title: Distinguishability of battery equivalent-circuit models containing CPEs: Updating the work of Berthier, Diard, & Michel

authors: Poihipi, Eden Kathleen

subjects: Constant Phase Elements

abstract: This manuscript revisits the assertion of Berthier et al. that competing fractional-element equivalent-circuit models of battery cells are indistinguishable in the presence of noise. Starting with Westerhoff’s general equivalent-circuit model (ECM) of 2016 and an idealized impedance spectrum of a lithium battery, a contemporary set of possible ECMs are chosen. Their distinguishability is investigated. Using the extended frequency range recommended by Mauracher & Karden in 1997 or Hasan & Scott in 2019, an approach is presented that permits selection of the appropriate model, even in the presence of noise. For the given frequency range, models with up to five elements or eight real parameters are studied. Fitting to measured data with straightforward numerical methods and choosing the most primitive appropriate sub-circuit is shown to reproduce the data. Typically a three-element, five-parameter ECM is shown to model real, measured data with precision comparable to individual sample error.

text: Distinguishability of battery equivalent-circuit models containing CPEs: Updating the work of Berthier, Diard, & Michel This manuscript revisits the assertion of Berthier et al. that competing fractional-element equivalent-circuit models of battery cells are indistinguishable in the presence of noise. Starting with Westerhoff’s general equivalent-circuit model (ECM) of 2016 and an idealized impedance spectrum of a lithium battery, a contemporary set of possible ECMs are chosen. Their distinguishability is investigated. Using the extended frequency range recommended by Mauracher & Karden in 1997 or Hasan & Scott in 2019, an approach is presented that permits selection of the appropriate model, even in the presence of noise. For the given frequency range, models with up to five elements or eight real parameters are studied. Fitting to measured data with straightforward numerical methods and choosing the most primitive appropriate sub-circuit is shown to reproduce the data. Typically a three-element, five-parameter ECM is shown to model real, measured data with precision comparable to individual sample error.

year: 2022

title: Models of q-algebra representations: Matrix elements of the q-oscillator algebra

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: This article continues a study of function space models of irreducible representations of q analogs of Lie enveloping algebras, motivated by recurrence relations satisfied by q-hypergeometric functions. Here a q analog of the oscillator algebra (not a quantum algebra) is considered. It is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a Lie algebra to its Lie group and the corresponding matrix elements of the ``group operators'' on these representation spaces are computed. This ``local'' approach applies to more general families of special functions, e.g., with complex arguments and parameters, than does the quantum group approach. It is shown that the matrix elements themselves transform irreducibly under the action of the algebra. q analogs of a formula are found for the product of two hypergeometric functions 1F1 and the product of a 1F1 and a Bessel function. They are interpreted here as expansions of the matrix elements of a ``group operator'' (via the exponential mapping) in a tensor product basis (for the tensor product of two irreducible oscillator algebra representations) in terms of the matrix elements in a reduced basis. As a by-product of this analysis an interesting new orthonormal basis was found for a q analog of the Bargmann–Segal Hilbert space of entire functions.

text: Models of q-algebra representations: Matrix elements of the q-oscillator algebra This article continues a study of function space models of irreducible representations of q analogs of Lie enveloping algebras, motivated by recurrence relations satisfied by q-hypergeometric functions. Here a q analog of the oscillator algebra (not a quantum algebra) is considered. It is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a Lie algebra to its Lie group and the corresponding matrix elements of the ``group operators'' on these representation spaces are computed. This ``local'' approach applies to more general families of special functions, e.g., with complex arguments and parameters, than does the quantum group approach. It is shown that the matrix elements themselves transform irreducibly under the action of the algebra. q analogs of a formula are found for the product of two hypergeometric functions 1F1 and the product of a 1F1 and a Bessel function. They are interpreted here as expansions of the matrix elements of a ``group operator'' (via the exponential mapping) in a tensor product basis (for the tensor product of two irreducible oscillator algebra representations) in terms of the matrix elements in a reduced basis. As a by-product of this analysis an interesting new orthonormal basis was found for a q analog of the Bargmann–Segal Hilbert space of entire functions.

year: 1993-11

title: An examination of DHB climate change policy and implementation: Responsiveness to Māori health

authors: Powell, Elisha

abstract: The impacts of climate change have become increasingly evident throughout the world and in Aotearoa. Frequency and intensity of extreme weather events such as flooding, coastal erosion, wildfires, and droughts are notably increasing. Climate-related disasters have devastating effects on human health, as is well documented in literature. These effects include cardiovascular disease, poorer mental health, food insecurity and water borne disease. 

Due to pre-existing health disparities, Māori are particularly vulnerable to the health impacts of climate change. Further, Māori have unique relationships with whenua wherein destruction of the natural environment will have a negative impact on the health of Māori people and communities. The health sector has an obligation to respond to Māori health in a way that honours Māori relationships with the environment and prioritises equitable health outcomes for Māori in climate change policy. 

Although Māori face potentially severe health impacts due to climate change, there is limited literature that considers health sector climate change policy and its responsiveness to Māori health. In an effort to address this gap in literature, this thesis aims to examine whether there is existing District Health Board (DHB) policy focused on implementing institutional responses to climate change. Further, this research seeks to understand the extent to which any identified DHB climate change policy responds to Māori health. 

At the time of study, DHBs were responsible for providing and funding health services throughout Aotearoa. During the late stages of this research, the health sector underwent reform, and two health authorities have replaced DHBs. The implications of this research have important ramifications within the newly established health authorities. A dedicated Māori health authority will provide the health sector with the chance to advance health equity by acting on holistic understandings of health for Māori. These actions would establish health policy that recognises Māori health as fundamentally linked to the environment and therefore uniquely impacted by climate change. 

To achieve the aims of this thesis, two research methods were implemented. Initially, an environmental scan of 17 DHB websites was completed to identify climate change and Māori health policies. This was followed by qualitative interviews with three DHB staff from diverse localities. Additionally, tāngata whenua interviews from the wider research project named Haumanu Hauora, were analysed to ensure Māori understandings of climate change were included in this research (Masters-Awatere et al., 2022). 

Research findings provide insights that point to highly fragmented climate change policies across the health sector. There is a glaring lack of direction in the health sector's response to climate change throughout existing policy. Māori health policies were in place across all DHBs, however, lacked recognition of the interconnection between Māori health and the natural environment, and therefore the impacts of climate change. 

Although policy was fragmented across regions, there is potential to enhance both climate change and Māori health policies by recognising the interconnected nature of Māori health and climate change. This will necessitate a significant change in the health systems policy response to climate change that prioritises mātauranga Māori and addresses the ongoing impacts of colonisation.

text: An examination of DHB climate change policy and implementation: Responsiveness to Māori health The impacts of climate change have become increasingly evident throughout the world and in Aotearoa. Frequency and intensity of extreme weather events such as flooding, coastal erosion, wildfires, and droughts are notably increasing. Climate-related disasters have devastating effects on human health, as is well documented in literature. These effects include cardiovascular disease, poorer mental health, food insecurity and water borne disease. 

Due to pre-existing health disparities, Māori are particularly vulnerable to the health impacts of climate change. Further, Māori have unique relationships with whenua wherein destruction of the natural environment will have a negative impact on the health of Māori people and communities. The health sector has an obligation to respond to Māori health in a way that honours Māori relationships with the environment and prioritises equitable health outcomes for Māori in climate change policy. 

Although Māori face potentially severe health impacts due to climate change, there is limited literature that considers health sector climate change policy and its responsiveness to Māori health. In an effort to address this gap in literature, this thesis aims to examine whether there is existing District Health Board (DHB) policy focused on implementing institutional responses to climate change. Further, this research seeks to understand the extent to which any identified DHB climate change policy responds to Māori health. 

At the time of study, DHBs were responsible for providing and funding health services throughout Aotearoa. During the late stages of this research, the health sector underwent reform, and two health authorities have replaced DHBs. The implications of this research have important ramifications within the newly established health authorities. A dedicated Māori health authority will provide the health sector with the chance to advance health equity by acting on holistic understandings of health for Māori. These actions would establish health policy that recognises Māori health as fundamentally linked to the environment and therefore uniquely impacted by climate change. 

To achieve the aims of this thesis, two research methods were implemented. Initially, an environmental scan of 17 DHB websites was completed to identify climate change and Māori health policies. This was followed by qualitative interviews with three DHB staff from diverse localities. Additionally, tāngata whenua interviews from the wider research project named Haumanu Hauora, were analysed to ensure Māori understandings of climate change were included in this research (Masters-Awatere et al., 2022). 

Research findings provide insights that point to highly fragmented climate change policies across the health sector. There is a glaring lack of direction in the health sector's response to climate change throughout existing policy. Māori health policies were in place across all DHBs, however, lacked recognition of the interconnection between Māori health and the natural environment, and therefore the impacts of climate change. 

Although policy was fragmented across regions, there is potential to enhance both climate change and Māori health policies by recognising the interconnected nature of Māori health and climate change. This will necessitate a significant change in the health systems policy response to climate change that prioritises mātauranga Māori and addresses the ongoing impacts of colonisation.

year: 2025