Известия Национальной академии наук Таджикистана. Отделение физикоматематических, химических, геологических и технических наук, №1(186), 2022 г. 
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Скачать  M.Sh.Shabozov , A.S.Quraishi  722 
Exact upper bounds of root mean square approximations some classes of periodic differentiable functions
in space L 
In the article, the exact values of the upper bounds of the best mean nonquadratic approximations of some classes of periodic of rendered functions by trigonometric polynomials, characterizing generalized modulus of continuity generated by a specific generalized shift operator in the space are found. Sharp JacksonStechkintype inequalities are obtained for both better joint approximation of functions and for functionals on the classes . 

Ключевые слова: best root mean square approximation functions; upper bounds; generalized modulus of continuity; generalization operator displacement; Petre functional.  

Скачать  E.Kh.Safarzoda  2332 
On the absolute convergence of the double Fourier series of almost periodic functions 
In this paper, we investigate sufficient conditions for the absolute convergence of double Fourier series of almost periodic functions in the sense of Bezikovich. Depending on the behavior of the Fourier exponents, the higher order continuity modulus and the averaging modulus of order are used as structural properties of the functions under consideration. 

Ключевые слова: almost periodic functions of Bezikovich; double Fourier series; Fourier exponents; modulus of continuity; averaging module; absolute convergence; range of functions.  

Скачать  K.E.Khaknazarov  3339 
Variational Dirichlet problem for nondivergence form elliptic operators with uncoordinated degeneracy 
The paper has a proof of a theorem on solvability of the variational Dirichlet problem for nondivergence form elliptic operators in a bounded domain of ndimensional Euclidean space with uncoordinated power degeneracy along the entire boundary of the domain. The solution of the problem under study is sought in a weighted Sobolevtype space, which is the closure of the class of infinitely differentiable finite functions. The concept of higher forms is introduced, and only the degrees of degeneracy of the coefficients of the higher forms are involved in the definition of the solutions space. 

Ключевые слова: variational Dirichlet problem; nondivergence form elliptic operator; uncoordinated power degeneracy; bounded domain.  

Скачать  G.I.Kokhirova , P.B.Babadzhano , M.N.Latipov , A.I.Jonmuhammadi , U.H.Khamroev  4061 
New nearearth objects in the Taurid complex 
The Taurid meteoroid stream, comet 2P/Encke being the parent of the stream and more than 30 nearEarths asteroids which are in fact extinct fragments of the parent comet have form the Taurid cometasteroidmeteoroid complex. The Taurid stream produces the meteor showers and subshowers observable on the Earth annually during OctoberNovember and MayJune. We carried out a new search for asteroids belonging to the Taurid complex. On the base of calculation of orbital evolution of a sample of NEAs discovered in 20042015 and determination of theoretical features of related showers a search for observable active showers close to theoretically predicted ones was performed. As a result, predicted showers of 16 NEAs were identified with the showers produced by the Taurid meteoroid stream. Revealed association points to their common cometary origin. New nearEarths objects alongside with already established ones are moving within the Taurid stream and are very likely extinct fragments of comet 2P/Encke  parent of the Taurid complex or remnants of a larger cometprogenitor that was disintegrated 2030 thousand years ago. 

Ключевые слова: comet; asteroid; extinct comet; meteoroid stream; meteor shower; orbit; radiant; evolution.  

Скачать  F.Sh.Shokirov  6270 
Majorana representation for quantum spin systems 
The description of the states of a quantum system with a high spin value in a multidimensional Hilbert space is associated with the complexity of an intuitive understanding of the geometric interpretation of the processes under study. In this paper, using Majorana's method of representing pure spin systems based on the basic states with spin S=1/2, a system of Majorana polynomials for the general case is determined. 

Ключевые слова: Majorana representation; Bloch sphere; Hilbert space; mathematical modeling.  

Скачать  Sh.Kh.Khalifaeva  7177 
Heavy metals in soils of south and central parts of Tajikistan 
Statistical characteristics of heavy metals (HM) in soil samples of the south and central parts of the country are given. The interannual variation of some heavy metals (zinc, arsenic, lead) is considered. 

Ключевые слова: heavy metals; soil; pollution; environment.  

Скачать  F.A.Khamidov , M.Yu.Akramov , J.N.Eshov , D.T.Isozoda , A.Badalov  7887 
System analysis of thermochemical properties of binary hydrides of selements, lanthanides (II) and modeling of their change regularities 
The known and/or specified values of thermodynamic properties of binary hydrides of selements, lanthanides (II) have been summarized. The system analysis of thermodynamic characteristics of binary hydrides of mentioned elements have been carried out by means of semiempirical and computational methods. The regularities of their change in the range of IА, IIА groups and lanthanides (II), as well as periods have been defined. A clear deviation of hydrides properties of typical elements of IА and IIА periods from subsequent typical analogs has been shown.
It has been defined that change of thermodynamic characteristics of lanthanide hydrides depending on their nature has complicated character with appearance of tetradeffect.
The mathematical models of defined regularities have been drawn up. 

Ключевые слова: system analysis; thermodynamic properties; binary hydrides; lanthanides; regularity; modeling.  

Скачать  К.О.Boboev , М.D.Boboyorov , J.N.Eshov , B.B.Barotov , U.М.Mirsaidov  8892 
Thermodynamic analysis of processing processes
in decomposition of uraniumcontaining ore
with sulfuric acid 
The article presents the results of a thermodynamic calculation of the decomposition of uraniumcontaining ores from the Oktyabrsky deposit with sulfuric acid, the thermodynamic characteristics of the minerals that make up the raw materials and the calculation of the Gibbs energy for each reaction are also determined. 

Ключевые слова: uranium ore; enthalpy; entropy; Gibbs energy; decomposition; sulfuric acid.  

Скачать  U.R.Jobirov , I.N.Ganiev , M.Ch.Shirinov , Z.R.Obidov  9397 
Influence of additives of erbium on anode behaviour Zn0.5Al zinc alloy in alkaline environment 
In paper results of potentiostatical researches influence of additives of erbium on anode behaviour of Zn0.5Al zinc alloy, in the alkaline environment are presented. Showed, that speed of corrosion of Zn0.5Al zinc alloy decreases at the additives in it 0.011.0 wt.% Cr. 

Ключевые слова: Zn0.5Al alloy; erbium; potentiostatically method; HCl electrolyte; corrosion potential; corrosion rate.  

Скачать  M.M.Mamadvafoev , D.A.Davlatshoev  98109 
Carbon in the rocks of the intrusive complexes in Kafandara ore field (Eastern Gissar) 
The article examines the distribution function of carbon, its abundance, dependence on petrochemical characteristics and correlations with petrogenic elements of intrusive complexes of the Southern Tien Shan in the position of the Kafandara ore field. 

Ключевые слова: carbon; distribution function; occurrence; correlational relation; Kafandara ore field.  

Скачать  S.Kh.Negmatullaev , R.U.Juraev , T.R.Ulubiev  110122 
The manifestation of strong earthquakes on the territory of Tajikistan in 2020 
The data on Tajikistan's strong earthquakes are presented that occurred in the year 2020. The description and analysis of the distribution of their epicenters in the territory of Tajikistan is given. Isoseist maps of surveyed seismic events had be used on April 24 and July 4, the nature of manifestation on the surface and their confinement to geological structures are given. Some information about the vulnerability of local buildings in the epicentral zones of earthquakes is presented. 

Ключевые слова: earthquake epicenter; magnitude; earthquake intensity; isoseist; macroseismic; aftershock.  

Скачать  Sh.A.Yoqubov , A.R.Ischuk  123132 
Hazardous exogenous geological processes and seismic hazard of the Surkhob river basin 
The article assesses the susceptibility of the mountain slopes of the Surkhob river valley to the formation of mass displacements on the slopes under seismic impacts. Using modern GIS technologies, it is shown that almost the entire populated and developed territory of the Surkhob river basin is at risk of landslides, mudflows and strong earthquakes. Based on the results of the assessment, a map of the susceptibility of slopes to landslides was constructed, on which the susceptibility varies from medium to high, with the dominance of zones with high susceptibility. Based on the assessment, the necessity of taking measures to reduce the risk of earthquakes and secondary exogenous phenomena is shown. 

Ключевые слова: Surkhob river; hazard; landslide; mudflow; earthquake; geological processes; seismic hazard; sustainability.  

Скачать  I.M.Azizxonov , B.L.Talgamer  133144 
Assessment of the feasibility of involving the ancient ephels and dumps of the Tereklikan section of the Kandzhol deposit into operation 
The expediency of involving technogenic deposits formed during the extraction of nonferrous metals in operation is justified. The description of ancient efels and dumps of the Tereklikan section of the Kanjol deposit is given. The method and results of furrow testing are presented and its reliability is evaluated. An underestimation of the silver content was found in the manual method of furrow testing performed by the predecessors. The industrial value of these deposits for silver mining has been established. A basic technology for extracting valuable components is proposed. 

Ключевые слова: technogenic deposits; furrow testing; control testing; material analysis; development technology.  

Скачать  M.A.Mirakov , F.Sh.Iskandarov , Y.N.Nurulloev  145152 
First find of hessite at Sangvor golden deposit
(NorthWestern Darvaz) 
The article provides a detailed description of silver telluride  hessite from the gold  placer Sangvor deposit with its chemical composition, Xray data and other physical and optical properties. 

Ключевые слова: hessite; concentrate; placer; silver minerals; tellurium minerals; Sangvor deposit; gold admixture; microhardness; Darvaz; Tajikistan.  

Скачать  G.N.Petrov , S.Rasulov , M.Ilolov , Kh.Akhmedov , M.G.Khulmi  153160 
Economic efficiency of construction of a small hydroelectric power station in the protected area of the Karatag river basin 
The issues of assessing the absolute and comparative economic efficiency of electricity supply to consumers in the protected area of the Karatag River are considered. The only two possible options are the construction of a 100 kW SHPP and the connection to a centralized power supply by constructing a 35 kV transmission line with a length of 31 km. 

Ключевые слова: project life cycle; discount rate; payback; electricity losses; present value; efficiency radius; electricity tariff; electricity transit; financial flows; net present value.  

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