title: Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: This paper is part of a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in real or complex conformally flat spaces. Here we consider classical superintegrable systems with nondegenerate potentials in three dimensions. We show that there exists a standard structure for such systems, based on the algebra of 3×3 symmetric matrices, and that the quadratic algebra always closes at order 6. We show that the spaces of truly second-, third-, fourth-, and sixth-order constants of the motion are of dimension 6, 4, 21, and 56, respectively, and we construct explicit bases for the fourth- and sixth order constants in terms of products of the second order constants.

text: Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory This paper is part of a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in real or complex conformally flat spaces. Here we consider classical superintegrable systems with nondegenerate potentials in three dimensions. We show that there exists a standard structure for such systems, based on the algebra of 3×3 symmetric matrices, and that the quadratic algebra always closes at order 6. We show that the spaces of truly second-, third-, fourth-, and sixth-order constants of the motion are of dimension 6, 4, 21, and 56, respectively, and we construct explicit bases for the fourth- and sixth order constants in terms of products of the second order constants.

year: 2005-10

title: Lignin oxidation products in soil, dripwater and speleothems from four different sites in New Zealand

authors: Heidke, Inken

abstract: Lignin oxidation products (LOPs) are widely used as vegetation proxies in climate archives, such as sediment and peat cores. The total LOP concentration, Σ8, provides information on the abundance of vegetation, while the ratios C/V and S/V of the different LOP groups also provide information on the type of vegetation. Recently, LOP analysis has been successfully applied to speleothem archives. However, there are many open questions concerning the transport and microbial degradation of LOPs on their way from the soil into the cave system. These processes could potentially alter the original source-dependent LOP signals, in particular the C/V and S/V ratios, and thus complicate their interpretation in terms of past vegetation changes. We analyzed LOPs in leaf litter and different soil horizons as well as dripwater and flowstone samples from four different cave sites from different vegetation zones in New Zealand using ultrahigh-performance liquid chromatography coupled to high-resolution mass spectrometry. We test whether the original source-dependent LOP signal of the overlying vegetation is preserved and can be recovered from flowstone samples and investigate how the signal is altered by the transport from the soil to the cave. The LOP concentrations range from mg g−1 in the soil to ng g−1 in the flowstones. Our results demonstrate that, from the soil to the flowstone, the C/V and S/V ratios both increase, while the total lignin content, Σ8, strongly decreases. This shows that the LOP signal is strongly influenced by both transport and degradation processes. Nevertheless, the relative LOP signal from the overlying soil at the different cave sites is preserved in the flowstone. We emphasize that for the interpretation of C/V and S/V ratios in terms of past vegetation changes, it is important to compare only samples of the same type (e.g., speleothem, dripwater or soil) and to evaluate only relative variations.

text: Lignin oxidation products in soil, dripwater and speleothems from four different sites in New Zealand Lignin oxidation products (LOPs) are widely used as vegetation proxies in climate archives, such as sediment and peat cores. The total LOP concentration, Σ8, provides information on the abundance of vegetation, while the ratios C/V and S/V of the different LOP groups also provide information on the type of vegetation. Recently, LOP analysis has been successfully applied to speleothem archives. However, there are many open questions concerning the transport and microbial degradation of LOPs on their way from the soil into the cave system. These processes could potentially alter the original source-dependent LOP signals, in particular the C/V and S/V ratios, and thus complicate their interpretation in terms of past vegetation changes. We analyzed LOPs in leaf litter and different soil horizons as well as dripwater and flowstone samples from four different cave sites from different vegetation zones in New Zealand using ultrahigh-performance liquid chromatography coupled to high-resolution mass spectrometry. We test whether the original source-dependent LOP signal of the overlying vegetation is preserved and can be recovered from flowstone samples and investigate how the signal is altered by the transport from the soil to the cave. The LOP concentrations range from mg g−1 in the soil to ng g−1 in the flowstones. Our results demonstrate that, from the soil to the flowstone, the C/V and S/V ratios both increase, while the total lignin content, Σ8, strongly decreases. This shows that the LOP signal is strongly influenced by both transport and degradation processes. Nevertheless, the relative LOP signal from the overlying soil at the different cave sites is preserved in the flowstone. We emphasize that for the interpretation of C/V and S/V ratios in terms of past vegetation changes, it is important to compare only samples of the same type (e.g., speleothem, dripwater or soil) and to evaluate only relative variations.

year: 2021

title: The embodied and lived experiences of welfare and care for highly impaired, high performance para-sport athletes in Aotearoa New Zealand

authors: Lowry, Amanda

abstract: Aligning with calls in critical disability studies to bring the body and impairment into disability sport, this thesis examines the welfare and care experiences of highly impaired athletes in high-performance sport. While a focus on athlete welfare has gained some international prominence, and a duty of care is increasingly invoked as an organisational and coaching responsibility, these developments remain largely disconnected from disability.  
The research is centred around two main objectives. First, to amplify the lived and embodied experiences of highly impaired, high performance disabled athletes as they prepare for, train, and compete in sport, and those who support them. Second, to understand how sporting institutions and regulations (within the broader context of government funding and national health care provision) influence welfare and care practices for high performance disabled athletes. 
Crip methodologies and Indigenous Māori storytelling methodologies such as pūrākau centres lived experience as a site of resistance and knowledge production. Using a reflexive, qualitative approach, including semi-structured interviews, autoethnographic vignettes, and visual ethnography, I expose how impairment effects are managed in ableist sporting environments that valorise normative athlete ideals. I interviewed 11 high-performance paraathletes, seven organisational representatives and two support workers. 
The research highlights the material, emotional, and temporal labour of care in highperformance sport. Findings are organised around three core themes: the embodied labour of care, impairment effects and interdependence; the tension between crip time, care time, and performance time; the intersecting structural, institutional, and ableist barriers that shape and constrain highly impaired athletes’ participation in disability sport.  
The first theme shows how high-performance sport privileges autonomous, efficient, and normative bodies, while marginalising those whose messy, gritty embodied impairment effects demand more time, support, and interdependence. The findings bring to the fore biosocial, psycho-emotional costs of navigating care and its impact on athlete welfare. The second theme uncovers how the rhythms of highly impaired bodies disrupt the linear, clockbound time of high-performance sport, revealing the incompatibility between care time and high performance cultures. It highlights the vital yet invisible labour of support workers, ii unacknowledged in contemporary sporting discourse. The third theme addresses the barriers that highly impaired athletes face when navigating ableist institutional and organisational structures. It exposes the complexity of the ableist disability sporting landscape and the gap between duty of care rhetoric and practice. 
Ultimately, this thesis calls for a radical reimagining of disability sport, one that centres interdependence, affirms bodily difference, and addresses the structural failures that marginalise highly impaired athletes.

text: The embodied and lived experiences of welfare and care for highly impaired, high performance para-sport athletes in Aotearoa New Zealand Aligning with calls in critical disability studies to bring the body and impairment into disability sport, this thesis examines the welfare and care experiences of highly impaired athletes in high-performance sport. While a focus on athlete welfare has gained some international prominence, and a duty of care is increasingly invoked as an organisational and coaching responsibility, these developments remain largely disconnected from disability.  
The research is centred around two main objectives. First, to amplify the lived and embodied experiences of highly impaired, high performance disabled athletes as they prepare for, train, and compete in sport, and those who support them. Second, to understand how sporting institutions and regulations (within the broader context of government funding and national health care provision) influence welfare and care practices for high performance disabled athletes. 
Crip methodologies and Indigenous Māori storytelling methodologies such as pūrākau centres lived experience as a site of resistance and knowledge production. Using a reflexive, qualitative approach, including semi-structured interviews, autoethnographic vignettes, and visual ethnography, I expose how impairment effects are managed in ableist sporting environments that valorise normative athlete ideals. I interviewed 11 high-performance paraathletes, seven organisational representatives and two support workers. 
The research highlights the material, emotional, and temporal labour of care in highperformance sport. Findings are organised around three core themes: the embodied labour of care, impairment effects and interdependence; the tension between crip time, care time, and performance time; the intersecting structural, institutional, and ableist barriers that shape and constrain highly impaired athletes’ participation in disability sport.  
The first theme shows how high-performance sport privileges autonomous, efficient, and normative bodies, while marginalising those whose messy, gritty embodied impairment effects demand more time, support, and interdependence. The findings bring to the fore biosocial, psycho-emotional costs of navigating care and its impact on athlete welfare. The second theme uncovers how the rhythms of highly impaired bodies disrupt the linear, clockbound time of high-performance sport, revealing the incompatibility between care time and high performance cultures. It highlights the vital yet invisible labour of support workers, ii unacknowledged in contemporary sporting discourse. The third theme addresses the barriers that highly impaired athletes face when navigating ableist institutional and organisational structures. It exposes the complexity of the ableist disability sporting landscape and the gap between duty of care rhetoric and practice. 
Ultimately, this thesis calls for a radical reimagining of disability sport, one that centres interdependence, affirms bodily difference, and addresses the structural failures that marginalise highly impaired athletes.

year: 2025-10