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

On the Linearization of the Painleve' III-VI Equations and Reductions of the Three-Wave Resonant System

We extend similarity reductions of the coupled (2+1)-dimensional three-wave resonant interaction system to its Lax pair. Thus we obtain new 3x3 matrix Fuchs--Garnier pairs for the third and fifth Painleve' equations, together with the previously known Fuchs--Garnier pair for the fourth and sixth Painleve' equations. These Fuchs--Garnier pairs have an important feature: they are linear with respect to the spectral parameter. Therefore we can apply the Laplace transform to study these pairs. In this way we found reductions of all pairs to the standard 2x2 matrix Fuchs--Garnier pairs obtained by M. Jimbo and T. Miwa. As an application of the 3x3 matrix pairs, we found an integral auto-transformation for the standard Fuchs--Garnier pair for the fifth Painleve' equation. It generates an Okamoto-like B\"acklund transformation for the fifth Painleve' equation. Another application is an integral transformation relating two different 2x2 matrix Fuchs--Garnier pairs for the third Painleve' equation.Comment: Typos are corrected, journal and DOI references are adde

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

Maximizing the optical performance of planar CH3NH3PbI3 hybrid perovskite heterojunction stacks

A vapour-phase reaction process has been used to deposit smooth and uniform CH3NH3PbI3 perovskite material to enable the measurement of its optical dispersion relations, n and k, by ellipsometry. Fitting was achieved with a combination of Tauc-Lorenz, critical point parabolic band (CPPB) and harmonic oscillators. We have used the dispersion relations in an all-optical model of new planar device architectures in order to establish design rules for future materials choices to maximize the short-circuit current (Jsc) performance. For 500nm of MAPI with no window layer, the maximum performance expected from the model is Jsc=21.63mAcm-2. The ability of thin layers (in the range 20-60nm) of a range of window layer materials (TiO2, WO3, ZnO, Nb2O5, CdS, and Cd0.4 Zn0.6S) to enhance the short-circuit current of the devices was investigated. The performance of the oxides showed interference behaviour, with the first maxima in their J sc curves exceeding the value achievable without a window layer. However, after the first maximum, the performance generally fell off with increasing thickness. The only material to stay greater than the no-window condition for the entire investigated range is WO3. The highest performance (J sc of 22.47mAcm-2) was obtained with 59nm of WO3, with that of TiO2, ZnO, and Nb2O5 being marginally lower. Parasitic absorption in CdS window layers caused the J sc to decrease for all non-zero thicknesses - it gives no interference enhancement and its use cannot be recommended on optical grounds. Use of the wider gap alloy Cd0.4Zn0.6S gave higher currents than did CdS but its performance was not so high as for the oxides. Observations are made on the practicalities of fabricating the target structures in the fabrication of practical PV devices

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

The cystic fibrosis transmembrane recruiter the alter ego of CFTR as a multi-kinase anchor

This review focuses on a newly discovered interaction between protein kinases involved in cellular energetics, a process that may be disturbed in cystic fibrosis for unknown reasons. I propose a new model where kinase-mediated cellular transmission of energy provides mechanistic insight to a latent role of the cystic fibrosis transmembrane conductance regulator (CFTR). I suggest that CFTR acts as a multi-kinase recruiter to the apical epithelial membrane. My group finds that, in the cytosol, two protein kinases involved in cell energy homeostasis, nucleoside diphosphate kinase (NDPK) and AMP-activated kinase (AMPK), bind one another. Preliminary data suggest that both can also bind CFTR (function unclear). The disrupted role of this CFTR-kinase complex as ‘membrane transmitter to the cell’ is proposed as an alternative paradigm to the conventional ion transport mediated and CFTR/chloride-centric view of cystic fibrosis pathogenesis. Chloride remains important, but instead, chloride-induced control of the phosphohistidine content of one kinase component (NDPK, via a multi-kinase complex that also includes a third kinase, CK2; formerly casein kinase 2). I suggest that this complex provides the necessary near-equilibrium conditions needed for efficient transmission of phosphate energy to proteins controlling cellular energetics. Crucially, a new role for CFTR as a kinase controller is proposed with ionic concentration acting as a signal. The model posits a regulatory control relay for energy sensing involving a cascade of protein kinases bound to CFTR

Lifetime self-reported arthritis is associated with elevated levels of mental health burden: A multi-national cross sectional study across 46 low- and middle-income countries

Population-based studies investigating the relationship of arthritis with mental health outcomes are lacking, particularly among low- and middle-income countries (LMICs). We investigated the relationship between arthritis and mental health (depression spectrum, psychosis spectrum, anxiety, sleep disturbances and stress) across community-dwelling adults aged ≥18 years across 46 countries from the World Health Survey. Symptoms of psychosis and depression were established using questions from the Mental Health Composite International Diagnostic Interview. Severity of anxiety, sleep problems, and stress sensitivity over the preceding 30 days were self-reported. Self-report lifetime history of arthritis was collected, including presence or absence of symptoms suggestive of arthritis: pain, stiffness or swelling of joints over the preceding 12-months. Multivariable logistic regression analyses were undertaken. Overall, 245,706 individuals were included. Having arthritis increased the odds of subclinical psychosis (OR = 1.85; 95%CI = 1.72–1.99) and psychosis (OR = 2.48; 95%CI = 2.05–3.01). People with arthritis were at increased odds of subsyndromal depression (OR = 1.92; 95%CI = 1.64–2.26), a brief depressive episode (OR = 2.14; 95%CI = 1.88–2.43) or depressive episode (OR = 2.43; 95%CI = 2.21–2.67). Arthritis was also associated with increased odds for anxiety (OR = 1.75; 95%CI = 1.63–1.88), sleep problems (OR = 2.23; 95%CI = 2.05–2.43) and perceived stress (OR = 1.43; 95%CI = 1.33–1.53). Results were similar for middle-income and low-income countries. Integrated interventions addressing arthritis and mental health comorbidities are warranted to tackle this considerable burden

Validation of the questionnaire on beliefs about medication with type 2 diabetic patients

O presente trabalho teve como objectivo validar o Questionário Crenças sobre a Medicação, que avalia Crenças Gerais e Crenças Específicas, estudando suas propriedades psicométricas em uma amostra de 387 pacientes diabéticos tipo 2. O estudo de validade para as Crenças Gerais revelou uma solução de um factor, com um alfa de 0,76, e para as Crenças Específicas, dois factores – Necessidades e Preocupações –, com um alfa de 0,77 e 0,69 respectivamente. Quanto à validade de constructo, verificou-se uma relação entre as Crenças Gerais e a subescala Necessidades das Crenças Específicas com Adesão à Medicação, avaliada pela Escala de Avaliação de Aderência Médica. O instrumento apresenta boas qualidades psicométricas para ser utilizado em pacientes diabéticos tipo 2.The present paper focused on the validation of the Questionnaire on Beliefs about Medication, which assesses both General Beliefs and Specific Beliefs. The psychometric properties of the instrument were analyzed on a sample of 387 type 2 diabetic patients. The validity study for General Beliefs found a unifactorial solution, with an alpha of .76, and for Specific Beliefs, a two-factor solution – Necessities and Concern –, with an alpha of .77 and .69, respectively. In terms of construct validity, a relationship between General Beliefs, subscale Necessities from Specific Beliefs, and adherence to medication, as evaluated by Medical Adherence Rating Scale, was found. The instrument presents good psychometric qualities to be used in type 2 diabetic patients.Fundação para a Ciência e Tecnologia (FCT

Depression and anxiety in patients with rheumatoid arthritis: prevalence rates based on a comparison of the Depression, Anxiety and Stress Scale (DASS) and the hospital, Anxiety and Depression Scale (HADS)

<p>Abstract</p> <p>Background</p> <p>While it is recognised that depression is prevalent in Rheumatoid Arthritis (RA), recent studies have also highlighted significant levels of anxiety in RA patients. This study compared two commonly used scales, the Depression Anxiety and Stress Scale (DASS) and the Hospital Anxiety and Depression Scale (HADS), in relation to their measurement range and cut points to consider the relative prevalence of both constructs, and if prevalence rates may be due to scale-specific case definition.</p> <p>Methods</p> <p>Patients meeting the criteria for RA were recruited in Leeds, UK and Sydney, Australia and asked to complete a survey that included both scales. The data was analysed using the Rasch measurement model.</p> <p>Results</p> <p>A total of 169 RA patients were assessed, with a repeat subsample, resulting in 323 cases for analysis. Both scales met Rasch model expectations. Using the 'possible+probable' cut point from the HADS, 58.3% had neither anxiety nor depression; 13.5% had anxiety only; 6.4% depression only and 21.8% had both 'possible+probable' anxiety and depression. Cut points for depression were comparable across the two scales while a lower cut point for anxiety in the DASS was required to equate prevalence.</p> <p>Conclusions</p> <p>This study provides further support for high prevalence of depression and anxiety in RA. It also shows that while these two scales provide a good indication of possible depression and anxiety, the estimates of prevalence so derived could vary, particularly for anxiety. These findings are discussed in terms of comparisons across studies and selection of scales for clinical use.</p