# No 3 (2008)

**Year:**2008**Articles:**11**URL:**https://journals.rudn.ru/miph/issue/view/531

## Articles

### Generalized Solution of Direct Problem for Modified Time-Dependent Transport Equation

#### Abstract

Solvability of the generalized solution for the time-dependent modified transport equation with initial and boundary conditions problem is proved. Modified transport equation differs from the common equation by replacement integrated composed function, being the solution, by a constant function, from the same class of the solution. That modification is more convenient for some nonlinear inverse problems in comparison with the common transport equation.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(3):5-12

5-12

13-21

22-30

### Analysis of Adaptive Multi-Rate System for Elastic Traffic

#### Abstract

Wide expansion of 3G networks in many countries and since the end of 2007 year in Russia as well sets new teletraffic problems. A lot of interactive services and high speed internet access produce great volume of elastic (data) traffic that composes significant part of total traffic in modern wireless networks. The use of classical Erlang multiservice model for 3G networks modelling is restricted due to the system assumes only constant bandwidth utilization by calls. In this work we propose adaptive multirate system in the form of multiserivce queueing system with elastic calls, which removes above restriction from Erlang multiservice system. An effective approximate algorithm for calculation of steady-state distribution and formulas for main QoS parameters are given. Obtained results can be applied by cellular 3G operators in their activities.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(3):31-39

31-39

### Foundational Aspects of Theory of Statistical Function Estimation and Pattern Recognition

#### Abstract

This paper provides a gentle introduction to the foundational ideas, concepts and results in the field of science dedicated to the theory of statistical function estimation and pattern recognition. The so-called VC Theory of Vapnik and Chervonenkis is introduced and explored gradually. The emphasis is placed on helping the reader appreciate the importance of the extension of the classical law of large numbers to function spaces, and the key role that "new" concepts such as Empirical Risk Minimization (ERM) principle, ERM consistency, VC dimension, and complexity control play in constructing algorithms that yield function estimators with optimal properties. As much as possible, each key concept is introduced via a tangible example, with the hope of helping the reader grasp the essential core of the foundational concept under exploration.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(3):40-54

40-54

### Asymptotic Solution of Boundary Problem for Relativistic Finite-Difference Schrцdinger Equation with Singular Oscillator Quasipotential

#### Abstract

Using the asymptotic methods the solution of boundary problem for the relativistic finite-difference Schrцdinger equation with the singular oscillator quasipotential is studied. For this problem eigenvalues and eigenfunctions are considered. It is shown that they have correct non-relativistic limits.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(3):55-68

55-68

### Multi-Layer Schemes for Solving Time-Dependent Schrцdinger Equation by Finite Element Method

#### Abstract

The symmetric implicit operator-difference multi-layer schemes for solving the timedependent Schrцdinger equation based on decomposition of the evolution operator via the explicit Magnus expansion up to the sixth order of accuracy with respect to the time step are presented. Reduced schemes for solving the Cauchy problem of a set of coupled timedependent Schrцdinger equations with respect to the hyperradial variable are devised by using the Kantorovich expansion of the wave packet over a set of appropriate parametric basis angular functions. The implicit algebraic schemes for numerical solving the problem with symmetric operators, using discretization of the component of the wave package by hyperradial variable by the high order finite-element method are formulated. The convergence and efficiency of the numerical schemes are demonstrated in numerical calculations of the exactly solvable models of one-dimensional oscillator with time-dependent frequency, two-dimensional oscillator in time-dependent external field by using the conventual angular basis.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(3):69-84

69-84

### Mathematical Modeling of Sexual Ratio of Biological Populations

#### Abstract

Using a modified simple model proposed by Redfield we try to explain population dynamics of species with changing sexual ratio. In the model the probability of offspring's sex is represented by a number in parents' genes and so that can be an adopted parameter to the current environment. According to our results the population can survive under harsh condition only if the number of males and the number of females are equal, only in this case the population posses more genetic viability.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(3):85-91

85-91

### On Nonlinear Generalization of Yukawa Meson Theory of Nuclear Forces

#### Abstract

We consider a nonlinear generalization of the Yukawa meson theory of nuclear forces that belongs to the class of theories with the Lagrangians proposed by L. Shiff. Relying on this basis, we study nonlinear equations for a nuclear potential and dynamic equations for nuclear particles which contain one unknown function of this potential. To found it, we suggest a principle which implies the proportionality of the nuclear field potential to the potential energy of nucleons in the field. The found equations are applied to study the dynamics of nuclear particles moving under the simultaneous action of nuclear and electromagnetic forces. It is shown that in the case of sufficiently intensive interaction of nucleons, the suggested equations give the value 14.9 for the dimensionless constant of strong interaction close to the experimental value.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(3):92-98

92-98

### Influence of Salinity on Water Flow in Porous Media

#### Abstract

The percolation model for electrokinetic flow of electrolyte in porous media is developed. In the context of this model taking into account ionic concentration of solution, zeta-potential, pore-metric curve and surface properties of porous media analytic dependence for filtration rate is obtained. The model results are in good agreement with experimental data obtained by authors (filtration of saline water in sandstone samples). Determined that in the presence of sufficient amount of capillaries with radius comparable with the thickness of EDL, the rate of filtration noticeably decreases as against the velocity of filtration without influence of EDL, that is interpreted as electro-viscous effect in porous media.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(3):99-106

99-106

### Pravila oformleniya statey

**Discrete and Continuous Models and Applied Computational Science**. 2008;(3):107-107

107-107