Доклады Академии наук Республики Таджикистан, том 63, №0708, 2020 г. 
File  Article title and abstract  Pages 


Download  Rakhmonov Z.Kh., Sobirov A.A., Fozilova P.A.  405415 
Estimate of short cubic exponential sums with primes in major arcs 
In major arcs , except for a small neighborhood of its centers at , , , is given a nontrivial estimate of the form
where , ,  arbitrary fixed positive numbers. 

Key words: Short exponential sum with primes; major arcs; density theorem; Dirichlet Lfunction.  

Download  Tuychiev А.M.  416426 
On the mean square polynomial approximation of functions by FourierChebyshev sums 
Exact estimates of the rate of convergence of the FourierChebyshev series are given for some classes of functions defined by a secondorder differential operator and characterized by a generalized module of continuity of th order in the space . Exact inequalities of Jackson Stechkin type between the value of best approximation of functions by private sums of the FourierChebyshev and generalized moduli of continuity of the th order defined by a differential operator of second order. 

Key words: best approximation; generalized shift operator; modulus of continuity of morder; FourierChebyshev series; differentiation operator.  

Download  Аbdukarimzoda М.К.  427435 
On the best weighted quadrature formulas for curvilinear integrals of the first kind 
The optimal quadrature formula for the class of functions of mvariables continuous along the curve is found whose norm of the gradient in the norm of the space is bounded. 

Key words: curvilinear integral; quadrature formula; error; weight function; nodes; gradient.  

Download  Safarov D.S., Abdulvokhidi О.  436440 
Generalized doubleperiodic solutions of the Poisson equation with given main parts 
In the paper for a Poisson equation on a plane with given principal parts, a generalized biperiodic solution using the elliptic Weierstrass function is found. 

Key words: generalized solutions; doubly periodic solution; antianalytic function; analytic function.  

Download  Gadoev M.G., Iskhokov J.S.  441449 
On a distribution of eigenvalues of nonselfadjoint elliptic operators in a bounded domain with uncoordinated degeneration 
We study a class of higherorder elliptic diﬀerential operators in a bounded domain whose coeﬃcients have uncoordinated powerlaw degeneracy along the entire boundary of the domain. The sesquilinear form associated with the operator under consideration may not satisfy the coercivity condition. Conditions for discreteness of the spectrum of operators under consideration are obtained and an asymptotics of function of distribution of their eigenvalues is studied. 

Key words: elliptic operator; power degeneration; noncoercive form; uncoordinated degeneration; bounded domain.  

Download  Radjabova L.N.  450460 
To the theory of twodimensional integral equations of Volterr type with two singular lines when the parameters are not related 
In this work explicit solutions of twodimensional integral equations of the Volterra type with a singularity and a logarithmic singularity in the kernel, containing arbitrary constants are obtained. The solution to the integral equation in the case when the parameters are not related to each other is sought in the form of a uniformly convergent generalized power series. To determine arbitrary functions, problems of the Cauchy type are solved. 

Key words: twodimensional integral equations; singular lines; arbitrary constants; Cauchytype problem.  

Download  Usmanov Z.D., Kosimov A.A.  461466 
About the automatic recognition of the language of works 
On an example of a model collection of 10 texts in five languages using Cyrillic graphics, the applicability of the γclassifier for automatic recognition of the language of the works based on the frequency of common 29 Cyrillic alphabetic letters is established. 

Key words: text; language; alphabet; frequency; classifier.  

Download  Mirzoev S.Kh., Nasridinova T.N.  467473 
Information model for monitoring and forecasting the ecological state of the atmosphere in Dushanbe city 
The article is devoted to the issue of an information model for monitoring and forecasting the ecological state of the atmosphere in Dushanbe. It is compiled a conceptual model of the ecological system, consisting of four main factors: observation, assessment of the actual state, forecast and assessment of the predicted state. An analytical dependence is obtained for changing the level of atmospheric pollution. This change is also plotted in a graph. 

Key words: atmosphere; harmful particles; monitoring.  

Download  Kokhirova G.I., Bakhtigaraev N.S., Levkina P.A., Chazov V.V., Khamroev U.Kh.  474480 
Features of rotational motion of some space debris fragments from observations at the Sanglokh observatory 
The regular session of observations of a sample of the space debris (SD) fragments was held at the International astronomical observatory Sanglokh of the Institute of Astrophysics of the Academy of Sciences of the Republic of Tajikistan using the Zeiss1000 telescope from July 31 to August 9, 2019. The aim is a study of variations in their brightness and the features of their rotational motion. The found features of the dependence of the brightness variations of the SD fragments with a large areatomass ratio and its correlation with the phase angle, the calculated values of the areatomass ratio and the periods of variations of brightness of the observed objects are presented in the paper. A stability of the rotational motion of the SD fragment having a large areatomass ratio equal to 29 m/kg is shown that is not typical for the rest fragments. 

Key words: space debris; positional observations; photometry; brightness; areatomass ratio; per.  

Download  Sharipov S.R., Abdullaev S.F., Maslov V.A., Madvaliev U.  481487 
Variability in the composition of the carboncontaining fraction of atmospheric aerosol in the semiarid zone
of Tajikistan 
The results of a twoyear (20142016) experiment to measure the content in organic and elementary carbon aerosols conducted at the Atmospheric Monitoring Station (Dushanbe, 38º33´34´´N, 68º51´22´´E) are presented. The article describes the possible sources of atmospheric carbon, the results of the application of the method of polynomial regression to data on carbon content. The Back Trajectories of air masses are given with the maximum content of elemental and organic carbon. 

Key words: atmospheric composition; carboncontaining aerosol; twostage thermographic method; polynomial regression.  

Download  Kuchakshoev D.S., Dzhabarov A.G., Kholov A.  488493 
Properties of glasses based on compounds of BiO and NaBO 
On the basis of compound BiOand NaBOsamples of glasses of different concentration of initial substances in a mix are received. In obtaining samples of glasses the method preliminary solidphase synthesis was used, thus some samples are received without such preliminary synthesis. The properties of glass samples  color, density, microhardness, refractive index vary depending on the technology of their manufacture. 

Key words: glass; solidphase synthesis; temperature; furnace; concentration.  

Download  Soliev L., Tursunbadalov Sh.  494499 
Structure of the diagram of the phase complex of the system NaClKclMgClCaClHO at 0 
Using the translation method, the phase equilibria of the NaClKClMgClCaClHO system at 0 were studied. It has been established that the system under study at 0 is characterized by the presence of 2 invariant points, 7 monovariant curves, and 9 divariant fields. Based on the data obtained, her phase complex diagram at a given temperature was first constructed. 

Key words: diagram; phase complex; invariant points; monovariant curves; divariant fields.  

Download  Juraev J.Kh., Kurbonov A.S., Nematov A.M., Tagoev M.M., Mirsaidov U.M.  500504 
Study of kinetics of the decomposition process of sintered borosilicate ore with a mixture of nitric and ortophosphoric acids 
In this paper the results of studies on kinetics of the decomposition of the sintered borosilicate ore concentrate of the Tajikistan AkArkhar deposit with a mixture of nitric and phosphoric acids are presents. The apparent activation energy, reaction rate constants, and the preexponential factor of the Arrhenius equation are determined, which are indicate the flow of the process in the diffusion region. 

Key words: borosilicate concentrate; processing; decomposition; extraction; kinetics; nitric acid; phosphoric acid.  

Download  Mamadvafoev M.M., Davlatshoev D.A.  505514 
Hydrogen in the rocks of the intrusive complexes
of Kafandara ore field (Eastern Gissar) 
The article is the first to consider the distribution function of hydrogen, its abundance, correlation with petrogenic elements and dependence on the petrochemical parameters of rocks of intrusive complexes of the Southern Tien Shan in the position of the Kafandara ore field. 

Key words: hydrogen; distribution function; abundance; correlations; dependence on petrochemical parameters; Kafandara ore field.  

Download  Shodibekov M.A., Mirakov M.A., Pautov L.A., Khvorov P.V., Fayziev A.R.  515519 
Loolingit from granite miarol pegmatit VezDara (Southwestern Pamir) 
In the nearamiar complex of the VezDarin vein, iron diarsenite, löllingite, is relatively rare for granite pegmatites. This is probably the first discovery of lellingite in the pagmatites of the Pamirs. 

Key words: löllingite; granite pegmatite; VezDara; miarola; vein; chemical composition.  

Download  Khabirov Z., Нakimzod S.  520522 
Seasonal summer dynamics of horseflaies (Diptera, Tabanidae) of Ramitsky gorge 
In this article the results of research on the seasonal summer of horseflies and the influence of climatic conditions on changes in the number of these insects in the Ramit Gorge provides. It was found that the flight of the first specimens was observed near the decoy trap on 7 June at an air temperature of + 23°C, relative humidity of 38% and wind speed of up to 1.0 m/s. upon the occurrence of lover temperatures (+13°C) and increased wind (up to 26 m/s), the flight of horseflies stops. The duration of the active phase and blood sucking is 90 days. 

Key words: horseflies; number; bloodsucking; season; flight; activity; Romit Gorge.  

Download  Jalilov A.U.  523529 
Molecular diagnostics of rust mushrooms forming etsial stage on barberis (Berberis spp.) 
In this article information about the role of the intermediate host of the rust fungi barberry (Berberis spp.) are presents. It is shown that in the sexual stage of reproduction in the life cycles of Puccinia graminis Pers. and Puccinia striiformis West. 

Key words: barberry; intermediate host; spermoginal and social stages; uredinal; teleto and basidial stages.  

Download  Sattorov B.N.  530533 
Yield structure of local and introduced varieties of weat grown in conditions of wind rain 
In this article yield structure of local and introduced wheat varieties grown in conditions of the wind rain was studied. It is shown that in the same conditions of sowing of highly productive wheat local variety and varieties from Russia (Volzhskaya 100, Volzhskaya K (qualitative) and Volzhskaya S3), the maximum expression of elements of the crop structure is observed. 

Key words: wheat; wind rain; structure of ear; mass of 1 ear; weight of 1000 grains.  

Download  Avezov T.Sh., Ergashev A.  534538 
Influence of presowing processing of wheat seeds by antioxidant on quantitative traits of ear structure in drought conditions 
In this article shown that seed treatment before sowing by the antioxidants (aTOK, ascorbic acid, ZnODEPK) under the conditions of soil drought increases the drought resistance of wheat varieties and favours a better formation of the ear structure of wheat. 

Key words: wheat; antioxidants; soil drought; ear structure.  
