CONTENTS &
ABSTRACTS

In
English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics * Mathematics

** **

Volume 54 No. 2
June 2005

Extropy-based
quantitative evaluation of finite functions; 67–78

Tõnu Lausmaa

**Abstract.** In this paper finite functions as one of the simplest
information processing models are analysed. The notion of partition is applied
in analysing these functions with its quantitative evaluation based on the
notion of extropy as an inherent measure of its complexity. Finite functions
are represented by partition pairs serving as their homomorphic images. The
treatise develops further the classical work of Hartmanis and Stearns [*Algebraic
Structure Theory of Sequential Machines*. Prentice-Hall, Englewood Cliffs,
New York, 1966] on finite automata that can be interpreted as a special case of
finite functions. The results allow us to evaluate the informational properties
of finite functions.

**Key words: **extropy, informational measure, partition, partition pair, finite
function, finite state machine.

Problems
of optimization: an exact algorithm for finding a maximum clique optimized for
dense graphs; 79–86

Deniss
Kumlander

**Abstract. **An algorithm for the maximum clique problem on
arbitrary undirected graphs is described. The algorithm presumes, as has been
proved, that vertices from an independent set cannot be included into the same
maximum clique. The independent sets are obtained from a heuristic
vertex-colouring, where each set constitutes a colour class. The colour classes
are then used to prune branches of the maximum clique search tree.
Computational results show that the algorithm performs better than those
published earlier, showing a substantial improvement with dense graphs.
Moreover, the new algorithm is easy to implement.

**Key words: **maximum clique,
independent set, branch-and-bound algorithm.

A note
on the minimal index (*M*-index) of time-like ruled surfaces;
87–97

Murat Tosun, Mehmet A. Gungor, and Soley Ersoy

**Abstract.** Minimal indices **(***M*-indices)
of time-like ruled and time-like hyperruled surfaces in _{} are investigated.
Additional results regarding developable, totally developable, and
nondevelopable ruled surfaces are also given.

**Key words:** Minkowski space,
time-like ruled surfaces, *M*-index.

Two-component scenario, cuprate related gaps,
and superconducting density; 98–110

Nikolai Kristoffel and Pavel Rubin

**Abstract.** A simple model of cuprate superconductivity with an electron
spectrum prepared by doping is developed. The pair-transfer interaction couples
the itinerant band with two components (“hot” and “cold”) of the defect
subsystem. Basic defect-itinerant gaps are quenched by progressive doping. Band
overlaps appear as novel sources for critical doping concentrations. Insulator
to metal transitions in the normal state are expected here. Minimal
quasiparticle excitation energies determine the pseudo- and superconducting
gaps according to the doping-dependent disposition of bands. Two pseudogaps can
be present at underdoping and two superconducting gaps can be manifested at
overdoping. Various transformations and connections between the gaps,
pseudogaps, and normal state gaps agree with various experimental findings. The
superconducting density does not reflect the presence of “extrinsic” gaps because
of the interband nature of the pairing. A Uemura-type sublinear plot at
underdoping with further recession is obtained. A mixed Fermi-liquid is
restored near optimal doping where the chemical potential intersects all the
band components.

**Key words:** cuprate superconductivity, two-band model, doping, gaps,
superfluid density.

The first scientific results from the Estonian
Grid; 111–127

Andi Hektor, Lauri Anton, Mario Kadastik, Konstantin
Skaburskas,

and Hardi Teder

**Abstract.** We present the first scientific results, technical details,
and recent developments in the Estonian Grid (EG). Ideas and concepts behind
Grid technology are described. We mention some most crucial parts of the Grid
system, as well as some unique possibilities in the Estonian situation. Scientific
applications currently running on the EG are listed and the first scientific
computations and results of the EG are discussed. The computations show that
the middleware is well chosen and the EG has remarkable stability and
scalability. We present the collected results and experiences of the
development of the EG and add some ideas of its near future.

**Key words:** radiation physics, Grid technology, scientific computations.

Copyright
Transfer Agreement; 128