A theory of continuous rates and applications to the theory of growth and obsolescence rates

doi:10.1016/0306-4573(94)90070-1

Information Processing & Management

Volume 30, Issue 2, March–April 1994, Pages 279-292

https://doi.org/10.1016/0306-4573(94)90070-1 Get rights and content

Abstract

For functions ƒ of a continuous variable t, we define the term “rate” (as, e.g., rate of growth or of obsolescence) as the exponential function of the derivative of the logarithm of this function (i.e., e^(logƒ)'). This replaces discrete calculations, such as $ƒ(t + 1) ƒ(t)$ , which is not so appropriate in this continuous context. We investigate this transformation (which is in fact the exponential function of the Fechner law), and show that it indeed has all properties that we can expect from a “rate” function. We then apply these findings to the results of three previous papers and again prove the main results in this continuous setting.

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Generally, obsolescence studies are synchronous because these are easier than diachronous studies to conduct. For functions of a continuous variable, Egghe (1994) defined the term rate of growth or obsolescence as an exponential function of the derivative of the log of the function. Egghe (1993); Egghe et al. (1995) observed that the rate of obsolescence varies and that this variation can be calculated as a utilization (mathematical) function.
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Five years later, Stevens (1953) publishes and paper citing Vickery (1948) and Bradford (1948) in which he explains the features of dispersion of specialized literature. In the early 1960s, three references to Bradford appear, i.e., Fourmont and Kervégant (1960), Kendall (1960) and Cole (1962). Every year from 1966 and until 2012 an average of 12 papers per year employing the strategies proposed by Bradford (1934, 1948) were found in the sample under study.
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Se analiza la literatura producida sobre la ley de Bradford desde 1934 hasta junio del 2012. Se encontraron 936 documentos producidos por 1 123 autores diferentes. Estos autores utilizaron 16 idiomas para comunicar los resultados de sus investigaciones; el inglés fue el idioma dominante, seguido del chino, español y portugués. Se identificó también a 15 autores como los más productivos, quienes publican sus investigaciones en inglés, en la forma de artículos en revistas académicas, y las presentan en congresos del área. Esta literatura crece de forma exponencial (R² = 0.974), a una tasa de 5.4% al año y duplica su tamaño cada 13.2 años.
Growth of Literature on Bradford's Law
2016, Investigacion Bibliotecologica
Se analiza la literatura producida sobre la ley de Bradford desde 1934 hasta junio del 2012. Se encontraron 936 documentos producidos por 1 123 autores diferentes. Estos autores utilizaron 16 idiomas para comunicar los resultados de sus investigaciones; el inglés fue el idioma dominante, seguido del chino, español y portugués. Se identificó también a 15 autores como los más productivos, quienes publican sus investigaciones en inglés, en la forma de artículos en revistas académicas, y las presentan en congresos del área. Esta literatura crece de forma exponencial (R² = 0.974), a una tasa de 5.4 % al año y duplica su tamaño cada 13.2 años.
This paper analyzes the literature produced on Bradford’ Law from 1934 to June 2012. The study compiled 936 documents produced by 1,123 authors, working in sixteen languages to communicate the results of their research, with English the leading language, followed by Chinese, Spanish and Portuguese. The study reveals the fifteen most productive authors, all of which work in English in both academic journals and conference settings. This literature is growing exponentially (R² = 0.974), at a rate of 5.4% per year and doubling in size every 13.2 years.
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Se analiza la obsolescencia de la literatura producida sobre la Ley de Lotka hasta 2010. En ese periodo no parece haber un patrón de obsolescencia definido. Sin embargo, los datos acumulados muestran una comportamiento obsolescente con una tasa de decrecimiento anual del 3.9 % y una tasa de duplicación cada 17.4 años. La estadística indica un buen ajuste al modelo exponencial, con un R² de 0.985 para la literatura a un nivel de significancia de 0.01.
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A theory of continuous rates and applications to the theory of growth and obsolescence rates

Abstract

Information Processing & Management

The size and growth of serial literature 1950–1987, in terms of the number of articles per serial

Scientometrics

Obsolescence of special library periodicals: Sampling errors and utility contours

Journal of the American Society for Information Science

The growth, utility and obsolescence of scientific periodical literature

Journal of Documentation

A note on ageing in a library circulation model

Journal of Documentation

A second note on ageing in a library circulation model: The correlation structure

Journal of Documentation

A third note on ageing in a library circulation model: Application to future use and relegation

Journal of Documentation

On the growth of bibliographies with time: An exercise in bibliometric prediction

Journal of Documentation

Changes in the use of sociological articles with time: A comparison of diachronous and synchronous data

British Library Lending Review