title: Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: This paper is the conclusion 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. For two-dimensional and for conformally flat three-dimensional spaces with nondegenerate potentials we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension. We also correct an error in an earlier paper in the series (that does not alter the structure results) and we elucidate the distinction between superintegrable systems with bases of functionally linearly independent and functionally linearly dependent symmetries.

text: Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems This paper is the conclusion 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. For two-dimensional and for conformally flat three-dimensional spaces with nondegenerate potentials we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension. We also correct an error in an earlier paper in the series (that does not alter the structure results) and we elucidate the distinction between superintegrable systems with bases of functionally linearly independent and functionally linearly dependent symmetries.

year: 2006-09

title: Idealism operationalized: Charles Peirce’s theory of perception

authors: Legg, Catherine

abstract: This paper begins by outlining Hume's understanding of perception according to which ideas are copies of impressions, which are thought to constitute a foundational confrontation with reality. This understanding is contrasted with Peirce's theory of perception according to which percepts give rise to perceptual judgements, but perceptual judgements are not a copy but an index (or 'true symptom' - just as a weather-cock indicates the direction of the wind) of the percept. Percept and perceptual judgement are thereby able to mutually inform and correct one another in rich ways, as the perceiver develops mental habits of interpreting their surroundings.

text: Idealism operationalized: Charles Peirce’s theory of perception This paper begins by outlining Hume's understanding of perception according to which ideas are copies of impressions, which are thought to constitute a foundational confrontation with reality. This understanding is contrasted with Peirce's theory of perception according to which percepts give rise to perceptual judgements, but perceptual judgements are not a copy but an index (or 'true symptom' - just as a weather-cock indicates the direction of the wind) of the percept. Percept and perceptual judgement are thereby able to mutually inform and correct one another in rich ways, as the perceiver develops mental habits of interpreting their surroundings.

year: 2014

title: Geothermal energy, decarbonisation and the just transition: developments in governance and regulation

authors: Parson, Phoebe

abstract: This review article pursues this special issue’s theme of renewable energy and just transition into the field of geothermal energy, an energy source which has a special role in Aotearoa New Zealand, and which raises clear questions of justice in the energy transition. It evaluates the track record, and examines the legal, regulatory and institutional challenges and opportunities for a just transition for geothermal in New Zealand. It particularly considers the role of Māori, and the challenges presented by emerging technological change. It considers the problems of renewability and sustainability that are special to geothermal resources. It evaluates the just transition issues that have particularly affected Māori landowners and holders of mana whenua. It finds that what constitutes a just transition must be seen against a longer historical time frame than many observers might assume. It shows that the distinctive regulatory framework for geothermal has been considerably affected by addressing these problems but may need to adapt further in the future. It considers the technical features that have shaped geothermal regulation and are likely to shape it in the future as new technological options emerge.

text: Geothermal energy, decarbonisation and the just transition: developments in governance and regulation This review article pursues this special issue’s theme of renewable energy and just transition into the field of geothermal energy, an energy source which has a special role in Aotearoa New Zealand, and which raises clear questions of justice in the energy transition. It evaluates the track record, and examines the legal, regulatory and institutional challenges and opportunities for a just transition for geothermal in New Zealand. It particularly considers the role of Māori, and the challenges presented by emerging technological change. It considers the problems of renewability and sustainability that are special to geothermal resources. It evaluates the just transition issues that have particularly affected Māori landowners and holders of mana whenua. It finds that what constitutes a just transition must be seen against a longer historical time frame than many observers might assume. It shows that the distinctive regulatory framework for geothermal has been considerably affected by addressing these problems but may need to adapt further in the future. It considers the technical features that have shaped geothermal regulation and are likely to shape it in the future as new technological options emerge.

year: 2025