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Energy levels of electrons in semiconductor quantum dots are obtained within the framework of perturbation theory taking into account the Rashba and Dresselhaus spin-orbit interactions and an external magnetic field. The circular quantum dots are simulated by a new smooth confinement potential of a finite depth and width. The dependence of energy levels on a constant uniform magnetic field and potential parameters is presented.

The main purpose of the article was to study the gender equality principles in the Ukrainian justice system. This paper covered the main mechanisms of the state of modern international legal regulations on the impact of gender equality in the administration of justice. The main issues arising upon the implementation of gender equality issues in the justice system of Ukraine were identified. It was suggested that new mechanisms of further improvement of the corresponding law enforcement practice. It was concluded that particularly during the COVID-19 pandemic, the recognition of gender equality in Ukraine as a key aspect of sustainable development requires the introduction of a gender integration policy in all areas, including in the justice system, where it is necessary to recognise gender aspects upon delivering justice.

BACKGROUND Clinical trials are essential to the advancement of modern evidence-based medicine. The number of healthcare professionals (HCPs) participating in clinical research is continuously declining. Collecting patient data for clinical research can be challenging and time-consuming. OBJECTIVE This study aimed to evaluate the use of the ZS Moments mobile phone application (app) as a real-time data collection tool in a survey of Healthcare Professionals (HCPs) treating patients with cow's milk protein allergy (CMPA). METHODS A secondary analysis of prospectively collected de-identified survey data obtained from HCPs treating patients with CMPA in an outpatient setting was conducted. HCPs downloaded the ZS Moments app to their mobile device. After evaluating a patient and recommending a clinical management strategy (visit 1), HCPs completed a 10-minute survey using the ZS Moments app to document patient symptoms in real time. At the next follow-up visit (visit 2), the HCP completed a second survey assessing how symptoms changed since initiating treatment. RESULTS Data from 404 patients (808 visits) were collected from 61 HCPs using the ZS Moments app. Of the 61 HPCs, 52 (85%) were included in the analysis. The most common reason for HCP exclusion was incomplete or non-submission of data. Of the 404 patient surveys collected, 75 (19%) were excluded due to the absence of visit 2 information, the discrepancy between the collected information on visit 1 and visit 2, or the poor quality of responses. Twenty-three patients were excluded from final symptom analysis calculations due to treatment switching but were included in the overall sample size. CONCLUSIONS The study found that a majority of healthcare professionals successfully completed surveys for both visit 1 and visit 2 using the ZS Moments mobile app. The use of high-quality, real-time data collection software like ZS Moments may help to simplify the process of data entry and increase HCPs’ participation in clinical research. This highlights the potential benefits of technology in improving data collection and promoting clinical research.

Although extensively hydrolyzed formula is widely accepted for managing cow’s milk protein allergy (CMPA) long-term, there is a lack of evidence on its short-term efficacy. This study’s objective was to investigate the short-term symptom changes (within 3–6 weeks) of infants diagnosed with CMPA and managed with extensively hydrolyzed formula containing Lactobacillus rhamnosus at their subsequent physician visit. Healthcare providers treating 202 patients diagnosed with CMPA under six months old completed de-identified surveys, which were then analyzed in this prospective study. After their first visit, the patients were started on extensively hydrolyzed formula, and their baseline symptoms were scored on a severity scale of 0–3. Patients were then reevaluated at their next follow-up visit to assess changes in symptom severity. The study found statistically significant improvements in gastrointestinal (93%), skin (83%), respiratory (73%), and uncategorized symptoms (90%). These symptom improvements were consistent across different follow-up visit durations. This study is the largest prospective analysis conducted in the United States evaluating short-term change in CMPA symptoms severity in infants under six months old using extensively hydrolyzed formula. These findings suggest that extensively hydrolyzed formula is associated with clinical symptom relief, which is often noticeable by the next follow-up visit. However, additional randomized control trials are needed to validate these results.

The two-dimensional circular quantum dot in a double semiconductor heterostructure is simulated by a new axially symmetric smooth potential of finite depth and width. The presence of additional potential parameters in this model allows us to describe the individual properties of different kinds of quantum dots. The influence of the Rashba and Dresselhaus spin-orbit interactions on electron states in quantum dot is investigated. The total Hamiltonian of the problem is written as a sum of unperturbed part and perturbation. First, the exact solution of the unperturbed Schrödinger equation was constructed. Each energy level of the unperturbed Hamiltonian was doubly degenerated. Further, the analytical approximate expression for energy splitting was obtained within the framework of perturbation theory, when the strengths of two spin-orbit interactions are close. The numerical results show the dependence of energy levels on potential parameters.

In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing highly accurate results. This work is meant to show that the RBM is an efficient and accurate emulator for the strong correlations induced by the pairing interaction in a variety of finite systems like ultrasmall superconducting grains, interacting topological superfluids and mesoscopic hybrid superconductor-semiconductor devices, all of which require an expensive, beyond-mean-field, particle-number conserving description. These systems are modelled by the number-conserving Richardson pairing Hamiltonian and its appropriate generalizations. Their ground state is solved for exactly using the Density Matrix Renormalization Group. The reduced basis is assembled iteratively from a small number of exact ground state vectors, well-chosen from across the relevant parameter space using a fast estimate of the emulation error and a greedy local optimization algorithm. The reduced basis emulation is found to accurately describe the weak-to-strong pairing cross-over in small grains, the third-order topological phase transition of the interacting Richardson-Kitaev chain, and the complex charge stability diagram of a hybrid quantum dot - superconductor device. RBMs are thus confirmed to be cheap and accurate emulators for the widely encountered superconducting phenomena. Capable of providing orders of magnitude computational speed-up with respect to approaches based only on traditional many-body solvers, they open new possibilities in building and solving models of interacting many-body systems and in better interfacing them with experimental design and data analysis., 16 pages, 17 figures

The surface morphology, elemental composition, and nanohardness of thin fullerite–aluminum films with different atomic fractions of metal are investigated by scanning electron and atomic-force microscopies, X-ray spectral microanalysis and nanoindentation. The films are obtained by the method of resistive evaporation in vacuum from a combined atomic-molecular flux of Al atoms and C60 molecules on single-crystal silicon substrates with the surface orientation (111). It is established that during deposition on unheated substrates, a nanocrystalline structure of films with an atomic fraction of metal of 20, 25 and 35%, with an average size of structural elements of 10, 15, and 25 nm, respectively, is formed. At the same time, internal mechanical stresses arise in the films, the relaxation of which leads to the exfoliation of significant sections of the film. During the deposition of films on substrates heated to 420 K, films with an average size of structural elements of 50–100 nm without exfoliation are formed, but in this case the nanohardness of the films decreases compared to the films obtained on unheated substrates.

The circular quantum dots localized in the double heterostructures are simulated by means of the axially symmetric smooth confinement potential of finite depth. For the proposed potential of new type, the exact wave functions and the energy levels of electron are found. The dependence of energy spectrum on potential parameters is investigated.

Nanostructured thin films on a silicon substrate were obtained by high-frequency pulse-periodic laser action (f ~ 10–15 kHz) with wavelength λ = 1.064 μm and power density q = 85 MW/cm2 on zinc oxide ceramic doped with scandium oxide in a vacuum chamber with pressure p = 2·10–2 mm Hg. The morphology of the obtained films was studied by atomic-force microscopy. Features of the transmission spectra in the visible and near and middle infrared regions were shown. The luminescence spectra obtained by excitation at various wavelengths were practically unchanged. The electrophysical properties of the ZnO + 0.9% Sc2O3/Si heterostructure were analyzed. It was established that the main conduction mechanism is current limited by space charge in an oxide film with deep traps.

The thin films deposited in vacuum (2 ⋅ 10–2 mm Hg) on the silicon and glass substrates under the multi-pulse high-frequency (10 –15 kHz) laser exposure (laser radiation power density 100 MW/cm2 and the distance from the target to the substrate 40 mm) for zirconium oxide ZrO2 ceramics doped with yttrium oxide 5 % Y2O3. The morphology of the obtained films was studied using atomic force microscopy. The features of transmission spectra in the visible, near infrared and middle infrared region were revealed. The transmission of the zirconium oxide film on the silicon substrate reached 12 % in the spectral region from 1.0 to 2.5 μm, and in the region from 2.6 to 6.0 μm was 4.7 %. On a glass substrate, the transmittance at a wavelength of 643 nm was 60 %, and at a wavelength of 2500 nm it reached 87 %. In the middle infrared region, transmission at a frequency of 2548 cm–1 was 70 % and reached 75 % at a frequency of 3566 cm–1. The volt-ampere and capacitance-voltage characteristics of the obtained zirconium oxide films were characterized by non-linearity, including hysteresis, and are probably due to the presence of discrete surface states with a wide energy spectrum associated with nanoparticles and nanocrystalline film inclusions.

The changes in the structure, surface roughness, and phase composition of thin fullerite-bismuth films deposited onto substrates from oxidized single-crystal silicon under thermal action in vacuum are studied by means of atomic-force microscopy and X-ray diffraction analysis. It is established that as-deposited bismuth films have a polycrystalline structure in the form of thin plates with an average arithmetic surface roughness of 13.72 nm. The thermal annealing of films at 490 K results in fractional recrystallization of the films and a decrease in the average arithmetic roughness to 12.74 nm. After thermal action at 540 K, the average arithmetic roughness of the films is 10.32 nm, the crystallites take the form of globules with an average size of 100 nm, new X-ray reflections appear on the X-ray patterns that indicate the formation of bismuth fulleride.

—Scanning electron and atomic force microscopy, X-ray diffraction, X-ray spectral microanalysis, and diffraction of reflected electrons were used to study changes in the structure, elemental, and phase composition of fullerite–copper films with an atomic metal fraction of 0.5, 1, 2 and 4%, deposited on oxidized single-crystal silicon substrates and subjected to thermal exposure in vacuum at different temperatures (470, 520, 570 and 620 K). It was found that thermal annealing at T = 520 K (t = 1 h) leads to the formation of a nanocrystalline structure with an average structural elements size of 33, 42, 50, and 65 nm for fullerite–copper films with an atomic fraction of metal of 0.5, 1, 2, and 4% respectively. An increase in temperature and annealing time leads to an increase in the size of structural elements and the formation of a new of CuxC60 phase, which belongs to the monoclinic space group P2/m. Electric force microscopy and the four-probe method were used to study changes in the local electrical properties and electrical resistivity of copper-containing fullerite films during vacuum annealing.

ZnO thin films of zinc oxide doped with 10 % ITO (indium tin oxide) on anodic aluminum oxide substrates are formed in vacuum during high-frequency repetitively pulsed laser deposition. The morphology of films on porous and non-porous surfaces of substrates was studied by atomic force microscopy. The optical properties of the films in the visible, near, and middle IR regions of the electromagnetic radiation spectrum, the Raman spectra, and also the features of the photoluminescence characteristics have been experimentally investigated. Zinc oxide films can be used in optoelectronic transducers, as luminescent material, in the form of transparent electrodes, sensitive layers of gas and biological sensors, catalysts, X-ray and gamma-radiation detectors.

9 pags., 5 figs., The ground-state pairing correlations in finite fermionic systems are described with a high degree of accuracy within a variational approach based on a combined coupled-cluster and particle-number-projected BCS ansatz. The flexibility of this symmetry-preserving wave function enables a unified picture valid from weak to strong coupling, both in small and large systems. The present variational approach consistently yields an energy upper bound while operating at the same level of precision as the nonvariational particle-number-projected Bogoliubov-coupled-cluster theory [Phys. Rev. C 99, 044301 (2019)2469-998510.1103/PhysRevC.99.044301]., This work was supported by a grant from the Romanian Ministry of Education and Research, CNCS-UEFISCDI, Project No. PNIII-P1-1.1-PD-2019-0346, within PNCDI III, and Project No. PN-19060101/2019-2022; and Spanish Ministerio de Ciencia e Innovación and European Regional Development Fund (FEDER) Project No. PGC2018-094180-B-I00.

The formal equivalence between the quartetting picture and the symmetry restored BCS picture is established for the ground state correlations induced by the general isovector-isoscalar pairing interaction. Multiple ground state structures compatible with the particle number and isospin symmetries are evaluated. The competition of isovector and isoscalar correlations is discussed for the $N=Z$ nuclei above $^{100}$Sn., Comment: 5 pages, 1 figure

The structure, phase composition, and mechanical properties of three-layer chromium-fulleritechromium films subjected to implantation with B+ ions (E = 80 keV, D = 5 × 1017 ion/cm2) are studied using the methods of atomic force microscopy, X-ray diffraction phase analysis, and nanoindentation. It is established that, as a result of ion implantation, the chromium and fullerite layers are intermixed and a solid-phase interaction occurs, owing to which a heterophase structure is formed with an increased nanohardness as compared with samples not subjected to implantation.

The advanced theory of the first and higher symmetric Frechet differentials and K-sub-differentials is constructed including the mean value theorem and the Taylor formula. We give simple sufficient conditions for symmetric K-subdifferentiability and consider some applications to Fourier series and variational functionals.

We study the pre-equilibrium dipole response in the charge-asymmetric reaction $^{132}$Sn+$^{58}$Ni at $E_{lab}=10$ MeV/A, within a semi-classical transport model employing effective interactions for the nuclear mean-field. In particular, we adopt the recently introduced SAMi-J Skyrme interactions, whose parameters are specifically tuned to improve the description of spin-isospin properties of nuclei. Within the same framework, we also discuss pre-equilibrium nucleon emission. Our results show that both mechanisms, i.e., pre-equilibrium dipole oscillations and nucleon emission, are sensitive to the symmetry energy below the saturation density $\rho_0$ (in the range $0.6\rho_0-\rho_0$), to the effective mass and to the nucleon-nucleon cross section. Finally, a covariant analysis is applied to study the correlations between the model parameters and observables of experimental interest., Comment: 6 pages, 4 figures

We study the description of single-species and isovector pairing correlations in the framework of the projected-BCS (PBCS) and the Quartet Condensation Model (QCM) from a particle-hole perspective and we introduce the representation of the QCM quartet condensate state in terms of particle-hole excitations with respect to the Hartree-Fock state. We also present a new bosonic approximation for both PBCS and QCM. In each case, the starting point is the reformulation of the pair/quartet condensate state in terms of particle-hole excitations with respect to the Hartree-Fock state. The main simplification of our approach is the assumption that the pair operators corresponding to both particle and hole states obey bosonic commutation relations. This simplifies tremendously the computations and allows for an analytic derivation of the averaged Hamiltonian on the condenstate state as a function of the mixing amplitudes. We study both the pure bosonic approach and the renormalized version, and compare the particle-hole bosonic version to the naive prescription of applying the boson approximation directly to the original condensate state. We compare the fermionic and the renormalized particle-hole bosonic approach in the case of a picket fence model of doubly degenerate states and in a realistic shell model space with an effective interaction for the $N=Z$ nuclei above $^{100}$Sn., 17 pages, 8 figures

Within the Quartet Condensation Model (QCM), the isovector pairing correlations for $N = Z$ nuclei are described with a very high accuracy by a condensate of $\alpha$-like quartets. The usual approach involves cumbersome recurrence relations in order to compute numerically the relevant quantities of the model: the norm of the quartet states and the mean value of the isovector pairing Hamiltonian as functions of the pair mixing amplitudes. We present the final analytical expressions for the above mentioned quantities, for all cases up to four quartets in the valence shell. The analytical QCM expressions were obtained by a straightforward implementation of the SO(5) algebra in the symbolic computer algebra system Cadabra2. The norm of the quartet states and the mean value of the Hamiltonian are polynomial functions of the mixing amplitudes. The numerical implementation of the QCM model is thus made trivial as matter of copying and pasting the presented formulas. We introduce in this work the method of computer aided analytical calculus for a many body setting. In particular, we provide precise and easy to use tools for the description of isovector pairing correlations., Comment: 5 pages

We study the nontrivial interplay of the well known \emph{pairing} and the more complex \emph{quarteting} correlations in the particular case of $N>Z$ atomic nuclei. Within the new Analytical Disentangled Condensate model, by implementing the notion of \emph{fractional degeneracy} we obtain the clear physical picture of a rather weakly interacting mixture of quartet and neutron pair condensates which mainly feel each other's influence through Pauli blocking. The basic idea of our approach may be generalized in order to scrutinize the extent to which similar manifestations are present in various many-body systems., 5 pages, 2 figures

We consider an interesting class of composite optimization problems with a gradient dominance condition and introduce corresponding analogue of the recently proposed concept of an inexact oracle. This concept is applied to some classes of smooth functional.

A laser method was proposed for the deposition of drop-shaped silver nanoparticles on the surface of polished silicon for use as active substrates in surface-enhanced Raman spectroscopy (SERS). The detection limit of rhodamine 6G when a drop of a solution of the dye is applied to the prepared substrates is

By SEM, AFM, electrostatic force microscopy, and X-ray diffraction methods, the structure, phase composition, and local electrical properties of tin–fullerite films implanted with B+ ions (E = 80 keV, F = 5 × 1017 ions/cm–2) are investigated. Ion mixing and solid- phase interaction of tin and fullerite layers are found to occur under ion implantation, and a heterophase structure with nonuniform local electrical properties is formed at the same time.

The influence of the number of layers and thermal annealing on the structure, elemental and phase compositions, and nanohardness of multilayer fullerite/aluminum films has been studied by scanning electron microscopy, atomic force microscopy, X-ray diffraction, X-ray microanalysis, and nanoindentation. The results demonstrate that sequential growth of five aluminum layers and four fullerite layers, each 50 nm in thickness, on oxidized single-crystal silicon substrates leads to the formation of textured films, which retain 111 texture after vacuum annealing at 620 K (τ = 5 h). In the case of the growth of bilayer films of greater thickness, C60(200 nm)/Al(300 nm), the fullerite and aluminum have a polycrystalline structure with no growth texture. Thermal annealing of the bilayer films leads to the formation of a new phase, AlxC60. The materials studied here possess enhanced nanohardness compared to pure aluminum and fullerite films.

The excitation of the Dynamical Dipole mode along the fusion path was investigated for the first time in the formation of a heavy composite system in the A~190 mass region, in fusion-evaporation and fission events. The composite system was formed at identical conditions of excitation energy and spin from two reactions with different charge asymmetry: the charge asymmetric 40Ca + 152Sm and the nearly charge symmetric 48Ca + 144Sm at E lab =11 and 10.1 MeV/nucleon, respectively. In this paper, we report the results on fusion evaporation events and the preliminary analysis on fission channel.

The excitation of the dynamical dipole mode along the fusion path was investigated for the first time in the formation of a heavy compound nucleus in the A ∼ 190 mass region. The compound nucleus was formed at identical conditions of excitation energy and spin from two entrance channels: the charge-asymmetric 40 Ca + 152 Sm and the nearly charge-symmetric 48 Ca + 144 Sm at E lab = 11 and 10.1 MeV / nucleon, respectively. High-energy γ rays and light charged particles were measured in coincidence with evaporation residues by means of the MEDEA multidetector array (Laboratori Nazionali del Sud, Italy) coupled to four parallel plate avalanche counters. The charged particle multiplicity spectra and angular distributions were used to pin down the average excitation energy, the average mass, and the average charge of the compound nucleus. The γ -ray multiplicity spectrum and angular distribution related to the nearly charge-symmetric channel were employed to obtain new data on the giant dipole resonance in the compound nucleus. The dynamical dipole mode excitation in the charge-asymmetric channel was evidenced, in a model-independent way, by comparing the γ -ray multiplicity spectra and angular distributions of the two entrance channels with each other. Calculations of the dynamical dipole mode in the 40 Ca + 152 Sm channel, based on a collective bremsstrahlung analysis of the reaction dynamics, are presented. Possible interesting implications in the superheavy-element quest are discussed.

The excitation of the Dynamical Dipole mode along the fusion path was investigated for the first time in the formation of a heavy compound nucleus in the A~190 mass region. The compound nucleus was formed at identical conditions of excitation energy and spin from two entrance channels having different charge asymmetry: the charge asymmetric 40 Ca + 152 Sm and the nearly charge symmetric 48 Ca + 144 Sm at Elab =11 and 10.1 MeV/nucleon, respectively. Both fusion–evaporation and fission events were studied simultaneously for the first time. The Dynamical Dipole mode excitation in the charge asymmetric channel was evidenced, in a model-independent way, by comparing the γ -ray multiplicity spectra and angular distributions of the two entrance channels with each other.

Proton-neutron (pn) correlations in nuclei above the Z=50 shell closure are investigated in order to understand the peculiar behaviour of the 2+ and 4+ states in Te and Xe isotopes. It turns out that by increasing the pn pairing interaction, which becomes important for N ≈ Z nuclei, the collectivity decreases. We thus conclude that the ratio between the B(E2) value and 2+ energy is a ”fingerprint” of pn collectivity. The available experimental data indeed indicate an enhanced pn pairing interaction by also approaching double magic Z=N=20 and Z=N=28 regions. It is known that the α-particle reduced width has the largest values in the region above 100Sn. In order to reproduce the reduced α-decay width we use an additional pocket-like surface potential in the single particle mean field, simulating four-body correlations. The strength of this interaction has a universal linear dependence on the experimental reduced width above the double magic nuclei 100Sn and 208Pb. Moreover, we demonstrate that pn pairing correlations have a small influence on this dependence and therefore cannot explain the larger reduced decay widths above 100Sn.

The γ -ray emission from the dynamical dipole formed in heavy-ion collisions during the process leading to fusion was measured for the N/Z asymmetric reaction 16 O + 116 Sn at beam energies of 8.1 and 15.6 MeV/nucleon. High-energy γ -rays and charged particles were measured in coincidence with the heavy recoiling residual nuclei. The data are compared with those from the N/Z symmetric reaction 64 Ni + 68 Zn at bombarding energies of 4.7 and 7.8 MeV/nucleon, leading to the same CN with the same excitation energies as calculated from kinematics. The measured yield of the high-energy γ -rays from the 16 O-induced reaction is found to exceed that of the thermalized CN and the excess yield increases with bombarding energy. The data are in rather good agreement with the predictions for the dynamical dipole emission based on the Boltzmann–Nordheim–Vlasov model. In addition, a comparison with existing data in the same mass region is performed to extract information on the dipole moment dependence.

The article discusses the national component in the missionary activity of the Russian orthodox church during the first occupation of Galicia in the 1914­1915. The national question in the Russian Empire closely associated with the religious situation, and confessional aspect occupied an important place as the domestic policy and foreign policy concepts, attitudes towards minorities. Especially brightly this is manifested in the First World War. The author should aim to delineate the main activities of the Russian Orthodox Church in Galicia, as part of the occupation apparatus during the first capture edge in the years 1914­1915 The Russian Orthodox Church activity in Galicia has been an integral part of the state. Geostrategic importance of the region was not too substantial and did not require such efforts to obtain and maintenance it. The main reasons aspirations of the Russian Empire in Western Ukraine were lying precisely in the national plane. And the results of anti­Ukrainian activities members of the Russian orthodox church in Galicia appeared opposite expected. The high level of religious society was one of the characteristic characteristics of the Russian Empire, suggesting the importance of church­state relations and require special attention to it. Government management system did not allow the possibility of atheistic beliefs, and individual rights are inseparable from human denomination. Orthodox clergy were completely integrated into the autocratic system of government, along with religious and performing certain functions of state officials. This fixation of civil status acts and participation in administrative activities provincial boards, and marked by a well known scientist and religious studies Boris Kandidovym participate in law enforcement activities. Since the beginning of the twentieth century. practical task priests all confessions expanded functions stabilization of the population within the limits the parish and maintaining trust in government. In the last decades of the tsarist political role of the church has increased. Trend have become stronger its closure with conservative political forces. Anti­Ukrainian activities The Russian orthodox church failed. Imposed by Tsarist administration structure of the Russian Orthodox Church in Galicia soon cease to exist ­ the clergy escaped, and those who switched to Orthodoxy who failed to withdraw from the Russian army repressed the Austrian authorities. Ukrainian movement has not only failed to destroy, he was strong. Seriously was discredited and the entire Russophile movement, which soon ceased to exist.