In English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics * Mathematics


Volume 50 No. 2 June 2001


Two-based duplicate-clones; 67–75

(full article in PDF format)

Ellen REDI

Abstract. The notion “two-based clone” on a pair of sets (universes) is defined. Some properties of two-based duplicate-clones are proved. The lattice of all double-dually closed duplicate-clones on a pair of 2-element sets is described.

Key words: two-based clone, lattice, two-based duplicate-clone, double-dually closed clone.

On conservative and coercive SM-methods; 76–85

(full article in PDF format)


Abstract. We study the space  of double sequences  satisfying  for some number a. In this note, using gliding hump arguments, we give necessary and sufficient conditions for a 3-dimensional matrix (i.e. SM-method) to transform every convergent or bounded sequence  into the space  or  the space of elements in  with bounded columns.

Key words: summability, SM-methods, gliding hump method, theorems of Toeplitz–Silverman type.

Coercivity inequality for the quasilinear finite difference operator; 86–97

(full article in PDF format)


Abstract. The coercivity inequality is established for the finite difference operator which approximates in two- or three-dimensional unit cube the quasilinear elliptic operator for the second boundary value problem. The obtained results are based on special discrete analogues of the Sobolev imbedding theorems.

Key words: finite difference method.

A quadratic programming approach to robust controller design; 98–111

(full article in PDF format)


Abstract. The procedure of robust controller design by quadratic programming makes use of a stability measure defined as the minimal distance between a preselected stable simplex and vertices of the characteristic polynomial of an uncertain system. A constructive procedure for generating stable simplexes in polynomial coefficients space is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward: an appropriate stable point is chosen and then the edges of the stable simplex will be generated by reflection vectors of this polynomial.

Key words: robust stability, discrete-time systems, pole placement, quadratic programming.


Karl Rebane 75; 112

Annual award of the Estonian Physical Society (inside back cover)