No 4 (2010)

The functional-differential -order equation with unbounded operational coefficient and deviations of arguments is considered. The existence theorem of the existence of solutions decreasing rapidly compared to exponent, is proved in the article.

The nonlocal well-posedness of the mixed problem for the Kawahara equation in a boundary rectangle under natural conditions on a boundary data is proved.

The problem of necessary and sufficient couditions of validity for discrete inequalities of Hardy type with variable limits of summation in the sequence spaces is studied.

Most information services contact with their clients through the call-centers. In this paper, we give a mathematical model of a call-center with two customer classes and three skillbased agent groups. Customers of each class are served not only by the one-skilled agent group but by one two-skilled agent group too. We propose formulas to obtain the main model performance measures such as blocking probabilities, mean queue lengths and probabilities of receiving service immediately. A computational example shows that the proposed model is more effective that the model with one-skilled agent groups.

The relativistic generalization of potential model of a quarkonium leads to the solution of a spectroscopic problem for quasipotential equations. In that specific case the problem is reduced to the investigation of a boundary problem for the ordinary differential equation of the terminating order with arbitrary parameter at the higher derivatives. In the work the algorithm of investigation of boundary problems for the differential equations of high orders is offered. The algorithm is realized with the use of system of symbolical evaluations MAPLE. It is erected, that at → 0 some solutions coincide with the solution of the nonrelativistic Schrodinger equation. Besides, are found out, so-called frontier layer solutions; transition of one type of the solution (for example, the solution with one junction) in to another (the solution without junctions). Investigations of properties of eigenvalues and eigenfunctions are carried out at various values of .

In the frame of constructive Kuryshkin-Wodkiewicz model of quantum measurements theory problem of calculating measured moments of observables is considered. This problem is closely related to the problem of calculating dispersions of measured values of observables, examined in details in papers of V. Kuryshkin. Values of moments and dispersions of measured observables are uniquely determined by quantum distribution function of Kuryshkin- Wodkiewicz.

We consider Dark Sector fields evolution on the basis of dynamical equations on the background of inflationary stage of Universe. We consider energy characteristics of Dark Sector fields to be of the same order as perturbations of gravitation field and inflaton. Effects of influence of Dark Sector fields on large-scale structure formation within the example of exponential inflation are researched.

model of gravitation in the frameworks of the Hamiltonian (Dirac) approach is considered. The equations, setting dependence of observable density of number of scalar particles on the initial data and invariant parametre of evolution, are constructed in an explicit form. Problems of unification of principles of the General Theory of Relativity (GTR) and the Quantum Theory of Fields (QTF) within a simple example of a vacuum creation of scalar particles in conformal-invariant model of gravitation [1-3,10-14] are considered. It is shown that such model can describe both possible mechanism of such creation, and ways of its generalisation to more complex models, including Standard Model (SM). It allows to formulate some new approach to quantization of the relativistic gravitational systems, which essence is in quantization of the phase space of initial quantities as integrals of motion of the system, obtained by Bogoljubov diagonalization of the motion equations in Hamiltonian formalism, and in the proof of equivalence of such quantization to transition from classical commutative variables to their noncommutative quantum analogues. The above described scheme can be applied to initial manifolds of any finite dimension and topology.