# No 1 (2008)

**Year:**2008**Articles:**11**URL:**https://journals.rudn.ru/miph/issue/view/514

### About Construction of No Autonomous System of DifferentialEquations on Given Particular Integrals

#### Abstract

The present paper recommends method of construction of no autonomous system of differential
equations with given properties of particular solutions. The conditions of stability
of the set of systems solutions are defined. The problem of construction of two-order system
of differential equations on given particular solution is considered.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(1):5-11

5-11

12-19

### A MathematicalModel of Call Center with Interactive Requests

#### Abstract

Now in Russia call centers market is growing roughly. All large companies have chosen
call centers as main way to contact their clients. Modern call centers allow to process both
voice requests and so-called internet-requests that not demand immediate reaction from an
operator: received by e-mail, fax, chat, etc. According market researches a share of internetrequests
makes 30% from the general number of client inquiries. The traffic this type of
requests produce have quite different characteristics from voice calls traffic. Nevertheless
majority of call centers performance evaluation techniques make no distinctions between
voice and internet-requests and use common Erlang-C model for calculations.
This work presents a model of call center with both types of requests as a priority queuing
system with bunker and two types of incoming traffic. An algorithm for calculation of stationary
probabilities for number of requests in service is proposed and comparative analysis
with Erlang-C model is given

**Discrete and Continuous Models and Applied Computational Science**. 2008;(1):20-27

20-27

### Calculation of Newton Potential of the Gravitating Configurationswith the Surface Close to the Spheroid by Symbolic andNumerical Methods

#### Abstract

An exact analytical representation of the heterogeneous perturbed ellipsoidal configuration
of the Newton gravitational potential to the inner point in is obtained. An expression for
the potential in is obtained in the form of a polynomial of the coordinates by the program
prepared in the system of symbolic mathematics MAPLE, and by numerical calculations
based on the regularized analogue of the Newton method. A formula for the potential to the
outer point out is found by the quadrupole approximation.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(1):28-42

28-42

### Multi-Layer Schemes for Solving the Time-Dependent Shr.odinger Equation

#### Abstract

The algorithm based on unitary evolution operator decomposition to generate in a
MAPLE and REDUCE packages multi-layer implicit schemes for numerical solving the
time-dependent Shroedinger equation is presented. The optimal methods for construction
of additional gauge transformations to extract symmetric operators needed for generation
economical algebraic evolution schemes with respect to spatial variables by the finite element
method are studied. The efficiency of the developed computational schemes till sixth
order with respect to the time step and till seven order with respect to the spatial step, are
demonstrated on the integrable model of oscillator in a time-dependent external field.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(1):43-53

43-53

### Elaboration of THz Surface Plasmon Spectroscopy Method

#### Abstract

Development of surface plasmon (SP) spectroscopy method in teraHertz (THz) spectral
range (30-100 сm 1 or 0.1-10 THz) utilizing free-electron laser (FEL) radiation is described
in the paper. The following issues are considered in it: 1) methods for THz SP excitation by
bulk radiation, as well as the ways of measuring their characteristics; 2) experimental results
on THz SP excitation on aluminum and copper surfaces by FEL radiation with wavelength of
110 and 150 m; 3) the procedure for the sample material THz dielectric constant calculation
using the measured SP complex refractive index; 4) a number of methods implementing THz
SP spectroscopy technique.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(1):54-65

54-65

### On the Structure of an Oscillating Neutrino. The StationaryTheory of Neutrino Oscillations

#### Abstract

The structure of the oscillating neutrino wave function is discussed in the context of the
stationary theory of neutrino oscillations. If one requires the superposition of neutrino states
with differing masses to be a solution of a single Dirac equation, then one can obtain the
equation for the oscillating neutrino mass. The problem of the fragmentation decay of an
oscillating neutrino to the incoherent mixture of neutrino mass states as well as the problem
of interaction of the incoherent neutrino mixture with neutrino detectors are also discussed.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(1):66-70

66-70

### The Palladium Phase Diagramin the Region of Liquid-Vapour Phase Transition

#### Abstract

On the basis of generalized Van-der-Waals equation, parameters of critical point of palladium,
for the first time were determinate. The new method of determination of thermodynamic
similarity parameter was developed. The binodal of palladium was calculated from
normal boiling point up to critical point. The spinodal of liquid phase in the region of positive
pressures and negative pressures was calculated. It is shown, that frequency homogeneous
nucleation of vapour bubbles in a vicinity of spinodal achieves values near 1028 cm 3s 1.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(1):71-75

71-75

### Standard Model in Hamiltonian Approachand Higgs Effect

#### Abstract

The vector bosons models including Standard Model (SM) are investigated in the framework
of the Dirac Hamiltonian method with explicit resolving the Gauss constraints in order
to eliminate variables with zero momenta and negative energy contribution in accordance
with the spectral postulate of operator quantization. This elimination leads to static interactions
in a frame of reference of the Hamiltonian formulation. We list a set of observational
and theoretical arguments in favor of these static interactions in SM. We show that the
Dirac Hamiltonian method admits the mechanism of spontaneous symmetry breaking in SM
by the initial data of the zeroth Fourier harmonic of the Higgs field that provokes masses
of vector and spinor fields without the Higgs potential of this zeroth harmonic. In this case,
the extremum of the quantum Coleman-Weinberg effective potential obtained from the unit
vacuum-vacuum transition amplitude leads to a new sum-rule for masses of fermions and
bosons and predicts a mass of the Higgs field 250 GeV.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(1):76-91

76-91

### On Physical Interpretation of Stationary Vacuum Axially SymmetricSolutions to the Einstein Equations

92-95

### Mass Spectrum ofScalar Particles in External Gravitational Field of Charged Black Holewith One Horizon

#### Abstract

In an external gravitational field of the charged black hole with one horizon the complex
scalar field is considered. By means of appropriate selection of the coefficients in the initial
equation of a scalar field it is led to the generalized equation of hyper geometrical type,
then to a canonical form of this equation, representing degeneration of the hyper geometrical
equation. Solving this equation which satisfies the requirements of limitation, is Laguerres
polynomial with a corresponding spectrum of special values. On the basis of this spectrum
expression for masses of the charged and neutral scalar particles is received.
As the charged astrophysical object will usually quickly be neutralized by surrounding
plasma it is considered, that the charged black holes do not represent the big interest from the
astrophysical point of view [1]. However, as it is marked by Chandrasekhar [2], the studying
of Reisner-Nordstrom solution describing charged black holes, allows understanding more
deeply properties of space-time in extreme conditions.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(1):96-99

96-99