# No 2.1 (2010)

**Year:**2010**Articles:**15**URL:**https://journals.rudn.ru/miph/issue/view/523

## Articles

### The Asymptotic Behavior of Solutions of Two Problems of Dynamic of Exponentially Stratiﬁed Fluid

#### Abstract

This article is devoted to studying the components of solutions of two problems of dynamics. The problems describe the small ﬂuctuations of the exponentially stratiﬁed and uniformly rotating ﬂuid in the Cartesian system of coordinates (x1,x2,x3) rigidly connected with the rotating ﬂuid. The ﬂuid is stratiﬁed along the axis Ox3 coinciding with the axis of rotation: ρ0(x3) = Aexp(−2βx3), where β > 0 is a parameter of stratiﬁcation. The asymptotics of the components of solution are constructed for both problems.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):5-10

5-10

11-25

### The MAP/G/1/ Discrete-Time Queueing System with Inversive Service Order and Probabilistic Priority

#### Abstract

This paper considers a discrete-time queueing system MAP∕G∕1∕∞ that is determined as follows. Upon arrival into the system of a new customer its length is compared with the (remaining) length of the customer in the device and with some probability which depends only on this two lengths, a new arrival will occupy the server while pushing out a servicing customer to the ﬁrst place in the queue, and with the supplemental probability, alternatively, the newly arrived one occupies the ﬁrst position in the queue (inversive service order and probabilistic priority). The main stationary characteristics of such systems behavior have been found. A number of numerical examples are presented according to found analytical formulae.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):26-36

26-36

### On Two Queuing Systems with «Transparent» Calls Applying to the Multicast Network Analysis

#### Abstract

Two multicast service models with diﬀerent users behavior are considered. We present corresponding mathematical models as queuing systems M|G|1|0|T with arbitrary distributed service times and transparent (T) calls. Calculation formulas for stationary probabilities of service customers and other characteristics are obtained.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):37-41

37-41

### A Method to Solve the Resource Allocation Problem in the Design of Virtual Private Networks with Unicast and Multicast Connections

#### Abstract

This paper is concerned with the resource allocation problem in the design of virtual private networks (VPNs) with unicast and multicast connections. The objective is to maximize the total network revenue that depends on blocking probabilities. Requests to set up connections are blocked if there is not enough available bandwidth on links of the infrastructure network, e.g. IP/MPLS (Multiprotocol Label Switching). We develop an approximate method to allocate bandwidth to VPNs based on revenue sensitivities calculation considering the implied costs - expected revenue loss due to capacity reduction when a new unicast or multicast connection is set up.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):42-53

42-53

### Mathematical Model of the Dynamic Behavior of RED-Like System Parameters

#### Abstract

In this paper a mathematical model of an autonomous system of three ordinary diﬀerential equations depending on parameters algorithm for active queue management such as Random Early Detection (RED) is constructed. The method for self-oscillation area evalution and critical (stationary) point selection is introduced. The patametric and phase portraits for systems with algorithms RED, GRED, DSRED and ARED are analyzed.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):54-64

54-64

### On the Solving of Stochastic Problem of Closure by Designings Method

#### Abstract

One of the inverse problems of dynamics - the closures problem by given properties of motion, no depending from velocities, into the class of stochastic diﬀerential Itos equations of second order is considered. The necessary and suﬃcient conditions of the existence of given integral manifold of constructed system of stochastic equations are received. The linear case of posed problem are separately investigated.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):65-71

65-71

### Stability of Program Manifold Single-Tuned System

#### Abstract

The single-tuned systems possessing by given program manifold are considered. The necessary and suﬃcient conditions of the programm manifolds absolute stability with respect to vector-function ω are obtained when the matrix of state has special structure.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):72-78

72-78

### On Some Aspects of Applying Polynorms on the Algebras in Physics

#### Abstract

In this article it is considered some opportunities of using in physics the pseudo-norms of degree above 2 (polynorms) on the hypercomplex algebras, ﬁrst of all on the example of the biquaternion algebra. Due to above a new point of view on the number of the known questions appears. In particular it is shown that the 4-norm consideration in the ﬁeld theory makes natural the transition from the Maxwells electrodynamics to the Born-Infelds nonlinear electrodynamics. Besides the algebraic approach shows naturalness of the addition the nonlinear term into the mezon Lagrangian of the nuclear forces oﬀered by T. Skyrme what supposedly can improve some properties of the model. Thus the algebraic consideration allows to clear some intuitive ﬁndings in the nonlinear ﬁeld theories, and also to bring in them some additional elements of rigidity.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):79-94

79-94

### Extension of Abelian Gauge Symmetry

#### Abstract

A generalization of the U(1) gauge symmetry group by permutation of the generator and the unity is proposed. Thus a commutative extension of the symmetry group is obtained. The two-dimensional matrix representation of this group contains matrices with determinants both 1 and −1. The aim of the present work consists in establishing the necessity of existence of so-called imaginary charges and electromagnetic ﬁelds with negative energy density. Some cosmological issues of the existence of such ﬁelds are discussed.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):95-100

95-100

### Computer Detection of Skin Fragments on Face Images

#### Abstract

The problem of the automatic skin fragments detection on images of the persons is considered. The algorithm and corresponding program were designed. The series of sample images on which one must to determine skin fragments are used as input data. C# language was used for realization of the program. Designed application has a good search speed and has the suitable user interface.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):101-103

101-103

### Solution of the Electromagnetic Waves Propagation Through a Stratiﬁed Medium Problem

#### Abstract

The problem of plane monochromatic linearly polarized electromagnetic wave diﬀraction through a stratiﬁed nonabsorbing medium is solved by means of general Maxwell equations solution expansion on fundamental solutions system for each layer, in case of isotropic media - for each separate polarization. In case of isotropic media for one (TE or TM) polarization the problem is equivalent to one of solving a linear algebraic equations system - two boarder equations on each boarder. In case of general monochromatic polarized electromagnetic wave the problem is equivalent to the solution of linear algebraic equations system with four equations on each boarder. In general the dimension of linear algebraic equations system is 4(m + 1), where m is the number of layers. In case of anisotropic media the problem must be solved for both TE and TM polarizations simultaneously, the coeﬃcient matrix of diﬀerential equations system for each layer doesnt have zero blocks.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):104-106

104-106

107-109

### On Stable Solution for a Mixed Boundary Value Problem for Laplace Equation with the Approximately Deﬁned Boundary

#### Abstract

A non-stationary heat conduction equation treated as an incorrect Cauchy problem is considered. Temperature ﬁeld is given on an arbitrary surface. The continuation of that temperature ﬁeld toward heat sources is performed.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):110-112

110-112

### Our authors

**Discrete and Continuous Models and Applied Computational Science**. 2010;(2.1):113-114

113-114