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, №1(174), 2019 г.

Article title and abstractPages
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M.Ilolov , D.N.Guljonov , J.Sh.Rahmatov
Hale type fractional integro-differential inclusions in Banach space
In this paper, sufficient conditions for the existence of weak solutions of fractional differential and integro-differential inclusions of Hale type in a Banach space are given. Methods of fractional integro-differential calculus and fixed point theories of multivalued mappings underlie the present research. It is known that the dynamics of economic, social and environmental macrosystems is a multi-valued dynamic process and differential and fractional integro-differential inclusions are natural models for macrosystem dynamics. Such inclusions are also used to describe some physical and mechanical systems with hysteresis.

Ключевые слова: functional-differential inclusion; Caputo fractional derivative; multivalued mapping; fixed point.

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N.U.Usmonov , N.N.Usmonzoda
A system of singular integral equations in a special case
The main goal of this paper is to determine the impact of zeros of determinant and poles of elements on the number of homogeneous functions and number of conditions of solubility. Presence of zeroes of the coefficient does not change the number linear independent solutions, but presence of the pole reduces this number on the order of pole.

Ключевые слова: zero; pole; integral equations; Holder condition; special case; canonical function; integral of Cauchy type.

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M.B.Kholikova , M.A.Usmonov
General conjugate boundary value problems with first order derivative in singular case
In the paper the case is considered, when factors have zeroes and poles of non-integer order, and non-analytical nature. It is proved that presence of zeroes of factor on counter do not influence on the number linear independent solution of the uniform problem and number of the conditions to solubility of the non-uniform problem, and pole influence on the number of solutions of the uniform problem and number of conditions of solubility of the non-uniform problem.

Ключевые слова: analytical function; breakup of the first sort; number of decision uniform problem; number of the conditions to solubility of the non-uniform problem; interpolation`s polynomial; singular case.

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S.Z.Kurbanshoev , U.R.Rustambekova
Stability of solutions quasistationary systems of the linear differential equations
The paper considers and offers the method of splitting-off 0f critical variables at the stability study of solutions of the system of quasilinear differential equations by means of integral manifold. The sufficient conditions of applicabbility pf small parametr method are determined for the search of the split-off replacement.

Ключевые слова: stability of solutions; integrated variety; own numbers of a matrix; consecutive approach.

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About solvability of some classes of two-dimensional singular integral operators on a limited area
Solvability of some classes of system of two dimensional singular integral operators on a limited area is analysed in this article. The effective and sufficient conditions for Noetherian in the space of Lebeg and the formula to rate index is given.

Ключевые слова: singular integral operation; Noetherian operators; symbol operator; the index of operator.

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М.А.Umarov , К.С.Bakhteev
On the prospects of the use the consonant writing
Some issues of the use of consonant texts for usual text and its consonant image is invested by means of comparing some parameters.

Ключевые слова: consonant letter; N-grams; metrics.

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P.B.Babadzhanov , G.I.Kokhirova , U.Kh.Khamroev , I.V.Kulaev , A.I.Jonmukhammadi
Theoretical radiants and velosities of the meteor showers associated with near earth asteroids discovered during 2009-2014
The dynamical properties of near Earth asteroids (NEAs) discovered during 1.01.2009-31.12.2014 were studied. It was established that according to the Tisserand invariant 274 NEAs are moving on comet-like orbits that intersect the Earths orbit. Investigation of the orbital evolution of these NEAs under the planetary perturbations has shown that during one cycle of the argument of perihelion variation 216 asteroids cross the Earths orbit for the four times and 50 asteroids - for the eight times. Consequently, if these NEAs are really the nuclei of extinct comets then according to the theory of formation and evolution of meteoroid streams, each of them can be a parent body of the meteoroid stream that is producing four or eight meteor showers. The results of calculations of the theoretical geocentric radiants, velocities, and dates of maximum activity of 1287 meteor showers, possible associated with 274 NEAs, are given in the paper. Since the parent bodies under consideration are moving within the relevant meteoroid streams the theoretical radiants of meteor showers yield the directions, velocities and dates of possible impacts of these bodies with the Earth.

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

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The study of the photometric parameters of Saturn family comets
The evolution of the absolute brightness (m) and photometric parameter (n) of comets during the entire time of their observation and the possible connection of these photometric parameters from solar activity has been studied. It is revealed that the changes of these parameters are insignificant, not associated with small changes in the elements of the orbits of comets and with the activity of the Sun.

Ключевые слова: comet; absolute brightness; photometric parameter; correlation; solar activity.

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Kh.Kh.Muminov , Sh.F.Muhamedova
Dissipative solitons of breather type of a scalar non-linear Shrödinger equation with the attraction potential
Numerical simulation methods are used to analyze the breather dynamics of nonlinear excitations of the multisoliton type described by the scalar nonlinear Schrödinger equation with the potential of attraction taking into account dissipation and pumping by external fields. Formation of coherent dissipative structures and the manifestation of a classical attractor in the phase space of the scalar nonlinear Schrödinger equation with a the potential of attraction are observed.

Ключевые слова: coherent structures; breather dynamics; classical attractor; scalar nonlinear Schrödinger equation with the potential of attraction; dissipation; pumping.

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M.Sh.Imom , Kh.Kh.Muminov , V.L.Romodanov , F.Rahimi , S.F.Odinaev
Development of qualuty digital analysis of neutron pulses and gamma quants with various scintillation counters
The paper presents the results of study of the digital separation of the responses of neutrons and gamma rays in non-destructive testing facilities for nuclear fissile materials with combinations of various scintillators. It has been shown that the stilbene crystalline scintillator, in comparison with the EJ-309 and BC-501 scintillators, has the best neutron channel loading.

Ключевые слова: non-destructive analysis; analog-digital converter; nuclear fissionable materials; photomultiplier tubes - photomultiplier tubes; nanosecond.

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S.F.Odinaev , F.Rahimi , Kh.Kh.Muminov , V.L.Romodanov , M.Sh.Imom
Optimization of parameters of the installation for U measurement in fuel assembly
Measurements are made of informative parameters of the installation with various sizes of large and small moderators. The best installation size was found, which gives the best measurement accuracy.

Ключевые слова: heat-extensive assembly; fissile materials; pulsed neutron generator; nondestructive analysis.

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D.S.Mansuri , A.Djurayev , H.O.Rahimova , M.M.Nasimova , G.Shuhratzoda
Method of determination of the shock-shifter shift deformation of composite gear wheel transmissions
The paper presents a new scheme and principle of operation of the gear train with compound wheels including shock absorbers-bushes made of rubber. Analytical method was used to obtain formulas for calculating the angular shifts (strains) of stock absorber-bushings taking into account their thickness, shear modulus and transmission parameters.

Ключевые слова: gear train; shock absorber-bush; shear; torque; radius; gear ratio.

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D.N.Nizomov , I.K.Kalandarbekov , A.M.Sanginov , R.Sh.Karimov
Numerical solution of the dynamic problem for calculation of carrying wall of low-floor buildings by the concentrated deformation method
The paper discusses the solution of the dynamic two-dimensional problem of the theory of elasticity by the method of concentrated deformations. The developed algorithm is implemented on the example of a doubly connected domain. The results of the calculation of the model of the load bearing wall of the clay building at different dynamic effects are obtained.

Ключевые слова: modulus of deformation; testing; free oscillations; numerical modeling; static load.

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Kh.B.Boboev , F.H.Nasrulloev , Sh.B.Nazarov
Contemporary state in the handling with industrial and solid domestic wastes in the Republic of Tajikistan
The paper presents the current state of the sphere of handling industrial and solid domestic wastes of the Republic of Tajikistan in order to minimize the harmful impact of waste on the environment and human health and create conditions for reducing the volumes of their formation and maximizing their involvement in economic circulation as secondary raw materials.

Ключевые слова: industrial and industrial waste; solid household waste; landfill.