title: Separation of variables on n-dimensional Riemannian manifolds. I. The n-sphere Sn and Euclidean n-space Rn

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: The following problem is solved: What are all the ``different'' separable coordinate systems for the Laplace–Beltrami eigenvalue equation on the n-sphere Sn and Euclidean n-space Rn and how are they constructed? This is achieved through a combination of differential geometric and group theoretic methods. A graphical procedure for construction of these systems is developed that generalizes Vilenkin's construction of polyspherical coordinates. The significance of these results for exactly soluble dynamical systems on these manifolds is pointed out. The results are also of importance for the analysis of the special functions appearing in the separable solutions of the Laplace–Beltrami eigenvalue equation on these manifolds.

text: Separation of variables on n-dimensional Riemannian manifolds. I. The n-sphere Sn and Euclidean n-space Rn The following problem is solved: What are all the ``different'' separable coordinate systems for the Laplace–Beltrami eigenvalue equation on the n-sphere Sn and Euclidean n-space Rn and how are they constructed? This is achieved through a combination of differential geometric and group theoretic methods. A graphical procedure for construction of these systems is developed that generalizes Vilenkin's construction of polyspherical coordinates. The significance of these results for exactly soluble dynamical systems on these manifolds is pointed out. The results are also of importance for the analysis of the special functions appearing in the separable solutions of the Laplace–Beltrami eigenvalue equation on these manifolds.

year: 1986-07

title: Eliciting usage contexts of safety-critical medical devices

authors: Bowen, Judy

subjects: computer science

abstract: This position paper outlines our approach to improve the usage choice of suitable devices in different health care environments (contexts). Safety-critical medical devices are presumed to have undergone a thorough (user-centred) design process to optimize the device for the intended purpose, user group and environment. However, in real-life health care scenarios, actual usage may not reflect the original design parameters. We suggest the identification of further usage contexts for safety-critical medical devices through ethnographic and other studies, to assist better modelling of the challenges of different usage environments. In combination with system and interaction models, these context models can then be used for decision-support in choosing medical devices that are suitable for the intended environment.

text: Eliciting usage contexts of safety-critical medical devices This position paper outlines our approach to improve the usage choice of suitable devices in different health care environments (contexts). Safety-critical medical devices are presumed to have undergone a thorough (user-centred) design process to optimize the device for the intended purpose, user group and environment. However, in real-life health care scenarios, actual usage may not reflect the original design parameters. We suggest the identification of further usage contexts for safety-critical medical devices through ethnographic and other studies, to assist better modelling of the challenges of different usage environments. In combination with system and interaction models, these context models can then be used for decision-support in choosing medical devices that are suitable for the intended environment.

year: 2014

title: He huringa āhuarangi, he huringa ao: A changing climate, a changing world

authors: Awatere, S

subjects: climate change adaptation

abstract: Iwi/hapū (tribe/subtribe) governance institutions are increasingly asserting their rangatiratanga (autonomy) to manage climate change risks and meet the well-being of whānau (family)/ hapū/iwi. Howevere, there is a shortange of specific guidance for whānau/hapū/iwi with respect to climate change adaptation and mitigation. We provide a commentary about risk and uncertainty, knowledge gaps, and options for climate change mitigation and adaptation for whānau/hapū/iwi.

text: He huringa āhuarangi, he huringa ao: A changing climate, a changing world Iwi/hapū (tribe/subtribe) governance institutions are increasingly asserting their rangatiratanga (autonomy) to manage climate change risks and meet the well-being of whānau (family)/ hapū/iwi. Howevere, there is a shortange of specific guidance for whānau/hapū/iwi with respect to climate change adaptation and mitigation. We provide a commentary about risk and uncertainty, knowledge gaps, and options for climate change mitigation and adaptation for whānau/hapū/iwi.

year: 2021-10