An elliptic property of parabolic trajectories

The curve joining the points of maximum height in the parabolas of ideal projectile motion is shown to be an ellipse. Some features of the motion are illustrated with the help of such ellipse.Comment: 4 pages, 1 figure. A shorter version of this typescript is scheduled to be published in the Am. J. Phys. probably in May 200

Bioindicators as a tool for monitoring and control biofilm reactors : a simplified approach

The control of wastewater treatment plants requires an extensive monitoring programme based on physicochemical costly routine analysis. Microbial populations are well known indicators of operational conditions in biological reactors. This research was carried out by the CENTA and the University of Minho in the scope of the Erasmus programme. The aim of the work was the development of a simplified approach, based on biological indicators, for monitoring small biofilm wastewater treatment processes. In that regard, protozoa and metazoan were monitored at CENTA experimental plants - namely a trickling filter and a rotating biological contactor -, and correlated with influent wastewater and effluent composition. The relationship between wastewater performance and the microbiological composition of the biofilm was identified and assessed. Results indicate that a methodology based on the bioindicators provides useful data for process monitoring and control of small wastewater treatment plants, thus diminishing the associated costs of routine analysis and providing information when such analysis aren’t easily available

Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.Comment: 22 pages, no figure