title: Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: This paper is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. Here we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different spaces. Through the use of this tool we derive and classify for the first time all two-dimensional (2D) superintegrable systems. The underlying spaces are exactly those derived by Koenigs in his remarkable paper giving all 2D manifolds (with zero potential) that admit at least three second order symmetries. Our derivation is very simple and quite distinct. We also show that every superintegrable system is the Stäckel transform of a superintegrable system on a constant curvature space.

text: Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform This paper is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. Here we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different spaces. Through the use of this tool we derive and classify for the first time all two-dimensional (2D) superintegrable systems. The underlying spaces are exactly those derived by Koenigs in his remarkable paper giving all 2D manifolds (with zero potential) that admit at least three second order symmetries. Our derivation is very simple and quite distinct. We also show that every superintegrable system is the Stäckel transform of a superintegrable system on a constant curvature space.

year: 2005-04

title: Response to Questionnaire - Focus: Taiwan

authors: Rolls, Mark G.

abstract: The desire of China to potentially invade Taiwan, mirroring historical actions like the annexation of Tibet, is met with significant challenges due to the unique circumstances surrounding Taiwan's status. Recent incursions into Taiwan's airspace by the People's Liberation Army Air Force (PLAAF) coincide with domestic and international factors, including President Xi's political positioning and international tensions. Despite President Biden's ambiguous statements, the U.S. exhibits a firm stance in supporting Taiwan, albeit with occasional policy confusion. Japan, recognizing the strategic importance of Taiwan, strengthens ties and prepares for potential conflict. European Union support for Taiwan grows amid concerns about China's global behavior. Taiwan faces external pressure from China to limit its diplomatic ties and international engagement. Efforts by countries like India to strengthen ties with Taiwan risk provoking China and complicating existing regional tensions. Despite international challenges, Taiwan remains resilient, seeking diplomatic support and strategic partnerships to counter Chinese pressure and maintain its sovereignty.

text: Response to Questionnaire - Focus: Taiwan The desire of China to potentially invade Taiwan, mirroring historical actions like the annexation of Tibet, is met with significant challenges due to the unique circumstances surrounding Taiwan's status. Recent incursions into Taiwan's airspace by the People's Liberation Army Air Force (PLAAF) coincide with domestic and international factors, including President Xi's political positioning and international tensions. Despite President Biden's ambiguous statements, the U.S. exhibits a firm stance in supporting Taiwan, albeit with occasional policy confusion. Japan, recognizing the strategic importance of Taiwan, strengthens ties and prepares for potential conflict. European Union support for Taiwan grows amid concerns about China's global behavior. Taiwan faces external pressure from China to limit its diplomatic ties and international engagement. Efforts by countries like India to strengthen ties with Taiwan risk provoking China and complicating existing regional tensions. Despite international challenges, Taiwan remains resilient, seeking diplomatic support and strategic partnerships to counter Chinese pressure and maintain its sovereignty.

year: 2021

title: Social deprivation in New Zealand

authors: Harcourt, Brian James

subjects: Deprivation

abstract: The purpose of the thesis was to better understand the phenomenon of social deprivation, world-wide and in particular in New Zealand. Social deprivation has been defined in many ways with multiple surrogates used to ‘measure’ its prevalence. The aim of this research was to provide examples of the lived experiences of social deprivation.

Social constructivist and interpretive lenses were used to portray the voices of those living in deprivation, as well as those people tasked to assist them. A narrative case study approach was employed with participants from Whānau Ora. This social and health initiative offered a holistic approach to assistance in contrast to the usual State agencies operating in a silo fashion, with separate agencies providing for different aspects of social deprivation such as housing, employment, mental health and other services. The approach of Whānau Ora is to support clients’ needs holistically and encourage people to develop their own plans for self- improvement. Navigators help people develop their plans and assist in their interactions with the various State agencies whose services they require. This approach allowed a better understanding of ways to overcome people’s feelings of powerlessness and desperation.

The findings from the study lead to suggestions for the application of evidence-based, complementary, integrated assistance programmes rather than having segregated public service agencies acting independently. The recommendations are simple yet require profound changes in public service operations when attempting to ameliorate or prevent social deprivation among citizens.

text: Social deprivation in New Zealand The purpose of the thesis was to better understand the phenomenon of social deprivation, world-wide and in particular in New Zealand. Social deprivation has been defined in many ways with multiple surrogates used to ‘measure’ its prevalence. The aim of this research was to provide examples of the lived experiences of social deprivation.

Social constructivist and interpretive lenses were used to portray the voices of those living in deprivation, as well as those people tasked to assist them. A narrative case study approach was employed with participants from Whānau Ora. This social and health initiative offered a holistic approach to assistance in contrast to the usual State agencies operating in a silo fashion, with separate agencies providing for different aspects of social deprivation such as housing, employment, mental health and other services. The approach of Whānau Ora is to support clients’ needs holistically and encourage people to develop their own plans for self- improvement. Navigators help people develop their plans and assist in their interactions with the various State agencies whose services they require. This approach allowed a better understanding of ways to overcome people’s feelings of powerlessness and desperation.

The findings from the study lead to suggestions for the application of evidence-based, complementary, integrated assistance programmes rather than having segregated public service agencies acting independently. The recommendations are simple yet require profound changes in public service operations when attempting to ameliorate or prevent social deprivation among citizens.

year: 2019