Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

Happiness and Well-Being of Young Carers: Extent, Nature and Correlates of Caring Among 10 and 11 Year Old School Children

Young carers often take on practical and/or emotional caring responsibilities that would normally be expected of an adult. For many of these children and young people, caring has been shown to have a detrimental effect on their lives. For example, caring at a young age appears to be associated with poor health and well-being, bullying and poorer educational outcomes. However, previous research has tended to be retrospective, carried out using small surveys of secondary school-aged children or to use qualitative methods with young people associated with caring projects. In contrast, little is known about the extent and nature of caring undertaken by younger children. This paper reports findings from a random sample survey of 10 and 11 year old children in the final year of their primary school education. 4,192 children completed the Kids’ Life and Times (KLT) online survey in 2011. Twelve percent of respondents to KLT said they helped look after someone in their household who was sick, elderly or disabled. Supporting previous qualitative research, this survey showed that children who were carers had poorer health and well-being, reported less happiness with their lives, were more likely to be bullied at school and had poorer educational aspirations and outcomes than their peers who were not carers. These findings suggest that teachers need to discuss the issue of caring with children in the classroom in a general and supportive way so that young carers feel able to confide in them and seek support if they need it.

“It’s like a problem that doesn’t exist”: The emotional well-being of mothers caring for a child with brain injury.

Background: Although research has shown that significant burden and adverse psychological impact are associated with caring for a child with brain injury, limited knowledge exists concerning the qualitative experience and impact of this burden.
Objective: To provide an account of the experiences of mothers who care for a childhood survivor of brain injury.
Research design: Postal survey.
Methods and procedures: A self-report questionnaire was sent to a consecutive sample of mothers (n=86) of children (aged 8-28) with acquired brain injury, registered with a UK children’s brain injury charity. Five essay style questions enabled mothers to reflect on and describe at length their caring experiences, with particular emphasis placed on the perceived impact on emotional well-being.
Main outcomes and results: Thematic analysis identified five key themes: Perpetually Anxious, The Guilty Carer, The Labour of Caring, A Self-Conscious Apologist and Perpetually Grieving. Collectively, these themes highlight two core processes shaping mothers’ caring experiences and concomitant mental well-being. Firstly, the collective and enduring nature of caregiver burden over time. Second, the crucial role played by socio-cultural values in perpetuating caregiver burden.
Conclusions: Societal norms, particularly those relating to the nature and outcome of brain injury and motherhood, serve to marginalise mothers and increase feelings of isolation. Findings suggest the value of peer support programs as an effective means of providing appropriate social support.

The importance of oral health for the systemic well being of an ageing population

The proportion of adults over the age of 60 years is expanding rapidly across European Union countries, including the Republic of Ireland. As the older population has grown faster than the total population, the proportion of older persons relative to the rest of the population has increased considerably (Figure 1). This trend mirrors the arrival of the “baby boomer� generation into early old age and will have wide ranging effects on social, political and economic spheres as well as presenting significant challenges for healthcare delivery and public healthcare policy.

Multiple source quantum well model of porous silicon light emission

Based on photoluminescence, Fourier transform infrared spectroscopy, and atomic force microscopy results, a new light emitting model for porous silicon (multiple source quantum well model) is proposed.

Systematic review of interventions to improve the psychological well-being of general practitioners

BACKGROUND: The health of doctors who work in primary care is threatened by workforce and workload issues. There is a need to find and appraise ways in which to protect their mental health, including how to achieve the broader, positive outcome of well-being. Our primary outcome was to evaluate systematically the research evidence regarding the effectiveness of interventions designed to improve General Practitioner (GP) well-being across two continua; psychopathology (mental ill-health focus) and 'languishing to flourishing' (positive mental health focus). In addition we explored the extent to which developments in well-being research may be integrated within existing approaches to design an intervention that will promote mental health and prevent mental illness among these doctors.

METHODS: Medline, Embase, Cinahl, PsychINFO, Cochrane Register of Trials and Web of Science were searched from inception to January 2015 for studies where General Practitioners and synonyms were the primary participants. Eligible interventions included mental ill-health prevention strategies (e.g. promotion of early help-seeking) and mental health promotion programmes (e.g. targeting the development of protective factors at individual and organizational levels). A control group was the minimum design requirement for study inclusion and primary outcomes had to be assessed by validated measures of well-being or mental ill-health. Titles and abstracts were assessed independently by two reviewers with 99 % agreement and full papers were appraised critically using validated tools.

RESULTS: Only four studies (with a total of 997 GPs) from 5392 titles met inclusion criteria. The studies reported statistically significant improvement in self-reported mental ill-health. Two interventions used cognitive-behavioural techniques, one was mindfulness-based and one fed-back GHQ scores and self-help information.

CONCLUSION: There is an urgent need for high quality, controlled studies in GP well-being. Research on improving GP well-being is limited by focusing mainly on stressors and not giving systematic attention to the development of positive mental health.

Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.