title: Families of classical subgroup separable superintegrable systems

authors: Kalnins, Ernie G.

subjects: mathematics

abstract: We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for some families of generalized oscillator and Kepler–Coulomb systems, hence demonstrating their superintegrability. The latter generalizes recent results of Verrier and Evans, and Rodríguez, Tempesta and Winternitz. Another example is given of a superintegrable system on a non-conformally flat space.

text: Families of classical subgroup separable superintegrable systems We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for some families of generalized oscillator and Kepler–Coulomb systems, hence demonstrating their superintegrability. The latter generalizes recent results of Verrier and Evans, and Rodríguez, Tempesta and Winternitz. Another example is given of a superintegrable system on a non-conformally flat space.

year: 2010

title: Using ultra-small radiocarbon dates to obtain reliable ages on shells affected by hard water

authors: Milson, Catherine Elizabeth

abstract: Radiocarbon dating is used across a wide range of scientific disciplines including archaeology, forensics, and geosciences. Interest in reducing the minimum sample size limit required for obtaining reliable radiocarbon dates has grown over the years as this would offer many new research opportunities. Contamination introduced by the radiocarbon dating process becomes more problematic for samples <0.10 mgC, and in order to reliably radiocarbon date ultra-small samples, contamination is one of the issues that needs to be resolved.

Reducing the amount of sample required for radiocarbon analysis has been specifically applied to an archaeological problem. The Mariana Islands, located in the Western North Pacific, are home to the archaeological site Bapot-1. While the exact date of human arrival is currently under debate, it is thought to have occurred between 3300 – 3500 years ago. Establishing a date of human arrival is important because it represents the longest ocean voyage of its time, more than 2000 km, and is necessary for modelling when Neolithic expansion in Island Southeast Asia occurred.

Obtaining reliable radiocarbon dates from Bapot-1 is difficult as short-lived terrestrial materials, such as charred twigs, are often degraded or scarce. While shell material is abundant, the presence of limestone bedrock hinders its use. As freshwater travels through limestone, it picks up bicarbonate ions depleted in ¹⁴C. This ‘old’ water is discharged into the water at the shore where it is then incorporated into the shells of some, but not all, shell taxa that live close to the shore. This results in older radiocarbon ages for some shellfish. To overcome this problem, it is hypothesized that ¹³C can be used to identify shellfish that have been affected by hard water. However, for shellfish that have a tolerance for both marine and estuarine environments, different ¹³C/¹⁴C values will be obtained depending on where sampling occurs on the shell. To accurately radiocarbon date a single shell that may have been influenced by old ¹⁴C at different times, it is necessary to identify which shell growth bands have been deposited while influenced by the different water sources. This necessitates the ability to date very small samples of shell material. 

To overcome contamination issues associated with radiocarbon dating ultra-small samples, a series of vacuum line and chemical modifications were selected and substituted into current Waikato Radiocarbon Dating Laboratory (WRDL) procedures. To assess the effect of each modification, three standards (of known age) that are used at the WRDL were radiocarbon dated. The radiocarbon dating results from the standards showed that the volume and chemical modifications did not have any significant impact on improving contamination issues for ultra-small samples. However, there were some noteworthy observations. The graphitisation reaction was significantly faster when a quartz tube with “slush” was used instead of magnesium perchlorate. This time reduction has the potential to minimise contamination. Furthermore, the use of a six-decimal point balance for weighing ultra-small samples resulted in more precise CO₂ yields compared to the four-decimal point balance routinely used at the WRDL.

Selected volume modifications were used to radiocarbon date three growth bands from a Gafrarium sp. shellfish from the Mariana Islands. Two results from the same Gafrarium sp. shellfish that were previously radiocarbon dated were incorporated into this thesis, resulting in a representation of three “marine” and two “estuarine” growth bands. Radiocarbon results provided preliminary evidence supporting the hypothesis of a relationship between ¹³C, ¹⁴C, and hard water exposure. Using Chi-square statistics, the five radiocarbon dates were calculated to be statistically distinguishable, a significant result considering the five radiocarbon dates were from the same shell. Furthermore, the pooled radiocarbon age of the “marine” growth bands was statistically distinguishable from one of the estuarine samples, where a difference of 304 ¹⁴C years was observed. Conversely, when the pooled radiocarbon age of the “marine” growth bands was compared to the other estuarine sample, the two radiocarbon dates were statistically the same. The reason for this was hypothesised to be due to variability in old ¹⁴C. The tide, along with wind and storms, results in variable concentrations of marine and fresh water held close to the shoreline by onshore currents, and so these variable conditions result in variability of the concentration of old ¹⁴C in the water.

text: Using ultra-small radiocarbon dates to obtain reliable ages on shells affected by hard water Radiocarbon dating is used across a wide range of scientific disciplines including archaeology, forensics, and geosciences. Interest in reducing the minimum sample size limit required for obtaining reliable radiocarbon dates has grown over the years as this would offer many new research opportunities. Contamination introduced by the radiocarbon dating process becomes more problematic for samples <0.10 mgC, and in order to reliably radiocarbon date ultra-small samples, contamination is one of the issues that needs to be resolved.

Reducing the amount of sample required for radiocarbon analysis has been specifically applied to an archaeological problem. The Mariana Islands, located in the Western North Pacific, are home to the archaeological site Bapot-1. While the exact date of human arrival is currently under debate, it is thought to have occurred between 3300 – 3500 years ago. Establishing a date of human arrival is important because it represents the longest ocean voyage of its time, more than 2000 km, and is necessary for modelling when Neolithic expansion in Island Southeast Asia occurred.

Obtaining reliable radiocarbon dates from Bapot-1 is difficult as short-lived terrestrial materials, such as charred twigs, are often degraded or scarce. While shell material is abundant, the presence of limestone bedrock hinders its use. As freshwater travels through limestone, it picks up bicarbonate ions depleted in ¹⁴C. This ‘old’ water is discharged into the water at the shore where it is then incorporated into the shells of some, but not all, shell taxa that live close to the shore. This results in older radiocarbon ages for some shellfish. To overcome this problem, it is hypothesized that ¹³C can be used to identify shellfish that have been affected by hard water. However, for shellfish that have a tolerance for both marine and estuarine environments, different ¹³C/¹⁴C values will be obtained depending on where sampling occurs on the shell. To accurately radiocarbon date a single shell that may have been influenced by old ¹⁴C at different times, it is necessary to identify which shell growth bands have been deposited while influenced by the different water sources. This necessitates the ability to date very small samples of shell material. 

To overcome contamination issues associated with radiocarbon dating ultra-small samples, a series of vacuum line and chemical modifications were selected and substituted into current Waikato Radiocarbon Dating Laboratory (WRDL) procedures. To assess the effect of each modification, three standards (of known age) that are used at the WRDL were radiocarbon dated. The radiocarbon dating results from the standards showed that the volume and chemical modifications did not have any significant impact on improving contamination issues for ultra-small samples. However, there were some noteworthy observations. The graphitisation reaction was significantly faster when a quartz tube with “slush” was used instead of magnesium perchlorate. This time reduction has the potential to minimise contamination. Furthermore, the use of a six-decimal point balance for weighing ultra-small samples resulted in more precise CO₂ yields compared to the four-decimal point balance routinely used at the WRDL.

Selected volume modifications were used to radiocarbon date three growth bands from a Gafrarium sp. shellfish from the Mariana Islands. Two results from the same Gafrarium sp. shellfish that were previously radiocarbon dated were incorporated into this thesis, resulting in a representation of three “marine” and two “estuarine” growth bands. Radiocarbon results provided preliminary evidence supporting the hypothesis of a relationship between ¹³C, ¹⁴C, and hard water exposure. Using Chi-square statistics, the five radiocarbon dates were calculated to be statistically distinguishable, a significant result considering the five radiocarbon dates were from the same shell. Furthermore, the pooled radiocarbon age of the “marine” growth bands was statistically distinguishable from one of the estuarine samples, where a difference of 304 ¹⁴C years was observed. Conversely, when the pooled radiocarbon age of the “marine” growth bands was compared to the other estuarine sample, the two radiocarbon dates were statistically the same. The reason for this was hypothesised to be due to variability in old ¹⁴C. The tide, along with wind and storms, results in variable concentrations of marine and fresh water held close to the shoreline by onshore currents, and so these variable conditions result in variability of the concentration of old ¹⁴C in the water.

year: 2022

title: Student voice and agency for Indigenous Maori students in higher education transitions

authors: Amundsen, Diana Leigh

subjects: Social Sciences

abstract: This article reveals the complexities of Indigenous students navigating the neoliberal model of education through an examination of Māori transitions into higher education contexts in Aotearoa New Zealand. In a recently completed doctoral study, the lived transition experiences of Indigenous Māori higher education students were critically investigated from a student voice perspective. Data were collected and analysed through repeated semi-structured interviews, focus groups and visual stories in a semi-longitudinal study with 20 Māori students enrolled in a wānanga, a polytechnic and a university. Using a Bourdieuan theoretical framework for analysis, findings revealed that participants experienced their transition as a journey. Students perpetually evolved their identities and agency in relation to the tertiary education environments and social structures they encountered which supported or constrained transition experiences. Within wānanga, participants felt their Māori cultural identity was highly valued; within polytechnics, there was a sense that Māori culture is included but more could be done; within universities, a need for more inclusive practices to support Māori learner requirements was identified. This empirical research outlines learning for Māori students in higher education, and is a timely addition to knowledge revealing the complexities of teaching in the neoliberal model of higher education with Indigenous people.

text: Student voice and agency for Indigenous Maori students in higher education transitions This article reveals the complexities of Indigenous students navigating the neoliberal model of education through an examination of Māori transitions into higher education contexts in Aotearoa New Zealand. In a recently completed doctoral study, the lived transition experiences of Indigenous Māori higher education students were critically investigated from a student voice perspective. Data were collected and analysed through repeated semi-structured interviews, focus groups and visual stories in a semi-longitudinal study with 20 Māori students enrolled in a wānanga, a polytechnic and a university. Using a Bourdieuan theoretical framework for analysis, findings revealed that participants experienced their transition as a journey. Students perpetually evolved their identities and agency in relation to the tertiary education environments and social structures they encountered which supported or constrained transition experiences. Within wānanga, participants felt their Māori cultural identity was highly valued; within polytechnics, there was a sense that Māori culture is included but more could be done; within universities, a need for more inclusive practices to support Māori learner requirements was identified. This empirical research outlines learning for Māori students in higher education, and is a timely addition to knowledge revealing the complexities of teaching in the neoliberal model of higher education with Indigenous people.

year: 2019