Vol. 40 No. 2 (210) (2006)

In the present paper the developments of Queueing Theory is described, its belongness to Operations Research and Probability Theory is substantiated. The Regularities of Many Servers Queues with infinite waiting room are explained on the example of $GI|G|s|\infty$ model. The explicit formulas, limit theorems in c, stability, inequalities for the main characteristics, extremal problems are presented. The main attention in future is given to $GI|G|s|\infty$ model with FIFO service discipline. Not only known results are formulated, but also some results, which were established by authors. For instance, in $GI|G|s|\infty$ model two groups of assumptions are suggested, which lead to the Little formulas. In particular, $M|G|s|\infty$ model is considered.

The existence of eigenvalues for Dirac's two-parameter boundary-value problem is proved.

In this paper following initial boundary value problem  is considered: $$\begin{cases}  A\left(\dfrac{\partial u}{\partial t}\right)+Bu=f, \\ u(0)=u_0, \\D^{\gamma}|_{\Gamma}=0, |\gamma|\leq m. \end{cases}$$ Operators $A$ and $B$ are nonlinear and have the following form: $$Au=\displaystyle\sum_{|\alpha|\leq m}(-1)^{|\alpha|}D^{\alpha}A_{\alpha}(x, t, D^{\gamma}u), ~~Bu=\displaystyle\sum_{|\alpha|\leq m}(-1)^{|\alpha|}D^{\alpha}B_{\alpha}(x, t, D^{\gamma}u), |\gamma|\leq m. $$

Conditions for functions $A_{\alpha}$ and $B_{\alpha}$ are obtained that lead to existence and uniqueness of solution of the problem in the spaces $L^p(0, T, ^0W^m_p), p\geq 2$.

The present paper, consisting of two parts, is devoted to constructing algebraic multigrid preconditioners for stiffness matrices arising in finite element approximation of elliptic problems in rectangular domains. The Dirichlet condition is placed on one part of the boundary and third type condition on the rest of the boundary. In the second part, using a sequence of two-grid preconditioners from [1], the multigrid preconditioner with inner Chebyshev iterations is constructed.

Conditions are obtained by which the solutions in the case of several goal sets and the systems with varying dynamics are stable with respect to informational disturbance. The stability of solution of pursuit-evasion to m goal sets game problem is analyzed when the object follows a system of nonlinear nonstationary differential equations with varying dynamics. So the dynamic of the system is changing step by step. The sequence of meetings with the goal sets is fixed. The moments of systems switching are assumed to be constant values. A family of u-stable bridges is constructed. A piecewise positional strategy extremal to that family and the theorem about the solution's stability with respect to informational disturbance of the pursuit-evasion to one goal set game problem, proved by N.N. Krasovskii, are applied. Conditions are obtained by which the solutions are stable with respect to informational disturbance.

The method of approximate determination of parameters of stationary axial-symmetric fields of rotating configurations at the third and the forth approximation of angular velocity is proposed.

The presence of constant flux of particles falling on the target is presupposed while determining the yields of residual nuclei by the induced activity method. However in reality the beam of particles possesses fluctuation. In the present work these fluctuations were considered when determining the intensity of the beam of particles. In some cases the corrections of the fluctuations are of about 30%.

In the given work it is theoretically and experimentally stated that the decrease of dislocation density in a crystalline block of X-ray interferometer leads to the decrease of the frequency of moire fringes.