A remark on embedded bipartite graphs
Abstract A use of Euler's formula in Zaks ( J. Combin. Theory Ser. B 32 (1982) , 95–98) is replaced by an elementary argument on permutations.
Extending an extension of Grinberg's theorem
Abstract Grinberg's well-known necessary condition for a planar graph to be Hamiltonian was extended by Shimamoto to a condition for having a 2-factor. We derive a necessary condition for a planar graph to contain a collection of n disjoint circuits, none of which separates any other two. All is done in terms of the numbers p k which denote the numbers of k -gonal faces.
Remotely-Piloted Helicopter Citrus Yield Map Estimation
A remotely-piloted Gas Xcell mini-helicopter with GPS, wireless Ethernet, and a machinevision system was flown over orange trees to take overhead images. The individual tree images were processed to estimate the number of orange pixels in the images. The fruit yield of individualtrees at harvest a month later had an r-squared value of 0.373 with the number of orange pixels onthe irrigated tree images. While it was demonstrated that a remotely-piloted mini-helicopter could beused to acquire useful overhead images of citrus trees, substantial further research is needed toimprove the accuracy of estimates of individual tree yields or health.