title: Construction of Good Rank-1 Lattice Rules Based on the Weighted Star Discrepancy

authors: Joe, Stephen

subjects: mathematics

abstract: The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrepancy. If the weights for the weighted star discrepancy are summable, then we show that for n prime there exist n-point rank-1 lattice rules whose weighted star discrepancy is O(n−1+δ) for any δ>0, where the implied constant depends on δ and the weights, but is independent of d and n. Further, we show that the generating vector z for such lattice rules may be obtained using a component-by-component construction. The results given here for the weighted star discrepancy are used to derive corresponding results for a weighted Lp discrepancy.

text: Construction of Good Rank-1 Lattice Rules Based on the Weighted Star Discrepancy The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrepancy. If the weights for the weighted star discrepancy are summable, then we show that for n prime there exist n-point rank-1 lattice rules whose weighted star discrepancy is O(n−1+δ) for any δ>0, where the implied constant depends on δ and the weights, but is independent of d and n. Further, we show that the generating vector z for such lattice rules may be obtained using a component-by-component construction. The results given here for the weighted star discrepancy are used to derive corresponding results for a weighted Lp discrepancy.

year: 2006

title: Connecting key competencies and social inquiry in primary social studies pedagogy: initial teacher education students' planning decisions and reflections.

authors: Hunter, Philippa Anne

subjects: key competencies

abstract: Over 2007-2009 we have worked with the national curriculum's key competencies to establish their place and purpose in the social sciences learning area. As a result, our initial teacher education (ITE) primary social studies programmes involve pedagogy that conceives key competencies as analogous to social inquiry thinking and skills processes. Our team was keen to research ways ITE students identify and embed key competencies in their social inquiry planning decisions. The research also sought student reflection of how engagement with key competencies might influence their future social studies teaching and learning. The article offers a storying of ways the curriculum element of key competencies has been developed, implemented, researched and reflected upon within ITE primary social studies curriculum.

text: Connecting key competencies and social inquiry in primary social studies pedagogy: initial teacher education students' planning decisions and reflections. Over 2007-2009 we have worked with the national curriculum's key competencies to establish their place and purpose in the social sciences learning area. As a result, our initial teacher education (ITE) primary social studies programmes involve pedagogy that conceives key competencies as analogous to social inquiry thinking and skills processes. Our team was keen to research ways ITE students identify and embed key competencies in their social inquiry planning decisions. The research also sought student reflection of how engagement with key competencies might influence their future social studies teaching and learning. The article offers a storying of ways the curriculum element of key competencies has been developed, implemented, researched and reflected upon within ITE primary social studies curriculum.

year: 2010

title: Portfolio of compositions

authors: Hoadley, Benjamin Russell

subjects: New Zealand composition

abstract: The music in this portfolio of original compositions is steeped in the Western tradition of tonal music. The pieces were written while also pursuing a professional career as a bassoonist touring internationally and performing a wide variety of western art music, from Renaissance to contemporary. I have responded to these influences consciously and unconsciously in my music. The overarching focus of this composition portfolio is to provide an answer to the question — to what extent do musical influences impact on the compositions of an international touring performer?

Underpinning the portfolio is the fact that the pieces were all written in New Zealand during periods of intense reflection and study. While I am constantly collecting ideas and inspiration for my music while travelling, I consolidate and realise these ideas only when I am home.

I identify with being a New Zealand composer, with cosmopolitan influences on my music reflecting the global influences on New Zealand’s culture and art. Working closely with composers performing their music has also informed my composition. I mention Gillian Whitehead in particular, whose music I have performed widely.

The two outer pieces in the portfolio, Huia and Manaia 4 are the most directly associated with New Zealand in their subject matter. Other pieces have foreign themes, from my nocturnal impressions of New York in Night Music to the Ancient Greece of Ostrakon to the West African poetry of Four Songs.

All of the pieces were written for professional musicians to perform, including the Auckland Philharmonia Orchestra and the Sydney Omega Ensemble. Having these outstanding performers in mind while writing, and interacting with these musicians during the composition process, has informed my writing.

text: Portfolio of compositions The music in this portfolio of original compositions is steeped in the Western tradition of tonal music. The pieces were written while also pursuing a professional career as a bassoonist touring internationally and performing a wide variety of western art music, from Renaissance to contemporary. I have responded to these influences consciously and unconsciously in my music. The overarching focus of this composition portfolio is to provide an answer to the question — to what extent do musical influences impact on the compositions of an international touring performer?

Underpinning the portfolio is the fact that the pieces were all written in New Zealand during periods of intense reflection and study. While I am constantly collecting ideas and inspiration for my music while travelling, I consolidate and realise these ideas only when I am home.

I identify with being a New Zealand composer, with cosmopolitan influences on my music reflecting the global influences on New Zealand’s culture and art. Working closely with composers performing their music has also informed my composition. I mention Gillian Whitehead in particular, whose music I have performed widely.

The two outer pieces in the portfolio, Huia and Manaia 4 are the most directly associated with New Zealand in their subject matter. Other pieces have foreign themes, from my nocturnal impressions of New York in Night Music to the Ancient Greece of Ostrakon to the West African poetry of Four Songs.

All of the pieces were written for professional musicians to perform, including the Auckland Philharmonia Orchestra and the Sydney Omega Ensemble. Having these outstanding performers in mind while writing, and interacting with these musicians during the composition process, has informed my writing.

year: 2016