title: Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties

authors: Kalnins, Ernie G.

subjects: mathematics

abstract: A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n−1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible. Such systems have remarkable properties: multi-integrability and multiseparability, an algebra of higher order symmetries whose representation theory yields spectral information about the Schrödinger operator, deep connections with special functions, and with quasiexactly solvable systems. Here, we announce a complete classification of nondegenerate (i.e., four-parameter) potentials for complex Euclidean 3-space. We characterize the possible superintegrable systems as points on an algebraic variety in ten variables subject to six quadratic polynomial constraints. The Euclidean group acts on the variety such that two points determine the same superintegrable system if and only if they lie on the same leaf of the foliation. There are exactly ten nondegenerate potentials. ©2007 American Institute of Physics

text: Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n−1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible. Such systems have remarkable properties: multi-integrability and multiseparability, an algebra of higher order symmetries whose representation theory yields spectral information about the Schrödinger operator, deep connections with special functions, and with quasiexactly solvable systems. Here, we announce a complete classification of nondegenerate (i.e., four-parameter) potentials for complex Euclidean 3-space. We characterize the possible superintegrable systems as points on an algebraic variety in ten variables subject to six quadratic polynomial constraints. The Euclidean group acts on the variety such that two points determine the same superintegrable system if and only if they lie on the same leaf of the foliation. There are exactly ten nondegenerate potentials. ©2007 American Institute of Physics

year: 2007

title: Pasifika women affected by domestic violence: The case of Teuila

authors: Masters-Awatere, Bridgette

abstract: Domestic violence is a pervasive social issue in New Zealand, with the majority of victims being women and children. In 2008, the New Zealand Crime and Safety Survey found that one in five Pasifika had experienced violence at the hands of their partner in the previous year.2 Six years later the results of the same survey reported a 19 per cent decrease of intimate partner violence among Pasifika. Despite this reduction, domestic violence is still prevalent in Pasifika communities. Women in general are known to have low rates of accessing the services available to assist them in navigating themselves and their children to safety, and Pasifika women, with even fewer social and economic resources than other women, are thus left in an even more precarious position. The research presented in this chapter focuses on identifying the barriers and supports women encounter when they attempt to access external agency support to gain protection from their abusers in order to deal with the impacts of abuse.

text: Pasifika women affected by domestic violence: The case of Teuila Domestic violence is a pervasive social issue in New Zealand, with the majority of victims being women and children. In 2008, the New Zealand Crime and Safety Survey found that one in five Pasifika had experienced violence at the hands of their partner in the previous year.2 Six years later the results of the same survey reported a 19 per cent decrease of intimate partner violence among Pasifika. Despite this reduction, domestic violence is still prevalent in Pasifika communities. Women in general are known to have low rates of accessing the services available to assist them in navigating themselves and their children to safety, and Pasifika women, with even fewer social and economic resources than other women, are thus left in an even more precarious position. The research presented in this chapter focuses on identifying the barriers and supports women encounter when they attempt to access external agency support to gain protection from their abusers in order to deal with the impacts of abuse.

year: 2017

title: From colonial categories to local culture: Evolving state practices of ethnic enumeration in Oceania, 1965-2014

authors: Kukutai, Tahu

subjects: Social Sciences

abstract: Numerous scholars have examined how governments in particular times and places have classified their populations by ethnicity, but studies that are both cross-national and longitudinal are rare. Using a unique database of census questionnaires, we examine state practices of ethnic enumeration over a 50-year period (1965–2014) in the 24 countries and areas that comprise Oceania. The region’s extraordinary linguistic and cultural diversity, combined with its complex colonial history and indigenous politics, make it an ideal site for comparative analyses. We find a shift from biological conceptions of difference to a more cultural understanding of group identity, exemplified by a sharp rise in language questions and the decline of race-based inquiries. While local identity labels have largely displaced colonial categories, the imprimatur of previous regimes still lingers, particularly in Melanesia. These shifts in official constructions of ethnoracial differences reflect a gradual lessening of colonial influences on demographic practices.

text: From colonial categories to local culture: Evolving state practices of ethnic enumeration in Oceania, 1965-2014 Numerous scholars have examined how governments in particular times and places have classified their populations by ethnicity, but studies that are both cross-national and longitudinal are rare. Using a unique database of census questionnaires, we examine state practices of ethnic enumeration over a 50-year period (1965–2014) in the 24 countries and areas that comprise Oceania. The region’s extraordinary linguistic and cultural diversity, combined with its complex colonial history and indigenous politics, make it an ideal site for comparative analyses. We find a shift from biological conceptions of difference to a more cultural understanding of group identity, exemplified by a sharp rise in language questions and the decline of race-based inquiries. While local identity labels have largely displaced colonial categories, the imprimatur of previous regimes still lingers, particularly in Melanesia. These shifts in official constructions of ethnoracial differences reflect a gradual lessening of colonial influences on demographic practices.

year: 2016