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基于文献老化负指数模型与生命周期曲线并借助函数推导与曲线分析方法,揭示出文献老化率在负指数模型中为常量,而在生命周期曲线下则为时间函数且具有复杂的数学特征。在此基础上,深入探讨了文献生命周期数学模型的理论特征、模型构建与数学验证问题。结果表明对数正态模型能够较好地拟合学科引文历时分布数据且符合文献生命周期理论曲线与老化率函数的典型数学特征。
Based on the literature aging negative index model and life cycle curve and using function derivation and curve analysis method, it is revealed that the aging rate of the document is constant in the negative exponential model and time function in the life cycle curve and has complex mathematical characteristics. On this basis, the theoretical characteristics, model construction and mathematical verification of mathematical model of literature life cycle are deeply discussed. The results show that the log-normal model can well fit the citation distribution data and meet the typical mathematical characteristics of the theoretical life cycle curve and the aging rate function.