title: (F,G)-abundant semigroups

authors: Stokes, Tim E.

subjects: Science & Technology

abstract: On a semigroup S, define the equivalence relation

F={(a,b)∈S×S∣∀x∈S:xa=x⇔xb=x},
and define G dually. We say S is F-abundant if there is an idempotent in every F-class, and similarly for G-abundance, and we say S is (F,G)-abundant if it is both F-abundant and G-abundant. These concepts are analogous to the notions of regularity and one- and two-sided abundance, defined in terms of Green’s relations L and R, and their generalisations L∗ and R∗, respectively. We relate this new form of abundance to the earlier ones, considering in particular the analogs of superabundance and amiability.

text: (F,G)-abundant semigroups On a semigroup S, define the equivalence relation

F={(a,b)∈S×S∣∀x∈S:xa=x⇔xb=x},
and define G dually. We say S is F-abundant if there is an idempotent in every F-class, and similarly for G-abundance, and we say S is (F,G)-abundant if it is both F-abundant and G-abundant. These concepts are analogous to the notions of regularity and one- and two-sided abundance, defined in terms of Green’s relations L and R, and their generalisations L∗ and R∗, respectively. We relate this new form of abundance to the earlier ones, considering in particular the analogs of superabundance and amiability.

year: 2022

title: Factors Affecting Caregiver Outcomes

authors: Calder, Nicole

subjects: caregiver

abstract: Research in the area of caregiving has tended to focus on the impact of the caregiving experience itself without consideration of continued psychological distress for caregivers after institutionalisation or death. Seven caregivers of loved ones with Alzheimer's Dementia (mostly spousal) were interviewed about their experiences of caregiving and their emotional well-being after placement of their loved one into a residential care facility or death. The  nature of the carers relationship with their loved one (e.g.  highly dependent), lack of social supports, inactivity and a poor experience of transition into care seemed to be factors relating to poorer outcomes for these caregivers. Utilisation of social supports, involvement in pleasant events, adequate preparation and information relating to the disease and collaboratively planned transition into care played protective roles for the remaining carers who reported decreased levels of anxiety, guilt, depression and stress post-institutionalisation/death. The implications of the current research for practise, policy change and prevention are extensive and suggest that risk factors may be identifiable and thus poorer mental health outcomes in caregivers preventable. A need for greater support to be made available to caregivers is necessary.

text: Factors Affecting Caregiver Outcomes Research in the area of caregiving has tended to focus on the impact of the caregiving experience itself without consideration of continued psychological distress for caregivers after institutionalisation or death. Seven caregivers of loved ones with Alzheimer's Dementia (mostly spousal) were interviewed about their experiences of caregiving and their emotional well-being after placement of their loved one into a residential care facility or death. The  nature of the carers relationship with their loved one (e.g.  highly dependent), lack of social supports, inactivity and a poor experience of transition into care seemed to be factors relating to poorer outcomes for these caregivers. Utilisation of social supports, involvement in pleasant events, adequate preparation and information relating to the disease and collaboratively planned transition into care played protective roles for the remaining carers who reported decreased levels of anxiety, guilt, depression and stress post-institutionalisation/death. The implications of the current research for practise, policy change and prevention are extensive and suggest that risk factors may be identifiable and thus poorer mental health outcomes in caregivers preventable. A need for greater support to be made available to caregivers is necessary.

year: 2008

title: Protecting the heartwood: How can tikanga Māori and mātauranga Māori inform the construction of digital identities and relational responsibilities to data in Aotearoa New Zealand?

authors: Lucas, Danielle

abstract: A report prepared by Danielle Lucas as part of the Tikanga in Technology research project

text: Protecting the heartwood: How can tikanga Māori and mātauranga Māori inform the construction of digital identities and relational responsibilities to data in Aotearoa New Zealand? A report prepared by Danielle Lucas as part of the Tikanga in Technology research project

year: 2025-02-11