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本文揭示了一明显而尚未被开发的特征,即在作者——出版物系统和期刊——论文系统之间存在着结构上的差异,因为一份期刊中可刊出若干篇文章,而每篇文章可能有若干个作者。为了从每篇文章只有一位作者的情况中导出几位作者的情况,文中使用了卷积理论从数学上对这种差异作了研究。我们指出,Lotka定律φ(i)=c/(1+i)~a,式中的i≥0,对所有的α=2,3,4,…,都是近似稳定的,这就是说,如果Lotka定律对每篇文章只有一位作者的系统能成立,那么(从数学上看在α相同时)它对每篇文章有一个以上作者的一般系统也近似成立。这对几何分布也同样适用。因此,该理论是对Lotka函数和几何函数的本质解释。
This article reveals an obvious and untapped feature that there is a structural difference between the author-publication system and the journal-paper system, since there can be several articles in a journal, and each article Articles may have several authors. To derive several authors from the case of only one author per article, the paper uses the convolution theory to mathematically study this discrepancy. We point out that Lotka’s law φ (i) = c / (1 + i) ~ a, where i≥0 is approximately stable for all α = 2,3,4, ..., that is to say, If Lotka’s law holds for systems that have only one author per article, then the general system that has more than one author per article (mathematically, when a is the same) holds approximately. The same applies to the geometric distribution. Therefore, the theory is an essential explanation of Lotka function and geometric function.