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: International symposium on volcanic-ash soils and field workshop in Mt Fuji area, Japan - conference report

authors: Lowe, David J.

abstract: An international symposium on Andisols and related soils, comprising one day of invited lectures at the Ikuta campus of Meiji University (17 March, 2006) and a two-day field trip in the Mt Fuji-Hakone area (18–19 March), was convened by soil scientist Professor Hiroshi Takesako, School of Agriculture, Meiji University (Ikuta campus), Kawasaki city, Kanagawa prefecture (near Tokyo). The 44 symposium and field trip were followed by the 50th anniversary meeting of the Japanese Society of Pedology (JSP), which consisted of one day of presentations (20 March) in the College of Bioresource Sciences, Nihon University (Shonann campus), Fujisawa city, Kanagawa prefecture. The symposium was sponsored by the Institute of Science and Technology of Meiji University, and by JSP.  
Prof. Hiroshi Takesako, who twice has visited the Department of Earth Sciences at University of Waikato (in September, 2001 – see Lowe, 2001 – and in August-September, 2004), organized the symposium partly to expose his students to an international panel of English-speaking soil scientists with some expertise in Andisols or related volcanic-ash derived soils. Hiroshi was also keen to sponsor and support scientists from developing Asian countries (and New Zealand). Consequently, six invited speakers each presented ~40-minute lectures on the first day of the symposium. All wrote up their lectures as papers for publication in the Proceedings (edited by Hiroshi Takesako). Copies of powerpoint presentations were made available as handouts (most in colour) for the participants to help enable them to follow the talks. Around 50 geoscientists and students attended the symposium lectures.

text: International symposium on volcanic-ash soils and field workshop in Mt Fuji area, Japan - conference report An international symposium on Andisols and related soils, comprising one day of invited lectures at the Ikuta campus of Meiji University (17 March, 2006) and a two-day field trip in the Mt Fuji-Hakone area (18–19 March), was convened by soil scientist Professor Hiroshi Takesako, School of Agriculture, Meiji University (Ikuta campus), Kawasaki city, Kanagawa prefecture (near Tokyo). The 44 symposium and field trip were followed by the 50th anniversary meeting of the Japanese Society of Pedology (JSP), which consisted of one day of presentations (20 March) in the College of Bioresource Sciences, Nihon University (Shonann campus), Fujisawa city, Kanagawa prefecture. The symposium was sponsored by the Institute of Science and Technology of Meiji University, and by JSP.  
Prof. Hiroshi Takesako, who twice has visited the Department of Earth Sciences at University of Waikato (in September, 2001 – see Lowe, 2001 – and in August-September, 2004), organized the symposium partly to expose his students to an international panel of English-speaking soil scientists with some expertise in Andisols or related volcanic-ash derived soils. Hiroshi was also keen to sponsor and support scientists from developing Asian countries (and New Zealand). Consequently, six invited speakers each presented ~40-minute lectures on the first day of the symposium. All wrote up their lectures as papers for publication in the Proceedings (edited by Hiroshi Takesako). Copies of powerpoint presentations were made available as handouts (most in colour) for the participants to help enable them to follow the talks. Around 50 geoscientists and students attended the symposium lectures.

year: 2006

title: The cultural and ecological health of the Tokaanu Stream

authors: Eastwood, Kevin

abstract: Freshwater ecosystems worldwide face increasing threats from human activities like land development and altered flow regimes. These pressures, along with climate change, jeopardize water quality and quantity. Despite these challenges, effective management can improve water quality and habitat, thus sustaining biodiversity and ecosystem services.
Lake Taupō, Aotearoa New Zealand’s largest freshwater lake, holds immense significance for the local iwi, Ngāti Tūwharetoa. The Tokaanu Stream is a tributary of Lake Taupō that was once considered a premier fly-fishing spot. However, the stream has been severely impacted by the Tongariro Power Scheme, which required it to be bisected and channelized to accommodate the Tokaanu tailrace. Coupled with land-use changes in the catchment, these alterations have caused the local hapū, Ngāti Kurauia, who have mana whenua over the lower stream, to raise concerns about its ecological and cultural degradation. To address this problem, I developed a cultural monitoring framework (CMF) in collaboration with Ngāti Kurauia, alongside conventional stream monitoring, at six sites in the lower Tokaanu Stream.
The bespoke CMF was developed through kōrero and wānanga (discussions and workshops) with Ngāti Kurauia. This participatory approach resulted in a CMF with 16 attributes covering vegetation, birdlife, water quality, pollution, engineering, and substrate. Regular assessments revealed a longitudinal decline in stream condition from the most upstream site (Site 1) to the most downstream (Site 6). The state of Site 3 was identified as the most desirable, whilst Site 5 was the most degraded.
Alongside the CMF, I assessed stream health using conventional scientific measures. This monitoring also showed a longitudinal decline in stream ecosystem health moving downstream. Water quality worsened, with indicator bacteria increasing from 45 to 190 CFU/100 ml and total ammoniacal nitrogen from 0.029 to 0.125 g/m3 over the 4 km segment. Deposited fine sediment cover was high, increasing from 69% cover at Site 1 to 83% at Site 6. Cellulose degradation rates (a functional indicator) were diminished at Sites 5 and 6 in both years, even with warming from geothermal springs. Macroinvertebrate communities, monitored in 2023 and 2024, initially showed a linear decline moving downstream in 2023. However, in-stream remediation in early 2024, undertaken by a private contractor, significantly improved macroinvertebrate indicators at impacted sites (Sites 4-6).
The challenges facing the Tokaanu Stream are complex, stemming from geothermal inputs, urbanisation, upstream agriculture, and channelization. Declining water quality may be linked to faulty sewage infrastructure in Tokaanu Village. The stream's diversion includes a tailrace spillway that prevents larger downstream flows, potentially reducing scouring events crucial for natural sediment dynamics. These changes have significant ecological and cultural ramifications for Ngāti Kurauia.
To better understand and address these issues, I argue for an additional downstream State of the Environment (SOE) monitoring site. The current site, near the upstream spring, fails to capture the full impact of catchment inputs, including diffuse pollution from Tokaanu Village and altered sediment dynamics from the diversion. An additional SOE site, coupled with the findings of my thesis, would provide crucial knowledge to support efforts in restoring the Tokaanu Stream's ecological health and the mana of Ngāti Kurauia.

text: The cultural and ecological health of the Tokaanu Stream Freshwater ecosystems worldwide face increasing threats from human activities like land development and altered flow regimes. These pressures, along with climate change, jeopardize water quality and quantity. Despite these challenges, effective management can improve water quality and habitat, thus sustaining biodiversity and ecosystem services.
Lake Taupō, Aotearoa New Zealand’s largest freshwater lake, holds immense significance for the local iwi, Ngāti Tūwharetoa. The Tokaanu Stream is a tributary of Lake Taupō that was once considered a premier fly-fishing spot. However, the stream has been severely impacted by the Tongariro Power Scheme, which required it to be bisected and channelized to accommodate the Tokaanu tailrace. Coupled with land-use changes in the catchment, these alterations have caused the local hapū, Ngāti Kurauia, who have mana whenua over the lower stream, to raise concerns about its ecological and cultural degradation. To address this problem, I developed a cultural monitoring framework (CMF) in collaboration with Ngāti Kurauia, alongside conventional stream monitoring, at six sites in the lower Tokaanu Stream.
The bespoke CMF was developed through kōrero and wānanga (discussions and workshops) with Ngāti Kurauia. This participatory approach resulted in a CMF with 16 attributes covering vegetation, birdlife, water quality, pollution, engineering, and substrate. Regular assessments revealed a longitudinal decline in stream condition from the most upstream site (Site 1) to the most downstream (Site 6). The state of Site 3 was identified as the most desirable, whilst Site 5 was the most degraded.
Alongside the CMF, I assessed stream health using conventional scientific measures. This monitoring also showed a longitudinal decline in stream ecosystem health moving downstream. Water quality worsened, with indicator bacteria increasing from 45 to 190 CFU/100 ml and total ammoniacal nitrogen from 0.029 to 0.125 g/m3 over the 4 km segment. Deposited fine sediment cover was high, increasing from 69% cover at Site 1 to 83% at Site 6. Cellulose degradation rates (a functional indicator) were diminished at Sites 5 and 6 in both years, even with warming from geothermal springs. Macroinvertebrate communities, monitored in 2023 and 2024, initially showed a linear decline moving downstream in 2023. However, in-stream remediation in early 2024, undertaken by a private contractor, significantly improved macroinvertebrate indicators at impacted sites (Sites 4-6).
The challenges facing the Tokaanu Stream are complex, stemming from geothermal inputs, urbanisation, upstream agriculture, and channelization. Declining water quality may be linked to faulty sewage infrastructure in Tokaanu Village. The stream's diversion includes a tailrace spillway that prevents larger downstream flows, potentially reducing scouring events crucial for natural sediment dynamics. These changes have significant ecological and cultural ramifications for Ngāti Kurauia.
To better understand and address these issues, I argue for an additional downstream State of the Environment (SOE) monitoring site. The current site, near the upstream spring, fails to capture the full impact of catchment inputs, including diffuse pollution from Tokaanu Village and altered sediment dynamics from the diversion. An additional SOE site, coupled with the findings of my thesis, would provide crucial knowledge to support efforts in restoring the Tokaanu Stream's ecological health and the mana of Ngāti Kurauia.

year: 2025