No 4 (2012)

Cover Page
Articles
Necessary Optimality Conditions in the Problem with Phase Space Change
Maksimova I.S.

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
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Research of Analytical Function of the Conformal Field Theory
Vishnevskaya N.I.

Abstract

The integral of hypergeometric type is considered. This integral is met in the conformal field theory. The ordinary linear differential equation is received which decision is the studied integral.
Discrete and Continuous Models and Applied Computational Science. 2012;(4):15-24
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The Study of Splitting Method of Singularly Perturbed Initial Value Problems for Non-Autonomous Systems of ODE
Workneh A.Z.

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
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An Optimal Control Applied Problem with a Mixed Constraint
Skiba A.K.

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
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Analytical and Computational Investigations of Solutions of Boundary-Value Problems for the Quasipotential Equation
Amirkhanov I.V., Sarker N.R., Sarhadov I., Tukhliev Z.K., Sharipov Z.A.

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
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Laser Acceleration of Channeled Light Particles in Periodically Modulated Crystal
Serov V.V., Sergeeva T.A.

Abstract

An approach for the laser acceleration of the charged particles channeled in a periodically bent crystal have been investigated under the accounting for the transverse energy leveles quantization.
Discrete and Continuous Models and Applied Computational Science. 2012;(4):53-67
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Numerical Recovery of the Distribution Function on the Electrons Energyin Plasma on Radiation Spectrum
Andreev V.V., Ibragim B.I., Laneev E.B., Mouratov M.N.

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
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On Numerical Solution of Direct and Inverse Scattering Problems for Spherically Symmetric Potentials Dependingon Parameters
Puzynina T.P., Thach V.T.

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
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Analytical Approach to Analysis of Extremal Trajectories and Stability of Programmed Motion
Azimov D.M., Mukharlyamov R.G.

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
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Intrusion Detection using Genetically Generated Finite Automata
Fralenko V.P.

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
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Riemann’s Wavesin Chaplygin Gas
Vilca Chaicha M.B., Rybakov Y.P., Shikin G.N.

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
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The Concept of Reactive Power in Electrodynamics and Lagrange Structures of Wave Electromagnetic Fields
Kazakov O.A.

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
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Signal-to-Noise Ratio Enhancement by Spatial Averaging at Image Registration
Evtikhiev N.N., Krasnov V.V., Rodin V.G., Solyakin I.V., Starikov S.N., Cheryomkhin P.A., Shapkarina E.A.

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
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On the Description of Relativistic Motions in Terms of Coordinate Time
Kapȕscik E.

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
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DNA Nonlinear Dynamics With Non-classic Solitary Waves
Najera M.L., Aguilar J.A., Aguero M.A.

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
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Hawking Radiation in de Sitter Space: Calculation of the Reflection Coefficient for Quantum Particles
Red’kov V.M., Ovsiyuk E.M., Krylov G.G.

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
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Some Problems of Modern Cosmology and Spinor Field
Saha B.

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
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High-Energetic Radiation from Gas Discharge Associated with the Maximum Rate of Current Change
Sorokin L.V.

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
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Nashi avtory
- -.

Abstract

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