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: 'Does anyone else have this?' The role of emotion in forum discussions about medical conditions affecting sex characteristics

authors: Roen, Katrina

subjects: Social Sciences

abstract: When people experience rare medical conditions or variations, searching online may be the only way to find others with similar experiences. This study examines what happens when people do just that. The dataset for the research has been generated from online posts by people living with variations of sex characteristics, which some call intersex variations. Our analysis focuses on how emotion appears in online posts, how affect becomes embodied in digital contexts, and how norms are negotiated as people relate to one another about the variations that some of them experience. We offer an analysis grounded in digital affect theory to contribute to health research literature. We suggest how health researchers and healthcare providers might develop more nuanced understandings of the emotional realities of people living with variations of sex characteristics.

text: 'Does anyone else have this?' The role of emotion in forum discussions about medical conditions affecting sex characteristics When people experience rare medical conditions or variations, searching online may be the only way to find others with similar experiences. This study examines what happens when people do just that. The dataset for the research has been generated from online posts by people living with variations of sex characteristics, which some call intersex variations. Our analysis focuses on how emotion appears in online posts, how affect becomes embodied in digital contexts, and how norms are negotiated as people relate to one another about the variations that some of them experience. We offer an analysis grounded in digital affect theory to contribute to health research literature. We suggest how health researchers and healthcare providers might develop more nuanced understandings of the emotional realities of people living with variations of sex characteristics.

year: 2021

title: Lessons learned from the MV Rena: Reimagining maritime and resource management law

authors: Paul, Adrienne Joy

subjects: Resource Management Law - New Zealand

abstract: The main research question in this thesis is what lessons can Aotearoa New Zealand learn from the MV Rena grounding accident? This research is an historical account of the legal framework existing at the time of the MV Rena grounding. In addition, the thesis will outline the surrounding marine environment to examine the relevant regulatory system.
In the early morning of 5th October 2011, the MV Rena vessel struck Ōtāiti (Astrolabe Reef).  Initially, the accident concerned a response to the safety of the crew on board the MV Rena. However, the seriousness of the damage to the hull with part of Ōtāiti reef protruding through the keel, presented issues concerning the recovery strategy for the vessel and cargo from the coastal marine area.  The MV Rena grounding released oil, cargo, and equipment into the surrounding marine environment of Ōtāiti. The oil, cargo and equipment travelled by the ocean currents, spreading across large areas of the ocean. This caused environmental effects across the coastal marine area in the Bay of Plenty region. The grounding was the “worst maritime environmental disaster” Aotearoa New Zealand had ever seen. 

The government of the day and the MV Rena owner are committed to international obligations for preparing and responding to maritime disasters and marine pollution. However, the government of Aotearoa New Zealand was not a party to international obligations addressing groundings relative to bunker oil. In addition, when responding to environmental effects from the grounding the legal processes regulating the maritime and resource management system, caused distress to the local community in the Bay of Plenty region. Specifically, the people of Motiti Island (“Motiti”), relative to preserving and protecting their cultural and spiritual relationship with Ōtāiti and Motiti.

An analysis of maritime and resource management law at the international level and domestic level is explored in this thesis. Such as, marine pollution, and indigenous peoples’ rights (iwi Māori) in connection with the Maritime Transport Act 1994, the Resource Management Act 1991, the Waitangi Tribunal process and related planning and policy instruments.  The research concludes that, had the government of the day ratified relevant conventions prior to the MV Rena grounding incident, the outcome of the location of the ship may have been a completely different result, such as a full wreck removal, without opposition. Additionally, the research concludes that the gap in the laws regulating marine environments did not equip iwi Māori with protecting their interests, resulting in a spiritual injustice to the people of Motiti. This research reveals that maritime and resource management law still has a long way to go with supporting the indigenous people’s voice in Aotearoa New Zealand for sustainable marine solutions. This thesis conclude with recommendations directed at better maritime and resource management regulations and indigenous peoples’ involvement.

text: Lessons learned from the MV Rena: Reimagining maritime and resource management law The main research question in this thesis is what lessons can Aotearoa New Zealand learn from the MV Rena grounding accident? This research is an historical account of the legal framework existing at the time of the MV Rena grounding. In addition, the thesis will outline the surrounding marine environment to examine the relevant regulatory system.
In the early morning of 5th October 2011, the MV Rena vessel struck Ōtāiti (Astrolabe Reef).  Initially, the accident concerned a response to the safety of the crew on board the MV Rena. However, the seriousness of the damage to the hull with part of Ōtāiti reef protruding through the keel, presented issues concerning the recovery strategy for the vessel and cargo from the coastal marine area.  The MV Rena grounding released oil, cargo, and equipment into the surrounding marine environment of Ōtāiti. The oil, cargo and equipment travelled by the ocean currents, spreading across large areas of the ocean. This caused environmental effects across the coastal marine area in the Bay of Plenty region. The grounding was the “worst maritime environmental disaster” Aotearoa New Zealand had ever seen. 

The government of the day and the MV Rena owner are committed to international obligations for preparing and responding to maritime disasters and marine pollution. However, the government of Aotearoa New Zealand was not a party to international obligations addressing groundings relative to bunker oil. In addition, when responding to environmental effects from the grounding the legal processes regulating the maritime and resource management system, caused distress to the local community in the Bay of Plenty region. Specifically, the people of Motiti Island (“Motiti”), relative to preserving and protecting their cultural and spiritual relationship with Ōtāiti and Motiti.

An analysis of maritime and resource management law at the international level and domestic level is explored in this thesis. Such as, marine pollution, and indigenous peoples’ rights (iwi Māori) in connection with the Maritime Transport Act 1994, the Resource Management Act 1991, the Waitangi Tribunal process and related planning and policy instruments.  The research concludes that, had the government of the day ratified relevant conventions prior to the MV Rena grounding incident, the outcome of the location of the ship may have been a completely different result, such as a full wreck removal, without opposition. Additionally, the research concludes that the gap in the laws regulating marine environments did not equip iwi Māori with protecting their interests, resulting in a spiritual injustice to the people of Motiti. This research reveals that maritime and resource management law still has a long way to go with supporting the indigenous people’s voice in Aotearoa New Zealand for sustainable marine solutions. This thesis conclude with recommendations directed at better maritime and resource management regulations and indigenous peoples’ involvement.

year: 2022