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.

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