title: The average order of the Dirichlet series of the gcd-sum function

authors: Broughan, Kevin A.

subjects: mathematics

abstract: Using a result of Bordellès, we derive the second term and improved error expressions for the partial sums of the Dirichlet series of the gcd-sum function, for all real values of the parameter.

text: The average order of the Dirichlet series of the gcd-sum function Using a result of Bordellès, we derive the second term and improved error expressions for the partial sums of the Dirichlet series of the gcd-sum function, for all real values of the parameter.

year: 2007

title: µ-Charts and Z: Extending the translation

authors: Reeve, Greg

subjects: computer science

abstract: This paper describes extensions and modifications to the µ-charts as given in earlier papers of Philipps and Scholz. The charts are extended to include a command language, integer-valued signals and local integer variables. The command language is based on the syntax presented in Scholz’ thesis and the integer-valued signals and local variables are based loosely on Scholz’ earlier work. After presenting the new semantics we turn to extending the µ-charts-to-Z translation that we developed in previous work. The extensions to the translation process describe both the changes due to the extensions to the µ-charts and a modification to the translation method to more fully capture the beneficial modularisation encouraged by the µ-charts formalism. We finish by giving three complete translation examples. The paper should be read as a record of our gradual development of a Z semantics for µ-charts–hence its sometimes exploratory character or laborious explanations as we come to terms (thinking out loud) with the (sometimes very subtle) meaning of µ-charts, especially with regard to pathological and unusual examples of their use.

text: µ-Charts and Z: Extending the translation This paper describes extensions and modifications to the µ-charts as given in earlier papers of Philipps and Scholz. The charts are extended to include a command language, integer-valued signals and local integer variables. The command language is based on the syntax presented in Scholz’ thesis and the integer-valued signals and local variables are based loosely on Scholz’ earlier work. After presenting the new semantics we turn to extending the µ-charts-to-Z translation that we developed in previous work. The extensions to the translation process describe both the changes due to the extensions to the µ-charts and a modification to the translation method to more fully capture the beneficial modularisation encouraged by the µ-charts formalism. We finish by giving three complete translation examples. The paper should be read as a record of our gradual development of a Z semantics for µ-charts–hence its sometimes exploratory character or laborious explanations as we come to terms (thinking out loud) with the (sometimes very subtle) meaning of µ-charts, especially with regard to pathological and unusual examples of their use.

year: 2000-08

title: The revitalisation roles of Māori-medium whānau

authors: Bryant, Braden

abstract: For over a century and a half, te reo Māori (the Māori language) has suffered from linguistic marginalisation, causing significant language shift to English, and, with it, generations of Māori who are unable to speak their indigenous language. While efforts since the 1970s to rebuild te reo Māori have primarily focused on educational initiatives such as kōhanga reo and kura kaupapa, there is now a move to shift the revitalisation strategy towards encouraging te reo Māori use in the home, and to rebuilding the language intergenerationally. Unfortunately, little is known about whānau perceptions regarding te reo Māori revitalisation, which is what this research investigates.

This research investigates five whānau who have committed their children to Māori-medium education. It aims to understand what influenced their decision-making around Māori-medium and what they see as the key benefits for their children. It also looks at what whānau consider to be obstacles regarding their use of te reo Māori, and at their commitment to Māori-medium education. Finally, this research aims to uncover how whānau perceive the wider revitalisation effort, and their roles in it.

The qualitative method of semi-structured interviews was used to conduct this research. The conversational nature of this method gives whānau the freedom to express their beliefs, while remaining on the main themes of this study. As the participants and themes of this research are Māori, the study used Kaupapa Māori theory and principles to guide it. This supported the overall aim of aligning with Māori aspirations, and safeguarding participants from exploitation.

This research found that perceptions of whānau often reflected the extent to which they had been affected by intergenerational language shift. Whānau still highly affected by language shift, and whose te reo Māori is less normalised in the home, prioritised te reo Māori learning at school as the key benefit of Māori-medium education. This group also faced more opposition to their Māori-medium choices from friends and whānau, and perceived their revitalisation roles to be more concerned with the immediate whānau. By contrast, the whānau who had managed to regenerate te reo Māori in their homes to a greater extent placed more emphasis on tikanga and values as benefits of Māori-medium education. They identified opposition from friends and whānau as a barrier to their promotion of te reo Māori, while also identifying their own subconscious lapses into English as a major barrier to maintaining normalised te reo Māori environments for their children. Finally, they perceived their revitalisation roles as revolving around normalising te reo Māori for their whānau and for their communities. They played important roles in establishing language domains for further use of what is their home language.

This small study shows the importance of understanding the perceptions of those who are central to the regeneration of te reo Māori because they are the key agents of successful change, and have the attitudes and skills to do so. A larger study would provide more data to support the formation of new language revitalisation strategies.

text: The revitalisation roles of Māori-medium whānau For over a century and a half, te reo Māori (the Māori language) has suffered from linguistic marginalisation, causing significant language shift to English, and, with it, generations of Māori who are unable to speak their indigenous language. While efforts since the 1970s to rebuild te reo Māori have primarily focused on educational initiatives such as kōhanga reo and kura kaupapa, there is now a move to shift the revitalisation strategy towards encouraging te reo Māori use in the home, and to rebuilding the language intergenerationally. Unfortunately, little is known about whānau perceptions regarding te reo Māori revitalisation, which is what this research investigates.

This research investigates five whānau who have committed their children to Māori-medium education. It aims to understand what influenced their decision-making around Māori-medium and what they see as the key benefits for their children. It also looks at what whānau consider to be obstacles regarding their use of te reo Māori, and at their commitment to Māori-medium education. Finally, this research aims to uncover how whānau perceive the wider revitalisation effort, and their roles in it.

The qualitative method of semi-structured interviews was used to conduct this research. The conversational nature of this method gives whānau the freedom to express their beliefs, while remaining on the main themes of this study. As the participants and themes of this research are Māori, the study used Kaupapa Māori theory and principles to guide it. This supported the overall aim of aligning with Māori aspirations, and safeguarding participants from exploitation.

This research found that perceptions of whānau often reflected the extent to which they had been affected by intergenerational language shift. Whānau still highly affected by language shift, and whose te reo Māori is less normalised in the home, prioritised te reo Māori learning at school as the key benefit of Māori-medium education. This group also faced more opposition to their Māori-medium choices from friends and whānau, and perceived their revitalisation roles to be more concerned with the immediate whānau. By contrast, the whānau who had managed to regenerate te reo Māori in their homes to a greater extent placed more emphasis on tikanga and values as benefits of Māori-medium education. They identified opposition from friends and whānau as a barrier to their promotion of te reo Māori, while also identifying their own subconscious lapses into English as a major barrier to maintaining normalised te reo Māori environments for their children. Finally, they perceived their revitalisation roles as revolving around normalising te reo Māori for their whānau and for their communities. They played important roles in establishing language domains for further use of what is their home language.

This small study shows the importance of understanding the perceptions of those who are central to the regeneration of te reo Māori because they are the key agents of successful change, and have the attitudes and skills to do so. A larger study would provide more data to support the formation of new language revitalisation strategies.

year: 2017