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  • Author or Editor: L. Egghe x
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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  

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

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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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 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  

The uncitedness factor of a journal is its fraction of uncited articles. Given a set of journals (e.g. in a field) we can determine the rank-order distribution of these uncitedness factors. Hereby we use the Central Limit Theorem which is valid for uncitedness factors since it are fractions, hence averages. A similar result was proved earlier for the impact factors of a set of journals. Here we combine the two rank-order distributions, hereby eliminating the rank, yielding the functional relation between the impact factor and the uncitedness factor. It is proved that the decreasing relation has an S-shape: first convex, then concave and that the inflection point is in the point (μ′, μ) where μ is the average of the impact factors and μ′ is the average of the uncitedness factors.

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Abstract

The single publication H-index, introduced by A. Schubert in 2009 can be applied on all articles in the Hirsch-core of a researcher. In this way one can define the “indirect H-index” of a researcher.

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Abstract

We present a mathematical derivation of the scale-dependence of the h-index. This formula can be used in two cases: one where the units are scale-dependent and one where the units are not scale-dependent. Examples are given.

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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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