Permutable entire functions satisfying algebraic differential equations

It is shown that if two transcendental entire functions permute, and if one of them satisfies an algebraic differential equation, then so does the other one.Comment: 5 page

An exactly solvable phase transition model: generalized statistics and generalized Bose-Einstein condensation

In this paper, we present an exactly solvable phase transition model in which the phase transition is purely statistically derived. The phase transition in this model is a generalized Bose-Einstein condensation. The exact expression of the thermodynamic quantity which can simultaneously describe both gas phase and condensed phase is solved with the help of the homogeneous Riemann-Hilbert problem, so one can judge whether there exists a phase transition and determine the phase transition point mathematically rigorously. A generalized statistics in which the maximum occupation numbers of different quantum states can take on different values is introduced, as a generalization of Bose-Einstein and Fermi-Dirac statistics.Comment: 17 pages, 2 figure

'Sink or swim': an evaluation of the clinical characteristics of individuals with high bone mass.

SUMMARY: High bone mineral density on routine dual energy X-ray absorptiometry (DXA) may indicate an underlying skeletal dysplasia. Two hundred fifty-eight individuals with unexplained high bone mass (HBM), 236 relatives (41% with HBM) and 58 spouses were studied. Cases could not float, had mandible enlargement, extra bone, broad frames, larger shoe sizes and increased body mass index (BMI). HBM cases may harbour an underlying genetic disorder. INTRODUCTION: High bone mineral density is a sporadic incidental finding on routine DXA scanning of apparently asymptomatic individuals. Such individuals may have an underlying skeletal dysplasia, as seen in LRP5 mutations. We aimed to characterize unexplained HBM and determine the potential for an underlying skeletal dysplasia. METHODS: Two hundred fifty-eight individuals with unexplained HBM (defined as L1 Z-score ≥ +3.2 plus total hip Z-score ≥ +1.2, or total hip Z-score ≥ +3.2) were recruited from 15 UK centres, by screening 335,115 DXA scans. Unexplained HBM affected 0.181% of DXA scans. Next 236 relatives were recruited of whom 94 (41%) had HBM (defined as L1 Z-score + total hip Z-score ≥ +3.2). Fifty-eight spouses were also recruited together with the unaffected relatives as controls. Phenotypes of cases and controls, obtained from clinical assessment, were compared using random-effects linear and logistic regression models, clustered by family, adjusted for confounders, including age and sex. RESULTS: Individuals with unexplained HBM had an excess of sinking when swimming (7.11 [3.65, 13.84], p < 0.001; adjusted odds ratio with 95% confidence interval shown), mandible enlargement (4.16 [2.34, 7.39], p < 0.001), extra bone at tendon/ligament insertions (2.07 [1.13, 3.78], p = 0.018) and broad frame (3.55 [2.12, 5.95], p < 0.001). HBM cases also had a larger shoe size (mean difference 0.4 [0.1, 0.7] UK sizes, p = 0.009) and increased BMI (mean difference 2.2 [1.3, 3.1] kg/m(2), p < 0.001). CONCLUSION: Individuals with unexplained HBM have an excess of clinical characteristics associated with skeletal dysplasia and their relatives are commonly affected, suggesting many may harbour an underlying genetic disorder affecting bone mass

Measurement invariance of Personal Well-Being Index (PWI-8) across 26 countries

This report examines the measurement invariance of the Personal Well-being Index with 8 items (PWI-8). University students (N = 5731) from 26 countries completed the measure either through paper and pencil or electronic mode. We examined uni-dimensional structure of PWI and performed a Multi-group CFA to assess the measurement invariance across the 26 countries, using conventional approach and the alignment procedure. The findings provide evidence of configural and partial metric invariance, as well as partial scalar invariance across samples. The findings suggest that PWI-8 can be used to examine correlates of life satisfaction across all included countries, however it is impossible to compare raw scores across countries

Injectivity of sections of convex harmonic mappings and convolution theorems

In the article the authors consider the class ${\mathcal H}_0$ of sense-preserving harmonic functions $f=h+\overline{g}$ defined in the unit disk $|z|<1$ and normalized so that $h(0)=0=h'(0)-1$ and $g(0)=0=g'(0)$, where $h$ and $g$ are analytic in the unit disk. In the first part of the article we present two classes $\mathcal{P}_H^0(\alpha)$ and $\mathcal{G}_H^0(\beta)$ of functions from ${\mathcal H}_0$ and show that if $f\in \mathcal{P}_H^0(\alpha)$ and $F\in\mathcal{G}_H^0(\beta)$, then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters $\alpha$ and $\beta$ are satisfied. In the second part we study the harmonic sections (partial sums) $$s_{n, n}(f)(z)=s_n(h)(z)+\overline{s_n(g)(z)},$$ where $f=h+\overline{g}\in {\mathcal H}_0$, $s_n(h)$ and $s_n(g)$ denote the $n$-th partial sums of $h$ and $g$, respectively. We prove, among others, that if $f=h+\overline{g}\in{\mathcal H}_0$ is a univalent harmonic convex mapping, then $s_{n, n}(f)$ is univalent and close-to-convex in the disk $|z|< 1/4$ for $n\geq 2$, and $s_{n, n}(f)$ is also convex in the disk $|z|< 1/4$ for $n\geq2$ and $n\neq 3$. Moreover, we show that the section $s_{3,3}(f)$ of $f\in {\mathcal C}_H^0$ is not convex in the disk $|z|<1/4$ but is shown to be convex in a smaller disk.Comment: 16 pages, 3 figures; To appear in Czechoslovak Mathematical Journa

The mental health continuum-short form: the structure and application for cross-cultural studies-A 38 nation study

Objective: The Mental Health Continuum-Short Form (MHC-SF) is a brief scale measuring positive human functioning. The study aimed to examine the factor structure and to explore the cross-cultural utility of the MHC-SF using bifactor models and exploratory structural equation modelling. Method: Using multigroup confirmatory analysis (MGCFA) we examined the measurement invariance of the MHC-SF in 38 countries (university students, N = 8,066; 61.73% women, mean age 21.55 years). Results: MGCFA supported the cross-cultural replicability of a bifactor structure and a metric level of invariance between student samples. The average proportion of variance explained by the general factor was high (ECV =.66), suggesting that the three aspects of mental health (emotional, social, and psychological well-being) can be treated as a single dimension of well-being. Conclusion: The metric level of invariance offers the possibility of comparing correlates and predictors of positive mental functioning across countries; however, the comparison of the levels of mental health across countries is not possible due to lack of scalar invariance. Our study has preliminary character and could serve as an initial assessment of the structure of the MHC-SF across different cultural settings. Further studies on general populations are required for extending our findings.info:eu-repo/semantics/acceptedVersio

Belief in a zero-sum game and subjective well-being across 35 countries

This article presents a short research report on the relationship between perceived antagonism in social relations measured using the Belief in a Zero-Sum Game (BZSG) scale, life satisfaction, and positive and negative affect. Given that individuals who believe that life is like a zero-sum game are likely to perceive their daily interactions with others as unfair, we expected that individuals with high BZSG experience more negative affect and fewer positive one, resulting in a lower satisfaction with life. In addition, we examined whether country-level BZSG may play a moderating role in these associations. Data were collected from student samples (N = 7146) in 35 countries. Multilevel modelling revealed that perceived social antagonism in social relations is negatively associated with satisfaction with life and that this relationship is mediated by both positive and negative affect at the individual level. The relation of individual BZSG and negative affect on satisfaction with life were weaker in societies with higher country-level BZSG, suggesting that the effects of BZSG may be less detrimental in these countries. These findings extend previous knowledge about predictors of life satisfaction and suggest that social beliefs might also be an important factor that influences subjective well-being. The contribution of the study is that the separate treatment of life satisfaction and positive and negative affect may be helpful in many research situations, particularly from a cross-cultural perspective.info:eu-repo/semantics/publishedVersio

Long-term effectiveness of tumour necrosis factor-α inhibitor treatment for psoriatic arthritis in the UK: A multicentre retrospective study

Objective. Real-world evidence of the long-term effectiveness of TNF-α inhibitor (TNFi) therapy in patients with PsA is limited. This study was conducted to describe patterns of TNFi therapy and treatment responses in patients with PsA treated in UK clinical practice. Methods. A multicentre, retrospective, observational cohort study of consenting patients treated with TNFi for PsA with ≥ 3 years follow-up from first TNFi initiation (observation period) was carried out in 11 UK National Health Service hospitals. Data were collected concerning baseline patient characteristics, PsA-related treatment pathways and TNFi treatment responses (PsA response criteria components: swollen/tender joint counts, physician and patient global assessments). Results. The mean age of patients (n=141) was 50.3 (S.D.: 12.1) years (50% male). During a median observation period of 4.5 (range: 3.4-5.5) years, patients received a median of one (range: one to five) TNFi. Twelve-week response rates for first TNFi (where available) were as follows: 80% (n=64/80) for swollen joint counts, 79% (n=63/79) for tender joint counts, 79% (n=37/47) for physician global assessments, 69% (n=41/59) for patient global assessments and 79% (n=37/47) for PsA response criteria. At the end of the observation period, the proportions of patients remaining on first, second, third and fourth/fifth TNFi were 56, 15, 5 and 3%, respectively; 21% of patients permanently discontinued TNFi therapy. Conclusion. Long-term TNFi therapy is generally well tolerated and may be effective; however, after initial TNFi failure, there appears to be progressively less benefit and more adverse effects with successive TNFi switches. Strategies are needed for effective therapy for PsA beyond the first TNFi failure

Capture the fracture: a best practice framework and global campaign to break the fragility fracture cycle

Summary The International Osteoporosis Foundation (IOF) Capture the Fracture Campaign aims to support implementation of Fracture Liaison Services (FLS) throughout the world. Introduction FLS have been shown to close the ubiquitous secondary fracture prevention care gap, ensuring that fragility fracture sufferers receive appropriate assessment and intervention to reduce future fracture risk. Methods Capture the Fracture has developed internationally endorsed standards for best practice, will facilitate change at the national level to drive adoption of FLS and increase awareness of the challenges and opportunities presented by secondary fracture prevention to key stakeholders. The Best Practice Framework (BPF) sets an international benchmark for FLS, which defines essential and aspirational elements of service delivery. Results The BPF has been reviewed by leading experts from many countries and subject to beta-testing to ensure that it is internationally relevant and fit-for-purpose. The BPF will also serve as a measurement tool for IOF to award ‘Capture the Fracture Best Practice Recognition’ to celebrate successful FLS worldwide and drive service development in areas of unmet need. The Capture the Fracture website will provide a suite of resources related to FLS and secondary fracture prevention, which will be updated as new materials become available. A mentoring programme will enable those in the early stages of development of FLS to learn from colleagues elsewhere that have achieved Best Practice Recognition. A grant programme is in development to aid clinical systems which require financial assistance to establish FLS in their localities. Conclusion Nearly half a billion people will reach retirement age during the next 20 years. IOF has developed Capture the Fracture because this is the single most important thing that can be done to directly improve patient care, of both women and men, and reduce the spiralling fracture-related care costs worldwide.</p