NDLI: Solving a Generalized Gauss Problem

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Generalised Trapezoid-Type Inequalities for Complex Functions Defined on Unit Circle with Applications for Unitary Operators in Hilbert Spaces

Some Monotonicity Properties of Convex Functions with Applications

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Generalized Weyl Spectrum of Upper Triangular Operator Matrices

Solving a Generalized Gauss Problem

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Solving a Generalized Gauss Problem

Content Provider	Springer Nature Link
Author	Zachos, Anastasios N.
Copyright Year	2014
Abstract	We solve a generalized Gauss problem in the Euclidean plane which states that: Given a convex quadrilateral, a positive number (weight) that corresponds to each of its vertices and a length of a linear segment which connects two mobile interior points of the quadrilateral find the minimum weighted network, which connects two of the vertices with one interior point and the other two with another interior point (Generalized Gauss tree). Furthermore, we introduce a generalized Gauss variable which corresponds to the unknown weight of the given distance which connects the two mobile interior points and obtain a degenerate generalized Gauss tree which corresponds to a specific value of the generalized Gauss variable that minimizes the length of the induced generalized Gauss trees and the weighted Fermat–Torricelli tree for a specific value of the generalized Gauss variable that maximizes the length of the induced generalized Gauss trees. Following this technique, we introduce a new class of generalized Gauss trees that we call absorbing generalized Gauss trees and a new class of Fermat–Torricelli trees that we call absorbing Fermat–Torricelli trees with respect to the sum of the four given weights of the convex quadrilateral.
Ending Page	1083
Page Count	15
Starting Page	1069
File Format	PDF
ISSN	16605446
e-ISSN	16605454
Journal	Mediterranean Journal of Mathematics
Issue Number	3
Volume Number	12
Language	English
Publisher	Springer Basel
Publisher Date	2014-08-06
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	weighted Fermat–Torricelli point Convex sets in $2$ dimensions (including convex curves) Generalized Gauss problem absorbing Fermat–Torricelli tree generalized Gauss variable Steiner systems Mathematics weighted Fermat–Torricelli problem absorbing generalized Gauss tree Spherical and hyperbolic convexity Generalized quadrangles, generalized polygons
Content Type	Text
Resource Type	Article
Subject	Mathematics

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An analytical solution of the weighted Fermat–Torricelli problem on a unit sphere

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Analytical solution of the weighted Fermat-Torricelli problem for convex quadrilaterals in the Euclidean plane: The case of two pairs of equal weights

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Realization of abstract convex geometries by point configurations, Part 1

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The discrete horospherical $p$-Minkowski problem in hyperbolic space

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