545 research outputs found
q-series and L-functions related to half-derivatives of the Andrews--Gordon identity
Studied is a generalization of Zagier's q-series identity. We introduce a
generating function of L-functions at non-positive integers, which is regarded
as a half-differential of the Andrews--Gordon q-series. When q is a root of
unity, the generating function coincides with the quantum invariant for the
torus knot.Comment: 21 pages, related papers can be found from
http://gogh.phys.s.u-tokyo.ac.jp/~hikami
New Finite Rogers-Ramanujan Identities
We present two general finite extensions for each of the two Rogers-Ramanujan
identities. Of these one can be derived directly from Watson's transformation
formula by specialization or through Bailey's method, the second similar
formula can be proved either by using the first formula and the q-Gosper
algorithm, or through the so-called Bailey lattice.Comment: 19 pages. to appear in Ramanujan
Uncovering Ramanujan's "Lost" Notebook: An Oral History
Here we weave together interviews conducted by the author with three
prominent figures in the world of Ramanujan's mathematics, George Andrews,
Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the
"lost" notebook, Andrews and Berndt's effort of proving and editing Ramanujan's
notes, and recent breakthroughs by Ono and others carrying certain important
aspects of the Indian mathematician's work into the future. Also presented are
historical details related to Ramanujan and his mathematics, perspectives on
the impact of his work in contemporary mathematics, and a number of interesting
personal anecdotes from Andrews, Berndt and Ono
The influence of an oil recycler on emissions with oil age for a refuse truck using in service testing
A method of cleaning lubricating oil on line was
investigated using a fine bypass particulate filter followed
by an infra red heater. Two bypass filter sizes of 6 and 1
micron were investigated, both filter sizes were effective
but the one micron filter had the greatest benefit. This
was tested on two nominally identical EURO 1 emissions
compliance refuse trucks, fitted with Perkins Phazer
210Ti 6 litre turbocharged intercooled engines and coded
as RT320 and RT321. These vehicles had emissions
characteristics that were significantly different, in spite of
their similar age and total mileage. RT321 showed an
apparent heavier black smoke than RT320. Comparison
was made with the emissions on the same vehicles and
engines with and without the on-line bypass oil recycler.
Engine exhaust emissions were measured about every
400 miles. Both vehicles started the test with an oil drain
and fresh lubricating oil. The two refuse trucks were
tested in a different sequence, the RT320 without the
recycler fitted and then fitted later and the RT321 with
the recycler fitted and then removed later in the test and
both without any oil change. The RT320 was also the
one with the finer bypass filter. The test mileage was
nearly 8,000 miles both trucks. The air/fuel ratio was
worked out by the exhaust gas analysis. The correlation
between air/fuel ratio and emission parameters was
determined and appropriate corrections were made in
the case of that the air/fuel ratio had an effect on
emissions. The results showed that the on line oil
recycler cleaning system can reduce the rate of increase
of the NOx with oil age. There appeared little influence of
the oil recycler on carbon monoxide and hydrocarbon
emissions. The rate of increase in particulate emissions
was reduced by 50% for RT320 and an immediate
decrease in particulate emissions was seen on RT320
test after fitting the recycler. The black smoke was
reduced by 30% for RT320 in terms average value and
an immediate decrease in smoke after fitting the recycler
on RT320 test and an immediate increase in smoke after
the removal of the recycler on RT321 test were shown
Effects of an on line bypass oil recycler on emissions with oil age for a bus using in service testing
A method of cleaning lubricating oil on line was
investigated using a fine bypass particulate filter
followed by an infra red heater. Two bypass filter
sizes of 6 and 1 micron were investigated, both filter
sizes were effective but the one micron filter had the
greatest benefit. This was tested on two nominally
identical EURO 2 emissions compliance single
decker buses, fitted with Cummins 6 cylinder 8.3 litre
turbocharged intercooled engines and coded as Bus
4063 and 4070. These vehicles had emissions
characteristics that were significantly different, in
spite of their similar age and total mileage. Bus 4063
showed an apparent deterioration on emissions with
time while Bus 4070 showed a stabilised trend on
emissions with time for their baseline tests without
the recycler fitted. Comparison was made with the
emissions on the same vehicles and engines with
and without the on-line bypass oil recycler. Engine
exhaust emissions were measured about every 2000
miles. All tests started with an oil drain and fresh
lubricating oil. The two buses were tested in a
different sequence, Bus 4063 with the recycler fitted
and then removed later in the test after an oil change
and Bus 4070 with no recycler fitted at first and then
fitted after 29,000 miles with no oil change. The Bus
4070 was also the one with the finer bypass filter.
The test mileage was 45,000 miles for Bus 4063 and
48,000 miles for Bus 4070. The air/fuel ratio was
worked out by the exhaust gas analysis. The
correlation between air/fuel ratio and emission
parameters was determined. The results showed that
the on line oil recycler cleaning system reduced the
rate of increase of the NOx from 5% to 1.6% for Bus
4063 and from 4.1% to 0% for Bus 4070 per 10,000
miles. Hydrocarbon emissions increased 30 ppm per
10,000 miles with the recycler removed compared to
a stabilised level with the recycler fitted for Bus 4063.
There was a small decrease in hydrocarbon
emissions after fitting the recycler for Bus 4070. The
particulate emissions were reduced by 35% for Bus
4063 and 24% for Bus 4070 on average. The
reductions on total particulate mass were due to
reductions on particulate carbon and lube oil VOF
emissions. The black smoke was reduced by 56% for
Bus 4063 in terms of rate of increase and 40% for
Bus 4070 in terms of average value
q-Newton binomial: from Euler to Gauss
A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made
less mysterious by virtue of being generalized through the introduction of an
additional parameter
Quantitying the Effects of Traffic Calming on Emissions Using on-road Measurement
The objective of this work was to determine the effect of
one form of traffic calming on emissions. Traffic calming
is aimed at reducing average vehicle speeds, especially
in residential neighborhoods, often using physical road
obstructions such as speed bumps, but it also results in
a higher number of acceleration/deceleration events
which in turn yield higher emissions. Testing was
undertaken by driving a warmed-up Euro-1 spark ignition
passenger car over a set of speed bumps on a level
road, and then comparing the emissions output to a noncalmed
level road negotiated smoothly at a similar
average speed. For the emissions measurements, a
novel method was utilized, whereby the vehicle was
fitted with a portable Fourier Transform Infrared (FTIR)
spectrometer, capable of measuring up to 51 different
components in real-time on the road. The results
showed that increases in emissions were much greater
than was previously reported by other researchers using
different techniques. When traffic-calmed results were
compared to a smooth non-calmed road, there were
substantial increases in CO2 (90%), CO (117%), NOx
(195%) and THC (148%). These results form the basis
for a good argument against traffic calming using speed
bumps, especially for aggressive drivers. Slowing traffic
down with speed restrictions enforced by speed
cameras is a more environmentally friendly option
Evaluation of a FTIR Emission Measurement System for Legislated Emissions Using a SI Car
A series of chassis dynamometer test trials were
conducted to assess the performance of a Fourier
Transform Infra Red (FTIR) system developed for
on-road vehicle exhaust emissions measurements.
Trials used a EURO 1 emission compliant SI passenger
car which, alongside the FTIR, was instrumented to
allow the routine logging of engine speed, road speed,
throttle position, air-fuel ratio, air flow and fuel flow in
addition to engine, exhaust and catalyst temperatures.
The chassis dynamometer facility incorporated an
‘industry standard’ measurement system comprising
MEXA7400 gas analyzer and CVS bag sampling which
was the ‘benchmark’ for the evaluation of FTIR
legislated gas-phase emissions (CO, NOx, THC and
CO2) measurements.
Initial steady state measurements demonstrated strong
correlations for CO, NOx and THC (R2 of 0.99, 0.97
0.99, respectively) and a good correlation for CO2 (R2 =
0.92). Subsequent transient and total mass emissions
measurements from replicate samplings of four different
driving cycles (two standard cycles, FTP75 and NEDC,
and two novel cycles based on real-world data collected
in Leeds) also show good response of FTIR and
satisfied agreement between the FTIR and CVS bag
sampling measurements.
In general, the trial results demonstrate that the
on-board FTIR emission measurement system provides
reliable in-journey emissions data
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
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