http://journals.vnu.volyn.ua/index.php/physics/issue/feedPhysics and Educational Technology2025-07-02T11:48:57+03:00Open Journal Systems<p><strong><img style="float: left; padding-right: 10px; padding-bottom: 10px;" src="http://journals.vnu.volyn.ua/public/site/images/admin/physics-.png" alt="" width="319" height="448" /></strong><strong>ISSN (Print): </strong><a href="https://portal.issn.org/resource/ISSN/2786-5444" target="_blank" rel="noopener">2786-5444</a><strong><br /><span lang="EN-US">ISSN <span lang="UK">(</span>Online<span lang="UK">): </span></span></strong><a href="https://portal.issn.org/resource/ISSN/2786-5452" target="_blank" rel="noopener"><span lang="EN-US"><span lang="UK">2786-5452</span></span></a><strong><br /></strong><strong>DOI: </strong>https://doi.org/10.32782/physics<br /><strong>Branch of science: </strong>education/pedagogy; natural sciences.<br /><strong>Periodicity:</strong> 4 times a year.<br /><strong>Professional registration (category «B»):<br /></strong><a href="https://mon.gov.ua/ua/npa/pro-zatverdzhennya-rishen-atestacijnoyi-kolegiyi-ministerstva-vid-30-listopada-2021-roku" target="_blank" rel="noopener">Decree of MES No. 1290 (Annex 3) dated November 30, 2021</a>; <a href="https://mon.gov.ua/ua/npa/pro-zatverdzhennya-rishen-atestacijnoyi-kolegiyi-ministerstva-530" target="_blank" rel="noopener">Decree of MES No. 530 (Annex 2) dated June 6, 2022</a>.<strong><br /></strong><strong>Specialities: </strong>014 – Secondary education (by subject specialties); 104 – Physics and astronomy; 105 – Applied physics and nanomaterials.</p>http://journals.vnu.volyn.ua/index.php/physics/article/view/2397APPROXIMATION IN PHYSICS LABORATORY CLASSES AT TECHNICAL UNIVERSITIES2025-07-02T10:24:40+03:00Kateryna HERASYMOVAtereshchuk.helvetica@gmail.com<p>The article discusses the methods of approximation of experimental data in the course of a laboratory practicum in physics at technical universities. The relevance of the chosen topic is explained by the fact that the choice of an approximation method determines the success and correctness of determining the quantitative and qualitative characteristics of the objects under study. The problem is to choose the right approximation method to solve specific practical problems.The paper reviews scientific publications and studies on the chosen topic, provides the basic concepts and definitions of the approximation theory. Two types of approximation are defined: strict mathematical and physical (technical) approximation. The methods are analyzed, the requirements for approximation of experimental data are specified and formulated. The general task of approximation is defined – the correct choice of the approximating function. The concepts of curve smoothing and the least squares method are revealed. The types of approximation used in the MS Excel computer programs are defined. The possibility of using linear approximation by the least squares method in physical research is considered. Mathematical formulas related to this method are presented. The peculiarities of the methodology for performing laboratory work using physical approximation for first-year students are indicated, taking into account their insufficient basic mathematical training to perform calculations. A specific example is used to demonstrate the application of the least squares method used in a physics laboratory workshop. The relevant calculations are presented, the advantages and disadvantages of the chosen method are determined, and a conclusion is made about the feasibility of its application.The direction of further research of other types of approximation for the purpose of their effective implementation in the educational process in physics is determined.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2398ON THE ISSUE OF ORGANIZATION AND CONDUCT OF EDUCATION PRACTICE “EDUCATIONAL PROJECT TECHNOLOGIES”2025-07-02T10:27:17+03:00Nina HOLOVINAtereshchuk.helvetica@gmail.comHOLOVIN Mykolatereshchuk.helvetica@gmail.comOksana OSTREItereshchuk.helvetica@gmail.comHryhoriy KOBELtereshchuk.helvetica@gmail.comOleksandr MARTYNIUKtereshchuk.helvetica@gmail.comGalina MYRONCHUKtereshchuk.helvetica@gmail.com<p>Educational practices are one of the key types of activity of education seekers. During the practice, education seekers gain practical experience of their future profession. The authors reveal the meaning of the educational practice "Educational Project Technologies" and show its place in the training of teachers of computer science and physics of a general secondary education institution. Possible types of activity of education seekers during the practice are considered. Practical work of education seekers of pedagogical direction is especially useful because it allows them to be in two statuses at the same time: student and teacher. Project technologies are an effective tool for the development of general cultural, information and communication, communicative, interdisciplinary, social and project and technological competencies of education seekers.The paper presents a mental map illustrating the concepts of a project, educational project, project technologies, characteristics and classification of an educational project. The stages of project implementation are considered. The planning stage, which is the foundation of the successful implementation of any project, is detailed. It is emphasized that the implementation of an educational project is based on previously acquired primary knowledge, search and research work. The final result of project activity is a report with a presentation of the created IT product, which is implemented using the means of mastered information technologies (text file, presentation, program code, video, website, etc.).To test the implementation of educational projects according to the school curriculum, the following are proposed: development of an individual project “Our Assistant Computer” in computer science for grade 5; development of an individual project “Experimental Problem in Physics” in physics for grade 7; development of a collective project “We Buy Computers for School”. It is indicated what should be the result of each project.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2399OPTICAL PROPERTIES OF CRYSTALS (TlGaSe2)1-x(SnSe2)x2025-07-02T10:33:58+03:00Dmytro IVANYUKtereshchuk.helvetica@gmail.comAndriy KEVSHYNtereshchuk.helvetica@gmail.com<p>The development of modern technologies requires the search for new promising materials as the main source of expanding and improving the functionality of semiconductor electronics devices. The scientific basis of such a search is the study of the physical properties of multicomponent systems, the study of the structure and properties of the identified phases.The potential that layered semiconductors open for the study of a number of new phenomena in solid-state physics is far from exhausted, and the interest of researchers in them is constantly growing. The properties of solid solutions based on Thallium chalcogenides make it possible to control their physical parameters and use them as detectors, optical analyzers, photo- and X-ray converters, and receivers of the visible and IR regions of the spectrum.Studies of the TlInSe2–SnSe2 system (Mozolyuk, 2011) indicate the formation of a wide range of solid solutions in the range of 0–28 mol.% SnSe2. For Tl1-xIn1-xSnxSe2 crystals (x=0; 0,1; 0,2; 0,25), the achieved values of the parameters of the third-order nonlinear optical effects are maximally critical, which allows us to predict their wide use as effective materials for nonlinear frequency conversion in the IR region of the spectrum, which is critical for IR lidar systems. Of particular interest may be their use in photonic gratings (Myronchuk, 2013).The family of binary compounds TlX (X= S, Se, Te) and their derivatives are well known as semiconductors for optical applications (Itoga, 1971). There are also ordered ternary representatives of TlTtX2 (Tt= Al, Ga, In) with two crystallographic centers with different coordination environments, but the existence of solid solutions for different chalcogenides cannot be excluded. Crystals (TlGaSe2)1-x(SnSe2)x (x=0,05; 0,1) were synthesized to increase the possibilities of controlling the physical properties of thallium-based compounds. This work presents the results of experimental studies of the optical properties of these compounds to understand their potential in optoelectronic and photonic devices.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2400METHODOLOGICAL ASPECTS OF DEVELOPING STUDENTS’ PROFESSIONAL COMPETENCIES BY SOLVING PHYSICS PROBLEMS2025-07-02T10:41:41+03:00Andriy KEVSHYNtereshchuk.helvetica@gmail.comVolodymyr HALYANtereshchuk.helvetica@gmail.comNazar KEVSHYNtereshchuk.helvetica@gmail.com<p>One of the important ways to develop the mental and creative abilities of educational students is the development of tasks that are related to the general mastered physics course – the basis for the development of special educational components. A physical task, as an element of the illumination process, is the most effective form of independent acquisition of knowledge and consolidation of theoretical material. In the course of solving problems, all the basic mental operations are involved, such as abstraction, analysis, deduction, inference, equation and synthesis.Varto notes that most first-year students experience difficulties when solving problems. This is due to the fact that they often formally remember laws, meanings, concepts and formulas, without understanding the peculiarities of minds and the stagnation between them. As a result, this knowledge is incorrectly or incorrectly interpreted in specific physical situations.In modern minds, the process of learning physics at most initial stages is a complex task, since many students are not prepared before acquiring new information. They don’t know how to identify food, explain the safety of boxes, handle equipment, don’t know fundamental physical laws, etc. Connected with this is the role of the student, who is responsible for creating the minds for the development of creativity, learning interests, and intellectual abilities of students, focusing on humanization, differentiation, and Individualization begins.To prepare a competent specialist, competitive, who has experimental knowledge and skills, who is able to operate with current terminology and new developments, scientific concepts, laws, concepts, traditions and theories of natural sciences, it is necessary to ensure a high level of fundamental training as the basis of professional competencies. The connection of physical tasks is an element in the formation of professional competencies of students. This process contributes to the acquisition of not only theoretical knowledge, but also the development of practical skills, critical thinking and the development of knowledge in real minds (Burhun, 2016).</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2401FEATURES OF CONDUCTING LABORATORY CLASSES ON THE RESEARCH OF RESONANCE PHENOMENA IN ELECTRICAL CIRCUITS OF ALTERNATING CURRENT2025-07-02T10:50:35+03:00Andriy KEVSHYNtereshchuk.helvetica@gmail.comVolodymyr HALYANtereshchuk.helvetica@gmail.comOleksii NOVOSADtereshchuk.helvetica@gmail.comNazar KEVSHYNtereshchuk.helvetica@gmail.comAndriy SEMENYUKtereshchuk.helvetica@gmail.com<p>The modern stage of education development is characterized by the wide introduction of information technologies into professional pedagogical activity, which ensure the education system reaches a qualitatively new level due to the effective use of electronic educational resources. The increasing speed of change in science-intensive technologies in the field of electronics brings to the fore the need to implement such training in electrical engineering disciplines, the content of which is not so much in the transfer of knowledge, but rather in the preparation of university graduates with a predominant focus on the development of high professional competence. Learning the basics of electronics is extremely important for future teachers, especially in today’s world, where technology is rapidly developing and actively integrated into the educational process. A future teacher who is familiar with the basics of electronics is better oriented in the modern technical environment. This allows him to understand the principles of operation of electronic devices used in education (for example, interactive whiteboards, laboratory equipment, computers), to use technology to improve the effectiveness of education.Electronics is an important component of STEM education. Future teachers who know the basics of this discipline can organize interesting classes with elements of robotics, programming or designing electronic circuits, motivate students to study technical sciences. The skills of working with electronics contribute to the development of logical thinking and understanding of cause and effect relationships, the ability to solve technical problems and apply knowledge in practice.A modern teacher must keep up with the times and know how to use new electronic tools and devices. For example, using Arduino or Raspberry Pi for integrated lessons, teaching students to create simple electronic projects. Teachers who know the basics of electronics are more valuable in the labor market because they can perform not only an educational but also a technical function. They are able to conduct electives, groups or special courses related to modern technologies. Basic knowledge of electronics allows you to teach the rules of safe use of electrical appliances, prevent danger, and develop a conscious attitude to work with technology in children.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2402EXPERIMENTAL PROBLEMS IN THE STRUCTURE OF PRACTICAL CLASSES OF THE UNIVERSITY COURSE OF PHYSICS2025-07-02T10:56:15+03:00Hryhoriy KOBELtereshchuk.helvetica@gmail.comNina HOLOVINAtereshchuk.helvetica@gmail.comValentyn SAVOSHtereshchuk.helvetica@gmail.comGalina MYRONCHUKtereshchuk.helvetica@gmail.com<p>The search for the optimal model of conducting a practical lesson in physics at universities is relevant. Based on the authors’ many years of experience in teaching physics in higher education institutions, it can be argued that the experimental skills of students need to be improved. The traditional structure of the educational process in higher education institutions involves the development of skills and abilities that a student needs to conduct experimental research during laboratory work, where, in most cases, his activity is reproductive, because it occurs in accordance with the algorithm proposed to him. The use of experimental problems in the structure of practical classes will help to successfully implement the relevant program learning outcomes. The use of experimental problems does not replace laboratory work and solving computational problems, but is their creative addition.The aim of the work is to show that the introduction of experimental problems into the structure of a practical lesson allows: to verify theoretical statements experimentally; to create a problem situation in the lessons, to develop creative thinking of the subject; to show the reality and validity of specific numerical values of physical quantities given in the problem condition. The novelty of this work is the idea of using experimental problems when conducting practical lessons in physics in a university course.In particular, experimental problems in mechanics and molecular physics are proposed, which can be successfully used when conducting practical lessons, their scientific and didactic functions are demonstrated. The content of a practical lesson using experimental problems is disclosed; examples of experimental problems are given. The advantages of combining practical lessons with experimental problems are highlighted: active learning, development of practical skills, deepening of understanding, development of research skills, increasing interest in physics. In general, experimental problems are an integral part of teaching physics. They combine theory with practice, making the learning process more effective.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2403MICROCONTROLLER CIRCUIT TECHNIQUE AND THREE-DIMENSIONAL MODELING TOOLS IN THE STEM-TRAINING SYSTEM OF ROBOTICS2025-07-02T11:00:41+03:00Oleksandr MARTYNIUKtereshchuk.helvetica@gmail.com<p>The concept of STEM education is based on the practical application of knowledge and skills for their further use in professional activities. The project approach allows students to understand how STEM knowledge is applied in real life. The paper analyzes the developed and tested concept of combining the capabilities of educational robotics tools, three-dimensional prototyping and programming microcontroller platforms. 3D prototyping in robotics is effective because the user can quickly obtain results and implement their ideas in the design process. A robotic STEM project completed in the learning process can be not only an object of study, but also a tool for modeling, design, a tool in an educational experiment, a digital laboratory, a tool for programming microcontrollers. As an example, the technological aspects of manufacturing and programming SMARS platforms are given. SMARS (Screwless Modular Assemblable Robotic System) is a screwless modular assembled robotic system, a currently popular technological educational tool. These are simple robotic platforms designed for educational purposes with a minimum number of components that can be assembled without special additional tools. The sequence of project implementation and the specifics of programming their electronic parts – Arduino microcontroller platforms – are described. The main functions that SMARS can perform and additional design elements that expand the possibilities of its use are analyzed. Work on the design and manufacture of structures opens up wide opportunities for studying issues of a technological nature and activating the cognitive activity of students.In the process of project work, design and creative abilities are developed, and the foundations of professional and digital competence are formed.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2404MULTISPECTRAL LIDAR SYSTEMS AND THEIR APPLICATIONS2025-07-02T11:03:46+03:00Igor MASHEVSKYtereshchuk.helvetica@gmail.com<p>The article presents the theoretical foundations of the functioning of multispectral LiDAR (MSL) systems, their hardware implementation, methodological approaches to data acquisition and processing, as well as outlines the key areas of practical application of this technology. The fundamental architecture of MSL is considered, which includes radiation sources operating at various wavelengths, scanning mechanisms, optical receiving modules, photodetector systems, and auxiliary navigation components (GPS/IMU). Particular attention is paid to the use of supercontinuum lasers and frequency doubling techniques to expand the spectral range. It is emphasized that a key advantage of MSL is the capability of simultaneous acquisition of both spatial and spectral information while maintaining high spatial resolution.The potential of MSL in providing accurate spectral discrimination of materials and structural elements based on spectrally sensitive reflected signals is analyzed. The article describes digital signal processing algorithms, including radiometric calibration, atmospheric distortion compensation, and machine learning techniques applied for classification, segmentation, and visualization of multidimensional data. Empirical results indicate a high object recognition accuracy using MSL data, which significantly exceeds the performance of traditional single-wavelength LiDAR systems and passive multispectral imagery.The study outlines the main applied directions for the use of multispectral LiDAR, including agro-monitoring, forestry, geodesy and cartography, environmental monitoring, urban planning, geology, and archaeology. It is demonstrated that the synergy of spatial and spectral data opens new possibilities for interpreting complex natural and anthropogenic systems.Market trends are also analyzed, highlighting a steady increase in investments in the field of MSL technologies and the infrastructure needed for their integration into multisensor platforms. In particular, significant growth of the global LiDAR market is anticipated, which also encompasses the multispectral segment.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2405PHOTOELECTRIC PROPERTIES OF In/CuInS2-ZnIn2S4 AND In–Ga/CuInS2-ZnIn2S4 DIODE STRUCTURES2025-07-02T11:06:29+03:00Oleksii NOVOSADtereshchuk.helvetica@gmail.comAndriy KEVSHYNtereshchuk.helvetica@gmail.com<p>The paper presents the results of studies on the photovoltaic properties of surface-barrier structures based on monocrystalline CuInS2–ZnIn2S4 films. These structures were obtained using thermal vacuum deposition of semitransparent In films on the CuInS2–ZnIn2S4 surface and mechanical rubbing of In–Ga eutectic into the surface of monocrystalline CuInS2–ZnIn2S4 fractures. The semitransparent indium films were deposited by thermal vacuum evaporation in a VUP- 5 system at a pressure of 1,3×10-5 Pa and a temperature of 300 K. The surface area onto which the semitransparent In layer was deposited was approximately ≈3×3 mm².When illuminating the In/CuInS2–ZnIn2S4 structure with 8 mol.% ZnIn2S4 from the CuInS2–ZnIn2S4 side, a single well-defined maximum was observed. The energy position of the maximum in the photovoltage spectrum corresponds to the photon energy of hν≈1,53 eV. When illuminating the samples from the side of the semitransparent In layer, two maxima were observed with energy positions of hν≈1,44 eV and hν≈1,60 eV. Similar results were obtained for diode structures with 12 mol.% ZnIn2S4. In samples with 12 mol.% ZnIn2S4, when illuminated from the monocrystalline substrate side, a shift of the photovoltage maximum to 1,56 eV was observed, which correlates well with the increase in the band gap of CuInS2–ZnIn2S4 as the ZnIn2S4 content increases.The highest photovoltage values among the diode structures In-Ga/CuInS2–ZnIn2S4 were observed in structures with 12 mol.% ZnIn2S4. When illuminated from the semiconductor substrate side, a narrow maximum with an energy position of hν≈1,44 eV was observed. When illuminated from the In–Ga eutectic side, alongside the maximum caused by intrinsic optical transitions (hν≈1,68 eV), a less pronounced step was observed in the long-wavelength region. This step was attributed to impurity light absorption, primarily caused by VCu.Having narrow maxima in the photovoltage spectra, the In(In–Ga)/CuInS2–ZnIn2S4 structures can be used as narrow-band light receivers. The energy position of the maxima in the photovoltage spectra depends on the composition of the CuInS2–ZnIn2S4 monocrystals, the method of obtaining the bilayer structure, and the illuminated side of the structure.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2406MAGNETIC PROPERTIES OF JOSEPHSON JUNCTIONS WITH A SECOND HARMONIC IN THE CURRENT-PHASE RELATIONSHIP2025-07-02T11:09:42+03:00Pavlo SAKHNIUKtereshchuk.helvetica@gmail.comОksana ZAMURUIEVAtereshchuk.helvetica@gmail.com<p>The conducted research is devoted to a relevant problem in superconductivity physics, namely the study of current states in superconducting junctions that exhibit deviations from the standard sinusoidal current-phase relationship. This problem is a subject of intensive scientific research from both fundamental and applied perspectives, as the non-sinusoidal dependence can significantly affect the characteristics of Josephson junctions used in various technological applications.The main goal of the research is to establish the quantitative impact of an external magnetic field on the current-phase relationship and critical current of such junctions, considering the presence of a second harmonic.An analytical study of the influence of the anharmonicity parameter α on the critical current of the junction in the absence of an external magnetic field was performed. It was shown that with an increase in the anharmonicity parameter, the critical current increases, and this dependence is quadratic at small values of α and approaches linear at large values.The dependence of the junction’s critical current on the magnetic flux magnitude and the anharmonicity parameter α was obtained. The research results are presented as graphs of the total current versus the phase difference at different magnetic flux values, the phase at which the current maximum is achieved versus the magnetic flux, and the critical current versus the magnetic flux for different values of the anharmonicity parameter α. It was established that with an increase in the anharmonicity parameter α, the critical current becomes more sensitive to the action of an external magnetic field, especially in the region of small magnetic flux values. This manifests as a faster decrease in the critical current with an increase in the magnetic field for junctions with a non-zero value of α compared to junctions with a purely sinusoidal current-phase relationship.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2407DEVELOPMENT OF COGNITIVE ABILITIES OF STUDENTS UNDER THE INFLUENCE OF DIFFERENT GENRES OF MUSIC2025-07-02T11:14:06+03:00Liubov SOBOLENKOtereshchuk.helvetica@gmail.comSvitlana SOROKINAtereshchuk.helvetica@gmail.comVictoria STOLYARtereshchuk.helvetica@gmail.com<p>The main cognitive functions of the brain are perception, memory, thinking and attention. At the initial stage of perception, the first signaling system prevails, i.e., the sensation of sound, light, chemical and other stimuli by our analyzers on the basis of an unconditional orienting reflex. From the point of view of the physiology of nervous activity, attention is a process of consciously focusing on relevant information, initiating mechanisms of memorization and movement, and forming new connections between excited neurons. From the psychological point of view, attention is a factor that determines the selectivity of perception. The physiological basis of concentration is the activation of certain cortical centers. Selectivity is a defining feature of attention.Therefore, the purpose of the study is to investigate the musical preferences of adolescents and to determine the influence of different genres of music on the development of high school students’ attention.In the life of modern adolescents and young people, music culture is an important means of communication and influence on the emotional state of a person. Modern research shows that a well-chosen composition can both activate and inhibit the assimilation of information.This article presents detailed results of research on the impact of different genres of music on the development of cognitive functions of the brain.The study experimentally proved the positive influence of different genres of music, namely: popular (pop), rock, electronic, classical on the dynamics of students’ attention parameters.The analysis of the influence of music as a factor suggests that it generally increases the effectiveness of the cognitive functions of the brain of high school students, in particular such properties of attention as concentration, volume, and switching. Taking into account the musical preferences of the administration of educational institutions, reflected in the form of the author’s music playlist “Listen and Learn” and the studied patterns, will help to organize comfortable learning and recreation conditions, as well as develop innovative methods to improve the efficiency of perception of educational material.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2408SOME PROBLEMS OF WHITE DWARF MODELLING2025-07-02T11:18:35+03:00Petro TROKHIMCHUCKtereshchuk.helvetica@gmail.com<p>Main peculiarities of formulation main principles and criteria of white dwarf theories are analyzed. Short comparative analysis of main methods of modeling is represented. All these methods are based on the conditions of equilibrium. The role of A. Eddington, R. Fowler, E. Stoner and S. Chandrasekar researches in the creation this theory is discussed. A. Eddington proposed to use the Lane-Emden equations to construct the theory of white dwarfs, which allow us to describe processes in polytropic gas spheres. It is shown that Stoner method, Lane-Emden equations and Einstein equations is based on the search of equilbrium comditions for sphere or semple to sphere symmetries. The role of the development of theoretical physics (Fermi-Dirac statistics) in the creation of this theory is shown. It should be noted that thanks to Stoner’s research, the Pauli principle and one of the first applications of Fermi-Dirac statistics for degenerate electronic systems appeared in the Bohr theory of the atom precisely in the theory of white dwarfs. Main peculiarities of Stoner method and Lane- Emden equtions are observed. Stoner’s method is based on the idea of studying the equilibrium of a star based on energetic considerations. The Lane-Emden equations were constructed for gaseous spheres with different polytropic indices. It was Emden’s introduction of thermodynamics into these equations that allowed them to be used in astrophysics. For these equations, it is necessary to additionally introduce the conditions for the rotation of the star. Einstein’s equation is also on the one hand a condition of energy equilibrium (effective potential energy equals kinetic energy) for inhomogeneous systems, and on the other hand it is a generalization of the special theory of relativity to curvilinear geometry. The generalization of the interval itself is nothing more than a metric of the corresponding space-time. Rotation is included in the equation from the very beginning. Peculiarities of application methods of general relarivity for modelling white dwarf structure and processes are analyzed too.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2409VOLTERRA AND LOTKA-VOLTERRA SYSTEMS OF KINETIC EQUATIONS AND THEIR EXPANSION AND APPLICATIONS2025-07-02T11:36:32+03:00Petro TROKHIMCHUCKtereshchuk.helvetica@gmail.comVladyslav SAKHANtereshchuk.helvetica@gmail.com<p>A systematic analysis of the systems of kinetic equations of Volterra and Lotka-Volterra is given. Population problems that had to be solved and their brief analysis are given. These problems include demographic, ecological, etc. problems.From a conceptual point of view, these problems are divided into two types: the problem of two species eating the same food (Volterra equation) and the predator-prey problem (Lotka-Volterra equation). The first problem arose from the problem of rabbit reproduction in Australia. In addition, in the same population biology, the problem arose when one species eats another (predator and prey). This problem was solved by many researchers in the field of biology and medicine, in particular virology. Its partial solution is given in the book of A. Lotka, and a more general one in the lectures of V. Volterra.Because of this, these equations are sometimes called the Lotka-Volterra equations. As in the first and second problems, it is necessary that there is enough resource (food) for the stationary stable existence and development of the dynamical system. We have analyzed the problems that are solved or that are expedient to be solved using these methods. Problems with a non-uniform temporal hierarchy of processes have also been analyzed. It has been shown that for solving such problems it is expedient to use the method of adiabatic elimination of variables. This method was used to solve kinetic problems in relaxation optics. These equations are expedient to use when there are several competing in-phase processes.Based on the general analysis of the systems of Volterra equations, it is possible to construct system criteria for controlling and predicting the corresponding processes and phenomena. To move to spatial problems, it is necessary to introduce the corresponding transport and diffusion coefficients into the systems of equations of Volterra and Lotka-Volterra. In this case, these equations can also be considered as systems of nonlinear diffusion equations. A list of problems for which it is expedient to use such a formalism is given.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2410THERMOELECTRIC AND OPTICAL PROPERTIES OF SOLID SOLUTION CRYSTALS ACROSS THE Pb4Ga4GeSe12-Pb4Ga4GeS12 SECTION2025-07-02T11:39:40+03:00Oleksii NOVOSADtereshchuk.helvetica@gmail.comOleg SHYGORINtereshchuk.helvetica@gmail.comHadj Kaddur BELLAGRAtereshchuk.helvetica@gmail.comLyudmyla PISKACHtereshchuk.helvetica@gmail.comVictor GOMILKOtereshchuk.helvetica@gmail.com<p>The paper presents the results of studies on the thermoelectric and optical properties of Pb4Ga4GeSe12– Pb4Ga4GeS12 crystals. The Pb4Ga4GeSe12–Pb4Ga4GeS12 crystals corresponded to the compositional content of 10, 20, and 30 mol.% Pb4Ga4GeS12.The aim of the study was to experimentally determine the specific electrical conductivity, conductivity type, Seebeck coefficient, estimate the band gap width, and calculate the thermoelectric power of Pb4Ga4GeSe12–Pb4Ga4GeS12 crystals.All studies were conducted at room temperature (T≈300 K). The highest values of specific electrical conductivity (σ≈170 Ω⁻¹·m⁻¹) were observed in Pb4Ga4GeSe12–Pb4Ga4GeS12 crystals with a 20 mol.% Pb4Ga4GeS12 content. High values of σ may indicate that the materials are in a state close to degeneracy. Thermoelectric methods have established that Pb4Ga4GeSe12–Pb4Ga4GeS12 crystals belong to n-type semiconductors. The Seebeck coefficient values were 205 µV/K, 220 µV/K, and 240 µV/K for Pb4Ga4GeSe12–Pb4Ga4GeS12 crystals with 10, 20, and 30 mol.% Pb4Ga4GeS12 content, respectively. Having high Seebeck coefficient values, Pb4Ga4GeSe12–Pb4Ga4GeS12 compounds are promising materials for the fabrication of sensitive thermal sensors. It has been established that the highest values of thermoelectric power (α²·σ=8.2×10⁻⁶ W/m·K²) are characteristic of Pb4Ga4GeSe12–Pb4Ga4GeS12 crystals with a 20 mol.% Pb4Ga4GeS12 content.To estimate the band gap width, light absorption spectra were studied in the region of the fundamental absorption edge.The band gap values estimated from the optical absorption spectra were 1.89 eV, 1.92 eV, and 1.95 eV for Pb4Ga4GeSe12– Pb4Ga4GeS12 solid solutions with 10, 20, and 30 mol.% Pb4Ga4GeS12, respectively. It was established that the investigated crystals are indirect band gap semiconductors.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2411OPTICAL THERMOSENSORS BASED ON THE GLASSES Er2S3–Ag0,05Ga0,05Ge0,95S22025-07-02T11:44:19+03:00Tetiana YATSYNIUKtereshchuk.helvetica@gmail.comVolodymyr HALYANtereshchuk.helvetica@gmail.comAndrii KEVSHYNtereshchuk.helvetica@gmail.comHanna SHAVAROVAtereshchuk.helvetica@gmail.comVolodymyr HALIANtereshchuk.helvetica@gmail.com<p>Optical sensors are one of the most promising technologies in modern solid-state physics and chemistry. They enable precise measurements and control of temperature, radiation levels, and monitoring of the pollution of various objects without physical contact. The use of such sensors significantly expands the capabilities in industrial production, medicine, and ecology. The relevance of optical sensor research is increasing with the development of modern technologies and the growing demands for accuracy, speed, and safety of measurements. They are used in fields that require high sensitivity to changes in temperature, pressure, humidity, gas concentrations, etc. The luminescent properties of chalcogenide glass alloys with the composition Er2S3–Ag0,05Ga0,05Ge0,95S2 at 0.42 mol.% Er2S3 were investigated. Photoluminescence was observed with emission peaks at 660, 860, and 980 nm upon excitation with a 532 nm wavelength laser. With an increase in temperature, the ratio between the intensities of the photoluminescence changes. The most sensitive to temperature variations was the photoluminescence peak at 860 nm. Based on the formula describing the probability of radiative and non-radiative processes, a model was built to determine the dependence of the photoluminescence intensity on temperature. According to the experimental dependence I(T), the activation energy was calculated (ΔE = 90 meV), which defines the energy required for the transition of erbium ions from the 4S3/2 state to the 2H11/2 state.A linear relationship between the intensity ratio of photoluminescence Ln (I980/I660) and the sample temperature was established. The sensor sensitivity was calculated to be 0.43 K⁻¹. Thus, the investigated glasses, within a limited temperature range, can be used as optical thermosensors.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025 http://journals.vnu.volyn.ua/index.php/physics/article/view/2412OPTICAL ABSORPTION OF GLASSES IN THE Ga2S3-GeS2-Sb2S3 SYSTEM DOPED WITH Er AND Nd2025-07-02T11:48:57+03:00Tetiana YATSYNIUKtereshchuk.helvetica@gmail.comVolodymyr HALYANtereshchuk.helvetica@gmail.comAndrii KEVSHYNtereshchuk.helvetica@gmail.comHanna SHAVAROVAtereshchuk.helvetica@gmail.comVitaly ARTYUKHtereshchuk.helvetica@gmail.comBohdan SVITLIKOVSKYItereshchuk.helvetica@gmail.com<p>Optical absorption in chalcogenide semiconductors is important from both fundamental and applied perspectives. The analysis of optical absorption spectra in chalcogenide glassy alloys helps reveal the electronic structure and the nature of chemical bonds in these materials, contributing to a deeper understanding of the physics of disordered systems. Studies of the optical properties of chalcogenide glasses assist in the development of new materials with improved characteristics and help identify defects and impurities that may influence their optical and photoelectrical properties.The optical absorption spectra of glasses with compositions of 20 mol.% Ga2S3 – 60 mol.% GeS2 – 20 mol.% Sb2S3 and 25 mol.% Ga2S3 – 30 mol.% GeS2 – 45 mol.% Sb2S3 simultaneously doped with Er and Nd were studied in the range of 550 – 2000 nm at room temperature. The edge of optical absorption of the glasses is located around 600 nm and does not undergo significant changes upon doping with Er and Nd. Narrow absorption bands were registered with maxima at 655, 755, 810, 885, 980, and 1540 nm, corresponding to transitions in the f-shells of Er3+ and Nd3+ ions.From the graph defining the edge of optical absorption, the optical band gap of the glasses was estimated by extrapolating the linear portion of the experimental curve to the intersection with the abscissa axis. It was found that with an increase in the Sb2S3 content (from 20 to 45 mol.%), the optical absorption edge shifts towards longer wavelengths, resulting in a decrease in the band gap of the studied glassy alloys. The addition of (1 – 3) mol.% Er2S3 does not lead to significant changes in the band gap, and with further increases in this component, a slight increase (~ 0.04 eV) in the band gap was recorded.The low values of the absorption coefficient in the 1000 – 2000 nm range indicate promising prospects for the use of these glasses in optoelectronic devices operating in the near-infrared range.</p>2025-04-30T00:00:00+03:00Copyright (c) 2025