title: Orthogonal trades in complete sets of MOLS

authors: Cavenagh, Nicholas J.

subjects: mathematics

abstract: Let Bₚ be the Latin square given by the addition table for the integers modulo an odd prime p (i.e. the Cayley table for (Zₚ, +)). Here we consider the properties of Latin trades in Bₚ which preserve orthogonality with one of the p−1 MOLS given by the finite field construction. We show that for certain choices of the orthogonal mate, there is a lower bound logarithmic in p for the number of times each symbol occurs in such a trade, with an overall lower bound of (log p)² / log log p for the size of such a trade. Such trades imply the existence of orthomorphisms of the cyclic group which differ from a linear orthomorphism by a small amount. We also show that any transversal in Bₚ hits the main diagonal either p or at most p − log₂ p – 1 times. Finally, if p ≡ 1 (mod 6) we show the existence of a Latin square which is orthogonal to Bₚ and which contains a 2 × 2 subsquare.

text: Orthogonal trades in complete sets of MOLS Let Bₚ be the Latin square given by the addition table for the integers modulo an odd prime p (i.e. the Cayley table for (Zₚ, +)). Here we consider the properties of Latin trades in Bₚ which preserve orthogonality with one of the p−1 MOLS given by the finite field construction. We show that for certain choices of the orthogonal mate, there is a lower bound logarithmic in p for the number of times each symbol occurs in such a trade, with an overall lower bound of (log p)² / log log p for the size of such a trade. Such trades imply the existence of orthomorphisms of the cyclic group which differ from a linear orthomorphism by a small amount. We also show that any transversal in Bₚ hits the main diagonal either p or at most p − log₂ p – 1 times. Finally, if p ≡ 1 (mod 6) we show the existence of a Latin square which is orthogonal to Bₚ and which contains a 2 × 2 subsquare.

year: 2017

title: Review: The Collection

authors: Cheesman, Sue

subjects: dance

abstract: Review of the dance performance, The Collection

text: Review: The Collection Review of the dance performance, The Collection

year: 2006

title: Young Māori mothers and bed-sharing with their pēpi/baby: A case study focusing on the relevance and influence of three varying health promotion resources

authors: Haereroa, Nikki M.

subjects: Māori

abstract: Māori Sudden Unexpected Death in Infancy (SUDI) rates are significantly higher than non-Māori. Bed-sharing is considered to be one of the major modifiable risk factors associated with SUDI rates (Mitchell et al., 1992), although there is strong opposition that suggests bed-sharing can act as a preventative measure against SUDI (McKenna & McDade, 2005). As a result of quantitative research and statistical data, many health promotion messages now focus on discouraging the practice of bed-sharing, whether it be through policy implementation throughout hospitals or through to health promotion guidelines. Although there is a high incidence of Māori SUDI rates, there has been little emphasis on Māori perspectives and insights into the practice. Of the few qualitative studies that focus on infant sleep practices, a significant finding is the high prevalence of Māori who bed-share regularly (Tipene-Leach et al., 2010). This paper will investigate the motivations and rationale of bed-sharing amongst young urban Māori mothers to gain a deeper understanding and appreciation into the lived realities of this group. The lack of consultation with a group that has been classed by New Zealand Government bodies, the Health Quality and Safety Commission and Child and Youth Mortality Review Committee Group, as ‘most at risk’ of experiencing a SUDI, maybe a contributing factor to the high Māori SUDI rates. This has brought about the question of whether current health resources are relevant and/or influence young Māori mothers. Using a Te Whare Tapa Wha framework within a Kaupapa Māori Research methodology, this paper provides a unique and much-needed perspective into the lives of young Māori mothers. The purpose of this research overall is: if health resources and messages are not relevant to a community and they have little or no influence over infant care practices, then do health professionals and researchers need to rethink current strategies and working models to ensure we focus on the real, lived needs of our community?

text: Young Māori mothers and bed-sharing with their pēpi/baby: A case study focusing on the relevance and influence of three varying health promotion resources Māori Sudden Unexpected Death in Infancy (SUDI) rates are significantly higher than non-Māori. Bed-sharing is considered to be one of the major modifiable risk factors associated with SUDI rates (Mitchell et al., 1992), although there is strong opposition that suggests bed-sharing can act as a preventative measure against SUDI (McKenna & McDade, 2005). As a result of quantitative research and statistical data, many health promotion messages now focus on discouraging the practice of bed-sharing, whether it be through policy implementation throughout hospitals or through to health promotion guidelines. Although there is a high incidence of Māori SUDI rates, there has been little emphasis on Māori perspectives and insights into the practice. Of the few qualitative studies that focus on infant sleep practices, a significant finding is the high prevalence of Māori who bed-share regularly (Tipene-Leach et al., 2010). This paper will investigate the motivations and rationale of bed-sharing amongst young urban Māori mothers to gain a deeper understanding and appreciation into the lived realities of this group. The lack of consultation with a group that has been classed by New Zealand Government bodies, the Health Quality and Safety Commission and Child and Youth Mortality Review Committee Group, as ‘most at risk’ of experiencing a SUDI, maybe a contributing factor to the high Māori SUDI rates. This has brought about the question of whether current health resources are relevant and/or influence young Māori mothers. Using a Te Whare Tapa Wha framework within a Kaupapa Māori Research methodology, this paper provides a unique and much-needed perspective into the lives of young Māori mothers. The purpose of this research overall is: if health resources and messages are not relevant to a community and they have little or no influence over infant care practices, then do health professionals and researchers need to rethink current strategies and working models to ensure we focus on the real, lived needs of our community?

year: 2015