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: Claims for manuka honey activity

authors: Molan, Peter C.

abstract: Whilst standards have been established to define whether or not a honey can be called manuka, little progress has been made with establishing a standard for describing the antibacterial activity of manuka honey. In New Zealand and in other countries there are laws that protect consumers from being misled, and laws to protect traders from unfair competition. Anyone making a claim for honey having a particular level of antibacterial activity when selling it needs to take care that they are not falling foul of these laws. This article has been written to ensure that false claims are not made unknowingly.

text: Claims for manuka honey activity Whilst standards have been established to define whether or not a honey can be called manuka, little progress has been made with establishing a standard for describing the antibacterial activity of manuka honey. In New Zealand and in other countries there are laws that protect consumers from being misled, and laws to protect traders from unfair competition. Anyone making a claim for honey having a particular level of antibacterial activity when selling it needs to take care that they are not falling foul of these laws. This article has been written to ensure that false claims are not made unknowingly.

year: 2012

title: Decolonizing Lamanite Studies – A Critical and Decolonial Indigenist Perspective

authors: Simon, Hemopereki

abstract: The emergence of Lamanite Studies exemplifies the need for decolonial and Indigenous-centered reevaluations of Mormon–Indigenous relations. This article advocates for the reclamation of Indigenous identity independent of the constraints imposed by Mormon doctrine. The incorporation of Indigenous genealogies into Mormon theology results in epistemic violence, disconnecting Indigenous peoples from their ancestral identities and substituting the latter with the settler/invader colonial construct of “Lamanite”. This paper advocates for the decolonization of Indigenous identities within Mormonism, emphasizing the need for a radical intervention that prioritizes Indigenous sovereignty and self-definition over the maintenance of colonial categories. I present approaches and scholarship in Lamanite Studies that align with Indigenous land and spiritual repatriation, promoting the restoration of Indigenous epistemologies to Indigenous communities. Theoretical colonialism must be supplemented by grassroots initiatives that empower Indigenous communities to reclaim their spiritual and cultural identities.

text: Decolonizing Lamanite Studies – A Critical and Decolonial Indigenist Perspective The emergence of Lamanite Studies exemplifies the need for decolonial and Indigenous-centered reevaluations of Mormon–Indigenous relations. This article advocates for the reclamation of Indigenous identity independent of the constraints imposed by Mormon doctrine. The incorporation of Indigenous genealogies into Mormon theology results in epistemic violence, disconnecting Indigenous peoples from their ancestral identities and substituting the latter with the settler/invader colonial construct of “Lamanite”. This paper advocates for the decolonization of Indigenous identities within Mormonism, emphasizing the need for a radical intervention that prioritizes Indigenous sovereignty and self-definition over the maintenance of colonial categories. I present approaches and scholarship in Lamanite Studies that align with Indigenous land and spiritual repatriation, promoting the restoration of Indigenous epistemologies to Indigenous communities. Theoretical colonialism must be supplemented by grassroots initiatives that empower Indigenous communities to reclaim their spiritual and cultural identities.

year: 2025