Asymptotic Expansions for the Conditional Sojourn Time Distribution in the M/M/1M/M/1-PS Queue

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison \cite{MO} and Flatto \cite{FL}.Comment: 30 pages, 3 figures and 1 tabl

Measurement of the Charged Multiplicities in b, c and Light Quark Events from Z0 Decays

Average charged multiplicities have been measured separately in $b$, $c$ and light quark ($u,d,s$) events from $Z^0$ decays measured in the SLD experiment. Impact parameters of charged tracks were used to select enriched samples of $b$ and light quark events, and reconstructed charmed mesons were used to select $c$ quark events. We measured the charged multiplicities: $\bar{n}_{uds} = 20.21 \pm 0.10 (\rm{stat.})\pm 0.22(\rm{syst.})$, $\bar{n}_{c} = 21.28 \pm 0.46(\rm{stat.}) ^{+0.41}_{-0.36}(\rm{syst.})$ $\bar{n}_{b} = 23.14 \pm 0.10(\rm{stat.}) ^{+0.38}_{-0.37}(\rm{syst.})$, from which we derived the differences between the total average charged multiplicities of $c$ or $b$ quark events and light quark events: $\Delta \bar{n}_c = 1.07 \pm 0.47(\rm{stat.})^{+0.36}_{-0.30}(\rm{syst.})$ and $\Delta \bar{n}_b = 2.93 \pm 0.14(\rm{stat.})^{+0.30}_{-0.29}(\rm{syst.})$. We compared these measurements with those at lower center-of-mass energies and with perturbative QCD predictions. These combined results are in agreement with the QCD expectations and disfavor the hypothesis of flavor-independent fragmentation.Comment: 19 pages LaTex, 4 EPS figures, to appear in Physics Letters

Measurement of Rb in e+e- Collisions at 182 - 209 GeV

Measurements of Rb, the ratio of the bbbar cross-section to the qqbar cross- section in e+e- collisions, are presented. The data were collected by the OPAL experiment at LEP at centre-of-mass energies between 182 GeV and 209 GeV. Lepton, lifetime and event shape information is used to tag events containing b quarks with high efficiency. The data are compatible with the Standard Model expectation. The mean ratio of the eight measurements reported here to the Standard Model prediction is 1.055+-0.031+-0.037, where the first error is statistical and the second systematic.Comment: 21 pages, 5 figures, Submitted to Phys. Letts

Measurement of the B0 Lifetime and Oscillation Frequency using B0->D*+l-v decays

The lifetime and oscillation frequency of the B0 meson has been measured using B0->D*+l-v decays recorded on the Z0 peak with the OPAL detector at LEP. The D*+ -> D0pi+ decays were reconstructed using an inclusive technique and the production flavour of the B0 mesons was determined using a combination of tags from the rest of the event. The results t_B0 = 1.541 +- 0.028 +- 0.023 ps, Dm_d = 0.497 +- 0.024 +- 0.025 ps-1 were obtained, where in each case the first error is statistical and the second systematic.Comment: 17 pages, 4 figures, submitted to Phys. Lett.

The effect of a curriculum-based physical activity intervention on accelerometer-assessed physical activity in schoolchildren: a non-randomised mixed methods controlled before-and-after study

Classroom-based physical activity (PA) interventions offer the opportunity to increase PA without disrupting the curriculum. We aimed to explore the feasibility and potential effectiveness of a classroom-based intervention on moderate to vigorous PA (MVPA) and total PA. The secondary aim was to assess the acceptability and sustainability of the intervention. In a mixed-methods, non-randomised, exploratory controlled before-and-after study, 152 children (10 ± 0.7 years) were recruited from five schools; two intervention (n = 72) and three control (n = 80) schools. School teachers delivered an 8-week classroom-based intervention, comprising of 10 minutes daily MVPA integrated into the curriculum. The control schools maintained their usual school routine. Mean daily MVPA (min), total PA (mean cpm), physical fitness, and health-related quality of life measurements were taken at baseline, end of intervention, and 4-weeks post-intervention (follow-up). Data were analysed using a constrained baseline longitudinal analysis model accounting for the hierarchical data structure. For the primary outcomes (MVPA and total PA) the posterior mean difference and 95% compatibility interval were derived using a semi-Bayesian approach with an explicit prior. The acceptability and sustainability of the intervention was explored via thematic content analysis of focus group discussions with teachers (n = 5) and children (n = 50). The difference in mean daily MVPA (intervention-control) was 2.8 (-12.5 to 18.0) min/day at 8 weeks and 7.0 (-8.8 to 22.8) min/day at follow-up. For total PA, the differences were -2 (-127 to 124) cpm at 8-weeks and 11 (-121 to 143) cpm at follow-up. The interval estimates indicate that meaningful mean effects (both positive and negative) as well as trivial effects are reasonably compatible with the data and design. The intervention was received positively with continuation reported by the teachers and children. Classroom-based PA could hold promise for increasing average daily MVPA, but a large cluster randomised controlled trial is required