title: Structure Theory for Extended Kepler-Coulomb 3D Classical Superintegrable Systems

authors: Kalnins, Ernie G.

subjects: superintegrability

abstract: The classical Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under Poisson brackets. This polynomial closure is typical for 2nd order superintegrable systems in 2D and for 2nd order systems in 3D with nondegenerate (4-parameter) potentials. However the degenerate 3-parameter potential for the 3D extended Kepler-Coulomb system (also 2nd order superintegrable) is an exception, as its quadratic symmetry algebra doesn't close polynomially. The 3D 4-parameter potential for the extended Kepler-Coulomb system is not even 2nd order superintegrable. However, Verrier and Evans (2008) showed it was 4th order superintegrable, and Tanoudis and Daskaloyannis (2011) showed that in the quantum case, if a second 4th order symmetry is added to the generators, the double commutators in the symmetry algebra close polynomially. Here, based on the Tremblay, Turbiner and Winternitz construction, we consider an infinite class of classical extended Kepler-Coulomb 3- and 4-parameter systems indexed by a pair of rational numbers (k1,k2) and reducing to the usual systems when k1=k2=1. We show these systems to be superintegrable of arbitrarily high order and work out explicitly the structure of the symmetry algebras determined by the 5 basis generators we have constructed. We demonstrate that the symmetry algebras close rationally; only for systems admitting extra discrete symmetries is polynomial closure achieved. Underlying the structure theory is the existence of raising and lowering constants of the motion, not themselves polynomials in the momenta, that can be employed to construct the polynomial symmetries and their structure relations.

text: Structure Theory for Extended Kepler-Coulomb 3D Classical Superintegrable Systems The classical Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under Poisson brackets. This polynomial closure is typical for 2nd order superintegrable systems in 2D and for 2nd order systems in 3D with nondegenerate (4-parameter) potentials. However the degenerate 3-parameter potential for the 3D extended Kepler-Coulomb system (also 2nd order superintegrable) is an exception, as its quadratic symmetry algebra doesn't close polynomially. The 3D 4-parameter potential for the extended Kepler-Coulomb system is not even 2nd order superintegrable. However, Verrier and Evans (2008) showed it was 4th order superintegrable, and Tanoudis and Daskaloyannis (2011) showed that in the quantum case, if a second 4th order symmetry is added to the generators, the double commutators in the symmetry algebra close polynomially. Here, based on the Tremblay, Turbiner and Winternitz construction, we consider an infinite class of classical extended Kepler-Coulomb 3- and 4-parameter systems indexed by a pair of rational numbers (k1,k2) and reducing to the usual systems when k1=k2=1. We show these systems to be superintegrable of arbitrarily high order and work out explicitly the structure of the symmetry algebras determined by the 5 basis generators we have constructed. We demonstrate that the symmetry algebras close rationally; only for systems admitting extra discrete symmetries is polynomial closure achieved. Underlying the structure theory is the existence of raising and lowering constants of the motion, not themselves polynomials in the momenta, that can be employed to construct the polynomial symmetries and their structure relations.

year: 2012

title: “My culture is like comfortable clothing”: Parenting experience of first-generation South Korean immigrants in Aotearoa New Zealand

authors: Kwon, Soyeon Bella

subjects: Korean

abstract: Although the parenting experience among first-generation South Korean immigrants in New Zealand has been documented, a further qualitative study was needed to understand the complexities of adjusting to New Zealand, where different parenting values and practices exist compared with South Korea. Through interviews with ten first-generation South Korean parents, this study explored the processes of participants re-evaluating their original values and practices. This study was guided by existing research on the cultural differences between Korea and New Zealand and theories of acculturation, immigrant parenting modification, dual route to value change, and cultural translation.

Three themes were extracted through thematic analysis. First, participants appeared to have found some values and practices easier to adapt and change, and some were more effortful. For example, many participants tended to encourage their children’s autonomy and independence in academics and careers domain sooner or later. However, some participants found it difficult to encourage their children’s independence in the financial and self-care domain because these new practices clashed with their original values. For example, adolescent children paying rent to their parents clashed with the importance of accumulating jeong (정), while making young children do house chores clashed with their belief that children should devote their time for self-development.

Second, parents and children’s bi-cultural socialisation emerged as a new parenting goal. Participants were concerned about them acquiring the New Zealand culture (e.g., family leisure life, involvement in their child’s school, and English fluency) and transmitting Korean culture to their children. Nevertheless, they seemed to have found practical, cultural, and language barriers to translate their values into action. In discussion, we discuss the importance of this issue and provide recommendations for immigrants.

Third, many participants reported having enhanced their relationships with their children. Male participants reported increasing time spent with their children because New Zealand work and family lifestyles enabled it. In contrast, female participants appeared to have found the overlap between the mother’s role as a comforter in Korean culture and the New Zealand parents’ communication style, and they reported becoming more validating of children’s emotions and less demanding and controlling. 
Our findings support the theory of the dual route to value change and the hierarchical nature of the value system (e.g., independence vs jeong). Also, we found our participants demonstrating cultural translation process to maintain values, which involves creating new solutions when tension arose between Korean and New Zealand cultures (e.g., private tutoring, communication method to overcome language differences, and family trips).

Supporting migrant parents may require extra attention to the family’s experience of reconstructing their ethnic identity, cultural socialisation to the mainstream culture and cultural maintenance as these lead to understanding their practices and behaviours. Also, migrant families may benefit from exploring creative solutions or applying the skills mentioned. At community and policy level, creating opportunities for participation in cross-cultural activities and increasing access to translation services can support migrant families. It is recommended for schools to invest time to clarify cultural expectations with newly migrated families.

text: “My culture is like comfortable clothing”: Parenting experience of first-generation South Korean immigrants in Aotearoa New Zealand Although the parenting experience among first-generation South Korean immigrants in New Zealand has been documented, a further qualitative study was needed to understand the complexities of adjusting to New Zealand, where different parenting values and practices exist compared with South Korea. Through interviews with ten first-generation South Korean parents, this study explored the processes of participants re-evaluating their original values and practices. This study was guided by existing research on the cultural differences between Korea and New Zealand and theories of acculturation, immigrant parenting modification, dual route to value change, and cultural translation.

Three themes were extracted through thematic analysis. First, participants appeared to have found some values and practices easier to adapt and change, and some were more effortful. For example, many participants tended to encourage their children’s autonomy and independence in academics and careers domain sooner or later. However, some participants found it difficult to encourage their children’s independence in the financial and self-care domain because these new practices clashed with their original values. For example, adolescent children paying rent to their parents clashed with the importance of accumulating jeong (정), while making young children do house chores clashed with their belief that children should devote their time for self-development.

Second, parents and children’s bi-cultural socialisation emerged as a new parenting goal. Participants were concerned about them acquiring the New Zealand culture (e.g., family leisure life, involvement in their child’s school, and English fluency) and transmitting Korean culture to their children. Nevertheless, they seemed to have found practical, cultural, and language barriers to translate their values into action. In discussion, we discuss the importance of this issue and provide recommendations for immigrants.

Third, many participants reported having enhanced their relationships with their children. Male participants reported increasing time spent with their children because New Zealand work and family lifestyles enabled it. In contrast, female participants appeared to have found the overlap between the mother’s role as a comforter in Korean culture and the New Zealand parents’ communication style, and they reported becoming more validating of children’s emotions and less demanding and controlling. 
Our findings support the theory of the dual route to value change and the hierarchical nature of the value system (e.g., independence vs jeong). Also, we found our participants demonstrating cultural translation process to maintain values, which involves creating new solutions when tension arose between Korean and New Zealand cultures (e.g., private tutoring, communication method to overcome language differences, and family trips).

Supporting migrant parents may require extra attention to the family’s experience of reconstructing their ethnic identity, cultural socialisation to the mainstream culture and cultural maintenance as these lead to understanding their practices and behaviours. Also, migrant families may benefit from exploring creative solutions or applying the skills mentioned. At community and policy level, creating opportunities for participation in cross-cultural activities and increasing access to translation services can support migrant families. It is recommended for schools to invest time to clarify cultural expectations with newly migrated families.

year: 2023

title: Research note: Empirical analysis of ethnic pay gaps in New Zealand

authors: Cochrane, William

abstract: This research note explores the factors contributing to ethnic pay gaps in New Zealand. The emphasis here is on description, as a causal analysis is beyond the capability of the methods used. The gaps between the average (as well as median) hourly wages for the European workforce relative to Māori and Pacific workers are substantial. A statistical analysis by Treasury in 2018 also showed that the ratio in average hourly wages (based on published survey estimates by Stats NZ) for both ethnic groups relative to European had stayed at a similar level for the last decade; as they state “there has been movement from year to year but no consistent upward or downward trend” (Treasury, 2018, p.1).

text: Research note: Empirical analysis of ethnic pay gaps in New Zealand This research note explores the factors contributing to ethnic pay gaps in New Zealand. The emphasis here is on description, as a causal analysis is beyond the capability of the methods used. The gaps between the average (as well as median) hourly wages for the European workforce relative to Māori and Pacific workers are substantial. A statistical analysis by Treasury in 2018 also showed that the ratio in average hourly wages (based on published survey estimates by Stats NZ) for both ethnic groups relative to European had stayed at a similar level for the last decade; as they state “there has been movement from year to year but no consistent upward or downward trend” (Treasury, 2018, p.1).

year: 2023-10-19