Basic Concepts of Graph Theory as the Instruments of Mathematical Formalization of Woven Structures

The paper presents the prerequisites of involving of topological elements and graph theory as an instrument of mathematical formalization of woven structures and technology of textile fabrics. Present research is based on analysis and comparison of the main concepts and conditions of textile technology and graph theory.

Mathematical Approaches to the Structural Analysis and Formalization of Woven Fabrics

The present paper shows the mathematical approach of formalization of textile fabrics, based on concepts and elements of graph theory and the structural analysis of woven structures and possibility of numerical evaluation of interlacing factor of warp and weft threads in woven structures through the weight of a structural graph vertex. Research observes quantitative aspect of structural evaluation of threads topology in fabric focusing in graph theory, in order to present an application productivity of this theory to solve the technological tasks.

杨慎的“四经二纬说”

“四经二纬说”中的“四经”指六书中能够造字的前四书 (象形、象事、象意、象声 ) ,“二纬”指不造字的后二书 (假借和转注 ) ,这是第一次对传统六书的科学分类。“四经二纬说”是受宋明“转声说”和班固“四象”之名的启发提出的 ,它对清代戴震“四体二用说”