Order statistics and the linear assignment problem

Under mild conditions on the distribution functionF, we analyze the asymptotic behavior in expectation of the smallest order statistic, both for the case thatF is defined on (–, +) and for the case thatF is defined on (0, ). These results yield asymptotic estimates of the expected optiml value of the linear assignment problem under the assumption that the cost coefficients are independent random variables with distribution functionF.asymptotic analysis;linear assignment problem;order statistic

Machine allocation problems in manufacturing networks

In this paper we discuss two server (machine) allocation problems that occur in manufacturing networks. The manufacturing network is modelled as an open network of queues. The server allocation problems are solved by means of a marginal analysis scheme. We show that for the first problem our algorithm generates undominated allocations. Furthermore, the algorithm provides us with bounds to check how close the allocation generated is to the optimal allocation. In the second problem the algorithm presented generates optimal allocations within time bounded by a polynomial function in the size of the network

Physical and chemical properties of lunar magma

Davies, G.R. [Promotor]Westrenen, W. van [Copromotor

The thermal equation of state of FeTiO_3 ilmenite based on in situ X-ray diffraction at high pressures and temperatures

We present in situ measurements of the unit-cell volume of a natural terrestrial ilmenite (Jagersfontein mine, South Africa) and a synthetic reduced ilmenite (FeTiO_3) at simultaneous high pressure and high temperature up to 16 GPa and 1273 K. Unit-cell volumes were determined using energy-dispersive synchrotron X-ray diffraction in a multi-anvil press. Mössbauer analyses show that the synthetic sample contained insignificant amounts of Fe^(3+) both before and after the experiment. Results were fit to Birch-Murnaghan thermal equations of state, which reproduce the experimental data to within 0.5 and 0.7 GPa for the synthetic and natural samples, respectively. At ambient conditions, the unit-cell volume of the natural sample [V_0 = 314.75 ± 0.23 (1 ) Å^3] is significantly smaller than that of the synthetic sample [V_0 = 319.12 ± 0.26 Å^3]. The difference can be attributed to the presence of impurities and Fe^(3+) in the natural sample. The 1 bar isothermal bulk moduli K_(T0) for the reduced ilmenite is slightly larger than for the natural ilmenite (181 ± 7 and 165 ± 6 GPa, respectively), with pressure derivatives K_0' = 3 ± 1. Our results, combined with literature data, suggest that the unit-cell volume of reduced ilmenite is significantly larger than that of oxidized ilmenite, whereas their thermoelastic parameters are similar. Our data provide more appropriate input parameters for thermo-chemical models of lunar interior evolution, in which reduced ilmenite plays a critical role

State anxiety improves prediction of pain and pain-related disability after 12 weeks in patients with acute low back pain:a cohort study

Question: Do measures of state anxiety and trait anxiety in people with acute low back pain (ALBP) improve prediction of chronic low back pain (CLBP), defined as pain or pain-related disability at 12 weeks? Design: Observational multi-centre prospective cohort study in primary physiotherapy care with measurements at baseline and at 12 weeks of state and trait anxiety, as well as other established prognostic factors for CLBP. Participants: People with nonspecific ALBP, aged 18 to 60 years, who had been pain free for ≥ 3 months before their current ALBP, and who were being treated according the Dutch clinical guidelines. Outcome measures and analysis: CLBP was defined as a pain score ≥ 3/10 on the Numerical Pain Rating Scale (primary outcome), and as a pain-related disability score ≥ 19/70 on the Pain Disability Inventory. Univariate and multivariate logistic regression analyses estimated how the risk of CLBP differed with state and trait anxiety and other established prognostic factors. Results: Most (204 of 225) participants completed both assessments. State anxiety was an independent predictor of CLBP, whether defined as pain or pain-related disability at 12 weeks, in contrast to trait anxiety. State anxiety improved the predictive performance of the model, with area under the curve (AUC) increasing from 0.64 (95% CI 0.56 to 0.71) to 0.75 (95% CI 0.68 to 0.82) and Nagelkerke's R2 increasing from 0.08 to 0.24 for the primary outcome measure, pain. For the secondary outcome measure, pain-related disability: AUC 0.63 (95% CI 0.54 to 0.72) improved to 0.73 (95% CI 0.65 to 0.82) and Nagelkerke's R2 increased from 0.05 to 0.16. Adding trait anxiety to the prognostic model for pain improved the AUC from 0.64 (95% CI 0.56 to 0.71) to 0.70 (95% CI 0.62 to 0.77) and Nagelkerke's R2 from 0.08 to 0.15. Conclusion: State anxiety in patients with ALBP improved prediction of CLBP, defined as pain and pain-related disability at 12 weeks