Katchanov Yurij L
National Research University Higher School of Economics (HSE), 20 Myasnitskaya Ulitsa, 101000 Moscow, Russia.
Springerplus. 2015 Nov 5;4:677. doi: 10.1186/s40064-015-1467-8. eCollection 2015.
The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation distributions in terms of the Ekeland variational principle and a mathematical exploration of the power law nature of citation distributions. Apart from its inherent value in providing a better understanding of the mathematical underpinnings of bibliometric models, such an approach can be used to derive a citation distribution from first principles.
本文的写作基于这样一种假设，即引文数学理论的目的是在数学形式主义层面解释文献计量规律。针对社会引文中幂律分布的出现提出了一种数学形式主义。本文的主要贡献在于根据埃克兰变分原理对引文分布进行公理刻画，以及对引文分布的幂律性质进行数学探究。除了在更好地理解文献计量模型的数学基础方面具有内在价值外，这种方法还可用于从第一原理推导出引文分布。
