Mathematics

Get Adobe Reader

2002, No. 4



S.V. Astashkin, R.F. Uzbekov

ON K-CLOSED SUBCOUPLES AND RELATIVE COMPLETIONS

Let (X0,X1) be a Banach couple such that X1 in X0. Subcouples of the form (X0,Y1) with a subspace Y1 of codimension 1 of the space X1 are considered.
By an analog of the Hahn-Banach theorem about extending of linear functionals, we find the criterion of (X0,Y1) being a K-closed subcouple of the couple (X0,X1). A new concept of (K*)-property of a Banach space is introduced. We prove that arbitrary "weighted" L1 - space is of this property.


M.M. Semenova

DECOMPOSITION OF MULTIRATE MODELS OF CONTROLLABLE SYSTEMS

A method of integral manifold is applied to study of multitempo nonlinear systems. The use of this method permits us to solve a problem of decomposition of multirate controllable systems. Local controllability of these systems is investigated. The application of the method is illustrated on example.


T.A. Sribnaya

THE CAFIERO CRITERION ON AN ORTHOMODULAR POSET

The uniform exhaustivity Cafiero criterion is proved in the case of functions defined on an orthomodular poset and taking values in an arbitrary topological space (without considering any algebraic operation on it).


Ch.A. Chikhanov

ON THE FUCHS CLASS THIRD ORDER EQUATION

In this paper 54 solutions of Fuchs class third order equation with three correct singular points are given.