of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Академии наук Республики Таджикистан, том 58, №2, 2015 г.

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Rakhmonov Z.Kh., Nazrubloev N.N.
Waring’s problem for fifth powers with almost equal summands
An asymptotic formula is obtained for the number of representations of sufficiently large natural number N by a sum fifth powers of natural numbers x , with conditions | x - ( N /33) | ≤ H , H ≥ N .

Key words: проблема Варинга; почти равные слагаемые; круговой метод; короткая тригонометрическая сумма; Waring’s problem; Almost equal summands; Circle metods; Short exponential summs.

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Yusupov G.A.
On the structural characteristics of functions from and exact values of widths of some classes functions
Several exact inequalities between the best approximations of differentiable periodic functions in the sense of Weyl trigonometric polynomials, and averaged with the weight of the moduli of continuity of arbitrary fractional order in the metric of L are found and their applications are also given. For some classes of functions, determined as the moduli of continuity and the exact values of various -widths in L are calculated.

Key words: неравенства типа Джексона-Стечкина; наилучшие полиномиальные приближения; модуль непрерывности дробного порядка; производная в смысле Вейля; n-поперечники; inequalities of Jackson-Stechkin; the best polynomial approximations; the modulus of continuity of fractional order; derivative in the sense of Weyl; n-widths.

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Jangibekov G., Odinabekov J.M.
In this paper the noethericity and index question of Neumann problem for general elliptic systems of differential equations of second order was studied. Investigation of this problem is carried out by method of bringing the equivalent into two-dimensional singular equation on a bounded domain on the plane.

Key words: эллиптическая система; задача Неймана; сингулярные интегральные уравнения; нётеровость и индекс задачи; elliptic systems; Neumann problem; singular integral equation; neothericity and index problem.

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Usmanov Z.D., Kosimov A.A.
Frequencies of the letters in tajik literature
Established that frequencies of Tajik letters in classical and contemporary poetry and prose are statistically indistinguishable. The data of the letter frequencies and an average information per the symbol of Tajik alphabet are presented.

Key words: таджикский язык; буквы; частотность; Tajik language; letter; frequency.

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Srumova F.V.
About asymptotic form of energy emitted by randomly arranged oscillation sources
The energy emitted by Poisson-distributed point source of oscillation has been calculated.

Key words: случайно расположенные источники колебаний; randomly arranged oscillation sources.

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Abdulloev S.Kh., Kokhirova G.I., Minikulov N.Kh., Mullo-Abdolov A.Sh.
Observations of potentially hazardouz asteroid 2014SS1
The photometric observations of asteroid 2014SS1 were carried out in astronomical observatory of the Institute of Astrophysics of the Republic of Tajikistan. As a result the light curves of the asteroid 2014SS1 were plotted. The determined period of rotation around of its axis is equal to 16 hours 43 minutes 12 seconds. Defined ratio of the asteroid’s radii at weak and bright positions is 2.1. Fulfilled astrometric reduction and calculated positions of asteroid during the observations are in good agreement with the data of MPC.

Key words: астероид; фотометрия; кривая блеска; период вращения; asteroid; photometry; light curve; period of rotation.

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Farhod Rahimi
Dynamic structural factors of dispersion of neutrons and infrared light on solitons of quasione-dimensional magnetics
The solitonic part of a dynamic structural factor of dispersion of neutrons and infrared light on solitons of quasione-dimensional magnetics is received. From the received decisions comes out that solitonic fashions lead to redistribution of intensity from the maximum peak in quasi-elastic part of a range which it is possible to observe in experiments on dispersion of neutrons.

Key words: солитон; динамический структурный фактор; магнетики; квазиодномерные магнетики; soliton; dynamic structural factor; magnetics; quasione-dimensional magnetics.

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Odinaev S., Mahmadbegov R.S.
Calculation of friction coefficients and relaxation times of ions aqueous solutions of KCl and СsCl depending on the state parameters
A certain choice of the model solution, the potential energy of interaction between ions and radial distribution function , as well as on the basis of analytical expressions for the coefficients of friction of the ions , , and the determination of relaxation times in momentum , and configuration spaces, the numerical calculations of these parameters for aqueous solutions of KCl and CsCl, at a temperature of 298 K in a wide range of changes in density and concentrations C were made. Received the theoretical results of these parameters are in good agreement with experimental data for aqueous solutions of KCl and СsCl.

Key words: потенциал межмолекулярного взаимодействия; радиальная функция распределения; коэффициент трения ионов; времена релаксации; molecular interaction potential; radial distribution function; the coefficient of friction of the ions; the relaxation times.

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Soliev L., Jumaev M.T., Avloev Sh.H., Toshov A.F.
Solubility in the system CaSO -СаCO -Ca(НСО ) -Н О at 0ºС temperature
In manuscript the investigation of solubility at invariant points in the system CaSO -СаCO -Ca(НСО ) -Н О при 0ºС is presented. The solubility diagram of the title system is modeled according to the evidences obtained.

Key words: метод растворимости; равновесие; жидкая фаза; твёрдые фазы; химический анализ; кристаллооптический анализ; нонвариантные точки; диаграмма растворимости; Method of solubility; balance; liquid phase; firm phases; chemical analysis; cristallooptical analysis; invariant of a point; diagram solubility.

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Mirsaidov U.M., Gafurov B.A., Badalov A., Nasrulloev Kh., Nasrulloeva D.Kh.
System analysis of formation enthalpy of gaseous lanthanide ions
The analysis of impact of various components for overall assessment of thermodynamic stability of complex compound is presented. The Born-Gaber cycle for determination of enthalpy formation of lanthanide borohydrides is made. By means of semiempirical method the complete data on formation enthalpy of gaseous ions of lanthanides is calculated. The change regularity of this value within lanthanides group is defined.

Key words: термодинамическая устойчивость; энтальпия образования; борогидриды лантаноидов; цикл Борна-Габера; thermodynamic stability; formation enthalpy; lanthanide borohydrides; Born-Gaber cycle.

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Ganiev I.N., Nazarov Kh.M., Abdurahimov B.B., Ganieva N.I., Safarov A.G.
Monoand invariant equilibrium coordinates in the system of Аl - Li - ВаАl
By results of differentsialno-thermal and metal analyses it is studied polythermal cuts: ВаАl - AlLi; ВаА1 - Al Li ; ВаА1 - Al Li ; ВаА1 - Li. Coordinates mono- and invariant transformations into system A1-Li-ВaA1 are defined.

Key words: алюминиевые сплавы; система А1-Li-ВаА1 ; разрез; координаты нонвариантных равновесий; ликвидус; перитектика; эвтектика; aluminium alloys; system A1-Li-ВaA1 ; coordinate section; invariant equilibrium; liquidus; peritectic; eutectic.

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Azizov B.S., Kabirov Sh.O., Ruziev J.R., Safiev A.H., Rajabov Sh.Kh., Safiev H.
The technology of processing solid residues in sulfuric acid decomposition of aluminaand fluorine wastes of aluminum production
In the paper the results of studies on the development of technology for the processing of the solid residue formed after sulfuric decomposition of alumina- and fluorinecontaining wastes of aluminum production are presents. Installed rational modes of the water treatment solid residues and calc-alkaline, alkaline soda processing sulphatecontaining solution. A principal process scheme enables the preparation of hydrofluoric acid, alumina, aluminum fluoride and cryolite from these industrial wastes.

Key words: производство алюминия; глинозём-, фторсодержащие отходы; сернокислотное разложение; известково-щелочная обработка; содово-щелочная обработка; плавиковая кислота; глинозём; фторсоли; production of aluminum; alumina- and fluorinecontaining wastes; sulfuric decomposition; calc-alkaline processing; soda-alkaline processing; hydrofluoric acid; alumina; fluorinecontaining salts.

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Dadoboeva M.L., Giyasidinov B.B., Mirakilov Kh.M., Solieva B.A., Abdullaev Kh.A.
The leaves role in the formation of technological property of cotton fibers
In this work the data about of leaves role on the formation of technological traits of cotton fibers are presented. It is shown that after the mechanical removal 25, 50, 75 and 100% of leaves in squaring, flowering and boll set periods technological traits of cotton fiber as a staple length, length of break and strength fiber statistically is not changed, with the exception of metric number (fineness). The metric number increase on 63.1% to compare with control plants. Full defoliation in boll maturation period is not affected on quality of cotton fiber.

Key words: тонковолокнистый хлопчатник Gossypium barbadense L; дефолиация; технологические свойства волокна; long stable cotton Gossypium barbadense L; defoliation; fiber technological property.

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Khojamuradov G.M., Ismoilov M.M., Saidov M.S., Shaymonov A.H.
The exam of functional results of plastic defects of upper extremities with groin flap, using instrument of quickly exam of DASH
The results of the study degree of disability in patients with upper limb defects before and after reconstructive plastic surgery on the upper extremity using the inguinal flap. Disability assessment was carried out using a rapid assessment tool DASH.

Key words: паховый лоскут; дефекты верхней конечности; инструмент быстрой оценки трудоспособности DASH; groin flap; defects of the upper extremity; Rapid Assessment Tool disability DASH.