Vol. 45 No. 2 (225) (2011)

In the present paper some systems of operators generated by Riemann–Liouville integral and derivative of orders $\alpha\in(0,1)$, and functions generated by Mittag–Leffler type functions are introduced. Some properties of these systems are investigated and for a certain class of functions the generalizations of Taylor–Maclourin type formulae are obtained. 

In the present paper the linear operators that depend on a normal pair of weight functions $\{\varphi, \psi,\}$ in the Banach spaces $L^p(D)$, where $D$ is the unit disk in the complex plane, are considered. It is investigated, for which values of p these operators are bounded.

In the present article a class of first order linear differential operators with unbounded coefficients is investigated. The compactness of operators is proved.

In this paper we investigate the Fredholm property of Wiener–Hopf operator for anisotropic boundary value problem for the Helmholtz–Schrödinger equation with the boundary conditions of the first and second type on the line y=0.

In the present paper we consider the Dirichlet problem for the fourth order differential-operator equation $Lu \equiv(t^{\alpha}u^{\prime\prime})^{\prime\prime}+t^{-2}Au = f$ , where $t\in(1, +\infty), \alpha\geq 2, f \in L_{2,2}((1, +\infty), H),~A$ is a linear operator in the separable Hilbert space H and has a complete system of eigenvectors that form a Riesz basis in H. The existence and uniqueness of the generalized solution for the Dirichlet problem are proved, and the description of spectrum for the corresponding operator is given.

The paper studies some singular integral operators with the Carleman shift. Sufficient conditions ensuring the invertibility of these operators are obtained. The scheme for construction of an invertible operator is given.

For 2-categories the notion of S-universality is introduced and investigated.

In this paper a three-layer plate with symmetrical structure to solve the prob-lem of determining the properties of the middle layer, which can propagate the harmonic wave in three-layer plate with phase speed equal to the phase speed of a single-layer plate.

Chair of Programming and Information Technologies, YSU In the present paper the Δ-equivalence problem of monadic logic programs (logic programs using only monadic functional and predicate symbols) is investigated. It is shown that contrary to the general case, the relation of Δ-equivalence is decidable in case of monadic programs. Our proof is based on the decidability of Rabin’s monadic second order logic of successor functions.

The effect of an electric field on the basic parameters of confined and interface polarons in cylindrical nanowires embedded in a non-polar matrix are studied theoretically for the first time. Analytical expressions for the quasi-onedimensional Fröhlich polaron self-energy and effective mass are obtained as functions of wire radius and strength of the electric field applied perpendicular to the wire axis, which may be of use at the interpretation of optical phenomena related to polaron motion in cylindrical nanowire, when the effect of an applied electric field competes with the size quantization.

In this paper we show by using the laws of pseudo-distributivity that every idempotent and commutative algebra with one n-ary operation satisfying the generalized entropic property is entropic.