title: Critical Sets of Full n-Latin Squares

authors: Cavenagh, Nicholas J.

subjects: Science & Technology

abstract: The full n-Latin square is the n × n array with symbols 1, 2,..., n in each cell. In a way that is analogous to critical sets of full designs, a critical set of the full n-Latin square can be used to find a defining set for any Latin square of order n. In this paper we study the size of the smallest critical set for a full n-Latin square, showing this to be somewhere between (n3 − 2n2 + 2n)/2 and (n − 1)3 + 1. In the case that each cell is either full or empty, we show the size of a critical set in the full n-Latin square is always equal to n3 − 2n2 − n.

text: Critical Sets of Full n-Latin Squares The full n-Latin square is the n × n array with symbols 1, 2,..., n in each cell. In a way that is analogous to critical sets of full designs, a critical set of the full n-Latin square can be used to find a defining set for any Latin square of order n. In this paper we study the size of the smallest critical set for a full n-Latin square, showing this to be somewhere between (n3 − 2n2 + 2n)/2 and (n − 1)3 + 1. In the case that each cell is either full or empty, we show the size of a critical set in the full n-Latin square is always equal to n3 − 2n2 − n.

year: 2016-03-01

title: Plug flow versus mixed flow modelling of a pressure screen

authors: Walmsley, Michael R.W.

subjects: engineering

abstract: The plug flow and mixed flow methods of modelling a screen are analysed in terms of screen length, internal fibre concentration and screen separation performance. Experimental data for consistency changes in screens of narrow length are incorporated into the analysis and from this data an equation for determining the real thickening in the screen and the fibre concentration profile along the screen is derived. Lastly, thicken equations are related to common equations used for modelling overall screen performance. The work directly links screen performance equations to passage ratio measurements from narrow length screen sections.

text: Plug flow versus mixed flow modelling of a pressure screen The plug flow and mixed flow methods of modelling a screen are analysed in terms of screen length, internal fibre concentration and screen separation performance. Experimental data for consistency changes in screens of narrow length are incorporated into the analysis and from this data an equation for determining the real thickening in the screen and the fibre concentration profile along the screen is derived. Lastly, thicken equations are related to common equations used for modelling overall screen performance. The work directly links screen performance equations to passage ratio measurements from narrow length screen sections.

year: 2001

title: Contextualizing street homelessness in New Zealand: A case study approach

authors: Groot, Shiloh Ann Maree

subjects: homelessness

abstract: Homelessness is commonly associated with large urban settings. For people who sleep on the streets it encompasses experiences of stigma, regulation and displacement, marginalization, violence, loneliness, and bodily decline. This thesis addresses the lack of research into the everyday practices of homeless people in New Zealand through a detailed exploration of the experiences of four homeless people. Through critically engaging with relevant scholarly literature this study documents the importance of human fortitude, agency, and meaningful social engagements in the lives of homeless people. Attention is given to how four homeless people (Brett, Daniel, Joshua and Ariā) construct place-based identities and the relational, spatial and material dimensions of homelessness, which are central to participants’ everyday lives. Participants were recruited through experienced community workers at the Auckland City Mission. A case-based ethnographic approach was used to engage with participants through volunteer work, direct observations, biographical interviews, photo-production projects, and photo-elicitation interviews. Workshops with staff on each case study were conducted to bridge the divide between critical scholars and community groups through advocacy and joint action. The analysis considers each case in turn. Brett differentiates himself from other homeless people and works to find space for himself to gain respite and solitude. Daniel engages in domestic practices on the streets that are commonly associated with home-making, such as decorating a physical space with personal objects and cultivating a sense of place, routine, comfort, and familiarity. Joshua immerses himself in a street family and forms close relationships with other homeless people that provide him with a sense of belonging, purpose, connection, support and responsibility. Ariā exemplifies how Māori cultural practices can enrich and mould a person’s efforts to retain a positive sense of self while homeless. Māori cultural concepts relating to caring, leadership, unity, relationships, spirituality, history and place are evoked to ground understandings of Ariā’s everyday life. Strategies for making a life on the streets involves Brett, Daniel, Joshua and Ariā working to maintain a sense of self and place in the face of adversity. A core finding from this research relates to the resilience of these participants, which spans personal and relational dimensions and extends to the social and physical environment.

text: Contextualizing street homelessness in New Zealand: A case study approach Homelessness is commonly associated with large urban settings. For people who sleep on the streets it encompasses experiences of stigma, regulation and displacement, marginalization, violence, loneliness, and bodily decline. This thesis addresses the lack of research into the everyday practices of homeless people in New Zealand through a detailed exploration of the experiences of four homeless people. Through critically engaging with relevant scholarly literature this study documents the importance of human fortitude, agency, and meaningful social engagements in the lives of homeless people. Attention is given to how four homeless people (Brett, Daniel, Joshua and Ariā) construct place-based identities and the relational, spatial and material dimensions of homelessness, which are central to participants’ everyday lives. Participants were recruited through experienced community workers at the Auckland City Mission. A case-based ethnographic approach was used to engage with participants through volunteer work, direct observations, biographical interviews, photo-production projects, and photo-elicitation interviews. Workshops with staff on each case study were conducted to bridge the divide between critical scholars and community groups through advocacy and joint action. The analysis considers each case in turn. Brett differentiates himself from other homeless people and works to find space for himself to gain respite and solitude. Daniel engages in domestic practices on the streets that are commonly associated with home-making, such as decorating a physical space with personal objects and cultivating a sense of place, routine, comfort, and familiarity. Joshua immerses himself in a street family and forms close relationships with other homeless people that provide him with a sense of belonging, purpose, connection, support and responsibility. Ariā exemplifies how Māori cultural practices can enrich and mould a person’s efforts to retain a positive sense of self while homeless. Māori cultural concepts relating to caring, leadership, unity, relationships, spirituality, history and place are evoked to ground understandings of Ariā’s everyday life. Strategies for making a life on the streets involves Brett, Daniel, Joshua and Ariā working to maintain a sense of self and place in the face of adversity. A core finding from this research relates to the resilience of these participants, which spans personal and relational dimensions and extends to the social and physical environment.

year: 2010