The definitions of homogeneous and mosaic attractors of codimension one are given. A topological method for their purposeful formation by using the feedback control laws of controlled dynamical systems is suggested.

A matrix infinite-dimensional analog of the Wiener theorem on local inversion of Fourier transforms is proved.

The exact dependence of constants in Jackson-type inequalities on the rate of convergence of the Diophantine approximations of certain numbers is obtained.

We show that, in a Banach space, continuous random processes constructed by using solutions of the difference equationX n =A n X n+1+V n , n=1, 2,..., converge in distribution to a solution of the corresponding operator equation.

The lattice of characteristic subgroups of the Jonquere group over a field of characteristic zero is described.