A new method for analysing the equilibrium and time-dependent behaviour of Markovian models

Many large-scale stochastic systems, such as telecommunications networks, can be modelled using a continuous-time Markov chain. However, it is frequently the case that a satisfactory analysis of their time-dependent, or even equilibrium, behaviour is impossible. In this paper, we propose a new method of analyzing Markovian models, whereby the existing transition structure is replaced by a more amenable one. Using rates of transition given by the equilibrium expected rates of the corresponding transitions of the original chain, we are able to approximate its behaviour. We present two formulations of the idea of expected rates. The first provides a method for analysing time-dependent behaviour, while the second provides a highly accurate means of analysing equilibrium behaviour. We shall illustrate our approach with reference to a variety of models, giving particular attention to queueing and loss networks. (C) 2003 Elsevier Ltd. All rights reserved.

Environmental conditions and variation in levels of sun exposure among children in child care

Sun exposure in childhood is I of the risk factors for developing skin cancer, yet little is known about levels of exposure at this age. This is particularly important in countries with high levels of ultraviolet radiation. (UVR) such as Australia. Among 49 children 3 to 5 years of age attending child care centers, UVR exposure was studied under 4 conditions in a repeated measures design; sunny days, cloudy days, teacher's instruction to stay in the shade, and a health professionals instruction to apply sunscreen. Three different data collection methods were employed: (a) completion of questionnaire or diary by parents and researcher, (b) polysulphone dosimeter readings, and (c) observational audits (video recording). Results of this study indicated that more than half the children had been sunburnt (pink or red) and more than a third had experienced painful sunburn (sore or tender) in the last summer. Most wore short sleeve shirts, short skirts or shorts and cap, that do not provide optimal levels of skin protection. However, sunscreen was applied to all exposed parts before the children went out to the playground. Over the period of I hr (9-10 a.m.) the average amount of time children spent in full sun was 22 min. On sunny days there was more variation across children in the amount of sun exposure received. While the potential amount of UVR exposure for young children during the hour they were outside on a sunny day was 1.45 MED (Minimum Erythemal Dose), they received on average 0.35 MED, which is an insufficient amount to result in an erythemal response on fair skin even without the use of sunscreen.

Discrete cyanide-bridged mixed-valence Co/Fe complexes: Outer-sphere redox behaviour

The outer-sphere redox behaviour of a series of [LnCoIII-NCFeII(CN)(5)](-) (L-n = n-membered pentadentate aza-macrocycle) complexes have been studied as a function of pH and oxidising agent. All the dinuclear complexes show a double protonation process at pH approximate to 2 that produces a shift in their UV/Vis spectra. Oxidation of the different non-protonated and diprotonated complexes has been carried out with peroxodisulfate, and of the non-protonated complexes also with trisoxalatocobaltate(III). The results are in agreement with predictions from the Marcus theory. The oxidation of [Fe(phen)(3)](3+) and [IrCl6](2-) is too fast to be measured, although for the latter the transient observation of the process has been achieved at pH = 0. The study of the kinetics of the outer-sphere redox process, with the S2O82- and [Co(ox)(3)](3-) oxidants, has been carried out as a function of pH, temperature, and pressure. As a whole, the values found for the activation volumes, entropies, and enthalpies are in the following margins, for the diprotonated and non-protonated dinuclear complexes, respectively: DeltaV(not equal) from 11 to 13 and 15 to 20 cm(3) mol(-1); DeltaS(not equal) from 110 to 30 and -60 to -90 J K-1 mol(-1); DeltaH(not equal) from 115 to 80 and 50 to 65 kJ.mol(-1). The thermal activation parameters are clearly dominated by the electrostriction occurring on outer-sphere precursor formation, while the trends found for the values of the volume of activation indicate an important degree of tuning due to the charge distribution during the electron transfer process. The special arrangement on the amine ligands in the isomer trans[(L14CoNCFeII)-N-III(CN)(5)](-) accounts for important differences in solvent-assisted hydrogen bonding occurring within the outer-sphere redox process, as has been established in redox reactions of similar compounds. ((C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003).