of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Национальной академии наук Таджикистана, том 65, №1-2, 2022 г.

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Esterman problem for cubes of primes with almost equal summands
We prove an asymptotic formula for the number of representations of a sufficiently large natural number N as the sum of two primes p and p and the cube of a prime p satisfying the conditions , , , , .

Key words: almost equal summands; short exponential sum with primes; Diophantine equation.

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Estermans Ternary Problem for Cubes of Primes with Almost Proportional Summands
Let - a sufficiently large natural number, , , - positive fixed numbers satisfying the condition For an asymptotic formula is obtained for the number of solutions of a Diophantine equation with almost proportional terms of the form with respect to the primes , and .

Key words: almost proportional summands; short exponential sum with primes; diophantine equation; small neighborhood of the center of majors arcs.

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The best approximation of periodic differentiated functions and sharp values of widths of some classes of the function in L
The sharp inequalities of Jackson-Stechkin type for the averaged with the weight of moduli of continuity of -th order were obtained. For the classes of functions determined by majorant and averaged magnitudes, the sharp values of -widths satisfying stated constrains on majorant, were calculated.

Key words: the best approximation; modulus of continuity; upper bound; Jackson-Stechkin type inequality; n-widths.

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The best mutual polynomial approximation of periodic functions and solution of some extreme problems in L
The exact upper bounds are found for the best mean-square approximation of some periodic classes functions defined by the modulus of continuity of the -th order.

Key words: the best approximation; modulus of continuity; extreme characteristic; upper bounds values.

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G.Jangibekov , S.F.Savlatov
On the polykernel function of the half-plane Imz>0 and its connection with two-dimensional singular integral operators
An explicit expression is found for the polykernels - Bergman functions of the space for the half-plane . The algebra of integral operators with polykernels Bergman kernels is studied. Effective necessary and sufficient conditions are established for the Noetherian operators in Lebesgue spaces to be Noetherian, and the index of operators from this algebra is calculated.

Key words: polykern-function; polykern-Bergman operator; singular integral; operator symbol; operator index; operator Noetherian.

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About developing a basis to metrization of word's euphony at usage unigram
The article is devoted to the study of Tajik words euphoniousness at usage unigram, an algorithm for recognizing their euphoniousness is developed and the results obtained are presented.

Key words: word; algorithm; recognition; euphony; unigram.

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D.Radhidov , T.Kh.Salikhov , Sh.I.Aknazarova , S.Kh.Tabarov , A.Mirzo , D.M.Sharifov , F.Sodikov , M.R.Fayzieva
The effect of the fullerene C on the thermal diffusivity of polymethylmetacrilate
Using dilatometry and thermography methods, the temperature changes in relative deformation, density and coefficient of thermal shrinkage or expansion of samples of polymethacrylate containing C fullerene were studied. It is shown that the value of thermal diffusivity of PMMA + C composite samples decreases with increasing concentration of C, which is associated with an increase in the scattering of phonons by structural inhomogeneity and by the C fullerene nanoparticles themselves.

Key words: polymer; nanocomposite; fullerene; deformation; thermal diffusivity.

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D.S.Kuchakshoev , A.G.Dzhabarov , A.Kholov
X-ray phase analysis of glasses 2BiO‒BO and BiO‒2BO with different concentrations of NaOH in the molding sand
The influence of NaOH on the phase composition of 2BiO-BO and BiO-2BO glasses was studied by X-ray phase analysis. It is shown that with increasing NaOH concentration, the content of the crystalline phase decreases, while the content of the amorphous phase increases. In BiO-2BO glasses, the effect of small additions of NaOHwas found: the addition of up to 4-5 mole percent of NaOH leads to a decrease in crystallinity, large additions lead to its increase, and at concentrations greater than 12%, its value stabilizes. The addition of NaOH to the 2BiO-BO and BiO-2BO glasses leads to a change in the composition of the crystalline phase.

Key words: glasses; X-ray phase analysis; crystalline and amorphous phases.

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S.K.Karimov , M.Kh.Egamov , A.Abdumanonov
Conformational transitions in capsulated polymer liquid crystal films
It was shown that the most stable conformation of the 7CB molecule (X≡OCH, OCH) in the initial state is considered to be the twist conformation with the rotation angle of the monomeric isomerism. It was found that the rotation of benzene rings relative to each other is accompanied by a change in the relative orientation of the interacting orbitals of the bridging carbon atoms of the rings. It was revealed that the lengthening of the aliphatic chain in the C3H7 fragment does not lead to noticeable changes in the features of the geometric structure of the molecule.

Key words: liquid crystals; nematic; polyvinylbutyral; FTIR spectroscopy; absorption band; vibration frequency; conformation.

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J.N.Nizomov , S.S.Zarifov
Mathematical modeling of the underground structures located in uniform springy ambience
This article deals with mathematical modeling of interaction problems between a structure and an elastic half-space based on the method of boundary equations. An algorithm and mathematical model for solving problems of the half-space weakened by a hole of arbitrary shape under plane deformation under various influences have been developed.

Key words: mathematical modeling; boundary equations; half-space; half-plane; plane deformation; hole; fundamental solution.

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S.M.Gaforzoda , D.Kh.Mirzoev , D.O.Davlatov , N.M.Jamolov , U.M.Mirsaidov
Thermodynamic analysis of occured processes during the decomposition of kaolin clays of the Chashma-Sang deposit of Tajikistan with chloride acid
In this article the results of thermodynamic calculations for the decomposition of kaolin clays of the Chashma-Sang deposit with chloride acid are presents, the thermodynamic characteristics of the minerals included in the aluminosilicate raw material and the calculation of the Gibbs energy for each reaction have been determined.

Key words: kaolin clays; enthalpy; entropy; Gibbs energy; decomposition.

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Stability of 1-phenyl-2,3-dimethylpyrazolintion complexes of Fe(III) in sulfuric acid and hydrochloric acid solutions
The process of complexation of Fe(III) with 1-phenyl-2,3-dimethylpyrazolintion (FPt) in a solution containing 2 mol/l HSO (HCl) has been studied. It is established that the process of complexation of Fe(III) with this organic ligand proceeds stepwise. The values of stability constants of all complex forms are determined. It is shown that the stability of iron (III) complexes with FPt increases during the transition from HSO to HCl.

Key words: iron (III); 1-phenyl-2,3-dimethylpyrazolintion; stability constant; complexes; complex formation; potentiometric titration.

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A.Sharifov , Z.H.Gaibullaeva , D.S.Nematzoda , Z.A.Goziev
Effective methods for preventing corrosion of hydraulic concrete
The article is devoted to methods of preventing corrosion of concrete to increase the durability of hydraulic structures. Modifying the composition of cement mineral additives from natural wollastonite, waste enrichment of fluorite ores and ashs of coal, and organ-chemical additives from dextrin, modified technical lignosulfonate and alkaline cotton stalk extract. These additives during the hydration of cement minerals contributed to the formation of corrosion-resistant compounds and the low-pore structure of cement stone that increase the construction and technical quality of concrete. Additives increased strength, waterproofability and corrosion resistance of hydraulic concrete in distilled and mineralized waters, magnesium sulfate solutions and sulfuric acid.

Key words: hydraulic concrete; concrete corrosion; cement; clinker minerals; mineral and organic-chemical additives; strength; waterproof; resistance; durability of structures.

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Studying the content of natural radionuclides in the soils of certain regions of Tajikistan
The content of natural radionuclides in the soils of some regions of Tajikistan has been studied. The content of natural radionuclides is relatively small in sandy soils. A high content of natural radionuclides is observed in clay soils.

Key words: soil; specific activity; natural radioactivity; Khatlon region.

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M.S.Safarov , H.U.Karimov , A.S.Saidov , I.B.Kholmatov , L.S.Nabiev , A.U.Bobojonov
Biodiversity monitoring of the southern spurs of the Vakhsh ridge with the use of unmanned aerial vehicles
In this article the results obtained in the course of field studies using unmanned aerial vehicles on the Vakhsh ridge in order to monitor biodiversity are presents. For the first time, unmanned aerial vehicles were used to monitor the vegetation and animals of forest ecosystems, which made it possible to conduct environmental monitoring in a short time and obtain reliable data.

Key words: monitoring; unmanned aerial vehicles; aerial photography; vegetation; animals.

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O.Sh.Majidov , M.A.Niyozova
Current state of hydrography in the Kishtud river basin (Central Tajikistan)
For the first time, in this article detailed, complete and up-to-date information about the lakes of the river basin are presents. Kishtud is a left tributary of the Zeravshan River. Quantitative observations are based on large-scale topographic maps, Internet resources (Google Earth, Bing) and field observations. The emphasis is on comparing the current state of the basin's water resources with previous observations, their changes and trends. Due to the fact that the lakes of the region are also unstable due to climate change, special attention is paid to the current state of the lakes, their quantitative change and main characteristics have been identified. Comparison of changes in the area of lakes for 2007-2020 is carried out.

Key words: Tajikistan; Kishtud; hydrography; river; lake; glacier; climate change.

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Lipid peroxidation of Solanum tuberosum l. plants under ex vitro conditions
The intensity of lipid peroxidation and the enzymes of the antioxidant system protection in vitro and under long lasting exposure in water-salt solution (ex vitro) on the perspective potatos clone №26 were studied. It was shown, that accumulation level of the malondialdehyde (MDA) was lower both in leaves and in roots in vitro, and after transferring the plants into the Murashige and Skoog (MS) water-salt solution (diluted twice) the activity of the lipid peroxidation increased in ex vitro condition. The variation on MDA accumulation under ex vitro condition sufficiently influences the intensity of the hydrogen peroxide accumulation (ROS). Such drifting of the ROS accumulation influences activity of both catalase and guaiacol peroxidase enzymes. As a result, the organ specificity of the protective antioxidant system of plant ex vitro was determined.

Key words: potato; reactive oxygenspecies; lipid peroxidation; enzyme; hydrogen peroxide.

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Content of soluble carbohydrates in wheat grained in various ecological conditions
In this article the results of studies on the soluble carbohydrates in the organs of wheat of three varieties of wheat of local selection (Zafar and Khuroson) and introduced (Kupava) from Russia to Tajikistan in the main phases of vegetation of plants grown in rainfed and irrigation are presents. Differences in the level of soluble carbohydrates in different wheat genotypes were identified under conditions of rainfed and irrigation. It is shown that, in the conditions of dry water, the content of soluble carbohydrates is greater than under irrigation conditions. Due to the active synthesis and mobilization of soluble carbohydrates, plants safely continue their activity.

Key words: wheat; leaves; stems; ears; soluble carbohydrates; environmental conditions.