of National Academy of Sciences
of Tajikistan

News of the National Academy of Sciences of Tajikistan.
Department of physical, mathematical, chemical, geological and technical sciences

Известия Академии наук Республики Таджикистан. Отделение физико-математических, химических, геологических и технических наук, №4(173), 2018 г.

Article title and abstractPages
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On the zeros of arithmetic dirichlet series without Euler product
Inequalities A.A.Karatsuba for the number of zeros of the Davenport-Heilbronn function in the short intervals of the critical line when the space has a shorter length has been proven.

Ключевые слова: Davenport-Heilbronn function; exponential pair; critical line; Dirichlet character; trigonometric sum.

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M.Azizov , A.Mukhlis
Reconstruction and coding the solution of the Neymans task using trigonometrical polynomials and given information about boundary function
In the paper the problem of restoring and coding solutions of the Neumans boundary value problem for given information about the boundary function is solved.

Ключевые слова: reconstruction; coding; Neyman's marginal task; marginal function; trigonometrical polynom; information vector; optimal approximation.

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Mean squared approximation of two variables functions with averaged trigonometric polynomials
In this paper are described some problems of mean-squared approximation of differentiable functions of two variables by averaged trigonometric polynomials.

Ключевые слова: best mean squared approximation; generalized trigonometric polynomials.

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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 L is solved.

Ключевые слова: best approximation; periodic of functions; trigonometric polynomial; modulus of continuity; difference of the mth order; joint approximation.

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Conditions for the dependence of the degree of summability of Stepanov functions and Fourier coefficients
In this work, results are obtained that establish the dependences between the degree of summability of the almost periodic Stepanov functions and Fourier coefficients. As a characteristic of the structural properties of the function, the modulus of continuity of the considered function of higher order is used.

Ключевые слова: almost periodic functions of Stepanov; Fourier series; Fourier coefficients; orthonormal system; trigonometric sums; degree of summability.

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Analysis of one lineare nonhomogeneous differential equation of Eulers type
In this work a linear nonhomogeneous differential equation of Eulers type of - th order is considered. For equations of this class the formula reducibility to equation with constant coefficients is indicated. The formula of integral representation of solution depending on root of an characteristic equation is presented.

Ключевые слова: linear equation type of Euler; model equation; characteristics of equation; Cauchy function; determinant type Vandermonde.

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On the coercitive solvability of the non-linear Laplace-Beltrami equation in Hilbert space
In this paper we obtain coercive estimates the non-linear operator of Laplace-Beltrami flow in Hilbert space L(R) and on the basis of the coercive estimates its separability is proven. The coercive solvability of nonlinear equations of the Laplace-Beltrami in the space L(R) is investigated.

Ключевые слова: Laplace-Beltrami operator; coercitive inequalities; nonlinearity; separability; solvability; Hilbert space.

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Author identification by truncated text digital portraits
Free text in Tajik is matched with two digital portraits taking into account the distribution of high-frequency and low-frequency sentence lengths. On the example of three model collections of works, make it possible to determine individually the author of the printed text in nine cases of ten using different digital portraits.

Ключевые слова: text; sentence; identification; identifier; digital portrait.

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About the hybrid method of automatic representation of the tajik word form in persian graphical letter systems
A program of studies of regularities has been outlined on the basis of the developed conceptual model underlying the correction of grammatical errors, made in the formal conversion of Tajik words form in Persian graphical letter systems from the same word forms specified in Cyrillic.

Ключевые слова: language; Tajik; Persian; graphics; conversion.

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Kh.B.Sharipov , K.Kabutov , I.H.Juraqulov , A.Safarov , F.Sultonov
The synthesis of titanium dioxide nanoparticles from titanium trichloride and research of its photocatalytic properties
In the article, titanium trichloride was used to obtain various polymorphic modifications of titanium dioxide (anatase, rutile). TiO powders were obtained by thermal decomposition of amorphous TiO⋅nHO at various temperatures: 300, 400, 500 and 600°C. The influence of heat treatment conditions on the micromorphology and phase composition of TiO powders has been revealed. A study was carried out on the photocatalytic properties of TiO nanoparticles.

Ключевые слова: titanium dioxide nanoparticles; anatase; rutile; titanium trichloride (titanium (III) chloride); thermal treatment; photocatalytic properties; adsorption.

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D.O.Davlatov , Sh.B.Nazarov , Zh.A.Misratov , U.M.Mirsaidov
Technology joint processing of nepheline syenites of Turpi and damburites of the Ak-Arkhar deposits of Tajikistan by sintering with sodium sulfate
The results of complex processing of nepheline syenites of Turpy and danburate of Ak-Arkhar fields of Tajikistan by the sintering method with sodium sulfate are presented. The optimal conditions for the ore sintering process are determined. The principal technological scheme of complex processing of ores with obtaining of such products as fertilizer, alumina, boric acid, iron oxide pigments, coagulants and building materials is offered.

Ключевые слова: nepheline syenites; danburate; sodium sulfate; complex processing; sintering; alumina; boric acid; technological scheme.

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O.A.Azizov , S.I.Bakum , A.Badalov , U.M.Mirsaidov
Specific of isolation and cleaning alumohydrides of potassium, rubidium and cesium
The results of the purification of aluminum hydrides of potassium, rubidium, and cesium are presented. The conditions for cleaning and obtaining crystals with a basic substance content of more than 99% were found.

Ключевые слова: aluminum hydrides; potassium; rubidium; cesium; purification; crystallization.

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M.J.Isobaev , E.Kh.Pulatov , B.G.Mavlonov , T.Kh.Abdullaev , M.И.Djumaeva , I.F.Rakhimov
Amides and sulfamides of 1,3,4-thiadiazines
By interaction of thiosemicarbazone α-hydroxykethone with the acetic anhydride which canalized by trifluoroacetic acid the amidothiadiazines were prepared. Sulfamidothiadiazines were synthesized by the reaction of aminotiadiazine with toluene sulfur chloride. The quantum-chemical calculation of synthesized compounds carried out and based on results of minimum energy calculations. The conclusion about stable configuration of the intermediate and final products was done.

Ключевые слова: acyl- and sulfuramide derivatives; aminothiadiazines; thiosemicarbazones; quantum-chemical calculation.

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Z.H.Gaibullaeva , G.T.Nasimov
Full-factorial planning of the process of hydrometallurgical extraction of lead from the galenite-containing Bali concentrate (Turkey)
The article examines the process of hydrometallurgical extraction of lead from galena-containing concentrates from the Bali deposit (Turkey) in a solution of nitric acid. The obtained experimental data were analyzed using the full-factorial experimental method of calculation and using the statistical software Minitab 15.0.

Ключевые слова: lead; concentrate; hydrometallurgical method; leaching; ecology.

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E.N.Sirodjidinov , I.N.Ganiev , Z.R.Obidov
High-temperature oxidation of Zn55Al alloy, doped with indium, in the firm condition
The thermogravimetrical method the interaction of Zn55Al alloy, doped with indium, with air oxygen in an interval to temperature 473-623K in the firm condition is investigated. Kinetic parameters of process of high-temperature oxidation of alloys are defined. It has been shown, that additives of indium within 0.01-0.05 wt.% slightly increase oxidability of an initial alloy, and products of oxidation of alloys are oxides AlO, ZnO ва InO.

Ключевые слова: Zn55Al alloy; indium; thermo gravimetrical a method; high-temperature oxidation; speed of oxidation; energy of activation.

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I.Sh.Ahmadshoev , N.P.Moukhamediev , A.H.Safiev , R.S.Rafiev , J.R.Ruziev , Sh.S.Jumaev , H.Safiev
Technology for producing flux with application of electrolyt turnover
The dependence of the melting temperature of the flux on the content of the components of the charge was studied. The optimal composition of the charge was revealed: waste - 60%, fluorite concentrate of Talco Fluorite LLC - 10% and electrolyte turnover of aluminum production - 30%. Based on the results of the studies, a basic technological scheme for the production of flux based on electrolyte turnover of aluminum production was developed.

Ключевые слова: fluorite concentrate; electrolyte turnover; flux; refining; industrial waste.

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Dj.N.Fozilov , B.A.Alidodov
Trace element composition of coal deposits Shishkat
It has been identified that deposits in coal seams Shishkat has higher concentration compared with their values сlarke tungsten, vanadium, silver, phosphorus, arsenic and germanium which are of interest in terms of the associated extraction of deposits during operation. The total metal content of coal, expressed in terms of an additive factor can be attributed to a group of highly metalliferous.

Ключевые слова: field; the deposition; facies; clark; the concentration; ratio; the average content of; the mean anomaly; toxicity.

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Features of the deep structure and the choice of the optimal design of exploration wells with the aim of further exploration of the Mahram oil and gas area
In the formation of oil and gas deposits in the western part of the Fergana depression, including in the Mahram area, deep tectonic disturbances play an important role, which divide the structure into blocks and serve as a way for the migration of hydrocarbons and their accumulation in Paleogene sediments. Therefore, the optimal choice of well design for each block guarantees a reduction in the cost of construction and an increase in the possibility of obtaining a positive result.

Ключевые слова: tectonics; blocks; cost; construction; area; result; oil; gas; economy.

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M.S.Safarov , A.R.Fazilov
The risks of natural disasters related to water and remote methods of their monitoring
The article is devoted to the analysis of the risk of natural disasters in Tajikistan and the justification of the possibility of using unmanned aerial vehicles for monitoring and data collection.

Ключевые слова: natural disasters; unmanned aerial vehicles; aerial photography.