Volume 7 Number 1 (Jan. 2017)
Home > Archive > 2017 > Volume 7 Number 1 (Jan. 2017) >
IJAPM 2017 Vol.7(1): 12-23 ISSN: 2010-362X
doi: 10.17706/ijapm.2017.7.1.12-23

Analysis of Sparsely Populated Sets

Kiamran Radjabli
Abstract—Emptiness is usually considered to be absolute and equal to null or zero. This paper proposes to analyze conditions close to emptiness. A relaxation of abstract concepts of zero and emptiness is used to analyze sparsely populated sets. The proposed definition of emptiness is based on the Riemann’s zeta function and depends on the perspective of the point from which emptiness is perceived. The new symmetric and asymmetric analytic continuations are proposed to resolve the asymptotic behavior of the zeta function near the pole. Different levels of infinity and emptiness are associated with “analytic convergence” using the asymmetric analytic continuation for the zeta function. The classifications of emptiness and infinity improve efficiency of data search in sparsely populated large sets, especially, when the data retrieval effort depends on the distance to remote data source.

Index Terms—Sparse, population, infinity, sets, zero, emptiness, classification, zeta function, deformation, search.

Kiamran Radjabli is with Utilicast, La Jolla, California, USA (email: kradjabli@utilicast.com).

Cite: Kiamran Radjabli, "Analysis of Sparsely Populated Sets," International Journal of Applied Physics and Mathematics vol. 7, no. 1, pp. 12-23, 2017.

General Information

ISSN: 2010-362X (Online)
Abbreviated Title: Int. J. Appl. Phys. Math.
Frequency: Quarterly
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca 
Abstracting/ Indexing: INSPEC(IET), CNKI, Google Scholar, EBSCO, Chemical Abstracts Services (CAS), etc.
E-mail: ijapm@iap.org
  • Dec 27, 2021 News!

    IJAPM Vol 9 & Vol 10 have been indexed by Inspec   [Click]

  • Jan 04, 2023 News!

    The paper published in Vol 13, No 1 has received dois from Crossref

  • Jan 04, 2023 News!

    IJAPM Vol 13, No 1 has been published with online version   [Click]

  • Jan 04, 2023 News!

    All the papers published in Vol 10-Vol 12 have received dois from Crossref

  • Sep 23, 2022 News!

    IJAPM Vol 12, No 4 has been published with online version   [Click]

  • Read more>>