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Abstract

Naranan's important theorem, published in Nature in 1970, states that if the number of journals grows exponentially and if the number of articles in each journal grows exponentially (at the same rate for each journal), then the system satisfies Lotka's law and a formula for the Lotka's exponent is given in function of the growth rates of the journals and the articles. This brief communication re-proves this result by showing that the system satisfies Zipf's law, which is equivalent with Lotka's law. The proof is short and algebraic and does not use infinitesimal arguments.

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Abstract

Focuses on possible mathematical theories of citation and on the intrinsic problems related to it. Sheds light on aspects of mathematical complexity as encountered in, for example, fractal theory and Mandelbrot's law. Also discusses dynamical aspects of citation theory as reflected in evolutions of journal rankings, centres of gravity or of the set of source journals. Makes some comments in this connection on growth and obsolescence

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Abstract

Power laws as defined in 1926 by A. Lotka are increasing in importance because they have been found valid in varied social networks including the Internet. In this article some unique properties of power laws are proven. They are shown to characterize functions with the scalefree property (also called seif-similarity property) as weIl as functions with the product property. Power laws have other desirable properties that are not shared by exponential laws, as we indicate in this paper. Specifically, Naranan (1970) proves the validity of Lotka's law based on the exponential growth of articles in journals and of the number of journals. His argument is reproduced here and a discrete-time argument is also given, yielding the same law as that of Lotka. This argument makes it possible to interpret the information production process as a seif-similar fractal and show the relation between Lotka's exponent and the (seif-similar) fractal dimension of the system. Lotkaian informetric systems are seif-similar fractals, a fact revealed by Mandelbrot (1977) in relation to nature, but is also true for random texts, which exemplify a very special type of informetric system.

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Abstract

We present a rationale for the Hirsch-index rank-order distribution and prove that it is a power law (hence a straight line in the log-log scale). This is confirmed by experimental data of Pyykkö and by data produced in this article on 206 mathematics journals. This distribution is of a completely different nature than the impact factor (IF) rank-order distribution which (as proved in a previous article) is S-shaped. This is also confirmed by our example. Only in the log-log scale of the h-index distribution do we notice a concave deviation of the straight line for higher ranks. This phenomenon is discussed.

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Abstract

Type/Token-Taken informetrics is a new part of informetrics that studies the use of items rather than the items itself. Here, items are the objects that are produced by the sources (e.g., journals producing articles, authors producing papers, etc.). In linguistics a source is also called a type (e.g., a word), and an item a token (e.g., the use of words in texts). In informetrics, types that occur often, for example, in a database will also be requested often, for example, in information retrieval. The relative use of these occurrences will be higher than their relative occurrences itself; hence, the name Type/ Token-Taken informetrics. This article studies the frequency distribution of Type/Token-Taken informetrics, starting from the one of Type/Token informetrics (i.e., source-item relationships). We are also studying the average number my* of item uses in Type/Token-Taken informetrics and compare this with the classical average number my in Type/Token informetrics. We show that my* >= my always, and that my* is an increasing function of my. A method is presented to actually calculate my* from my, and a given a, which is the exponent in Lotka's frequency distribution of Type/Token informetrics. We leave open the problem of developing non-Lotkaian Type/TokenTaken informetrics.

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Abstract

Aims to inform researchers about metrics so that they become aware of the evaluative techniques being applied to their scientific output. Understanding these concepts will help them during their funding initiatives, and in hiring and tenure. The book not only describes what indicators do (or are designed to do, which is not always the same thing), but also gives precise mathematical formulae so that indicators can be properly understood and evaluated. Metrics have become a critical issue in science, with widespread international discussion taking place on the subject across scientific journals and organizations. As researchers should know the publication-citation context, the mathematical formulae of indicators being used by evaluating committees and their consequences, and how such indicators might be misused, this book provides an ideal tome on the topic. Provides researchers with a detailed understanding of bibliometric indicators and their applications. Empowers researchers looking to understand the indicators relevant to their work and careers. Presents an informed and rounded picture of bibliometrics, including the strengths and shortcomings of particular indicators. Supplies the mathematics behind bibliometric indicators so they can be properly understood. Written by authors with longstanding expertise who are considered global leaders in the field of bibliometrics

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Date

14. 2.2012 12:53:22

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Source

Journal of information science. 22(1996) no.3, S.165-170

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Date

14. 8.2004 19:17:22