Abstract

We introduce an evolutionary structure of Euclidean networks for boundary convex quadrilaterals in the two dimensional Euclidean space (botanological network) which has two roots, one main branch and two branches. A botanological network is a weighted full Steiner tree which is enriched by a collection of instantaneous images of the process of photosynthesis, by assuming mass flow continuity.

Author information

Contact details are reproduced from the original publication and may be historical.

Anastasios N. Zachos

Chiou 43 Street, Chalandri, 15231 Attiki, Greece

azachos@gmail.com

Gerasimos Zouzoulas

G. Zouzoulas Ltd, Meintani 25, 117-41 Athens, Greece

Keywords

  • Weighted Fermat-Torricelli problem
  • weighted Fermat-Torricelli point
  • botanological network
  • weighted Steiner minimal tree
  • inverse weighted Fermat-Torricelli problem
  • convex quadrilateral

Mathematics Subject Classification

51E12, 52A10, 52A55, 51E10

References

  1. K. Bopp: Über das kürzeste Verbindungssystem zwischen vier Punkten, Dissertation, Göttingen (1879).Google Scholar
  2. S. Gueron, R. Tessler: The Fermat-Steiner problem, Amer. Math. Monthly 109 (2002) 443–451.https://doi.org/10.1080/00029890.2002.11919871Google Scholar
  3. A. N. Zachos, G. Zouzoulas: An evolutionary structure of convex quadrilaterals, J. Convex Analysis 15(2) (2008) 411–426.https://doi.org/10.68381/jca15029Google Scholar
  4. A. N. Zachos, G. Zouzoulas: An evolutionary structure of convex quadrilaterals. Part II, J. Convex Analysis 20(2) (2013) 483–493.https://doi.org/10.68381/jca20029Google Scholar

Suggested citation

A. N. Zachos, G. Zouzoulas. “An Evolutionary Structure of Convex Quadrilaterals. Part III.” Journal of Convex Analysis 25 (2018), No. 3, 759–765. https://doi.org/10.68381/jca25052

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press LLC.