A similar argument with (20) and (21) proves that∂ * b,t∂ b G q,t ϕ = G q,t∂ * b,t∂ b ϕ, finishing the proof of (18).

We define weak Z(q), a generalization of Z(q) on bounded domains Ω in a Stein manifold M n that suffices to prove closed range of∂. Under the hypothesis of weak Z(q), we also show (i) that harmonic (0, q)-forms are trivial and (ii) if ∂Ω satisfies weak Z(q) and weak Z(n − 1 − q), then∂ b has closed range on (0, q)-forms on ∂Ω. We provide examples to show that our condition contains examples that are excluded from (q − 1)-pseudoconvexity and the authors' previous notion of weak Z(q).

Environmental conditions of Australia's Northern Territory are seasonally conducive to excessive body heat storage by outdoor workers. For electrical utility workers who periodically work at height, in confined space, and in proximity to live power sources, the impact of the climate may be considered a hazardous condition. Therefore, this study examined the physiological and fluid balance responses of 20 power network workers (31.5 years; 86.0 kg; 1.71 m; BMI 29.5) throughout work shifts in the Northern and Southern regions of the Northern Territory, Australia. Twenty male heat-acclimatized power network workers provided written informed consent to be monitored during maintenance of electrical infrastructure that included replacing power pole components and transformer and substation repairs in the Northern (n = 13) and Southern regions (n = 7) of the Northern Territory (mean wet-bulb globe temperatures of 32.0°C and 28.7°C, respectively). An ingestible telemetry pill provided measurement of gastrointestinal temperature (Tgi), that when combined with heart rate values, provided physiological strain index (PSI). Urine specific gravity, sweat rate, and level of dehydration were also determined. The Tgi values of this study were within the ISO9886 limit for monitored, heat-acclimatized workers, with a peak of 38.4°C. Mean PSI was 2.6, which represents overall low strain, with periods of moderate strain. Urinary analysis indicated that workers were dehydrated prior to and following the work shift, however the mean sweat rate of 0.44 L.h(-1) was matched by fluid consumption of 0.42 L.h(-1) to limit body mass loss to 0.1% during the shift. This study demonstrates that heat acclimatized electrical utility workers adhere to ISO9886 requirements when undertaking self-paced activity in hot conditions.

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Abstract. For a domain Ω ⊂ R n , we introduce the concept of a uniformly C m defining function. We characterize uniformly C m defining functions in terms of the signed distance function for the boundary and provide a large class of examples of unbounded domains with uniformly C m defining functions. Some of our results extend results from the bounded case.