Vol. 36 No. 3 (199) (2002)

In the paper are considered the generalized spaces of Nikolskii-Besov type with zero upper indexes born from some functions with polynomial growth. In contrast to the corresponding $H$-spaces of Sobolev-Liouville type, which in case of upper index do not depend the function born from, the considered spaces in general don’t have this property. The paper gives the proof of this fact and some embedding theorems are proved.

In the paper the existence of an optimal pair of an initial boundary problem for some class of the nonlinear evolutionary equations of the fourth order with variable coefficients is proved.

An algebra is called a quasi-Boolean algebra, if it satisfies hyperidentities of the variety of Boolean algebras. Elementary characterization is proven for quasi-Boolean algebras.

Sequential calculi of minimal Robinson’s arithmetic (with cut rule and cut- free) are defined in this paper. Equivalence of these calculi is proved.

In this article an algorithm is described, which brings every program, written in procedural language, to conformity with such a system of functional equations, that defines its denotational semantics and in each equation the number of variables is minimal. The algorithm uses the mathematical model, for which the existence of the least element is proved.

The problem of stability depending on acting force of the system of the linear differential equations with changeable coefficients is considered. It is shown that Liapunov’s reconstruction equivalence of tasks of stability depending on acting force of systems with changeable and with constant coefficients is preserved. Necessary and sufficient conditions are obtained, under which the resulted system of the linear differential equations with changeable coefficients is stable, asymptotic stable or unstable depending on acting force.

Two wave equations for isotropic, heterogeneous naturally gyrotropic media, based on two well-known formula of material equations are derived. It is shown that under certain conditions there exist substantial distinctions between solutions of wave equations corresponding to the two aforesaid equations.

The criterion of stability against radial adiabatic oscillations is considered for the models of neutron homogeneous stars in the framework of general relativity. The critical value of adiabatic exponent $\gamma_{cr}$ is obtained in the framework of general relativity, which corresponds to the limit of stability of the star and is applicable in the whole allowable range where the parameter $\eta_1=R/\alpha (R$ – star radius, $\epsilon$– energy density, $\alpha= \sqrt{3c^4/(8\pi G\epsilon)})$ varies. The obtained results are compared with the known result of Chandrasekhar.