XML结构与递阶数

XML Structures and Hierarchical Numbers

XML结构和计算机科学中其他数据结构可引出一种数学概念——递阶数.给出其公理和基本定义、定理、运算法则.定义了三类递阶函数,可用于各种变换,作为未来算法研究之基础.递阶结构是普遍存在的通用结构.用递阶数表示XML结构呈现一种简洁性.研究递阶结构的数学基础对其实际应用很有意义.

Hierarchical numbers, a mathematical concept, which is mtroduced from the phenomena ot XML structures and the other data structures in computing by the author. Axioms, basic definitions and operation rules are given. Three classes of hierarchical functions are defined, so that it would be as a basis for future research of algorithms. Hierarchical structures exist ubiquitously as a kind of universal structures. Representing XML structures as hierarchical numbers is compact and legible. The research in its mathematical fundamentals is interesting to a variety of applications.