No 4 (2012)

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.

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.

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.

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.

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.

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.

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.

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

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.