title: Decomposing complete equipartite graphs into short odd cycles

authors: Smith, Benjamin R.

subjects: mathematics

abstract: In this paper we examine the problem of decomposing the lexicographic product of a cycle with an empty graph into cycles of uniform length. We determine necessary and sufficient conditions for a solution to this problem when the cycles are of odd length. We apply this result to find necessary and sufficient conditions to decompose a complete equipartite graph into cycles of uniform length, in the case that the length is both odd and short relative to the number of parts.

text: Decomposing complete equipartite graphs into short odd cycles In this paper we examine the problem of decomposing the lexicographic product of a cycle with an empty graph into cycles of uniform length. We determine necessary and sufficient conditions for a solution to this problem when the cycles are of odd length. We apply this result to find necessary and sufficient conditions to decompose a complete equipartite graph into cycles of uniform length, in the case that the length is both odd and short relative to the number of parts.

year: 2010

title: Pedalling on: An autoethnographical journey of creative discovery

authors: Dunlop, Jonathan

abstract: My research is about exploring ways to use the sustain pedal in works by CPE Bach, JC Bach, 
Haydn and Mozart specifically. During their lifetimes, pedalling was considered to be a novelty 
on the fortepiano and was not seriously notated in the detailed style of later composers such as 
Beethoven and Schumann. 

The thesis explores ways to use the sustain pedal in keyboard works by CPE Bach, JC Bach, 
Haydn and Mozart, and also early Romantic Period composers like Beethoven, Schumann and 
Schubert. This artistic exploration is shaped and documented using an autoethnographic 
methodology, and the repertoire showcased in each recital is a mix of solo and chamber music. 
At the centre of this research is Carl Philipp Emanuel Bach’s treatise on keyboard playing 
entitled Essay on the True Art of Playing Keyboard Instruments from 1753. In it, Bach states 
that “the undamped register of the pianoforte is the most pleasing and, once the performer 
learns to observe the necessary precautions in the face of its reverberations, the most delightful 
for improvisation.

text: Pedalling on: An autoethnographical journey of creative discovery My research is about exploring ways to use the sustain pedal in works by CPE Bach, JC Bach, 
Haydn and Mozart specifically. During their lifetimes, pedalling was considered to be a novelty 
on the fortepiano and was not seriously notated in the detailed style of later composers such as 
Beethoven and Schumann. 

The thesis explores ways to use the sustain pedal in keyboard works by CPE Bach, JC Bach, 
Haydn and Mozart, and also early Romantic Period composers like Beethoven, Schumann and 
Schubert. This artistic exploration is shaped and documented using an autoethnographic 
methodology, and the repertoire showcased in each recital is a mix of solo and chamber music. 
At the centre of this research is Carl Philipp Emanuel Bach’s treatise on keyboard playing 
entitled Essay on the True Art of Playing Keyboard Instruments from 1753. In it, Bach states 
that “the undamped register of the pianoforte is the most pleasing and, once the performer 
learns to observe the necessary precautions in the face of its reverberations, the most delightful 
for improvisation.

year: 2024-05-29

title: ‘Pakeha Bill’: William John McClear, a Pakeha who lived at Te Aroha

authors: Hart, Philip

abstract: Born in Ireland to a Scottish soldier named McAleer, McClear, as he would re-name himself, was uncertain of his age, his birthplace, and the spelling of his name – for, like his parents, he was illiterate. After his drunken father, who abandoned his wife and family, sold him to unknown Maori at an unknown date, he was educated in a Maori school and was unable to speak English until the early 1870s, when he was living with Ngati Rahiri at Omahu pa, at Te Aroha. When Pakeha visitors first met him in 1877, he was a popular resident there and known as Pakeha Bill (or Pakeha William).
Possiby involved in mining before the Te Aroha rush, he both invested in and mined in several claims there from 1880 onwards, and at the end of that decade was one of a small group of Waiorongomai miners who took up a claim at Thames. When not mining, he took whatever jobs were available, struggling financially, in part because of a fondness for drink. As, unlike other Pakeha Maori, there was no evidence of his forming a close relationship with any Maori women, he did not benefit from a Maori wife’s landholdings, and he died in poverty.

text: ‘Pakeha Bill’: William John McClear, a Pakeha who lived at Te Aroha Born in Ireland to a Scottish soldier named McAleer, McClear, as he would re-name himself, was uncertain of his age, his birthplace, and the spelling of his name – for, like his parents, he was illiterate. After his drunken father, who abandoned his wife and family, sold him to unknown Maori at an unknown date, he was educated in a Maori school and was unable to speak English until the early 1870s, when he was living with Ngati Rahiri at Omahu pa, at Te Aroha. When Pakeha visitors first met him in 1877, he was a popular resident there and known as Pakeha Bill (or Pakeha William).
Possiby involved in mining before the Te Aroha rush, he both invested in and mined in several claims there from 1880 onwards, and at the end of that decade was one of a small group of Waiorongomai miners who took up a claim at Thames. When not mining, he took whatever jobs were available, struggling financially, in part because of a fondness for drink. As, unlike other Pakeha Maori, there was no evidence of his forming a close relationship with any Maori women, he did not benefit from a Maori wife’s landholdings, and he died in poverty.

year: 2016