of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Академии наук Республики Таджикистан, том 58, №9, 2015 г.

Article title and abstractPages
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Ilolov M., Jangibekov G., Chorshanbieva M.Ch.
The study of a class of systems of integral equations contain two-dimensional singular operators and operators of Bergman
In explores some classes of systems of two dimensional integral equations containing singular operators and operators Bergman on a limited area. Found effective necessary and sufficient conditions for Noetherian in the space of lebeg L ( D ), p >1 and the formula for the rate us index.

Key words: нётеровость оператора; индекс оператора; операторная матрица; двумерные сингулярные интегральные операторы; оператор Бергмана; Noetherian; the index of operator; operator matrix; two-dimensional singular integral operators; Bergman operators.

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Rahimov A.O.
An asymptotic formula in Estermann quartic problem with almost equal summands
An asymptotic formula is proveded for the number of representations of a sufficiently large positive integer as a sum of two primes , and the fourth degree of a natural number , satisfying

Key words: почти равные слагаемые; короткая тригонометрическая сумма; диофантово уравнение; almost equal summands; short exponential sum; circle method; diophantine equation.

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Farozova A.D.
The best approximation of classes differential functions in spaces
In article proved the exact inequality between of the best approximation of periodic function with trigonometric polynomial and modulus continuity its average derivative in L spaces. The exact values of n -widths of classes function, where the average modulus of continuity majorized by given function are found.

Key words: наилучшие приближения; модуль непрерывности; полином; мажоранта; n-поперечники; the best approximation; modulus of continuity; polynomial; majorant; n-widths.

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Ziemidinov B.M., Gulomnabiev S.G.
Limit solutions and the solvability condition for systems of differential equations of the first order in the spaces of Stepanov
In this article is solved the system of ordinary differential equations of order in the spaces of Stepanov. In the terms of pre-individual equations are obtained sufficient conditions for ornery-priori estimates for the solutions of the system in the case where the coefficients are continuous and continuous-limited.

Key words: система обыкновенных дифференциальных уравнений первого порядка; пространство Степанова; априорная оценка; предельные решения; модуль непрерывности интеграла; the system of ordinary differential equations; order Stepanovs space; the space of continuous; bounded on (on the whole axis) features; apriori estimate.

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Khudoyberdiev Kh.A., Kosimov A.A.
About a correlation of word form and word usage in russian translation of A.Firdousi "Shahnameh"
An unexpected coinsidence of quantitative regularities characterizing the ratio of between numbers of word forms and word usages in the original and the russian translation of A.Firdousi "Shahnameh" is discovered.

Key words: Фирдоуси; Шахнаме; русский перевод; словоупотребление; словоформа; зависимость; Firdousi; Shahnameh; russian translation; word usage; word form; dependence.

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Usmanov Z.D.
On a rotation of the mass point that moves under gravity along the hyperbolic orbit
Explicit formulas to the rigid body rotation through the true anomaly and four arbitrary constants of integration are received. Specific types of rotation when the rigid body goes to infinity are described.

Key words: материальная точка; гравитация; математическая модель; поступательное движение; вращение; mass point; gravity; mathematical model; translational motion; rotation.

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Odinaev S., Akdodov D.M.
Study of the frequency dispersion of the propagation velocity of thermal waves in aqueous solutions electrolyte
In the basis of the previously obtained expressions for the velocity of propagation of thermal waves in electrolyte solutions are investigated dispersion of the velocity of propagation of thermal wave in aqueous electrolyte solutions of NaCl, taking into account the contribution of the process structural relaxation.

Key words: скорость тепловых волн; структурная релаксация; потенциальная энергия межчастичного взаимодействия; радиальная функция распределения; velocity of thermal waves; process structural relaxation; potential energy of interaction; radial distribution function.

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Salikhov T.Kh., Mahmalatif A., Khojaev Yu.P., Rahmonov R.K.
The theory of thegeneration of second harmonic of the nonlinear photoacoustics signal of the optical inhomogeneous solids
The theory of second harmonic (SH) nonlinear PA - signal optically inhomogeneous and semi transparences solids has been presented. Depending on the amplitude and phase of the signal from the frequency modulation of the incident beam and thermal coefficient (TC) of thermal and optical parameters for most of interest cases are obtained.

Key words: фотоакустика; тепловая нелинейность; нелинейный фотоакустический отклик; вторая гармоника; photoacoustic; thermal nonlinearity; nonlinear photoacoustic response; second harmonic.

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Yusupov I.Kh., Umarov N.N., Marupov R.
EPR spectroscopic properties of burdock leaves ( Mill.) depending on radiation background areas
By ESR-method spectroscopy the content of free radicals in the leaves of burdock was studied, depending on the background of radiation areas. According to the spectral parameters of the signal, it was found that the amount of free radicals contained in the composition burdock leaves depends on the location and environmental condition (background radiation) environment.

Key words: лекарственное растение репейник; ЭПР-спектры; листья; свободные радикалы; medical plant burdock; spectra’s EPS; leaves; free radicals.

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Kodirova H.I., Nazarov B.I., Abdullaev S.F., Karieva R.A., Davlatshoev T.
Research of soil and atmospheric dust aerosol of Tajikistan
The analysis of soils of different regions of the territory of Tajikistan gamma radiometric method using a gamma spectrometer manufactured by "Canberra". It measures the concentration of isotopes of uranium and thorium (Pb-214, Bi-214, Pb-212, Pb-210, Ac-228, Tl-208) as well as K-40 isotope in soil and dust samples haze. A high level of concentration of lead isotopes in soils Zafarabad area and Istaravshan.

Key words: изотопный анализ; пылевой аэрозоль; радиоактивный изотоп; пылевая буря; пылевая мгла; isotope analysis; dust aerosol; a radioactive isotope; dust storm; dust haze.

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Soliev L., Jumaev M.T., Nizomov I.M., Toshov A.F.
Solubility in the system NaSO-NaCO-NaHCO-HO at 25ºС temperature
In manuscript the investigation of solubility at invariant points in the system NaSO-NaCO-NaHCO-HO at 25ºС is presented. The solubility diagram of the title system is modeled according to the evidences obtained.

Key words: растворимость; равновесие; жидкая фаза; твёрдая фаза; химический анализ; кристаллооптический анализ; рентгенофазовый анализ; нонвариантные точки; диаграмма; геометрические образы; solubility; balance; liquid phase; firm phase; chemical analysis; cristallooptical analysis; X-ray diffraction analysis; invariant of a point; diagram; geometrical images.

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Odinaev F.R., Safarov A.G., Kuchakshoev D.S., Akobirov A.A., Ganiev I.N.
Influence of tin on the anodic behavior of the alloy AI4.5 in a medium electrolyte NaCl
By anodic potentiodynamic method behavior of alloy Al+4.5% Fe (AlI4.5), tin-doped medium in NaCl electrolyte of various concentrations are studied. It has been shown that alloying the tin reduces the corrosion rate of the alloy is 1.5-2 times in NaCl electrolyte medium.

Key words: сплав AЖ4.5; анодное поведение; коррозия; электролит NaCl; потенциал коррозии; скорость коррозии; alloy AlI4.5; anodic behavior; corrosion; electrolyte NaCl; corrosion potential; corrosion rate.

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Vazirov N.Sh., Ganiev I.N., Ganieva N.I., Berdiev A.E., Norova M.T.
Praseodymium influence on the kinetics of oxidation of the alloy in the solid state AMg6
By thermogravimetric method the interacting of АMg6 alloy, which contains praseodymium with atmospheric oxygen on the range 673-873 К has been analyzed. Addition of praseodymium decreases the speed of corrosion (oxidation), which is accompanied by increasing the volume of apparent energy of corrosion process activation from 37,8 to 73,4 кДж/моль.

Key words: сплав АMг6; празеодим; термогравиметрический метод; кинетика окисления; истинная скорость окисления; энергия активации; alloy AMg6; praseodymium; thermal gravimetric method; oxidation kinetics; the real rate of oxidation; the activation energy.

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Mamadvafoev M.M., Bakhtdavlatov R.D., Mirzoev B., Bakhronov N.
Farob ore field (Central Tajikistan): geology and assessment of perspectives of industrial gold mineralisation
The article characterizes features of geological foramtion at Farob ore field, provides information on ore-controlling structures, mineral content of ores, forms of gold presence in ores, beneficiation technologies of gold-containing ores, reserves and expected resources of Sharshaga deposit. The article also contains recommendation for preparing more detailed geological and surveying works on the ore field sites, in order to create a reserve of in-situ resources for Zeravshan gold-extracting enterprise.

Key words: Фаробское золоторудное поле; рудопроявления Кундабаст, Якота, Якота Северная, Якбача, Зебо, месторождение Шаршага; запасы и прогнозные ресурсы золота; перспективы рудного поля; Farob ore field; mineral occurrences of Kundabast, Yakota, North Yakota, Yakbacha, Zebo, Sharshaga deposit; reserves and expected resources of gold; perspectives of ore field.

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Salimov J., Ergashev A.
The influence of high concentration of coand different ecological stress factors on growth and productivity of the durum wheat’s
In this article the results the experimental findings about the effect of high concentration of CO and different ecological stress factors (high temperature of air, soil drought) on growth and productivity of wheat an example of two sorts are shown. On the basis of the analysis of physiological and genetic systems of adaptation of plants and attractions assimilates, the various stability of two sorts of wheat to action of high concentration of CO and different ecological factors is established.

Key words: пшеница; рост; продуктивность; распределение ассимилятов; высокая температура; почвенная засуха; повышенная концентрация СО; wheat; growth; productivity; distribution assimilates; soil drought; high temperature of air; high concentration of CO.

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Felaliev A.S., Ismoilov M.T., Felaliev R.S.
The productivity of perspective form of endemic apple tree (Ledeb.) M.Roem in the condition of Western Pamir
In this article the results of many years expeditional research work on studying productivity of more than 30 perspective endemic form of apple tree in the condition of highmountain area of Western Pamir are present.

Key words: яблоня; местные формы; продуктивность; урожайность; productivity; endemic form; apple tree; yield.