of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Национальной академии наук Таджикистана, том 64, №09-10, 2021 г.

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Fuzzy integro-differential equation of Uryson type
Observation problems in dynamic control systems with incomplete information and uncertain parameters are described by fuzzy integro-differential equations and systems of such equations. In this regard, it is important to analyze the solvability and study the qualitative properties of solutions of fuzzy equations. In this paper, we study a finite-dimensional system of fuzzy integro-differential equations with a nonlinear Uryson operator.

Key words: fuzzy integro-differential equation; nonlinear Uryson operator; Zadeh extension principle.

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Exact type of inequality of the Jeckson-Stechkin for one characteristic of smoothness in the Bergman space and the width of classes of functions

Key words: continuity modulus; characteristics of smoothness; Jackson-Stechkin type inequality; upper bound; -widths.

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The upper boundaries of the best approximations of certain classes of vectors by Fourier sums in the orthonormal system of vectors in the hilbert space
In this paper the exact values of the upper bound for the best approximations of some classes of vectors by Fourier sums over an arbitrary system of orthonormal vectors in an arbitrary separable Hilbert space are found.

Key words: upper bound; system of orthonormal vectors; averaging operator; generalized modulus of continuity; best approximations.

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D.S.Safarov , S.K.Miratov
Оn solution of one class of second-order differential equations with constant deviations of the argument
In this work, for a nonlinear second-order differential equation with constant deviating argument with constant coefficients, exact solutions are found using the Jacobi elliptic function - delta amplitude dnu.

Key words: solution; modulus of function; periods of solution; doubly periodic solution; elliptic function; elliptic integral; delta-amplitude.

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S.A.Iskhokov , A.Y.Kudzhmurodov , M.Sultonzoda
Variational Dirichlet problem for degenerate elliptic operators in the hole space
In the paper we study solvability of the Dirichlet variational problem for non-divergent form elliptic operator in the hole space which coefficients have power degeneracy at the infinity. Theorem on Fredholm solvability of the problem is proved.

Key words: Sobolev-type space; elliptic operator; power degeneration; non-divergent form; Dirichlet problem.

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A boundary value problems for elliptic systems of equations in the plane
In this article the purpose is to establish an effective necessary and sufficient conditions Noetherian in (considered over the field) and getting the formula for the calculation of the index.

Key words: noetherian property; two-dimensional singular integral operators; Dirichlet problem; problem index.

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B.I.Makhsudov , I.Kh.Fayzulloyev , M.Kh.Egamov
Temperature dependence of optical properties in composites based on polymer-nematic liquid crystal under uniaxial deformation
An experimental setup for studying the temperature dependence of the optical properties of polymer-liquid crystal composites with controlled surface adhesion under uniaxial deformation is presented. It has been shown experimentally that in polymer-liquid crystal composites based on nematic liquid crystal (NLC) 4-n-heptyl-4'-cyanobiphenyl (7CB), a temperature dependence of the optical property is observed under uniaxial deformation.

Key words: polymer-liquid crystal composites; surface adhesion; uniaxial deformation; polarization; injection laser; optical properties; photonics.

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R.J.Akramzoda , A.S.Kurbonov , M.M.Tagoev , U.M.Mirsaidov
Boric acid extraction from the brine of lake Sasyk-Kul Tajikistan with isobutyl alcohol and tributylphosphate
In this paper the results of the extraction of boric acid with isobutyl alcohol and tributylphosphate from the lake Sasyk Kul brine are presents. The optimal conditions for the boric acid transition to the organic phase from the lake Sasyk-Kul brine during extraction have been determined. It has been found that isobutyl alcohol and tributylphosphate are effective reagents for the extraction of boric acid.

Key words: extraction; isobutyl alcohol; tributylphosphate; boric acid; brine.

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Biologically active methionin and its protolytic properties
The protolytic properties of aqueous methionine solutions in the temperature range from 293.16 to 328.16 K at a constant ionic strength of the solution of 0.1 mol / l (Na (H) CIO) by the method of pH-metric titration were investigated. The presence of interionic forces of attraction and repulsion of basic particles affects the values of the ionization constants of methionine.

Key words: methionine; protolytic properties; dissociation; pH; ionic strength; temperature; amino acid; pK.

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M.D.Isobaev , E.Kh.Pulatov , B.G.Mavlonov
Bromine and amino derivatives of thiazolidine-2-thione
A schematic diagram of the synthesis of bromo- and amino derivatives of thiazolidine-2-thione was developed and the analysis of the stability of the thion-thiol transition in depending on external factors, was carried out.

Key words: thiazolidine thione; thion-thiol tautomerism; bromine and amino derivatives.

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T.M.Umarovа , S.S.Holova
Anodic behavior of Al-Ti alloys with metals of lanthanide groups in the medium of NaCl electrolyte
The results of electrochemical investigations of alloys of eutectic composition aluminum-titanium system, alloyed by metals of the cerium subgroup (lanthanum, praseodymium and neodymium) in the 3% NaCl solution are presented.

Key words: aluminum alloy; rare earth metals; Lanthanum; Рraseodymium; Neodymium; anodic behavior; polarization curves.

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Technology of obtaining coagulants from kaolin clays of the Ziddi deposit by the method of sulphatization
In this article the results of physicochemical studies on the technology of obtaining crude and purified coagulants for water purification from kaolin clays of the «Ziddi» deposit by the method of sulfatization and testing the coagulating ability of the crude coagulant in laboratory conditions are presents. The optimal technological parameters of the kaolin clay sulfatization process have been determined: temperature - 260-280°C, duration - 90-120 minutes, sulfuric acid concentration - 90-95%, acid dosage up to 110% of stoichiometric calculation. The process of water treatment of sulfated cake was also studied in order to obtain a purified liquid coagulant - the optimal parameters of water treatment: temperature - 85-95°C, duration - 30-45 minutes, ratio - S:L=1:4. In this case, the degree of extraction of aluminum sulfate is more than 97%. On the basis of the laboratory studies carried out, a basic technological scheme for obtaining crude and purified kaolin coagulants was developed. The study of the coagulating ability of the obtained coagulant showed that its main physical and chemical parameters correspond to the requirements of GOST 5155-74 for crude aluminum sulfate and in terms of «dose of coagulant» meet the requirements of GOST 12966-75 for purified aluminum sulfate.

Key words: sulfatization; crude coagulant; purified coagulant; kaolin clay; coagulating ability; aluminum sulfate.

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I.N.Ganiev , Sh.G.Rajabova , F.A.Rahimov , Z.R.Obidov
Anode behaviour of Zn55Al alloy, doped with molybdenum, in the sour environment
In this paper the results potentiodynamical researches of anode behaviour of Zn55Al alloy, doped with molybdenum, in the sour environment are presented. Showed, that doped zinc-aluminium alloy molybdenum promotes reduction of corrosion rate of an alloy initial at 1.5-2.0 times.

Key words: Zn55Al alloy; molybdenum; potentiostatically method; HCl electrolyte; corrosion potential; corrosion rate.

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Kh.Sh.Rakhimov , A.A.Kodirov , A.B.Badalov
Chlorinating roasting of mechanically activated antimony sulfide concentrates with sodium chloride
An effective method of chlorinating roasting of mechanically activated sulphide-antimony concentrate with sodium chloride has been developed. The optimal mode of the roasting process has been determined, which provides a high yield of antimony compounds, which are easily processed technologically.

Key words: sulfide antimony concentrate; mechanical activation; oxidative chlorination roasting; chlorination roasting; chloride natrium.

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Geotectonic and structural factors of the location of silver and silver-bearing deposits in Northern and Central Tajikistan
The object of research is the silver and silver-bearing deposits of the Kuramin structural-formation zone (Northern Tajikistan) and the Zeravshan-Gissar zone (Central Tajikistan). The leading in the formation of the first zone is considered to be the Middle-Late Hercynian volcano-intrusive formations, and in the second - Hercynides with poorly developed Caledonian and Baikal cycles. The main factor in the localization of these deposits is the structural factor. Deposits of Northern Tajikistan are confined to graben-synclines, subsidence troughs, handfuls and horst-anticlines, and the objects of Central Tajikistan are controlled by a system of submeridional and northwestern faults in the zone of interformational disruptions.

Key words: geotectonic and structural factors; silver and silver-bearing deposits; hercynides; metallogenic province; structural-formation zones.

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Qualitative and quantitative characteristics of the bird fauna of the Pamir Botanical Garden
The article provides data on the bird fauna of the Pamir Botanical Garden. For the first time, a generalized list of species composition is presented. Information is given about the nature of the birds' stay and the nature of the occurrence of nesting and sedentary species on the territory of the Botanical garden.

Key words: species composition; nature of stay; nature of occurrence; sedentary; nesting; quantitative characteristics.