Fixed-orientation equilateral triangle matching of point sets

Given a point set P and a class C of geometric objects, G(C)(P) is a geometric graph with vertex set P such that any two vertices p and q are adjacent if and only if there is some C is an element of C containing both p and q but no other points from P. We study G(del)(P) graphs where del is the class of downward equilateral triangles (i.e., equilateral triangles with one of their sides parallel to the x-axis and the corner opposite to this side below that side). For point sets in general position, these graphs have been shown to be equivalent to half-Theta(6) graphs and TD-Delaunay graphs. The main result in our paper is that for point sets P in general position, G(del)(P) always contains a matching of size at least vertical bar P vertical bar-1/3] and this bound is tight. We also give some structural properties of G(star)(P) graphs, where is the class which contains both upward and downward equilateral triangles. We show that for point sets in general position, the block cut point graph of G(star)(P) is simply a path. Through the equivalence of G(star)(P) graphs with Theta(6) graphs, we also derive that any Theta(6) graph can have at most 5n-11 edges, for point sets in general position. (C) 2013 Elsevier B.V. All rights reserved.

Comparison of performance of solar photovoltaics on dual axis tracker with fixed axis at 13 degrees N latitude

Tracking systems, that continually orient photovoltaic (PV) panels towards the Sun, are expected to increase the power output from the PV panels. Tremendous amount of research is being done and funds are being spent in order to increase the efficiency of PV cells to generate more power. We report the performance of two almost identical PV systems; one at a fixed latitude tilt and the other on a two-axis tracker. We observed that the fixed axis PV panels generated 336.3 kWh, and the dual-axis Sun-tracked PV panels generated 407.2 kWh during August 2012 March 2013. The tracked panels generated 21.2% more electricity than the optimum tilt angle fixed-axis panels. The cost payback calculations indicate that the additional cost of the tracker can be recovered in 450 days.