Vol 71, No 6 (2016)

Let {γn(V)}_n≥1 be the sequence of proper codimensions of some variety V of Poisson algebras over a field of characteristic zero. A class of minimal varieties of Poisson algebras of polynomial growth of the sequence {γn(V)}_n≥1 is presented, i.e., the sequence {γn(V)}_n≥1 of any such variety V grows as a polynomial of some degree k, but the sequence {γn(W)}_n≥1 of any proper subvariety W in V grows as a polynomial of degree strictly less than k.

The paper develops a study of closed geodesics on piecewise smooth constant curvature surfaces of revolution initiated by I.V. Sypchenko and D. S. Timonina. The case of constant negative curvature is considered. Closed geodesics on a surface formed by a union of two Beltrami surfaces are studied. All closed geodesics without self-intersections are found and tested for stability in a certain finite-dimensional class of perturbations. Conjugate points are found partly.

The problem under consideration is the construction of an attainability set’s internal approximation for a full controllable linear time-invariant system. This approximation is obtained as an intersection of two domains given by quadratic forms. One of these forms is based on parameters of the original system. The other form is produced by the solution to some linear matrix inequality. The method proposed here is illustrated by a numerical example.