Mathematics |
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2004, The Second Special Issue
D.V. Repin
GRADED IDENTITIES OF A SIMPLE THREE-DIMENSIONAL LIE ALGEBRA
Let K be a field of characteristic zero and sl2 be the Lie algebra of 2x2 matrices with zero trace over a field F. It is well known three classic non-trivial gradings on sl2: Z2, Z2 x Z2 and Z3 - gradings. In the case of these gradings a complete description of the vector space of multilinear graded identities in the terms of representation theory of symmetric group and the Young diagrams is given.
O.P. Filatov
UNIFORM EXPONENTIAL STABILITY OF DIFFERENTIAL INCLUSIONS
A criterion of the uniform exponential stability of differential inclusions with slow variables based on a comparative differential inclusion is given. The comparative differential inclusion may be obtained by partial averaging the initial problem. Sufficient conditions for the uniform exponential stability of a given differential inclusion are obtained.
N.P. Balabayeva
STABILITY OF SYSTEMS OF DIFFERENTIAL INEQUALITIES AND INCLUSIONS WITHIN AN INFINITE INTERVAL
In the paper the problem of stability of a system of differential inequalities and inclusions with slow and rapid variables is considered. A stability theorem within an infinite interval is proved.
Å.V. Sokolovskaya
In the paper a theorem about reciprocal approximation of the systems of differential inclusions with one-sided Lipschitz right-hand side without rapid variables is proved. The range of problems for which the Krylov-Bogolybov principle of averaging can be applied to is then extended.