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Journal of Convex Analysis 25 (2018), No. 3, 759--765
Copyright Heldermann Verlag 2018

An Evolutionary Structure of Convex Quadrilaterals. Part III

Anastasios N. Zachos
Chiou 43 Street, Chalandri, 15231 Attiki, Greece

Gerasimos Zouzoulas
Meintani 25, 117-41 Athens, Greece

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.

Keywords: Weighted Fermat-Torricelli problem, weighted Fermat-Torricelli point, botanological network, weighted Steiner minimal tree, inverse weighted Fermat-Torricelli problem, convex quadrilateral.

MSC: 51E12, 52A10, 52A55, 51E10

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