title: Lie theory and separation of variables. 6. The equation iUt + ∆2U = 0

authors: Boyer, C.P.

subjects: Mathematics

abstract: This paper constitutes a detailed study of the nine−parameter symmetry group of the time−dependent free particle Schrödinger equation in two space dimensions. It is shown that this equation separates in exactly 26 coordinate systems and that each system corresponds to an orbit consisting of a commuting pair of first− and second−order symmetry operators. The study yields a unified treatment of the (attractive and repulsive) harmonic oscillator, linear potential and free particle Hamiltonians in a time−dependent formalism. Use of representation theory for the symmetry group permits simple derivations of addition and expansion theorems relating various solutions of the Schrödinger equation, many of which are new.

text: Lie theory and separation of variables. 6. The equation iUt + ∆2U = 0 This paper constitutes a detailed study of the nine−parameter symmetry group of the time−dependent free particle Schrödinger equation in two space dimensions. It is shown that this equation separates in exactly 26 coordinate systems and that each system corresponds to an orbit consisting of a commuting pair of first− and second−order symmetry operators. The study yields a unified treatment of the (attractive and repulsive) harmonic oscillator, linear potential and free particle Hamiltonians in a time−dependent formalism. Use of representation theory for the symmetry group permits simple derivations of addition and expansion theorems relating various solutions of the Schrödinger equation, many of which are new.

year: 1975-03

title: Kinetic and isotherm studies on adsorption of arsenic using silica based catalytic media

authors: Aremu, James Oyediji

abstract: This study investigates the removal of arsenic (both As (III) and As (V)) from drinking water using a silica based catalytic media (DMI-65). In this study, BET, FTIR, XRD, SEM and XRF were used to characterize the adsorbent before and after contact with As (III) and As (V). Batch experiments were performed to evaluate the adsorption kinetics at different pH (5, 6, 7 and 8.5). The kinetic study showed that a contact time of 6 h was needed to reach equilibrium and the experimental data were best fitted to the pseudo second-order kinetic model for both As (III) and As (V). Several batch tests were conducted with different concentration of arsenic at different pH conditions (5, 6, 7 and 8.5). During the adsorption test, the maximum adsorption of As (III) occurred at pH 5, while As (V) adsorption reached its maximum at pH 8.5. The adsorption data showed a good fit to Langmuir isotherm models and the maximum adsorption capacity of the silica based catalytic media for As (III) and As (V) were estimated to be 0.318 mg/g and 0.237 mg/g respectively.

text: Kinetic and isotherm studies on adsorption of arsenic using silica based catalytic media This study investigates the removal of arsenic (both As (III) and As (V)) from drinking water using a silica based catalytic media (DMI-65). In this study, BET, FTIR, XRD, SEM and XRF were used to characterize the adsorbent before and after contact with As (III) and As (V). Batch experiments were performed to evaluate the adsorption kinetics at different pH (5, 6, 7 and 8.5). The kinetic study showed that a contact time of 6 h was needed to reach equilibrium and the experimental data were best fitted to the pseudo second-order kinetic model for both As (III) and As (V). Several batch tests were conducted with different concentration of arsenic at different pH conditions (5, 6, 7 and 8.5). During the adsorption test, the maximum adsorption of As (III) occurred at pH 5, while As (V) adsorption reached its maximum at pH 8.5. The adsorption data showed a good fit to Langmuir isotherm models and the maximum adsorption capacity of the silica based catalytic media for As (III) and As (V) were estimated to be 0.318 mg/g and 0.237 mg/g respectively.

year: 2019

title: He whare mātātuhi Tūhoe:  A Tūhoe re-visioning of English language literary texts

authors: Salsano, Marama

subjects: Māori writers

abstract: This thesis urges more Māori to undertake iwi-based readings of English language literary texts. I have chosen to privilege my father’s iwi, Ngāi Tūhoe, and to examine what Tūhoetana means to me and how it might thus enrich my reading of texts. In our ancestral tongue, Ngāi Tūhoe have a rich and pronounced history of storytelling, literary composition, analysis and critique. Unfortunately, this richness is woefully underappreciated within the English language literary landscape. Yet, as the ranks of Māori writers swell, along with the diversity of literary forms that Māori create, so too must Māori – and more specifically iwi – literary scholarship flourish, for if we do not critique the texts that are written about, of, and on behalf of us, who will? Throughout this thesis, I use the terms ‘iwi literary scholars’ and ‘iwi literary scholarship’ to consciously and repeatedly remind the reader of the rich, literary legacies residing within iwi archives; I also hope to highlight the exciting and endless possiblitites for the English language literary landscape to be enriched by readings that are founded within these archives – including the histories, everyday experiences and understandings from our tīpuna. 

Structurally, this thesis is divided into three broad strands. Chapters 1-3 focus on whakawhanaunatana and background information to my research. Because this thesis also represents the singular piece of writing that I wish I had read prior to enrolling in the thesis paper for this Master’s degree, my academic hīkoi – frustrations and all – is a necessary component and is covered in chapter 2. Chapters 4-6 then examine three different types of literary texts created by wāhine. These texts include the short story “Birth Rights” by Ngāi Tahu science fiction and fantasy writer, J.C. Hart (2010), the Instagram post Te Kuharere tapes by Ngāti Kahungungu and Ngāti Tuwharetoa songwriter and storyteller @tekahureremoa (2019) – also known as the performer Ladyfruit – and the young adult novel Dark Souls by Ngāti Wai, Ngāti Manuhiri, and Ngāti Whatua writer, Paula Morris (2011). While 21st century texts published on platforms such as Instagram may not sit easily within a traditional English literary curriculum, and indeed the novelty of these specific forms may well prove fleeting, the ‘everydayness’ of online texts yields rewarding analysis opportunities and is currently amiss within mainstream English literary studies. Each of these analysis chapters contains a focused introduction and conclusion, since chapter 7, the concluding chapter of this thesis, is a letter to future iwi literary scholars. 

Woven throughout this rangahau is a call for iwi scholars to consciously: engage with the literary traditions of their own iwi; identify the colonial thoughts and motives that they bring to the reading of literary texts; bring their tīpuna to the reading, but let the text itself breathe life into the critique and; consider the genres and types of texts that they critique. Ultimately, this thesis considers how engaging with the literary legacies of our tīpuna might broaden the English language literary landscape and thus enhance the body of iwi literary scholarship in Oceania and beyond.

text: He whare mātātuhi Tūhoe:  A Tūhoe re-visioning of English language literary texts This thesis urges more Māori to undertake iwi-based readings of English language literary texts. I have chosen to privilege my father’s iwi, Ngāi Tūhoe, and to examine what Tūhoetana means to me and how it might thus enrich my reading of texts. In our ancestral tongue, Ngāi Tūhoe have a rich and pronounced history of storytelling, literary composition, analysis and critique. Unfortunately, this richness is woefully underappreciated within the English language literary landscape. Yet, as the ranks of Māori writers swell, along with the diversity of literary forms that Māori create, so too must Māori – and more specifically iwi – literary scholarship flourish, for if we do not critique the texts that are written about, of, and on behalf of us, who will? Throughout this thesis, I use the terms ‘iwi literary scholars’ and ‘iwi literary scholarship’ to consciously and repeatedly remind the reader of the rich, literary legacies residing within iwi archives; I also hope to highlight the exciting and endless possiblitites for the English language literary landscape to be enriched by readings that are founded within these archives – including the histories, everyday experiences and understandings from our tīpuna. 

Structurally, this thesis is divided into three broad strands. Chapters 1-3 focus on whakawhanaunatana and background information to my research. Because this thesis also represents the singular piece of writing that I wish I had read prior to enrolling in the thesis paper for this Master’s degree, my academic hīkoi – frustrations and all – is a necessary component and is covered in chapter 2. Chapters 4-6 then examine three different types of literary texts created by wāhine. These texts include the short story “Birth Rights” by Ngāi Tahu science fiction and fantasy writer, J.C. Hart (2010), the Instagram post Te Kuharere tapes by Ngāti Kahungungu and Ngāti Tuwharetoa songwriter and storyteller @tekahureremoa (2019) – also known as the performer Ladyfruit – and the young adult novel Dark Souls by Ngāti Wai, Ngāti Manuhiri, and Ngāti Whatua writer, Paula Morris (2011). While 21st century texts published on platforms such as Instagram may not sit easily within a traditional English literary curriculum, and indeed the novelty of these specific forms may well prove fleeting, the ‘everydayness’ of online texts yields rewarding analysis opportunities and is currently amiss within mainstream English literary studies. Each of these analysis chapters contains a focused introduction and conclusion, since chapter 7, the concluding chapter of this thesis, is a letter to future iwi literary scholars. 

Woven throughout this rangahau is a call for iwi scholars to consciously: engage with the literary traditions of their own iwi; identify the colonial thoughts and motives that they bring to the reading of literary texts; bring their tīpuna to the reading, but let the text itself breathe life into the critique and; consider the genres and types of texts that they critique. Ultimately, this thesis considers how engaging with the literary legacies of our tīpuna might broaden the English language literary landscape and thus enhance the body of iwi literary scholarship in Oceania and beyond.

year: 2021