title: Harmonic sets and the harmonic prime number theorem

authors: Broughan, Kevin A.

subjects: harmonic prime number theorem

abstract: We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+ O(log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem” π H(x)/ π(x) → log2.

text: Harmonic sets and the harmonic prime number theorem We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+ O(log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem” π H(x)/ π(x) → log2.

year: 2005

title: The inherent liminality of lesbian detectives: Shifting spaces and lesbian crime fiction 1984-2022

authors: Antoniolli, Claudia

subjects: Crime fiction

abstract: This thesis studies lesbian detective fiction and specifically considers this genre in its early decades (1980s-1990s) from the United States, United Kingdom, Australia, and New Zealand. This thesis postulates that out of a sample pool of a hundred novels, there are recurring patterns of behaviours and attitudes among the protagonists of this genre within certain physical and metaphorical spaces. These patterns demonstrate a destabilised identity, as the lesbian sleuth never ceases to explore and test the boundaries of her authority as an enforcer of law and order and of her suppressed spatiality as a member of a sexual minority. This causes her to live in a perpetual state of Insider/Outsider liminality and it causes queer trauma to be a fundamental aspect of her character. This thesis considers this concept as the result of long-standing, systemic homophobia and heterosexist normativity, and utilises the notion of queer trauma to interpret the way the lesbian sleuth is inescapably stuck between a sense of duty and justice and a yearning for belonging and self-affirmation. The interpretive process is supported by an extensive and in-depth theoretical research into the fields of history, culture, geography, feminist criticism, gender, and sexuality studies for the selected subject matter. The spaces selected and analysed in this thesis are the queer closet, the medical establishment, domestic settings, and the gay bar. These spaces have been chosen for the significant, emblematic ways in which the lesbian detectives interact with them and have been analysed in order of their importance for the protagonists’ characterisation. The introduction includes introductory statements and the theoretical framework, the first chapter overviews major detectives in the history of crime literature from a spatial perspective; the second chapter discusses the queer closet; the third chapter considers the space of the clinic and the topics of queer trauma and of the pathologisation of homosexuality; the fourth chapter analyses the domestic settings of the protagonists; the fifth chapter examines the context of the gay bar and its history; finally, the conclusion offers closing statements about the focus and originality of this thesis. The originality of this thesis lies in its focus on spaces and on the relationship between the protagonist and society, law and order, and Self and Other. This thesis contributes to the knowledge of queer literature by specifically considering the unescapable liminality of the lesbian/Outsider detective/Insider.

text: The inherent liminality of lesbian detectives: Shifting spaces and lesbian crime fiction 1984-2022 This thesis studies lesbian detective fiction and specifically considers this genre in its early decades (1980s-1990s) from the United States, United Kingdom, Australia, and New Zealand. This thesis postulates that out of a sample pool of a hundred novels, there are recurring patterns of behaviours and attitudes among the protagonists of this genre within certain physical and metaphorical spaces. These patterns demonstrate a destabilised identity, as the lesbian sleuth never ceases to explore and test the boundaries of her authority as an enforcer of law and order and of her suppressed spatiality as a member of a sexual minority. This causes her to live in a perpetual state of Insider/Outsider liminality and it causes queer trauma to be a fundamental aspect of her character. This thesis considers this concept as the result of long-standing, systemic homophobia and heterosexist normativity, and utilises the notion of queer trauma to interpret the way the lesbian sleuth is inescapably stuck between a sense of duty and justice and a yearning for belonging and self-affirmation. The interpretive process is supported by an extensive and in-depth theoretical research into the fields of history, culture, geography, feminist criticism, gender, and sexuality studies for the selected subject matter. The spaces selected and analysed in this thesis are the queer closet, the medical establishment, domestic settings, and the gay bar. These spaces have been chosen for the significant, emblematic ways in which the lesbian detectives interact with them and have been analysed in order of their importance for the protagonists’ characterisation. The introduction includes introductory statements and the theoretical framework, the first chapter overviews major detectives in the history of crime literature from a spatial perspective; the second chapter discusses the queer closet; the third chapter considers the space of the clinic and the topics of queer trauma and of the pathologisation of homosexuality; the fourth chapter analyses the domestic settings of the protagonists; the fifth chapter examines the context of the gay bar and its history; finally, the conclusion offers closing statements about the focus and originality of this thesis. The originality of this thesis lies in its focus on spaces and on the relationship between the protagonist and society, law and order, and Self and Other. This thesis contributes to the knowledge of queer literature by specifically considering the unescapable liminality of the lesbian/Outsider detective/Insider.

year: 2023

title: Exploring the potential of Te Whāriki in supporting a decolonising educational reform in classroom

authors: Corlett, Melissa Jane

abstract: This thesis begins with a deep belief in the potential of Te Whāriki, a bicultural curriculum document born of the dual heritages of Aotearoa/New Zealand, to support the educational reform needed. There is a need to decolonise our classrooms and create contexts for learning where Māori students feel they can belong and also thrive. The pathway to achieving this reality is complex. It requires a deep foundational understanding of our shared histories in order to move from deficit positions about Māori learners to ones of agency and hope. While strong relationships are important it was by connecting with Māori metaphors that we were able to move beyond the rhetoric and begin to build shared understandings and greater respect for knowledge from te ao Māori. The process of whakawhiti kōrero or dialogic and iterative sense making furthered our combined theorising. The whakataukī and metaphors embedded in Te Whāriki were foundational to these contexts as they strengthened our collective abilities as teachers to make the learning more meaningful and fun.
This research process provided me with valuable insights into the way my own power and beliefs can inhibit potential collective learning. Despite this it was the content of Te Whāriki that helped to enable the learning of myself and my participants, creating safe and supportive contexts for our collective learning to begin to grow. 
While this research strengthened my own beliefs in the potential of Te Whāriki it also assisted my participants to become more open to this potential as well. In this endeavour, time was required to engage with the more expert other, whether this was from other people or through the use of artefacts. The relational and culturally responsive pedagogy that we had learned to implement in our classrooms was also able to be connected with, as our shared unlearning and learning flowed.

text: Exploring the potential of Te Whāriki in supporting a decolonising educational reform in classroom This thesis begins with a deep belief in the potential of Te Whāriki, a bicultural curriculum document born of the dual heritages of Aotearoa/New Zealand, to support the educational reform needed. There is a need to decolonise our classrooms and create contexts for learning where Māori students feel they can belong and also thrive. The pathway to achieving this reality is complex. It requires a deep foundational understanding of our shared histories in order to move from deficit positions about Māori learners to ones of agency and hope. While strong relationships are important it was by connecting with Māori metaphors that we were able to move beyond the rhetoric and begin to build shared understandings and greater respect for knowledge from te ao Māori. The process of whakawhiti kōrero or dialogic and iterative sense making furthered our combined theorising. The whakataukī and metaphors embedded in Te Whāriki were foundational to these contexts as they strengthened our collective abilities as teachers to make the learning more meaningful and fun.
This research process provided me with valuable insights into the way my own power and beliefs can inhibit potential collective learning. Despite this it was the content of Te Whāriki that helped to enable the learning of myself and my participants, creating safe and supportive contexts for our collective learning to begin to grow. 
While this research strengthened my own beliefs in the potential of Te Whāriki it also assisted my participants to become more open to this potential as well. In this endeavour, time was required to engage with the more expert other, whether this was from other people or through the use of artefacts. The relational and culturally responsive pedagogy that we had learned to implement in our classrooms was also able to be connected with, as our shared unlearning and learning flowed.

year: 2022