of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Академии наук Республики Таджикистан, том 60, №10, 2017 г.

Article title and abstractPages
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Rahmonov F.Z.
The approximate functional equation for Dirichlet -function
Theorem about the approximate functional equation for Dirichlet -function with uniform estimates modulo and imaginary part has been proved via formulas allowing to approximate exponential sums by a shorter ones

Key words: характер Дирихле; формула Ван дер Корпута; короткая тригонометрическая сумма; Dirichlet character; formula of Van der Corput; short trigonometric sum.

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Khabibullo A., Davlatbekov A.A.
Linear А-quasigroups
In the article the ability to define class ratio linear A-quasigroups were found also the relationship linear quasigroups with A-quasigroups is revealed.

Key words: линейная квазигруппа; А-квазигруппа; трансляция; примитивная квазигруппа; внутренняя подстановка; linear quasigroups; linear А-quasigroups; translations; primitive quasigroup; inward productions.

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Jangibekov G., Koziev G.
On the conditions of noetherian and index of one class of two-dimensional singular integral equations with odd characteristic and breaking coefficients
Two dimensional singular operator with odd characteristic and breaking coefficients is studied in the paper. Effective necessary and sufficient conditions for Noetherian in the space of lebeg and the formula for the rate of index are found.

Key words: нётеровость оператора; индекс оператора; операторная матрица; двумерные сингулярные интегральные операторы; оператор Бергмана; singular integral operators; noetherian operators; the index of operator; operator.

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Kokhirova G.I., Devyatkin A.V., Khamroev U.Kh., Buriev A.M., Bakanas E.S., Gorshanov D.L., Abdulloev S.H., Yusupov M.Z., Mullo-Abdolov A.S.H., Ibragimov A.A., Safarov A.G.
Observations of the potentially hazardous asteroid 2014JO25 in Tajikistan
The results of astrometric and photometric in BVRI bands observations of the potentially hazardous asteroid 2014JO25 carried out by the Zeiss-1000 and AZT-8 telescopes in the Sanglokh and Gissar observatories at the period of its close approach to the Earth in April 2017 have presented. The asteroid’s coordinates were determined as well as the apparent and absolute brightness in four bands and color indexes were obtained. The light curves show that object’s magnitude has practically not been changed during observations and the value of absolute magnitude corresponds to the ephemerid value. Estimation of the diameter and rotation period by our observations is in well accordance with known data.

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

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Muminov Kh.Kh., Shokirov F.Sh.
Numerical simulation of processes of formation the topological vortices on two-dimensional domain walls
By numerical simulation methods the formation processes of topological vortices on domain walls within the framework of a supersymmetric (2+1)-dimensional nonlinear sigma model is investigated. The models describing the formation of topological vortices in the interaction of localized (topological) perturbations moving along the plane of domain walls and deformation waves are obtained. Also the models of emission a topological vortex by the domain wall were obtained and the T-symmetry property of the model under investigation is confirmed.

Key words: топологический вихрь; доменная стенка; нелинейная сигма-модель; Т-инвариантность; численное моделирование; topological vortex; domain wall; nonlinear sigma model; T-invariance; numerical simulation.

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Tuichiev Sh., Rashidov D., Tabarov S.Kh., Aknazarova Sh.I.
Influence of nanocarbon particles on the thermal and deformational properties of polymer nanocomposites
The paper discusses the results of studies of the effect of nanocarbon particles on fluidity, mechanical and thermal properties of polymer nanocomposites. It has been established that as the concentration of nanocarbon particles increases, the limit of the forced elasticity, the length of the neck formation, the reversibility of the geometry of the samples upon heating, and also the combustibility of the nanocomposites decrease.

Key words: раствор; растворитель; нанокомпозит; структура; свойства; горючесть; solution; solvent; nanocomposite; structure; properties; flammability.

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Maslov V.A., Abdullaev S.F., Nazarov B.I.
About the nature of fast aerosol settling in the atmosphere
The dynamics of aerosol settling in the temperature inversion layer, determined by the phenomenon of double diffusion, which associated with the difference in the diffusion coefficients of temperature and impurity concentration, was investigated. The theoretical model of double diffusion convection, which is the cause of the effect of fast aerosol deposition, was used to explain a number of atmospheric phenomena. The parameters of double diffusion convection for dusty air are estimated. The diurnal variation of the mass concentration of dust aerosol and soot confirms this model of fast aerosol settling.

Key words: аэрозоль; двойная диффузия; приземная инверсия; быстрое осаждение; атмосферные осадки; dust aerosol; double diffusion; surface inversion; fast settliпg; atmospheric precipitation.

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Ganiev I.N., Achyrmatov J.T., Gulov S.S., Berdiev A.E.
The influence of scandium on kihetic oxidation of the hard alloy AK9M2
The kinetics of oxidation of the alloy of АК9М2. alloyed by scandium in the hard state by termogravimetric method is investigated. It is shown that additions of scandium within the limits of the studied concentration diminish oxidableness of initial alloy of АК9М2.

Key words: сплав АК9М2; скандий; термогравиметрический метод; кинетика окисления; истинная скорость окисления; энергия активации; AK9M2 alloy; scandium; thermogravimetric method; oxidation; kinetics of the oxidation; rate is the true activation energy.

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Soliev L.
Structure of a phase complex to sixcomponent of system Na,K,Mg,Ca // SO,Cl-HO at 50°С in area crystallization of sakiit (MgSO∙6HO)
By method of compilation of phase balance of system Na,K,Mg,Ca//SO,Cl-HO at 50°С in area crystallization of sakiit (MgSO∙6HO) are investigated. Is established that as the equilibrium phase of the investigated system at 50°С participates in formation 4 invariant of points, 13 monoalternative curves and 15 divariant of fields. On the basis of the received data a fragment of the diagram phase equilibrium investigated of system Na,K,Mg,Ca//SO,Cl-HO for the first time is constructed at 50С in area crystallization of sakiit.

Key words: равновесие; система; сакиит; фаза; нонвариантные точки; моновариантные кривые; дивариантные поля; диаграмма; компонент; diagram; system; phase; balance; sakiit; invariant point; monoalternative curve; divariant of a field.

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Samikhov Sh.R., Kholov Kh.I., Zinchenko Z.A.
Technology of concentration of the ores of the lower horizons of the Dzhyzhikrut deposit
A study of the effect of various modifiers and other factors on the flotation of the investigated ores of the Lower horizons of the Djizhikrutsk deposit revealed the expediency of using a simple scheme for obtaining a given ore with the production of antimony concentrate. Based on the conducted studies, a technological scheme of flotation of ore of this field is proposed.

Key words: флотация; месторождение; степень извлечения; сурьмяной концентрат; расход реагентов; сурьмяной руда; flotation; deposit; recovery; antimony concentrate; reagent consumption; antimony ore.

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Bohirova M.K., Ergashev A., Atoev M.Kh., Khakimova R.Sh., Abdullaev Kh.A.
About some characteristics of cotton plants water exchang in abiotic stresses
In this paper the results of study of transpiration, water deficit and water keeping ability in different growth and development phases of longstable cotton plants after various grade of defoliation are given. It shown that the high intensity of transpiration maximally observed in control plants in midday (12 o'clock), but is not observed in experimental plants. Is discovere that between of water keeping ability of control and experimental plants reliable differences is not eхist. Is established that the increasing extent of defoliation is not influence on water deficit of plants. To sum up that the abiotic stresses-defoliation considerable in not changed of water balance in cotton plants.

Key words: тонковолокнистый хлопчатник Gossypium barbadense L; водный обмен; транспирация; водный дефицит; водоудерживающая способность листа; long-stable cotton; Gossypium barbadense L; defoliation; water keeping ability; transpiration; water deficit.