Ukrains’kyi Matematychnyi Zhurnal
(Ukrainian Mathematical Journal)
Ukrains'kyi Matematychnyi Zhurnal (UMZh) was founded in May 1949. Journal is issued by Institute of Mathematics NAS of Ukraine. English version is reprinted in the Springer publishing house and called Ukrainian Mathematical Journal.
Ukrains'kyi Matematychnyi Zhurnal focuses on research papers in the principal fields of pure and applied mathematics. The journal is published monthly, each annual volume consists of 12 issues. Articles in Ukrainian, Russian and English are accepted for review.
Latest Articles (November 2019)
Ukr. Mat. Zh. - 2019. - 71, № 11. - pp. 1553-1569
In this paper, we present a series of definitions and properties of lifting dynamical systems (LDS) corresponding to the notion of deterministic diffusion. We give heuristic explanations of the mechanism of formation of deterministic diffusion in LDS and the anomalous deterministic diffusion in the case of transportation in long billiard channels with spatially periodic structures and nonideal reflection law. The expressions for the coefficient of deterministic diffusion are obtained.
A method for the construction of exact solutions to the nonlinear heat equation $u_t = \left(F(u)u_x \right)_x +G(u)u_x +H(u)$
Ukr. Mat. Zh. - 2019. - 71, № 11. - pp. 1443 -1454
We propose a method for the construction of exact solutions to the nonlinear heat equation based on the classical method of separation of variables and its generalization. We consider substitutions used to reduce the nonlinear heat equation to a system of two ordinary differential equations and construct the classes of exact solutions by the method of generalized separation of variables.
Generalization of resonance equations for the Laguerre- and Legendre-type polynomials to the fourth-order equations
Ukr. Mat. Zh. - 2019. - 71, № 11. - pp. 1529-1538
A recurrent algorithm for finding particular solutions of а fourth-order resonance equation connected with the generalization of Laguerre and Legendre polynomials is constructed and substantiated. For this purpose, we use the general theorem on the representation of partial solutions of resonance equations in Banach spaces, which was proved by V. L. Makarov in 1976. An example of general solution to the resonant equations with a differential operator for the Laguerre-type polynomials is presented.