of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Национальной академии наук Таджикистана, том 64, №01-02, 2021 г.

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Hotamova R.L., Sharifzoda M.S.
Behavior of short cubic exponential sums with primes in a small neighborhood of the center of major arcs
Behavior of Weyls short quadratic exponential sums with prime numbers for , is studied in a small neighborhood , of the center of major arcs.

Key words: Short quadratic exponential sum with primes; major arcs; density theorem; Waring-Goldbach problem.

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Shabozov M.Sh., Quraishi A.S.
Some inequalities of Jackson-Stechkin type related to nonclassical module of continuity of higher order in L
In paper the estimate of best approximation () for arbitrary complex valued of 2π-periodic function by subspace of trigonometric polynomials not higher -1 order and averaged values of nonclassical module of continuity was obtained. The sharp constant in Jackson-Stechkin inequalities between the best approximation and nonclassical module of continuity at the point π/2 was found.

Key words: best approximation; nonclassical modulus of continuity; Jackson-Stechkin type inequalities; shift operator; weight function.

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Yusupov G.A., Mirkalonova M.M.
Inequalities for best approximations of analytical functions in Hardys banach space
Some exact inequalities between the value of the best polynomial approximation of the function and the integrals containing the first-order modulus of continuity of the th derivative of the function with respect to the argument are found. Along the way, some well-known results of L.V.Taykov are generalized to the case of simultaneous polynomial approximation of analytic functions in the unit disk and their best approximations sequences of derivatives with respect to the argument

Key words: best approximation; modulus of continuity; analytic function; derivative with respect to argument; diameter.

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Mamadayozov N.M., Saadi Sh.
The best polynomial approximation and widths of set in L space
The exact inequality between the best polynomial approximation and the value of moduli continuity of function in f Î L on norm space L were found in the article. For some classes of functions which are defined by these moduli of continuity, were calculated by exact value of n-widths.

Key words: the best approximation; modulus of continuity; the weight function; n-widths.

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Safarov D.S., Odinabekov Kh.V.
Solution of one class of pseudoparabolic equation systems on plane with given chain parts
In the article for one class of pseudo-parabolic systems of equations of the form found a generalized solution to a mixed problem in a class of functions is found that is bounded in and doubly periodic in the variable z, and with given principal parts.

Key words: doubly periodic solution; pseudo-parabolic systems of equations; generalized solution.

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Mukhsinov E.M.
On the pursuit problem in nonlinear differential games with retarded argument
The paper considers the pursuit problem in the sense of L.S. Pontryagin for a nonlinear differential game with retarded argument. Using an analogue of the Lyapunov function and methods of the theory of differential inequalities in a Banach space, the solvability of pursuit problem is proved.

Key words: pursuit problem; nonlinear differential games; retarded functional differential equations; terminal set; Banach space.

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Kayumov M.M.
About recognition of the author of the text based on the frequency of multi-signed αβ-codes of word forms
The article solves the problem of recognizing the authors of works for classical and modern poetry, as well as modern prose. The works are compared with a digital portrait, characterized by the distribution of the frequency of multivalued αβ -codes in them. The effectiveness of the use of the -classifier and digital portraits of texts based on αβ -codes for the identification of authors of works is confirmed.

Key words: text; digital portrait; αβ-codes; classifier.

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Kokhirova G.I., Babadzhanov P.B., Khamroev U.H., Zhonmuhammadi A.I., Kulaev I.V.
Virginid asteroid-meteoroid complex. Near-Earth asteroids associated with the Mu-Virginid meteoroid stream
Presented results complete the study aimed to finding new near-Earth asteroids belonging to the Virginid asteroid-meteoroid complex. On the base of calculation of orbital evolution of a sample of NEAs and determination of theoretical features of related showers a search for observable active showers close to theoretically predicted ones was carried out within published databases. As a result, predicted showers of 4 NEAs were identified with the active showers produced by the m-Virginid meteoroid stream. Revealed association points to a cometary nature of NEAs that are moving within the stream and may be considered as extinct fragments of a larger comet-progenitor of the stream. Coming from the presented series of papers a summary conclusion was made, namely, the Virginid asteroid-meteoroid complex consists of a lot of streams and substreams producing meteor showers, and of 31 object of a cometary nature presenting themselves extinct fragments of a larger comet-progenitor of the complex.

Key words: comet; asteroid; extinct comet; meteoroid stream; meteor shower; orbit; radiant.

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Ibragimov A.A.
About of comets tail orientation
Based on the available data on the aberration of the plasma tail of comets, the possibility of using the method for determining the velocity of the solar wind from the orientation of plasma tails of comets was investigated. The results of a comparative analysis of the velocities measured by the spacecraft and the calculated data obtained from the deviation of comet tails relative to the extended radius vector are presented. The condition of correspondence between measured and calculated data is shown.

Key words: comet; plasma tail; aberration; tangential solar wind.

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Qurbonien M.S., Umar Z., Yamamoto Tomoyuki, Rahimi F.
The first-principles calculations of the electronic structure of Mn doped AMO (A=Ca, Sr, M=Sn, Zr, Ti, Hf)
The article presents the results of quantum-mechanical calculations of the electronic structure of Mn doped AMO (A=Ca, Sr, M=Sn, Zr, Ti, Hf) with density functional theory. The mBJ estimated of band gap of the AMO systems are closer to the experimental ones. The crystal field parameters (10Dq) and the red emission wavelength of the phosphors are estimated. The electronic structure of the split 3d-Mn orbitals and their contribution to the t and e states are studied in detail here.

Key words: phosphor; density functional theory; band gap; crystal field parameter (10Dq); red emission.

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Tuichiev Sh., Rashidov D., Tabarov S.Kh., Tuichiev L., Aknazarova Sh.I., Sodikov F.Kh.
The photoaging of amorphous polymeric nanocomposites
Investigation of the change in the structure and properties of amorphous PMMA and PS nanocomposites in the field of UV irradiation were studied. It is shown that during photoaging an extremal changes in the structure, mechanical and thermal properties of the composites are observed.

Key words: polymer; fullerene; composite; irradiation; structure; strength; deformation; photoaging.

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Gafurov S.J., Boboev T.B.
Effect of fullerene C on photodestruction of polymethylmetakrilat
The effect of fullerene on the lightfastness of polymethyl methacrylate under UV radiation has been studied. It is shown that the introduction of chemical additives into the polymer leads to a decrease in photodestructive processes. It was found that with an increase in the fullerene concentration, the drop in the molecular weight of the polymer sharply decreases and its lightfastness increases.

Key words: polymethylmethacrylate; fullerene; UV irradiation; tensile strength; tensile deformation; molecular weight; lightfastness.

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Tagoev M.T., Malysheva E.Yu., Otaev Sh.D., Azamov Sh.O., Mirsaidov U.M.
Aluminum and iron oxides obtaining from Tajikistan aluminosilicate ores by sintering with NaOH
The article presents the sintering results of aluminosilicate ores: kaolin clays, green kaolin clays and argillites with NaOH. The optimal parameters for the extraction of aluminum and iron oxides after the water-acid treatment of the sinter have been found. Among aluminosilicate ores, argillites are most preferred when sintered with NaOH.

Key words: sintering; decomposition; water-acid treatment; extraction; aluminum oxide; iron oxide; NaOH.

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Boboyorov M.D., Barotov B.B., Mirsaidzoda I., Boboev K.O., Mirsaidov U. M.
Physico-chemical basis of sulfuric acid decomposition of uranizing ores of Tajikistan
The article presents the results of sulfuric acid decomposition of uranium-containing ores in Tajikistan. The optimal parameters of processing of uranium-containing ores: Northern, Central and Western Tajikistan have been found. The basic technological scheme of uranium ore processing is proposed.

Key words: uranium ores; sulfuric acid decomposition; processing; optimal parameters.

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Samikhov Sh.R., Asriev J.B.
Thiosulphate leaching of gold and silver from concentrates of Duoba deposit
This article presents the results of the study of thiosulfate leaching kinetics of gold and silver containing concentrates, and optimum conditions of this process are specified. It is shown that during a 12 hour leaching process the extraction of gold in the solution makes 88,1%.

Key words: thiosulphate leaching; deposit; gold recovery; silver recovery; process temperature; concentrate; baked concentrate.

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Aminjoni G., Naimov N.A., Suyarov Q.J., Ruziev J.R., Safiev H.
Thermodynamics of processing of flotation muscovite concentrate by the method of sulphatization
In work presents the results of the thermodynamic parameters of the process of processing the flotation muscovite concentrate of the Kurgovad deposit by the sulfatization method. To clarify the possibility of chemical reactions during the interaction of minerals of the flotation muscovite concentrate with sulfuric acid in the temperature range from 393 to 573 K, a thermodynamic calculation of the change in the Gibbs free energy and the calculation of the equilibrium constants of the reactions were carried out. Also, for the reactions taking place according to the Kirchhoff equation, the enthalpy values were calculated. Comparison of the temperature dependences of the change in enthalpy and Gibbs free energy of reactions indicates a decrease in the values of the two compared thermodynamic quantities.As a result of the calculations of the thermodynamic values of the reactions under study at different temperatures, it was found that in the process of sulfatization, the values of changes in the Gibbs energy are negative.

Key words: muscovite concentrate; alumina; sulfatization; aluminum sulfate; aluminum hydroxide; Gibbs energy; enthalpy; heat capacity.

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Hisoriev H.H., Mirsaburov Sh.M.
Green algae - Chloropyta of the Isfara river basin
The article provides information on the new floristic finds of green algae (Chlorophyta) in water bodies of Isfara river. Diversity of algae of this river have not been studied before. Totaly 26 species of green algae were found in this river, which belonging to 3 classes, 7 orders, 11 families and 14 genera. Scenedesmaceae, Ulotrichaceae family and the Ulothrix, Scenedesmus genera are dominant in species diversity.

Key words: green algae; biodiversity; algoflora; Isfara river; Tajikistan.

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Solieva B.A., Oyzoda N.Kh., Sattorov B.N., Ergashev A.E., Khakimova R.Sh., Maniyazova N.A., Abdullaev Kh.A.
Water keeping ability of cotton leaves with different shapes and colors
In this paper the results of study of water keeping ability leaves of inbred lines uplant cotton with different shapes and colors leaves are presents. It is shown the water keeping ability is dependent from leaves shapes and colors, times of the day and, possibly, from leaf ages.

Key words: middle stable cotton Gossypium hirsutum L .; inbred lines; shape and colour of leaf; water keeping ability.