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Minimal Impact One-Dimensional Arrays

Author

Listed:
  • Leo Egghe

    (University of Hasselt, 3500 Hasselt, Belgium)

  • Ronald Rousseau

    (Faculty of Social Sciences, University of Antwerp, 2020 Antwerpen, Belgium
    Department MSI, KU Leuven and Centre for R&D Monitoring (ECOOM), 3000 Leuven, Belgium)

Abstract

In this contribution, we consider the problem of finding the minimal Euclidean distance between a given converging decreasing one-dimensional array X in ( R + ) ∞ and arrays of the form A a = ( a , a , … , a ︸ , 0 , 0 , … a t i m e s ) , with a being a natural number. We find a complete, if not always unique, solution. Our contribution illustrates how a formalism derived in the context of research evaluation and informetrics can be used to solve a purely mathematical problem.

Suggested Citation

  • Leo Egghe & Ronald Rousseau, 2020. "Minimal Impact One-Dimensional Arrays," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:811-:d:359224
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    References listed on IDEAS

    as
    1. Egghe, Leo & Rousseau, Ronald, 2019. "Infinite sequences and their h-type indices," Journal of Informetrics, Elsevier, vol. 13(1), pages 291-298.
    2. Leo Egghe, 2006. "Theory and practise of the g-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 131-152, October.
    3. Ludo Waltman & Nees Jan van Eck, 2012. "The inconsistency of the h-index," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 63(2), pages 406-415, February.
    4. Ludo Waltman & Nees Jan van Eck, 2012. "The inconsistency of the h‐index," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 63(2), pages 406-415, February.
    5. Denis Bouyssou & Thierry Marchant, 2011. "Ranking scientists and departments in a consistent manner," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 62(9), pages 1761-1769, September.
    6. van Eck, N.J.P. & Waltman, L., 2008. "Generalizing the h- and g-indices," ERIM Report Series Research in Management ERS-2008-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Egghe, Leo & Rousseau, Ronald, 2019. "Solution by step functions of a minimum problem in L2[0,T], using generalized h- and g-indices," Journal of Informetrics, Elsevier, vol. 13(3), pages 785-792.
    8. Denis Bouyssou & Thierry Marchant, 2011. "Ranking scientists and departments in a consistent manner," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 62(9), pages 1761-1769, September.
    9. van Eck, Nees Jan & Waltman, Ludo, 2008. "Generalizing the h- and g-indices," Journal of Informetrics, Elsevier, vol. 2(4), pages 263-271.
    10. Alonso, S. & Cabrerizo, F.J. & Herrera-Viedma, E. & Herrera, F., 2009. "h-Index: A review focused in its variants, computation and standardization for different scientific fields," Journal of Informetrics, Elsevier, vol. 3(4), pages 273-289.
    11. Egghe, Leo & Rousseau, Ronald, 2020. "Polar coordinates and generalized h-type indices," Journal of Informetrics, Elsevier, vol. 14(2).
    Full references (including those not matched with items on IDEAS)

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