of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Академии наук Республики Таджикистан, том 62, №07-08, 2019 г.

Article title and abstractPages
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Karimov U.H.
Hereditary homology equivalency of topological spaces
The concept of homological equivalence of topological spaces is introduced and investigated.

Key words: homology Sklyarenko; hereditary homological equivalency.

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Zevarshoev U.N.
The accurate assessment in interpolation error by bilinear splines on some classes of functions
In this paper, we find exact upper bounds for the approximation of functions by interpolation bilinear splines on some classes of functions of two variables defined by continuity modules.

Key words: bilinear splines; continuity modules; upper bounds for the approximation.

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Kurbonov I.
Solvability of a system of some nonlinear integral equations in image space
The paper studies the solvability of a system of nonlinear integral equations of special type. For solvability, the Laplace transform is applied using the convolution multiplication theorem. The application of the Laplace transform makes it possible to transform a system of nonlinear integral equations to a system of nonlinear algebraic equations into image space. It is shown on the example of the solvability of system of nonlinear algebraic equations.

Key words: nonlinear; convolution; systems; image spaces and originals.

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Gadoev M.G., Iskhokov J.S.
On a class of degenerate elliptic operators in a bounded domain, generated by noncoercive forms
We study a class of higher-order elliptic differential operators in a bounded domain whose coefficients have uncoordinated power-law degeneracy along the entire boundary of the domain. The sesquilinear form associated with the operator under consideration may not satisfy the coercivity condition. It is presented in the form of a finite sum of auxiliary forms, and among them we separate out leader forms. By applying embedding theorems of different metrics for spaces of differentiable functions of many real variables with power weights, it is proved that only the degeneracy of the coefficients of leader forms affects the domain of the studied elliptic operator.

Key words: elliptic operator; power degeneration; noncoercive form; uncoordinated degeneration; bounded domain.

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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 norm of the classical Fourier operator (a Lebesgue constant), expressed through the integrals of Riemann from trigonometric functions with shifted argument, and on this basis then the problem of the top assessment of Lebesgue constant is completely solved and its lower assessment is improved the fixed value of the parameter has presented.

Key words: frequent sums of Fourier series; norm of Fourier operator; estimation of Lebesgue constant; lower and upper bounds; exact values of the constants; asymptotic formula.

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Naskov D.S.
Research of the improper problem of the linear programming with restriction budget of the pension insurance system
In this article the solving of the improper problem of the liner programming, which is contents the contradicted system of restriction in order to budget deficits and surpluses of the pension insurance system, proving the solvability of the problem and demonstrating the results its numerical implementation is presents.

Key words: improper problem; liner programming; financial stability; budget planning; insurance rates; pension insurance.

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Kabilov M.M., Barotov A.S.
Main characteristics of the wave of combustion of the propan-air mixture in models of the filtration combustion of gases
The main characteristics of the combustion wave of the propane-air mixture are considered within the framework of two mathematical models of filtration combustion of gases. The curves of the dependence of the wave velocity and the equilibrium temperature on the rate of feed of the mixture and the fuel excess coefficient calculated by these models are presented and their comparative analysis is carried out. The values ​​of the wave velocity correspond to the low-velocity regimes, and the wave velocity in the two-temperature model is relatively lower compared to the single-temperature one. The curves of the wave velocity versus the coefficient of excess fuel have a wedge-shaped shape and the minimum corresponds to the stoichiometric mixture.

Key words: temperature; concentration; filtration combustion; wave velocity; porous medium; injection rate; fuel excess.

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Kokhirova G.I., Buriev A.M.
Analysis of the precision of astrometric reduction of observations using various softwares
The results of analysis of the precision of astrometric reduction of observations made using software APEX-II and Astrometrica are given. For astrometry observations of asteroid (596) Sheila by the Zeiss-1000 telescope at the International Astronomical Observatory Sanglokh IA AN RT were used. It was shown that the best accuracy of the coordinates determination is provided by the APEX-II.

Key words: asteroid; astrometry; coordinates; orbit; processing; accuracy; Astrometrica; APEX-II.

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Tuichiev Sh., Rashidov D., Abdulov Kh.Sh., Aknazarova Sh.I., Tuichiev Kh.
The photoaging of crystalline polymeric nanocomposites
The changes in the structure and properties of the crystalline nanocomposite of LDPE and IPP under the action of UV light are studied. It is shown that during photoaging the mechanical and thermal properties of composites undergo the greatest changes, while their structure remains unchanged. These changes are associated with the development of the processes of cross-linking and destruction of chain molecules upon irradiation.

Key words: polymer; fullerene; composite; irradiation; structure; strength; deformation; photoaging.

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Yusupov I.Kh., Yusupov O.I., Bakhdavlatov A.D., Marupov R.
The influence of environmental factors on the rotational mobility of a spin-labeled medicinal plant of a ferula smelly (Ferula foetida (Bunge) Regеl)
The rotational mobility of a nitroxyl radical and the properties of a wild-growing medicinal plant ferule stinky (Ferula foetida (Bunge) Regel) have been studied by EPR spectroscopy.It is shown that the parameters of rotational diffusion of a radical attached to the structures of the main parts: in the stems and leaves of the ferule depends on the place of its growth and the ecological state of the environment. It was established that at room temperature above 300 K and in dependences on the height above sea level, structural transitions occur, accompanied by a marked increase in the rotational diffusion of the radical in all the studied samples.

Key words: EPR-spectra; spin labels; medicinal plants; molecular dynamics; leaves; stem; diffusion; mobility.

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Nazarov B.I., Abdullaev S.F., Lugmonova Sh.O.
The phenomenon of anomalous behavior of meteorological, optical and microphysical characteristics of the atmosphere before the seismic events
The paper reports of the phenomenas of anomalous behavior of the atmospheric parameters before seismic events.

Key words: earthquakes; meteorological parameters; aerosol optical thickness; Angstrom parameter; ozone; water vapor.

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Azizov O.A., Bakum S.I., Khikmatov M., Mirsaidov U.M.
Determination of densityof alumohydrides of potassium, rubidium and cesium
In this article the results of determining the density of potassium, rubidium and cesium alumohydrides by liquid pycnometry are presents. It has been shown that the densities of these alumohydrides monotonously increase and their dependences are characterized by straight lines.

Key words: alumohydrides; potassium; rubidium; cesium; pycnometry; density.

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Abdusalyamova M.N., Kabgov H.B., Makhmudov F.A.
Physico-chemical characteristics of Yb14MnSb11 doped with yttrium
The methods of synthesis and growth of monocrystals of Zintl phases are considered. Solid solutions of the type Yb14-xYxMnSb11 were obtained. It is shown that all the obtained samples have a tetragonal structure of the type Ca14AlSb11. The lattice parameters were found. The coefficients of thermal expansion, melting temperature and Debye temperature were calculated.

Key words: rare-earth elements; Zintl phases; thermal expansion; melting points.

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Babazhanova M.A., Sayfudinov A.K.
The kinetic behavior robotfactory multienzyme complex of Calvin cycle in extracts from leaves of arabidopsis thaliana race Enkheim
In this article results of kinetic studies robotfactory reactions in a multienzyme complex of Calvin cycle in extracts from leaves of Arabidopsis thaliana race Enkheim are present. The dependence robotfactory activity multienzyme complex of reaction time, protein concentration and ribozo-5-phosphate in the reaction medium. It is established that robotfactory refers to allosteric enzymes. The sigmoid form of the curve of the reaction rate dependence on the protein and substrate concentration indicates a positive cooperative interaction between the active centers of the enzyme subunits.

Key words: Arabidopsis; robotfactory; reaction; rate; kinetics; multienzyme complex; of Calvin cycle.

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Mamadvafoev M.M., Davlatshoev D.A.
To petrochemistry and the genesis of xenolites in the inversion granodiorites of the Kafandara skarn ore field (Eastern Hissar)
In this article the most comprehensive data on the petrochemistry and genesis of xenoliths of quartz gabbro, diorite-quartz diorite and monzonite in the inversion (C) granodiorites of Central Tajikistan in the position of the Kafandara skarn ore field are presents. It is assumed that they belong to metaxenolites.

Key words: Kafandara skarn ore field; petrochemistry; xenolith; metasomatosis; metaxenolites; quartz gabbro; diorites-quartz diorites; monzonites containing xenoliths inverse (C) granodiorites.

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Sabirov А.А.
New names for the genera of Spinosella Sabirov, 2014 and Brenckleina Sabirov, 2019 (Foraminifera)
Instead of the pre-occupied names for the two genera of foraminifera described from the Devonnian deposits of the Zeravshan Ridge, new ones were proposed in accordance with the requirements of the International Code of Zoological Nomenclature.

Key words: Foraminifera; Devonian system; Tajikistan.

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Isoyev K.S.
Information on bugs from the genus Lethrus (Coleoptera, Scarabaeidae) widespread in Tajikistan
This is the first time that the article provides information on distribution and ecology of 19 species of scarabaeidae of Lethrus family in Tajikistan.

Key words: Tajikistan; ecology; distribution; the ridge; Coleoptera; Scarabaidae; Lethrus.

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Kosimova S.I., Hojamurodova J.A.
Efficacy of treatment of hyperprolactinemia in fertile women in the iodin deficiency region
In this article the effectiveness of the use of complex pathogenetic therapy of hyperprolactinemia in women with infertility in subclinical hypothyroidism in iodine deficiency region is discusses. Marked pregnancy in 42.0% (63/150) of women. Of these, 12.7% (8/150) of women had a clinical pregnancy against the background of complex therapy with L-thyroxine according to the regimen.

Key words: female infertility; hyperprolactinemia; iodine deficiency disorders; galactorhea; metabolic syndrome.