About a conjecture for uniformly isochronous polynomial centers
We study a specific family of uniformly isochronous polynomial systems. Our results permit to solve a problem about centers of such systems.
COMMUTATORS AND LINEARIZATIONS OF ISOCHRONOUS CENTRES
— We study isochronous centers of some classes of plane differential systems. We consider systems with constant angular speed, both with homogeneous and nonhomogenous nonlinearities. We show how to construct linearizations and first integrals of such systems, if a commutator is known. Commutators are found for some classes of systems. The results obtained are used to prove the isochronicity of some classes of centers, and to find first integrals for a class of Liénard equations with isochronous centers.
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.