On the Heisenberg invariance and the Elliptic Poisson tensors

We study different algebraic and geometric properties of Heisenberg invariant Poisson polynomial quadratic algebras. We show that these algebras are unimodular. The elliptic Sklyanin-Odesskii-Feigin Poisson algebras $q_{n,k}(\mathcal E)$ are the main important example. We classify all quadratic $H-$invariant Poisson tensors on ${\mathbb C}^n$ with $n\leq 6$ and show that for $n\leq 5$ they coincide with the elliptic Sklyanin-Odesskii-Feigin Poisson algebras or with their certain degenerations.Comment: 14 pages, no figures, minor revision, typos correcte

Quality of life in a clinical sample of obese children

To measure health-related quality of life (HRQoL) in a clinical sample of obese children by child self-report and parent-proxy report; to compare quality of life assessments provided by obese children and their parents; to assess differences in quality of life between the obese clinical sample and healthy control children. Pairwise comparison of obese children matched for age, gender and socio-economic status with non-obese controls. One hundred and twenty-six obese children (body mass index (BMI) 98th centile) and 71 lean control children (BMI <85th centile). Controls were matched with 71 children from the obese clinical group (mean age 8.6, standard deviation (s.d.) 1.9 years; 33 M/38 F). Measurement: The Paediatric Quality of Life Inventory (UK) version 4 was self-administered to parents and to children aged 8–12 years and interview was administered to children aged 5–7 years. This questionnaire assessed physical, social, emotional and school functioning from which total, physical and psychosocial health summary scores were derived. In the obese clinical group (n=126), parent proxy-reported quality of life was low for all domains. In the obese clinical group, parent-reported scores were significantly lower than child self-reported scores in all domains except physical health and school functioning. Parent-proxy reports were significantly higher for healthy controls than obese children in all domains (median total score 85.2 vs 64.7; 95% confidence interval (CI) 15.6, 24.1). For child self-reports, only physical health was significantly higher for healthy controls than obese children (median score 81.3 vs 75.0; 95% CI 3.1, 12.5). HRQoL is impaired in clinical samples of obese children compared to lean children, but the degree of impairment is likely to be greatest when assessed using the parent perspective rather than the child perspective