### STUDY OF TEMPERATURE DEPENDENCE OF SEMICONDUCTOR PHOTORESISTORS

A description is given of a laboratory setup for studying the temperature dependence of the photocurrent of semiconductor photoresistors and the results of experimental measurements of the lifetime of minority carriers of a photocurrent of conductivity depending on the temperature and frequency of light irradiation waves. It is established that the temperature dependence of the lifetime of minority photocurrent carriers in the studied semiconductor photoresistors is linear when illuminated with the green spectrum light. The magnitude of the lifetime monotonously decreases with an increase in temperature up to a statistical distribution of the measured quantity. The dependence of the lifetime of minority carriers on the frequency of light waves is almost linear. The lifetime of the minority carriers of the photocurrent monotonously increases with an increase in the wavelength of the irradiated light.

Read More### STATISTICS OF MODE CONTENT OF VORTEX MATRIX BEAMS DURING DISTRIBUTION IN ATMOSPHERE

This paper analyzes the mode composition of the radiation from vortex matrix laser beams synthesized by a coherent fiber-optic emitter matrix. The energy transfer between the vortex azimuthal radiation modes during propagation in free space and turbulent atmosphere is analyzed on the basis of numerical simulation. It is shown that most of the radiation energy is pumped into the main mode in the far-field zone, which is determined by the topological charge of the synthesized beam. Statistical characteristics of the mode composition of the synthesized vortex matrix beam are similar to those of the Laguerre-Gaussian beam in case of turbulence.

Read More### APPROXIMATION AND INTERPOLATION OF WAVE SIGNALS IN THE BASIS OF BORDERING FUNCTIONS IN THE STUDY OF MECHANICAL AND OTHER PHYSICAL FIELDS

A formula for trigonometric approximation and interpolation of signals based on the bordering functions is proposed, which simplifies the process of modeling and reconstructing changes of wave signals from measured samples. Proposed modifications of the formula for simultaneous parallel filtering of signals based on the use of families of new bordering and filtering functions. The advantages of using the proposed approach and formulas over the known ones are shown. The interrelation of the formula with the known sampling theorem of is shown.

Read More### MAGNON FOCUSING IN CRYSTALS WITH ALPHA-IRON STRUCTURE

The features of the propagation of spin waves (magnons) in crystals with the alpha-iron structure are studied within the framework of a model that takes into account the interaction of an atom with the atoms of the first and second coordination spheres in a layer of a cubic body-centered crystal lattice. It is shown that there is no magnon focusing in long-wave approximation, as for short waves in case of no external constant magnetic field, a focusing effect is observed. The features of focusing are considered with a negative interaction parameter with neighbors.

Read More### MODELING OF DISTRIBUTION DEPENDENCE OF POLLUTANT SUBSTANCES IN THE MOUNTAIN GORGES FROM DAILY CHANGES OF TEMPERATURE

При помощи математической модели в двумерной постановке исследуются течения воздуха и распространение загрязняющих веществ в горных ущельях при учете вызываемых солнечной радиацией суточных изменений температуры поверхности. Рассмотрены ущелье идеализированной формы и ущелье, расположенное в Северной Осетии в районе хвостохранилища вблизи селения Унал в долине реки Ардон. Проведено сравнение динамики течений и распространения загрязняющих веществ. Показано, что учет суточных изменений температуры сказывается на закономерностях распространения загрязняющих веществ в этих ущельях. Также отличия наблюдаются между дневными и ночными режимами проветривания горных ущелий.

Read More### FEATURES OF EXPERIMENTAL RESEARCH ON SUPERSONIC ATMOSPHERIC VACUUM DRIVEN TUNNEL

В настоящее время экспериментальные исследования сверхзвуковых течений проводятся на сложных экспериментальных установках, таких как аэродинамические и ударные трубы. Для исследования сверхзвуковых течений с числами Маха меньше 4 возможно использование вакуумных аэродинамических труб. В статье приводятся результаты исследования процессов, происходящих в вакуумной аэродинамической трубе при пуске. Анализ полученных результатов показал, что реализуемый в трубе стационарный режим сверхзвукового течения имеет продолжительность около 3 секунд, что подтверждается представленными в работе теневыми картинами течения. Это обстоятельство позволяет использовать имеющуюся атмосферно-вакуумную трубу для исследования аэродинамических характеристик летательных аппаратов при числах Маха от 1,5 до 4.

Read More### ON LEVY-CHIVITA METRIC CONNECTIVITY ON DISTRIBUTION OF PLANES

In n-dimensional projective space, the distribution of m-dimensional planes with a given metric tensor is investigated in the paper. The object of tangent connection is considered, and it is shown that the affine distributed connection can be generalized with a Levi-Civita connection in the case of a holonomic distribution and in the case of a semi-normalized distribution of the 1st kind with the corresponding adaptation of the frame. It is proved that the subobject of the tangent distributed connection can also be covered by the field of the metric tensor, but only in the adapter frame.

Read More### ON MECHANISM OF ALKALI METALS LINES FORMATION IN SONOLUMINESCENCE SPECTRA

О МЕХАНИЗМЕ ФОРМИРОВАНИЯ ЛИНИЙ ЩЕЛОЧНЫХ МЕТАЛЛОВ В СПЕКТРАХ СОНОЛЮМИНЕСЦЕНЦИИ Научная статья Казачек М.В.1, Гордейчук Т.В.2, * 1 ORCID:...

Read More### ON NUMERICAL SOLUTION OF SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS WITH ILL-CONDITIONED MATRICES

The results of the numerical solution of systems of linear algebraic equations (SLAE) with symmetric and asymmetrical ill-conditioned matrices by the regularization method are presented in the paper. Positive-definite and oscillatory matrices are considered. The article shows that in order to regularize the computational process according to the Tikhonov method, it is enough to replace the system matrix A_n with the matrix A_n + αE_n where E_n is the identity matrix, and α is some positive number (regularization parameter) that tends to zero.

Read More### ELECTRICAL CURRENT AND CONDUCTIVITY IN ULTRACOLD PLASMA. CALCULATION BY THE METHOD OF MOLECULAR DYNAMICS

Electric current in the ultracold highly collisional plasma was considered in the work by the method of molecular dynamics. The current is caused by the electric field applied to plasma. Calculations are made for different values of the collisional parameter. Plasma conductivity was determined from the ratio of current and electric field. Comparison with the results obtained by other methods was performed. The difference from the results obtained earlier on the basis of the analysis of the diffusion coefficient and the autocorrelation function of the current is discussed.

Keywords: molecular dynamics, collisional plasma.

### INTEGRATION OF EULER EQUATIONS FOR 2D MOTION OF COMPRESSIBLE MEDIUM FLOW

The Euler equations for 2D unsteady motion of compressible medium flow are under consideration. Two components of velocity vector, density and pressure supposed as the main unknowns. We propose the procedure of integration which based on introduction of new variables and general statements of theory of partial differential equations. As the result we obtain ratios for simple algebraic combinations of main unknowns which convenient for solution of fluid mechanics problems and for simulation of real fluid and gaseous flow.

Read More### PHASE TRANSITION OF THE FIRST CLASS IN GAS OF RESONANTLY ACTIVATED RYDBERG ATOMS

The equation of the state of the gas model of resonantly activated Rydberg atoms was calculated in the work with the help of the Monte Carlo method in the NVT ensemble. Variants of systems with arbitrarily and equally oriented dipole moments are considered. In both cases, critical parameters of the phase transition as well as binodal are determined. Critical temperatures almost coincide in both variants. However, the critical density for equally oriented dipoles is 20 times lower. It is shown that a specific feature of the phase transition in dipole systems is the absence of spatial separation in the region of the coexistence of dense and rarefied phases, which is due to the topological features of clusters of the dense phase. The parameters for the experimental observation of the self-organization of ultra-cold Rydberg atoms on the existing experimental stands are determined. The discovered self-organization of atoms in resonantly activated gas in the form of chains opens up new possibilities for creating quantum computers on Rydberg atoms.

Read More### INFLUENCE OF ELECTRIC FIELD ON RYDBERG ND-STATES OF COLD LITHIUM ATOMS

The effect of the weak electric field on the coherent two-photon resonance 2S-nD is considered in the work by means of recording the fluorescence incidence of Li atoms in the magneto-optical trap. In the course of experiments, it was observed that a separate line is transformed into a band due to the Stark effect under the effect of the weak uncompensated electric field. In this case, the width of the band increases with the increase of the value of the principal quantum n number (or the value of the electric field). It is shown that resonant radiation tuned to the left or right edge of the line allows obtaining gas of Rydberg atoms with a constant large dipole moment 11-01-2019 14-14-35 oriented along or against the field, respectively. The radiation tuned to the center of the band will allow obtaining atomic states with a zero dipole moment but with a large contribution of states with a maximum value of the orbital quantum number 11-01-2019 14-17-58.

Read More### STRUCTURAL AND PHOTOLUMINESCENT PROPERTIES OF COLLOIDAL SEMICONDUCTOR QUANTUM POINTS IN SUSPENSION AND ON SUBSTRATE

Quantum dots (QD) of semiconductor compounds CdSe, PbS, InSb were chemically synthesized. Laboratory technology of applying layers on the substrate was tested. By means of 3D-AFM-topography, it was determined that QDs in a layer on a substrate are aggregated into conglomerates having a polygonal flattened shape and consisting of tightly packed smaller particles. The experimentaly measured photoluminescence spectra are in good agreement with the theoretical ones. PbS and InSb QDs have the quantum yield level is about 5-10 times lower than the best results for colloidal CdSe / CdS quantum dots. When transferring quantum dots from a suspension to a substrate, a decrease in the quantum yield is observed, which can be explained by the weakening of the quantum size effect in the QD due to their aggregation.

Read More### VISUALIZATION OF MATRIX OF ELASTIC PROPERTIES OF CRYSTALS USING SPECIALIZED GRAPHIC PACKETS

A review of the means of visualizing elastic properties of cubic crystals by the matrix of elastic constants is performed. As an example, the measurement data for cij cubic TiNi single crystals is used. It is known for its martensitic transformations, shape memory effects and super-elasticity, as well as TiFe crystals isomorphic to nickelide titanum. The matrix of elastic constants of crystals was visualized using the program of computer algebra Mathcad, ELATE calculation and graphics programs: Elastic tensor analysis and SC-EMA: Self-Consistent Elasticity of Multi-phase Aggregates. The characteristic surfaces of Young’s modulus, the shift, and the Poisson’s ratio are obtained.

Read More### FEATURES OF NANOSTRUCTURAL STATES OF MECHANO-SYNTHESIZED POWDER STEELS ALLOYED BY CR AND SI

The paper studies the influence of alloying elements of substitution (Cr, Si) on the formation of nanostructures in powder nanocrystalline steels based on Fe-1mas. of % C obtained by means of mechano-alloyage of the initial powders of iron and graphite. The study was carried out by X-ray diffraction and magnetic structuroscopy. Carbon is distributed between the volumes of ferrite nanograin and grain boundary segregations in the nanostructure of steels. The carbon concentration in the ferrite varies between 0.2 and 0.37 at. % depending on the alloyage. Cr and Si increase the concentration of carbon in the ferrite as compared to non-alloy steel. The carbon concentration in grain boundary segregations varies within the range (1.1 – 1.7)•10-5 mol/m2. Cr lowers the concentration of carbon in segregations, while Si causes little change. The concentration of carbon in segregations is determined mainly by the grain size and the associated extent of the boundaries obtained by mechano-alloyage.

Read More### MIXED PROBLEM FOR ONE QUASILINEAR PARABOLIC EQUATION WITH HYSTERESIS

The paper considers an initial-boundary value problem for a quasilinear parabolic equation with a memory operator in a bounded domain with a sufficiently smooth boundary. A theorem on the existence of solutions of the initial-boundary value problem with a memory operator is proved. We used the method of discretization with respect to time to prove this theorem. The uniqueness of the solutions of this problem is also proved if the memory operator is a hysteresis nonlinearity of the generalized backlash type.

Read More### ON SOLVABILITY OF CAUCHY PROBLEM FOR SYSTEMS OF NON-LINEAR INTEGRO-DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES WITH PARAMETERS

It is possible to carry out the method of transforming solutions to study the problem of solvability of the Cauchy problem for non-linear integro-differential partial differential equations. The essence of this approach is the transformation of the initial Cauchy problem into an equivalent Volterra integral equation of the second kind, to which one can apply the topological method – the principle of condensed mappings. Sufficient conditions are defined for given functions for which the original problem is solvable from the conditions of contraction of the operator u.

In this paper we study the solvability of the Cauchy problem for systems of non-linear integro-differential partial differential equations of the first order with a parameter and an integral representation of the solutions obtained. Further, for a new class of systems of non-linear integro-differential partial differential equations of the third order, sufficient conditions for the existence of solutions of the Cauchy problem are found, and, in addition, an integral representation of such solutions is constructed. In view of the non-linearity of the initial problems, sufficient conditions do not guarantee the uniqueness of the solutions obtained.

Read More### CONSTRUCTION OF LABELED MULTITUDES USING POTENTIAL FUNCTIONS

In this paper, based on earlier papers, we constructed a labeled area using potential functions. The definitions and designations of labeled areas are given, specific cases of labeled areas are considered. The paper also introduces the concept of oriented labeled areas. Examples of oriented labeled areas are given. We consider a linear singularly perturbed ordinary differential equation of the first order as an example of the application of labeled area. A labeled area is constructed to study the asymptotic behavior of the solution of the initial problem. It is proved that there is a part of the labeled area that is the area of the attraction of the solution of the degenerate equation.

Read More### EXTREME VALUES OF ELASTIC MODULI AND POISSON’S RATIO OF TiFe AND TiNi WITH SHAPE MEMORY

Among the macroscopic characteristics of solids, elastic properties play a crucial role in the analysis of the loss of stability of the crystal lattice of materials to phase transitions. For shear-type transitions, such as martensitic transformations in metals and alloys, the study of the anisotropy of the parameters of crystal structures: elastic moduli and constants, Poisson’s ratio, and others is of particular importance. In this paper, the surfaces of Young’s and shear moduli of crystals, as well as the Poisson’s ratio and their central sections are constructed. Extreme values of the moduli and the Poisson’s ratio of the crystals are calculated. Transformation of surfaces and their central sections is given in the context of loss of stability of alloys to martensitic transformations.

Read More