Algorithmic Minimization of Non-zero Entries in 0,1-Matrices

In this paper we present algorithms which work on pairs of 0,1- matrices which multiply again a matrix of zero and one entries. When applied over a pair, the algorithms change the number of non-zero entries present in the matrices, meanwhile their product remains unchanged. We establish the conditions under which the number of 1s decreases. We recursively define as well pairs of matrices which product is a specific matrix and such that by applying on them these algorithms, we minimize the total number of non-zero entries present in both matrices. These matrices may be interpreted as solutions for a well known information retrieval problem, and in this case the number of 1 entries represent the complexity of the retrieve and information update operations.

Key Agreement Protocol Using Elliptic Curve Matrix Power Function

* Work is partially supported by the Lithuanian State Science and Studies Foundation.

On the Operational Solution of a System of Fractional Differential Equations

MSC 2010: 26A33, 44A45, 44A40, 65J10

Online Dictionary - Tool for Preservation of Language Heritage

The paper aims to represent a bilingual online dictionary as a useful tool helping preservation of the natural languages. The author focuses on the approach that was taken to develop compatible bilingual lexical database for the Bulgarian-Polish online dictionary. A formal model for the dictionary encoding is developed in accordance with the complex structures of the dictionary entries. These structures vary depending on the grammatical characteristics of Bulgarian headwords. The Web-application for presentation of the bilingual dictionary is also describred.

Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring

2000 Mathematics Subject Classification: 15A15, 15A24, 15A33, 16S50.