of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Академии наук Республики Таджикистан, том 61, №3, 2018 г.

Article title and abstractPages
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Jurakhonov O.A.
Least upper bounds of approach some classes of functions of two variables the triangular sums fourier in space
In work the exact least upper bounds of approximation of functions of two variables the triangular partial sums of a double series Fourier by general orthogonal polynomials on a class of functions in space are calculated.

Key words: наилучшие приближения; модуль непрерывности; ряд Фурье; неравенство; ортогональные многочлены; best approximation; modulus of continuity; sums Fourier; orthogonal polynomials; inequalities.

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Mustafokulov R.
Equation model for one lineare homogeneous equation of Euler’s type of th order
In this work the generalized form of lineare equation of Euler’s type of n - th order is considered. For equation of this class the conditions reducibility to equation with constants coefficients is reduce. The model equations is determined. The method of solve of model equations is indicate.

Key words: уравнение типа Эйлера; модельное уравнение; формула Фаа-ди-Бруно; характеристическое уравнение; характеристические числа; equation of Euler’s type; model equation; formula of Faa-du-Bruno; characteristic equation; characteristic number.

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Iskhokov S.A., Rakhmonov B.A.
On solvability and smoothness of a solution of variational Dirichlet problem for degenerate elliptic operators in the whole space
We study the variational Dirichlet problem for a class of higher order degenerate elliptic operators in the whole n-dimensional Euclidian space. A theorem on unique solvability of the problem is proved and under some additional condition on smoothness of coefficients and the right-hand side of the equation, differential properties of the solution are studied. Formulation of the problem under consideration is connected with integro-differential sesquilinear form that may not satisfy the coercitivity condition.

Key words: вариационная задача Дирихле; эллиптический оператор; степенное вырождение; некоэрцитивная форма; гладкость решения; variational Dirichlet problem; elliptic operator; power degeneration; noncoercive form; smoothness of solution.

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Rajabova L.N., Shukurova G.N.
On some cases of symmetric two-dimensional integral equations of type Volterra with the a singularity and logarithmic singularity in the kernel
In this paper, we investigate some cases of a symmetric two-dimensional integral equation of Volterra type with a singularity and a logarithmic singularity in the kernel. In the case when the parameters of the equation are related to each other, depending on the sign of the equation parameters, explicit solutions of the integral equation containing arbitrary functions are obtained.

Key words: симметричное интегральное уравнение; логарифмическая особенность; произвольные функции; асимптотическое поведение; непрерывные функции; обращение в нуль; symmetric integral equation; logarithmic singularity; arbitrary functions; asymptotic behavior; continuous functions; vanishing.

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Kabilov M.M., Khalimov I.I.
The superadiabatic mode of combustion hedrogen-air mixture in an inert porous medium
Behavior of an analytical solution of the mathematical model of filtration gas combustion, that allowes to describe the superadiabatic mode of combustion hydrogen-air mixture in an inert porous medium, is considered. Conditions for existence of superadiabatic mode of combustion of the mixture are studied. Dependences of difference of equilibrium and adiabatic temperatures and the speed of a stationary combustion wave on the speed of mixture and the coefficient of excess fuel are investigated in the paper. Patterns of change in the temperature distribution of the porous medium, a mixture of gases and the relative concentration of the missing component are also considered.

Key words: сверхадиабатический режим; скорость волны; равновесная температура; адиабатическая температура; распределения температур; коэффициент избытка топлива; состав смеси; концентрация; superadiabatic mode; wave speed; equilibrium temperature; adiabatic temperature; the temperature distribution; the coefficient of excess fuel; concentration; the composition of the mixture.

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Kokhirova G.I., Ivanova O.V., Rakhmatullaeva F.J., Khamroev U.Kh., Abdulloev S.H.
Results of observations of the asteroid (596) Scheila in Sanglokh observatory
The results of astrometric and photometric in BVRI standard bands observations of active asteroid (596) Sheila performed by the Zeiss-1000 telescope of the International astronomical observatory Sanglokh in the period of June 16 - 17 and July 30- August 1, 2017 are presented. The object’s coordinates were determined, as well as the absolute magnitudes in four bands and color-indexes of asteroid were obtained. The light curves do not shown variations of the brightness during the period of observations. The absolute magnitude values are close to the ephemerid value, estimations of diameter and rotation period of the asteroid by our observations are in good accordance with other data. The obtained data showed that the asteroid has saved absolute magnitude and other parameters, in spite of its collision with a small body in December 2010 that led to outburst of its brightness and developing of a comet activity of the asteroid. The impact of the asteroid Sheila was very likely not catastrophic, and did not lead to its complete decay.

Key words: астероид; астрометрия; фотометрия; координаты; кривая блеска; абсолютная яркость; диаметр; период вращения; asteroid; astrometry; photometry; coordinates; light curve; absolute magnitude; diameter; rotation period.

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Odinaev S., Idibeg Kh.
About the frequency behavior of the electroconductive properties of electrolyte solutions depending on the nature of the attenuation of relaxing flows
Analytical expressions for the dynamic coefficient of electroconductivity and modulus of electroelasticity of electrolyte solutions when relaxing the flows are damped by degree and exponential law are obtained. The frequency behaviour of these coefficients in a wide frequency range, and asymptotic behaviour at low and high frequencies were investigated.

Key words: коэффициент удельной электропроводности; модуль электроупругости; коэффициенты трения; времена релаксации; потенциальная энергия взаимодействия; радиальная функция распределения; the coefficient of electroconductivity; module of electroelasticity; the coefficients of friction; the relaxation times; the potential energy of interaction; the radial distribution function.

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Kadirov A.L.
Thermal energy converter on the basis of secondary cast polycrystalline silicon
Comparison of solar and thermal energy converters based on semiconductor silicon of various modifications is presented. A cheaper and more efficient thermal energy converter from secondary cast polycrystalline silicon is proposed. The prospects of using non-monocrystalline, nanostructured and composite materials are pointed out.

Key words: нефотоактивная составляющая солнечного излучения; преобразователи солнечной и тепловой энергии; вторичный литой поликристаллический кремний; non-photoactive component of solar radiation; converters of solar and thermal energy; secondary cast polycrystalline silicon.

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Abdulov Kh.Sh., Tuichiev L., Tuichiev Sh.
Calculation of parametres of a helical chain of polymer
It is shown that for a helical chain with number of various atoms in the period of identity more than 7 it is impossible to write formulas of type of Miyazawa in an analytical kind. Therefore on the basis of the equations of Miyazawa the algorithm is created and the program on a Fortran for calculation of parametres helical chain with any number of various atoms in the identity period is written. Under this program parametres of a helical chain for number of various atoms in the period of identity from 1 to 3 are calculated.

Key words: алгоритм; параметры спиральной цепи; период идентичности; программа; уравнения Миязавы; algorithm; parametres of a helical chain; the identity period; the program; the equations of Miyazawa.

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Hodjiev S.K., Nazarov Kh.M., Ermatov K.A., Mirsaidov I.U., Bobojorov M.D.
Effectiveness of hydrogen peroxide action as an oxidizer of uranium dioxide depending on the pH state
In the article the results of the action of hydrogen peroxide as an oxidizer of uranium dioxide depending on the pH state are presented. It was found that hydrogen peroxide in the sulfuric acid state is possessed a high oxidizing ability with respect to uranium, and the oxidation process proceeds energetically not only with the participation of iron ions, but also in their absence. Such combined processes using hydrogen peroxide as an oxidizer deserve more attention.

Key words: рН среды; пероксид водорода; диоксид урана; ион железа; степень окисления; реагент; окислитель; pH state; hydrogen peroxide; uranium dioxide; iron ion; oxidation grades; reagent; oxidant.

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Naimov N.A., Ruziev J.R., Aminjoni G., Safiev A.Kh., Boboev Kh.E., Muhamediev N.P., Rafiev R.S., Safiev Kh.
Complex processing of kaolin clays Ziddi deposit
In this work the results of studies on establishing the composition and optimal parameters for the complex processing of kaolin clays of the Ziddi deposit is showed. The conducted studies showed that during the process of sulfatization of kaolin clays, it is possible to obtain sulfated sintering, consisting mainly of silica, aluminum sulfate and iron sulfate. The resulting sulphated sinter according to known Bayer technology can be processed to produce alumina or used in the production of aluminum fluoride and cryolite.

Key words: каолиновые глины; сульфатизация; сульфатсодержащий раствор; десульфатизация; коагулянт; неочищенный коагулянт; коагулирующие свойства; сульфат алюминия неочищенный; глинозём; kaolin clays; sulfatization; sulfate-containing solution; desulfatization; coagulant; raw coagulant; coagulating properties; crude aluminum sulfate; alumina.

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Nazarov Kh.M., Boboev B.D., Ermatov K.A., Bahronov S., Muminov S.V.
Contents of radon in the air of the spetamen district of the Republic of Tajikistan
The results of monitoring of the radon content in the air of residential houses in the Spitamen district of Tajikistan are presented. It is shown that the average concentration of radon in the air is 72 Bq/m³.

Key words: радон; объёмная активность; радиометр; дозиметр; доза; жилые помещения; воздух; radon; volumetric activity; radiometer; dosimeter; dose; residential houses; air.

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Sabirov A.A.
Two new species of the primitive carboniferous foraminifera of the Tajikistan
In the Lower Carboniferous deposits of Tajikistan two new species of calcareous primitive Foraminifera, the youngest representatives of thin-walled Parathuramminidae, are found out first time, which have been still known from more ancient deposits.

Key words: фораминиферы; паратурамминиды; каменноугольная система; турнейский ярус; визейский ярус; Foraminiferа; Parathuramminidаe; Carboniferous system; Tournaisian stage; Visean stage.

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Abdullaev Kh.A., Valiev Yu.Ya., Gorenkova L.G., Kabgov Kh.B., Mamatov E.D.
The influence of superphosphate, making up from Karatag deposits on photosynthesis, assimilate partitioning and technological properties of cotton fiber
It shown that the fertilizer superphosphate, making up from Karatag deposits is raise of the photosynthesis intensity rate, weight of vegetative and generative organs give a higher yield

Key words: хлопчатник; фосфорит; микроэлементы; фотосинтез; распределение ассимилятов; технологические свойства волокна. биологический и хозяйственный урожай; cotton; phosphorite; microelements; photosynthesis; assimilate partitioning; technological properties of fiber; biological and economic harvest.

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Khamroeva Kh.M., Davlyatnazarova Z.B., Norkulov N.Kh., Dzhumaev B.B.
Influence of exogenous antioxidants on lipide peroxidation of arabidopsis plants in salinity conditions
The effect of ascorbic acid and α-tocopherol on the processes of lipid peroxidation in the wild type and mutant forms of Arabidopsis thaliana (L .) Heynh in conditions of chloride salinity was studied. It is shown that the adding of exogenous antioxidants to the aqueous growth medium separately and in a complex leads to different degrees of inhibition of lipid peroxidation processes. In the wild form of En and mutants forms as, cla and flavi , the level of MDA formation is different in the presence of NaCl , ascorbic acid acts as a pro-oxidant, i.e. facilitated the oxidation reaction, and α-tocopherol abruptly inhibited POL.

Key words: Arabidopsis thaliana (L.) Heynh; засоление; антиоксиданты; аскорбиновая кислота; α-токоферол; перекисное окисление липидов; Arabidopsis thaliana (L.) Heynh; salinity; antioxidants; ascorbic acid; α-tocopherol; lipid peroxidation.