No 2 (2008)

The problem of the potential field continuation we consider in a case of an approximately defined boundary. We have obtained the stability of an approximate solution with respect to boundary error and to field data error.

We introduce generalized threshold approach for multivariate extreme values modeling. Using this approach we suggest multivariate generalized Pareto distribution definition. Bivariate generalized Pareto distribution based on Pickands representation has been examined with different statistical dependence function models. Numerical experiments with stock indexes data have been performed showing high efficiency of suggested models and calculation algorithms.

The variational-iteration algorithms of the numerical solving of the bound state and scattering problems for coupled-channels radial equations are presented in the framework of the Kantorovich method (KM). Reduction of the boundary problems with conditions of the third type for systems of coupled radial equations is executed by a finite element method (FEM) with a high order accuracy on a non-uniform grid. As benchmark calculation to check rate of convergence and decomposition KM and efficiency of the FEM approximations of problem, we used exact values of energy, a phase and lengths of dispersion for model of three identical particles (bosons) on a straight line interacting by the pair zero-range potentials. A comparison of convergence rate of KM and Galerkin method in numerical calculations of the ground state energy of the given model is performed.

Three neutrino vacuum transitions and oscillations in the general case were considered and expressions for neutrino wave functions in three cases: with CP violation, without CP violation and the case when direct e $ transitions are absent,i.e., at (13) = 0 (some works indicate on this possibility) were obtained. There were also computed transition probabilities for the case of CP conservation and for absence of direct e $ transitions, i.e. (13) = 0. It was shown that the probability Pe!e (t) at e $ e neutrino transitions is definitely positive value if m2 13 = m2 12 + m2 23.

It is shown that in the low-energy limit the quantum mechanical differential cross-section of two identical charged particles generated by the central multipole interaction in the Coulomb field oscillates rapidly. This angular peculiarity of the cross-section is the discussed and new phenomenon called the coulomb-multipole analogue of the Mott effect.