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James Bible. (HTTP://WWW2.CCIM.ORG/BIBLE/DCB.HTML) [3] Li, Wentian 2002. Bibliography of references to Zipf's law. (HTTP

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Abstract  

Here, the quantitative theory of translation is shown to be of great utility in describing scientific networks. In fact, we deduce a new Zipf's Law for the descriptors of a set of documents, based on the concepts of centres of interest and of irreversible parallel translations. This new law can be generalized to other phenomena, such as the distribution of the sizes of cocitation clusters. Finally, we have established the model, for descriptor presence in a network, which closely fits the values recorded.

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presence of competition, and referred to the contributions of speakers to conferences and the performances of individuals or teams in various sports as further manifestations of the same pattern. He concluded that the Bradford's law, Zipf's law, Lotka's law

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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  

The definitions of the term bibliometrics as used in the literature are examined and evaluated. Most such definitions are held to be too broad. A new definition is proposed; then its advantages and possible defects pointed out. A crucial question is whether Zipf's law of word occurrence should be considered a part of this particular sub-discipline.

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Abstract  

N-grams are generalized words consisting of N consecutive symbols, as they are used in a text. This paper determines the rank-frequency distribution for redundant N-grams. For entire texts this is known to be Zipf's law (i.e., an inverse power law). For N-grams, however, we show that the rank (r)-frequency distribution is

\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} $${\text{P}}_{\text{N}} \left( {\text{r}} \right) = \frac{{\text{C}}}{{{\text{(}}\psi _{\text{N}} ({\text{r))}}^\beta }},$$ \end{document}
, where N is the inverse function of fN(x)=x lnN–1x. Here we assume that the rank-frequency distribution of the symbols follows Zipf's law with exponent .

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Scientometrics
Authors: L. Quoniam, F. Balme, H. Rostaing, E. Giraud, and J. Dou

Abstract  

Zipf's law was used to qualify all the key-words of documents in a data set. This qualification was used to build a graphical representation of the resulting indicator in each document. The graphical resolution leads to a document dispatch in a three dimensional space. This graphical representation was used as an information retrieval tool without using any keyword. The presentation of a case study is internet available. The graph is drawn in Virtual Reality Markup Language (VRML) allowing a dynamic picture which is linked to a Database Management System (FreeWais). The experimentation was drawn to get a first impression of documents data set by querying without any keyword.

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Abstract  

The hypothesis proposed by the author expresses that Zipf's law is only fulfilled on rank distributions which correspond to highly integrated (closed) subject fields. This hypothesis was tested on vast amount of empirical data. It was shown that document files in integrated fields are characterised by thematic, chronological (and sometimes geographical) closedness, as well as closedness by citation. Relationships were found between empirical facts usually considered in isolation within the frameworks of different scientometric and bibliometric theories (the theory of information concentration and scattering, obsolescence theory, theory of changing source productivity).

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reports that the Lotkaian exponent α varies between 1.3 and 3. Let (2) be Zipf's law ( g ( r ) is the item density in the source on rank density r and where T denotes the total number of sources). Then the following Theorem is valid

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