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Abstract  

The characteristic scores and scales (CSS), introduced by Glänzel and Schubert (J Inform Sci 14:123–127, <cite>1988</cite>) and further studied in subsequent papers of Glänzel, can be calculated exactly in a Lotkaian framework. We prove that these CSS are simple exponents of the average number of items per source in general IPPs. The proofs are given using size-frequency functions as well as using rank-frequency functions. We note that CSS do not necessarily have to be defined as averages but that medians can be used as well. Also for these CSS we present exact formulae in the Lotkaian framework and both types of CSS are compared. We also link these formulae with the h-index.

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Abstract  

Price's law asserts — in its simpliest version — that
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sqrt N$$ \end{document}
authors produce half of the papers made by the total ofN authors. More generally: the topN (0<<1) authors produce a fraction (0<<1) of the papers made by the total ofN authors and the Price's law says that . In this paper — using Lotka's law — we prove a mathematical relationship of in function of and the parameter (the mean number of papers per author) and investigate when . More-over our reasoning uses the theory of the 80/20 rule as developed in: L. EGGHE, On the 80/20-rule,Scientometrics, 10 (1986) 55–68, thereby also showing the relation betwwen the 80/20-rules (being an arithmetical form of measuring elitarism) and Price's law (being a geometric form of measuring elitarism).
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Abstract  

A relation, established by András Schubert (Scientometrics 78(3): 559–565, 2009) on the relation between a paper’s h-index and its total number of received citations, is explained. The relation is a concavely increasing power law and is explained based on the Lotkaian model for the h-index, proved by Egghe and Rousseau.

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Conclusion  

I think that most of the problems mentioned in the GS paper are caused by natural evolutionary aspects of the discipline. It cannot be doubted that BIS is growing into a more and more professional research discipline. There are indeed problems of quality and of the fact that researchers have different origins. The first problem is evoluating in the right direction and the second one should be considered as an enrichment rather than as a negative fact. One must admit, nevertheless, that different subdisciplines will tend to live their own life, but that continuing contacts (such as joint conferences) remain important and are necessary for the further development of all these subdisciplines.

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Abstract  

The paper focusses on possible mathematical theories of citation and on the intrinsic problems related to it. It sheds light on aspects of mathematical complexity as e.g. encountered in fractal theory and Mandelbrot's law. There is also a discussion on dynamical aspects of citation theory as reflected in evolutions of journal rankings, centres of gravity or of the set of source journals. Some comments are given in this connection on growth and obsolescence.

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Abstract  

The generalized (also called extended) transfer principles as introduced in two earlier papers by Egghe and Rousseau are known to be stronger properties than the classical transfer principle of Dalton. Hence, functions satisfying one of these generalized principles are very good concentration measures. This paper studies the following non-trivial problem: how many different generalized transfer principles can a function satisfy? We show that a function can, at most, satisfy one generalized transfer principle. This also shows that a further generalization of transfer principles, comprising the generalized ones, is not possible. The proof of this result involves the solution of a norm problem in mathematical analysis and analytical geometry.

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Abstract  

This paper proves two regularities that where found in the paper (Larivière et al. (2007). Long-term patterns in the aging of the scientific literature, 1900–2004. In Proceedings of ISSI 2007. CSIC, Madrid, Spain, pp. 449–456.). The first is that the mean as well as the median reference age increases in time. The second is that the Price Index decreases in time. Using an exponential literature growth model we prove both regularities. Hence we show that the two results do not have a special informetric reason but that they are just a mathematical consequence of a widely accepted simple literature growth model.

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Abstract

The single publication H-index of Schubert is applied to the papers in the Hirsch-core of a researcher, journal or topic. Four practical examples are given and regularities are explained: the regression line of the single publication H-index of the ranked papers in the Hirsch-core is decreasing. We propose two measures of indirect citation impact: the average of the single publication H-indices of the papers in the Hirsch-core and the H-index of these single publication H-indices, defined as the indirect H-index. Formulae for these indirect citation impact measures are given in the Lotkaian context.

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Abstract  

Consider a country's national output, measured by counting the number of authors from countryc that collaborate in every paper in a bibliography. Depending on whether countryc appears at least once in every paper, we are able to deduce the corresponding relationship betweenc's fractional score and its fraction of multinational papers to whichc belongs. One of these models, a slowly decreasing concave function is similar to the relation observed byNederhof andMoed 1 between the fractionated score of a countryc and its fraction of multinational papers. The proof of the models developed here uses a stochastic property of weighting schemes, namely that the average fractional score of a country equals its total score.

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Abstract  

The present paper studies fractal features (such as the fractal dimension) of hypertext systems (such as WWW) and establishes the link with informetric parameters. More concretely, a formula for the fractal dimension in function of the average number of hyperlinks per page is presented and examples are calculated. In general the complexity of these systems is high. This is also expressed by formulae for the total number of hypertext systems that are possible, given a fixed number of documents.

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