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.

Examination of Passwords’ Influation on the Compressing Process of Non-Encrypted Objects

The principal methods of compression and different types of non-encrypted objects are described. An analysis is made of the results obtained from examinations of the speed of compression for objects when using passwords with different length. The size of the new file obtained after compression is also analyzed. Some evaluations are made with regard to the methods and the objects used in the examinations. In conclusion some deductions are drawn as well as recommendations for future work.

Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.