Utilizing a method briefly hinted in the author’s paper written in 1991 jointly with V. C. Harris, we derive here a number of unpublished recursion formulae for a variety of product partition functions which we believe have not been considered before in the literature. These include the functionsp∗(n;k,h) (which stands for the number of product partitions ofn> 1 into k parts of which h are dist...

Diversity of opinion is an empirical fact often appearing in social networks. In the paper known statistical methods of evaluation is substituted by fuzzy concepts, namely Step Ordered Fuzzy Numbers (SOFN). SOFN are extentions of Ordered Fuzzy numbers (OFN) introduced by Kosiński, Prokopowicz and Ślȩzak in 2002. In 2011 Kacprzak and Kosiński observed that SOFN may be equipped with a lattice str...

Most of the multi-party computation frameworks can be viewed as oblivious databases where data is stored and processed in a secret-shared form. However, data manipulation in such databases can be slow and cumbersome without dedicated protocols for certain database operations. In this paper, we provide efficient protocols for oblivious selection, filtering and shuffle—essential tools in privacy-...

A time minimizing assignment problem (TMAP) dealing with the allocation ofn jobs to m(< n) persons is considered in this paper. One job is to be allocated to exactly one person and each person does at least one job. All the persons start working on the jobs simultaneously. If a person is to do more than one job, he does them one after the other in any order. The aim of the present study is to f...