Physics

2005, No. 5

I.V. Kulagina

BIRATIONAL INVARIANTS OF THE KLEIN FOUR-GROUP MODULES

In the paper birational invariants for the maximal torus T of the connected semisimple group of type are found. Here ? is a four-subgroup of the Weil’s group , is an arbitrary element of the Picard class. The Klyachko method allows to calculate these invariants by using the structure of the module of rational characters of T only. Following this method the explicit formula which simplifies the calculation of a cohomology invariant for an arbitrary Klein four-group module is obtained. The triviality of the groups is proved by using this formula.

O.P. Filatov

THE INTEGRAL EULER METHOD WITH PERTURBATIONS AND THE AVERAGING PRINCIPLE FOR DIFFERENTIAL INCLUSIONS

The accuracy of the approximation of the solution sets by means of the Euler integral discretization scheme with pertubations for one-sided Lipschitz differential inclusions with slow variables is estimated. The averaging theorem for the differential inclusions is derived from the main theorem.

V.G.Tsiroulik, D.V.Tsiroulik

SOLUTIONS OF INHOMOGENEOUS ORDINARY DIFFERENTIAL EQUATIONS AND SYSTEMS

In the paper the method of finding solutions of some class of inhomogeneous ordinary differential equations and systems with right-hand side of a special form is proposed. It is proved that for equations and systems of equations of this class the proposed method considerably reduces the amount of calculations in comparison with the known methods especially in the resonance case when right-hand side contains the polynomial of a high degree.