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