自相似常数和定量差异及其在体育科学中的应用

Self-similar constant and quantitative difference as well as their applications in sports science

传统的统计方法可以得出两组数据的定性分布差异,而定量差异(QD)可以得出它们的平均值差异。以黄金分割常数为底的对数称为黄金对数,研究发现一个新的自然常数可以表示黄金分割常数,且黄金对数保持不变,称其为自相似常数。自相似常数不但能表示部分基本物理常数,而且能表示部分运动记录和生理极限。用自相似常数表示QD在分子细胞水平、组织器官水平和整体水平功能3个方面与运动成绩的特征参数,并讨论了QD在体育科学中的初步应用。

As for two sets of data, their qualitative distribution difference can be derived by using traditional statis-tical methods, while their mean value difference can be derived from quantitative difference （QD）. A base-golden ratio logarithm is called as a golden logarithm, the authors found that a new natural constant can express the golden ratio, and its golden logarithm maintains unchanged, and called it as self-similar constant. The self-similar constant can not only express some fundamental physical constants, but also express some sports records and physiological limits. The authors used the self-similar constant to express the QD in athletic performance characteristic parameters in such 3 aspects as molecular cell level, tissue or organ level and overall level, and further discussed the QD’s pre-liminary applications in sports science.