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.

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 1)

Pages:

16-28

Citation:

K. Yordzhev and H. Kostadinova, "Mathematical Modeling in the Textile Industry", Bulletin of Mathematical Sciences and Applications, Vol. 1, pp. 16-28, 2012

Online since:

August 2012

Authors:

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

O. BOGOPOLSKI, Introduction to Group Theory", European Mathematical Society, Zurich (2008).

G. I. BORZUNOV, Textile Industry - Survey Information. Moscow, CNII ITEILP, vol. 3, 1983 (in Russian).

J. DAINTITH, R. D. NELSON, The Penguin Dictionary of Mathemathics. Penguin books, (1989).

S. R. DAVIS, C++ for Dummies. IDG Books Worldwide, (2000).

B. W. KERNIGAN, D. M RITCHIE, The C Programming Language. AT& T Bell Laboratories, (1998).

H. SCHILDT, Java 2 A Beginner's Guide. McGraw-Hill, (2001).

V. N. Sachkov, V. E. Tarakanov, Combinatorics of Nonnegative Matrices. Amer. Math. Soc., (1975).

J. -P. SERRE, Linear, Representations of Finite Groups. Springer-Verlag, New York, (1977).

TAN KIAT SHI, W. -H. STEEB, Y. HARDY, Symbolic C++: An Introduction to Computer Algebra using Object-Oriented Programming. Springer, (2001).

V. E. TARAKANOV, Combinatorial Problems and (0, 1)-matrices. Moscow, Nauka, 1985 (in Russian).

A. DE VOS, Reversible Computing: Fundamentals, Quantum Computing, and Applications. Wiley, (2010).

K. YORDZHEV, I. STATULOV, Mathematical Modeling and Quantitative Evaluation of Primary Weaving Braids. Textiles and Clothing, 10, (1999), 18-20 (in Bulgarian).

K. YORDZHEV, On an Equivalence Relation in the Set of the Permutation Matrices. Blagoevgrad, Bulgaria, SWU, Discrete Mathematics and Applications, (2004), 77-87.

K. YORDZHEV, An Example for the Use of Bitwise Operations in programming. Mathematics and education in mathematics, 38 (2009), 196-202.

K. YORDZHEV, H. KOSTADINOVA, Using Mathematical Methods in the Weaving for Receiving Quantity Valuations of the Textile Structure Variety. Textiles and Clothing, 1, (2011), 710 (in Bulgarian).