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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  

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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Abstract  

In this paper, the special place of Zipf's law and Pareto's law amongst other classical informetric laws (such as Bradford's graphical and verbal law, Weber-Fechner's or Brookes', Leimkuhler's and Mandelbrot's) is revealed and explained. Equivalencies amongst some of these laws are proved. We also determine the conditions under which Bradford's graphical law is a special case of Bradford's verbal law.

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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  

A model for measuring the congestion in library shelves after j years (j∈ ℕ) is obtained by taking j-fold convolutions of the distributions that describe the yearly growth of literature (e.g., periodicals, books on a certain topic,…) From this one can estimate the expected number of critical points in the shelf, after j years. One can also calculate the probability that there will be m (m∈ ℕ) critical points after j years. The paper closes by examining two concrete cases.

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Abstract

In this short communication we give critical comments on the paper of Perakakis et al. (Scientometrics 85(2):553–559, ) on “Natural selection of academic papers”. The criticism mainly focusses on their unbalanced criticism of peer review and their negative evaluation of the link of peer review with commercial publishing.

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