of National Academy of Sciences
of Tajikistan

News of the National Academy of Sciences of Tajikistan.
Department of physical, mathematical, chemical, geological and technical sciences

Известия Академии наук Республики Таджикистан. Отделение физико-математических, химических, геологических и технических наук, №2(175), 2019 г.

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On the joint approximation of a periodic function and its sequential derivatives
In the work, an extremal problem of joint approximation of the function itself and its sequence of derivatives by trigonometric polynomials for one class of functions was solved, of which the average value of the norm of the difference of m-th order in the L metric is bounded by a given mojarant.

Ключевые слова: the best polynomial approximation; finite difference of m-th order; partial sum of Fourier sum.

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About simultaneous polynomial approximation of functions and their derivatives in the Bergman space
In this paper the exact inequalities between sizes of the best mean square polynomial approximation of intermediate derivatives and the best polynomial approximation of the senior derivative of the analytical in a circle function satisfying the condition are found. The exact value of the top side of size of simultaneous approximation of functions and its intermediate derivatives in a metrics space are calculated.

Ключевые слова: exact inequality; the mean-square polynomial; best polynomial approximation; extremal problem; Bergman space.

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Solving one extreme problem in space L
In the article, we solve one extreme problem of the calculated least upper bounds the best polynomial approximation sequential derivatives of on some class of functions defined majorant , where is the differential operator Chebyshev second order

Ключевые слова: mean square best approximation; generalized modulus of continuity; double Fourier-Chebyshev series; majorant; Chebyshev operator.

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An estimation of the delay value in the predator-prey system of Wangersky and Cunningham, when the positive stationary solution of this system is asymptotically stable according to the exponential law
In this paper some earlier obtained results on the investigation of stability of periodic solutions of non-linear systems of delay-differential equation are used for an investigation of asymptotic stability according to the exponential law of the positive stationary solution of the predator-prey system of Wangersky P.J. and Cunningham W.J. It was made an estimation of the time lag value , when such type of stability takes place.

Ключевые слова: a mathematical model in ecology; the delay predator-prey system; stability in ecological systems; the asymptotic stability according to the exponential law of a solution of a delay-differential system; the orthogonal transformation of matrices similarity.

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G.I.Kokhirova , U.Kh.Khamroev , M.N.Latipov
Comparision of determination of the trajectories and velocities of fireballs photographed by the fireball and digital cameras
Photographic observations of the Perseids meteor shower activity during its maximum were carried out by the Tajikistan fireball network in 2007-2011. As a result of the astrometric reduction of obtained observational data the atmospheric trajectories, velocities and orbits of 29 Perseid meteoroids were determined. Part of them was detected by both the fireball and digital cameras, and the independent reduction was performed for them. A comparison analysis of the results of determination of the dynamical properties of meteoroids photographed by different techniques is presented here. A sufficient precision of the data determination has proved reliability and advances of the digital cameras usage in fireball observations.

Ключевые слова: meteor shower; fireball; atmospheric trajectory; height; geocentric trajectory.

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The density of the flow of internal energy in piezoelectric semiconductors at low temperatures
The process of stimulated scattering of two-frequency laser pumping in semiconductor compounds with a piezoelectric effect at low temperatures is studied. The effect of optical sound generation by two-frequency laser pumping in a piezoelectric semiconductor with a reflecting back surface was revealed when current flows towards the pump and across the magnetic field at low temperatures.

Ключевые слова: piezoelectric; semiconductor; optical sound generation; lazer pumping.

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Z.V.Kobuliev , Sh.A. Zaripov , J.A.Zaripov
Thermal conductivity of composite fittings for different temperatures
This paper presents the results of studies of the parametrs of thermal insulation and processes at different temperatures, as well as the process of rebuilding reinforcement for different temperatures. According to the results of research experiments, the heating of composite reinforcement in the temperature range of 298-380 K was estimated.

Ключевые слова: composite reinforcement; temperature; thermal conductivity.

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U.M.Mirsaidov , D.Kh.Mirzoev , Sh.D.Otaev , Sh.Azamov , N.M.Jamolov
Alumina extraction from aluminumsilicate ores of Tajikistan by decompositioning with chloride acid
The paper presents the results of obtaining alumina and iron oxide from aluminumsilicate ores of deposits in Tajikistan. It is shown that during the processing of the initial aluminumsilicate ores as nephelinesyenites, kaolin clays, mudstones of various deposits, the alumina extraction grade is not more than 50%. Iron oxide recovery grade varies from 22.5 to 93.0%. For calcinedaluminosilicate ores, the alumina extraction grade is from 62 to 97%, for iron oxide from 48 to 99%.

Ключевые слова: alumina; iron oxide; aluminumsilicate ore; nephelinesyenites; kaolin clays; mudstones; hydrochloric acid.

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D.S.Mansuri , A.Djurayev , H.O.Rahimova , M.M.Nasimova , G.Shuhratzoda
The calculation of the friction force of the rotational kinematic pair of the fifth class with longitudinal grooves
The paper presents the design scheme and the principle of operation of the developed new effective design scheme of the rotational kinematic pair of the fifth class with longitudinal grooves on the surface of the pair axis. A method for determining the friction force in a kinematic pair is given, a formula for calculating the friction force in a kinematic pair is derived. Graphic regularities of the change of the friction moment due to the variation of the width of the grooves, the length of the kinematic pair are built The parameters of the kinematic pair are justified.

Ключевые слова: rotational kinematic pair; grooves; length; width; friction torque; load; resource; lubrication; parameters.

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G.N.Petrov , Kh.Kh.Khalikov
Hydro-coal scenario of energetics development in Tajikistan
To achieve the global average level of economic development, the total production and consumption of electricity in Tajikistan should increase three times. At the same time, today, and for the foreseeable future, hydropower will be the base of all Tajikistans energy. But at the same time, in order to mitigate the shortcomings of hydropower, as an addition to it, development of coal energetics is also necessary in Tajikistan.

Ключевые слова: energy resources; economic development; hydropower; thermal energetics; coal; electricity tariff.

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Kaolinite clays and conditions of their formation and distribution the jurassic sediments of the Tajik depression
By the study of the petrographic and mineralogical composition of the Jurassic clay rocks it has been established, that the single light-grey and white clays layers that are found in sections of even-aged sediments mainly consist of kaolinite mineral, whose formation is closely related to the coal-bearing rocks of the Middle Jurassic formation.

Ключевые слова: kaolin; kaolinite; associative; formation; dispersion; depression; pattum; cut; gravelite; conglomerate.

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M.M.Mamadvafoev , D.A.Davlatshoev
On petrochemistry and genesis oflamprophyres of Kafandara skarn-ore field (East Gissar)
The paper provides information on the petro-chemistry of lamprophyres in the diorite series genetically related to the inversion (C) granitoid magmatism of the normal, calk-alkaline series. For comparison, data on other dyke rocks of increased alkalinity, as well as the normal, calc-alkaline series, are also given. These materials lead to the conclusion that lamprophyres could have been formed not only due to the effect of transmagmatic solutions of increased alkalinity on diabase dikes of normal alkalinity, during their crystallization, as D.S. Korzhinsky wrote earlier, also as a result of applying the same solutions to diorite dykes that is directly observed in Kafandara skarn-ore field.

Ключевые слова: East Gissar; Kafandar skarn-ore field; dikes; lamprophyres; quartz monzonites; syenites; diorites; diabases; petrochemistry; genesis.

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F.M.Babadzhanov , M.B.Rustamov
Characteristics of soil subsidence of the upper horizon of the upper quaternary Dushanbe complex in the central part of Dushanbe by the method of two curves
Loess rocks are widely spread on the territory of Tajikistan. In the Republic, all loess deposits have a cover character: almost all plains and valleys are cover with loess. Many loess rocks are often watered up due to increased rainfall, rising levels in rivers, due to engineering and economic activities of man (leakage from water pipes, irrigation of fields, the creation of artificial reservoirs and canals). Due to the increase in construction in Tajikistan, the need to study loess rocks increases.

Ключевые слова: loess; two-curve method; subsidence soils; lower horizon of the Upper Quaternary Dushanbe complex.

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The level of groundwater occurrence in the irrigated lands of the Yakhsu, Kyzylsu and Pyanj river basins of southeastern Tajikistan
The paper analyzes the results of research on the occurrence of groundwater levels on the irrigated lands of the Yakhsu, Kyzylsu and Pyanj river valleys. Studies have shown that in significant areas, groundwater is located at a critical level of 0 - 1.1, 0 - 1.5 m, which is a predisposing factor in soil salinization and prevents the production of high crop yields.

Ключевые слова: groundwater; the level of their occurrence; irrigated lands; fertility; salt balance; observations; precipitation; runoff regime; evaporation.

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