Based on two large data samples from ISI databases, the author evaluated the Hirsch model, the Egghe-Rousseau model, and the
Glänzel-Schubert model of the h-index. The results support the Glänzel-Schubert model as a better estimation of the h-index
at both journal and institution levels. If hc, hp and hpc stand for the Hirsch estimation, Egghe-Rousseau estimation, and Glänzel-Schubert estimation, respectively, then an inequality
hp < h ∼ hpc < hc holds in most cases.
There exists a quantitative relationship, which can be expressed as G=kF(lgP)N, where G is per capita GDP, F gross expenditure
on R&D as % of GDP, P patent applications, N Internet users per 10,000 inhabitants, and k a constant ranging from 0.4 to 1.2
in most countries. The mechanism of the relationship is explained in the paper.
The set of citations received by a set of publications consists of citations received by articles in the h-core and citations received by articles in the h-tail. Denoting the cardinalities of these fours sets as C, P, CH and CT we introduce the tail-core ratio (CT/CH) and show that in practical cases this ratio tends to increase. Introducing further the k-index, defined as k = (C/P)/(CT/CH), we show that this index decreases in most practical cases. A power law model is in accordance with these practical observations.
The phenomenon of all-elements-sleeping-beauties in science is revealed by four special cases. The ‘sleeping beauties’ prick their fingers on the ‘spindles’ so that they fall into sleep then are awakened by their ‘princes’. The authors speculate that the phenomenon could happen in scientific literatures with high quality.