Abstract: The link between coordinate transformations in the plane and their effects on the graph of a function can be difficult for students studying college level mathematics to comprehend. To solidify this conceptual link in the mind of a student Microsoft Excel can serve as a convenient graphing tool and pedagogical aid. The authors of this paper describe how various transformations and their related functional symmetry properties can be graphically displayed with an Excel spreadsheet.
Abstract: This paper reports the results of an experimental study
conducted to characterise the gas-liquid multiphase flows
experienced within a vertical riser transporting a range of gas-liquid
flow rates. The scale experiments were performed using an
air/silicone oil mixture within a 6 m long riser. The superficial air
velocities studied ranged from 0.047 to 2.836 m/ s, whilst
maintaining a liquid superficial velocity at 0.047 m/ s. Measurements
of the mean cross-sectional and time average radial void fraction
were obtained using a wire mesh sensor (WMS). The data were
recorded at an acquisition frequency of 1000 Hz over an interval of
60 seconds. For the range of flow conditions studied, the average
void fraction was observed to vary between 0.1 and 0.9. An analysis
of the data collected concluded that the observed void fraction was
strongly affected by the superficial gas velocity, whereby the higher
the superficial gas velocity, the higher was the observed average void
fraction. The average void fraction distributions observed were in
good agreement with the results obtained by other researchers. When
the air-silicone oil flows were fully developed reasonably symmetric
profiles were observed, with the shape of the symmetry profile being
strongly dependent on the superficial gas velocity.
Abstract: This paper presents a simple and original method for
the generation of short monocycle pulses based on the transient
response of a passive band-pass filter. The recorded sub-nanosecond
pulses show a good symmetry and a small ringing (13 % of the peak
amplitude). Their spectral density covers the range 3.1 GHz to
10.6 GHz. The possibility to adapt the pulse spectral density to the
indoor FCC frequency mask is demonstrated with a prototype
working at a reduced frequency (FCC/1000). A detection technique is
proposed.