CONTENTS &
ABSTRACTS

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

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

Maria ZELTSER

**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

Malle FISCHER

**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

Ülo NURGES

**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.

CHRONICLE

Karl Rebane 75; 112

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