Mathematical Modeling in the Textile Industry

Abstract

A mathematical model, describing some different weaving structures, is made in this article. The termsself-mirror and rotation-stable weaving structure are initiated here. There are used the properties and operationsin the set of the binary matrices and an equivalence relation in this set. Some combinatorial problems aboutfinding the cardinal number and the elements of the factor set according to this relation is discussed. We proposean algorithm, which solves these problems. The presentation of an arbitrary binary matrix using sequence ofnonnegative integers is discussed. It is shown that the presentation of binary matrices using ordered n-tuples ofnatural numbers makes the algorithms faster and saves a lot of memory. Implementing these ideas a computerprogram, which receives all of the examined objects, is created. In the paper we use object-oriented programmingusing the syntax and the semantic of C++ programming language. Some advantages in the use of bitwiseoperations are shown. The results we have received are used to describe the topology of the different weavingstructures.