Серия "Математика"
https://rep.ksu.kz//handle/data/44
2022-08-12T15:00:54ZAn 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.
2022-03-30T00:00:00ZConnection 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.
2021-03-30T00:00:00ZConstruction 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.
2022-03-30T00:00:00ZSeparability 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