No 1 (2008)

The present paper recommends method of construction of no autonomous system of differential equations with given properties of particular solutions. The conditions of stability of the set of systems solutions are defined. The problem of construction of two-order system of differential equations on given particular solution is considered.

Now in Russia call centers market is growing roughly. All large companies have chosen call centers as main way to contact their clients. Modern call centers allow to process both voice requests and so-called internet-requests that not demand immediate reaction from an operator: received by e-mail, fax, chat, etc. According market researches a share of internetrequests makes 30% from the general number of client inquiries. The traffic this type of requests produce have quite different characteristics from voice calls traffic. Nevertheless majority of call centers performance evaluation techniques make no distinctions between voice and internet-requests and use common Erlang-C model for calculations. This work presents a model of call center with both types of requests as a priority queuing system with bunker and two types of incoming traffic. An algorithm for calculation of stationary probabilities for number of requests in service is proposed and comparative analysis with Erlang-C model is given

The algorithm based on unitary evolution operator decomposition to generate in a MAPLE and REDUCE packages multi-layer implicit schemes for numerical solving the time-dependent Shroedinger equation is presented. The optimal methods for construction of additional gauge transformations to extract symmetric operators needed for generation economical algebraic evolution schemes with respect to spatial variables by the finite element method are studied. The efficiency of the developed computational schemes till sixth order with respect to the time step and till seven order with respect to the spatial step, are demonstrated on the integrable model of oscillator in a time-dependent external field.

The structure of the oscillating neutrino wave function is discussed in the context of the stationary theory of neutrino oscillations. If one requires the superposition of neutrino states with differing masses to be a solution of a single Dirac equation, then one can obtain the equation for the oscillating neutrino mass. The problem of the fragmentation decay of an oscillating neutrino to the incoherent mixture of neutrino mass states as well as the problem of interaction of the incoherent neutrino mixture with neutrino detectors are also discussed.

The vector bosons models including Standard Model (SM) are investigated in the framework of the Dirac Hamiltonian method with explicit resolving the Gauss constraints in order to eliminate variables with zero momenta and negative energy contribution in accordance with the spectral postulate of operator quantization. This elimination leads to static interactions in a frame of reference of the Hamiltonian formulation. We list a set of observational and theoretical arguments in favor of these static interactions in SM. We show that the Dirac Hamiltonian method admits the mechanism of spontaneous symmetry breaking in SM by the initial data of the zeroth Fourier harmonic of the Higgs field that provokes masses of vector and spinor fields without the Higgs potential of this zeroth harmonic. In this case, the extremum of the quantum Coleman-Weinberg effective potential obtained from the unit vacuum-vacuum transition amplitude leads to a new sum-rule for masses of fermions and bosons and predicts a mass of the Higgs field 250 GeV.

In an external gravitational field of the charged black hole with one horizon the complex scalar field is considered. By means of appropriate selection of the coefficients in the initial equation of a scalar field it is led to the generalized equation of hyper geometrical type, then to a canonical form of this equation, representing degeneration of the hyper geometrical equation. Solving this equation which satisfies the requirements of limitation, is Laguerres polynomial with a corresponding spectrum of special values. On the basis of this spectrum expression for masses of the charged and neutral scalar particles is received. As the charged astrophysical object will usually quickly be neutralized by surrounding plasma it is considered, that the charged black holes do not represent the big interest from the astrophysical point of view [1]. However, as it is marked by Chandrasekhar [2], the studying of Reisner-Nordstrom solution describing charged black holes, allows understanding more deeply properties of space-time in extreme conditions.