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A Lagrangian program detecting the Weighted Fermat-Steiner-Frechet multitree for a Frechet multisimplex in the dimensional Euclidean Space
Anastasios N. Zachos
In this paper, we introduce the Fermat-Steiner-Frechet problem for a given tuple of positive real numbers determining the edge lengths of an simplex in $\mat…
A generalized Fermat-Torricelli tree that has acquired a subconscious on a surface
Anastasios Zachos
We study a generalized Fermat-Torricelli (S.FT) problem for infinitesimal geodesic triangles on a C^2 complete surface M with variable Gaussian curvature a < K < b, for a, b in R,…
The plasticity of non-overlapping convex sets in R^{2}
Anastasios Zachos
We study a generalization of the weighted Fermat-Torricelli problem in the plane, which is derived by replacing vertices of a convex polygon by 'small' closed convex curves with we…
The plasticity of some mass transportation networks in the three dimensional Euclidean Space
Anastasios Zachos
We obtain an important generalization of the inverse weighted Fermat-Torricelli problem for tetrahedra in R^3 by assigning at the corresponding weighted Fermat-Torricelli point a r…
Solving a problem of angiogenesis of degree three
Anastasios N. Zachos
An absorbing weighted Fermat-Torricelli tree of degree four is a weighted Fermat-Torricelli tree of degree four which is derived as a limiting tree structure from a generalized Gau…
An analytical solution of the weighted Fermat-Torricelli problem on the unit sphere
Anastasios N. Zachos
We obtain an analytical solution for the weighted Fermat-Torricelli problem for an equilateral geodesic triangle A_1A_2A_3 which is composed by three equal geodesic arcs (sides) of…
Analytical solution of the weighted Fermat-Torricelli problem for tetrahedra: The case of two pairs of equal weights
Anastasios N. Zachos
The weighted Fermat-Torricelli problem for four non-collinear and non-coplanar points in the three dimensional Euclidean Space states that: Given four non-collinear and non-coplana…
Two new analytical solutions and two new geometrical solutions for the weighted Fermat-Torricelli problem in the Euclidean plane
Anastasios N. Zachos
We obtain two analytic solutions for the weighted Fermat-Torricelli problem in the Euclidean Plane which states that: Given three points in the Euclidean plane and a positive real…
Analytical solution of the weighted Fermat-Torricelli problem for convex quadrilaterals in the Euclidean plane: The case of two pairs of equal weights
Anastasios N. Zachos
The weighted Fermat-Torricelli problem for four non-collinear points in R^2 states that: Given four non-collinear points A_1, A_2, A_3,A_4 and a positive real number (weight) B_i w…
A plasticity principle of convex quadrilaterals on a convex surface of bounded specific curvature
Anastasios Zachos
We derive the plasticity equations for convex quadrilaterals on a complete convex surface with bounded specific curvature and prove a plasticity principle which states that: Given…