Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

HFD groups in the Solovay model

Hajnal and Juhasz proved that under CH there is a hereditarily separable, hereditarily normal topological group without non-trivial convergent sequences that is countably compact and not Lindelof. The example constructed is a topological subgroup H subset of 2(omega 1) that is an HFD with the following property (P) the projection of H onto every partial product 2(I) for I is an element of vertical bar omega(1)vertical bar(omega) is onto. Any such group has the necessary properties. We prove that if kappa is a cardinal of uncountable cofinality, then in the model obtained by forcing over a model of CH with the measure algebra on 2(kappa), there is an HFD topological group in 2(omega 1) which has property (P). Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Let M be a compact, connected non-orientable surface without boundary and of genus g >= 3. We investigate the pure braid groups P,(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 -> P(m)(M \ {x(1), ..., x(n)}) hooked right arrow P(n+m)(M) (P*) under right arrow P(n)(M) -> 1, where m, n >= 1, and p* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p: F(n+m)(M) -> F(n)(M) of configuration spaces, defined by p((x(1), ..., x(n), x(n+1), ..., x(n+m))) = (x(1), ..., x(n)). We show that p and p* admit a section if and only if n = 1. Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups. (C) 2009 Elsevier B.V. All rights reserved.

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

The gas-phase alcoholysis of protonated homoleptic alkoxysilanes

Tetra-alkoxysilanes are common and useful reagents in sol-gel processes and understanding their reactivity is important in the design of new materials. The mechanism of gas-phase reactions that mimic alcoholyis of Si(OMe)(4) (usually known as TMOS) under acidic conditions have been studied by Fourier transform ion cyclotron resonance techniques and density functional calculations at the B3LYP/6-311+G(d,p) level. The proton affinity of TMOS has been estimated at 836.4 kJ mol(-1) and protonation of TMOS gives rise to an ionic species that is best represented as trimethoxysilyl cations associated with a methanol molecule. Protonated TMOS undergoes rapid and sequential substitution of the methoxy groups in the gas-phase upon reaction with alcohols. The calculated energy profile of the reaction indicates that the substitution reaction through an S(N)2 type mechanism may be more favorable than frontal attack at silicon. Furthermore, the sequential substitution reactions are promoted by a mechanism that involves proton shuttle from the most favorable protonation site to the oxygen of the departing group mediated by the neutral reagent molecule.

Effectiveness of artemether-lumefantrine provided by community health workers in under-five children with uncomplicated malaria in rural Tanzania : an open label prospective study

Background: Home-management of malaria (HMM) strategy improves early access of anti-malarial medicines to high-risk groups in remote areas of sub-Saharan Africa. However, limited data are available on the effectiveness of using artemisinin-based combination therapy (ACT) within the HMM strategy. The aim of this study was to assess the effectiveness of artemether-lumefantrine (AL), presently the most favoured ACT in Africa, in under-five children with uncomplicated Plasmodium falciparum malaria in Tanzania, when provided by community health workers (CHWs) and administered unsupervised by parents or guardians at home. Methods: An open label, single arm prospective study was conducted in two rural villages with high malaria transmission in Kibaha District, Tanzania. Children presenting to CHWs with uncomplicated fever and a positive rapid malaria diagnostic test (RDT) were provisionally enrolled and provided AL for unsupervised treatment at home. Patients with microscopy confirmed P. falciparum parasitaemia were definitely enrolled and reviewed weekly by the CHWs during 42 days. Primary outcome measure was PCR corrected parasitological cure rate by day 42, as estimated by Kaplan-Meier survival analysis. This trial is registered with ClinicalTrials.gov, number NCT00454961. Results: A total of 244 febrile children were enrolled between March-August 2007. Two patients were lost to follow up on day 14, and one patient withdrew consent on day 21. Some 141/241 (58.5%) patients had recurrent infection during follow-up, of whom 14 had recrudescence. The PCR corrected cure rate by day 42 was 93.0% (95% CI 88.3%-95.9%). The median lumefantrine concentration was statistically significantly lower in patients with recrudescence (97 ng/mL [IQR 0-234]; n = 10) compared with reinfections (205 ng/mL [114-390]; n = 92), or no parasite reappearance (217 [121-374] ng/mL; n = 70; p <= 0.046). Conclusions: Provision of AL by CHWs for unsupervised malaria treatment at home was highly effective, which provides evidence base for scaling-up implementation of HMM with AL in Tanzania.

More than a reader and less than a critic: literary authority and women`s book-discussion groups

The phenomenon of women reading books collaboratively is largely invisible, and certainly under-researched. This study, based on extensive circulation figures and on a small sample of members of four Council of Adult Education reading groups in metropolitan Melbourne, argues that such groups have a reading repertoire which is seriously middlebrow, far removed from the “wish-fulfillment” or “lazy reader” stereotypes purveyed by some who would scorn such groups. The study finds that such groups are sensitively served by the institution which hosts them. While such groups do not question the aesthetic assumptions that underlie their practice, they are combative with some manifestations of the literary establishment. Their powerful preferences for contemporary Australian women's fiction and their participation in global debates via identity politics suggests they warrant closer examination, both within Australian culture, and to find out if such groups have counterparts in other cultures.

Nematode assemblages from Avicennia marina leaf litter in a temperate mangrove forest in south-eastern Australia

Meiofauna from Avicennia marina leaf litter in a temperate mangrove forest was enumerated, and the nematode assemblages compared on the bases of leaf colour (used as a guide to leaf age) and shore horizon where samples were collected. Twenty-one putative nematode species were collected from 48 leaf litter samples. Univariate analyses indicated that neither the colour of the leaf nor the shore horizon significantly affected abundance of nematodes. However, of the four (222) treatment groups, rarefaction curves revealed highest diversity on brown leaves from under the shade of the tree canopy (H'=0.751-0.126 SE, n=17). Species diversity of leaf litter nematodes was lower in this temperate mangrove system than reported from tropical mangrove studies. ANOSIM tests confirmed a significant effect of shore horizon on nematode assemblages. The dominant feeding group among nematodes was non-selective deposit feeders (7/21 species, but 77% of all nematodes). Epigrowth grazers were represented by 8/21 species of nematodes, but only 19% of the total number. Excised leaves became skeletonised by about 15 weeks. Shorter temporal scales of life cycles of nematodes compared with leaf degradation, and the dynamic nature of epibiontic assemblages, probably explain the similar assemblage structure on yellow and brown leaves.

Baby, it`s you : international capital discovers the under threes

Well-established international entertainment firms such as Disney and Fisher-Price are joining new start-up firms such as Baby Einstein to create a 'Baby' market of products (including toys, games and videos) specifically targeted at children aged 0-3 years. Despite its novelty, the 'Baby' market mirrors older markets that these firms have created around other demographic groups (e.g. older children, adolescents and adults) - it redefines its target demographic group around specific commodities and promotes its redefinition as 'common sense'. The 'Baby' firms redefine babies solely as early learners whose potential to learn can be released by these firms' brand-name 'educational' or 'developmental' products. Many adults buy these products because they accept the firms' redefinition of babies, but other adults ignore the firms' promotional messages and buy the products to give themselves some time apart from their babies. The 'Baby' market is significant for children and adults because it changes young children's relationships with adults and because it subordinates local cultural differences to a children's culture that purports to be 'global' but has, in reality, extremely narrow foundations in class, race and gender.

Extending abelian groups to rings

For any abelian group G and any function f : G → G we define a commutative binary operation or `multiplication' on G in terms of f. We give necessary and sufficient conditions on f for G to extend to a commutative ring with the new multiplication. In the case where G is an elementary abelian p-group of odd order, we classify those functions which extend G to a ring and show, under an equivalence relation we call weak isomorphism, that there are precisely six distinct classes of rings constructed using this method with additive group the elementary abelian p-group of odd order p².

Under-reporting of energy intake in the 1997 national nutrition survey

Aims To estimate the level of under-reporting of energy intake by gender, age, ethnicity and body size (normal, overweight, obese) in the 1997 National Nutrition Survey (NNS97) in New Zealand.
Methods Data were from 4,258 participants (1,808 men and 2,450 women aged 15 years and over) who completed the 24-hour diet recall; the primary methodology used in the NNS97. Under-reporting was assessed using the ratio of reported energy intake to estimated resting metabolic rate (EI: RMRest). Cut-off limits were used to identify percentages of under-reporters in the various subgroups.
Results Mean EI: RMRest was 1.40 for all participants (1.51 for men, 1.30 for women, p<0.001) with older age being associated with lower EI: RMRest (p<0.001). There were no significant differences in mean EI: RMRest between ethnic groups for men.
Mean EI: RMRest for women were: Maori 1.46, European 1.29, and Pacific 1.37 (p<0.01). A larger body size was associated with a significantly lower EI: RMRest especially for women.
Percentages of ‘definite’ under-reporters (individual EI: RMRest <0.9) were as follows: men 12%, women 21%; Europeans 16%, Maori 23% and Pacific 26%; normal weight (11%), overweight (19%) and obese (27%) participants; and from 10% in the youngest to 23% in the oldest age group (p<0.001 for all results).
Conclusion In this study, in agreement with the literature, women, older people and obese people under-reported more than men, younger people and non-obese people. Possible ethnic differences in under-reporting rates need further study. Care is needed in interpreting the energy intake data from the NNS97.

Friendships under strain : the work-personal life integration of middle managers

Middle managers in today's organisations have reported experiencing longer working hours and intensified work regimes. These increased pressures, in turn, have led to growing difficulty in addressing the integration of their work and personal lives. In an exploratory study of the daily workplace experiences of Australian middle managers and the impacts on their personal lives, one of the key themes to emerge was respondents' concerns about the negative effects on their friendships. This paper discusses middle managers' recognition of the value of friendships for their wellbeing, and the resultant anger and sadness reported at the strain on these relationships due to competing time demands. The significant role that friendships play in alleviating some of the stresses of work demands, while concurrently being impeded by these same demands, is an important issue for organisations to consider. These findings indicate the need for middle managers to truly have an ability to engage in activities - and friendships - which will aid them in their working lives. The study also indicates a need for further investigation into the development and maintenance of friendships for both middle managers and other groups of employees.

Investigation into the diffusion of innovation in technical and further education : implementing e-mail through action research

This research project examined the diffusion of change within one Victorian TAFE Institute by engaging action research to facilitate implementation of e-mail technology. The theoretical framework involving the concepts of technology innovation and action research was enhanced with the aid of Rogers's (1983) model of the diffusion of the innovation process. Political and cultural factors made up the initiation phase of innovation, enabling the research to concentrate on the implementation phase of e-mail Roger's (1983) model also provided adopter categories that related to the findings of a Computer Attitude Survey that was conducted at The School of Mines and Industries Ballarat (SMB), now the University of Ballarat—TAFE Division since amalgamation on 1st January 1998. Despite management rhetoric about the need to utilise e-mail, Institute teaching staff lacked individual computers in their work areas and most were waiting to become connected to the Internet as late as 1997. According to the action research reports, many staff were resistant to the new e-mail facilities despite having access to personal computers whose numbers doubled annually. The action research project became focussed when action researchers realised that e-mail workshop training was ineffective and that staff required improved access. Improvement to processes within education through collaborative action research had earlier been achieved (McTaggart 1994), and this project actively engaged practitioners to facilitate decentralised e-mail training in the workplace through the action research spiral of planning, acting, observing and reflecting, before replanning. The action researchers * task was to find ways to improve the diffusion of e-mail throughout the Institute and to develop theoretical constructs. My research task was to determine whether action research could successfully facilitate e-mail throughout the Institute. A rich literature existed about technology use in education, technology teaching, gender issues, less about computerphobia, and none about 'e-mailphobia \ It seemed appropriate to pursue the issue of e-mailphobia since it was marginalised, or ignored in the literature. The major political and cultural influences on the technologising of SMB and e-mail introduction were complex, making it impossible to ascertain the relative degrees of influence held by Federal and State Governments, SMB's leadership or the local community, Nonetheless, with the implementation of e-mail, traditional ways were challenged as SMB's culture changed. E-mail training was identified as a staff professional development activity that had been largely unsuccessful. Action research is critical collaborative inquiry by reflective practitioners who are accountable for making the results of their inquiry public and who are self-evaluating of their practice while engaging participative problem-solving and continuing professional development (Zuber-Skerritt 1992, 1993). Action research was the methodology employed in researching e-mail implementation into SMB because it involved collaborative inquiry with colleagues as reflective practitioners. Thoughtful questions could best be explored using deconstructivist philosophy, in asking about the noise of silence, which issues were not addressed, what were the contradictions and who was being marginalised with e-mail usage within SMB. Reviewing literature on action research was complicated by its broad definition and by the variability of research (King & Lonnquist 1992), and yet action research as a research methodology was well represented in educational research literature, and provided a systematic and recognisable way for practitioners to conduct their research. On the basis of this study, it could be stated that action research facilitated the diffusion of e-mail technology into one TAFE Institute, despite the process being disappointingly slow. While the process in establishing the action research group was problematic, action researchers showed that a window of opportunity existed for decentralised diffusion of e-mail training,in preference to bureaucratically motivated 'workshops. Eight major findings, grouped under two broad headings were identified: the process of diffusion (planning, nature of the process, culture, politics) and outcomes of diffusion (categorising, e-mailphobia, the survey device and technology in education). The findings indicated that staff had little experience with e-mail and appeared not to recognise its benefits. While 54.1% did not agree that electronic means could be the preferred way to receive Institute memost some 13.7% admitted to problems with using the voice answering service on telephones. Some 43.3% thought e-mail would not improve their connectedness (how they related) to the Institute. A small percentage of staff had trouble with telephone voice-mail and a number of these were anxious computer users. Individualised tuition and peer support proved helpful to individual staff whom action researchers believed to be 'at risk', as determined from the results of a Computer Attitude Survey. An instructional strategy that fostered the development of self-regulation and peer support was valuable, but there was no measure of the effects of this action research program, other than in qualitative terms. Nevertheless, action research gave space to reflect on the nature of the underlying processes in adopting e-mail. Challenges faced by TAFE action researchers are integrally affected by the values within TAFE, which change constantly and have recently been extensive enough to be considered as a 'new paradigm'. The influence of competition policy, the training reform agenda and technologisation of training have challenged traditional TAFE values. Action research reported that many staff had little immediate professional reason to use e-mail Theoretical answers were submerged beneath practical professional concerns, which related back to how much time teachers had and whether they could benefit from e-mail. A need for the development of principles for the sound educational uses of e-mail increases with the internationalisation of education and an increasing awareness of cultural differences. The implications for conducting action research in TAFE are addressed under the two broad issues of power and pedagogy. Issues of power included gaining access, management's inability to overcome staff resistance to technology, changing TAFE values and using technology for conducting action research. Pedagogical issues included the recognition of educational above technological issues and training staff in action research. Finally, seventeen steps are suggested to overcome power and pedagogical impediments to the conduct of action research within TAFE. This action research project has provided greater insight into the difficulties of successfully introducing one culture-specific technology into one TAFE Institute. TAFE Institutes need to encourage more action research into their operations, and it is only then that -we can expect to answer the unanswered questions raised in this research project.

Pulling schools up by their bootstraps : the case of a government intervention to raise standards in five 'under-performing' schools

This paper canvasses a school improvement intervention instigated by a government education department to raise the student achievement results of five schools in the outer eastern suburbs of Melbourne. The paper discusses the theory base of the intervention and the outcomes of its first stage which involved a preliminary survey of all students, teachers, assistant principals and principals from the schools involved. The survey results reveal discrepancies of opinions, perceptions, interests and ideas within these key groups. Future plans are discussed in light of both the findings from the first round of theory-building and other pertinent research concerning improving student learning outcomes.