS WHEN WORKING WITH CUTTING EQUIPMENT IN THE GARMENT INDUSTRY

V.V. Gerasimov — 2025-03-03

One of the main risks that arises when working with light industry equipment is injury from moving machine parts. Many sewing machines have moving parts that can lead to serious injury if the worker does not use them carefully or if the machine is not properly maintained or if there is a human factor of inattention to a particular operation. The latter is particularly dangerous when cutting materials on a draw frame. This situation becomes a particular problem when, as usual, less qualified workers start working on this rather dangerous technological operation instead of experienced male staff which is caused by the peculiarities of the enterprise's operation during martial law. In order to prevent the worker from being injured by a cutting tool while performing technological operations, the development of an individual hand protection device with the involvement of modern digital technologies have been proposed by authors. The main approaches to the manufacture of the protection device and propose basic circuit solutions that allow implementing the protection system in its final form have been analysed. The emphasis is placed on the protection device, the design of which can be implemented on a common and affordable element base. The authors also envisage expanding the capabilities of this security device by adapting other additional functional and technological options to it, which increases its efficiency and competitiveness.

EVALUATION OF THE INFLUENCEOF THE PARAMETERSOF THE CLAMPING CONVEYOR OF THE REABILITY OF STRAND CLAMPING

Y.V. Muravynets — 2025-03-07

In the article, the influence of the parameters of the pressure conveyor on the reliability of the compression of raw material strands in its channel was evaluated, and mathematical relations were obtained that allow determining the influence of the parameters of the pressing cylinders of the conveyor on the external pulling force of the strands. duct during heating operation.

DIRECTIONS FOR IMPROVING THE DESIGNS OF PLANER MACHINES

V. Zavarynskyi — 2025-03-07

The analysis of the schematic diagram of a planer machine has been presented, identifying the main mechanisms that influence processing accuracy. The designs of the feeding mechanisms of planer machines, the work piece clamping mechanisms, and the new cutting tool design have been analyzed. The main advantages and disadvantages of these designs have been established, and suggestions for their further improvement have been proposed.

COMPARISON OF RESOURCE-SAVING INDICATORS OF THE MICROPROCESSOR BASED MAGNETIC- PULSE UNIT AND EXISTING ELECTROHYDRAULIC PRESS EQUIPMENT WHEN CUTTING PARTS FROM TEXTILE MATERIALS

R. Rosul — 2025-03-07

The article deals with the comparison of the technical and economic indicators of the magnetic pulse installation and the existing electro-hydraulic press equipment. Taking into account the results of the research, magnetic pulse press equipment was developed and designed to perform technological operations in light industry. According to the results of experimental studies , it was established that at speeds of 4...7 m/s, the cutter can be immersed in the material to a depth of 0.7...0.9 of its thickness . As a result of the review of technical and patent literature, it was established that there is no consensus among scientists regarding the impact of tool speed on the cutting effort. These speeds can be achieved using press equipment with an electromagnetic motor and on magnetic pulse installations. In order to determine the technical and economic indicators of the magnetic pulse installation, a part made of natural soft leather with a thickness of 0.8 mm was cut. cutter with the maximum possible perimeter L=150 mm.
A system of well-known objective criteria was used to assess the achieved technical level of the magnetic pulse press, as well as to compare its technical and economic indicators with hydraulic press equipment. Calculation of the coefficient, which takes into account the energy consumption of the press per 1 linear mm of the cut part, was carried out experimentally. The essence of this coefficient was that the electrical energy consumed by the press equipment was determined experimentally using an electrical energy meter and compared with the electrical energy consumption of the magnetic pulse installation. As a result of the calculations, the energy consumption in each case was: for the PVG-8-2-0 press – 1.1•10 6 J; for MIU- 1.22•10 4 J. Then the energy consumption coefficient was 6.5 and 0.22, respectively. In addition to the given well-known objective criteria for assessing technical and economic efficiency, the technological cycle of the operations considered in this work should be analyzed to compare the performance indicators of the use of magnetic-pulse press equipment and electro-hydraulic press PVG-8-2-0. It has been established that when performing technological operations (TO) of cutting parts from textile materials on press equipment with a magnetic pulse unit (MIU), it is necessary to achieve the greatest possible correspondence between the effort created by the MIU and the technological effort of performing maintenance, which will lead to a significant saving of electricity by account of its discrete consumption.

EFFECT OF CHARACTERISTICS OF INITIAL POWDERS ON VELOCITIES OF ELASTIC WAVES PROPAGATION IN REACTION-SINTERED SiC-Cr3C2 COMPOSITES

O.V. Talko — 2025-03-07

Using the technology of reactive sintering of powders, composite ceramic materials based on silicon carbide of two modifications with an average particle size of 70 nm and 28 μm were obtained, containing in the charge from 3 to 10% (wt.) of Cr3C2 powder particles with an average particle size of ~0.2 μm. The influence of the Cr3C2 content and the size of silicon carbide particles on the regularities of change in the propagation velocities of longitudinal and transverse elastic waves, disturbed by pulse acoustic techniques, were studied.

COMPARATIVE ANALYSIS OF QUALITY MANAGEMENT SYSTEMS AND SELECTION OF THE MOST EFFECTIVE SYSTEM FOR MACHINING PRODUCTION

V.M. Franchuk — 2025-03-07

The article examines modern approaches to quality management in the mechanical engineering industry, in particular, Six Sigma, 5S and Total Quality Management (TQM) methodologies. The article analyses their effectiveness in improving the accuracy, reliability and productivity of production processes, as well as their impact on reducing the level of defects and optimizing costs. The practical experience of implementing these methods in leading companies such as Toyota, General Electric and Motorola is considered. It is determined that the combination of TQM, Six Sigma and 5S provides a systematic approach to quality improvement, increases production efficiency and contributes to the long-term success of enterprises.

INTERRELATION BETWEEN TOOTH STIFFNESS AND FEED RATE OF A FRAME SAW TOOTH

Z. Sirko — 2025-03-07

The accuracy and quality of lumber requires the use of modern equipment with wood-cutting tools of the required rigidity. The stability of the tool in the cut depends on the stiffness of the saw blade, which directly affects the quality of the machined surfaces. That's why wood cutting tools are made of special tool steels, in which alloying elements affect the physical and mechanical properties of the steels, in particular their stiffness. The stiffness of the saw tooth and the saw as a whole is influenced by the cutting forces, especially the lateral cutting force, which tends to bend the tooth and thus reduce the accuracy and quality of the cut. In turn, the cutting forces depend on the feed to the tooth, and the higher the feed to the tooth, the higher the cutting forces. Therefore, it is very important to establish the relationship between tooth stiffness and tooth feed to ensure high productivity of the sawing process and proper accuracy and quality of the machined surfaces.

DYNAMIC ELASTICITY AND ELECTRICAL RESISTIVITY OF REACTION-SINTERED NANOSIZED CERAMICS SiC-TiC

O.V. Vdovychenko — 2025-03-07

Using the technology of reactive sintering of nanosized powders, composite materials based on silicon carbide, containing in the charge from 1 to 8% (wt.) of titanium carbide powder particles were fabricated. The influence of the TiC content in the charge on the regularities of changes in the electrical resistivity and dynamic elastic moduli of composites, determined from the results of acoustic measurements of the propagation velocities of elastic waves of various types using pulsed and resonant methods, was investigated.

ENERGY MANAGEMENT IMPLEMENTATION SYSTEM AT THE ENTERPRISE

Z. Sirko — 2025-03-07

The article highlights the issues related to energy efficiency, which is an urgent problem for Ukraine. The author shows that Ukraine is currently facing the issue of stable energy supply and efficient use of energy resources. The rise in prices for fuel and energy resources has led to the search for ways to use them economically or replace them with alternative energy sources. Energy independence and energy efficiency of an enterprise is a key factor in achieving its successful operation. New approaches to the implementation of energy efficiency policy are now needed, and one of the ways to achieve this is through energy management at the enterprise. In today's business environment, energy management will provide a practical solution to the company's problems, a certain balance in the supply of fuel and energy and other material resources.

AN EQUATION RELATED TO THE RIEMANN PROBLEM WITH A RATIONAL COEFFICIENT THAT IS INVERTIBLE IN ONE OF THE SUBRINGS OF A FACTORIZATION PAIR

T.G. Voytik — 2025-03-07

We report the results of a continuation of the study on the solvability of an abstract equation involving two rational functions from subrings. By the equation can be describe the boundary conditions of a problem related to the Riemann (Riemann-Hilbert, Riemann-Hilbert-Privalov) boundary value problem in the theory of analytic functions. We consider the case when the coefficient is a rational function belonging to one of the subrings of a factorization pair of the ring and is invertible in this subring. The equation is solved in the entire complex plane, and the boundary condition is obtained by restricting it to the closed real axis. We employ an approach that is distinguished by its algebraicity and simplifies the proof. This approach combines fundamental principles of ring theory and functional analysis, the theory of linear operators, and equations in rings with factorization pairs. A theorem on existence and uniqueness is established, along with general formulas for the desired solutions. An illustrative example is provided. The method used avoids the theory of Cauchy and Fourier-type integrals, the requirement of function Holder’s and the concept of index.

A WAY TO GENERATE ELECTRICITY FROM TREES AND SOLAR RADIATION

Z. Sirko — 2025-03-07

The article highlights issues related to generating electricity from trees and solar radiation. It is emphasized that this topic is still poorly understood, but has great prospects as an alternative source of renewable energy. It is shown that at this stage, the energy efficiency of enterprises is of great importance. Rising prices for fuel and energy resources determine the ways to save them or replace them with other alternative sources. In order to select and implement energy efficiency measures at an enterprise, it is necessary to thoroughly study the actual state of use of fuel and energy resources and determine the potential for energy saving measures based on the main technological facilities available at the enterprise. It is noted that it is advisable to improve the energy efficiency of enterprises by introducing alternative sources of renewable energy, one of which is a method of generating electricity from trees and solar radiation.

RATING OF SAWS BY QUALITY AND MANUFACTURING ACCURACY BASED ON STATISTICAL CHARACTERISTICS

Z. Sirko — 2025-03-07

The article highlights the issues related to the properties of circular saws, in particular the accuracy of their manufacture and subsequent sharpening. Wood-cutting tools must ensure high labor productivity and product quality, which depend on their durability and resistance to wear. The properties of circular saws from well-known foreign manufacturers were evaluated for compliance with their regulatory and technical documentation, the accuracy of manufacturing and sharpening of flat and trapezoidal teeth, composite technical and economic indices, and ultimately an integral indicator that combines all of the above technical and economic indicators. In a new circular saw, the carbide blades must have the same overhang to the left and right of the blade. If this rule is violated for various reasons, the accuracy and quality of the cut decreases during sawing, chips and other defects are observed, which ultimately negatively affects the tool's properties.

CAD MODEL CORRECTIONS TO OPTIMIZE 3D PRINTING PROCESSES

S. Myskovets — 2025-03-14

The paper considers issues of improving the quality and functionality of products obtained using FDM printing
technologies. Based on studies of the influence of geometric parameters of digital models on the quality of forming parts, a
method of correcting their configuration at the stage of their preparation is proposed.

VIRTUAL RECONSTRUCTION OF HISTORICAL BUILDINGS USING 3D COMPUTER GRAPHICS

I. Burchak — 2025-03-14

This work is devoted to solving the scientific and practical problem of preserving the historical heritage of Ukraine. As
of today, there are many ways of museification of historical buildings, among which external museification is a mechanism for
transforming a historical complex into an open-air museum, regardless of the state of preservation or the presence of a museum
exposition. In fact, the monument acts as a museum object and is considered the main, and often the only, exhibit. The virtual
form of museification is modern information animation technology, which makes it possible to create 3D models of historical
buildings, restore the original architectural appearance and represent materials about the monument in an interactive
environment, which improves the visual perception of the object.
The work is multidisciplinary, it affects history, art, architecture, construction, and its most comprehensive part is
computer, multimedia technologies and computer graphics.
The paper analyzes modern types, forms and directions of museification of historical buildings. A computer
implementation of a 3D image of the Church of the Exaltation of the Holy Cross in Lutsk is proposed

OPTIMIZATION OF DIGITAL TWINS OF FESTO MODULAR PRODUCTION STATIONS

S. Myskovets — 2025-03-14

The paper considers the issues of creation, implementation and optimization of digital twins of FESTO modular
production stations. By means of modeling, the operation of the software and hardware part of the production center for the
assembly of a valve block based on FESTO work under the control of the Siemens SIMATIC S7-1500 PLC was investigated.

OPTIMIZATION OF THE REGIME OF CONTACT WELDING OF SHEET STRUCTURES BY THE METHOD OF MULTIFACTOR EXPERIMENT PLANNING

V. Kashytskyi — 2025-03-18

The influence of technological parameters of the process of contact welding of sheet structures on the strength of the welded joint was studied. The boundary conditions and the variability of the combination of different factors on the ability to form a high-quality and strong welded joint were determined. A mathematical model for finding the optimal values of the shear strength of the welded joint of sheet structures by the method of gradient descent along the response surface was developed. The optimal mode of the process of contact welding of steel sheets of a certain thickness was established.