of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Академии наук Республики Таджикистан, том 61, №2, 2018 г.

Article title and abstractPages
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Ilolov M., Kuchakshoev Kh.S., Guljonov D.N.
On fractional linear Volterra equations in Banach spaces
In this paper, the foundations of the theory of a class of fractional integrodifferential equations of Volterra type in Banach spaces is present. Conditions for the existence of -resolvent operators that are equivalent to the correctness of the corresponding initial abstract problems are established.

Key words: производная Капуто; резольвентный оператор; задача Коши; скалярное ядро; Caputo derivative; resolvent operators; Cauchy problem; scalar kernel.

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Mehmonzoda S.N.
Approximation of continuous functions of two variables by -spline in metric
In this paper for some class of functions with two variables given by module of continuity, the exact upper bounds approximation of functions by interpolation splines were found.

Key words: сплайн-функции; модуль непрерывности; интерполяционный сплайн; решётка узлов; spline functions; module of continuity; interpolation spline; lattice of nodes.

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Shakirov I.A., Khasanov Yu.Kh.
About some estimates of the norms of classical Fouriers operator
In this paper a new and more simple integral representation for the Lebesgues constants, expressed through the integrals of Riemann from trigonometric functions with shifted argument has presented, and on this basis a more accurate lower and upper bounds for the remainder term constants corresponding to the fixed value of the parameter were determined.

Key words: ряд Фурье; норма оператора Фурье; константа Лебега; нижняя и верхняя границы; оценка константы Лебега; точные значения константы; Fourier series; norm of Fourier operator; Lebesgues constant; lower and upper bounds; estimation of Lebesgues constant; exact values of the constants.

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Kabilov M.M., Kholov O.A.
Approximate analytical solution of the model problem of filtration combustion of gases
We consider a mathematical model describing the stationary propagation of the combustion wave of the gas mixture in inert porous medium that takes into account the diffusion phenomenon of the missing component. Sets out the method for determining the solution of the equations of balance of temperature and concentration of the missing reagent as a function of the longitudinal coordinate. A relation is derived for determining the speed of a stationary combustion wave.

Key words: температура; концентрация; диффузия; скорость волны; химическая реакция; фильтрационное горение; волна горения; число Льюиса; пористая среда; уравнение; temperature; concentration; diffusion; wave velocity; chemical reaction; filtration combustion; combustion waves; Lewis number; porous medium; equation.

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Usmanov Z.D.
About one heuristic clusterizer
We examine a one-parameter mathematical model of a clusterizer tuned by self-learning. The process is limited by two conditions: the number of classes, as well as the set of proposals for the possible distribution of objects by classes are known in advance. For each proposal, an index of efficiency is calculated, the maximum value of which defines the value of the parameter.

Key words: кластеризатор; математическая модель; clusterizer; mathematical model.

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Rahimi F., Mullo-Abdolov A.Sh., Kokhirova G.I., Relke H.V., Yuldoshev Q.X., Protsyuk Yu.I., Andruk V.M.
Investigation of the Microtek ScanMaker 1000XL Plus scanner for creation of the catalogue of Dushanbe part of the project «FON»
It is intended using the scanner "Microtek ScanMaker 1000XL Plus" to digitize about 1600 records, obtained within the FON project in the Institute of Astrophysics of the Academy of Sciences of the Republic of Tajikistan. This work was performed for the purpose of a detailed study of the scanner parameters and an estimation of the accuracy of the processing photographic plates. To evaluate the scanner's astrometry and photometric errors, six consecutive scans of one photographic plate were measured using the LINUX/MIDAS/ROMAFOT software, and the following error values were obtained:σ=±0.054 px and σ=±0.020 . The astrometry precision of processing the star field in the Tycho-2 catalogue system is σ=±0.13″. The found characteristics are quite favorable for the digitization of photographic records.

Key words: сканер; фотопластинка; координаты; каталог; ошибка; точность; scanner; photographic plates; coordinates; catalogue; error; accuracy.

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Ibadinov Kh.I., Konovalova N.A., Ibrohimov A.A., Davruqov N.Kh., Kalashnikova T.M.
Groups of meteorite-producing bodies from the orbits of Jupiter family comets
In the paper the families of small bodies of the Solar system, which contain Jupiter family comets, meteorite-producing meteoroids, formed as a result of a fragmentation of their parent bodies, and carbonaceous chondrites meteorites are considered. Grouping in families of the listed objects was established on the basis of the analysis of their orbits using the orbital similarity criterion D.

Key words: комета; семейство Юпитера; орбита; метеороид; метеорит; углистый хондрит; родительское тело; comet; Jupiter family; orbit; meteoroid; meteorite; carbonaceous chondrite; parent body.

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Maslov V.A., Abdullaev S.F., Nazarov B.I.
Observations of fast aerosol settling by means AERONET data
Measurements of the daytime course of the aerosol optical thickness, humidity, and particle size at the AERONET station in Dushanbe, with varying degrees of atmospheric dust, have shown that an accelerated deposition of a dust aerosol occurs in an inversely stratified temperature layer. The analysis showed that the dynamics of aerosol deposition in the temperature inversion layer is determined by the double diffusion effect, which arises from the difference in the diffusion coefficients of the components. Narrow vertical convection cells descending into the colder layer provide increased condensation of water vapor, an increase in the coagulation rate of aerosol particles, and fast settling of dust.

Key words: аэрозоль; аэрозольная оптическая толща; влагосодержание; параметр Ангстрема; двойная диффузия; приземная инверсия; быстрое осаждение; dust aerosol; aerosol optical density; humidity; Angstrom parameter; double diffusion; surface inversion; fast settling.

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Kurbonov A.S., Barotov A.M., Misratov Zh.A., Nazarov F.A., Mirsaidov U.M.
Hydrochloric acid decomposition of the sinter obtained after the joint sintering of the initial borosilicate ore and its concentration with sodium chloride
The results of studies of the hydrochloric acid decomposition of the sinter of the initial borosilicate ore and its concentrate with sodium chloride are presented. The optimal conditions for the hydrochloric acid decomposition of the sinter obtained during the joint sintering of borosilicate ore with sodium chloride are determined.

Key words: концентрат; боросиликатная руда; переработка; спекание; разложение; извлечение; concentrate; borosilicate ore; processing; sintering; decomposition; extraction.

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Barotov M.A., Ahmadov A.Sh., Akhmedov M.Z., Kobuliev Z.V.
The physico-chemical foundations of obtaining coagulants of zeolites and study of their coagulating ability
In this article the results of research on the preparation of the mixed coagulants of zeolites of Tajikistan with the study of their coagulating properties are provided. It is established that the obtained coagulant is effective at high turbidity. It is determined that coagulation ability of the mixed coagulants is not reduced by lowering the temperature from indoor temperature up to 5-12°C.

Key words: цеолиты; соляная кислота; смешанный коагулянт; хлорид железа; хлорид алюминия; zeolites; chloride acid; mixed coagulant; ferric chloride; aluminum chloride.

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Rajabov U.R., Shuhratzoda M., Yormamadova S.G., Kozihonov A.U.
Formation of coordination compounds of Ag(I) - metronidazole - HO
By the method of oxidative capacity and oxidative function it was established that in system Ag (I) - metronidazole - HO at ionic strength 0.1 mol/l, at temperature 308 К and at concentration Ag (I) С=1×10 mol/l, metronidazole Сmetr=1×10mol/l the following complexes are formed: 1) [AgНL(HO)]; 2) [Ag(НL)(HO)]; 3)[Ag(НL)HO]; 4) [Ag(НL)].

Key words: серебро (I); метронидазол; окислительный потенциал; окислительная функция; Argentum; metronidazole; oxidative potential; oxidative function.

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Hojiev S.K., Nazarov Kh.M., Boboyorov M.D., Mirsaidov U.M.
Physical and chemical properties of uranium ores of the «Central Tajikistan» deposit
In this article the results of the chemical and mineralogical analysis of uranium-containing ores of the “Central Tajikistan” deposit are presented. The results of X-ray spectral-fluorescent and differential-thermal analyzes of various uranium ore samples are described. The isotope composition of uranium ores is determined by the method of alpha and mass spectrometry.

Key words: урансодержащая руда; Центральный Таджикистан; альфа-спектрометрия; масс-спектрометрия; изотопный состав; химический анализ; минералогический анализ; uranium-containing ore; Central Tajikistan; alpha-spectrometry; mass-spectrometry; isotope composition; chemical analysis; mineralogical analysis.

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Samikhov Sh.R., Zinchenko Z.A., Kurbonov Sh.A., Safarov S.Sh., Ismoilova M.C., Gorenkova L.G.
Study of enrichment of phosphate ore of Rivat
The obtained results of the studies make it possible to conclude that the content of POin any analyzed classes is unsatisfactory, so the screening does not make it possible to obtain a ready concentrate. The possibility of flotation of the main bulk of nodular phosphorus ores, cationic reagents-collectors are shown.

Key words: флотация; месторождение; степень извлечения; фосфоритовая мука; расход реагентов; фосфорсодержащая руда; flotation; deposit; extraction degree; phosphorite flour; consumption of reagents; phosphorus-containing ore.

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Naimov N.A., Aminjoni G., Ruziev J.R., Rafiev R.S., Boboev Kh.E., Safiev H.
Physical and chemical aspects of processing stavrolite-muscovite by sulfathization method
In this work the physico-chemical aspects of the processing of staurolite-muscovite schists by the method of sulfatization are investigated. Optimum technological parameters of sulfatization processes (temperature, duration, concentration and dosage of acid) and aqueous treatment of sulfated sinter (temperature, duration and ratio of solid and liquid phases) are determined. The isolated aluminum sulphate can be used as a raw coagulant, during its subsequent processing it is possible to produce aluminum hydroxide and sodium aluminate, the raw material for fluoride salts, and alumina, the main raw material for the production of aluminum.

Key words: ставролит-мусковитовые сланцы; сульфатизация; сульфат алюминия; гидроксид алюминия; глинозем; фтористые соли; staurolite-muscovite schists; sulfatization; aluminum sulphate; aluminum hydroxide; alumina; fluoride salts.

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Khakimova R.Sh., Sattorov B., Rakhimov M.M., Niyazmukhamedova M.B., Bohirova M.K., Djumaev B.B., Abdullaev Kh.A.
Potential rate of photosyntesis, chlorophyll and starch contents in Thunb.
In this paper the results of analysis of potential rate of photosynthesis, chlorophyll and starch contents in variegated leaves Euonymus japonica Thunb. f. aureo-variegata (Rgl.), Rehd. is presents. It shown that in green parts of variegated leaves the photosynthesis rate and starch content is higher than in green leaves of normal plants.

Key words: бересклет японский; жёлто-зелёная форма; потенциальная интенсивность фотосинтеза; содержание хлорофилла; количество крахмала и фруктозанов; Euonymus japonica; variegated leaves; potential of photosynthesis; chlorophyll; starch contents.