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, №1, 2015 г.

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Tukhliev K.
Structural characteristics of functions and the precise widths of some classes function
Several exact inequalities are found between the best approximations of differentiable periodic functions in the sense of Weil trigonometric polynomials and averaged with the weight of the moduli of continuity of arbitrary fractional order in the metric of L and their applications are given. To calculate the exact value the widths of certain classes of functions in L .

Ключевые слова: функция Стеклова; модуль непрерывности m-го порядка; неравенства типа Джексона-Стечкина; наилучшие приближения; тригонометрический полином; производная в смысле Вейля; n-поперечники; Steklov function; module continuity of m-th order; inequalities of Jackson-Stechkin; best approach; trigonometric polynomial; derivative in the sense of Weyl; n-widths.

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Beknazarov J.Kh.
The upper face of the deviations of certain class of functions of their partial sums of Fourier-Chebyshev space
We consider the problem of computing the exact upper bound of the best polynomial approximation of certain classes of differentiable functions belonging to the Hilbert space with Chebyshev weight . The inequalities of Jackson-Stechkin type linking best polynomial approximation with mean positive weight special modulus of continuity of -th order where - a differential operator of second order. Calculated accurately value of -widths of some classes of functions from .

Ключевые слова: наилучшее полиномиальное приближение; верхние грани; обобщенный модуль непрерывности; константа Джексона-Стечкина; коэффициенты Фурье-Чебышева; n-поперечники; best polynomial approximation; upper bounds; a generalized modulus of continuity; the Jackson-Stechkin constant; the Fourier-Chebyshev; n-widths.

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Pirov R.
On the theory of non-linear over determined systems of three and four differential equations (p.d.e) in the second-order partial one unknown function in space
In the robot explores some nonlinear systems indicated in the title types. Explicit conditions for joint ensuring the unique solvability of the initial data.

Ключевые слова: условия совместности; переопределённые системы; conditions compatibility; over determined systems.

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Arabov M.K.
Analysis of stability of special point for non-smooth second order equation
This paper takes into consideration to the non-linear second order equation depending on parameters. Used advanced mathematical analysis for investigated equation. Here's been found conditions to stability of the critical point.

Ключевые слова: негладкие динамические системы; фазовые портреты; устойчивость; особая точка; ограниченность; A non-smooth dynamic systems; phase portraits; stability; critical point; limitation.

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Shakirov I.A., Khasanov Yu.Kh.
About estimations of Lébesque’s constants to Lagrange interpolation polynomials
In this work the task of evaluation of growth of considered Lébesque’s constants through defining them parameters is solved when at the fixed value of one of them the other parameter increases without restriction. In these two basic cases simple asymptotic equalities are got for them.

Ключевые слова: интерполяционные полиномы Лагранжа; функции и константы Лебега; оценка порядка роста и асимптотика констант Лебега; Lagrange interpolation polynomials; Lébesque’s functions and constants; estimation of the growth order and the asymptotic behavior of the Lébesque’s constants.

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Usmanov Z.D., Dovudov G.M.
Positional coding of tajik wordforms
Positional coding of Tajik wordforms is presented. It admits uniquely to recognize all grammatical characteristics of a wordform necessary for the automatic processing of text information.

Ключевые слова: таджикский язык; словоформа; граммема; код; Tajik language; wordform; grammeme + ; code.

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Abdulloev S.Kh., Minikulov N.Kh.
Photometry of asteroid (00533) Sara
The photometric observations of asteroid (00533) Sara were carried out in Аugust 2014. As a result, the light curve was obtained. The rotation period of asteroid is equal to 11.624 hours that coincides almost with the period determined previously by optical observations P=11.654 hours.

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

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Odinaev S., Makhmadbegov R.S.
Calculation of the frequency spectrum and Cole-Cole's diagramms of aquaeous solution of NaCl depending on state parameters
Calculations of frequency spectrum of coefficients of dielectric permeability and dielectric losses of aqueous solution of NaCl on the basis of which are constructed Cole-Cole's diagramms at the fixed values of parameters of a state and frequencies are carried out. The received results are compared to literary data which are in satisfactory consent.

Ключевые слова: коэффициенты диэлектрической проницаемости и диэлектрических потерь; частотный спектр; диаграмма Коула-Коула; coefficients of dielectric permeability and dielectric losses; a frequency range; Cole-Cole's diagramm.

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Nizomov J.N., Kalandarbekov I.
Comparative analysis method of the concentrated deformation and finite elements
Development and improvement of methods of calculation is one of the major problems of structural mechanics. The article presents the results of a comparative analysis of methods concentrated deformation and finite element obtained by examples of test problems.

Ключевые слова: метод сосредоточенных деформаций; метод конечных элементов; продольная деформация; аналитическое решение; concentrated deformation method; finite element method; longitudinal deformation; analytical solution.

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Rajabov U.R., Ermamadova S.G., Kozichonov A.U., Rachimova R.N.
Thermodynamic functions of reaction formation of coordination compounds of iron (III) and iron (II) with dibazolom and 0.25 mol/l
The method of oxidative capacity and oxidative function were calculated stability constants and thermodynamic functions of reactions identified the formation of complex compounds of iron with Dibazole: Fe HDb , Fe HDb ОН , Fe HDb(ОН) , Fe (HDb) (ОН) , Fe HDb .

Ключевые слова: железо (III) и железо (II); окислительный потенциал; окислительная функция; энтальпия; свободная энергия; энтропи; iron; dibazole; transition metals; coordination compounds; oxidative potential and oxidative function; enthalpy; free energy; ent.

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Mudinov H.G., Safarmamadov S.M., Husaynov A.D.
Complex formation silver (I) with 1,2,4-triazolom at 288-318 K
Potentiometric method is studied complexes formation silver (I) with 1,2,4-triazole in the temperature 288-318 K. It has been established that silver (I) with 1,2,4-triazole formed three complex forms. With increasing temperature, decreasing stepwise constant.

Ключевые слова: серебро; 1,2,4-триазол; комплексообразование; константа устойчивости; silver; 1,2,4-triazol; complexes generation; constant stability.

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Fayzilov I.U., Isobaev M.J., Saburov M.I.
Preparation of Z,E-isomeric monoethers of di-tretic enin dioxyaldehydes
In the paper the conditions and scheme of preparation of Z,E-isomeric monoethers of ditretic enin dioxyaldehydes was shown. This reaction was realized by the way of oxidation Z,E-isomeric simple monoethers of related enin triols. Oxidative agent was Manganese Dioxide (MnO ) in the media of dried ether or hexane at the temperature 40-50ºС.

Ключевые слова: простые моноэфиры; активированная двуокись марганца; ениновые диоксиальдегиды; simple ethers; manganese dioxide; enin dioxyaldehydes.

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Bobiev O.G., Shakhmatov A.N., Abulkhaev V.D.
Technological characteristics of some active dyes
Results of research of characteristics of diffusion, sorbtion, reactionary ability, fixing and hydrolysis degree monochlortriazine dyes bright red 6С, is bright-blue K and divinylsulphone remazol black B at dyeing of cellulose fibre are resulted.

Ключевые слова: диффузия; сорбция; реакционная способность; степень фиксации; константа гидролиза; ярко-красный 6С; ярко-голубой К; ремазол черный В; diffusion; sorbtion; reactionary ability; fixing degree; a hydrolysis constant; bright-red 6С; bright-blue K; remazol black B.

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Jamolzoda B.S., Murodiyon A., Shukurov T., Safarov A.G., Safiyev H.S.
Study IR-spectroscopic properties of anthracite of deposit "Nazarailok" before and after heat treatment
IR spectroscopy method to study the structure and properties of anthracite of field “Nazarailok” before and after thermal treatment. When thermal treatment (1000 - 1200°C) in the structure of anthracite comes significant change; completely lost and genetic adsorbed water, volatile, there is a splitting of CHx and CH - group. In the low frequency of the frequency-region (at 1200°C) four absorption bands observed with ѵmahs at 1618, 1480, 972 and 640 cm , which differs in shape and intensity. These absorption bands are bending vibrations of organic-compounds which may be associated with loss of hydrogen due to the relationship CH groups. Cavity №4 anthracite of deposit “Nazarailok” can be recommended for the production of cathode blocks for the purpose of lining of aluminum electrolytic. Thermal treatment anthracite is necessary to make at temperature not lower than 1200°C

Ключевые слова: ИК-спектроскопия; антрацит; термообработка; метаморфизм; молекулярная структура; витринит; IR-spectroscopy; anthracite; heattreatment; metamorphism; molecular structure; showcase.

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