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The paper presents theoretical investigations of the elastic and acoustic properties in crystals forming the solid solution system CuGa(S1 − xSex)2 . The structures with varying selenium content, x = 0, 0.25, 0.5, 0.75, and 1, were examined. Employing the supercell method, a series of solid solutions were modeled by replacing sulfur atoms with selenium atoms in the CuGaS2 crystal structure. The generated substitution structures underwent geometry optimization using density functional theory (DFT) in conjunction with the BFGS algorithm, describing the exchange-correlation interactions through generalized gradient approximation (GGA). The optimized structures of the solid solutions were found to be in good agreement with the available experimental data, with a slight overestimation of parameters, attributed to the known features of the GGA functional. The elastic constants matrix Cij for tetragonal symmetry was calculated, demonstrating compliance with Born's mechanical stability criterion for all compositions investigated. The evaluation of the material's elastic characteristics with changing composition revealed that the coefficients and C33 exhibited nearly twice as large values compared to the shear coefficients. Notably, the C11 coefficient reached 104.79 GPa, while the minimum value was obtained for C44 at 51.29 GPa. Isomorphic replacement of sulfur with selenium atoms resulted in a monotonic decrease in the elastic constants Cij. Employing the Green-Christoffel equation, the acoustic wave propagation velocities in a number of crystals were calculated using a home-made program written in Python. Acoustic wave velocities v were computed in (100) and (001) planes, with the highest observed velocity v max = 5586 m/s corresponding to the longitudinal acoustic wave (LA) in the (001) plane. The isomorphic replacement of S → Se resulted in a monotonic reduction in the propagation velocity v of acoustic waves within the investigated solid solution system. An analysis of anisotropy revealed that transverse TA2 waves exhibited the highest values for the A coefficient, accounting for 35-43% in the (100) plane and 28-40% in the (001) plane. In contrast, for LA waves, the propagation velocity was nearly isotropic (A parameter close to zero). [ABSTRACT FROM AUTHOR]

In this paper, we will systematically present the method of collective variables with a reference system for a classical many-particle interacting system in the grand canonical ensemble. The emphasis will be placed on the details of calculations. In particular, the usage of total correlation functions defined for the grand canonical ensemble allows us to investigate very accurately the cumulants of the grand partition function for the reference system. It is shown that any cumulant Mn can be expressed as a product of three components: the average particle number within the reference system. Kronecker's symbol for n wave vectors, and the n-particle structure factor. The functional expression for the grand partition function is derived, with all coefficients explicitly defined. The coordinates of the critical point are computed in the mean field approximation. [ABSTRACT FROM AUTHOR]

Deep Convolutional Neural Networks (CNNs) have exhibited remarkable eficacy in data analysis across various domains of physical research. Within the realm of particle and high-energy physics, an imperative challenge revolves around the scrutiny of particle tracks acquired through track detectors, exemplified by liquefied argon time projection chambers (LArTPCs). These cutting-edge neural networks have showcased unparalleled performance in tackling this intricate task, demonstrating their profound potential in enhancing particle track analysis. Since the scalability requirement is imposed on neutrino detectors, it is also imposed on CNN model implementations. The scalability for LArTPC data processing is achieved due to the sparsity of the data, which have the form of thin trajectories. To process sparse data, subspecies sparse convolutional networks (SSCNs) and sparse tensor networks (STNs) have been proposed. In this paper, we present the results of semantic segmentation of the LArTPC-simulated PILArNET data using STNs and test various modifications of the classical U-Net architecture: Attention U-ResNet, U-ResNet3+, U-ResNet with an additional deep supervision block, as well as loss functions: focal loss, balanced cross-entropy to improve the accuracy of Michel electron identification. The best results were obtained for balanced cross-entropy. Further improvement is possible by combining several methods. [ABSTRACT FROM AUTHOR]

The paper discusses the cosmological model with an interaction between dynamical quintessence dark energy and cold dark matter. Evolution of the dark energy equation of state parameter is defined by the dark energy adiabatic sound speed and the dark sector interaction parameter, which must be a more physically correct model then the one previously used, in which this evolution was determined by some fixed dependence on the scale factor. The constraints on the interaction parameter and other parameters of the model were obtained using the cosmic microwave background, baryon acoustic oscillations and the supernova SN Ia data. [ABSTRACT FROM AUTHOR]

We analyze the possibilities of detecting a signal in the hydrogen 21 cm line, which was formed in the early universe during the Dark Ages, using the Ukrainian radio telescopes UTR-2 and GURT of the National Academy of Sciences of Ukraine. As a result of cosmological expansion, this line is shifted to the decameter range of wavelengths (λobs ≈ 18 m, νobs ≈ 16 MHz) and is in the band of operating frequencies of these telescopes. The brightness temperature of the predicted sky-averaged global signal ranges from ∼ −0.08 to ∼ 0.02 K, depending on the cosmological model. Such a weak signal is a big challenge even for the world's largest radio telescope in the decameter wavelength range UTR-2, since the signal level of the synchrotron radiation of the Galaxy at these frequencies is 20 000-40 000 K. The paper highlights the peculiarities of spectroscopy at decameter waves, interfering factors of natural and instrumental origin and ways to eliminate them in order to reliably detect the signal in the 21 cm line, which can become an important source of information both about the environment in which the first stars and galaxies were born, and about the nature of dark matter particles and the magnitude of primordial magnetic fields. It was concluded that the detection of such a signal using the most sensitive radio telescopes of the decameter wavelength range is quite possible (with a frequency accumulation of 25 MHz, the detection time will be ∼ 50 days) and can be implemented in the coming years of peace in Ukraine. [ABSTRACT FROM AUTHOR]

The paper focuses on transport properties of double perovskite Sr2FeMoO6−δ, which were studied experimentally and using First principles calculations. The strontium ferromolybdate specimens were prepared using citrate-gel method followed by compacting and thermal treatment at different regimes. The Hall effect was calculated using Quantum Espresso and Wannier90 software packages. The study conformed high sensitivity of Sr2FeMoO6 to the processing parameters such as pressure and temperature of powder compacting as well as the temperature and duration of the subsequent annealing in Ar/O2 atmosphere. The optimal regime of compacting to avoid cracking involved pressing under 4 GPa at T = 800 K. Further heat treatment of the compacted specimens in Ar/O2 atmosphere has shown that three types of electric conductivity, namely metallic, semiconducting and mixed one can be realized in the Sr2FeMoO6 specimens. The highest magnitude of magnetoresistance was found in the semiconducting specimen (about 44%), while the specimen of metallic type demonstrated magnetoresistance of about 21%. The elevated values of magnetoresistance in the semiconducting specimen were achieved due to conduction mechanism related to tunneling through intergrain dielectric layers formed by secondary SrMoO4 phase. The Hall effect was computed by constructing the Hamiltonian in the maximally-localized Wannier functions basis. Calculations of the Berry curvature, which is the origin of the high intrinsic Hall effect showed that its highest magnitudes concentrate near avoided band crossings gapped out due to spin-orbit coupling. The Hall conductivity calculated by integrating the Berry curvature over all occupied bands was found to be ~22 S/cm. [ABSTRACT FROM AUTHOR]

This paper is concerned with the influence of rotation on the onset of ferromagnetic fluid convection in the presence of both modulated and unmodulated magnetic fields. The effects of magnetic field modulation and rotation on the onset of ferroconvection are of interest from both practical and theoretical points of view. Modulation of an appropriate parameter may significantly affect the motion and improve the stability of various systems, including charges in an electrostatic field and ferromagnetic resonance. Rotating ferrofluids have potential uses in a variety of fields including rotating turbomachines and chemical processing industry. The resulting eigenvalue problem is solved using isothermal boundary conditions and the regular perturbation method under the assumption of a small modulation amplitude. On the assumption that the principle of exchange of stabilities is valid, the onset criteria are formulated. The magnetic parameter, the Taylor number, the Prandtl number, and the magnetic field modulation frequency are all functions of the thermal Rayleigh number shift. The influence of various physical factors is perceived to be significant at moderate values of the magnetic field modulation frequency. The study shows that, in the presence of both magnetization and rotation, the magnetic field modulation has a destabilizing impact on the system with convection occurring faster than in the unmodulated system. [ABSTRACT FROM AUTHOR]

Samuil Kaplan (1921-1978) was a productive and famous astrophysicist. He was affiliated with a number of scientific centers in different cities of the former Soviet Union. During the earliest 13 years of his career, namely in 1948-1961, he worked at the Lviv University in Ukraine. In the present paper, the Lviv period of his life and scientific activity is described on the basis of archival materials and his published studies. Kaplan arrived in Lviv in June 1948, the same month when he obtained the degree of the Candidate of Science. He was a head of the astrophysics sector at the Astronomical Observatory of the University, a professor of the department for theoretical physics, as well as the founder and head of a station for optical observations of artificial satellites of the Earth. He was active in the organization of an astronomical observatory outside the city. During the years in Lviv, Kaplan wrote more than 80 articles and 3 monographs in 9 areas. At that time, his focus was on the stability of circular orbits in the Schwarzschild field, on the white dwarf theory, on space gas dynamics, on cosmic plasma physics and turbulence, on the acceleration of cosmic rays, on the physics of interstellar medium, on the physics and evolution of stars, on cosmology and gravitation, and on the optical observations of the Earth's artificial satellites. Some of his findings are fundamental to the development of theory in those fields as well as of observational techniques. The paper presents a complete bibliography of Kaplan's works published during the Lviv period and reviews his respective scientific achievements in the light of the current state of research in those areas. [ABSTRACT FROM AUTHOR]

The review presents the results of modeling of the solvation of nanoparticles with deep eutectic solvents that act as stabilizers of metal nanoparticles, which provide a new platform for nanoparticle technology. It is calculated that there is a slower dynamics of solvent molecules, i.e., a slowing down of water near solutes. Such water has limited movement and cannot be organized into tetrahedral forms, in contrast to water in volume. Also, the paper describes systematic studies of the adsorption configuration, distribution density and adsorption energy of molecules H$_{2}$O, CO$_{2}$, CH$_{4}$, N$_{2}$, C$_{8}$H$_{18}$ and fluorocarbons C$_{3}$F$_{8}$ and C$_{5}$F$_{12}$ on the surface of kaolinite (0 0 1). Water adsorption is initiated and occurs due to the growth of clusters around surface groups, which is mainly regulated by the interactions of hydrogen bonds. Further, the paper investigates theoretically physical and mechanical properties of nanoscale systems, in particular, nanotips, amorphous carbon monolayer and nanoparticles. It is shown that the single-layer amorphous carbon is surprisingly stable and is deformed with a high ultimate strength without the propagation of cracks from the point of failure. The sliding on amorphous polyethylene and silicon studied using the method of molecular dynamics is described. The paper also discusses the dependencies of the friction force, acting on nanoparticles, on their velocity and sizes, in particular, the contact area, the structure and the type of the material, as well as on the direction of their shear and temperature. At an angle of rotation $ 45^\circ $, the silicon friction forces reach a minimum value, which can be termed superlubricity. The molecular dynamics modeling of the surface of carbon nanotubes, chitosan, polyvinyl acetate, titanium dioxide, $α$-quartz and zeolite is described to solve application problems ranging from reaction control to targeted delivery and creation of new drugs. The general principles have been identified that artificial water channels made of carbon nanotubes porins must satisfy, which can serve as a basis for further experiments. The organic modification mainly forms a modifier layer by crosslinking the hydrogen bond with the substrate, the flatness of the modified layer is strongly influenced by the type and concentration of the modifier. [ABSTRACT FROM AUTHOR]

In this paper, the three-dimensional Casson flow of a ternary hybrid nanofluid over a porous linearly stretching/shrinking surface in the presence of an external magnetic field is considered. The surface deformation process is described by introducing two parameters of stretching/shrinking in the lateral directions. Using similarity transformations, the basic set of nonlinear partial differential equations is converted into ordinary differential equations. An exact analytical solution to this boundary value problem is obtained. The influence of the Casson parameter, magnetic field, porosity medium, and stretching/shrinking parameter, taking into account mass transpiration, on the velocity profiles and the skin friction coefficients is considered in detail. It has been established that the results obtained in some limited cases are in excellent agreement with the available data. Tables show the new results for the skin friction coefficients in the lateral directions (x and y) for different variants of surface deformation. [ABSTRACT FROM AUTHOR]

This paper investigates the changes in the properties of a bulk amorphous metallic alloy based on the ferrum (Fe55Ni8Co6)69-(Mo4Cr2V1)7-Al2-(P9C6B5Si2)22 under the influence of an alternating magnetic field (AMF). The level of the structural ordering of the bulk samples is higher than that of their tape counterparts. A slower cooling rate causes a partial nanocrystallization. The surface of such bulk samples is covered by surface layers, which were formed during the synthesis. These layers determine the corrosion resistance of amorphous alloys in the investigated solutions. After holding the samples in the AMF, some alteration of their elemental composition can be observed. An analysis of the electrochemical characteristics of the alloy samples under the conditions of cyclic scanning of the electrode potential indicates a higher corrosion resistance of the tested samples in a solution of hydrochloric acid. The lowest corrosion resistance was in the aqueous NaOH solution. During multiple cyclic polarization of bulk samples in aggressive media, a passivation of the surface occurs, and the destruction of the surface protective layers. The samples of the alloy (Fe55Ni8Co6)69-(Mo4Cr2V1)7-Al2-(P9C6B5Si2)22 modified by an alternating magnetic field have increased corrosion resistance in a 0.5 M aqueous solution of NaCl and HCl. By choosing the duration of the modification in the alternating magnetic field, it is possible to change the electrochemical parameters of the alloy (Fe55Ni8Co6)69-(Mo4Cr2V1)7-Al2-(P9C6B5Si2)22. An alternating magnetic field contributes to the diffusion of atoms in the bulk, which will determine not only the electrochemical parameters of amorphous alloys, but also other physical and chemical properties of a multicomponent sample. Under the influence of AMF, the electrical resistance of the amorphous samples is significantly reduced with increasing exposure to the magnetic field [ABSTRACT FROM AUTHOR]

The Hirota-Ramani equation is considered. Its two-kink solutions are known and may be constructed, for example, by direct methods if the parameters ki, i = 1, 2 of the solution components are not equal to each other. In this paper, such solution is constructed for k1 = k2. [ABSTRACT FROM AUTHOR]

We present and analyse the performance of different combinations of four higher-order numerical integrators and up to nine interpolation schemes applied to the problem involving the Sun and four Gas-giants (outer planets), namely, Jupiter, Saturn, Uranus, and Neptune. The Hermite interpolation schemes obtained by one, two, and three time-step and interpolants for ODEX2 and ERKN integrators are considered in this paper. The interpolants are a special example of an interpolation scheme, which produce an approximation that is continuous across one step and across the complete interval of integration. The interpolants are quite expensive in comparison with the other interpolation schemes. Therefore, one of the objectives of this paper is to investigate the possibilities of replacing the interpolants of certain integrators by other interpolation schemes, perhaps at a cost of a little bit of accuracy. The experiments are performed to examine the error growth in the positions, velocities, and relative error in energy and angular momentum using different combinations of integrators and interpolation schemes over a long interval of integration, as long as 100 million years for the Jovian problem with local error tolerances ranging from 10-16 to 10-08. [ABSTRACT FROM AUTHOR]

The paper presents theoretical investigations of the elastic and acoustic properties in crystals forming the solid solution system CuGa(S1 − xSex)2 . The structures with varying selenium content, x = 0, 0.25, 0.5, 0.75, and 1, were examined. Employing the supercell method, a series of solid solutions were modeled by replacing sulfur atoms with selenium atoms in the CuGaS2 crystal structure. The generated substitution structures underwent geometry optimization using density functional theory (DFT) in conjunction with the BFGS algorithm, describing the exchange-correlation interactions through generalized gradient approximation (GGA). The optimized structures of the solid solutions were found to be in good agreement with the available experimental data, with a slight overestimation of parameters, attributed to the known features of the GGA functional. The elastic constants matrix Cij for tetragonal symmetry was calculated, demonstrating compliance with Born's mechanical stability criterion for all compositions investigated. The evaluation of the material's elastic characteristics with changing composition revealed that the coefficients and C33 exhibited nearly twice as large values compared to the shear coefficients. Notably, the C11 coefficient reached 104.79 GPa, while the minimum value was obtained for C44 at 51.29 GPa. Isomorphic replacement of sulfur with selenium atoms resulted in a monotonic decrease in the elastic constants Cij. Employing the Green-Christoffel equation, the acoustic wave propagation velocities in a number of crystals were calculated using a home-made program written in Python. Acoustic wave velocities v were computed in (100) and (001) planes, with the highest observed velocity v max = 5586 m/s corresponding to the longitudinal acoustic wave (LA) in the (001) plane. The isomorphic replacement of S → Se resulted in a monotonic reduction in the propagation velocity v of acoustic waves within the investigated solid solution system. An analysis of anisotropy revealed that transverse TA2 waves exhibited the highest values for the A coefficient, accounting for 35-43% in the (100) plane and 28-40% in the (001) plane. In contrast, for LA waves, the propagation velocity was nearly isotropic (A parameter close to zero). [ABSTRACT FROM AUTHOR]

The text describes a scientific event held in Lviv, Ukraine, dedicated to World Quantum Day. The event aimed to popularize quantum theory and its practical applications, with over 200 participants from various countries attending. The program included presentations, lectures, and panel discussions on quantum computing and programming. The event received positive feedback from students, scientists, and IT representatives. The text also includes two research papers discussing topics related to quantum metrology and photodetection techniques. It discusses the need for quantum computing in condensed matter physics and proposes alternative methods for describing strongly correlated quantum systems. The text also presents an analytical solution for maximally entangled states of four quantum dice, demonstrating the quantum advantage. It provides an introduction to quantum information theory, discussing quantum superposition, entanglement, and the potential of quantum computers. The text also discusses the existence of discrete spectrum points and bound states in weakly deformed waveguides, as well as the concept of quantum correlations and their importance in understanding quantum mechanics. It presents research on the transfer of entanglement and steering properties in linear chain systems and proposes a method for calculating the partition function of spin systems on quantum computers. The results of the quantum calculation are in good agreement with theoretical predictions. [Extracted from the article]

Precise analysis of complex gas mixtures is an urgent task today, since its accuracy and quality is important not only for human health, but also for the ecology of population centers or the planet as a whole. Traditional methods of gas environment analysis are imperfect, and those that have the necessary sensitivity and selectivity do not yield results in a particularly short time. Nowadays, the Fabry- Pérot interferometry is used for research in a significant number of industrial and scientific areas. The analysis of the works presented in this paper confirms the relevance of research in the field of multibeam interferometry and the prospects of developing modifications of the Fabry- Pérot interferometer. The article is devoted to classical optical correlation methods for the analysis of gas mixtures with a quasi-periodic structure of the spectrum. A modification of the analyzer was developed and it was shown that the use of the modified Fabry- Pérot interferometer as a correlation mask ensures the express realization of the selectivity of the measurement components. An experimental study was conducted to test the possibility of scanning the SO2 absorption spectrum in the 220 nm region. Laboratory tests of the described layout of the SO2 analyzer demonstrated its high metrological parameters. The main reported error was 1% on the 0 -10000 ppm scale and 10% on the 0 -1000 ppm scale. The length of the cuvette was 170 mm, the warm-up time of the model was 30 minutes, the minimum measured concentration was 25 ppm. We can state that the correlation masks based on the IFP can be widely used for the analysis of gas components with a quasi-periodic structure of the spectrum. Compared to other devices of a similar type, they have a much higher luminous intensity: U = ΩA, where Ω is the solid angle; A is the light diameter of the IFP with the same resolution. This is crucial for remote instruments [V. R. Kozubovskii, Yu. Yu. Bilak, Ukr. J. Phys. 66, 664 (2021)]. In addition, their small weight and dimensions allow one to create portable devices based on them. However, since the IFP is a multi-beam interferometer, the procedure for optimizing its parameters is rather complicated, although technical methods for solving this problem exist [V. R. Kozubovskii, V. L. Goldovskii, O. D. Kraysler, AS 1182345 USSR, MKI G01N 21/61]. The conducted analysis and research open up new opportunities for the optimization of interferometric devices and interferometric methods of gas analysis. [ABSTRACT FROM AUTHOR]

In the paper, a review of the results for recovering the weak equivalence principle in a space with deformed commutation relations for operators of coordinates and momenta is presented. Different types of deformed algebras leading to a space quantization are considered, among them noncommutative algebra of a canonical type, algebra of the Lie type, the Snyder algebra, the Kempf algebra and nonlinear deformed algebra with an arbitrary function of deformation depending on momenta. The motion of a particle and a composite system in a gravitational field is examined and the implementation of the weak equivalence principle is studied. We conclude that the Eötvös parameter is not equal to zero even in the case when the gravitational mass is equal to the inertial mass. The principle is preserved in a quantized space if we consider parameters of deformed algebras to be dependent on mass. It is also shown that the dependencies of parameters of deformed algebras on mass lead to preserving the properties of the kinetic energy in quantized spaces and solving the problem of the significant effect of space quantization on the motion of macroscopic bodies (the problem is known as the soccer-ball problem). [ABSTRACT FROM AUTHOR]

Every year, human energy consumption is constantly growing, so the role of nuclear energy will only increase over time. However, the reserves of 235 which is the main fissile nuclide in nuclear energy, are limited and should be depleted in the coming decades. But this problem can be avoided if we use the huge reserves of 238 U. This article aims to investigate the feasibility of implementing one of the regimes of a fundamentally new and not yet practically implemented process in nuclear energy – the nuclear traveling wave in a uranium-plutonium medium, where plutonium-239 is formed from 238 U. A nuclear traveling wave may form in a uranium-plutonium medium as a moving wave of plutonium-239 fission. This paper considers the possibility of the formation of such a wave in a spherical uranium-plutonium medium, and the study is conducted in spherical geometry. A majority of works studying the traveling wave mode of nuclear fission consider 1D or cylindrical 3D geometry. There are only a few works devoted to the study of this problem in spherical geometry. It should also be noted that the nuclear reactions considered in the present paper involve the participation of epithermal neutrons, which also significantly distinguishes our work from previous works on this topic, because most of them consider thermal neutrons. Since this problem is spherically symmetric, it allowed us to replace 3D modeling of the whole sphere with 1D modeling along the radius of this sphere. We have developed kinetic equations describing a nuclear traveling wave and modeled it by numerically solving these kinetic equations. An improved explicit-implicit numerical calculation scheme was used, which allowed us to increase the temporal step of the simulation. [ABSTRACT FROM AUTHOR]

The paper presents the results of the studies into the photoluminescence of cytosine molecules in a neutral liquid medium induced by the radiation of a xenon lamp with a wavelength of 280 nm. It was found that the luminescence is represented by a wide band with a vague threshold at a wavelength of 340 nm and a blurred maximum in the spectral region of 365-380 nm. It is shown that the presented luminescence curve reflects fluorescence, while phosphorescence is absent entirely. The lack of phosphorescence can be explained by the effect of the solvent. The obtained results are compared with the data of known studies. The discrepancies found may be primarily due to the pH of the solvents used in the previous studies. It is the first time that experiments with the excitation of luminescence of a neutral liquid solution of cytosine molecules under the simultaneous action of xenon lamp radiation with a wavelength of 280 nm and a continuous laser beam with a wavelength of 530 nm and a power of 0.25 W have been performed. It has been established that under these experimental conditions the luminescence curve acquires a qualitatively new form - the luminescence threshold is shifted to the short-wavelength region, and the luminescence curve has an additional maximum at a wavelength of 410 nm. An explanation of the physical nature of this phenomenon is given, which is that the intense electromagnetic field generated by the laser promotes the efficient formation of singlet exciters of cytosine (photodimers). In the process of their decay, cytosine photodimers form excited monomers in singlet states which, by intercombinational conversion (intersystem crossing), intensively populate metastable triplet states. The radiation decay of the formed metastable triplet states causes phosphorescence, which is the reason for the appearance of the second maximum in the wavelength range of 410 nm. Attention is drawn to the fact that metastable triplet states play a key role in the photochemistry of nucleic acid bases and presumably will have a major impact on the development of new biotechnologies. [ABSTRACT FROM AUTHOR]

The paper investigates the stability of small axisymmetric disturbances in a nonuniformly rotating viscous electrically conductive fluid taking into account galvanometric and thermo-magnetic phenomena. In the local geometrical optics approximation, we obtained a dispersion equation taking into account the Hall, the Nernst, the Right-Leduc effects and gradients of temperature ⛛T0 and thermo-electromotive force coefficient ⛛α in constant magnetic field B0 0 and gravitational field g. The growth rates of thermomagnetic instability (TMI) in a nonuniformly rotating electrically conducting fluid without an external magnetic field (B0 = 0) are obtained for the case of "smooth" (a weakly inhomogeneous medium) gradients (⛛T0 and ⛛α). The regions of the development of TMI are established depending on the profile of the angular velocity of rotation (Rossby number Ro) and the radial wave number kR. The conditions under which the generation of a magnetic field with sharp gradients of temperature and thermo-electromotive force coefficient in the media with low (σ → 0) and high (σ → ∞) conductivity are found. The regions of the development of the Hall magnetorotational instability in an external magnetic field (B0 ≠ 0) are established depending on the profile of the angular rotation velocity (Rossby number Ro) and the axial wavenumber kz. The growth rates of TM instabilities for the propagation of perturbations with a wave vector k in the radial direction k∥eR are obtained taking into account the Nernst effect in an external magnetic field B0, the Righi-Leduc effect, the inhomogeneity of the equilibrium temperature and specific thermopower, and the buoyancy force in a temperature-stratified medium. [ABSTRACT FROM AUTHOR]

The paper presents emission spectra of an overstressed nanosecond discharge between zinc electrodes in air and nitrogen at pressures of 13.3 kPa and 20 kPa, respectively. In the process of microexplosions of inhomogeneities on the working surfaces of zinc electrodes in a strong electric field, zinc vapor is introduced into the discharge gap during the formation of ectons. This creates prerequisites for the formation of molecules and clusters of zinc, oxide and zinc nitride in plasma and the synthesis of thin nanostructured films of zinc, oxide and zinc nitride, which can be deposited on a glass or quartz substrate installed near the center of the discharge gap. The spectral characteristics of the discharge were investigated from the central part of the discharge gap 2 mm in size. The main excited components of the plasma of vapor-gas mixtures based on zinc vapor and air and nitrogen have been identified, which, when deposited outside the discharge plasma, can lead to the formation of thin nanostructured films of zinc, nitride and zinc oxide. [ABSTRACT FROM AUTHOR]

The paper contains the biographical data and the list of publication of the staff of the Department for Experimental Physics, University of Lviv, in 1872-1939. The following staff members are included (in the alphabetical order): Jan Bochnik, Szczęsny Gnatowski, Kazimierz Gostkowski, Luiza Gregor, Jakub Klinger, Jadwiga Klonowiecka (married Halaunbrenner), Zofja Krzysik (married Orlicz), Kazimierz Krzyżanowski, Andrij Lastovećkyj, Stanisław Loria, Stanisław Malec, Jan Marszał, Roman Negrusz, Wincenty Podlacha, Marjan Puchalik, Franciszek Słuszkiewicz, Zdzisław Specht, Tomasz Stanecki, Zdzisław Stanecki, Jan Stock, Józef Szpilecki, Ignacy Zakrzewski, Jan Załuski, Franciszek Zelena, and Władysław Żłobicki. The list of publications discovered so far contains 192 items. [ABSTRACT FROM AUTHOR]

The paper describes the accelerator Mikrotron M-30 (1-18 MeV) of the Institute of Electronic Physics of the National Academy of Sciences of Ukraine and its main characteristics. Also, it briefly reviews articles on the formation of radiation fields and discusses their characteristics for nuclear physics installations. It includes application of various methods of measuring the currents of charged particles, methods of detecting radiation Fields using various recording media and changing the spatial distribution using attening lters. Attention is also paid to an alternative low-cost registration method using commercial window glass. For the Mikrotron M-30 accelerator, parameters of the radiation fields were investigated on a metrological bench oriented along the electron beam at distances of 0-400 cm from the M-30 beam output node. Diametric characteristics were determined using ionization chambers of the ROBOTRON dosimeter and a Faraday cylinder designed for diagnostics of electron beams with energies up to 30 MeV. In this work, to control the spatial uniformity of the radiation field, we used a registration method based on glass plates; the degree of uniformity of the radiation field was determined by a change in their optical characteristics, namely, the degree of darkening. For correctness of the obtained distributions, the radiation dose was limited to the region of linearity of glass darkening from the absorbed dose. The use of a radiation shaper ensured irradiation of samples with radiation of a uniform Field in the irradiation plane of 30%, which satisfies the conditions of radiation tests for most objects. Analytical dependencies of the radiation dose on the distance to the output node M-30 were obtained using a Faraday cylinder. The combination of these dose dependencies of glass darkening, the spatial homogeneity of the fields, along with the dose dependence on the distance to the source node, made it possible to develop protocols for dosimetric tracking of the irradiation process for materials and devices for various purposes. [ABSTRACT FROM AUTHOR]

This paper presents the results of ultrasonic measurements in trigonal LiTaO3 crystals. The samples of direct section with faces perpendicular to the main crystallographic axes and X/45 sections of LiTaO3 crystals were manufactured for experimental studies. The velocities of longitudinal and transverse acoustic waves along the three principal crystallographic axes and two additional axes in theYZ plane in trigonal crystals of point group 3m LiTaO3 crystals were measured using the pulse-echo overlap method. In the piezoelectric crystals, elastic and electrical properties are related and the propagation of an acoustic wave is accompanied by the appearance of electric fields, which must be taken into account in the calculations. The relations for the complete determination of all components of the matrices of elastic stiffness and piezoelectric coefficients based on all necessary acoustic wave velocities measured were derived from the Christoffel equation for the piezoelectric crystals. Using the obtained ratios, all components of the tensors of piezoelectric coefficients, elastic stiffness constants, as well as all elastic compliances of LiTaO3 crystals are calculated. The obtained results are consistent with the literature data and will be used in further measurements and calculation of the spatial anisotropy of induced (electro-, piezo- and acousto-optical) effects on the same crystal samples in order to select the most effective geometry of their possible practical use. [ABSTRACT FROM AUTHOR]

The paper studies structure and dynamics of the crystal lattice of solid solutions based on zirconium dioxide. Structural experiments were performed on a KSN-2 neutron spectrometer (in the "diffractrometer" mode) and DRON-3.0 X-ray diffractrometer. The phonon spectrum of solid solutions was obtained using the method of inelastic scattering of thermal neutrons. Dispersion ratios were obtained with KSN-2 (in a "triple-axes-spectrometer" mode) on monocrystal samples. It is known that the introduction of such ions as Ca, Y, Nd, Sc into the ZrO2 crystal lattice stabilizes the cubic structure of the lattice. Particular attention was paid to the ZrO2 system - 33% mol. Y2O3. In this system, the possibility of formation of a pyrochlor structure was considered. It has been suggested that a phase transition occurs in ZrO2-based solid solutions under the influence of neutron irradiation and temperature, which can lead to disruption of coatings made of these materials. [ABSTRACT FROM AUTHOR]

This paper presents the results of a study of the existence of nine near-Earth meteorite-producing groups in asteroidal orbits, containing sporadic fireballs from the IAU MDC-2007 database, sporadic meteors from the SonotaCo database, meteorites − namely, L5, L6 and H4−H6 ordinary chondrites and an ureilite, for which atmospheric and orbital parameters are known from instrumental observations. Orbits of the selected members of meteorite-producing groups were classified as asteroid orbits according to the Tisserand parameter Tj > 3.1. Dynamic links between the members of the identified meteorite-producing groups and instrumentally observed known meteorites which were taken as a reference for the search of potential group members were tested using orbital similarity criteria, in particular the Drummond criterion − DD and the Southworth and Hawkins criterion − DSH. As a result, several meteorite-dropping sporadic fireballs and small meteors, whose orbits are similar to the asteroid orbits of nine known meteorites, were detected and reckoned as possible members of meteorite-producing groups. [ABSTRACT FROM AUTHOR]

The paper draws attention to some theoretical problems of the Standard Model. In particular, the “phi-four” self-action of the Higgs field in the Standard Model is not a consequence of the derivatives “extension” in order to localize some symmetry. The same applies to the Yukawa interaction of the fermion fields with the Higgs field. The only manifestation of such interactions which are being discussed is the mass generation by particles of the Standard Model. Therefore it is unclear how the existence of such interactions can be confirmed experimentally. In the paper, it is proposed to consider the Higgs boson as a bound state of two gauge bosons and describe it by the multi-particle fields method [13, 14]. Within this approach, the self-action of the Higgs field is the consequence of the self-action of a non-Abelian gauge field, i.e. it is not a manifestation of a “new” non-gauge interaction. Unfortunately, within the proposed approach it is impossible to describe the Yukawa interaction in a similar way. Moreover, the “unnatural” sign in the Lagrangian under the squared Higgs field is not postulated as in the Standard Model, but it is the result of the dynamic equations of the two-particle gauge field. Therefore a physical interpretation of the spontaneous symmetry breaking is proposed by analogy with the phenomenon of the critical condensation. The bound state of two gauge bosons is described by the two-particle gauge field that takes values on the linear space of weak-isospin second rank tensors. Under the global group SU(2)-transformations, this linear space can be decomposed into a direct sum of invariant subspaces: tensors multiple of unit tensor, antisymmetric and symmetric tensors with zero trace. If we write the Lagrangians of these fields, the local SU(2)-symmetry of these Lagrangians will be achieved by the derivatives “extension”. Thus, the interaction of irreducible tensor fields with the Higgs field can be introduced. It is shown that the interaction of the antisymmetric part of the field with the gauge field contributes to the mass of W±-bosons, and the interaction of the symmetric part with a zero trace with the gauge field contributes to the mass of all three gauge bosons, as W± and Z0-bosons. Hence the parameters of the model can be given that the Z0-boson mass will be greater than the mass of the W±-bosons, as required by the experiment. [ABSTRACT FROM AUTHOR]

This paper studies, the generation of magnetic fields in a nonuniformly rotating layer of finite thickness of an electrically conducting fluid by thermomagnetic (TM) instability. This instability arises due to the temperature gradient ▽T0 and thermoelectromotive coefficient gradient ▽α . The influence of the generation of a toroidal magnetic field by TM instability on the convective instability in a nonuniformly rotating layer of an electrically conductive fluid in the presence of a vertical constant magnetic field B0 || OZ is established. By applying the method of perturbation theory for the small parameter ϵ = √ Ra-Rac/Rac of the supercriticality of the stationary Rayleigh number Rac, a nonlinear equation of the Ginzburg-Landau type was obtained. This equation describes the evolution of the finite amplitude of perturbations. Numerical solutions of this equation made it possible to determine the heat transfer in the fluid layer with and without TM effects. It is shown that the amplitude of the stationary toroidal magnetic field noticeably increases with allowance for TM effects. [ABSTRACT FROM AUTHOR]

The paper studies quantized space described by a time reversal invariant and rotationally invariant noncommutative algebra of a canonical type. A particle in a uniform field is considered. We find exactly the energy of a particle in a uniform field in the quantized space and its wavefunctions. It is shown that the motion of the particle in the field direction in time reversal invariant and rotationally invariant noncommutative space is the same as in an ordinary space (a space with the ordinary commutation relations for the operators of coordinates and the operators of momenta). The noncommutativity of the coordinates has an influence only on the motion of the particle in the directions perpendicular to the field direction. Namely, space quantization has an effect on the mass of the particle. [ABSTRACT FROM AUTHOR]

Context. The paper presents a computational scheme and a number of techniques for increasing the efficiency of mathematical modeling of the energy characteristics of metal clusters with vacancies. The object of the research is the process of calculating wave functions and finding eigenvalues using the Numerov and the shooting methods. Objective. The objective of the research is to improve the quality of the calculation of the wave functions of electrons in a metal cluster by using optimally selected methods and techniques in the computational scheme, to ensure the adequacy, stability and cost-effectiveness of self-consistent calculations of the energy characteristics of metal clusters by limiting the change in the electrostatic potential within a single iteration, choosing the optimal integration step and data presentation format. Method. At the modeling stage, to increase the efficiency, the electron Density Functional Theory was used in conjunction with the Kohn-Sham version for the stabilized jellium model taking into account the local density approximation for calculating the energy characteristics of nanoclusters. At the simulation stage, the one-electron wave function was calculated by “stitching” it from two parts at an empirically selected point with normalization before and after the procedure. A number of techniques have been developed to improve the quality of the simulation: calculating the optimal step, limiting changes in the electrostatic profile, managing the resulting data arrays, etc. For calculations on a supercomputer, the distribution between the flows was carried out. Results. At the modeling stage, economic models of the metal sphere with a vacancy in the center were developed. For the simulation stage, a method of stable two-sided calculation of the wave function using the shooting and the Numerov methods with the optimal step has been developed. The full computational scheme for the simulation is implemented in C ++ for calculation on a PC and on a supercomputer. The simulation results were compared with the \emph{ab-initio} calculation data and experimental data for Cs, Rb, K, Na, Li, Mg, and Al clusters with and without vacancies (calculation error < 15\ Conclusions. The developed computational scheme and modeling technique allow increasing the simulation efficiency and obtaining adequate energy characteristics of metal spherical nanoclusters with and without vacancies. Further research might focus on the modification of models and simulation techniques for the study of layered nanoscale systems. [ABSTRACT FROM AUTHOR]

This paper presents the results of computer simulation of the ideality factor of silicon n+–p–p+ structure with iron contamination. The Solar Cells Capacitance Simulator (SCAPS) was the tool used for numerical simulation of these devices. The iron concentration range of 1010 – 1013 cm–3, the acceptor doping level range of 1015 –1017 cm–3, the temperature range of 290 – 340 K, and the base thickness range of 150 – 240 μm were used in the investigation. The double diode model was used to extract the ideality factor. The following cases were considered: (i) uniformly distributed lone interstitial iron atoms; (ii) coexistence of non-uniformly distributed Fei and FeiBs. It has been shown that the ideality factor value is determined by a hole occurring on the Fei level, a trap location, and an intrinsic recombination contribution. The increase in the base thickness leads to a decrease in n value. The sign of change in the ideality factor after FeiBs dissociation depends on temperature, doping level, and iron concentration. [ABSTRACT FROM AUTHOR]

The origin and development of teaching and research in theoretical physics at the Lviv Polytechnic for the period from 1922 to 1933 is studied. The role of theoretical physicists of the Polytechnic in the development of physical research and training in post-war Poland and Ukraine is shown. The paper contains short biographical sketches of Professor Wojciech (Adalbert) Rubinowicz, who headed the Chair for Theoretical Physics at the Lviv Polytechnic, as well as of his students: Jan Blaton, Roman Stanisiaw Ingarden, and Wasyl (Bazyli) Milianczuk. All of them are known not only for scientific achievements, but also for organizational activities. іп particular, Jan Blaton (1907-1948) contributed to the organization of the Maria Curie-Sklodowska University in Lublin. Roman Stanislaw Ingarden (1920-2011) spend a major part of his life, from 1966 to 1991, at the Nicolaus Copernicus University in Torun; he also was a founder of the journal Reports in Mathematical Physics (in 1970). Wasyl Milianczuk (1905-1958) headed the Department for Theoretical Physics at the University of Lviv in 1945-58. He is the only link between pre- and post-WWII traditions of theoretical physics in Lviv as a whole and at the University of Lviv in particular. Prof. Milianczuk was also one of the founders of the Lviv school of spectroscopy. The bibliography of works in theoretical physics at the Lviv Polytechnic from the period of 1922-1933 is presented. The list counts thirty titles. The papers mostly concern one of Rubinowicz's primary research fields, quantum theory of radiation. More specifically, the topics include the theory of diffraction, Zeeman effect, multipole radiation, “forbidden” lines, etc. Professor Rubinowicz also authored several popular scince papers. [ABSTRACT FROM AUTHOR]

This papers presents the results of the influence of a weak magnetic field (MF) (0.354 T) on the electrophysical properties of surface structures based on p-Si. A 300-hours exposure of singlecrystal silicon samples in a magnetic field stimulates the decay of hydrogen-containing and oxygencontaining surface complexes (C-HX, Si-O-H, O-H) and the formation of Si-H3 centers. As a result, the surface resistance increases and the barrier properties of the Bi-Si(p) contact deteriorate. [ABSTRACT FROM AUTHOR]

The increasing scientific interest in Sn-based nanocomposite alloys with minor additions of oxides, metals and carbon in nanosized form is explained by the possible application of these materials as an alternative to commercial lead-free solders. As pointed out in recent literature reviews, the improved mechanical properties and reinforced microstructure of solder joints using nanocomposite Sn-Ag-Cu (SAC) alloys, compared to those without nanoinclusions, revealed new possibilities for the development of the currently used commercial lead-free solders. The main benefit of the nanosized additions is related to the suppression of the extensive growth of the Cu6Sn5 intermetallic compound (IMC) at the solder/Cu interface towards the solder side. This is achieved due to the spreading of nanoparticles over the IMC's surface, thereby suppressing the growth of Cu6Sn5 on the interface as well as in the bulk solder. In particular, the adsorbed nanoparticles on the IMC layer interface hinder the diffusion of Sn atoms from the bulk solder towards the interface and thereby suppress the IMC growth. Compared to the solid state, there is a limited number of papers dealing with experimental investigations of nanocomposite SAC solders in the liquid state after melting as well as in the semi-solid state. It has been shown that minor metal nanoadditions have an impact on the microstructure of solidified SAC solders, but practically without any significant change of the melting temperatures. The effect of small nanosized (up to 3 wt.%) nickel impurities on the electrical conductivity of Sn95.5Ag3.8Cu0.7 (SAC387) alloy has been investigated. It has been shown that the electrical conductivity gradually decreases with an increase in the impurity content of Ni. Conductivity, as a structure-sensitive transport characteristic of the liquid state of a substance, is important for modeling the processes of melting and solidification. The conductivity data provide additional information on the influence of admixtures on the structure and physicochemical properties of the metal matrix, which is important for understanding the microstructural transformations in a liquid state. Morphology of the samples was examined using REMMA-102-02 Scanning Electron Microscope- Analyzer (JCS SELMI, Sumy, Ukraine). [ABSTRACT FROM AUTHOR]

The paper presents the results of a comparative analysis of time series of Wolf numbers, total squares of spots groups, daily characteristics of the solar large-scale magnetic field (LSMF), its two components — photospheric and polar magnetic fields – with time series of the geomagnetic planetary index Ap. The cyclic changes of solar and magnetic activity and the asymmetry of magnetic field polarity reversal in two solar hemispheres were observed. The focus of this study was to determine the level of dependence of the geomagnetic activity on the dynamics of magnetic activity during the periods of the solar magnetic field polarity reversal. We used the complete homogeneous data series of magnetographic LSMF measurements (http://wso.stanford.edu), the synoptic maps of photosphere magnetic fields polarities (http://solis.nso.edu), the averaged daily squares of spots groups (http://solarscience.msfc.nasa.gov/greenwch.shtml), and the average daily values of Ap (ftp.swpc.noaa.gov/pub/warehouse). The pair of 22-23 cycles and the running 24 cycle of solar activity were investigated. We used a cumulative method of graphical representation of the studied observational data. The results are: • The north-south asymmetry of spots formation was found during 22–24 cycles. It has been established that the maxima of activity in different hemispheres are shifted by more than 1.5 years. This may be indicative of the independence of the solar cycles’ development in these hemispheres. • In the leading spots, the polarities change signs at the beginning of each cycle. At the solar poles, the magnetic field polarity reversal takes place during periods of solar activity maximum and not always at the same time. It is supposed that such an evolution of the solar magnetic field leads to the appearance of coronal holes and geomagnetic activity. • The evolution of the distribution of both solar and geomagnetic activity in the last three cycles (1986–2019) was investigated in detail. The geomagnetic disturbances are not maximal during the period of maximal spots formation, but 1–2 years later. The geomagnetic activity reflects the north-south asymmetry of the solar cycle and also the process of the solar magnetic field polarity reversal assotiated with it. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the Fisk–Tait equation in interaction with an external magnetic field in noncommutative space-time. The space-time noncommutativity is introduced through the Moyal– Weyl product method. Consequently, we studied the continuity equation in both commutative and noncommutative space-time; there we examined the influence of the space-time noncommutativity on the current density quadri-vector. Moreover, we find that the total charge obtained from the probability density is still indefinite even when space does not commute. Furthermore, we found the spin current density in the two different spin directions. We also investigated the linking between the fermions and the bosons in the Fock space using the Holstein–Primakoff transformation. [ABSTRACT FROM AUTHOR]

The paper describes an experimental setup for the measurement of the isobaric thermal conductivity of molecular crystals in the temperature range from 80 K to 300 K. A scheme of the developed experimental setup for measuring the thermal conductivity by the linear-flow steadystate method under saturated vapor pressures has been presented. A modified heat potentiometer method with one thermometer was used, which allowed us to minimize the error in the estimation of the thermal conductivity due to the uncontrollable heat flows and different calibration of thermometers. The noncontrollable heat flows from thermal radiation were reduced considerably with a radiation shield on which the temperature field of the measuring cell was reproduced using a set of thermocouples and precision heat controllers. The total systematic error in the measurement of the thermal conductivity does not exceed 5%. [ABSTRACT FROM AUTHOR]

Active galactic nuclei (AGN) are the brightest objects in the Universe and their brightness is mainly caused by accretion of m atter onto supermassive black holes (SMBH). This is the common reason of the AGN activity. However, every AGN has differences and fine features, which are the subject of an intensive investigation. The occurrence of such highly-relativistic objects as SMBH residing at the AGN core makes them an excellent laboratory for testing the fundamental physical theories. The X-rays and gamma-rays generated in a corona of an accretion disc around SMBH yield valuable information for these tests, the radiation in the range of 1-100 keV being at present the most informative source. However, there are a number of obstacles for such a study due to different physical processes that complicate the interpretation of observations in different bands of the electromagnetic radiation. In this paper, we review the current concepts concerning the structure of AGNs with a focus on the central part of these objects th at require relativistic theories for their understanding. The basic notions of the unified AGN schemes are considered; some modifications are reviewed. The paper contains the following sections. I. Introduction; II. Observational manifestations and classification of galaxies with active nuclei (II.A. Optical observations; II.B. Radio observations; II.C. X-ray data; II.D Infrared data; II.E. AGN anatomy with multywave data); III. AGN “central machine”; III.A. Black holes; III.B. Accretion disc types; III.C. Corona; III.D. AGN unified scheme); IV. Simulation X-ray AGN spectra (IV.A. The power-law contimuum and the exponential cut-off; IV.B. The absorption of X-rays; IV.C. Reflection; IV.D. Fe K a line; IV.E. Spin paradigm); V. AGN as a laboratory to test the fundamental interactions (V.A. Strong gravitational fields; V.B. Dynamic dark energy near compact astrophysical objects [ABSTRACT FROM AUTHOR]

The paper reports the effect of low-temperature annealing (up to 150°C) and light irradiation from a quartz mercury lamp (up to 20 min) on the structural, optical, and electrical properties of Indium tin oxide (ITO) films. 0.8 μm thick ITO films were obtained by RF magnetron sputtering of a commercial target on the optically transparent glass substrates in an argon atmosphere without heating. Information about the morphology of the ITO films' surface was obtained and the surface parameters were calculated using the method of atomic force microscopy. It has been found that the low temperature annealing for one hour and short-term irradiation with a quartz mercury lamp lead to an increase in the average size of crystallites and root-mean-square (RMS) surface roughness, a decrease in the resistivity of ITO films as well as an increase in the optical transparency in the visible spectral range. After annealing the ITO film at 150°C, the average crystallite size and RMS roughness of the surface increased approximately three times, and after 20 min irradiation – approximately 1.6 times, respectively. The lowest optical transparency in the visible spectral range among the studied experimental samples was found to be for the non-annealed and non-irradiated ITO films, whereas the highest – for the samples annealed at the highest temperature (150°C) and irradiated for 5 min with the light from the DRT-125 lamp. On the basis of the analysis of optical absorption spectra of ITO films, we detected an increase in their optical band gap from 3.59 eV for the unannealed film up to 3.66 eV with an increase in the annealing temperature of the samples up to 150°C. The resistivity of ITO films decreases with an increase in the annealing temperature up to 150°C and with an increase in the irradiation time with a light of the quartz mercury lamp up to 20 minutes. These results may be useful in the engineering of electronic devices based on the materials of low thermal stability. [ABSTRACT FROM AUTHOR]

We analyze the spectra of two sunspots of July 8, 2015 and September 5, 2021 which were observed with the ATsU-5 solar telescope of the Main Astronomical Observatory of the National Academy of Sciences of Ukraine. The main goal of the study was to search for signs of superstrong magnetic fields in the sunspots (>10³G), taking into account the fact that such magnetic fields can have mixed magnetic polarity. An SBIG ST-8300 CCD camera was used to record a spectral interval of about 8 Å near the FeI 5434.5 Å line, where six metal lines with effective Landé factors geff from −0.014 to 2.14 are located. Also, FeI 5397.1 line with geff = 1.426 was studied too for the second sunspot. In the first spot, we found a splitting of the I ± V profiles in the FeI 5434.5 line, corresponding to a magnetic field with a strength of ≈ 25 kG which has the opposite magnetic polarity with respect to the " kilogaussian" magnetic field (≈ 2 kG) determined from lines with large Landé factors. A detailed comparison of the spectral widths in the Stokes I profiles of two lines of the 15th iron multiplet, FeI 5434.5 and 5397.1 Å showed that their additional widening (local peaks of splitting) sometimes occurs at different places on the Sun. Considering that these lines have almost the same temperature sensitivity and formation height in the atmosphere, it is unlikely that this is a non-magnetic effect due to variations in thermodynamic conditions and the velocity field. Regarding the possible influence of spectral blends, the paradox is that it is the more " clean" line Fe I 5434.5 that demonstrates the most incomprehensible splitting peaks. This strengthens the assumption that the observed splitting peaks are of a magnetic nature. But then, if we assume that the additional widening of the 5434.5 line is due to the magnetic field, then its value should be ~ 105 G. The semi-empirical model for the first sunspot was built using the so-called Tikhonov stabilizers, which modify the objective function to ensure the smoothness and stability of the solutions of the inverse problem. This model has an anomalous feature, namely, the maximum of micro-turbulent velocities in the region of the temperature minimum, i. e. where the minimum of these velocities is present in the model of a quiet photosphere. Perhaps this feature indicates very strong magnetic fields in this sunspot. On the whole, we cannot draw a final conclusion about the existence of the abovementioned superstrong magnetic fields in the sunspots, but we draw attention to interesting and mysterious effects in the line profiles, which require additional studies. [ABSTRACT FROM AUTHOR]

The paper describes the capabilities and the current state of the horizontal solar telescope AZU-26, as well as considers a control hardware–software complex targeting and guiding the telescope. Studies of flares in a large range of heights in the solar atmosphere have been carried out. The physical state of the photosphere before solar flares and at their initial stage has been determined on the basis of the observations. We have observed and studied some variations of chromospheric thermodynamic parameters at the initial stage of a flare and a two-ribbon flare. Nonhomogeneous semiempirical models of the flare chromosphere and surge have been built for the moments of the flare observations. Our calculations in the framework of two-component chromospheric models point to a possible existence of some details with deep heating chromospheric layers. Some twist motions were observed in the active region photosphere and chromosphere. The temporal changes of the horizontal velocities in the kernel sites and their surroundings were of a wave character and were nearly synchronous throughout the whole height of the photosphere. A detailed analysis of the motion of matter initially in the low-temperature atmospheric layers and in the flare regions on the Sun is an important factor for understanding the processes of propagation of turbulence from the region of the primary energy release as a result of magnetic reunions in flares of various types. The study of the field of velocity of the flare area by observations in a wide spectral range enables us to verify the validity of existing ideas about the mechanisms of the transfer of flare energy. [ABSTRACT FROM AUTHOR]

In this paper, we studied the string theory in its original form of Nambu-Goto. We found that the calculation of the variation of the Nambu-Goto action with respect to the metric of the word sheet leads to a nonlinear action which is not strictly equivalent to the Polyakov action. Then the equation of motion corresponding to this action is nonlinear. This was the reason why we decided to solve the nonlinear Nambu-Goto equation of motion directly. This has been done for a string interacting with a constant, antisymmetric tensor field B in the Nambu-Goto formulation, and we derive the noncommutativity among the string end points coordinates. [ABSTRACT FROM AUTHOR]

The paper deals with an approach to the study of classical systems of interacting particles including distribution functions using random field theory and integration following the Wiener measure. For a Liouville distribution function, statistical functionality is determined for which a string of equations in the Wiener space similar in shape to the Bogoliubov chain of equations for the distribution functions in the phase space is derived. With the use of the development of statistical functionals included in the output string of equations in a row built by Wiener, in “transition” from the Wiener into the phase space, corresponding approximations for the different functions of the particles are determined, for which systems of linear differential equations are derived. The solution to the equation for the zero approximation of the one-particle distribution function represents the local equilibrium distribution, which, when t —— ^o, enters the well-known Maxwell function. All the solutions to homogeneous equations for different approximations of the one-particle distribution function if t = 0 are the same, which makes it possible to determine the unknown two-particle approximation, three-particle, etc. distribution function at t = 0. It is also indicated separately that the Bogoliubov chain of equations can produce a sequence of closed systems of linear differential equations matching the systems discussed in this paper. In the case of the statistical equilibrium all time derivatives for all approximations of the distribution function equal zero, and the time-independent functions fall into the product of two independent functions of the coordinates and impulses. The equations obtained for the distribution functions of certain approximations are easily solved. For the zero and first approximations of two-particle distribution function we obtain the known values. For the second approximation of the distribution function an expression is obtained in which one of the components is divergent, but in the combination with the following addend of the same order their sum is zero - in accordance with the general requirements for orthogonal expansions of the stochastic functional, following which the next approximation is finite. For the third approximation of this very distribution function is an expression that consists of 214 different types of addends by different amounts of the Mayer functions' products. Given the above-mentioned requirements for the orthogonal statistical functional expansion, the third approximation takes finite values too. [ABSTRACT FROM AUTHOR]

The number of exactly solvable potentials is rather limited. Therefore, much attention has been devoted to quasi exactly solvable (QES) problems for which it is possible to find exactly in an explicit form only a few energy levels and the corresponding wave functions. It was found that supersymmetric (SUSY) quantum mechanics is a powerful tool for this purpose. In our paper [V. M. Tkachuk, Phys. Lett. A 245, 177 (1998)] we proposed SUSY method for generating QES potentials with two known eigenstates. In the frame of this method the general expressions for the superpotential, the potential energy and two wavefunctions which correspond to the two energy levels were obtained. Using this method, we obtained QES potentials for which we found in the explicit form the energy levels and wave functions of the ground and first excited states. Later in [V. M. Tkachuk, J. Phys. A 34, 6339 (2001)] this method was generalized for the case of an arbitrary two energy level. In this paper the method of supersymmetric quantum mechanics has been used for discovering the quasiexactly solvable potentials for systems with position-dependent mass. We have established the conditions which provide regular potential energy in the case of a singular generating function. The examples of the quasi-exactly solvable potentials for a particle with position-dependent mass with two known eigenstates have been considered in the cases of regular and singular generating functions. We have found the exact eigenfunctions of a particle with position dependent mass which correspond to the two energy levels. [ABSTRACT FROM AUTHOR]

This paper presents a short review of the activities of physicists -- the full members of the Shevchenko Scientific Society in Lviv (abbreviated as NTSh -- from its name in Ukrainian: {\em Naukove tovarystvo imeni Shevchenka}). The society was founded in Lviv in 1873 and named after famous Ukrainian poet, writer, artist, public and political figure Taras Shevchenko. After reorganization in 1892, the society came to resemble a typical scientific association, and it was in fact the first Ukrainian Academy of Arts and Sciences. Structurally, in consisted of three sections, one of them was devoted to mathematics, natural sciences and medicine. NTSh was dissolved by the Soviet authorities in 1940; in 1947 it resumed its activities in Western Europe and in the USA; in 1989 it was reactivated in Ukraine. In this paper, we analyze the activities of the physicists that received the title of NTSh full members (academicians) by 1940. Different fields of physics were represented in the society during this period, and among the full members of the NTSh 21 scientists were engaged in physics. Publications in the field of physics appeared regularly in the {\em Collection of the mathematical-natural sciences-medical section of NTSh} -- a total of 74 articles were published on physical subjects, including 3 terminological and 10 bibliographic ones. The physicists took an active part in the organization and activities of the clandestine Ukrainian university in Lviv (1919-1925). Papers of NTSh full members appeared in leading European physical journals. Internships in leading European centres of physical thought were widely practiced. At the beginning of 1920s, physicists from other countries were elected as NTSh full members. Among them were Max Planck, Albert Einstein, Stepan Timoshenko, Mykola Krylov, Dmytro Rozhansky, Abram Ioffe. [ABSTRACT FROM AUTHOR]

In this paper we consider a model that describes rumors spreading process in the social community, whose members tend to opportunistic behavior. The model is based on the assumption that information is spread by agents (the members of the community). There are four possible states for every agent. Namely, an agent can bein the neutral state, which means that the agent doesn't spread information (but potentially can do it). Being in the active state means that the agent is the source of information spreading. In the opportunistic state the agent acts to decrease the infouence of those agents which are in the active state. In the relaxation state the agent can't spread information. The agents can make transitions from one state to another. Possible transitions are from the neutral state to the active state or to the opportunistic state, from the active and opportunistic states to the relaxation state, and from the relaxation state to the neutral state. To describe how the transitions are realized, we use a system of nonlinear differential equations. The equations determine how the number of agents in different states changes depending on the current distribution of the agents by states. In particular, transition from the neutral state to the active state is realized due to passing the information from the agents in the active state to the agents in the neutral state. An additional effect of this interaction is the transition of the agents from the neutral state to the opportunistic state. Interaction of the agents in the active and opportunistic states forces the active state agents to transit to the relaxation state. It is shown that a stationary solution exists in the system, and the stationary number of agents in the active state depends nonlinearly on the parameter which characterizes the intensity of the transition from the neutral state to the active state. [ABSTRACT FROM AUTHOR]

It is shown that the classical theory of phase transitions cannot be used to describe the melting of a nanocrystal. This is due to the zero-dimensionality of the nanocrystal in terms of thermodynamics. This paper contains a new model of nanocrystal melting, which takes into account the zero-dimensionality characteristic. Based on the proposed model, we obtained the formulas that describe the size dependence of the nanocrystal melting temperature and nanocrystal melting heat. [ABSTRACT FROM AUTHOR]

The spectroscopy of cold gas-dust envelopes of supernovae is the subject of this article. To define the quantitative characteristics of the matter in these envelopes, a possibility of additional sources of energy is discussed — in particular, the intense, diffusely distributed flows of high-energy positrons formed by the recently discovered chain of radioactive decays: 4422Ti 85 y −−→ 4421Sc 6 h −→ 4420Ca. The quantitative characteristics of radiation distribution function S(E, r) and electron distribution function F(E, r) are obtained for certain rarefied layers of the supernova remnant SN1987A. An additional feature of the kinetic ensemble of the envelope’s gas with the mentioned radioactive decay is the presence of the recoil nuclei of the final elements of this decay’s chain. In the case under consideration, these are the nuclei of 4420CaII. The paper notes that the motion of recoil nuclei in a rarefied supernova gas at a sufficiently high kinetic energy accumulated by radioactive decay determines that the recoil nuclei exist only in an ionized state, and the remaining nuclei, after hydrogen recombination, — in a neutral state. In the discussed case, 4420CaII can be observed only in an ionized state, and 4420CaII — only in a neutral state. This remark can be applied to the recoil nuclei of other elements formed at earlier times during the hydrogen recombination. It is shown that this method is suitable for isotopic separation of the final elements of radioactive decay chains occurring in young supernova envelopes. The presence of a nonthermal component in the obtained distributions of S(E, r) and F(E, r) causes an additional IR emission of the dust formed during the expansion of a supernova envelope in the modern epoch of observations. The presence of spectral lines at the moment of the Hubble telescope observation allowed us to conclude that the existence of the numerous observed spectral lines in the optical, UV, and near-infrared regions of the spectrum requires the presence of the astronomical silicates with extensive passbands extending over these spectral intervals in the observed dust shells. The presence of graphite dust in these bunches excludes the existence of the observed optical component of the spectrum and requires its presence in separate shell structures enriched with C–N–O elements. However, in this case, the presence of decaying 4422TiII isotopes which form the fast positrons is unlikely. The graphite particles, as well as H2 molecules, are influenced by positrons only when the density of the shell allows them to reach its outer layers. In this case, the number of collisions with atoms should not exceed several thousands. It is necessary to decelerate them before the complete annihilation with atomic electrons of the shell’s atoms and molecules. [ABSTRACT FROM AUTHOR]

We present a brief essay about the statistical physics of complex systems - a research direction that now acquires features of a well established field of science with its object of study, conceptual background, and methods of analysis. A complex system consists of many interacting parts (agents) and manifests collective behaviour nontrivially following from the behaviour of its individual components. Examples of complex systems are found in condensed matter, ecological and biological systems, human society, stock markets and economy. The concept of a complex system refers to many traditional disciplines of science and forms a new, inter-disciplinary branch of knowledge. Peculiar features of complex systems are self-organization, emergence of new functionalities, adaptive nature of interactions, high sensitivity to small changes in the initial conditions, governing power laws ("fat-tailed" distributions). In our paper, we concentrate on applying methods and concepts of statistical physics in a complex system analysis. We discuss how such approach allows for conceptual understanding and interpretation of a wide range of phenomena in various systems, not necessarily of physical origin. Together with the general description of the properties of complex systems, we give a brief overview of some studies performed in this field at the Institute for Condensed Matter Physics of the NAS of Ukraine (Lviv, Ukraine). In particular, these studies cover critical behaviour of complex magnets, scaling behaviour of complex polymer macromolecules, phase transition of spin system on complex networks, sociophysical approaches to studying human activities, scientometrics. [ABSTRACT FROM AUTHOR]

We calculated morphological parameters for a test sample of 4659 galaxies from VIPERS (spectroscopic galaxy survey performed on VIMOS spectroscope at VLT). These parameters include Gini, M20, Concentration, Asymmetry, and Smoothness, also known as CAS parameters. The results correlate with the distribution of these parameters for other simulated and observed samples. We also studied the dependence of these parameters with the Sersic power index of the radial distribution of the surface brightness of the galaxy image. Our aim was to find a clear division of VIPERS galaxies into elliptical and spiral. This is necessary for testing the method of the Sersic index (ns) calculation in the statmorph program. To find such bimodality, we use B-V color index from VIPERS database. To perform the error analysis of morphological parameters, we simulated galaxy images with a random background of different magnitudes and estimated the errors as the dispersion of the parameters. We also found asymptotic values of errors of morphological parameters by increasing the numbers of mock images. To analyse the possible variation of each morphological parameter during the convolution of close galactic images, we have simulated them to research. As a result of this investigation, we have analysed the dependence of every morphological parameter from CAS and Gini-M20 statistics, from the distance between galactic centers. The differences between our results for VIPERS and Gini-M20 distribution for PanStarrs galaxies at z < 0.5 could be explained by cosmological evolution of galaxies. We found out that in modern Universe there are many more elliptical galaxies than at z > 0.5 which corresponds to VIPERS sample. Also we concluded that galaxy mergers were more frequent in the early Universe. [ABSTRACT FROM AUTHOR]