of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Национальной академии наук Таджикистана, том 64, №07-08, 2021 г.

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Generalised problem for amounts multiplicative function in arithmetical progression
Asymptotic formulation is put on in work for amounts multiplicative function in arithmetical progression, on number to simple divisors which lies in given interval.

Key words: amount multiplicative function; asymptotic formulation; nature Dirichlet; generalised function Mangolidta.

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M.Sh.Shabozov , A.Mukhlis
Jackson-Stechkin inequalities and the widths of some classes of function in L
In this work the exact value of an extremal characteristic of a special from, which connects the best polynomial approximation of functions with an expression containing the averaged value of the modulus of continuity of the -th oder of the derivative of the -th order is obtained. The exact values of the -widths of some class of functions in the space are calculated.

Key words: best approximation; extremal characteristic; Jackson-Stechkin type inequality; -widths.

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Upper bounds of best approximation of some classes of periodic functions of two variables by circular Fourier sums in L(Q)
In the article the exact upper bounds of the best approximation some classes of two variables by circular Fourier sums characterized by a generalized modulus of continuity in the Hilbert space are found. Sharp constants in the Jackson-Stechkin type inequality between the best approximations and the generalized modulus of continuity in are also found.

Key words: complex Fourier series; generalized modulus of continuity; Laplace operator; "circular" sums.

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A speed of convergence of "hyperbolic" partial sums of the double Fourier series on the Fourier-Hermite orthogonal polynomials
In work exact upper bounds approximations for bivariate functions by "hyperbolic" partial sums of the double Fourier series on the orthogonal polynomials Fourier-Hermite on classes of functions are calculated.

Key words: best approximation; "hyperbolic" sums; modulus of continuity; orthogonal polynomials; inequalities.

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Sharp inequalities between best approximations and some characteristics of smoothness in the Bergmans space

Key words: In the article exact constant in Jackson-Stechkin type for the characteristic of smoothness; determined by averaging the finite differences of the -th order of function to the Bergman space are found. For the classes of functions defined using the smoothness characteristics; the extremal problem of the simultaneous approximation of the function and it's successive derivatives is solved; sharp inequalities; best approximations; smoothness characteristics; modulus of continuity.

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S.A.Iskhokov , K.E.Khaknazarov
Variational Dirichlet problem with homogeneous boundary conditions for non-divergent form degenerate elliptic operators
We study the variational Dirichlet problem with homogeneous boundary conditions for a class of non-divergent form elliptic operators in a bounded domain of the -dimension euclidian space with degeneracy along the entire boundary of the domain. In contrast to published papers, the operators under investigation may have non-zero middle coefficients.

Key words: variational Dirichlet problem; non-divergent form elliptic operator; power degeneration; bounded domain.

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G.I.Kokhirova , A.M.Buriev , S.N.Safarov
Determination of the physical properties of a potentially hazardous asteroid 2003 SD220 from observations in the Gissar Astronomical Observatory
In this paper the results of photometric processing of multicolor observations of the potentially hazardous asteroid 2003 SD220 carried out by the AZT-8 telescope of the Hissar Astronomical Observatory during its approach to Earth in December 2018 are presents. The apparent and absolute brightness of the asteroid in four filters is obtained, the brightness of the object practically did not change during the observation period, the absolute value of the brightness corresponds to the ephemeris value. Color indices correspond to S-type asteroids. The estimates of the asteroid's diameter based on our observations are in good agreement with the available data. The approach of the asteroid with the Earth did not change it physical properties.

Key words: asteroid; observations; photometry; brightness; light curve; color index; diameter.

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B.I.Mahsudov , N.U.Mulloev , N.Zaydullo
Effect of low flows of thermal neutrons on the IR spectrum of Rhizobium phaseoli IS TAAS-80TJ and Bacillus megaterium var. phosphaticum bacteria
The IR spectra of bacteria Rhizobium phaseoli IS TAAS-80TJ and Bacillus megaterium var. phosphaticum and the effect of a low flux of thermal neutrons on the spectral characteristics of these biobacteria intended for use in the production of microfertilizers were studied. It was found that in some bands of the IR spectrum of bacteria, when they are irradiated with small fluxes of thermal neutrons, an increase in optical density occurs. The greatest change is observed at a thermal neutron flux of 5.4 * 10 neutron / cm, which correlates with a 5-6-fold decrease in the germination time of bacteria. It has been shown experimentally that one of the possible mechanisms of the effect of thermal neutrons on the IR spectrum of bacteria Rhizobium phaseoli IS TAAS-80TJ and Bacillus megaterium var. phosphaticum is the nuclear reaction of radiative capture of thermal neutrons by nuclei of nitrogen atoms of the form .

Key words: IR spectrum of biobacteria; thermal neutrons; nuclear reaction; radiation capture; Rhizobium phaseoli IS TAAS-80TJ; Bacillus megaterium var. phosphaticum; hormesis.

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Determination of enrichment of uranium samples using delayed neutrons
In this work the experimental determination of unknown enrichment of uranium samples using delayed neutrons and modeling of irradiation processes of uranium samples of different enrichment using delayed neutrons are considered.

Key words: DT-thermonuclear reaction; heat-extensive assembly; fissile materials; pulsed neutron generator; nondestructive analysis.

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Digital method for analysis of the counting rate of time coincidence of γ-γ and n-n Cf pulses
The paper investigates a digital method for analyzing the count rates of time coincidences of pulses γ-γ and n-n of a californium source. It was required to measure the time coincidences of gamma quanta and neutrons of various multiplicity in an installation with a neutrostop protective layer and without a protective layer in order to determine the content of fissile materials.

Key words: time coincidence count rate; non-destructive analysis; digital analyses; protective layer; double match; analog-digital converter; nuclear fissionable materials; photomultiplier tubes; nanos.

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S.F.Abdullaev , V.A.Maslov
On the relationship of the degradation of Medvezhy glacier with dust injuries
The atmospheric factors affecting the accelerated melting of glaciers in Tajikistan, which has been observed for several years, are considered. On the example of the pulsating Medvezhy glacier, an analysis of the trajectories of air masses is carried out. It has been established that during dust intrusions in the central part of Tajikistan, dust is further carried by air currents towards glaciers, which are sources of water for mountain rivers. The deposition of dust on the ice surface reduces the surface albedo, enhancing light absorption, and accelerates glacier melting.

Key words: glaciers; back trajectories; aerosol; dust transport.

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N.M.Jamolov , D.Kh.Mirzoev , M.M.Tagoev , S.M.Gaforzoda , U.M.Mirsaidov
Kinetic aspects of decomposition of aluminosilicate ore in Tajikistan by mineral acids
In this article the kinetic aspects of mudstones and kaolin clays decomposition by mineral acids are studied. The decomposition kinetics of mudstones of Chashma-Sang deposit by hydrochloric, sulfuric, nitric and orthophosphoric acids has been studied, and decomposition kinetics of kaolin and green (kaolin) clays by nitric and hydrochloric acids have been studied as well. It has been defined that during the decomposition of mudstones by nitric acid, the process flows in the kinetic region. In other cases, the process takes place in diffusion or mixed areas.

Key words: kinetic aspects; decomposition; kaolin clays; mineral acid; aluminosilicate ore.

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A.S.Jafarov , K.B.Nurov
Research of binary systems with special temperature points
In this paper the results of determining the coordinates of the critical decay in the In-Se system by measuring the propagation velocity of ultrasound are presents. The ultrasonic method was used to investigate the delamination region in the In-Se system. On the basis of the experimental data, a line of monovariant equilibrium was constructed, which bounds the indicated region. The coordinates of the critical point (critical temperature and critical composition) have been determined. It is shown that the ultrasonic method can be successfully used to reliably establish the boundary of the separation region of metallic and semiconducting liquids in the phase diagram, as well as to study the separation process itself.

Key words: ultrasonic method; ultrasound propagation velocity; phase diagram; melt separation; metal and semiconductor systems.

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Thermal characteristics of the process of steam formation of transmission oil brand LUMIX transmission oil: SAE 80W-90; API GL-5
The process of vaporization of transmission oil brand LUMIX transmission oil: SAE 80W-90; API GL-5 by tensimetry with a membrane zero pressure gauge was studied. Investigations carried out in the temperature range of 300-500 K under isochoric and equilibrium conditions have shown that the process of vaporization of an object consists of three stages and their thermal characteristics have been determined.

Key words: lubricating oils; technical and economic indicators; vaporization process; grading; thermodynamic characteristics.

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U.R.Jobirov , I.N.Ganiev , M.Ch.Shirinov , Z.R.Obidov
Anode behaviour of Zn0.5Al zinc alloy, doped with erbium, in the sour environment
In this paper the results potentiodynamical researches of anode behaviour of Zn0.5Al zinc alloy, doped with erbium, in the sour environment, are presented. Showed, that introduction in Zn0.5Al zinc alloy erbium promotes reduction of corrosion rate of anodic alloy.

Key words: Zn0.5Al alloy; erbium; potentiostatically method; HCl electrolyte; corrosion potential; corrosion rate.

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Kh.Sh.Rakhimov , A.A.Kodirov , A.B.Badalov
Mechanical activations of the sulfide-antimony concentrates
A method of mechanical activation of sulphide - antimony concentrate has been developed. The optimal conditions for processing concentrate, allowing growth to extract antimony from it.

Key words: antimony sulfide concentrate; mechanical activation; useful conditions; antimony isolation.

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N.K.Usmonov , F.A.Fayziev , A.R.Fayziev
Geological and mineralogical characteristics Tutli-Kuduk gold-sulfide deposit (South-Western Karamazar)
The article provides information on the Tutly-Kuduk gold-sulfide deposit. The mineral composition of the ores is simple. The main vein mineral is quartz and ore pyrite. Other minerals include sericite, halloysite, iron hydroxides, and jarosite.

Key words: Tutly-Kuduk; deposit; secondary quartzite; quartz; pyrite; sericite; iron hydroxides; halloysite.

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M.O.Ubaydullo , G.K.Mirojov , M.M.Yakubova , M.K.Kurbonov
Antiviral and hepatoprotective effect of tincture Lagenaria siceraria (Molina) Stendl in experimental viral hepatitis "B"
In this article the results of the effect of tincture of Lagenaria vulgaris on white mice infected with the hepatitis B virus are presents. The DNA level of the virus during the development of hepatitis and after treatment was determined by the polymerase chain reaction (PCR) method, the biochemical parameters of the activity of the enzymes ALT, AST and bilirubin were studied in the blood serum. The results of the experiments allow us to recommend tincture of Lagenaria for the treatment of hepatitis of viral and mixed etiology.

Key words: tincture; lagenaria; medicinal viral hepatitis B.

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Kh.A.Abdullaev , B.A.Solieva , N.Kh.Oyzoda , M.M.Saidnabiev
Reperative regeneration of cotton leaves after defoliation
In this paper, the result of reparative regeneration of the leaves after defoliation of inbred lines of cotton with different shapes and colors of the leaves are presents. It is shown, that in lines L-501 and L-549 with integri form of the leaves and after full removed in the end of vegetation period, low ability of the leaves regeneration was observed. But in line L-3 (with okra leaves type) and L-601 (with broad leaves) in results of second grow of leaves after 90 days of defoliation a new leaves area was formed, exceeding of control plants in 23% and 56.3% accordingly. This result is evidence about reparative regeneration of the leaves in cotton.

Key words: middle stable cotton Gossypium hirsutum L.; inbred lines; shape and colors of leaf; leaf and leaf area.