No 3.1 (2010)

Properties of special solutions of potential type for a linearized Kawahara equation in a half-strip are studied.

We consider Banach spaces continuous sections when every fiber is Banach lattice. A some versions of the Banach-Stone theorem was obtained.

In the paper we deal with a Markovian queueing system with heterogeneous servers and constant retrial rate. The system operates under a threshold policy. The system is described by quasi-birth-and-death process with infinitesimal matrix depending on the threshold levels. Using a matrix-geometric approach we perform a stationary analysis of the system, derive expressions for the mean performance measures and formulas for optimal threshold levels.

We consider a model of a single-link network serving multicast traffic. A recursive algorithm for computing blocking probabilities and other characteristics is given. It is also shown that the inaccuracy of computing blocking probabilities for multicast traffic with the use of Kaufman-Roberts recursive formula is unacceptable.

The problem of propagation of a plane monochromatic linearly polarized electromagnetic wave through a piecewise homogeneous dielectric structure (diffraction grating) without absorption, the characteristic dimensions of inhomogeneities is comparable with the wavelength of optical radiation or less than it. The problem is solved for the polarization. The case of conical diffraction is described, also the problem is formulated in the case of a lattice of optically anisotropic material.

By a rigorous logical analysis we show that the Ehrenfest paradox related to the relativistically rotating disc is not a paradox of the Special Theory of Relativity as it is usually treated in the literature because, as we proved rigorously, it does not follow from the principles of the Special Theory of Relativity but - contrary to this - contradicts them. We also analyse the logical status of the widely spread statement "moving clocks go slow" within the framework of the Special Theory of Relativity. Using the methods of the symbolic logic we show that this statement with correct interpretation of the meaning of the notion that the clock goes slow is, strictly speaking, at least misleading. We discuss the obtained results.

For the describing of a system under the combined quantum and thermal influences, it is offered two approaches each of them is a thermofield analogue of Clausius'classical and Einstein's statistical thermodynamics accordingly. We call them as Thermofield Thermodynamics and Thermofield Statistical Thermodynamics. We start from the thermofield vacuum and make a consent between basic notions of the quantum mechanics and thermodynamics. We suppose to consider the thermofield vacuum as an effective thermobath and ground stationary state as an thermal equilibrium state. On this ground we introduce such notions as effective temperature and effective entropy and get possibility to describe systems under combined quantum and thermal influences.

For the first time, we have measured adhesion forces between normal and malignated tissues extracted from human stomach epithelium and the tip of an atomic force microscope. We have found a significant decrease (more than by an order of value) of the adhesion forces of malignated cells, and their contact stiffness, as well.