## No 4 (2009)

**Year:**2009**Articles:**11**URL:**http://journals.rudn.ru/miph/issue/view/513

Articles

Fixed Points of h-completely Continuous Multivalued Mappings and Inequalities in Spaces with the Cone

###### Abstract

In the first part of the paper a new class of multivalued mappings is introduced and studied. This mappings have convex but non-compact images. For the mappings of this particular class we are proving fixed points theorems, which are used in the second part of the paper to study solvability of inequalities in spaces with the cone.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):5-13

Application of the Method of Guiding Functions to Problem of Bifurcation of Periodic Solutions of Differential Inclusions

###### Abstract

In this paper, applying the method of guiding functions and of integral guiding functions we consider the problem of global bifurcation of periodic solutions of the family of one-parameter ordinary differential inclusions.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):14-24

A Nonparametric Stochastic Dynamics Model of Interest Rates

###### Abstract

We propose a new arbitrage-free nonparametric stochastic dynamics model of interest rates within the Heath-Jarrow-Morton framework using infinite dimensional stochastic calculus. The model yields strictly positive spot forward rates, allows for observation errors and has a straightforward algorithmic implementation.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):25-37

Numerical Investigation of Renormalization Group Equations in a Model of Advected Vector Field by Anisotropic Stochastic Environment

###### Abstract

Using the field theoretic renormalization group the influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of passively advected transverse vector field by an incompressible turbulent flow is investigated. The velocity field is taken to have a Gaussian statistics with zero mean and defined noise with finite time correlations. It is shown that the inertial-range scaling regimes are given by the existence of infrared stable fixed points of the corresponding renormalization group equations with some angle integrals. The analysis of integrals is given. The problem is solved numerically and borderline spatial dimension below which the stability of the scaling regime is not present is found as a function of anisotropy parameters.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):38-46

Some Iteration Methods with High-Order Convergence for Nonlinear Equations

###### Abstract

In this paper the iteration methods with high-order convergence for nonlinear equations are studied. It is shown that all the iteration methods with third-order convergence are equivalent to the standard Tchebyshev method. The acceleration of the convergence of the Newton method is also considered. New iteration methods on the procedure discussed above are proposed. Comparison between different iteration methods is given by test examples.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):47-55

A Study of Impedance, Frequency and Parametric Excitation of Oscillators

###### Abstract

One dimensional and tow dimensional harmonic oscillators are described. According to B. I. Zeldovich article the definition of impedance is introduced. Exploration of small parametric oscillations of impedance and frequency is made. By numerical solution of lineal ODE systems (for 1D and 2D case) it was shown, that impedance plays the key role in the parametric resonance phenomena.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):56-62

Torsion of a Multilayer Prismatic an Anisotropic Rod of Rectangular Cut, Composed from Orthotropic Materials

###### Abstract

Properties of distribution of pressure and displaycements is carried out for separate layers of a multilayered anisotropic rod. Efficiency of a layered design under the torsion can be estimated through the received results.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):63-75

Letter to Editor: Paradox. An Electrical Current Circuit in Electric Field

###### Abstract

The Poynting vector, which exists in crossing electric and magnetic fields, in reality represents energy flux density.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):76-78

Correlations in Quantum Mechanics as Origin of Modified Newtonian Dynamics

###### Abstract

We present derivation of modified Newtonian force from quantum mechanics with Coulomb potential. We show, that MOND-like theory arises in classical limit of quantum dynamics if nontrivial correlations of canonical variables are taken into account.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):79-82

Fluctuation Theory of Protective Nanolayers on Metals in the Aggressive Electrolytes

###### Abstract

In this article the mathematical model of inhibitiring nanolayer is exposed. The latter is formed by the mechanism of heterogeneous germ-formation on energetically non-uniformed surface S of the real anodic dissolution metal. There considered the rise of a fluctuation ΔVф of electrolyte on the surface S. Their saturation by the ions components is described by the classical equations of the ionic mass transfer. Every volume ΔVф can be a mother phase for the germ of inhibitor. There considered the kinetics of germ-formation and the evolution of germ given by the change of the mother phase.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):83-94

Investigations of an Optoelectronic Device for Angular Displacements Measurements with Use of a Deep Phasetype Reflective Grating

###### Abstract

An optoelectronic device for measurements of small angular displacements based on a diffraction of a laser beam on a deep reflective phasetype grating was suggested and investigated. The grating's depth is about several wavelengths. The zero diffraction order's power dependency on the incident angle of a laser beam was investigated theoretically and experimentally. There were found conditions when linear conversion of angular vibrations into changes of power of zero order took place. The experimentally measured sensitivity of the device was rad with channel bandwidth of 800 Hz and signal-to-noise ratio 10.

**Discrete and Continuous Models and Applied Computational Science**. 2009;(4):95-101