title: Near-automorphisms of Latin squares

authors: Cavenagh, Nicholas J.

subjects: intercalate

abstract: We define a near-automorphism α of a Latin square L to be an isomorphism such that L and αL differ only within a 2 × 2 subsquare. We prove that for all n≥2 except n∈{3, 4}, there exists a Latin square which exhibits a near-automorphism. We also show that if α has the cycle structure (2, n − 2), then L exists if and only if n≡2 (mod 4), and can be constructed from a special type of partial orthomorphism. Along the way, we generalize a theorem by Marshall Hall, which states that any Latin rectangle can be extended to a Latin square. We also show that if α has at least 2 fixed points, then L must contain two disjoint non-trivial subsquares.

text: Near-automorphisms of Latin squares We define a near-automorphism α of a Latin square L to be an isomorphism such that L and αL differ only within a 2 × 2 subsquare. We prove that for all n≥2 except n∈{3, 4}, there exists a Latin square which exhibits a near-automorphism. We also show that if α has the cycle structure (2, n − 2), then L exists if and only if n≡2 (mod 4), and can be constructed from a special type of partial orthomorphism. Along the way, we generalize a theorem by Marshall Hall, which states that any Latin rectangle can be extended to a Latin square. We also show that if α has at least 2 fixed points, then L must contain two disjoint non-trivial subsquares.

year: 2011

title: The characteristics and life difficulties associated to non-suicidal self-injury and suicidality in a community sample.

authors: Robertson, Charlotte Rose

abstract: Non-Suicidal Self-Injury (NSSI) is a complex and understudied topic within the New Zealand literature. Risk factors, and functions of NSSI and suicidality within the socio-cultural context of New Zealand is an important area of research, having both clinical and research implications, such as enhancing or fuelling further investigation into prevention and therapeutic strategies. 
A revised version of the Survey of College and Mental Health and Well Being and the Depression, Anxiety, Stress Scale (21) were used to explore NSSI, mental health, physical health and other characteristics of participants. Surveys were anonymous and self-selected by New Zealand community members. There were 304 participants, primarily identifying as female and of European descent. 
Young women were the highest risk demographic for engagement in NSSI. Psychological distress, any type of abuse, suicidality, and experiencing the suicide of a friend or acquaintance were significant predictors of participant’s engagement in NSSI. Multiple types of abuse and experiencing the death of a family member or friend to suicide significantly predicted suicidality, suggesting merit for acquired capability theory. Emotional regulation remains the most endorsed function of NSSI. There is no type of abuse that correlates to a function of NSSI, which highlights the complexity and idiosyncrasy of NSSI for each individual. Clinicians should focus on the behaviours’ functions specific for that individual to promote positive treatment outcomes.

text: The characteristics and life difficulties associated to non-suicidal self-injury and suicidality in a community sample. Non-Suicidal Self-Injury (NSSI) is a complex and understudied topic within the New Zealand literature. Risk factors, and functions of NSSI and suicidality within the socio-cultural context of New Zealand is an important area of research, having both clinical and research implications, such as enhancing or fuelling further investigation into prevention and therapeutic strategies. 
A revised version of the Survey of College and Mental Health and Well Being and the Depression, Anxiety, Stress Scale (21) were used to explore NSSI, mental health, physical health and other characteristics of participants. Surveys were anonymous and self-selected by New Zealand community members. There were 304 participants, primarily identifying as female and of European descent. 
Young women were the highest risk demographic for engagement in NSSI. Psychological distress, any type of abuse, suicidality, and experiencing the suicide of a friend or acquaintance were significant predictors of participant’s engagement in NSSI. Multiple types of abuse and experiencing the death of a family member or friend to suicide significantly predicted suicidality, suggesting merit for acquired capability theory. Emotional regulation remains the most endorsed function of NSSI. There is no type of abuse that correlates to a function of NSSI, which highlights the complexity and idiosyncrasy of NSSI for each individual. Clinicians should focus on the behaviours’ functions specific for that individual to promote positive treatment outcomes.

year: 2021

title: Different coloured tears: Dual cultural identity and Tangihanga

authors: Edge, Kiri

subjects: bereavement

abstract: Although whānau/family that are configured by both Pākehā and Māori identities number significantly within New Zealand, there has been little or no attention paid to the ways in which these identities influence the bereavement processes that will inevitably impact upon the lives of these whānau/family. The present study explored the experiences of an individual, whose whānau/family included two life ways: Māori and Pākehā. Of specific focus was the ways in which these identities influenced his bereavement subsequent to the death of his beloved wife, who was of Māori descent. One elderly male Pākehā participant was interviewed, using an open ended narrative approach. The interview was semi-structured around five broad themes, but the focus was upon the participant’s experiences and his preference in expressing these. The data analysis utilised a thematic process which allowed the participant’s experiences to determine the emergent themes. The results depicted the diversity of issues that may be raised for dual cultural whānau/family within bereavement processes. Two central themes are discussed in relation to intercultural conflict and the eventual resolution that was created. Decision-making processes, cultural and language differences played significant roles within the conflict and exclusion experienced by the participant. Communication and compromise provided resolution to the prior conflicts experienced. This created positive and unexpected outcomes which resulted in increased understandings and the strengthening of links between the participant, his whānau/family and his wife’s marae.

text: Different coloured tears: Dual cultural identity and Tangihanga Although whānau/family that are configured by both Pākehā and Māori identities number significantly within New Zealand, there has been little or no attention paid to the ways in which these identities influence the bereavement processes that will inevitably impact upon the lives of these whānau/family. The present study explored the experiences of an individual, whose whānau/family included two life ways: Māori and Pākehā. Of specific focus was the ways in which these identities influenced his bereavement subsequent to the death of his beloved wife, who was of Māori descent. One elderly male Pākehā participant was interviewed, using an open ended narrative approach. The interview was semi-structured around five broad themes, but the focus was upon the participant’s experiences and his preference in expressing these. The data analysis utilised a thematic process which allowed the participant’s experiences to determine the emergent themes. The results depicted the diversity of issues that may be raised for dual cultural whānau/family within bereavement processes. Two central themes are discussed in relation to intercultural conflict and the eventual resolution that was created. Decision-making processes, cultural and language differences played significant roles within the conflict and exclusion experienced by the participant. Communication and compromise provided resolution to the prior conflicts experienced. This created positive and unexpected outcomes which resulted in increased understandings and the strengthening of links between the participant, his whānau/family and his wife’s marae.

year: 2011