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: Coastal hazards of the Bay of Plenty coast [Field Trip FT3]

authors: de Lange, Willem P.

abstract: The latest GSNZ fieldtrip to examine coastal processes in the Bay of Plenty ran in 1988. In the intervening 13 years there have been changes in both the legislative framework and our scientific understanding that affect coastal management at the start of the 21st Century. The most important legislative change has been the Resource Management Act (RMA) introduced in October 1991. and the associated Coastal Policy Statement. Amongst other requirements has been the need to define Coastal Hazard Zones for the entire 10-15,000 km of the New Zealand coast.
This field trip (Environment Court permitting) will particularly examine the advances in our understanding of coastal processes and hazards in the context of coastal development in the western Bay of Plenty between Waihi and Little Waihi.

text: Coastal hazards of the Bay of Plenty coast [Field Trip FT3] The latest GSNZ fieldtrip to examine coastal processes in the Bay of Plenty ran in 1988. In the intervening 13 years there have been changes in both the legislative framework and our scientific understanding that affect coastal management at the start of the 21st Century. The most important legislative change has been the Resource Management Act (RMA) introduced in October 1991. and the associated Coastal Policy Statement. Amongst other requirements has been the need to define Coastal Hazard Zones for the entire 10-15,000 km of the New Zealand coast.
This field trip (Environment Court permitting) will particularly examine the advances in our understanding of coastal processes and hazards in the context of coastal development in the western Bay of Plenty between Waihi and Little Waihi.

year: 2001

title: Monitoring first year Maori students enrolled in selected Faculty of Arts and Social Sciences courses: A report prepared for the Dean of the Faculty of Arts and Social Sciences

authors: Levy, Michelle Patricia

subjects: maori students

abstract: Monitoring first year Maori Students Enrolled in Selected Faculty of Arts andSocial Sciences Courses. The total number of Maori students targeted by this project was 182, representing 93% of the total number of Maori students enrolled in Semester B level one courses. The majority of students participating in this initiative were first year students, although a small number of students taking 100 level courses were second, third or graduate year students. 11 Student views on the monitoring and support initiative Students were provided with the opportunity to comment on the monitoring and support initiative. All students contacted (49) recommended that this intervention continue for future first year Maori students enrolled in FASS.

text: Monitoring first year Maori students enrolled in selected Faculty of Arts and Social Sciences courses: A report prepared for the Dean of the Faculty of Arts and Social Sciences Monitoring first year Maori Students Enrolled in Selected Faculty of Arts andSocial Sciences Courses. The total number of Maori students targeted by this project was 182, representing 93% of the total number of Maori students enrolled in Semester B level one courses. The majority of students participating in this initiative were first year students, although a small number of students taking 100 level courses were second, third or graduate year students. 11 Student views on the monitoring and support initiative Students were provided with the opportunity to comment on the monitoring and support initiative. All students contacted (49) recommended that this intervention continue for future first year Maori students enrolled in FASS.

year: 2003-03-01