, Volume 34, Issue 2, pp 285–315 | Cite as

On the influence of production on utilization functions: Obsolescence or increased use?

  • L. Egghe
  • I. K. Ravichandra Rao
  • R. Rousseau


We study the influence of production on utilization functions. A concrete example of this is the influence of the growth of literature on the obsolescence (aging) of this literature. Here, synchronous as well as diachronous obsolescence is studied. Assuming an increasing exponential function for production and a decreasing one for aging, we show that, in the synchronous case, the larger the increase in production, the larger the obsolescence. In the diachronous case the opposite relation holds: the larger the increase in production the smaller the obsolescence rate. This has also been shown previously byEgghe but the present proof is shorter and yields more insight in the derived results. If a decreasing exponential function is used to model production the opposite results are obtained. It is typical for this study that there are two different time periods: the period of production (growth) and — per year appearing in the production period — the period of aging (measured synchronously and diachronously). The interaction of these periods is described via convolutions (discrete as well as continuous).


Convolution Utilization Function Exponential Function Opposite Result Production Period 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B. C. Brookes, Obsolescence of special library periodicals: sampling errors and utility contours,Journal of the American Society for Information Science, 21 (1970) 320–329.Google Scholar
  2. 2.
    B. C. Brookes, Aging in scientific literature,Journal of Documentation, 36 (1980) 164–165.Google Scholar
  3. 3.
    Q. L. Burrell. On the growth of bibliographies with time: an exercise in bibliometric prediction,Journal of Documentation, 45 (1989) 302–317.Google Scholar
  4. 4.
    L. Egghe, I. K. R. Rao, Citation age data and the obsolescence function: fits and explanations,Information Processing and Management, 28 (1992) 201–217.Google Scholar
  5. 5.
    L. Egghe, I. K. R. Rao, Classification of growth models based on growth rates and its applications,Scientometrics, 25 (1992) 5–46.Google Scholar
  6. 6.
    B. C. Griffith, P. Servi, A. Anker, C. Drott, The aging of scientific literature: a citation analysis,Journal of Documentation, 35 (1979) 179–196.Google Scholar
  7. 7.
    F. Xiaorong, A study of the problem of the aging of books in university libraries: strategies for countering its effects,Journal of the American Society for Information Science, 43 (1992) 501–505.Google Scholar
  8. 8.
    D. K. Gapen, S. P. Milner, Obsolescence,Library Trends, 30 (1981) 107–124.Google Scholar
  9. 9.
    M. B. Line, Changes in the use of literature with time — obsolescence revisited,Library Trends, 41 (1993) 665–683.Google Scholar
  10. 10.
    L. Egghe, R. Rousseau,Introduction to Informetrics, Amsterdam, Elsevier, 1990.Google Scholar
  11. 11.
    G. A. Barnett, E. L. Fink, M. B. Debus, A mathematical model of academic citation age,Communication Research, 16 (1989) 510–531.Google Scholar
  12. 12.
    E. S. Aversa, Citation patterns of highly cited papers and their relationship to literature aging: a study of the working literature,Scientometrics, 7 (1985) 383–389.Google Scholar
  13. 13.
    I. K. R. Rao, B. M. Meera, Growth and obsolescence of literature: an empericial study, In:Informetrics-91,I. K. R. Rao (Ed.), Bangalore, Sarada Ranganathan Endowment for Library Science, 1992, 377–394.Google Scholar
  14. 14.
    E. R. Stinson, F. W. Lancaster, Synchronous versus diachronous methods in the measurement of obsolescence by citation studies,Journal of Information Science, 13 (1987) 65–74.Google Scholar
  15. 15.
    L. L. Hargens, D. H. Felmlee, Structural determinants of stratification in science,American Sociological Review, 49 (1984) 685–697.Google Scholar
  16. 16.
    L. Egghe, On the influence of growth on obsolescence,Scientometrics, 27 (1993) 195–214.Google Scholar
  17. 17.
    L. Egghe, A theory of continuous rates and applications to the theory of growth and obsolescence rates,Information Processing and Management, 30 (1994) 279–292.Google Scholar
  18. 18.
    W. Rudin,Functional Analysis, New York, McGraw-Hill, 1973.Google Scholar
  19. 19.
    R. L. Graham, D. E. Knuth, O. Patashnik,Concrete Mathematics, Reading (MA), Addison-Wesley, 1989.Google Scholar
  20. 20.
    L. Egghe, Consequences of Lotka's law in the case of fractional counting of authorships an of first author counts,Mathematical and Computer Modelling, 18 (1993) 63–77.Google Scholar
  21. 21.
    L. Egghe, Special features of the author-publication relationship and a new explanation of Lotka's law based on convolution theory,Journal of the American Society for Information Science, 45 (1994) 422–427.Google Scholar

Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • L. Egghe
    • 1
    • 3
    • 2
  • I. K. Ravichandra Rao
    • 3
  • R. Rousseau
    • 3
    • 4
    • 2
  1. 1.LUCDiepenbeekBelgium
  2. 2.Informatie-en BibliotheekwetenschapUIAWilrijkBelgium
  3. 3.DRTC, ISIBangaloreIndia
  4. 4.KIHWVOostendeBelgium

Personalised recommendations