Доклады Национальной академии наук Таджикистана, том 64, №0506, 2021 г. 
File  Article title and abstract  Pages 


Download  S.A.Iskhokov , B.A.Rakhmonov  243248 
About isomorphism of some fractional order Sobolev type spaces 
In the paper, we first study the interpolation properties of one type of normed spaces of differentiable functions in the entire Euclidean space with a powerlaw weight, and then, using an elliptic operator with degeneration, an isomorphism of some scale of such spaces is constructed. 

Key words: Sobolevtype space of fractional order; interpolation of functional spaces; elliptic operator; power degeneration; an isomorphism of functional spaces.  

Download  M.Sh.Shabozov , A.S.Quraishi  249261 
On the joint approximation of functions and its derivatives in the average on the real axis by algebraic polynoma with the weight of ChebyshevHermit 
Sharp JacksonStechkintype inequalities are obtained on the sets , in which the values of the best joint polynomial approximations are estimated from above by the generalized modulus of continuity of the mth order. 

Key words: joint approximation; JacksonStechkin type inequalities; upper bound; generic module continuity; Kfunctional.  

Download  A.G.Aydarmamadov , N.U.Qadamshoev  262268 
On approximation of analytic functions
in weight Bergmans space 
In the weighted Bergman B space for classes of analytic in the unit circle function defined by generalized modules continuity of higher order th derivatives on argument some inequalities between best approximation and medium meaning of modules continuity high order are praved. 

Key words: analytical function; the generalized modulus of continuity of mth order; best approximation; weight Bergman's space; complex algebraic polynomial; nwidths.  

Download  A.A.Shabozova , G.Farzom  269274 
The best joint approximation of some classes of periodic functions determined by the module of continuity of the mth order in L 
In this paper, one extremal problem the best approximation of a function and their sequential derivatives for a class of functions given by the averaged value of the modulus of of continuity of the th order of the highest derivative of the th order fÎL and bounded from above by a given majorant are considered. 

Key words: complexvalued polynomial; modulus of continuity; joint approximation; upper bounds; best joint polynomial approximation.  

Download  A.Zahurbekov  275282 
Upper bounds of the best meansquare approximation of function of many variables by triangular Fourier sums over arbitrary orthogonal systems 
In this article, the exact upper bounds of the best meansquare approximations of functions of many variables by partial Fourier sums over arbitrary orthogonal systems of functions on some classes of functions of many variables, characterized by a generalized modulus of continuity generated by the generalized shift operator are found. 

Key words: Fourier series; orthogonal system; shift operator; generalized modulus of continuity; "triangular sums".  

Download  L.N.Rajabova , F.M.Akhmadov  283290 
On some cases of twodimensional integral equations
of Volterra type with boundary singular and
stronglysingular lines 
Some cases of a twodimensional integral equation of Volterra type with a singular and strongly  singular lines are studied, in which, depending on the roots of the characteristic equation and the sign of the parameters of the equation, explicit representations of the variety of solutions in terms of arbitrary functions are obtained. 

Key words: twodimensional integral equations; special line; strongspecial line; characteristic equation.  

Download  G.I.Kokhirova , F.Dzh.Rakhmatullaeva , S.A.Borysenko  291302 
Results of observations of comet P/2019 LD2
in the Sanglokh observatory 
A shortperiod comet P/2019 LD2 (Atlas) was discovered in June 2019. The object was originally classified as a Trojan asteroid, but later included in the Jupiter family of comets. The origin of the object has not been established for certain and therefore the study of the comet continues to be of particular scientific interest. The optical observations of the comet were carried out in August 2020 at the Sanglokh International Astronomical Observatory (IAOS) of the Institute of Astrophysics of the National Academy of Sciences of Tajikistan. The apparent and absolute brightness of the comet in the R filter is determined, the dust production parameter and the upper limit of the radius of the nucleus are estimated. The distribution of brightness along the tail is shown and the structure of the dust tail is revealed. Photometric data indicate that during the monitoring period, the comet was in a state of normal cometary activity, associated mainly with the recent passage of perihelion. 

Key words: comet; photometry; light; dust production; radius; isophote; FinsonProbstein diagram.  

Download  D.Rashidov , T.Kh.Salikhov , S.Kh.Tabarov , A.Mirzo , D.M.Sharifov , F.Kh.Sodikov  303307 
Thermaldiffusivity of fullerenefilled polyethylene 
Temperature changes in thickness, density, and coefficients of thermal shrinkage or thermal expansion of fullerenecontaining samples of low density polyethyleneСhas been studied by dilatometers and thermography methods. It is shown that the coefficient of thermaldiffusivity of the composite samples of LDPEС decreases with increasing concentration of С, which is associated with an increase in phonon scattering on crystallites and the nanoparticles of fullerene С. 

Key words: polymer; nanocomposite; fullerene; phonons; thermaldiffusivity.  

Download  N.S.Beknazarova , J.O.Shoalifov  308313 
Complex formation in the system Hg (II)  1phenyl2,3dimethylpyrazoline5thion  0.1 mol / l HNO  298 K 
The process of complexation of mercury (II) ions in a medium of 0.1 mol / L HNO at a temperature of 298 K was studied by potentiometry using a redox electrode based on 1phenyl2,3dimethylpyrazoline5thione and its oxidized form. It is shown that titration of the Hg (II)1phenyl2,3dimethylpyrazoline5thione  0.1 mol /L HNO  298 K system leads to a regular increase in the potential of the indicator electrode. It was found that the process of complexation proceeds stepwise with the formation of four complex forms of compositions: [HgL(HO)], [HgL(HO)], [HgL(HO)] and [HgL] For each complex particle, their stability constants are determined by the Bjerrum method. 

Key words: complexation; 1phenyl2; 3dimethylpyrazoline5thione; mercury(II); redox electrode; stability constant; equilibrium concentration.  

Download  A.S.Kurbonov , M.M.Tagoev , R.Akramzoda , A.P.Tagaev , U.M.Mirsaidov  314317 
Comparative assessment of thermodynamic characteristics of borosilicate ore decomposition with mineral acids and acetic acid 
In the paper a comparative thermodynamic analysis of the possibility of a number of chemical reactions during the processing of Tajikistan borosilicate ores with nitric, sulfuric, hydrochloric, orthophosphoric and acetic acids are presents. The analysis showed that the probabilities of the occurring reactions of minerals of borosilicate ores with nitric acid are more preferable in comparison with other acids. 

Key words: borosilicate ores; decomposition; thermodynamic analysis; mineral acids; acetic acid.  

Download  M.M.Mamadvafoev , D.A.Davlatshoev  318325 
To the petrochemistry of basaltoids and alkaline basaltoids of the Kafandara ore field (Eastern Gissar) 
The article contains the most complete data on the petrochemistry of basaltoid and alkalinebasaltoid subvolcanic dikes, which are products of the final taphrogenic magmatism of the Kafandara ore field and the southern Tien Shan. 

Key words: petrochemistry; taphrogenic; subvolcanic; basaltoid and alkalinebasaltoid dikes; Kafandar ore field; East Gissar; South Tien Shan.  

Download  N.S.Saidov , D.S.Sattarov  326334 
Results of the introduction of hoseed plants in the North American area the Central Botanical Garden of Tajikistan for 85 years 
In this article the results of the introduction of conifers in the North American section of the Central Botanical Garden of Tajikistan over the past 85 years of activity are presents. It has been ascertained that over the past 30 years, the biodiversity of this site has decreased by 16 species, which belong to 1 family and 2 genera, and for this period more than 40 taxa have been preserved on the site. This number is dominated by representatives of the cypress family  Cupressaceae Bartl., which is represented by 5 genera and 28 species. 

Key words: introduction; garden; North American site; conifers; family; genus.  

Download  M.B.Niyazmukhamedova  335340 
The content of nitrogen and protein in green biomass and in grain tritikalе 
In this article the results of the analysis of the content of nitrogen and protein in the leaves, stem, spike, as well as in the mature grain of the triticale samples in different phases of development are presents. The study of nitrogen and protein in vegetative organs in the process of vegetation of triticale plants revealed a clear relationship  the increased nitrogen concentration in the leaf stem mass in D83, T25 and Vose3 contributes to an increased protein content in the grain. 

Key words: triticale; wheat; rye; leaf; stem; spike; nitrogen content; protein.  

Download  К.Aliev , N.S.Dilovarova , N.Kh.Norkulov , M.Kh.Shukurova , Z.Kh.Norkulova  341345 
Organ specificity of pro and antioxidant system of potato
in vitro and ex vitro 
In this article the organspecificity of the antioxidant defense system of potato plants ex vitro has been established. The main mechanism of the plant resistance against to upcoming stress mainly by the concentration of antioxidants in the root system is determined. It is supposed that the root system has a high resistance potential in contrast to leaves. Moreover, the activity of the studied enzymes was higher in roots than in leaves. 

Key words: potato; reactive oxygen species; lipid peroxidation; enzyme; hydrogen peroxide.  
