title: Bôcher contractions of conformally superintegrable Laplace equations

authors: Kalnins, Ernie G.

abstract: The explicit solvability of quantum superintegrable systems is due to symmetry, but the symmetry is often “hidden”. The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define quadratic algebras, a generalization of Lie algebras. Distinct systems on constant curvature spaces are related by geometric limits, induced by generalized Inönü–Wigner Lie algebra contractions of the symmetry algebras of the underlying spaces. These have physical/geometric implications, such as the Askey scheme for hypergeometric orthogonal polynomials. However, the limits have no satisfactory Lie algebra contraction interpretations for underlying spaces with 1- or 0-dimensional Lie algebras. We show that these systems can be best understood by transforming them to Laplace conformally superintegrable systems, with flat space conformal symmetry group SO(4, ℂ), and using ideas introduced in the 1894 thesis of Bôcher to study separable solutions of the wave equation in terms of roots of quadratic forms. We show that Bôcher’s prescription for coalescing roots of these forms induces contractions of the conformal algebra so(4, ℂ) to itself and yields a mechanism for classifying all Helmholtz superintegrable systems and their limits. In the paperActa Polytechnica, to appear, arXiv:1510.09067], we announced our main findings. This paper provides the proofs and more details.

text: Bôcher contractions of conformally superintegrable Laplace equations The explicit solvability of quantum superintegrable systems is due to symmetry, but the symmetry is often “hidden”. The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define quadratic algebras, a generalization of Lie algebras. Distinct systems on constant curvature spaces are related by geometric limits, induced by generalized Inönü–Wigner Lie algebra contractions of the symmetry algebras of the underlying spaces. These have physical/geometric implications, such as the Askey scheme for hypergeometric orthogonal polynomials. However, the limits have no satisfactory Lie algebra contraction interpretations for underlying spaces with 1- or 0-dimensional Lie algebras. We show that these systems can be best understood by transforming them to Laplace conformally superintegrable systems, with flat space conformal symmetry group SO(4, ℂ), and using ideas introduced in the 1894 thesis of Bôcher to study separable solutions of the wave equation in terms of roots of quadratic forms. We show that Bôcher’s prescription for coalescing roots of these forms induces contractions of the conformal algebra so(4, ℂ) to itself and yields a mechanism for classifying all Helmholtz superintegrable systems and their limits. In the paperActa Polytechnica, to appear, arXiv:1510.09067], we announced our main findings. This paper provides the proofs and more details.

year: 2016

title: Carbonate Alteration of the Sams Creek Gold Deposit

authors: Lee, Ryan John

subjects: Sams Creek Gold Depsoit

abstract: Located near Upper Takaka, NW Nelson, the Sams Creek Gold Deposit is host to significant gold mineralisation, which has been extensively explored since being first discovered in 1974 by CRA exploration. The gold mineralisation, hosted largely within the Sams Creek Granite Dyke has since been the focus of continual ongoing exploration and research by various companies and academia. The dyke is a peralkaline microgranite, is up to 60 meters wide and has a strike length totalling 7 kilometres. Multiple stages of hydrothermal alteration have affected the granite dyke which is host to a series of sheeted, stock work and irregular fracture veins. At the time of writing, Sams Creek is New Zealand’s largest undeveloped gold project.

Despite extensive research and exploration, the origin of Au bearing fluids and hence classification of the deposit is still debated. Little is also known about the role of which the widespread carbonate alteration has had during the genesis of this deposit. Siderite/ankerite (carbonate) veins are a common occurrence at Sams Creek, occurring in both the highly mineralised granite and seemingly unaltered metasedimentary rock, of which the Sams Creek Granite and various other mafic dykes intrude.

This study presents a detailed paragenetic study of the multiple phases of carbonate alteration throughout the prospect. Trace element geochemistry for individual vein generations was obtained by in-situ analysis of the carbonate vein minerals using LA-ICP-MS. Oxygen and carbonate stable isotope ratios were also determined for many of the carbonate minerals.

The carbonate alteration was found to be largely structurally controlled and coeval with the multiple stages of Au mineralisation and alteration. The veins were often comprised of multiple siderite and ankerite intergrowths, reflecting temporally distinct fluids of varying Ca/Fe/Mn/Mg concentrations. Whole vein geochemical analysis confirmed an overall ankerite composition, contrary to the previous reports of siderite only veins. Major and trace element signatures showed geochemically distinct ankerite veins for each host rock. Notably, the geochemistry of the veins indicates that the surrounding metasediments are an unlikely fluid source for the carbonate alteration. This has implications for models which suggest an orogenic fluid is responsible for the alteration. The fluid likely received its trace element and isotopic signature from a high temperature, reduced and 18O-depleted fluid source, consistent with a fluid source that is not metamorphogenic. The carbonate minerals associated with the mineralisation and/or the dyke have a unique trace element signature in relation to carbonate of other lithologies.

Overall, this study provides evidence that is in agreement with the Sams Creek Dyke being classified as an Intrusion Related Gold System. Further implications for exploration potential are the distinctions between metamorphogenic and hydrothermal carbonate minerals, which could be easily undertaken using pXRF based upon anomalous Mn and Mg contents.

text: Carbonate Alteration of the Sams Creek Gold Deposit Located near Upper Takaka, NW Nelson, the Sams Creek Gold Deposit is host to significant gold mineralisation, which has been extensively explored since being first discovered in 1974 by CRA exploration. The gold mineralisation, hosted largely within the Sams Creek Granite Dyke has since been the focus of continual ongoing exploration and research by various companies and academia. The dyke is a peralkaline microgranite, is up to 60 meters wide and has a strike length totalling 7 kilometres. Multiple stages of hydrothermal alteration have affected the granite dyke which is host to a series of sheeted, stock work and irregular fracture veins. At the time of writing, Sams Creek is New Zealand’s largest undeveloped gold project.

Despite extensive research and exploration, the origin of Au bearing fluids and hence classification of the deposit is still debated. Little is also known about the role of which the widespread carbonate alteration has had during the genesis of this deposit. Siderite/ankerite (carbonate) veins are a common occurrence at Sams Creek, occurring in both the highly mineralised granite and seemingly unaltered metasedimentary rock, of which the Sams Creek Granite and various other mafic dykes intrude.

This study presents a detailed paragenetic study of the multiple phases of carbonate alteration throughout the prospect. Trace element geochemistry for individual vein generations was obtained by in-situ analysis of the carbonate vein minerals using LA-ICP-MS. Oxygen and carbonate stable isotope ratios were also determined for many of the carbonate minerals.

The carbonate alteration was found to be largely structurally controlled and coeval with the multiple stages of Au mineralisation and alteration. The veins were often comprised of multiple siderite and ankerite intergrowths, reflecting temporally distinct fluids of varying Ca/Fe/Mn/Mg concentrations. Whole vein geochemical analysis confirmed an overall ankerite composition, contrary to the previous reports of siderite only veins. Major and trace element signatures showed geochemically distinct ankerite veins for each host rock. Notably, the geochemistry of the veins indicates that the surrounding metasediments are an unlikely fluid source for the carbonate alteration. This has implications for models which suggest an orogenic fluid is responsible for the alteration. The fluid likely received its trace element and isotopic signature from a high temperature, reduced and 18O-depleted fluid source, consistent with a fluid source that is not metamorphogenic. The carbonate minerals associated with the mineralisation and/or the dyke have a unique trace element signature in relation to carbonate of other lithologies.

Overall, this study provides evidence that is in agreement with the Sams Creek Dyke being classified as an Intrusion Related Gold System. Further implications for exploration potential are the distinctions between metamorphogenic and hydrothermal carbonate minerals, which could be easily undertaken using pXRF based upon anomalous Mn and Mg contents.

year: 2016

title: Cultural justice, ethics and practice: Summary of presentation

authors: Herbert, Averil May Lloyd

subjects: psychology

abstract: The following cases and remarks are based on the author’s employment over six years
in the Department of Social Welfare in Rotorua Specialist Services. The author
discusses definitions that relate to the topic of cultural justice, ethics, and practice and
our awareness and understanding of the issues; and presents three case studies from practitioner experience.

text: Cultural justice, ethics and practice: Summary of presentation The following cases and remarks are based on the author’s employment over six years
in the Department of Social Welfare in Rotorua Specialist Services. The author
discusses definitions that relate to the topic of cultural justice, ethics, and practice and
our awareness and understanding of the issues; and presents three case studies from practitioner experience.

year: 1993