IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i5p811-d359224.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/5/811/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/5/811/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. van Eck, Nees Jan & Waltman, Ludo, 2008. "Generalizing the h- and g-indices," Journal of Informetrics, Elsevier, vol. 2(4), pages 263-271.
    3. 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.
    4. Leo Egghe, 2006. "Theory and practise of the g-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 131-152, October.
    5. 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.
    6. Egghe, Leo & Rousseau, Ronald, 2020. "Polar coordinates and generalized h-type indices," Journal of Informetrics, Elsevier, vol. 14(2).
    7. Egghe, Leo & Rousseau, Ronald, 2019. "Infinite sequences and their h-type indices," Journal of Informetrics, Elsevier, vol. 13(1), pages 291-298.
    8. 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.
    9. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Leo Egghe & Ronald Rousseau, 2021. "The h-index formalism," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 6137-6145, July.
    2. Bouyssou, Denis & Marchant, Thierry, 2014. "An axiomatic approach to bibliometric rankings and indices," Journal of Informetrics, Elsevier, vol. 8(3), pages 449-477.
    3. Leo Egghe & Ronald Rousseau, 2019. "Measures of linear type lead to a characterization of Zipf functions," Scientometrics, Springer;Akadémiai Kiadó, vol. 121(3), pages 1707-1715, December.
    4. Marcin Kozak & Lutz Bornmann, 2012. "A New Family of Cumulative Indexes for Measuring Scientific Performance," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-4, October.
    5. Egghe, Leo & Rousseau, Ronald, 2020. "Polar coordinates and generalized h-type indices," Journal of Informetrics, Elsevier, vol. 14(2).
    6. Deming Lin & Tianhui Gong & Wenbin Liu & Martin Meyer, 2020. "An entropy-based measure for the evolution of h index research," Scientometrics, Springer;Akadémiai Kiadó, vol. 125(3), pages 2283-2298, December.
    7. Lathabai, Hiran H., 2020. "ψ-index: A new overall productivity index for actors of science and technology," Journal of Informetrics, Elsevier, vol. 14(4).
    8. Serge Galam, 2011. "Tailor based allocations for multiple authorship: a fractional gh-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(1), pages 365-379, October.
    9. Yang, Alex Jie & Wu, Linwei & Zhang, Qi & Wang, Hao & Deng, Sanhong, 2023. "The k-step h-index in citation networks at the paper, author, and institution levels," Journal of Informetrics, Elsevier, vol. 17(4).
    10. Kuan, Chung-Huei & Huang, Mu-Hsuan & Chen, Dar-Zen, 2011. "Ranking patent assignee performance by h-index and shape descriptors," Journal of Informetrics, Elsevier, vol. 5(2), pages 303-312.
    11. Wei, Shelia X. & Tong, Tong & Rousseau, Ronald & Wang, Wanru & Ye, Fred Y., 2022. "Relations among the h-, g-, ψ-, and p-index and offset-ability," Journal of Informetrics, Elsevier, vol. 16(4).
    12. Maor Weinberger & Maayan Zhitomirsky-Geffet, 2021. "Diversity of success: measuring the scholarly performance diversity of tenured professors in the Israeli academia," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(4), pages 2931-2970, April.
    13. J. E. Hirsch, 2019. "hα: An index to quantify an individual’s scientific leadership," Scientometrics, Springer;Akadémiai Kiadó, vol. 118(2), pages 673-686, February.
    14. Bornmann, Lutz & Mutz, Rüdiger & Hug, Sven E. & Daniel, Hans-Dieter, 2011. "A multilevel meta-analysis of studies reporting correlations between the h index and 37 different h index variants," Journal of Informetrics, Elsevier, vol. 5(3), pages 346-359.
    15. Christoph Steinbrüchel, 2019. "A citation index for principal investigators," Scientometrics, Springer;Akadémiai Kiadó, vol. 118(1), pages 305-320, January.
    16. Egghe, Leo & Rousseau, Ronald, 2022. "Rank-frequency data and impact in a continuous model: Introducing impact bundles," Journal of Informetrics, Elsevier, vol. 16(3).
    17. Ana Paula dos Santos Rubem & Ariane Lima Moura & João Carlos Correia Baptista Soares de Mello, 2015. "Comparative analysis of some individual bibliometric indices when applied to groups of researchers," Scientometrics, Springer;Akadémiai Kiadó, vol. 102(1), pages 1019-1035, January.
    18. Egghe, Leo, 2024. "Mathematical informetrics: Hirsch-type equations and bundles," Journal of Informetrics, Elsevier, vol. 18(1).
    19. Kuan, Chung-Huei & Huang, Mu-Hsuan & Chen, Dar-Zen, 2011. "Positioning research and innovation performance using shape centroids of h-core and h-tail," Journal of Informetrics, Elsevier, vol. 5(4), pages 515-528.
    20. J. E. Hirsch, 2010. "An index to quantify an individual’s scientific research output that takes into account the effect of multiple coauthorship," Scientometrics, Springer;Akadémiai Kiadó, vol. 85(3), pages 741-754, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:811-:d:359224. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.