Vol. 46 No. 2 (228) (2012)

In this paper it has been proved that each normal automorphism of the n-periodic product of cyclic groups of odd order $r\geq1003$ is inner, whenever r divides n.

The paper studies a initial-boundary value problem for a class of second order degenerate pseudohyperbolic equations. We prove the existence and uniqueness of the problem in the appropriately constructed functional space.

One of the problems in the theory of coding is the code building of a maximum volume for the proposed additive channel. In this paper we have found and consequently presented the upper and the lower bounds for the code volume, which corrects the errors of the additive channel.

In the present work it is shown that the set $D=\{\sum \limits^{\infty}_{i=o}\delta_i2^{N_i} : \delta_i=0,~1\},$ for every sequence $N_0 < N_1 <…< N_i <… $ of natural numbers can be changed into the set of the form $\Lambda = \{k + o(\omega(k)) : k \in D\},$ where $\omega(k)$ is an arbitrary, tending to infinity at $k\rightarrow\infty$ sequence, such that $\Lambda$ is the spectrum of universality for Walsh system. 

In this paper a few new types of random contraction and dilation schemes are considered. In particular, four one-sided additive schemes and two two-sided additive schemes are represented. All schemes has been built for sample extremes and exponential random variables. Characterizations of distributions for all those schemes are obtained.

A contact problem for a solid isotropic homogeneous elastic semi-infinite plate, strengthened by a solid homogeneous infinite elastic stringer (IES), has been investigated under assumption that the homogeneous IES is welded (glued) to the semi-infinite plate parallel to its boundary and is at a finite distance from that boundary. The contact pair (plate–stringer) was simultaneously deformed by uniformly distributed horizontal tensile stresses of constant intensity acting on the infinity of the plate, and by a concentrated force applied to the stringer and directed along the axis of stringer. The problem was formulated as a singular integral equation with kernel consisting of singular and regular parts. Then for solution of this equation the generalized Fourier integral transform was used, by means of which this integral equation was reduced to a functional equation with respect to the Fourier transform of unknown function. The closed solution of the contact problem was constructed in an integral form. The tangential contact forces and normal stresses arising in the IES were determined. Asymptotic formulas describing the behavior of stresses both near and far from the application point of concentrated force were obtained.

The functional programming language, which uses the set {car, cdr, cons, atom, eq, if_then_else} of built-in functions is Turing complete (see [1]). In the present paper the minimality of this set of functions is proved.

We study the minimum linear arrangement of the graphs (MINLA) on transitive oriented graphs. We prove that MINLA of transitive oriented graphs is NP-complete.

The possibility of forced quenching of defects in cholesteric liquid crystals with negative dielectric anisotropy has been experimentally examined. It was experimentally shown for the first time that under homeotropic boundary condi-tions the sharpness of edges of photonic band gap in cholesteric liquid crystals with negative dielectric anisotropy increases in the course of quenching of defects.

Recently the Fermi LAT collaboration reported on the detection of high energy $\gamma$-ray signal from giant lobes of the radio galaxy Centaurus A. It is shown that if the $\gamma$-rays had originated from the inverse-Compton scattering of cosmic microwave background photons for the equipartition magnetic field of 2 μG, the Fermi LAT would not detect $\gamma$-rays from the lobes of Centaurus A. However, the detected $\gamma$-rays may be produced in hadronic interactions, namely in interactions of high energy protons with low density plasma followed with the production of pions, the neutral component decaying into 2 $\gamma$-quanta. In this article we study the hadronic origin of $\gamma$-rays, and estimate the total energy of protons assuming a power-law proton distribution with an exponential cut-off.