Vol. 48 No. 1 (233) (2014)

There are five precomplete classes of De Morgan functions, four of them are defined as sets of functions preserving some finitary relations. However, the fifth class – the class of zigzag De Morgan functions, is not defined by relations. In this paper we announce the following result: zigzag De Morgan functions can be defined as functions preserving some finitary relation.

In the present paper an approach to construct algebraic two-level preconditioners for the matrices of normal systems arising in data fitting by least squares method with piecewise linear basis functions is proposed. The approach is based on using hierarchical grids with their subdivision into substructures and corresponding partition of the matrices. Estimates for condition numbers of preconditioned matrices are obtained.

In this article obtained operator analogue of well-known S. Bernstein Theorem about approximation on the real axis of a bounded and uniformly continuous function by entire functions of Bernstein space.

In this paper we investigate the deformation of the real part of $\beta$-uniform algebra on a locally compact Hausdorff space. We prove that if the deformation semigroup contains at least one deformation other than the affinity, then $\beta$-uniform algebra coincides with the algebra of all complex-valued bounded continuous functions.

In the present paper we will consider the behavior of Fourier coefficients with respect to the Walsh double system after modification of functions. We prove that for any function $f(x,y)\in L^{p}[0,1]^2$ one can find a function $g\in L^{p}[0,1]^{2}$ coinciding with $f(x,y)$ on a small measure such that the non-zero coefficients of $g(x,y)$ are monotonically decreasing over all rays by absolute values.

In the paper [1] the notion of the $\langle\rho_j,\ W_j\rangle$ absolutely monotone function was introduced. In the present paper we give some examples of sequences $\{W_j(x)\}_0^{\infty},$ consider the corresponding classes of $\langle\rho_j,\ W_j\rangle$ absolute monotone functions and study the problems of thei representation.

Bending vibrations of electroconductive plate-strip in the longitudinal magnetic field are being investigated. The problem is solved on the basis of hypothesis of magnetoelasticity of thin bodies by the use of the model of the perfect conductor for boundary condition on the surface faces of plate-strip. The numerical results of the frequency vibrations and damping coefficients are brought, based on the intensity of magnetic field.

The article is devoted to the optimization of monadic logic programs and goals (programs and goals, which do not use functional symbols of arity $>1$ and use only predicate symbols of arity 1). A program$\ P$ is terminating with respect to a goal $G$ if an SLD-tree of $P$ and $G$ is finite. In general, monadic programs are not terminating. Program and goal transformations are introduced, by which a monadic program $P$ and a variable-free monadic goal $G$ are transformed into $P{'}$ and $G{'}$, such that $P{'}$ is terminating with respect to $G{'}$ and $P\models G$ if and only if $P{'}\models G{'}$.  Note that the transformed program $P{'}$ is the same for all goals.

In this paper a recursive approach is suggested for the problem of Minimum Linear Arrangement (MINLA) of a graph by length. A minimality criterion of an arrangement is presented, from which a simple proof is obtained for the polynomial solvability of the problem in the class of bipartite, G-oriented graphs.

The influence of water soluble cationic 3N- and 4N-pyridyl porphyrins with different peripheral substituents on melting parameters of Calf Thymus DNA has been studied. It was shown, that the presence of porphyrin changes the shape and parameters of DNA melting curve. The decrease of T in the presence of 3N-porphyrins is observed. Because of the intercalation binding mechanism occurs in GC-rich regions of DNA, which is the reason for the decrease melting interval. While even at the low relative concentration for 4N-porphyrins already the external binding mechanism “turns on” and as a result the change in the melting parameters of DNA upon complexation with these porphyrins is not observed.

The liquid crystalline phase formation by short DNA fragments within the flexible polymer water containing matrix as well as the influence of interaction parameters and volume fraction of polymer on the orientational ordering have been investigated. It has been shown that liquid crystalline order formation in ds-DNA, immeresed in the polymeric matrix occurs with increase of the volume fraction. The volume fraction of transition between isotropic and nematic phases depends on value of the temperature dependendt Flory–Huggins parameter. The obtained results show the effect of the polymer matrix on the ordering in DNA molecules.

We consider the formation of the surface plasmon polariton whispering gallery modes in the convex cylinder cavity. Developed theoretical model allows obtaining the closed-form expressions for the mode field distributions, resonant frequency, as well as the emitting and dissipative losses in the structure in a broad wavelength range. The obtained results give opportunity to find optimal conditions for efficient emission in convex cylinder cavity and serve as practical guidelines for stimulated emission.