title: A recurrence relation approach to higher order quantum superintegrability

authors: Kalnins, Ernie G.

subjects: superintegrability

abstract: We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method provides rigorous proofs of superintegrability and explicit constructions of higher order generators for the symmetry algebra. We apply the method to 5 families of systems, each depending on a parameter k, including most notably the caged anisotropic oscillator, the Tremblay, Turbiner and Winternitz system and a deformed Kepler-Coulomb system, and we give proofs of quantum superintegrability for all rational values of k, new for 4 of these systems. In addition, we show that the explicit information supplied by the special function recurrence relations allows us to prove, for the first time in 4 cases, that the symmetry algebra generated by our lowest order symmetries closes and to determine the associated structure equations of the algebras for each k. We have no proof that our generating symmetries are of lowest possible order, but we have no counterexamples, and we are confident we can can always find any missing generators from our raising and lowering operator recurrences. We also get for free, one variable models of the action of the symmetry algebra in terms of difference operators. We describe how the Stäckel transform acts and show that it preserves the structure equations.

text: A recurrence relation approach to higher order quantum superintegrability We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method provides rigorous proofs of superintegrability and explicit constructions of higher order generators for the symmetry algebra. We apply the method to 5 families of systems, each depending on a parameter k, including most notably the caged anisotropic oscillator, the Tremblay, Turbiner and Winternitz system and a deformed Kepler-Coulomb system, and we give proofs of quantum superintegrability for all rational values of k, new for 4 of these systems. In addition, we show that the explicit information supplied by the special function recurrence relations allows us to prove, for the first time in 4 cases, that the symmetry algebra generated by our lowest order symmetries closes and to determine the associated structure equations of the algebras for each k. We have no proof that our generating symmetries are of lowest possible order, but we have no counterexamples, and we are confident we can can always find any missing generators from our raising and lowering operator recurrences. We also get for free, one variable models of the action of the symmetry algebra in terms of difference operators. We describe how the Stäckel transform acts and show that it preserves the structure equations.

year: 2011

title: A Literary and Cultural History of Military Science Fiction and the United States of America, 1870s-2010s

authors: Nicholson, Blair

subjects: History

abstract: This thesis is both a literary history of the military science fiction (military SF) subgenre and a cultural history of the United States of America during the twentieth and early-twenty-first centuries. This thesis academically rehabilitates a neglected literary subgenre, and utilises it to prove the efficacy of using literary texts, specifically science fiction (SF) texts, in the study of cultural history. It expands both the sources and methods of interpretation open to cultural historians. Employing the military SF subgenre as its archive, it examines the military SF narratives’ engagement – through extrapolation, metaphor and allegory, as well as didacticism – with their historical-cultural contexts and those contexts’ popular rhetorics, adopting methodologies from cultural history, the history of ideas, and the literary New Historicism. In addition to looking at period-specific themes – ranging from the emergence of the military-industrial complex and consensus anticommunism during the 1950s, through soldier alienation and the ‘cult of the mercenary’ during the Vietnam and post-Vietnam era of the 1970s and 1980s, to the renewed American Exceptionalism and military-civilian divide of the 2000s – this thesis focuses on American attitudes towards militarism and militarisation. The concept of militarism also provides a foundational division in the subgenre, between the two ‘streams’ of militaristic military SF and antimilitaristic military SF. This thesis, however, shows that the subgenre has primarily been sympathetic to militaristic and right-wing rhetorics, support for which has become increasingly strident in modern military SF.

text: A Literary and Cultural History of Military Science Fiction and the United States of America, 1870s-2010s This thesis is both a literary history of the military science fiction (military SF) subgenre and a cultural history of the United States of America during the twentieth and early-twenty-first centuries. This thesis academically rehabilitates a neglected literary subgenre, and utilises it to prove the efficacy of using literary texts, specifically science fiction (SF) texts, in the study of cultural history. It expands both the sources and methods of interpretation open to cultural historians. Employing the military SF subgenre as its archive, it examines the military SF narratives’ engagement – through extrapolation, metaphor and allegory, as well as didacticism – with their historical-cultural contexts and those contexts’ popular rhetorics, adopting methodologies from cultural history, the history of ideas, and the literary New Historicism. In addition to looking at period-specific themes – ranging from the emergence of the military-industrial complex and consensus anticommunism during the 1950s, through soldier alienation and the ‘cult of the mercenary’ during the Vietnam and post-Vietnam era of the 1970s and 1980s, to the renewed American Exceptionalism and military-civilian divide of the 2000s – this thesis focuses on American attitudes towards militarism and militarisation. The concept of militarism also provides a foundational division in the subgenre, between the two ‘streams’ of militaristic military SF and antimilitaristic military SF. This thesis, however, shows that the subgenre has primarily been sympathetic to militaristic and right-wing rhetorics, support for which has become increasingly strident in modern military SF.

year: 2016

title: Maori perspectives of the environment: A review of resource use consent submissions made by iwi to Environment Waikato.

authors: Whangapirita, Laura

subjects: Maori

abstract: As part of our broader brief to gather, summarise, analyse and distribute information held by Environment Waikato on Maori and the environment, we reviewed and summarised iwi consent submissions made on various resource use consent applications. This report refers to values and beliefs sourced from iwi submissions held by Environment Waikato and are presented within a Maori values framework to highlight environmental perspectives of tangata whenua in the Waikato region.

text: Maori perspectives of the environment: A review of resource use consent submissions made by iwi to Environment Waikato. As part of our broader brief to gather, summarise, analyse and distribute information held by Environment Waikato on Maori and the environment, we reviewed and summarised iwi consent submissions made on various resource use consent applications. This report refers to values and beliefs sourced from iwi submissions held by Environment Waikato and are presented within a Maori values framework to highlight environmental perspectives of tangata whenua in the Waikato region.

year: 2003-11