SPEEDING UP THE GENERATION OF NEAR-RINGS ON FINITE CYCLIC GROUPS USING PARALLEL PROCESSING IN C#

TitleSPEEDING UP THE GENERATION OF NEAR-RINGS ON FINITE CYCLIC GROUPS USING PARALLEL PROCESSING IN C#
Publication TypeJournal Article
Year of Publication2018
AuthorsMALINOVA MARIA, GOLEV ANGEL, RAHNEV ASEN
JournalNeural, Parallel, and Scientific Computations
Volume26
Issue3
Start Page345
Pagination10
Date Published11/2018
ISSN1061-5369
Keywords16Y30
Abstract

The main purpose of this article is to reduce the generation time of near-rings on finite cyclic groups using the parallel processing provided by C#. We divide the near-rings into independent subsets and generate them simultaneously. The calculations are further accelerated after refactoring and defining appropriate compiler optimizations.

URLhttps://acadsol.eu/npsc/articles/26/3/9.pdf
DOI10.12732/npsc.v26i3.9
Refereed DesignationRefereed
Full Text

[1] Clay J.R., The near-rings on a finite cycle group, Amer. Math. Monthly, 71 (1964), 47-50. 
[2] Jacobson R.A., The structure of near-rings on a group of prime order, Amer. Math. Monthly, 73 (1966), 59-61. 
[3] Clay J.R., The near-rings on groups of low order, Math. Zeitschr., 104 (1968), 364-371. 
[4] Pilz G., Near-rings, North-Holland, Amst., 23 (1977). 
[5] Pilz G., Near-rings, North-Holland, Amst., Revised edition, 23 (1983). 
[6] Yerby R., H.Heatherly, Near-Ring Newsletter, 7 (1984), 14-22. 
[7] Rakhnev A.K., G.A.Daskalov, Construction of near-rings on finite cyclic groups, Math. and Math. Education, Sunny Beach, Bulgaria, (1985), 280-288. 
[8] Rakhnev A.K., On near-rings, whose additive groups are finite cyclics, Compt. rend. Acad. bulg. Sci., 39 No. 5 (1986), 13-14. 
[9] Aichinger E., F.Binder, J.Ecker, R.Eggetsberger, P.Mayr and C.N¨obauer. SONATA: Systems Of Nearrings And Their Applications, Package for the group theory system GAP4. Johanes Kepler University Linz, Austria, (2008). http://www.algebra.uni-linz.ac.at/sonata/ 
[10] Rahnev A., A. Golev, Some New Lower Bounds for the Number of Near-rings on Finite Cyclic Groups, Int. Journal of Pure and Applied Mathematics, 59, No.1 (2010), 59-75. 
[11] Rahnev A.K., A.A. Golev, Computing Near-rings on Finite Cyclic Groups, Compt. rend. Acad. bulg. Sci., 63, book 5 (2010), 645-650. 
[12] Golev A., A. Rahnev, Computing Classes of Isomorphic Near-rings on Cyclic Groups of Order up to 23, Scientific Works, Plovdiv University, 37, book 3, Mathematics (2010), 53-66. 
[13] Golev A., Algorithms for Generating Near-rings on Finite Cyclic Groups, Proceedings of the Anniversary International Conference REMIA 2010, Plovdiv, 255-262, 10-12 December 2010. 
[14] Golev A. A., A. K. Rahnev, Computing Near-rings on Finite Cyclic Groups of Order up to 29, Compt. rend. Acad. bulg. Sci., 64, No. 4, (2011), 461-468. 
[15] Golev A., A. Rahnev, New results for near-rings on finite cyclic groups, Proceedings of Annual Workshop “Coding Theory and Applications”, 51-54, Gabrovo, December 2011. 
[16] Pavlov N., A. Golev, A. Rahnev, Distributed Software system for Testing NearRIngs Hypotheses and New Constructions for Near-Rings on Finite Cyclic Groups, Int. Journal of Pure and Applied Mathematics, 90, No.3 (2014), 345-356. 
[17] Malinova M., A. Golev, A. Rahnev, Generating SQL Queries for Filtering NearRings on Finite Cyclic Groups, Int. Journal of Pure and Applied Mathematics, 119, No. 1 (2018), 225-234. 354