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)