On the Linearization of the First and Second Painleve' Equations

We found Fuchs--Garnier pairs in 3X3 matrices for the first and second Painleve' equations which are linear in the spectral parameter. As an application of our pairs for the second Painleve' equation we use the generalized Laplace transform to derive an invertible integral transformation relating two its Fuchs--Garnier pairs in 2X2 matrices with different singularity structures, namely, the pair due to Jimbo and Miwa and the one found by Harnad, Tracy, and Widom. Together with the certain other transformations it allows us to relate all known 2X2 matrix Fuchs--Garnier pairs for the second Painleve' equation with the original Garnier pair.Comment: 17 pages, 2 figure

The Generalized Dirichlet to Neumann map for the KdV equation on the half-line

For the two versions of the KdV equation on the positive half-line an initial-boundary value problem is well posed if one prescribes an initial condition plus either one boundary condition if $q_{t}$ and $q_{xxx}$ have the same sign (KdVI) or two boundary conditions if $q_{t}$ and $q_{xxx}$ have opposite sign (KdVII). Constructing the generalized Dirichlet to Neumann map for the above problems means characterizing the unknown boundary values in terms of the given initial and boundary conditions. For example, if $\{q(x,0),q(0,t) \}$ and $\{q(x,0),q(0,t),q_{x}(0,t) \}$ are given for the KdVI and KdVII equations, respectively, then one must construct the unknown boundary values $\{q_{x}(0,t),q_{xx}(0,t) \}$ and $\{q_{xx}(0,t) \}$, respectively. We show that this can be achieved without solving for $q(x,t)$ by analysing a certain ``global relation'' which couples the given initial and boundary conditions with the unknown boundary values, as well as with the function $\Phi^{(t)}(t,k)$, where $\Phi^{(t)}$ satisifies the $t$-part of the associated Lax pair evaluated at $x=0$. Indeed, by employing a Gelfand--Levitan--Marchenko triangular representation for $\Phi^{(t)}$, the global relation can be solved \emph{explicitly} for the unknown boundary values in terms of the given initial and boundary conditions and the function $\Phi^{(t)}$. This yields the unknown boundary values in terms of a nonlinear Volterra integral equation.Comment: 21 pages, 3 figure

In-depth analysis of chloride treatments for thin-film CdTe solar cells

CdTe thin-film solar cells are now the main industrially established alternative to silicon-based photovoltaics. These cells remain reliant on the so-called chloride activation step in order to achieve high conversion efficiencies. Here, by comparison of effective and ineffective chloride treatments, we show the main role of the chloride process to be the modification of grain boundaries through chlorine accumulation, which leads an increase in the carrier lifetime. It is also demonstrated that while improvements in fill factor and short circuit current may be achieved through use of the ineffective chlorides, or indeed simple air annealing, voltage improvement is linked directly to chlorine incorporation at the grain boundaries. This suggests that focus on improved or more controlled grain boundary treatments may provide a route to achieving higher cell voltages and thus efficiencies

‘We’ll be okay together’: navigating challenges as queer university students in Aotearoa New Zealand

Queer university students face multiple stressors which can contribute to mental health difficulties, including minority stressors unique to their queer identities. However, there is little literature exploring stressors faced by queer individuals in university settings. The aim of this study was to qualitatively explore the current challenges and strengths faced by queer university students in Aotearoa New Zealand, in order to contextualise their mental health experiences. Twenty-eight queer students participated across 12 focus groups or interviews. Two queer researchers thematically analysed the data. Three themes were interpreted from the data: ‘That’s not feminine enough’: the impact of societal ideologies on queer students; ‘There’s one rainbow person in the room’: Tokenism, social isolation, and then finding community; and ‘You know what it’s like to not be heard’: The transformation of challenges into strengths. The findings illustrate how queer university students make meaning of their challenges, and the strengths they develop to mitigate these. Educational institutions are highlighted as important sites of systemic change, to reduce minority stressors in students’ lives

‘Is it worth potentially dealing with someone who won't get it?’: LGBTQA+ university students’ perspectives on mental health care

LGBTQA+ university students have unique mental health needs and high rates of mental distress compared to their cisgender heterosexual peers; however, it is likely that many LGBTQA+ individuals remain untreated or receive inappropriate or insensitive care. The aim of this study was to explore the experiences and preferences in mental health care of LGBTQA+ university students in Aotearoa New Zealand. Twenty-eight young adults participated across 12 focus groups or interviews in which they were asked about their experiences and preferences. We used thematic analysis to identify patterns of meaning in the data. Researchers developed three themes of I can do this on my own, but others should seek help; you have to be lucky to access mental health care; and ‘therapists just need to be a bit more like up with the programme’. The results of this study mirror those found in more general studies of LGBTQA+ mental healthcare experiences, however, also adds to considerations for university campus healthcare services. The findings of this study should be considered by all mental health providers working with LGBTQA+ young adult university students

Women’s experiences of wearing therapeutic footwear in three European countries

Background: Therapeutic footwear is recommended for those people with severe foot problems associated with rheumatoid arthritis (RA). However, it is known that many do not wear them. Although previous European studies have recommended service and footwear design improvements, it is not known if services have improved or if this footwear meets the personal needs of people with RA. As an earlier study found that this footwear has more impact on women than males, this study explores women’s experiences of the process of being provided with it and wearing it. No previous work has compared women’s experiences of this footwear in different countries, therefore this study aimed to explore the potential differences between the UK, the Netherlands and Spain. Method: Women with RA and experience of wearing therapeutic footwear were purposively recruited. Ten women with RA were interviewed in each of the three countries. An interpretive phenomenological approach (IPA) was adopted during data collection and analysis. Conversational style interviews were used to collect the data. Results: Six themes were identified: feet being visibly different because of RA; the referring practitioners’ approach to the patient; the dispensing practitioners’ approach to the patient; the footwear being visible as different to others; footwear influencing social participation; and the women’s wishes for improved footwear services. Despite their nationality, these women revealed that therapeutic footwear invokes emotions of sadness, shame and anger and that it is often the final and symbolic marker of the effects of RA on self perception and their changed lives. This results in severe restriction of important activities, particularly those involving social participation. However, where a patient focussed approach was used, particularly by the practitioners in Spain and the Netherlands, the acceptance of this footwear was much more evident and there was less wastage as a result of the footwear being prescribed and then not worn. In the UK, the women were more likely to passively accept the footwear with the only choice being to reject it once it had been provided. All the women were vocal about what would improve their experiences and this centred on the consultation with both the referring practitioner and the practitioner that provides the footwear. Conclusion: This unique study, carried out in three countries has revealed emotive and personal accounts of what it is like to have an item of clothing replaced with an ‘intervention’. The participant’s experience of their consultations with practitioners has revealed the tension between the practitioners’ requirements and the women’s ‘social’ needs. Practitioners need greater understanding of the social and emotional consequences of using therapeutic footwear as an intervention