“Naukovi Notatki” is a peer-reviewed, open-access journal (Category B) that publishes review articles and the results of original fundamental and applied research in the field of “Mechanical Engineering and Machine Building.” Scientific papers are published in the following specialties: G8 Materials Science; G9 Applied Mechanics; G11 Mechanical Engineering (by specialization)
Луцький національний технічний університет
TO DETERMINATION OF DEFORMATION CHARACTERISTICS OF GLUE-LAIMED PINE AND SPRUCE WOOD AT DIFFERENT HUMIDITIES IN THE PRECRITICAL AND POSTCRITICAL STAGES OF WORK: EXPERIMENTAL STAGE
Solid and glued wood is often operated in environments with different humidity levels. Current regulatory documents limit such operation to the Kmod coefficient. In some cases, it is unclear how to determine certain mechanical characteristics with increased moisture content, including deformable ones. For example, the operation of elements in bridge structures, hydraulic structures, sea piers, shore protection structures, and others. Very often, materials, elements, and structures based on wood operate in a post-critical stage of operation (seismic vibrations, dynamic loads, progressive destruction, floods, changes in water levels, and others). The purpose of our research is to conduct experimental studies of structural glued laminated wood of pine and spruce with different moisture content under a strict regime of axial compression tests along the fibers during operation in river and marine aquatic environments. As well as to establish the main deformation parameters in the pre-critical and post-critical stages of operation under such operating conditions. Experimental studies of structural glued pine and spruce wood of different humidity after immersion in river and sea water environments by axial compression along the fibers under a rigid test regime were carried out. The main mechanical characteristics of glued pine and spruce wood in the pre-critical and post-critical stages of operation were experimentally established, including the temporary ultimate strength of wood, the modulus of elasticity, relative critical, limiting and residual deformations, under such operating conditions. Formulas were proposed for determining the relative limiting deformations of structural glued wood at different humidity. The main deformation characteristics of glued pine and spruce wood, both in river and sea water environments, relative critical, limiting and residual deformations were established. At humidity levels of 21% and 30%, they increase in comparison with the characteristics determined at a standard humidity of 12%.
INVESTIGATION OF HYDRODYNAMIC AND GAS DYNAMIC PROCESSES IN A CLOSED BYPASS CHANNEL WITH A RECTANGULAR CROSS-SECTION OF VARYING ASPECT RATIOS
The article addresses a scientific and applied problem of determining the hydrodynamic and gas dynamic characteristics of flow in closed channels with a rectangular cross-section. It is substantiated that classical analytical relations based on the Hagen-Poiseuille law are valid exclusively for channels with a circular cross-section, whereas in real engineering systems, rectangular or more complex geometries are predominant. The study presents an analytical investigation of laminar flow of liquids and gases in a rectangular channel based on the Navier-Stokes equations. For the rectangular channel, the solution was constructed using the method of expansion in trigonometric series, which allows proper consideration of boundary conditions and the geometric characteristics of the flow domain. It was established that the flow capacity of the channel depends on the aspect ratio of its sides, with the extreme value of the corresponding coefficient being achieved for a square cross-section. The analytical results were verified through numerical simulations using MATLAB and SOLIDWORKS Flow Simulation. Functional dependencies of velocity and flow characteristics on the geometric parameters of the channel were constructed.
ULTRASONIC NON-DESTRUCTIVE STUDY OF REACTION-SINTERED SILICON CARBIDE MODIFIED WITH TUNGSTEN CARBIDE
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 tungsten carbide powder particles were fabricated. The influence of the WC content in the charge on the regularities of changes in the electrical resistivity and elastic characteristics of composites, determined from the results of ultrasonic measurements of the propagation velocities of elastic waves of various types using pulse methods, was investigated.
PREREQUISITES FOR TAKING INTO ACCOUNT MODIFICATIONS OF CONIFERS OF WOOD SPECIES IN CALCULATIONS OF TIMBER ELEMENTS AND STRUCTURES
The study highlights the methodology for considering the impact of softwood modification in the design of timber structures. Although timber is a widely used building material due to its environmental friendliness, low weight, ease of processing, high longitudinal strength and cost-effectiveness, it has limitations such as moisture sensitivity, anisotropy and natural defects that limit its structural application. Modification of timber with various composite materials improves the physical and mechanical properties of timber, improves moisture resistance and increases durability. Such types of modifications change the behaviour of timber structures and their stress-strain state, which is not taken into account in current design standards, which highlights the need to update design approaches. The study focuses on structural elements, including beams, columns and cross-laminated panels, where longitudinal strength largely determines the load-bearing capacity and stiffness. Traditional design includes characteristic and design values of compressive, tensile, and flexural strengths, as well as elastic and shear moduli modified by reliability factors. This paper presents the possibility of using experimental data when taking into account the modification of coniferous wood species. In this case, experimental values are used to determine modification factors that correct the design resistance to bending, compression, tensile, and elastic moduli. Formulas are given to illustrate the application of these factors under uniaxial bending and combined loading conditions. A methodology is proposed that allows for accurate consideration of changes in mechanical behavior due to processing with composite materials, providing an accurate assessment of the strength and improved serviceability of wooden structures. The introduction of these factors into structural calculations demonstrates that modification can significantly improve the performance and service life of wooden structures. This approach lays the foundation for incorporating modified wood properties into future design standards and provides engineers with practical tools for more reliable and durable wood construction designs.
CURRENT ISSUES OF STRUCTURAL TRANSFORMATIONS IN POLYMER COMPOSITE MATERIALS UNDER THE INFLUENCE OF PHYSICAL FIELDS: A REVIEW
The article analyzes the literature in the aspect of the formation of polymer composites under the influence of physical fields, which provide intensive structuring of the composition based on thermosets. The characteristics of physical fields and the features of structural transformations at the level of fine structure and supramolecular formations, which occur as a result of external energy influence, are presented. The positive influence of physical fields on the processes of structuring of polymer composite materials based on reactive polymers is proven, which is determined by the processes of ordering structural components and the formation of polymer composites with a low stress state and a high degree of structuring of the polymer matrix.
SPECTROPHOTOMETRIC METHODS FOR QUALITY ASSESSMENT OF BIOFUEL MATERIALS DERIVED FROM OIL FLAX STEMS: IMPLICATIONS FOR SUSTAINABLE DEVELOPMENT
The study is devoted to the development of a spectrophotometric methodology for evaluating biofuel materials produced from non-conditioned oil flax (Linum usitatissimum L.) stems. Solid biofuel briquettes with different ratios of flax biomass and sapropel binder (L70/S30, L50/S50, L100) and a control wood sample were investigated. Aqueous extracts of combustion residues were analyzed using spectrophotometry in the wavelength range of 200–1100 nm. The obtained transmission spectra demonstrated similar overall patterns for all samples, indicating comparable structural features of combustion residues. A pronounced minimum at a wavelength of 975 nm was identified for all investigated samples. This spectral feature is attributed to the second overtone of O–H stretching vibrations and reflects the presence of hydroxyl-containing compounds and bound water in the analyzed systems. Comparative analysis showed that the differences in transmission values between flax-based biofuels and the control wood sample do not exceed 3–4%, indicating a high degree of similarity in the chemical composition of their combustion residues. The use of sapropel as a binder does not significantly affect the overall spectral characteristics, although it increases absorption intensity due to higher mineral content. The results confirm the feasibility of using oil flax stem biomass for the production of solid biofuels and demonstrate that spectrophotometric analysis can be applied as a rapid diagnostic tool for assessing their quality and environmental safety.
FORMATION OF EPOXY COMPOSITES BASED ON RECYCLED FILLERS OF SYNTHETIC ORIGIN
A method of processing glass-fiber polymer composite materials by mechanical grinding with subsequent classification of particles and formation of epoxy composite samples is presented. An increase in the physical and mechanical characteristics of epoxy composite materials based on secondary raw materials, structured at a final temperature of 170°C, is determined. A decrease in the compressive strength and gel fraction content of the epoxy composite material as a result of introducing a filler into the composition in an amount of more than 200 wt. parts is established. However, the use of a filler in an amount of 600 wt. parts provides an increase in the impact strength of epoxy composites. The using of smaller particles of secondary raw materials improves processability of the composition and increases the compressive strength of epoxy composites.
DYNAMIC SYNCHRONIZATION OF INERTIAL VIBRATION EXCITERSBIHARMONY VIBRATION DRIVE
The possibility of obtaining stable biharmonic oscillations of a vibration machine with kinematically uncoupled inertial vibration exciters is considered. The dynamic synchronization of two pairs of inertial vibration exciters with multiple rotation frequencies is investigated. The problem is solved using the integral stability criterion (extreme property) of synchronous movements. Phase shifts in possible synchronous movements of vibration exciters, conditions for the existence and stability of synchronous movements are established. Formulas for vibration moments that ensure self-synchronization of vibration exciters are obtained. Theoretical results are confirmed by numerical modeling.
DATA-DRIVEN DISCOVERY OF BORON CARBIDE-LIKE MATERIALS USING OPEN COMPUTATIONAL MATERIALS DATABASES
This study presents a data-driven approach for identifying materials with similar properties to target compounds using open computational materials databases. We use boron carbide (B₄C) with specific boron-to-carbon ratios (0.78-0.91) as our test case material and develop a robust pipeline for data collection, processing, and analysis. Six clustering algorithms representing different methodologies and several feature engineering techniques are employed to group materials based on structural, energetic, and mechanical properties. Our methodology successfully identifies clusters with high concentrations of target boron carbide compositions and reveals other boron-containing materials with similar properties. This approach demonstrates the potential of leveraging open materials databases for accelerated materials discovery and provides a framework applicable to various material systems beyond boron carbide.
EFFICIENCY OF MICROSTRUCTURE ANALYSIS IN EVALUATING THE STRENGTH CHARACTERISTICS OF POLYURETHANE FOAMS
The paper presents a comprehensive approach to evaluating the strength characteristics of polyurethane foams (PUF) based on a combination of macroscopic testing and microstructure analysis. The study is founded on varying the weight ratios of the primary components—polyol and isocyanate—enabling the formation of test specimens with diverse topological parameters of the porous matrix. Numerical and graphical interpretation of the compression results was conducted using cyclic loading within the plastic deformation zone to identify the stages of cell failure. The influence of the formulation on the stability of the plateau stress and the nature of residual deformation accumulation in the cell walls and struts was investigated. A comparative analysis of the mechanical response for both traditional and modified PUF compositions was performed across variations in structural energy absorption. Through geometric modeling of a hexagonal network, the relationship between changes in cell face tilt angles and the macroscopic yield strength of the material was established. Effects of local stress concentration at microstructure nodes, which dictate the onset of stability loss in the porous framework, were identified. The study demonstrates the versatility of the developed approach for the predictive design of polymer compositions with predetermined performance properties for critical engineering structures.
APPROACHES TO TOPOLOGICAL DATA ANALYSIS FOR DETECTING ANOMALIES IN MULTIDIMENSIONAL DATA SETS
Abstract. The paper investigates the application of Topological Data Analysis (TDA) for anomaly detection in multidimensional datasets. The rapid growth of data volumes in modern systems – including IoT, financial monitoring, cybersecurity, and medical diagnostics – necessitates the development of robust methods capable of detecting structural anomalies in high-dimensional spaces. Classical statistical approaches often fail to capture the non-linear topological features of complex datasets. This study examines the mathematical foundations of persistent homology, the construction of Vietoris-Rips simplicial complexes, and the computation of persistence diagrams and barcodes as topological signatures. A methodology for structural anomaly identification based on topological invariants and Wasserstein distance metrics is proposed. Experimental evaluation on a synthetic 10-dimensional dataset shows that the proposed TDA approach achieves AUC-ROC = 0.951 and Precision = 0.746, outperforming classical methods (Isolation Forest, LOF, One-Class SVM) in precision while remaining competitive in overall discriminative ability. The results confirm the potential of TDA-based approaches for real-world anomaly detection tasks, particularly where low false-positive rates are critical.
PRESERVATION OF THE QUALITY OF AUTOMOTIVE GASOLINE DURING LONG-TERM STORAGE
The article highlights issues related to studies of the quality of automotive gasoline during long-term storage. It is noted that Ukraine has small reserves of petroleum products, in particular gasoline. Therefore, it is necessary to create minimal reserves, as is practiced in developed countries. The preservation of the quality indicators of gasoline during long-term storage and environmental safety during their transportation and storage is quite relevant. It has been shown that many factors affect the physicochemical parameters of gasoline during long-term storage: interaction with the structural materials of tanks, the influence of external factors, storage and transportation conditions, etc. Therefore, it is important to test automobile gasoline after long-term storage for compliance of its quality parameters with the requirements of the standard.
GAS GENERATOR BASED ON CARBON COMPONENTS OF INDUSTRIAL WASTE
The article highlights issues related to the creation of a gas generator, its design, technical data, technical and technological operating conditions. It is noted that the design of the gas generator differs from analogues in that it has two combustion chambers, in one of which the primary combustion of fuel with hydrolysis elements takes place and in the other the final combustion, where fuel gases (CO, CH4, C2H6, H, etc.) burn and environmentally friendly fuel gases are supplied to the heat consumer. To ensure efficient combustion of fuel and fuel gases, the design of the gas generator provides two dispensers - primary and secondary air supply. For effective operation, the gas generator is equipped with additional equipment: a fuel supply screw, air pressure fans and flue gas removal, control and measuring instruments and an automation system. The main parameters of the gas generator, its technological indicators, operating conditions are given.
technical and technological operating conditions
RESULTS OF RESEARCH ON THE STRESS STATE OF THE CRANKSHAFT OF THE RV GEARBOX
The paper presents research on the static stress state of a crankshaft and the limit value of yield stress, which is necessary for improving the design and material of a crankshaft.
DETERMINATION OF THE ACCURACY OF LIQUID PRODUCTS DOSING USING ENERGY-SAVING AUTOMATED EQUIPMENT
The article presents the results of research into the processes of dosing liquid products with different rheological properties using a volumetric dispenser, and also proposes the design of an automated energy-saving device for feeding liquid products to the dispenser.
NANOTECHNOLOGY IN ENERGY: ADVANTAGES, CHALLENGES AND PROSPECTS
Based on the study and analysis of advanced world research related to the possibilities of applying nanotechnologies, in the article we assessed the prospects for the development of the use of nanotechnologies in the energy sector. The application of nanotechnology opens up new broad opportunities for improving the efficiency, stability and environmental friendliness of energy systems. However, along with potential advantages, it also introduces certain challenges and risks related to safety, ecology and regulatory aspects.
STATISTICS OF CHARGE CARRIERS IN A DEGENERATE AND NON-DEGENERATE SEMICONDUCTOR
Electrons in the conduction band and holes in the valence band can be considered as an ideal Fermi gas. In semiconductors at not very low temperatures, the kinetic energy of electrons is greater than the Coulomb energy, so electrons can be considered as free. For an ideal Fermi gas, the probability of filling a state with energy E at temperature T is found using the Fermi distribution. For a degenerate and non-degenerate semiconductor, expressions have been found for calculating the concentrations of charge carriers, electrons in the conduction band, and holes in the valence band, when the position of the Fermi level is known. The expressions for the concentrations of electrons and holes are greatly simplified if the semiconductor is non-degenerate.
SYNERGETICS OF TECHNOLOGICAL PROCESSES: PHILOSOPHICAL AND TECHNOLOGICAL MODELING OF UNIVERSAL PRINCIPLES OF PRODUCTION
The article presents a philosophical and technological analysis of synergistic principles in the organization of production processes. It is demonstrated that the current stage of industrial development is characterized by the integration of digitalization, automation, and environmentally oriented technologies, which requires the search for universal approaches to production modeling. The feasibility of applying synergetics as an interdisciplinary methodology is substantiated, enabling the combination of theoretical concepts of self-organization and nonlinear dynamics with engineering models. Universal principles of technological processes — cutting, forming, thermal treatment, and assembling — are identified, and their cross-industry similarity is confirmed. Production systems are proposed to be viewed as open, multi-level, and adaptive structures capable of self-recovery. The strategic importance of the synergistic approach for the reconstruction of Ukraine’s industrial infrastructure is emphasized, particularly in ensuring flexibility, resilience, resource efficiency, and technological sovereignty.
ROLE AND DEVELOPMENT OF ENGINEERING ETHICS IN UKRAINE
The article examines the formation, current state and prospects for the development of engineering ethics in Ukraine. The role of educational institutions, professional codes and socio-historical events (in particular, Chernobyl) in the formation of the ethical consciousness of engineers is analyzed. An overview of existing ethical codes in Ukrainian engineering communities, practical challenges and recommendations for integrating ethical training into curricula and corporate practice are presented.
EXPERIMENTAL DETERMINATION OF EFFICIENT PROCESSING PARAMETERS AND ANALYTICAL MODELING OF LOW-CARBON STEEL LASER CUTTING WITH A12 KW FIBER LASER
The paper presents the results of an experimental study of gas-assisted laser cutting of low-carbon steels using a high-power 12 kW fiber laser in an oxygen environment. The research was carried out on sheet steel of various thicknesses using full factorial experimental planning methods. The relationships between the optimal laser power and the maximum cutting speed as functions of material thickness were determined. Based on the experimental data, analytical approximation dependencies were obtained and a generalized technological model describing the cutting process was proposed. The model links cutting speed with laser power and sheet thickness and demonstrates good agreement with experimental results. In addition, an energy analysis of the process was performed, showing a significant increase in energy efficiency with increasing material thickness due to the contribution of exothermic oxidation and improved heat localization in the cutting channel. The obtained results can be used to predict efficient technological parameters for industrial laser cutting of low-carbon steels.
IMPROVING THE RELIABILITY OF ROBOTIC MANUFACTURING SYSTEMS BASED ON FAULT DIAGNOSIS, PREDICTIVE MAINTENANCE, AND REAL-TIME MONITORING
The paper considers current approaches to improving the reliability of robotic and automated manufacturing systems based on fault diagnosis, predictive maintenance, real-time condition monitoring, and supporting automated infrastructure. The relevance of the study is determined by the increasing structural and functional complexity of robotic complexes, in which local defects of drives, reducers, bearings, sensors, or auxiliary subsystems may cause unplanned downtime and loss of process stability. The paper generalizes diagnostic, prognostic, and monitoring approaches and proposes a generalized structure of a reliability assurance system for a robotic complex that integrates physical subsystems, data acquisition, local diagnostic processing, IIoT-based data exchange, technical state analytics, and service decision support.
SIMULATION ANALYSIS OF RIGID INCLUSIONS INTERACTION IN PLATE ELEMENTS UNDER DYNAMIC LOADS
The paper presents a simulation analysis and numerical implementation of a methodology for investigating the dynamic interaction of rigid inclusions in infinite plate elements. The problem is solved based on the combined application of the boundary integral equation method and the theory of functions of a complex variable, which allows for effective modeling of welded joints as rigid heterogeneities. The numerical implementation of the proposed approach was carried out using the method of mechanical quadratures and collocation to solve systems of singular integral equations. A study of the influence of geometric parameters on the distribution of radial and hoop stresses in the vicinity of a system of two inclusions was performed. A comparative analysis of the dynamic stress state for cases of identical and different inclusion lengths under varying frequencies of the external load was conducted. The effects of mutual shielding and reinforcement of local stress fields depending on the topology of the elements' arrangement were established. The versatility of the developed approach for assessing the strength of thin-walled structures with complex inclusion systems is demonstrated.
SELECTION OF CAST IRON WELDING METHOD FOR REPAIR AND RESTORATION OF AUTOMOTIVE COMPONENTS
The study investigates the features of cast iron welding without preheating, which can be applied in the repair and restoration of automotive components. The relevance of the topic is determined by the inherent difficulties of welding cast iron due to its brittleness, susceptibility to cracking, and the formation of hard structures in the heat-affected zone. An analysis of existing cast iron welding methods was carried out, demonstrating that the use of specialized electrodes and optimized welding parameters can significantly improve the quality of welded joints. Experimental studies were performed on gray cast iron samples obtained from an engine exhaust manifold. Welding was carried out without preheating using three types of electrodes: TsCh-4, MNCh-2, and UTP-8. The quality of the welded joints was evaluated through tensile testing on an MR-100 testing machine, with each sample tested five times followed by the determination of the average fracture load. The obtained results made it possible to objectively assess the mechanical properties of the welded joints. A strength analysis of butt welded joints was conducted, showing that all investigated variants meet the strength requirements and possess a sufficient safety margin. It was established that the TsCh-4 electrode provides a strong but relatively brittle weld, making it suitable for components not subjected to dynamic loads. The MNCh-2 electrode is versatile and ensures a good balance between strength and ductility, while the UTP-8 electrode produces the most ductile and high-quality weld, although it is characterized by a higher cost. The results of the study confirm the effectiveness of welding of cast iron and allow for a well-founded selection of electrode type depending on operating conditions and economic feasibility.
ROBOTICS – THE PATH TO IMPLEMENTING INDUSTRY 4.0 IN AGRICULTURE
At the current stage of development in the agricultural sector, the labor shortage is a particularly pressing issue for Ukrainian producers, significantly hindering the adoption of innovative technologies. This situation poses a direct threat to the country’s food security. One of the most promising approaches to solving this problem is the development and deployment of robots capable of replacing human labor and performing agricultural operations autonomously. As a review of research and existing robot designs has shown, they are capable of performing a variety of technological operations, from field monitoring to sowing and harvesting, thereby reducing dependence on manual labor. At the same time, the productivity of the work performed and the quality of the finished product increase significantly, while the negative impact on the environment decreases. This article provides an overview of robots that are being actively introduced into agricultural production. The advantages and challenges of robot implementation are outlined. It has been established that the creation of swarm robotic systems is a promising direction for the development of robotics in agriculture.
INFLUENCE OF TEMPERATURE-HUMIDITY REGIME ON THE DEFORMABILITY OF BENDING ELEMENTS AFTER LONG-TERM OPERATION
uences for timber as a building material is moisture exposure. There are many causes of failure in timber structures of buildings and сооружений. In most cases, failure results from a combination of specific factors and influences acting on structural elements. An analysis of the conducted studies indicates that such factors include, among others, an increase in timber moisture content and the aging of materials. The results of experimental tests of solid timber beams under different service conditions are presented. Within the framework of the tests, these conditions were simulated by varying the moisture content of the specimens from 12% to 15% and by considering different service lives. In total, twelve experimental beams with service lives of 25, 50, and 75 years were tested. The test specimens were divided into three series with different moisture contents and service lives. As a result of the conducted tests, the values of the relative deformations of the beams were determined from the beginning of loading until failure. The load-bearing capacity of the beams was established. The failure mode of the beams was identified, occurring in the pure bending zone. The maximum values of relative deformations in the compressed and tension zones were determined. It was established that an increase in timber moisture content leads to an increase in the relative deformations of the compressed zone of the beam by up to 12%, and of the tension zone by up to 7%. No consistent patterns regarding the influence of timber age on the development of deformations in the tested beams were identified. However, it should be noted that no clear generalized correlation can be established regarding the influence of service life on deformability. The deformation behavior and load-bearing capacity of beams depend on their service conditions and the presence of external adverse effects on timber as a building material.
MODERN TRENDS IN THE APPLICATION OF CHALCOGENIDE GLASSES IN ELECTRONICS AND RADIO ENGINEERING
The article provides a comprehensive analysis of modern trends in the application of chalcogenide glasses in electronics and radio engineering. Their key physicochemical properties, which enable a wide range of applications in optoelectronic and electronic devices, are considered. Particular attention is paid to their use in phase-change memory, neuromorphic systems, and sensor technologies. The prospects for integrating chalcogenide glasses into photonic structures, especially in the mid-infrared range, are analyzed. The role of erbium ion doping in the development of efficient waveguide optical amplifiers for telecommunication systems is highlighted. The main technological challenges related to thermal stability, material purification, and compatibility with CMOS technologies are outlined. It is concluded that chalcogenide glasses have significant potential as a fundamental material platform for next-generation electronics and radiophotonics.
OPTIMIZATION OF CULTURAL HERITAGE ROUTES USING GRAPH THEORY METHODS: MUSEUM NETWORK AND "LUTSK KLIKUNS"
Abstract. This paper addresses the problem of mathematical modeling and algorithmic optimization of tourist routes at macro- (regional) and micro- (urban) levels using graph theory. The research is based on two case studies in the Volyn region: a logistic network of seven key museums and a themed walking route featuring 21 "Lutsk Klikuns" bronze sculptures. The methodology involves representing the spatial distribution of cultural objects as weighted undirected graphs, where edges reflect real logistical costs (time, fuel, or pedestrian distance). The software implementation, performed in Python (Jupyter Notebook, NumPy), integrates distinct algorithmic strategies for different scales. For the regional museum network, Dijkstra’s algorithm, the Nearest Neighbor heuristic, and Kruskal’s algorithm were applied to construct a minimum spanning tree and cost-efficient cycles. For the urban pedestrian route, a combination of the Greedy algorithm and 2-opt local optimization was employed to solve the Traveling Salesman Problem. The results demonstrate the universality of the proposed approach: a logistically sound itinerary minimizing transit costs was created for automobile tourism, while an optimal pedestrian path of approximately 11.5 km (starting from point A1) was calculated for the city tour. The practical significance of the work lies in automating the planning of cultural expeditions and enhancing the tourist experience through scientifically grounded navigation.
MECHANIZATION AND AUTOMATION OF HORTICULTURE: THE PATH TO SUSTAINABLE AND EFFICIENT PRODUCTION
The issues of mechanization and automation are highly relevant in the context of introducing innovative technologies in horticulture. The application of modern solutions is aimed at achieving maximum yields, high-quality fruit, and a significant reduction in manual labor costs. The use of specialized machines and automated systems allows for the optimization of technological resources, minimization of human impact on the environment, and reduction of health risks for workers. Modern machines for maintaining tree-line strips feature a modular design, allowing working components to be adapted to specific conditions. To protect tree trunks, the units are equipped with an electro-hydraulic deflection mechanism, and the active components are powered by the tractor’s hydraulic system or an autonomous power unit. Manufacturers offer models with front, rear, or mid-mount hitches. Domestic manufacturers are already actively implementing these global standards in their own production. Research results confirm the global trend of transitioning from traditional mechanization methods to innovative systems based on automation principles. Most orchard processes are now automated: self-propelled chassis with autopilot operate autonomously, and irrigation systems are controlled remotely. Agricultural drones are used for plant protection, and harvesting is carried out by intelligently controlled combines. An important step toward the adoption of agricultural drones in horticulture will be the ability to integrate them into broader automation systems and improve decision-making, such as weather stations and irrigation and fertigation systems. Key elements of this process include monitoring and IoT solutions based on soil moisture sensors and canopy scanning systems. Technologies for the differentiated application of fertilizers and plant protection products are implemented taking into account the variability of plantings, while global navigation satellite systems (GNSS/GPS) ensure autonomous piloting of equipment between rows. The authors summarize global trends in the mechanization of the horticulture industry and justify priority areas for the use of automated systems in horticulture. The study found that horticulture is in the early stages of a transformation driven by a gradual shift from mechanized to automated technologies. This contributes to increased production efficiency and the sustainable development of the industry.
ANALYSIS OF METHODS FOR FORECASTING URBAN PUBLIC TRANSPORT MOVEMENT
The article presents the results of a study the problem of forecasting urban public transport movement under conditions of increasing mobility demand, growing traffic intensity and the need to improve intelligent transport systems. Accurate prediction of vehicle arrival time, travel time between stops, service headways, and vehicle occupancy is essential for route optimization, timetable planning, and improving passenger service quality. The research is motivated by the fact that transport systems operate in a highly dynamic environment influenced by congestion, weather conditions, infrastructure disruptions, and fluctuations in passenger demand. Analyzed the main methodological approaches used for forecasting urban public transport movement. These include statistical time-series methods (particularly regression analysis, moving average techniques, and ARIMA/SARIMA models), filtering approaches based on the Kalman filter, machine learning and deep learning methods, neural network architectures, hybrid and spatio-temporal models. Particular attention is paid to the strengths and limitations of each approach, their data requirements, computational complexity, and suitability for real-time applications in urban transport systems. The results show that statistical models remain useful for baseline forecasting due to their simplicity, transparency, and low computational cost, but their ability to capture nonlinear and rapidly changing transport conditions is limited. Kalman filter are effective for short-term real-time estimation when streaming GPS and sensor data are available. Machine learning, deep learning, and graph-based neural network models demonstrate higher predictive accuracy because they can process large-scale heterogeneous data and represent complex temporal and spatial dependencies. Hybrid models that combine statistical and artificial intelligence methods achieve the best overall performance in highly dynamic urban environments.
INVESTIGATION OF THE INFLUENCE OF THE SCREEN SYSTEM PARAMETERS OF DRUM WOOD CHIPPERS ON THE FRACTIONAL COMPOSITION OF INDUSTRIALWOOD CHIPS
A pattern has been established in the variation of the percentage of substandard fraction of wood chips in the total mass of industrial chips depending on the parameters of the screen system of drum wood chippers. A regression equation was obtained, which can be used to calculate the percentage of substandard fraction, taking into account the number of sections of the stepped screen, the radial distance between the screen and the drum, and the moisture content of the wood. Optimal parameters for the screen system of drum wood chippers have been established.