# No 1 (2009)

**Year:**2009**Articles:**12**URL:**https://journals.rudn.ru/miph/issue/view/512

## Articles

### Necessary Conditions of Optimality for 2-normality Systems

#### Abstract

In this paper controlled system with impulsive controls in the neighborhood of abnormal point is investigated. The concept of 2-normality which plays a greater role in the course of derivation of the first and second order necessary conditions for optimal control problem is introduced in this article. Sufficient conditions of 2-normality are resulted in this article. Besides that proximity of necessary and sufficient conditions of optimality for 2-normality systems is investigated.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):5-13

5-13

### Maximum Principle in a Problem of Maximization of the Income for Model of a Gas Deposit

#### Abstract

The model of functioning of a gas deposit is considered. The optimum control problem is put and dares over an Infinite Horizon. Cost of realisation of the gas is included in the criterion description, set by concave function.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):14-22

14-22

### Traffic Routing Problem on MPLS Network with Unicast Connections

#### Abstract

The Multiprotocol Label Switching (MPLS) technology is a solution to build multiservice network transport layer. When such networks are operated quality provisioning with optimal usage of network resources problems appear. In this paper traffic routing problem on MPLS network with unicast connections is formulated when network parameters are given. The network parameters are structure, bandwidth requirements, routing costs, delays and packet loss probabilities. The problem is formulated in terms of graph theory and multiobjective optimization. Numerical example calculated using simplex and weighted sum methods is also shown.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):23-33

23-33

### M|G|1 Queues with Batch Service and its Aplication to the Stream Control Transmission Protocol Performance Analysis. Part I

#### Abstract

In this paper we present a survey of M|G|1 batch service queues which was prepared under performance evaluation of the Stream Control Transmission Protocol (SCTP). The survey is organized in chronological order of the known publications and contains available until now results for probability measures of queues in which jobs are served in batches of fixed and variable size. Some probability measures of virtual waiting time are obtained for SCTP protocol performance analysis.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):34-44

34-44

### Some Symbolic-Numeric Methods for Calculation of Energy Eigenvalues for the Quantum Anharmonic Oscillators

#### Abstract

One-dimensional Shr.odinger's equation for the quartic, sexic and octic anharmonical oscillators is considered. The energy spectra of this quantum oscillators by the quantization of classical Lindstedt-Poincare trajectories, by the method of the Deprit-Hori normal forms and by using the power series are obtained. The comparison of obtained results are performed.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):45-55

45-55

### Equations of Motion of Rapidly Driven Systems

#### Abstract

A general theory of a large class of classical dynamical systems with an external rapidly oscillating driving action is proposed. The main results are the effective equations for the mean motion. The scope of the present work is to generalize the approach to the case when the fast perturbation contains odd and even terms and amplitudes may depend on velocities.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):56-61

56-61

### Data Processing by Method of Transformation of Functions and its Derivatives Values on Grids into Fourier Coefficients

#### Abstract

In this paper two practical problems are considered: function reconstruction from its or its partial derivatives perturbed values on a discrete grid. Formulation of stable reconstruction of a function with method of regularized expansion in Fourier series of Zernike polynomials is proposed. Calculations of stabilizing functionals are realized in computer algebra system Axiom.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):62-70

62-70

### Electroosmosis Flow in Slit Microchannel

#### Abstract

The process of electroosmotic flow in slit microchannel which thickness is of an order of several EDL thicknesses is investigated in this paper. The model and derived analytical solutions allow to predict velocity profiles and time of developing the steady state flow in cases of both altering and current electric field. The results of the simulation are in good agreement with the obtained experimental data.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):71-78

71-78

### Static Configuration with Spherical Symmetry in Conformal Gravitation: Vacuum Solution

#### Abstract

The oscillating model of conformal gravity is considered. The static solution is studied in vacuum-dominated conformal gravitation, which is modeled by scalar field χ(x). The vacuum solution (χ = 0, Tμν = 0) in Einstein's gauge φ(x) = φ0 = const being considered, the Newtonian potential is obtained. The significance of the additional term in the potential is also discussed.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):79-84

79-84

### Static, Cylindrically Symmetric Perfect Fluid Configurations

#### Abstract

We study the properties of static, cylindrically symmetric configurations of a perfect fluid in general relativity, with the equation of state p = ωε with arbitrary values ω = const. We thus include into consideration the types of fluids which are now actively studied in cosmology (dark matter, cosmic strings, domain walls, quintessence, cosmic vacuum, phantom matter). Exact solutions to the Einstein equations with such fluids have been obtained for arbitrary values of ω. For any ω, we prove the absence of a flat spatial asymptotic as well as an asymptotic like that of a cosmic string. We show that all such distributions, under some conditions on the integration constants, have a regular axis and a spatial infinity at which the energy density tends to zero (except for configurations with ω = −1/3, which corresponds to a gas of cosmic strings). Thus such a system has a finite energy per unit length along the symmetry axis. In particular, for stiff matter (ω = 1), this quantity is equal to the Planck value of energy per unit length.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):85-95

85-95

### Peculiarities of Light Scattering on the Rough Surface of a Gradient Waveguide

#### Abstract

Some peculiarities of light scattering in thin-film and gradient waveguides are found. For ion-exchange fabricated waveguides a developed model of refractive index function is proposed. The maximum sensibility of the roughness spectrum waveguide measurement method is derived for waveguides with different index functions in near-surface region.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(1):96-101

96-101

102-108