In an old paper [M.K. Buckland. Are obsolescence and scattering related? Journal of Documentation 28 (3) (1972) 242–246] Buckland poses the question if certain types of obsolescence of scientific literature (in terms of age of citations) implies certain types of journal scattering (in terms of cited journals). This problem is reformulated in terms of one- and two-dimensional obsolescence and linked with one- and two-dimensional growth, the latter being studied by Naranan. Naranan shows that two-dimensional exponential growth (i.e. of the journals and of the articles in journals) implies Lotka's law, a law belonging to two-dimensional informetrics and describing scattering of literature in a concise way. In this way we obtain that exponential aging of journal citations and of article citations imply Lotka's law and a relation is given between the exponent α in Lotka's law and the aging rates of the two obsolescence processes studied.
We show that the composition of two information production processes (IPPs), where the items of the first IPP are the sources of the second, and where the ranks of the sources in the first IPP agree with the ranks of the sources in the second IPP, yields an IPP which is positively reinforced with respect to the first IPP. This means that the rank-frequency distribution of the composition is the composition of the rank-frequency distribution of the first IPP and an increasing function φ, which is explicitly calculable from the two IPPs' distributions. From the rank-frequency distribution of the composition, we derive its size-frequency distribution in terms of the size-frequency distribution of the first IPP and of the function φ. The paper also relates the concentration of the reinforced IPP to that of the original one. This theory solves part of the problem of the determination of a third IPP from two given ones (so-called three-dimensional informetrics). In this paper we solved the “linear” case, i.e., where the third IPP is the composition of the other two IPPs.
The following problem has never been studied : Given A, the total number of items (e.g. articles) and T, the total number
of sources (e.g. journals that contain these articles) (hence A>T), when is there a Lotka function.
This paper studies four different h-index sequences (different in publication periods and/or citation periods). Lotkaian models
for these h-index sequences are presented by mutual comparison of one sequence with another one.
We also give graphs of these h-sequences for this author on which a discussion is presented. The same is done for the g-index
and the R-index.
In general information production processes (IPPs), we define productivity as the total number of sources but we present a
choice of seven possible definitions of performance: the mean or median number of items per source, the fraction of sources
with a certain minimum number of items, the h-, g-, R- and hw-index. We give an overview of the literature on different types of IPPs and each time we interpret “performance” in these
concrete cases. Examples are found in informetrics (including webometrics and scientometrics), linguistics, econometrics and
In Lotkaian IPPs we study these interpretations of “performance” in function of the productivity in these IPPs. We show that
the mean and median number of items per source as well as the fraction of sources with a certain minimum number of items are
increasing functions of the productivity if and only if the Lotkaian exponent is decreasing in function of the productivity.
We show that this property implies that the g-, R- and hw-indices are increasing functions of the productivity and, finally, we show that this property implies that the h-index is
an increasing function of productivity. We conclude that the h-index is the indicator which shows best the increasing relation
between productivity and performance.
In a general framework, given a set of articles and their received citations (time periods of publication or citation are
not important here) one can define the impact factor (IF) as the total number of received citations divided by the total number
of publications (articles). The uncitedness factor (UF) is defined as the fraction of the articles that received no citations.
It is intuitively clear that IF should be a decreasing function of UF. This is confirmed by the results in [van Leeuwen & Moed, 2005] but all the given examples show a typical shape, seldom seen in informetrics: a horizontal S-shape (first convex then
Adopting a simple model for the publication-citation relation, we prove this horizontal S-shape in this paper, showing that
such a general functional relationship can be generally explained.
From a list of papers of an author, ranked in decreasing order of the number of citations to these papers one can calculate
this author’s Hirsch index (or h-index). If this is done for a group of authors (e.g. from the same institute) then we can
again list these authors in decreasing order of their h-indices and from this, one can calculate the h-index of (part of)
this institute. One can go even further by listing institutes in a country in decreasing order of their h-indices and calculate
again the h-index as described above. Such h-indices are called by Schubert  “successive” h-indices.
In this paper we present a model for such successive h-indices based on our existing theory on the distribution of the h-index
in Lotkaian informetrics. We show that, each step, involves the multiplication of the exponent of the previous h-index by
1/α where α > 1 is a Lotka exponent. We explain why, in general, successive h-indices are decreasing.
We also introduce a global h-index for which tables of individuals (authors, institutes,...) are merged.
We calculate successive and global h-indices for the (still active) D. De Solla Price awardees.