http://dspace.nbuv.gov.ua:80/handle/123456789/106455 2026-04-05T17:46:05Z 2026-04-05T17:46:05Z Sklyar, G.M. Szkibiel, G. http://dspace.nbuv.gov.ua:80/handle/123456789/106509 2016-09-30T00:02:55Z 2008-01-01T00:00:00Z

Controllability from Rest to Arbitrary Position of the Nonhomogeneous Timoshenko Beam Sklyar, G.M.; Szkibiel, G. The controllability of a slowly rotating beam clamped to a disc is considered. It is assumed that at the beginning the beam remains at the position of rest and it is supposed to rotate by the given angle to achieve a desired position. The movement is governed by the system of two differential equations with nonhomogeneous coe cients: mass density, rotary inertia, exural rigidity and shear sti ness. The problem of controllability is reduced to the moment problem that is, in turn, solved with the use of the asymptotics of the spectrum of the operator connected with the movement.

2008-01-01T00:00:00Z Shu, Sh. http://dspace.nbuv.gov.ua:80/handle/123456789/106508 2016-10-05T21:28:12Z 2008-01-01T00:00:00Z

Complete Hypersurfaces in a Real Space Form Shu, Sh.

2008-01-01T00:00:00Z Petrov, Ye.V. http://dspace.nbuv.gov.ua:80/handle/123456789/106507 2016-09-30T00:02:54Z 2008-01-01T00:00:00Z

Submanifolds with the Harmonic Gauss Map in Lie Groups Petrov, Ye.V. In this paper we find a criterion for the Gauss map of an immersed smooth submanifold in some Lie group with left invariant metric to be harmonic. Using the obtained expression we prove some necessary and sufficient conditions for the harmonicity of this map in the case of totally geodesic submanifolds in Lie groups admitting biinvariant metrics. We show that, depending on the structure of the tangent space of a submanifold, the Gauss map can be harmonic in all biinvariant metrics or nonharmonic in some metric. For 2-step nilpotent groups we prove that the Gauss map of a geodesic is harmonic if and only if it is constant.

2008-01-01T00:00:00Z Milewski, J. http://dspace.nbuv.gov.ua:80/handle/123456789/106506 2016-09-30T00:02:54Z 2008-01-01T00:00:00Z

An Invariant Form of the Euler-Lagrange Operator Milewski, J. We define a class of almost S(M)-multilinear maps. The Euler-Lagrange operator is given by means of the trace of an almost S(M)-bilinear map.

2008-01-01T00:00:00Z