# No 4 (2012)

**Year:**2012**Articles:**19**URL:**https://journals.rudn.ru/miph/issue/view/535

### Necessary Optimality Conditions in the Problem with Phase Space Change

#### Abstract

Necessary optimality conditions are obtained for the optimal control problem with phase space change. Phase space change is caused by existence of several controlled objects. These problems have applications both in physics and economics.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):5-14

5-14

15-24

### The Study of Splitting Method of Singularly Perturbed Initial Value Problems for Non-Autonomous Systems of ODE

#### Abstract

With the help of non-autonomous version of the method of Splitting with new point of view, the paper studied singularly perturbed initial value problems for model systems of ODE. The proposed method will allow us to construct quasi-regular asymptotic solutions for linear Cauchy Problems and to formulate criteria for the stability of singularly perturbed quasi-linear problems.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):25-30

25-30

### An Optimal Control Applied Problem with a Mixed Constraint

#### Abstract

We consider a gas deposits group functioning model. The optimum control problem with a mixed constraint is stated and solved over a ﬁnite horizon. A maximum of accumulated production for a group of gas deposits is taken as the optimization criterion.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):31-43

31-43

### Analytical and Computational Investigations of Solutions of Boundary-Value Problems for the Quasipotential Equation

#### Abstract

Investigation of solutions of a boundary-value problem is carried out for the quasipotential equation with piecewise-constant potentials at various values of the parameters of the problem. The comparative analysis of the solutions of the quasipotential equation with the solutions of Schr̈odinger equation is performed.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):44-52

44-52

53-67

### Numerical Recovery of the Distribution Function on the Electrons Energyin Plasma on Radiation Spectrum

#### Abstract

The results of the numerical solution of the integral equation of the ﬁrst kind occurred under the operation of distribution function recovery on electrons energy through the spectrum of radiation are presented. The Tikhonov functional with the stabilizers of the ﬁrst and the second order is used.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):68-72

68-72

### On Numerical Solution of Direct and Inverse Scattering Problems for Spherically Symmetric Potentials Dependingon Parameters

#### Abstract

The scattering problem for the radial Schr̈odinger equation, in contrast to a statement of Cauchy’s problem, is formulated as a boundary value problem for a wave function with a non-linear asymptotic condition with exclusion of an unknown phase shift. The phase shift is determined after calculation of the wave function by taking into account its asymptotic behavior and applying the iteration schemes of a continuous analog of Newton’s method (CANM). The inverse problem for an equation with a potential depending on the parameters is reduced to minimization problem with respect to the parameters for the functional that describes the sum of squares of deviations of the speciﬁed values of phase shifts from the corresponding calculated values. Basic features of the computational schemes are demonstrated by solution of the problem with Morse’s potential which admits analytical solution and also by solving the problem with Woods–Saxon’s potential.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):73-86

73-86

### Analytical Approach to Analysis of Extremal Trajectories and Stability of Programmed Motion

#### Abstract

Analytical approach to analysis of optimal trajectories of a rocket and method of determining control actions for stable programmed motion are considered. It is shown that the analytical trajectory solutions can be used to test the existence of conjugate points on extremals. Control laws that can provide stable motion are discussed.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):87-95

87-95

### Intrusion Detection using Genetically Generated Finite Automata

#### Abstract

Two new methods for detecting network attacks using genetically generated ﬁnite automata with a) the transitions actions, and b) with the selected states are presented. The ﬁrst method is based on the “ﬂib” model that can predict changes in network activity on the basis of progressived analysis of network records in the KDD-99 format. The second method is an adaptation of a classical ﬁnite automata.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):96-102

96-102

### Riemann’s Wavesin Chaplygin Gas

#### Abstract

We have investigated propagation of Riemann waves in an ideal ﬂuid with negative pressure, the so-called Chaplygin gas. We consider barotropic motion of the medium when the pressure is P = P( ρ) in the assumption u = u( ρ), where u — the velocity, ρ — density of the medium. The system of hydrodynamic equations then reduces to a wave equation of the ﬁrst order, which describes a wave with variable speed. It is shown that these waves have deformed proﬁle, which leads to an ambiguous deﬁnition of ρ. In order to remove this lack in the original equation we have introduced a member with the second derivative, which leads to the appearance of waves with a stationary proﬁle which is a rarefaction wave.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):103-109

103-109

### The Concept of Reactive Power in Electrodynamics and Lagrange Structures of Wave Electromagnetic Fields

#### Abstract

The representation of reactive power for nonharmonic electromagnetic ﬁelds and divergent equation of reactive energy conservation are obtained. It is proved that reactive power and reactive power density are the functional of action and negative Lagrange’s function density (Lagrangian) respectively. It is shown that this Lagrangian can be used for detection the same space structure of electromagnetic ﬁeld as the structure of standing waves.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):110-121

110-121

### Signal-to-Noise Ratio Enhancement by Spatial Averaging at Image Registration

#### Abstract

Estimations of temporal and spatial noises and signal-to-noise ratios for image registration method of single exposure with spatial averaging were performed. Two necessary conditions for achievement of the maximum increase of signal-to-noise ratio were deﬁned. The obtained experimental results conﬁrm theoretical estimations of changing spatial resolution and achievable increase of signal-to-noise ratio in registered images. Joint usage for increase of signal-to-noise ratio of the considered method of single exposure with spatial averaging and the method of multiple exposure will allow to ﬂexibly combine requirements to the speed of image registration and to the quantity of resolvable elements in image.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):122-136

122-136

### On the Description of Relativistic Motions in Terms of Coordinate Time

#### Abstract

It is shown that it is possible to describe motions in a relativistically covariant way in terms of the coordinate time without using the notion of the proper time. For completeness we consider motions of Galilean and Einsteinian both subluminal and superluminal particles. The presented approach can easily be generalized to more general models of spacetime.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):137-143

137-143

### DNA Nonlinear Dynamics With Non-classic Solitary Waves

#### Abstract

The nonlinear Schr̈odinger equation was obtained by using the method of generalized coherent states (GCS) applied to the quasi spin conﬁguration of the DNA lattice model. In this model the DNA macromolecule is subjected to the inﬂuence of thermal phonons. By analyzing the nonlinear saturated Schr̈odinger equation, several non classical soliton-like solutions describing the hydrogen bonds are obtained. Among them there is a couple of compact-anticompact soliton that evolves as a healing mechanism for repairing the eventual open states of the hydrogen bonds.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):144-152

144-152

### Hawking Radiation in de Sitter Space: Calculation of the Reflection Coefficient for Quantum Particles

#### Abstract

Though the problem of Hawking radiation in de Sitter space-time, in particular details of penetration of a quantum mechanical particle through the de Sitter horizon, has been examined intensively there is still some vagueness in this subject. The present paper aims to clarify the situation. A known algorithm for calculation of the reﬂection coeﬃcient R j on the background of the de Sitter space-time model is analyzed. It is shown that the determination of R j requires an additional constrain on quantum numbers R ∕ℏ c ≫ j, where R is a curvature radius. When taking into account this condition, the value of R j turns out to be precisely zero. It is shown that the basic instructive deﬁnition for the calculation of the reﬂection coeﬃcient in de Sitter model is grounded exclusively on the use of zero order approximation in the expansion of a particle wave function in a series on small parameter 1 ∕ R 2, and it demonstrated that this recipe cannot be extended on accounting for contributions of higher order terms. So the result R j = 0 which has been obtained from examining zero-order term persists and cannot be improved. It is claimed that the calculation of the reﬂection coeﬃcient R j is not required at all because there is no barrier in the

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):153-169

153-169

### Some Problems of Modern Cosmology and Spinor Field

#### Abstract

In this report some burning problems of modern cosmology are discussed. The most popular models dealing with dark energy are also discussed in short. We specially stretch on the spinor model of ﬂuid and dark energy. It is shown that the model with spinor ﬁeld can resolve a number of standing problems of modern cosmology. It is noted that the non-trivial non-diagonal components of energy momentum tensor of spinor ﬁelds impose some severe restriction on the metric functions.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):170-180

170-180

### High-Energetic Radiation from Gas Discharge Associated with the Maximum Rate of Current Change

#### Abstract

The X-ray and gamma-ray radiation was registered in the moments of the maximum speed of current change (10 kA/ns) in the gas discharge tube. The collision of relativistic electrons with Krypton (Kr) and Xenon (Xe) as with metal vapor in the plasma discharge can intensify the X-ray emission due to their bigger atomic charge. Due to the freezing of heavy water in the cloud ice particles the concentration of Deuterium in them will be signiﬁcantly higher then in water vapor. The neutrons (2.45 MeV) and high energy protons (3.02 MeV) from lightning and thunderstorm can be produced in D–D nuclear fusion reactions. The high-energetic radiation from lightning and thunderstorm can be associated bought with proton capture and neutron capture. The fast neutrons should be slowdown to the thermal neutrons in the reaction of type ( n,n). The photon energies in gamma-ray spectrum can rise up to 19.8 MeV. The X-ray and gamma-ray signatures from lightning can be explained due to the Compton scattering eﬀect. The observation of the long period gamma ray radiation during the thunderstorm can be due to the decay of isotopes.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):181-188

181-188

### Nashi avtory

**Discrete and Continuous Models and Applied Computational Science**. 2012;(4):189-191

189-191