4,109 research outputs found
The Bailey chain and mock theta functions
Standard applications of the Bailey chain preserve mixed mock modularity but
not mock modularity. After illustrating this with some examples, we show how to
use a change of base in Bailey pairs due to Bressoud, Ismail and Stanton to
explicitly construct families of q-hypergeometric multisums which are mock
theta functions. We also prove identities involving some of these multisums and
certain classical mock theta functions.Comment: 17 pages, to appear in Advances in Mathematic
Hecke-type double sums, Appell-Lerch sums, and mock theta functions (I)
By developing a connection between partial theta functions and Appell-Lerch
sums, we find and prove a formula which expresses Hecke-type double sums in
terms of Appell-Lerch sums and theta functions. Not only does our formula prove
classical Hecke-type double sum identities such as those found in work Kac and
Peterson on affine Lie Algebras and Hecke modular forms, but once we have the
Hecke-type forms for Ramanujan's mock theta functions our formula gives
straightforward proofs of many of the classical mock theta function identities.
In particular, we obtain a new proof of the mock theta conjectures. Our formula
also applies to positive-level string functions associated with admissable
representations of the affine Lie Algebra as introduced by Kac and
Wakimoto
Oil quality in diesel engines with on line oil cleaning using a heated lubricating oil recycler
A method of cleaning the oil on line was investigatedusing a bypass fine particulate filter followed by an infra
red heater to remove water and light diesel fractions in
the oil. This was tested on a range of on road vehicles
and a Ford 1.8 litre IDI passenger car engine on a test
bed. Comparison was made with the oil quality on the
same vehicles and engines without the on-line recycler.
Test times were from 200 to 1500 hours of oil ageing and
some of the tests showed that the oil quality was still
good after 4 times the normal oil life. The results showed
that the on line oil recycler cleaning system reduced the
rate of fall of the TBN and rate of increase of the TAN.
There was a very significant reduction in the soot in oil
and the fuel dilution. There was also a consistent reduction
in all the wear metals apart from copper and a
decrease in the rate of reduction of oil additives. There
was also measured on the Ford IDI engine a 5% reduced
fuel consumption. Many of these effects were attributed
to an influence of the cleaner oil on reduced engine
deposits
Oil quality in diesel engines with on line oil cleaning using a heated lubricating oil recycler
A method of cleaning the oil on line was investigatedusing a bypass fine particulate filter followed by an infra
red heater to remove water and light diesel fractions in
the oil. This was tested on a range of on road vehicles
and a Ford 1.8 litre IDI passenger car engine on a test
bed. Comparison was made with the oil quality on the
same vehicles and engines without the on-line recycler.
Test times were from 200 to 1500 hours of oil ageing and
some of the tests showed that the oil quality was still
good after 4 times the normal oil life. The results showed
that the on line oil recycler cleaning system reduced the
rate of fall of the TBN and rate of increase of the TAN.
There was a very significant reduction in the soot in oil
and the fuel dilution. There was also a consistent reduction
in all the wear metals apart from copper and a
decrease in the rate of reduction of oil additives. There
was also measured on the Ford IDI engine a 5% reduced
fuel consumption. Many of these effects were attributed
to an influence of the cleaner oil on reduced engine
deposits
Application of a portable FTIR for measuring on-road emissions
The objective of this work was the development of an onroad
in-vehicle emissions measurement technique
utilizing a relatively new, commercial, portable Fourier
Transform Infra-Red (FTIR) Spectrometer capable of
identifying and measuring (at approximately 3 second
intervals) up to 51 different compounds. The FTIR was
installed in a medium class EURO1 spark ignition
passenger vehicle in order to measure on-road
emissions. The vehicle was also instrumented to allow
the logging of engine speed, road speed, global position,
throttle position, air-fuel ratio, air flow and fuel flow in
addition to engine, exhaust and catalyst temperatures.
This instrumentation allowed the calculation of massbased
emissions from the volume-based concentrations
measured by the FTIR. To validate the FTIR data, the
instrument was used to measure emissions from an
engine subjected to a real-world drive cycle using an AC
dynamometer. Standard analyzers were operated
simultaneously for comparison with the FTIR and the
standard analyzer results showed that most pollutants
(NOx, CO2, CO) were within ~10% of a standard analyzer
during steady state conditions and within 20% during
transients. The exception to this was total HC which was
generally 50% or less than actual total HC, but this was
due to the limited number of hydrocarbons measured by
the FTIR. In addition to the regulated emissions, five
toxic hydrocarbon species were analyzed and found to
be sensitive to cold starts in varying proportions. Finally,
FTIR data was compared to results from a commercially
available on-road measurement system (Horiba OBS-
1000), and there was good agreement
The effect of ambient temperature on cold start urban traffic emissions for a real world SI car
The influence of ambient temperature on exhaust
emissions for an instrumented Euro 1 SI car was
determined. A real world test cycle was used, based on
an urban drive cycle that was similar to the ECE urban
drive cycle. It was based on four laps of a street circuit
and an emissions sample bag was taken for each lap.
The bag for the first lap was for the cold start emissions.
An in-vehicle direct exhaust dual bag sampling
technique was used to simultaneously collect exhaust
samples upstream and downstream of the three-way
catalyst (TWC). The cold start tests were conducted
over a year, with ambient temperatures ranging from –
2°C to 32°C. The exhaust system was instrumented with
thermocouples so that the catalyst light off temperature
could be determined. The results showed that CO
emissions for the cold start were reduced by a factor of
8 downstream of catalyst when ambient temperature
rose from -2°C to 32°C, the corresponding hydrocarbon
emissions were reduced by a factor of 4. There was no
clear relationship between NOx emissions and ambient
temperature. For subsequent laps of the test circuit the
reduction of CO and HC emissions as a function of
ambient temperature was lower. The time for catalyst
light off increased by 50% as the ambient temperature
was reduced. The results show that the vehicle used is
unlikely to meet the new – 7oC cold start CO emission
regulations
What is 'binge drinking'? Perceptions of Australian adolescents and adults, and implications for mass media campaigns
Objective: While the term ‘binge drinking’ has no definitive definition, it is commonly used in lay conversation and mass media communication campaigns. It is important to understand how the general population interprets the term, and their positive and negative perceptions of this behaviour. Methods: A convenience sample of 549 participants from two Australian towns completed a survey on perceptions of binge drinking; 221 adolescents, 104 parents of adolescents and 224 adult community members. Results: Across all three groups, binge drinking was defined using broad descriptors; few respondents referred to specific consumption levels and those who did varied widely in the quantities specified. The majority of respondents described binge drinking negatively and, in most cases, more negatively for adolescents than adults. However, both adult groups perceived binge drinking to be more enjoyable and pleasant for adolescents than for adults, and more enjoyable and pleasant than adolescents did themselves. Conclusions and Implications: There is a need for shared understanding of terms to ensure that educational interventions and communication campaigns are using the same definitions as their target audiences. There is also a need to ensure adults are not providing young people with mixed messages about excessive alcohol consumption
On two 10th order mock theta identities
We give short proofs of conjectural identities due to Gordon and McIntosh
involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan Journa
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