Vol. 36 No. 2 (198) (2002)

This work is based on the theory of spaces with limit operation of a sequence constructed by the author. In a vector space X partially ordered set L of all linear limit operations of a sequence is considered, each of them generates the same system of bounded subsets in X as the given linear limit operation of a sequence. It is proved that L contains the smallest element, each nonempty subset from L has the greatest lower bound and the perfect ordered subset has the least upper bound that is L contains maximal elements. The characteristics of the smallest element and the maximal elements of L are obtained. For linear spaces with limit operation of a sequence statements about a neighborhood of zero, convex sets and differentiable mappings as well as statements that generalize the classical Banach-Steinhaus theorem and the theorem on open mapping are proved. In particular we obtain results reinforcing some known versions of Banach-Steinhaus theorem for topological vector spaces.

On the basis of mathematical models control algorithms are investigated for two elastic mechanical systems (flying object, elastic manipulator). Control parameters are found that provide damping of the first mode of elastic oscillations at the end of movement. The oscillation graphics of the elastic element of those systems are presented for the found control algorithms.

The question of equivalence of three-valued predicate calculi with the symbol of uncertainty of symmetric constructive logic is considered. For one of the considered calculi the mix elimination theorem is proved.

A new method for consideration of an electron stationary motion in the field of an arbitrary one-dimensional potential. It is shown that for a case of an electron infinite motion, the problem of determination of wave functions can be represented as Cauchy problem for the one-dimensional Schrodinger equation. For the case of finite motion the equation determining the energy spectrum is found. It is proved, when the spectrum of bound states is know, the problem of building the wave functions of the discrete spectrum can be formulated as Cauchy problem for wave equation as well.