Vol. 35 No. 3 (196) (2001)

In this paper problems on location of singularities of power series are investigated which lie outside of its circle of convergence and on prescribed spiral angle. Finite as well as infinite singularities are considered.

The notion of movability was itroduced, for metrizable compacts, by K. Borsuk. He proved that the any plane compact is a movable. In this paper the equivariant movability of plane invariant compacts is studied. It is proved that all plane invariant compacts are equivariant movable in the case of linear action of compact and connected group G on the plane.

Problem of rapprochement with m target sets is considered, when the movement of system is described by the system of linear stochastic differential equations. The extremal strategy is constructed by a method of extremal aiming.

In the work possible complexes of three-dimensional planes in six-measured projective space P⁶ are studied. It’s proved that one-parametric family of cones of second order in P⁶ with univariate top and with three-dimensional flat forming defines four-parametric possible family of planes E³, which are all three-dimensional forming to this cones.

In this paper we discuss questions concerning transformations of PROLOG-programs and PROLOG-queries intended for extension of intellectual abilities of the interpreter. Some subset of simple monadic PROLOG is considered. It is proved that one cannot transform any program and query from this subset in such a way that the interpreter will always stop with a definite answer, but it is possible to do it if the query is a logical consequence of the program.

Game problems for the double link manipulator movement are considered with the use of the extreme targeting method. Problems of rapprochement and deviation of linear systems are investigated. For certainty, two problems of rapprochement of the manipulator grasp to the target set are solved with respect to the speed and coordinates as well as two problems of the deviation from the target set with respect to the speed and coordinates.

The research is on the problem of the rotary motion stability of the heavy gyroscope around its axis of dynamic symmetry by the influential force. It is shown that with any angular speed and with any values of parameters, the rotary motion of the gyroscope is unstable by the influential force.

The propagation of electromagnetic waves through a layer of naturally gyrotropic media in an external magnetic field is considered. The problem is solved by a method $4\times 4$ matrix of Beremann. The Jones matrixes are constructed; the reflection and transmission coefficients, the polarization azimuth and ellipticity of a passing wave are calculated. The specific features of polarization functions of own modes, eigen polarizations and polarization functions of an incident wave at which one of the own modes is not exited are investigated. It is shown, that in these media under certain conditions three own modes are excited.´

In the given article the jump type boundary condition is proved, which was considered in a boundary problem discussed in [1], connected with a harmonic wave diffraction on the half-infinite inclusion.