of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Академии наук Республики Таджикистан, том 61, №09-10, 2018 г.

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Shabozov M.Sh., Akobirshoev M.O.
About Kolmogorov's type of inequalities for periodic functions of two variables in L
In this article the exact inequalities of Kolmogorov's type for a sequence of mixed derivatives of functions of two variables and the best approximate sequential derivatives of functions by quasi-polynomial in a Hilbert space L(Q) Q:={0 £ x, y £ 2π} were found.

Key words: Kolmogorov's type of inequalities; generalized polynomial; quasi-polynomial; the best approximation; quasi-width.

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Aminov A.S.
On the approximate functional equation of Davenport-Heilbronn's function
The paper is devoted to a new proof of the asymptotic formula for the sum , which appears when deriving the approximate functional equation for the Davenport-Heilbronn function.

Key words: Davenport-Heilbronn's function; exponentials sum; critical direct critical line.

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Kurbonov I., Igbolov S.I.
Waves in isotropic suspension-linear and nonlinear media with memory
The problems of propagation of electromagnetic waves in piecewise-inhomogeneous nonlinear media are considered. Substitutions of boundary value problems for obtained systems of nonlinear integro-differential equations of partial derivatives are given. Their approximate periodic solutions are sought by the method of equivalent linearization. A generalization of the Fresnel formula for media with memory properties is obtained. It is shown that for nonconducting environments without memory . The angle of incidence of reflection and refraction are equal.

Key words: рiecewise inhomogeneous medium; inhomogeneous; inheritance; linear; nonlinear; regularity; electromagnetic fields; ferromagnet.

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Pirov R., Rahimzoda F.Sh.
The theory of five over determined system of partial differential equations of second order with two unknown functions on a plane
We consider the class of over determined system of partial differential equations of second order with two unknown functions on a plane containing in the right side the second-order derivative. Explicit conditions of joint, proved the existence and uniqueness of solutions containing not more then seven permanent derivatives.

Key words: over determined systems; compatibility condition; the manifold solutions.

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Rakhmonov B.A.
On the smoothness of a solution of variational Dirichlet problem associated with noncoercive form in the whole space
We study the Dirichlet variational problem for one class of higher order elliptic operators in the whole n-dimensional Euclidean space in the case of uncoordinated degeneration of coefficients at infinity and we prove that under certain conditions on the smoothness of the coefficients of the elliptic operator and the righthand side of the equation, the smoothness of the solution of this problem is improving. The problem under investigation is connected with the integro-differential sesquilinear form, which may not satisfy the coercivity condition.

Key words: variational Dirichlet problem; elliptic operator; power degeneration; noncoercive form; uncoordinated degeneration; smoothness of a solution.

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Kokhirova G.I., Ivanova О.V., Buriev A.M., Khamroev U.Kh., Rakhmatullaeva F.J.
Complex observations of comet 29P/Schwassmann-Wachmann 1 in Sanglokh observatory
In the International astronomical observatory Sanglokh of the Institute of Astrophysics of the AS RT astrometric and photometric observations of comet 29P were carried out in July-August, 2017. In spite of short period the comet is classified as Centaurs group object. The coordinates of comet were determined and the orbit was calculated, apparent and absolute magnitudes in BVRI bands, and color-indexes were found as well the diameter of comet nucleus was estimated. The results of observations in the Sanglokh observatory are in good agreement with the data of world observations.

Key words: comet; astrometry; photometry; coordinates; orbit; light curve; color-index; diameter.

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Abdullaev S.F., Samiev S.B., Rasulzoda H.H., Maslov V.A., Nazarov B.I., Karieva R.A., Madvaliev U.
Seasonal and interannual variations of TSP (TSP - total sum of particles) in the atmosphere of Dushanbe city
Using the data of the AERONET station of the Atmospheric Physics Laboratory for 2010-2017 and the aerosol optical thickness the aerosol content of various fractions of TSP, PM10, PM2.5, PM1 by 1551 measurements was restored. The regularities of the seasonal variation of the contamination are established, correlations between TSP and the monthly precipitation amount and annual temperature are revealed; a number of important relationships between fractions of particle matter in the atmosphere was found; сorrelations were found between TSP and PM10, between TSP and PM2.5, between TSP and PM1 and the patterns of their variation were established.

Key words: PM10; PM2.5; PM1; TSP; monthly precipitation; annual mean of the temperature; fine dust; aerosol; atmospheric air.

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Karimova Z.I., Bahodurov U.F., Mabatkadamzoda K.S.
Complex formation of silver (I) with 2-mercaptobenzimidazole at temperatures 278-318 K
The process of complex formation of silver (I) with 2-merkaptobenzimidazol at temperatures of 278-318K by a potentiometric method was studied. It is established that silver connects two molecules of 2-merkaptobenzimidazol. The thermodynamics functions of the formation of the silver complex with 2-merkaptobenzimidazol are calculated and their effects on the depth of the complication reaction are shown.

Key words: silver(I); 2-merkaptobenzimidazol; complexation; thermodynamic function; stability constant.

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Sangov Z.G.
A new Method synthesis of 2-alkylthioethyl-5,7-dioxo-1,3,4-thiadiazolo [3,2-a] pyrimidine derivatives
In this paper new method for the synthesis of 2-alkylthioethyl-5,7-dioxo-1,3,4-thiadiazolo[3,2-a]pyrimidine derivatives by cyclization of malonic acid ether with derivatives 2-alkylthioethyl-5-amino-1,3,4-thiadiazole has been described.

Key words: 2-alkylthioethyl-57-dioxo-1,3,4-thiadiazolo [3,2-a] pyrimidine; cyclization; malonic acid diethyl ester.

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Zukhurova M.A., Vakhobova R.U.
Dependence of specific and equivalent electrical conductivity on the degree of dilution of concentrated solutions of ctrontiun
In the article, based on electrochemical studies, the nature of the proceeding reduction processes on the mercury-dropping electrode and in the electrode region was established. The forms of existence of the strontium element depending on the physicochemical parameters, the degree of reversibility or irreversibility of the processes, the degree of dissociation, the measurement of the quantities are determined.

Key words: specific and equivalent conductivity; element; convertibility; physic-chemical parameters; degree of dissociation; concentration; electrolyte; viscosity; cation of strontium; association; dilution.

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Abdusalyamova M.N., Kabgov H.B., Makhmudov F.A.
Physico-chemical characteristics of YbMnSb doped with yttrium
The methods of synthesis and growth of monocrystals of Zintl phases are considered. Solid solutions of the type YbYxMnSb were obtained. It is shown that all the obtained samples have a tetragonal structure of the type CaAlSb. The lattice parameters were found. The coefficients of thermal expansion, melting temperature and Debye temperature were calculated.

Key words: rare-earth elements; Zintl phases; thermal expansion; melting points.

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Rahimov F.A., Ganiev I.N., Obidov Z.R.
Kinetic oxidation of Zn5Al alloy, doped with chrome, in the firm condition
In this paper the results of research kinetic the oxidation of Zn5Al alloy, doped with chrome, in a firm condition are presents. It is showed that additives of an alloying component slightly reduce oxidability of alloy Zn5Al.

Key words: Zn5Al alloy; chrome; thermo gravimetrical method; alloys oxidation; speed of oxidation; energy of activation.

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Ragabov U.R., Sultonov R.A., Yusufi S.Dj., Yusupov I.Kh., Haydarov K.H.
Iron (II) with acetylcysteine synthesis and biological properties its investigations by spin marks method
The physico-chemical, physiological, and biological properties of the synthesized coordination compound of iron (II) with acetylcysteine using the spin label method to find new, more effective antioxidant agents, and conduct laboratory tests were studied. It has been established that in the compound of sulphate of iron(II) with acetylcysteine when adding ethanol to the solution with the presence of a nitroxyl radical, it is completely restored and affects to the chemical stability of the nitroxyl fragment which indicates a strong property of antioxidants.

Key words: coordination compound; ferrum acetylcysteine; nitroxyl radical; EPR spectra.

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Fayziev F.A., Fayziev A.R., Yatimov S.B.
Matildite from silver and silver containing deposits of Tajikistan
In this article the data on sulfosalts of silver and bismuth - matildite from silver and silver-containing deposits and occurrences of Tajikistan are summarised. At the Kandzhol field it was discovered and described for the first time. Established in more than ten deposits and silver ore manifestations, matildite makes it possible to say with confidence that it is more widespread than previously thought are summarizes.

Key words: matildite; shapbachite; galena; sphalerite; association; field.

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Li Yaoming, Маdaminov А.А., Li Kaihui, Fan Lianlian, Yusupov С.Y., Оkhonniyozov М.V., Тursunov У.А., Ma Xuexi
Productivity of the tаll forbs semisavannas pastures of Tajikistan
The results of changes in the productivity and structure of Prangos communities in the Ziddi (southern slope of the Hissar range, height 2000 m) under the influence of nitrogen fertilizers are presented. The gross yield of Prangos pastures increased from 45.1 (in control) to 91.9 c/ha (NP). Harvest dry weight of Prangos pabularia in the herbage of pastures has increased in 3.2 time.

Key words: Tajikistan; higher mountains; pasture; productivity; structure tаll forbs; semi savanna.

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Abdullaev Kh.A., Djumaev B.B., Bohirova M.K., Ergashev A.E.
Carbohydrate contents in leaves of defoliated cotton plants
In this article the results of analysis of carbohydrate contents in leaves of long stable cotton Gossypium barbadense L. after defoliation by thin layer one-dimensional chromatography in cellulose methods are presents. It is shown that indepently from the degree of defoliation of sucrose contents was higher with compare to contents of glucose and fructose. This date is evidence of sucrose direction of metabolism in cotton plants.

Key words: long stable cotton; leaf; defoliation; carbohydrate; thin layer chromatography; metabolism.