No 1 (2011)

In this article there defined one of generalization of classical notion of chromatic number of a plane or a space defined, that is chromatic number with an interval of forbidden distances. Some upper bounds are obtained for this value with different intervals and the method of finding these results are described.

A problem of stable continuation of the heat conduction equation solution is considered. The continuation of the solution is performed from approximately defined boundary. The whole problem is treated as an incorrect Cauchy problem for the heat conduction equation with Cauchy data given on an arbitrary approximately defined surface.

We perform a waiting time analysis of a retrial queue with several heterogeneous servers and threshold control policy. The blocked customers are dispatched to the infinitely large orbit with FCFS service discipline. The system is analyzed in steady-state by deriving expressions for the Laplace transforms of the waiting time, the probability generating functions for the number of retrials made by a customer and for various moments of corresponding quantities. Some illustrative numerical examples and their discussion are presented.

In this paper we investigate a multi-rate elastic and non-elastic BBP (Binomial-Poisson-Pascal) traffic with prioritized calls. A mathematical model taking into account a thresholdbased dynamical resource allocation scheme is developed. The allocation and service scheme are dependent on calls priority and system load. This algorithm offers new possibilities for QoS levels guaranty in multi-rate systems. The equilibrium probabilities and formulas for different parameters are derived.

This paper deals with several aspects in time series modeling concerning estimation and tests of long memory, fractional integration, and cointegration, as well as applications to financial data. The aim of the paper is to develop new and improved estimation and testing techniques, in particular to extend existing work concerning fractional processes and also to introduce new areas of application. The formulation allows the widely used fractional autoregressive integrated moving average ARFIMA models and our asymptotic results provide a theoretical justification of the findings in simulations that the local Whittle estimator is robust to deterministic polynomial trends. Finally, we explore the existence of long memory in some financial time series and conclude using a novel approach in their exploration.

In our recent paper [1] we have shown in detail that the Ehrenfest paradox is not a paradox of the Special Theory of Relativity (STR). We also analysed the logical status of the widely spread statement that "moving clocks go slow". We underlined that very often these problems are treated very dogmatically. On the example of Tyapkin's works [2, 3] we describe the regretable influence of dogmatic approach in the interpretation of the STR on the critical thinking and approach.

In view of development of unary relational approach to description of physical interactions theories of direct interparticle action are discussed, that include the Fokker-Feynman-Wheeler electrodynamics, the theory of direct interparticle gravitational interaction, and the Hoyle-Narlikar theory of gravitation. These theories have several resemblances, main of which is implication of Mach's principle in them, according to which there is a relation between distribution of particles in the universe, their masses and gravitation constant. In the Hoyle-Narlikar theory and in the unary relational approach free action of a chosen particle is represented in the form of its interaction with the rest part of the whole universe. In present work correspondence between the Hoyle-Narlikar theory and the relational theory is set up, relation between their parameters is found, differences between these theories are pointed out, and relation between Mach's principle and cosmological coincidences is discussed.

Review of methods for studying temperature dependence of characteristics of optical waveguides fabricated by sol-gel technique is presented. The method of studying temperature properties of effective refractive index of waveguide modes with the help of thermoelectric module Peltier is proposed and approved. This method allows to widely expand the temperature researches of materials and waveguides made of them.