汉字构件系统数学模型的创建与分析

Chinese Characters Component Part System: Model Establishment and Analysis

汉字是由构件构成的,字形的任何改变,终将由构件体现,构件的优化是汉字系统优化的充分必要条件,研究不同发展阶段的汉字构件系统具有的个性和共性,描述构件系统变化轨迹,探讨构件发展规律,对汉字教学、汉字信息处理、汉字规范等都具有非常重要的现实意义。如何从历代汉字事实入手,总结、探索汉字发展的内在规律,始终是学界关心的重要问题之一。在汉字构形拆分数据的基础上,采用数理统计的方法,建立了汉字构件数学模型,并通过对构件模型的导函数极限分析,揭示了汉字构件有限增长规律,即构件数随字符数的增加而增加,二者的增长速度成非线性函数关系,增长速度的极限趋于0。

Chinese characters can be analyzed into component parts, and hence into systems; but the previous researches lack such a nature for want of theoretical departures. It has become an urgent demand to summarize and explicate the natural laws in accordance with the characters reform and application in the new era. The present paper, by adopting a statistic methodology, namely, the derived function limit analysis, proves that the component number increases along character sets, the growth velocities of the two being in a nonlinear function relation, and the limit of the growth velocity tends to be zero.