title: Models for the 3D Singular Isotropic Oscillator Quadratic Algebra

authors: Kalnins, Ernie G.

subjects: Science & Technology

abstract: We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential—differential or differential—difference and difference—difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.

text: Models for the 3D Singular Isotropic Oscillator Quadratic Algebra We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential—differential or differential—difference and difference—difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.

year: 2010-02-01

title: Rates, controls and potential adverse effects of nitrate removal in a denitrification bed

authors: Warneke, Sören

subjects: denitrification

abstract: Denitrification beds are a simple approach for removing nitrate (NO₃⁻) from a range of point sources prior to discharge into receiving waters. These beds are large containers filled with woodchips that act as an energy source for microorganisms to convert NO₃⁻ to nitrogen (N) gases (N₂O, N₂) through denitrification. This study investigated the biological mechanism of NO₃⁻ removal, its controlling factors and its adverse effects in a large denitrification bed (176 m × 5 m × 1.5 m) receiving effluent with a high NO₃⁻ concentration (>100 g N m⁻³) from a hydroponic glasshouse (Karaka, Auckland, New Zealand). Samples of woodchips and water were collected from 12 sites along the bed every two months for one year, along with measurements of gas fluxes from the bed surface. Denitrifying enzyme activity (DEA), factors limiting denitrification (availability of carbon, dissolved organic carbon (DOC), dissolved oxygen (DO), temperature, pH, and concentrations of NO₃⁻, nitrite (NO₂⁻) and sulfide (S²⁻)), greenhouse gas (GHG) production – as nitrous oxide (N₂O), methane (CH₄), carbon dioxide (CO₂) – and carbon (C) loss were determined. NO₃⁻-N concentration declined along the bed with total NO₃⁻-N removal rates of 10.1 kg N d⁻¹ for the whole bed or 7.6 g N m⁻³ d⁻¹. NO₃⁻-N removal rates increased with temperature (Q₁₀ = 2.0). In laboratory incubations, denitrification was always limited by C availability rather than by NO₃⁻. DO levels were above 0.5 mg L⁻¹ at the inlet but did not limit NO₃⁻-N removal. pH increased steadily from about 6 to 7 along the length of the bed. Dissolved inorganic carbon (C-CO₂) increased in average about 27.8 mg L⁻¹, whereas DOC decreased slightly by about 0.2 mg L⁻¹ along the length of the bed. The bed surface emitted on average 78.58 μg m−² min⁻¹ N₂O-N (reflecting 1% of the removed NO₃⁻-N), 0.238 μg m⁻² min⁻¹ CH₄ and 12.6 mg m⁻² min⁻¹ CO₂. Dissolved N₂O-N increased along the length of the bed and the bed released on average 362 g dissolved N₂O-N per day coupled with N₂O emission at the surface about 4.3% of the removed NO₃⁻-N as N₂O. Mechanisms to reduce the production of this GHG need to be investigated if denitrification beds are commonly used. Dissolved CH₄ concentrations showed no trends along the length of the bed, ranging from 5.28 μg L⁻¹ to 34.24 μg L⁻¹. Sulfate (SO₄²⁻) concentrations declined along the length of the bed on three of six samplings; however, declines in SO₄²⁻ did not appear to be due to SO₄²⁻ reduction because S²⁻ concentrations were generally undetectable. Ammonium (NH₄⁺) (range: <0.0007 mg L⁻¹ to 2.12 mg L⁻¹) and NO₂⁻ concentrations (range: 0.0018 mg L⁻¹ to 0.95 mg L⁻¹) were always very low suggesting that anammox was an unlikely mechanism for NO₃⁻ removal in the bed. C longevity was calculated from surface emission rates of CO₂ and release of dissolved carbon (DC) and suggested that there would be ample C available to support denitrification for up to 39 years.
This study showed that denitrification beds can be an efficient tool for reducing high NO₃⁻ concentrations in effluents but did produce some GHGs. Over the course of a year NO₃⁻ removal rates were always limited by C and temperature and not by NO₃⁻ or DO concentration.

text: Rates, controls and potential adverse effects of nitrate removal in a denitrification bed Denitrification beds are a simple approach for removing nitrate (NO₃⁻) from a range of point sources prior to discharge into receiving waters. These beds are large containers filled with woodchips that act as an energy source for microorganisms to convert NO₃⁻ to nitrogen (N) gases (N₂O, N₂) through denitrification. This study investigated the biological mechanism of NO₃⁻ removal, its controlling factors and its adverse effects in a large denitrification bed (176 m × 5 m × 1.5 m) receiving effluent with a high NO₃⁻ concentration (>100 g N m⁻³) from a hydroponic glasshouse (Karaka, Auckland, New Zealand). Samples of woodchips and water were collected from 12 sites along the bed every two months for one year, along with measurements of gas fluxes from the bed surface. Denitrifying enzyme activity (DEA), factors limiting denitrification (availability of carbon, dissolved organic carbon (DOC), dissolved oxygen (DO), temperature, pH, and concentrations of NO₃⁻, nitrite (NO₂⁻) and sulfide (S²⁻)), greenhouse gas (GHG) production – as nitrous oxide (N₂O), methane (CH₄), carbon dioxide (CO₂) – and carbon (C) loss were determined. NO₃⁻-N concentration declined along the bed with total NO₃⁻-N removal rates of 10.1 kg N d⁻¹ for the whole bed or 7.6 g N m⁻³ d⁻¹. NO₃⁻-N removal rates increased with temperature (Q₁₀ = 2.0). In laboratory incubations, denitrification was always limited by C availability rather than by NO₃⁻. DO levels were above 0.5 mg L⁻¹ at the inlet but did not limit NO₃⁻-N removal. pH increased steadily from about 6 to 7 along the length of the bed. Dissolved inorganic carbon (C-CO₂) increased in average about 27.8 mg L⁻¹, whereas DOC decreased slightly by about 0.2 mg L⁻¹ along the length of the bed. The bed surface emitted on average 78.58 μg m−² min⁻¹ N₂O-N (reflecting 1% of the removed NO₃⁻-N), 0.238 μg m⁻² min⁻¹ CH₄ and 12.6 mg m⁻² min⁻¹ CO₂. Dissolved N₂O-N increased along the length of the bed and the bed released on average 362 g dissolved N₂O-N per day coupled with N₂O emission at the surface about 4.3% of the removed NO₃⁻-N as N₂O. Mechanisms to reduce the production of this GHG need to be investigated if denitrification beds are commonly used. Dissolved CH₄ concentrations showed no trends along the length of the bed, ranging from 5.28 μg L⁻¹ to 34.24 μg L⁻¹. Sulfate (SO₄²⁻) concentrations declined along the length of the bed on three of six samplings; however, declines in SO₄²⁻ did not appear to be due to SO₄²⁻ reduction because S²⁻ concentrations were generally undetectable. Ammonium (NH₄⁺) (range: <0.0007 mg L⁻¹ to 2.12 mg L⁻¹) and NO₂⁻ concentrations (range: 0.0018 mg L⁻¹ to 0.95 mg L⁻¹) were always very low suggesting that anammox was an unlikely mechanism for NO₃⁻ removal in the bed. C longevity was calculated from surface emission rates of CO₂ and release of dissolved carbon (DC) and suggested that there would be ample C available to support denitrification for up to 39 years.
This study showed that denitrification beds can be an efficient tool for reducing high NO₃⁻ concentrations in effluents but did produce some GHGs. Over the course of a year NO₃⁻ removal rates were always limited by C and temperature and not by NO₃⁻ or DO concentration.

year: 2011

title: Maori and epilepsy: Personal perceptions of the cause, treatment and consequences of epilepsy by Maori in the Bay of Plenty

authors: Simonsen, Kiri

subjects: Maori

abstract: This paper discusses the perceptions of epilepsy held by Maori in the Bay of Plenty. The paper
begins by introducing the purpose and rationale of the research. It then moves on to describe the
aims and qualitative research methods that were used to collect the data. Finally the paper
discusses the findings of the research, this includes: a close look at the unique perceptions of
epilepsy that were reported by Maori in the Bay of Plenty; the lack of resources and services
available in a small rural town of the Bay of Plenty; the services desired by Maori; attitudes
towards medication and the inappropriate behaviour many of the participants experienced by the
medical profession.

text: Maori and epilepsy: Personal perceptions of the cause, treatment and consequences of epilepsy by Maori in the Bay of Plenty This paper discusses the perceptions of epilepsy held by Maori in the Bay of Plenty. The paper
begins by introducing the purpose and rationale of the research. It then moves on to describe the
aims and qualitative research methods that were used to collect the data. Finally the paper
discusses the findings of the research, this includes: a close look at the unique perceptions of
epilepsy that were reported by Maori in the Bay of Plenty; the lack of resources and services
available in a small rural town of the Bay of Plenty; the services desired by Maori; attitudes
towards medication and the inappropriate behaviour many of the participants experienced by the
medical profession.

year: 1999