# No 1 (2011)

**Year:**2011**Articles:**19**URL:**https://journals.rudn.ru/miph/issue/view/527

## Articles

5-13

### On the Chromatic Numbers of R2 and R3 with an Intervalof Forbidden Distances

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):14-29

14-29

### Investigation of Controllability ofDifferential Systems with Special Type Control Effects

#### Abstract

The work is initiated by the physical applications. We investigate the controllability of the system
x˙ = f(x) + B(t)u,
where B(t) = B1 cos wt + B2 sin wt. The control action has the special structure set by the physical application. For example, the similar control actions exist in the problems of theaircraft landing in the conditions of wind disturbance, or changing the incline of the orbit plane of the space satellite. The article describes the controllability specifications for theproblem in the form of the corresponding theorems.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):30-35

30-35

### On Stable Continuation of the Heat Conduction Equation Solution from Approximately Defined Boundary

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):36-43

36-43

### On a Stability of Several-Side Differential Game with Many Goals Sets

#### Abstract

Stability of differential game of several sides with many aim sets relative to informational noise is considered. It is proved, that strategies, which are extremal to stable bridges guarantee stable task solution relative to informational noise.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):44-53

44-53

### Waiting Time Distribution of the Queue with FCFS Orbit and Threshold Policy

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):54-74

54-74

### A Queueing System with Negative Claims, InfiniteBuffer and Finite Bunker for Superseded Claims

#### Abstract

Study is performed of the queuing system with Poisson incoming flows of ordinary and negative claims. For ordinary claims, there is an infinite-capacity buffer. The arriving negative claim knocks out an ordinary claim queued in the buffer and moves it to a finite-capacity buffer of superseded claims (bunker). If upon the knock out of the ordinary claim bunker is full, knocked out claim is lost. If the buffer is empty, then the negative claim discharges the system without affecting it. After servicing the current claim, the server receives a claim from the buffer or, if the buffer is empty, the bunker. The claims arriving from both the buffer and bunker are served exponentially with the same parameter.
Expressions for the stationary joint probability distribution of number of claims in buffer and bunker and for main probabilistic characteristics of the system were obtained.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):75-81

75-81

### Mathematical Model of Multi-Rate BBP Traffic with Priorities Policy

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):82-90

82-90

### On Analysis of M[X]|G|1|r Queuing System

#### Abstract

The paper presents results of analysis of M[X]|G|1|r queuing system with vacations and batch arrival. The relationship between the probability distributions of systems with infinite and limited capacity is shown. An expression for generating function of queue length distribution for the case of r < ∞ is obtained, as well as formulas for stationary probabilities, call loss probability and other characteristics.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):91-97

91-97

### Long RangeMemory Modeling and Estimation for Financial Time Series

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):98-106

98-106

### Graviatoms Taking Account of Relativistic Corrections and Minihole Rotation

#### Abstract

Gravitationally bound quantum systems, so-called graviatoms, consisting of a minihole and a charged particle have been considered [1, 2]. Relativistic corrections, particle spin and minihole rotation were taken into account. A frequency, oscillator strength and intensity of radiation were calculated for the dipole transition 2p → 1s.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):107-115

107-115

### A Note on a Nonstandard Interpretation of the Special Theory of Relativity

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):116-117

116-117

118-120

### Mach's Principle in the Hoyle-Narlikar Theory and in the Unary Relational Approach

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):121-133

121-133

### New Method of Constructing Inflationary Solution in a Chiral Cosmological Model

#### Abstract

New method of constructing inflationary solution in a chiral cosmological model is proposed for spatially-flat, open and closed Universe. Inflationary solutions for the models with the exponent and power law scale factor in the framework of the two-component chiral cosmological model are obtained. The special distribution between chiral fields, when one of them is responsible for the dynamics in the spatially-flat section and another - for the warping of this section, is suggested.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):134-143

134-143

### Study of Thermooptical Coefficient of Sol-Gel Waveguides

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):144-155

144-155

### Towards 90th Anniversary of L. Deryugin

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):156-157

156-157

### Nashi avtory

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):158-159

158-159

### Pravila oformleniya statey

**Discrete and Continuous Models and Applied Computational Science**. 2011;(1):160-160

160-160