of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Академии наук Республики Таджикистан, том 63, №07-08, 2020 г.

Article title and abstractPages
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Rakhmonov Z.Kh., Sobirov A.A., Fozilova P.A.
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 L-function.

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Tuychiev А.M.
On the mean square polynomial approximation of functions by Fourier-Chebyshev sums
Exact estimates of the rate of convergence of the Fourier-Chebyshev series are given for some classes of functions defined by a second-order 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 Fourier-Chebyshev 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 m-order; Fourier-Chebyshev series; differentiation operator.

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Аbdukarimzoda М.К.
On the best weighted quadrature formulas for curvilinear integrals of the first kind
The optimal quadrature formula for the class of functions of m-variables 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.

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Safarov D.S., Abdulvokhidi О.
Generalized double-periodic 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; anti-analytic function; analytic function.

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Gadoev M.G., Iskhokov J.S.
On a distribution of eigenvalues of nonselfadjoint elliptic operators in a bounded domain with uncoordinated degeneration
We study a class of higher-order elliptic differential operators in a bounded domain whose coefficients have uncoordinated power-law 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.

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Radjabova L.N.
To the theory of two-dimensional integral equations of Volterr type with two singular lines when the parameters are not related
In this work explicit solutions of two-dimensional 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: two-dimensional integral equations; singular lines; arbitrary constants; Cauchy-type problem.

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Usmanov Z.D., Kosimov A.A.
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 γ-classifier 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.

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Mirzoev S.Kh., Nasridinova T.N.
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.

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Kokhirova G.I., Bakhtigaraev N.S., Levkina P.A., Chazov V.V., Khamroev U.Kh.
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 Zeiss-1000 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 area-to-mass ratio and its correlation with the phase angle, the calculated values of the area-to-mass 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 area-to-mass ratio equal to 29 m/kg is shown that is not typical for the rest fragments.

Key words: space debris; positional observations; photometry; brightness; area-to-mass ratio; per.

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Sharipov S.R., Abdullaev S.F., Maslov V.A., Madvaliev U.
Variability in the composition of the carbon-containing fraction of atmospheric aerosol in the semi-arid zone of Tajikistan
The results of a two-year (2014-2016) 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; carbon-containing aerosol; two-stage thermographic method; polynomial regression.

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Kuchakshoev D.S., Dzhabarov A.G., Kholov A.
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 solid-phase 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; solid-phase synthesis; temperature; furnace; concentration.

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Soliev L., Tursunbadalov Sh.
Structure of the diagram of the phase complex of the system NaCl-Kcl-MgCl-CaCl-HO at 0
Using the translation method, the phase equilibria of the NaCl-KCl-MgCl-CaCl-HO 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.

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Juraev J.Kh., Kurbonov A.S., Nematov A.M., Tagoev M.M., Mirsaidov U.M.
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 Ak-Arkhar 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.

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Mamadvafoev M.M., Davlatshoev D.A.
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.

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Shodibekov M.A., Mirakov M.A., Pautov L.A., Khvorov P.V., Fayziev A.R.
Loolingit from granite miarol pegmatit Vez-Dara (Southwestern Pamir)
In the near-a-miar complex of the Vez-Darin 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; Vez-Dara; miarola; vein; chemical composition.

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Khabirov Z., Нakimzod S.
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 2-6 m/s), the flight of horseflies stops. The duration of the active phase and blood sucking is 90 days.

Key words: horseflies; number; blood-sucking; season; flight; activity; Romit Gorge.

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Jalilov A.U.
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.

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Sattorov B.N.
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.

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Avezov T.Sh., Ergashev A.
Influence of pre-sowing 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 (a-TOK, ascorbic acid, Zn-ODEPK) 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.