Серия "Математика" https://rep.ksu.kz//handle/data/44 2022-08-12T15:00:54Z An inverse problem for Hilfer type differential equation of higher order https://rep.ksu.kz//handle/data/13187 An inverse problem for Hilfer type differential equation of higher order Yuldashev, T.K.; Kadirkulov, B.J.; Mamedov, Kh.R. In three-dimensional domain, an identification problem of the source function for Hilfer type partial differential equation of the even order with a condition in an integral form and with a small positive parameter in the mixed derivative is considered. The solution of this fractional differential equation of a higher order is studied in the class of regular functions. The case, when the order of fractional operator is 0 < < 1, is studied. The Fourier series method is used and a countable system of ordinary differential equations is obtained. The nonlocal boundary value problem is integrated as an ordinary differential equation. By the aid of given additional condition, we obtained the representation for redefinition (source) function. Using the Cauchy–Schwarz inequality and the Bessel inequality, we proved the absolute and uniform convergence of the obtained Fourier series. 2022-03-30T00:00:00Z Connection between the amalgam and joint embedding properties https://rep.ksu.kz//handle/data/13184 Connection between the amalgam and joint embedding properties Yeshkeyev, A.R.; Tungushbayeva, I.O.; Kassymetova, M.T. The paper aims to study the model-theoretic properties of differentially closed fields of zero and positive characteristics in framework of study of Jonsson theories. The main attention is paid to the amalgam and joint embedding properties of DCF theory as specific features of Jonsson theories, namely, the implication of JEP from AP. The necessity is identified and justified by importance of information about the mentioned properties for certain theories to obtain their detailed model-theoretic description. At the same time, the current apparatus for studying incomplete theories (Jonsson theories are generally incomplete) is not sufficiently developed. The following results have been obtained: The subclasses of Jonsson theories are determined from the point of view of joint embedding and amalgam properties. Within the exploration of one of these classes, namely the AP-theories, that the theories of differential and differentially closed fields of characteristic 0, differentially perfect and differentially closed fields of fixed positive characteristic are shown to be Jonsson and perfect. Along with this, the theory of differential fields of positive characteristic is considered as an example of an AP-theory that is not Jonsson, but has the model companion, which is perfect Jonsson theory, and the sufficient condition for the theory of differential fields is formulated in the context of being Jonsson. 2021-03-30T00:00:00Z Construction of the differential equations system of the program motion in Lagrangian variables in the presence of random perturbations https://rep.ksu.kz//handle/data/13181 Construction of the differential equations system of the program motion in Lagrangian variables in the presence of random perturbations Tleubergenov, M.I.; Vassilina, G.K.; Azhymbaev, D.T. The classification of inverse problems of dynamics in the class of ordinary differential equations is given in the Galiullin’s monograph. The problem studied in this paper belongs to the main inverse problem of dynamics, but already in the class of second-order stochastic differential equations of the Ito type. Stochastic equations of the Lagrangian structure are constructed according to the given properties of motion under the assumption that the random perturbing forces belong to the class of processes with independent increments. The problem is solved as follows: First, a second-order Ito differential equation is constructed so that the properties of motion are the integral manifold of the constructed stochastic equation. At this stage, the quasi-inversion method, Erugin’s method and Ito’s rule of stochastic differentiation of a complex function are used. Then, by applying the constructed Ito equation, an equivalent stochastic equation of the Lagrangian structure is constructed. The necessary and sufficient conditions for the solvability of the problem of constructing the stochastic equation of the Lagrangian structure are illustrated by the example of the problem of constructing the Lagrange function from a motion property of an artificial Earth satellite under the action of gravitational forces and aerodynamic forces. 2022-03-30T00:00:00Z Separability of the third-order differential operator given on the whole plane https://rep.ksu.kz//handle/data/13179 Separability of the third-order differential operator given on the whole plane Suleimbekova, A.O. In this paper, in the space L2(R2), we study a third-order differential operator with continuous coefficients in R(􀀀1;+1). Here, these coefficients can be unlimited functions at infinity. In addition under some restrictions on the coefficients, the bounded invertibility of the given operator is proved and a coercive estimate is obtained, i.e. separability is proved. 2022-03-30T00:00:00Z