Доклады Национальной академии наук Таджикистана, том 64, №0102, 2021 г. 
File  Article title and abstract  Pages 


Download  Hotamova R.L., Sharifzoda M.S.  510 
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; WaringGoldbach problem.  

Download  Shabozov M.Sh., Quraishi A.S.  1119 
Some inequalities of JacksonStechkin type related to nonclassical module of continuity of higher order in L 
In paper the estimate of best approximation () for arbitrary complex valued of 2πperiodic function by subspace of trigonometric polynomials not higher 1 order and averaged values of nonclassical module of continuity was obtained. The sharp constant in JacksonStechkin 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; JacksonStechkin type inequalities; shift operator; weight function.  

Download  Yusupov G.A., Mirkalonova M.M.  2025 
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 firstorder modulus of continuity of the th derivative of the function with respect to the argument are found. Along the way, some wellknown 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.  

Download  Mamadayozov N.M., Saadi Sh.  2634 
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 nwidths. 

Key words: the best approximation; modulus of continuity; the weight function; nwidths.  

Download  Safarov D.S., Odinabekov Kh.V.  3541 
Solution of one class of pseudoparabolic equation systems on plane with given chain parts 
In the article for one class of pseudoparabolic 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; pseudoparabolic systems of equations; generalized solution.  

Download  Mukhsinov E.M.  4246 
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.  

Download  Kayumov M.M.  4756 
About recognition of the author of the text based on the frequency of multisigned αβcodes 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; αβcodes; classifier.  

Download  Kokhirova G.I., Babadzhanov P.B., Khamroev U.H., Zhonmuhammadi A.I., Kulaev I.V.  5763 
Virginid asteroidmeteoroid complex.
NearEarth asteroids associated with the MuVirginid meteoroid stream 
Presented results complete the study aimed to finding new nearEarth asteroids belonging to the Virginid asteroidmeteoroid 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 mVirginid 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 cometprogenitor of the stream. Coming from the presented series of papers a summary conclusion was made, namely, the Virginid asteroidmeteoroid 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 cometprogenitor of the complex. 

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

Download  Ibragimov A.A.  6470 
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.  

Download  Qurbonien M.S., Umar Z., Yamamoto Tomoyuki, Rahimi F.  7177 
The firstprinciples calculations of the electronic structure of Mn doped AMO (A=Ca, Sr, M=Sn, Zr, Ti, Hf) 
The article presents the results of quantummechanical 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 3dMn 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.  

Download  Tuichiev Sh., Rashidov D., Tabarov S.Kh., Tuichiev L., Aknazarova Sh.I., Sodikov F.Kh.  7882 
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.  

Download  Gafurov S.J., Boboev T.B.  8387 
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.  

Download  Tagoev M.T., Malysheva E.Yu., Otaev Sh.D., Azamov Sh.O., Mirsaidov U.M.  8891 
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 wateracid treatment of the sinter have been found. Among aluminosilicate ores, argillites are most preferred when sintered with NaOH. 

Key words: sintering; decomposition; wateracid treatment; extraction; aluminum oxide; iron oxide; NaOH.  

Download  Boboyorov M.D., Barotov B.B., Mirsaidzoda I., Boboev K.O., Mirsaidov U. M.  9296 
Physicochemical basis of sulfuric acid decomposition of uranizing ores of Tajikistan 
The article presents the results of sulfuric acid decomposition of uraniumcontaining ores in Tajikistan. The optimal parameters of processing of uraniumcontaining 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.  

Download  Samikhov Sh.R., Asriev J.B.  97101 
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.  

Download  Aminjoni G., Naimov N.A., Suyarov Q.J., Ruziev J.R., Safiev H.  102107 
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.  

Download  Hisoriev H.H., Mirsaburov Sh.M.  108112 
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.  

Download  Solieva B.A., Oyzoda N.Kh., Sattorov B.N., Ergashev A.E., Khakimova R.Sh., Maniyazova N.A., Abdullaev Kh.A.  113116 
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.  
