of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Академии наук Республики Таджикистан, том 63, №11-12, 2020 г.

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Nozirov O.O.
Estimates for linear exponential sums with primes based on the mean values of Chebyshev functions
Based on the mean values of the Chebyshev functions over all Dirichlet characters of a given modulus, a new estimate for linear exponential sums with prime numbers is obtained.

Key words: exponentials sums with prime numbers; Tchebychev function; Dirichlet L-series; I.M.Vinogradov sieve.

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Komilov O.O.
Dissociative quasigroups of small order
In this paper examples of classification quasigroups of the 5th order by categories: right-diassociative (left-diassociative) quasigroups of degree k(l) and some isotopes of diassociative quasigroups of the 5th order are obtained.

Key words: quasigroups; loop; dissociative quasigroups; isotopes; subquasigroup; simple quasigroups.

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Dadaboev P.А.
Optimal square formula of Markov type for approximate calculation of curvolinear integral on some classes of differentiated functions and curves
In this paper, an optimal quadrature formula of Markov type is found for the approximate calculation of the curvilinear integral on some classes of functions and curves that are twice differentiable in a given domain. An exact estimate of the error of the best quadrature formula for the entire class of functions is calculated.

Key words: optimal formula; Markov-type quadrature formula; error estimate.

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Raimzoda F.
Exact inequalities containing best approximations and norm of differences in L
The exact inequalities between the value of the best mean-square approximation of functions and the average value of the norm of differences of functions are found. For some classes of functions defined by the indicated differences, the problem of simultaneous approximation of functions and its successive derivatives by trigonometric polynomials in the metric of the space is solved.

Key words: best approximation; periodic of functions; trigonometric polynomial; modulus of continuity; difference of the m order; joint approximation.

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Odinaev R.N., Gaforov A.B.
Investigation of mathematical model of cotton agrocenosis in the stationary case
In this paper the model of cotton agrocenosis of three trophic levels "cotton-harmful insects-useful insects" is investigated. For the model agrocenosis, the necessary and sufficient conditions for the existence of a solution to the stationary problem of plant protection are formulated and justified.

Key words: model; cotton; beneficial insect; harmful insect; agrocenosis; biomass; the number of insects; fertility function.

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Jangibekov G., Eshonqulov A.A.
About the algebra of some two-dimensional integral operators with an odd characteristic
In this article the algebra of two-dimensional singular integral operators with odd characteristic and new classes of polykernels of Bergman operators in Lebeg space is studied. Necessary and sufficient conditions for the above operators to be noetherian are found, and a formula is obtained for calculating the index.

Key words: polikernel-function; polikkernel-Bergman operator; singular integral; operator symbol; operator index; operator's noetherianness.

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Kokhirova G.I., Babadzhanov P.B., Khamroev U.H., Zhonmuhammadi A.I.
Virginid asteroid-meteoroid complex. Near-Earth asteroids associated with the Nu-Virginid meteoroid stream
Presented result is the continuation of the finding of new near-Earth asteroids (NEAs) belonging to the Virginid asteroid-meteoroid complex. On the base of calculation of orbital evolution of a sample of NEAs and determination of theoretical features of related showers a search for observable active showers close to theoretically predicted ones was carried out among published catalogues. As a result, predicted showers of 5 NEAs were identified with the showers produced by the Nu-Virginid meteoroid stream. Revealed association points to a cometary nature of NEAs that are moving within the stream and may be considered as extinct fragments of a larger comet-progenitor of the Virginid asteroid-meteoroid complex.

Key words: comet; asteroid; extinct comet; meteoroid stream; meteor shower; orbit; radiant.

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Salikhov T.Kh., Davlatjonova Sh.Kh., Rakhmonov R.K.
The features of the frequency dependence of the parameters of the photoacoustic signal of the superfluid Не-Не solution
The analysis of the frequency dependence of the parameters of the photoacoustic signal (PA) generated by the superfluid solution of Не-Не in the buffer gas is carried out. For two limiting (strongly and weakly absorbing) cases, fairly simple formulas for the amplitude and phase of the PA signal are obtained, and a numerical calculation of the frequency dependences of these parameters is performed. It turned out that the frequency dependence of the amplitude of the PA signal is a set of pulses (harmonics) caused by the presence of a weakly damped second sound in the system under study. It was found that the growth of the amplitude of the PA signal with the growth of the optical absorption coefficient is nonlinear, and its phase is weakly sensitive to the variation of the absorption coefficient.

Key words: optoacoustics; photoacoustics; superfluid solution; thermal mechanism; second sound.

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Mahsudov B.I., Salimov K.H., Zaydullo N.
Effect of small thermal neutron fluxes on the activation rate of Rhizobium is TAAS-80TJ bacteria
The effect of a small thermal neutron flux on the growth rate of bacteria Rhizobium phaseoli is TAAS-80 TJ, intended for the production of micronutrients, was studied. The hormesis phenomenon of the germination time of bacteria when they were irradiated with small fluxes of thermal neutrons was discovered. The best result is obtained with thermal neutron fluxes of 5.4 ∙ 10 neutrons / cm, at which the germination time of bacteria is reduced by 5-6 times.

Key words: thermal neutrons; radiation capture; nuclear biotechnology; Rhizobium phaseoli; hormesis.

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Tashbaev G.A., Tohirov J.J., Haydarov K.H.
Synthesis of sulfonamides 1,4-benzodioxane series
In this article the interactions of 1,4-benzodioxane-6-sulfochloride with secondary amines are described.

Key words: 1.4-Benzodioxan-6-sulfocloride; sulfoclorid; dimathylamin diethylamin; morpholin; piparidin; sulfonamid; N,N-diethy-1.4-Benzodioxan-6-sulfonamide.

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Khalikov D.Kh., Muhidinov D.S., Saidova R.S., Avloev Kh.Kh.
Ion-exchange equilibrium in system of pectin hydrogels and copper ions
The thermodynamic aspects of ion exchange reaction in system of hydrogel (microgel) of pectin polysaccharides of sunflower basket (MG SB) and bivalent copper ions were studied. Based on the data of copper ion sorption and swellability of MG SB at different degrees of sorbent filling, the total change in the isobar potential (ΔG) of the ion exchange reaction was estimated. Taking into account the presence of a large amount of water in the hydrogel composition, in the work was made an attempt to take into account the transition of the solvent from the polysaccharide phase to the external solution phase. To estimate the ion exchange the constant of equilibrium (K) and change of value ΔG, it was define not only ion distributions between phases (ΔG), but also as quantitative or semi-quantitative form, was carried out the calculation of the specific components of changes in free energy associated with changes in the concentration of resinates (ΔG), interfacial transfer of solvent (ΔG), differences in resinate activity coefficients (ΔG) in monionic forms of the hydrogel, as well as the presence of cooperativity (ΔG) when binding ions with a sorbent. It was shown that the total effect of the above parameters can lead to a negative change of value ΔG, which is the reason for mixing the equilibrium towards the formation of metal complexes of MG SB.

Key words: microgel; pectinaceous substances; copper ions; sorption; sorption isotherm; Lengmyur's equation; isobaric potentials.

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Abdusalyamova M.N., Barotov S.S., Makhmudov F.A., Shaimardanov E.N.
Obtaining and properties of nanostructured europe oxide
Nanostructured europium oxide (EuO) was synthesized by the template method. Using the IR method, it was found that CO is adsorbed on the sample surface. Aside from carbon oxide samples also absorb water vapor from the air. Analysis of X-ray diffraction patterns of samples of europium sesqui oxides obtained by thermal decomposition in air at 550°C and 700°C of europium nitrate taken at low concentration indicates the presence of a single EuO crystalline phase with the Bixbyite -MnO structural type.

Key words: properties nanostructured europium; RFS; IR-spectroscopy.

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Fayziev A.R., Fayziev F.A., Murodkulov M.Y.
About the source of ore-forming fluids (on the example of some ore deposits in Tajikistan)
In this paper the data on the relationship of derivatives of the main subcrustal igneous rocks in the formation of hydrothermal deposits of gold, polymetals, silver, antimony and mercury are presents. This assumption is supported by the confinement of deposits to deep long-lived faults, a significant time interval between the host igneous, often acidic rocks, and ore mineralization, the often colossal scale of deposits does not correlate with the volumes of the host magmatic bodies, the presence of representatives of basic igneous rocks in the areas of mineralization development, similar in age to mineralization, remoteness of deposits from intrusions of granitoids, which could be associated with mineralization, uniformity of mineralization in deposits, despite localization in rocks of different composition and age.

Key words: subcrustal magmatism; gold; silver; polymetals; antimony; mercury; mantle source.

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Sabirov A.A.
About genera of Palaeotextularia Schubert, 1921 and Eotextularia Mamet, 1970 (foraminifera)
In the article the data on the groundlessness of the identification of the genus Eotextularia Mamet, 1970 and the principles of taxonomy of the genus Palaeotextularia Schubert, 1921 are presented and one new species is identified.

Key words: foraminifera; taxonomy; Carboniferous system; Tajikistan.

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Khodzhayeva Z.G., Kurbonbekova Sh.Sh., Akhmedov F.A., Zubaydova T.M., Rakhimov I.F.
Investigation of acute toxicity of Artemisia santolinifolia and Artemisia tournefortiana infusion
Currently, medicines have become increasingly used in the treatment of various diseases and prevention in order to increase the body's resistance to adverse factors. Adopted by the Decree of the Government of the Republic of Tajikistan of October 28, 2020 "Program for the development of the pharmaceutical industry in the Republic of Tajikistan" for 2021-2025 is the Government's concern for the health of the people to improve medical and drug care to the population. In this article the results of a study on the acute toxicity of the infusion of sagebrush santolinifolia - Artemisia santolinifolia (Turcz. ex Pamp.) Krasch. and the wormwood of Tournefort - Artemisia tournefortiana Reichenb are presents. It is shown that when intragastric administration of the infusion of wormwood herb santolinolistnaya and Tournefort in doses from 50 to 3000 mg/kg of body weight to white rats, signs of toxicity do not appear. The average lethal dose (LD50) could not be determined due to the lack of toxicity. The studied infusion of the herb sagebrush santolinolistnaya and Tournefora can be attributed to the indicators of compliance with class IV-practically non-toxic substances.

Key words: toxicity; Artemisia santolinifolia; Artemisia Tournefortiana; intragastric administration; lethal dose.