Доклады Национальной академии наук Таджикистана, том 65, №0304, 2022 г. 
File  Article title and abstract  Pages 


Download  M.Sh.Shabozov , Z.А.Parvonaeva  143149 
About Jacksontype inequalities in L[1,1] and solutions
of some extremal problems 
In the space L[1,1] an exact Jacksontype inequality between E(f), the best approximation of a continuous function by the subspace  of algebraic polynomials of degree (1) the generalized modulus of continuity of the first order ω(f ,t) of the derivative f Î L[1,1] and introduced by A.A.Abilov was found. A similar inequality between E(f) and the functional Petre is proved. 

Key words: Jacksontype inequality; best meansquare approximation; Legendre polynomials; modulus of continuity.  

Download  Yu.Kh.Khasanov , M.M.Makhamadieva  150156 
About the summation of Fourier series by VoronoiNerlund method 
A measurable and Lebesgue integrable function f(x) belonging to the space L(1 ≤ p ≤ ∞) is considered. The question of the behavior of the Linear operator, or (W,p)  Voronoi averages, which are formed using partial sums of order k of the Fourier series of the function f(x), is investigated. A statement is proved in which, for each n>1, an upper bound of the value p(f;x;W) is established through a sequence of the best approximations of the function in a uniform metric. 

Key words: periodic function; Fourier series; linear operator; Voronoi averages; regularity of summation method; trigonometric polynomials; Fourier coefficients; uniform metric.  

Download  S.A.Iskhokov , K.E.Khaknazarov  157161 
On the finite dimensionality of the kernel of some nondivergece form degenerate elliptic operators 
We prove an inequality which contains the norm of a nondivergence form elliptic operator in a bounded domain of the dimensional Euclidean space that degenerates along the entire boundary of the domain. Then, with the help of this inequality, the finitedimensionality of the kernel of the operators under investigation is proved. In contrast to previously published papers, the coefficients of the operators under investigation are not differentiable, and therefore they cannot be reduced to divergence form. 

Key words: nondivergence form elliptic operator; power degeneration; bounded domain; a finitedimensional kernel; closeness of a range of operator.  

Download  I.Kurbonov , U.Bakhtovar  162170 
Eproblem of electrodynamics for an isotropic
suspensionlinear and nonlinear medium with memory 
The problems of propagation of electromagnetic waves in piecewise inhomogeneous nonlinear media are considered. Substitutions of boundary nonlinear integrodifferential problems are given to obtain systems of partial differential equations. Their approximate timeperiodic solutions are sought by the method of equivalent linearization. A generalization of the Fresnel formulas of the Eproblem of electrodynamics for media with memory properties is obtained. It is shown that for nonconducting media without memory . The is, the angles of incidence, reflection and refraction are equal. 

Key words: piecewise linear medium; inhomogeneous medium; memory; linear and nonlinear medium; Eproblems of electrodynamics.  

Download  Sh.B.Khalilov , B.N.Rushanov  171178 
On the theory of boundary problems for multidimensional Petrovsky elliptic systems of equations of the second order 
In the article, for one elliptic system of four secondorder equations depending on four unknown functions, the Neumann problem in a halfspace is considered. Using the Fourier transform method, it is proved that the problem posed is uniquely solvable and this solution is found in an explicit form. 

Key words: elliptic system; Neumann problem; Fourier transform; strongly elliptic systems; homotopy classification; characteristic determinant; matrix differential operator.  

Download  G.Kh.Khujanazarova , I.Z.Khonov  179185 
Basic boundaryvalue problems for elliptic systems
of differential equations of the fourth order with displacement coefficients 
The work has established effective necessary and sufficient Noetherianness conditions for elliptic systems of differential fourthorder equations with discontinuous coefficients and the formula for calculating the index is obtained. 

Key words: basic boundary value problems; elliptic systems; singular integral operator; symbol; index; operator impatience.  

Download  M.M.Kabilov  186191 
Thermal ignition of a mixture of gas in an inert porous medium 
A twotemperature model of thermal ignition of a mixture of gases in an inert porous medium is investigated in the adiabatic formulation. An approximate solution of the problem is obtained. 

Key words: wave; combustion; mixture; velocity; ignition; model; porous medium.  

Download  H.G.Asoev  192200 

In this article a possible connection between the activity of the Sun and the absolute brightness of comets of the families of Saturn and Jupiter are considered. The dependence of the brightness of some comets on the activity of the Sun has been revealed. It is shown that for comets of the Jupiter family this dependence is stronger than for comets of the Saturn family. This is due to the lack of observational data on comets of the Saturn family due to rarer encounters with the Sun compared to comets of the Jupiter family. Rare observations do not allow a fullfledged analysis. 

Key words: comet; photometric parameter; absolute brightness; correlation; solar activity.  

Download  A.M.Olimov , M.Subhoni , Tomoyuki Yamamoto , F.Rahimi  201209 
Effect of pressure on the geometric and elastic properties of CsPbX (X = Cl, Br, I) 
In this paper the results of studying the dependence of unit cell parameters, elasticity constants, bulk moduli of elasticity, and other elasticity parameters of CsPbX (X = Cl, Br, I) perovskites on pressure in the range from 0 to 30 GPa with a step of 5 GPa, in the framework of the density functional theory are presents. It is determined that for all structures, the values of the bulk modulus, the average speed of sound, the transverse and longitudinal speeds of sound, as well as the Debye temperature increase with increasing pressure. 

Key words: geometric properties; density functional theory; bond length; elasticity constants; average sound speed; transverse and longitudinal sound speeds; shear modulus; Debye temperature.  

Download  S.Odinaev , D.A.Abdurasulov , A.A.Abdurasulov  210219 
Molecular statistical study of the orientation elastic properties of nematic liquid crystals 
The orientational elastic properties of nematic liquid crystals are investigated on the basis of the locally equilibrium statistical distribution function generalized for the description of liquid systems with arbitrary shapes of molecules. Analytical expressions are obtained for the coefficients of orientation elasticity during deformation of transverse bending ( ) longitudinal bending ( ) and torsion ( ) In the framework of the approximation of the separability of the intermolecular interaction potential into radial and angular parts, using the LennardJones and MayerZaupe potentials as its radial and orientation parts, the dependence of the orientation elasticity coefficients ( ) is investigated from temperature, pressure and density for NLC (PAA). 

Key words: statistical distribution function; nematic liquid crystals; orientation elasticity; radial and orientation order.  

Download  Sh.S.Nurulhakov  220228 
An exact solution of the coupled equations in the theory of stimulated brillouin scattering using Riemann method 
In this article we have obtained an exact solution of the coupled equations in the theory of stimulated Riemann scattering of electromagnetic waves in the field of a twodimensionally localized pump wave for arbitrary scattering angles by the Riemann method. The spatial variation of the amplitudes of the interacting waves is studied for various values of the pump field and the sizes of its localization region. 

Key words: stimulated Riemann scattering; stimulated Brillouin scattering; ionacoustic wave.  

Download  М.D.Boboyorov  229232 
Таҷзияи кинетикии маъданҳои урандори Тоҷикистон 
Дар мақола тавсифи кинетикии таҷзияи маъданҳои урандори конҳои «Тоҷикистони Марказӣ», «Тоҷикистони Ғарбӣ», «Тоҷикистони Шарқӣ» ва «Октябрское» бо кислотаи сулфат оварда шудааст. 

Key words: кинетика; маъдани урандор; таҷзия; кислота; энергияи фаъолкунӣ.  

Download  A.S.Jafarov  233239 
Phase equilibrium in the InTe system 
In this article the results of a study of the temperaturedependence of the speed of propagation of ultrasound in exfoliating melts of the InTe system are presents. In the InTe system, anomalies in the polytherms ϑs. It was found that these anomalies increase gradually as the concentration of melts approaches the critical one. The lines of monovariant liquidliquid equilibrium and critical parameters have been refined. 

Key words: temperature; phase; system; indium; tellurium; ultrasonic method; concentration.  

Download  T.M.Umarovа , S.S.Holova , D.S.Kuchakshoev  240247 
Synthesis and physicochemical properties of AlTe alloys alloyed by neodymium 
The analysis of the available literature data on the aluminumtellurium phase diagram, shows the results of studies of Xray phase and metallographic analyzes of alloys of the AlTeNd system and the prospect of their application are briefly presented. 

Key words: state diagram; aluminum alloy; neodymium; aluminum telluride; diffractogram; microstructure.  

Download  A.Toshmakhmadzoda  248253 
Modification of bitumen with polymer additives using secondary raw materials and byproducts of the industry 
In this article the effect of polymer additives from dynistyrene thermoplastic elastomer (DST), vegetable oil tar, gossypol resin (GS) and the residue from the regeneration of used lubricating oils (ORSM) on the physical and mechanical properties of bitumen are studied. It is shown that the use of the abovementioned additives makes it possible to improve the physical and mechanical properties of bitumen. 

Key words: polymer; oils; additive; gossypol resin; properties.  

Download  F.M.Toshov , Sh.R.Samikhov , Sh.A.Kurbonov , N.Kh.Oyzoda , Kh.A.Abdullaev  254259 
Action of phosphate fertilizer, produced from phosphorites of the Rivat deposit on biological and economical tratts of midle staple cotton 
In the study found that by adding superphosphate to the soil with a P0 content of 1318% obtained from Rivat deposits, it positively affection on biological, economical and technological qualities of cotton fiber. It was found that as a result of the application of phosphate fertilizers obtained from Rivat deposits, increases the main stem (3/1 times), the total leaf surface area per plants (3.2 times), the number of formed fruit organs (3.7 times), total biological yield (2.7 times) with comparison to control plants of cotton. 

Key words: cotton; phosphate rock raw materials; superphosphate; morpophysioloqical patterns; distribution of assimilates; biological and economic harvest; technological properties of cotton fiber.  

Download  T.Sh.Avezov , A.Ergashev  260263 
Effect of seed treatment with physiologically active substances on the activity of antioxidant enzymes in wheat leaves under soil dry conditions 
It was shown that the treatment of seeds before sowing with antioxidants atocopherol (αTOK), ascorbic acid and Znhydroxyethyl phenolic acid (ZnODEPK) under soil drought conditions increases the drought resistance of plants of soft and durum wheat varieties and affects the activity of antioxidant enzymes in the leaves. 

Key words: wheat; antioxidants; soil drought; enzymes activity.  

Download  A.K.Sayfudinov , M.A.Babazhanova  264268 
The kinetic behavior robotfactory multienzyme complex of Calvin cycle in extracts from leaves of cotton leaves 
The results of kinetic studies robotfactory reactions in a multienzyme complex of Calvin cycle in extracts from cotton leaves of variety 108F. The dependence robotfactory activity multienzyme complex of reaction time, protein concentration and ribozo5phosphate 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: cotton; robotfactory; reaction; rate; kinetics; multienzyme complex; Calvin cycle.  

Download  B.I.Ganiev , S.A.Avezov  269274 
Hyperbilirubinamia in the development of encephalopathy in liver cirrhosis 
The importance of hyperbilirubinemia in the development of hepatic encephalopathy (HE) in patients with liver cirrhosis (LC) was studied. 27 patients of the viral etiology LC were examined (18  chronic hepatitis B, 9  chronic hepatitis C). The content of bilirubin in blood serum in patients with LC varies depending on the severity of the pathological process. In univariate analysis, the following measures were significantly (p≤0.05) associated with poor prognosis: HE, hyperbilirubinemia, hypercreatinemia, hypoalbuminemia, and reduced prothrombin time. Our studies confirm that bilirubin levels increase with irreversible impaired liver function. Increasing bilirubin over time helps reduce the likelihood of survival. On the base, the bilirubin content of patients with LC can be divided with a low or high risk of death from liver failure with the development of HE. 

Key words: cirrhosis of liver; hepatic encephalopathy; hyperbilirubinemia; survival.  
