A function f : V (G) → {0, 1, 2} is a Roman dominating function for a graph G = (V,E) if for every vertex v with f(v) = 0, there exists a vertex w ∈ N(v) with f(w) = 2. Emperor Constantine had the requirement that an army or legion could be sent from its home to defend a neighboring location only if there was a second army which would stay and protect the home. Thus, there are two types of armi...

AbstractThe purpose of this study was to investigate the controllable operating parameters influence, including pH, solid content, collector, co-collector, and depressant dose, and conditioning time, on apatite flotation kinetics. Four first order flotation kinetic models are tested on batch flotation time-recovery profiles. The results of batch flotation tests and the fitting of first-order ki...

Filtration under an ultrasonic field is a technique that is gaining importance in the wastewater treatment research field, not only due to its ability as a cleaning mechanism, but also as a filtration intensifier. The main objective of this research was the study of the influence of ultrasonic waves on the filtration of the oilfield wastewater (known as produced water) in order to increase the ...

Close observation at a number of South African water treatment plants has shown that media losses during backwashing are excessive – much higher than anticipated. The only likely reasons for this phenomenon are either that insufficient freeboard was provided by the designer or that the mechanical behaviour of the media gradually changes after being placed in the filters. A number of media tests...

To select the best available packing material for malodorous organic gases such as toluene and benzene, biofilter performance was compared in biofilters employed different packing materials including porous ceramic (celite), Jeju scoria (lava), a mixture of granular activated carbon (GAC) and celite (GAC/celite), and cubic polyurethane foam (PU). A toluene-degrading bacterium, Stenotrophomonas ...