Partial actions of monoids

We investigate partial monoid actions, in the sense of Megrelishvili and Schroeder [12]. These are equivalent to a class of premorphisms, which we call strong premorphisms. We describe two distinct methods for constructing a monoid action from a partial monoid action: the expansion method provides a generalisation of a result of Kellendonk and Lawson [10] in the group case, whilst the approach via globalisation extends results of both [12] and [10]

The transcriptional regulation of maspin : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Biochemistry at Massey University, Palmerston North, New Zealand

Maspin (mammary serine protease inhibitor) is a tumour suppressing member of the serpin superfamily. Maspin is expressed in normal breast and prostate cells, but reportedly down regulated during progression of cancer in these tissues. Maspin has been shown to inhibit cellular migration and invasion in vitro; while in vivo, maspin has been shown to inhibit tumour growth, metastasis, and angiogenesis. Maspin also plays a role in the sensitisation of cells to induced apoptosis. These functions of maspin are independent of serine protease inhibition; however the cellular mobility function is dependent on an intact reactive site loop. Despite this knowledge, the molecular mechanisms for all reported functions of maspin are currently unknown. Maspin is reported to be transcriptionally regulated: to date Ets, Ap1, and p53 transcription factors have been shown to activate transcription of maspin by binding directly to the promoter. Androgen is reported to be a negative regulator through the binding of the androgen receptor to a hormone response element within the promoter. This hormone response element is also responsible for an increase in maspin expression in response to tamoxifen, an anti-oestrogen drug. Transcriptional regulation of maspin has also been reported to be activated by other molecules, including gamma linolenic acid, manganese containing super-oxide dismutase, and nitric oxide, the mechanisms of regulation by these molecules is unknown. Loss of maspin expression in cancerous cells lines has been attributed to loss of one or more of the activating factors, and aberrant methylation of cytosine residues resulting in chromatin compaction. This study investigated the transcriptional regulation of maspin, with the aim of identifying transcriptional effectors important to the regulation of the gene. Identification of such factors may help identify a pathway in which maspin exerts its tumour suppressor functions. To this end, the maspin promoter was cloned and functional assays carried out. identifying several putative regions of the maspin promoter which may be important for the regulation of the gene. To date, the precise activator/repressor binding sites and the cognate proteins responsible for this regulation are unidentified

Extending the Ehresmann-Schein-Nambooripad Theorem

We extend the `join-premorphisms' part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive categories, following on from a result of Lawson (1991) for the `morphisms' part. However, it is so-called `meet-premorphisms' which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type theorem for meet-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem in the inverse case.Comment: 23 pages; final section on Szendrei expansions removed; further reordering of materia

Exact rings and semirings

We introduce and study an abstract class of semirings, which we call exact semirings, defined by a Hahn-Banach-type separation property on modules. Our motivation comes from the tropical semiring, and in particular a desire to understand the often surprising extent to which it behaves like a field. The definition of exactness abstracts an elementary property of fields and the tropical semiring, which we believe is fundamental to explaining this similarity. The class of exact semirings turns out to include many other important examples of both rings (proper quotients of principal ideal domains, matrix rings and finite group rings over these and over fields), and semirings (the Boolean semiring, generalisations of the tropical semiring, matrix semirings and group semirings over these).Comment: 17 pages; fixed typos, clarified a few points, changed notation in Example 6.

Conjugation in Semigroups

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing definitions, characterize the conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups when the set is infinite.Comment: 41 pages, 14 figure

Workplace violence in Queensland, Australia: the results of a comparative study

[Abstract]: This paper presents the results on workplace violence from a larger study undertaken in 2004. Comparison is made with the results of a similar study undertaken in 2001. The study involved the random sampling of 3000 nurses from the Queensland Nurses’ Union’s membership in the public (acute hospital and community nursing), private (acute hospital and domiciliary nursing) and aged care sectors (both public and private aged care facilities). The self-reported results suggest an increase in workplace violence in all three sectors. Whilst there are differences in the sources of workplace violence across the sectors, the major causes of workplace violence are: clients/patients, visitors/relatives, other nurses, nursing management and medical practitioners. Associations were also found between workplace violence and gender, the designation of the nurse, hours of employment, the age of the nurse, morale and perceptions of workplace safety. Whilst the majority of nurses reported that policies were in place for the management of workplace violence, these policies were not always adequate