Известия Академии наук Республики Таджикистан. Отделение физико-математических, химических, геологических и технических наук, №2(171), 2018 г.
|Article title and abstract||Pages|
|М.О.Аkobirshoev , V.D.Sainakov |
The value of quasiwidths of the some class of periodical functions with two variables in L
In the Hilbert space of square-integrable periodic in each variable functions accurate estimates of quasiwidths of certain classes of differentiable functions are found whose averaged moduli of continuity of higher-order partial derivatives are majorized by given functions.
Ключевые слова: best approximation; modulus of continuity; periodical function; normalized space; liner and Kolmogorovs quasiwidths.
|S.A.Iskhokov , B.A.Rakhmonov |
Variational Dirichlet problem associated
with noncoercive form in the whole space
We study the solvability of the Dirichlet variational problem for one class of higher order elliptic operators in the whole -dimensional Euclidean space in the case of uncoordinated degeneration of coefficients at infinity. The formulation of the problem under consideration is connected with the integro-differential sesquilinear form, which may not satisfy the coercivity condition. The notion of an leading form is introduced, and in accordance with the behavior of the coefficients of the leading forms, the basic weighted normed space is defined in which the solution of the main problem of the work is searched. A theorem on the unique solvability of this problem is proved and an estimate of the norm of the solution is established through the norm of the righthand side of the equation.
Ключевые слова: variational Dirichlet problem; elliptic operator; power degeneration; noncoercive form; uncoordinated degeneration.
About one class of nonlinear singular integral equations
In the paper a class of nonlinear singular integral equations is studied. It is established that number of solutions of the integral equation in the class of functions, limited on a countour, do not change due to presence of zeroes of coefficients of the integral equation and decrease by total order of all pole.
Ключевые слова: integral equations; condition of Hölderr; singular case; canonical function; Cauchi type integral; interpolation polynomial; zero and pole.
|T.A.Toshov , Kh.Kh.Muminov , A.T.Maksudov |
To the theory of magnetoelastic waves in S = 1 ferromagnets with strong single-ion anisotropy
Investigations of non-Heisenberg ferromagnets with spin S = 1 were carried out in the presence of a connection with the phonon subsystem by modulating the exchange integral. The ground state is found and a soliton solution is obtained for the system of equations describing the coupled spin-quadrupole wave with the deformation one in S = 1 ferromagnets with single-ion anisotropy of the "easy plane" type.
Ключевые слова: non-Heisenberg ferromagnet; single-ion anisotropy; spin-phonon interaction; magnetoelastic waves; spin-quadrupole waves.
|T.Kh.Salikhov , N.Melikkhudzha , A.Mahmalatif |
The contribution of absorbing substrate to the formation of the nonlinear photoacoustic response:
mathematical model and temperature field
A mathematical model for the generation of a nonlinear photoacoustic (PA) response is proposed for the case when the substrate, along with the sample, is absorbing. The system of nonlinear heat conduction equations for the gas layer, the sample and the substrate has been used. The temperature increments are represented as the sum of the locally equilibrium and oscillatory parts, and the oscillatory ones as the sum of the linear and nonlinear parts. The necessary system of differential equations for the fundamental and second harmonics of a nonlinear PA signal is obtained. The features of the formation of the temperature field in the PA chambers are studied in detail.
Ключевые слова: photoacoustic; optoacoustic; thermal nonlinearity.
|S.Odinaev , D.M.Akdodov , Kh.I.Idibegzoda |
Frequency dispersion of electric elasticity modulus of aqueous solution of sodium chloride
Based on the previously obtained analytical expression for the modulus of electroelasticity , when the relaxing flows are dumped exponentially, for a certain solution model and explicit expressions for the potential of intermolecular interaction and the radial distribution function , as well as the corresponding values of concentrations C and temperatures T, the dynamic modulus of electroelasticity of NaCl aqueous solution is calculated. The results of numerical calculations are in satisfactory agreement with the experiment.
Ключевые слова: the modulus of electroelasticity; friction coefficients; relaxation time; potential energy of interaction; radial distribution function.
|Kh.Kh.Muminov , Sh.F.Muhamedova , M.Asghari-Larimi |
Numerical simulation of multi-solitonic solution
of the vector nonlinear Schrödinger equation
with a self-consistent potential
Numerical simulation of the evolution of the multisolitonic solution of the vector nonlinear Schrödinger equation with a self-consistent potential , describing a two-component Bose-gas in field-theoretical models of physics of condensed matter is carried out. Analysis of the dynamics of the evolution of multisoliton solutions shows that there is no significant breather dynamics of the motionless soliton. The mobile soliton exhibits substantial breather dynamics at three fundamental frequencies of time modulation. Soliton demonstrates stability while retaining the integral of motion with high accuracy.
Ключевые слова: n-soliton solution; trivial boundary conditions; vector nonlinear Schrödinger equation; breather.
|D.Kh.Mirzoev , S.M.Gaforzoda , Sh.D.Otaev , Sh.B.Nazarov |
Aqueous-hydrochloric acid leaching of green clays
of Chashma-Sang of Republic of Tajikistan deposit
with preliminary sintering with calcium chloride
The results of study of aqueous-hydrochloric acid leaching of green clays of Chashma-Sang Deposit with preliminary sintering with calcium chloride are considered in the paper. The optimal conditions of extraction of valuable components from the ore are defined
Ключевые слова: green clay; aqueous-hydrochloric acid leaching; sintering; calcium chloride.
|Sh.H.Halikov , J.А.Oliftaeva , M.Umаrhon |
Release of humic acids in the form of the complex from coal of «Shurob»
In the paper the release of humic acids from brown coal of the Shurob field of the Republic of Tajikistan is considered. By the spectral and composition analysis the characteristic structurally - group composition of humic acids is defined. It is revealed that in brown Shurob coal presence of humic acids is connected with determination of genesis of humic acids in nature.
Ключевые слова: alkali; coal; humic acids; humuses; humates; ashes; extraction.
|M.M.Tagoev , Sh.B.Nazarov , Zh.A.Misratov , U.M.Mirsaidov |
Kinetics of the sintering process of borosilicate raw
material and its concentrate with sodium sulphate
The results of the studies of borosilicate raw materials of the Ak-Arkhar field and its concentrate decomposition by the sintering method with sodium sulfate are presented. The mechanisms of the reactions are determined and the kinetics of the process is studied.
Ключевые слова: borosilicate ore; concentrate; sintering; kinetics; sodium sulfate.
The accounting features of drilling technology
in intervals, characterized by the presence of
anomalously high seampressure in drawing up
of the technical project of construction of wells
at the square of a Mahram
Based on data from previous studies and results of drilling wells recommendations ore produced, when drafting new exploratory wells it is neussary to take into account the particularities of drilling technology in intervals characterized by the presence of anomalously high seam pressure.
Ключевые слова: abnormal; layer; hydrostatic; drilling; repression; area; lithological section; search; intelligence; pressure.
|D.A.Abdushukurov , D.Abdusamadzoda , A.S.Kodirov |
Initial salinization of rivers in the upper
of the Vakhsh river
The article deals with the initial salinization of rivers in the upper reaches of the Vakhsh river. It is determined that the share of underground feeding of rivers increases in the middle river formation, correspondingly the mineralization of water in the rivers increases. Measures have been developed to reduce the overall salinity of the Vakhsh river.
Ключевые слова: salinization; Vakhsh river; physical and chemical properties of water; turbidity.
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