On dominant contractions and a generalization of the zero-two law

Zaharopol proved the following result: let T,S:L^1(X,{\cf},\m)\to L^1(X,{\cf},\m) be two positive contractions such that $T\leq S$. If $\|S-T\|<1$ then $\|S^n-T^n\|<1$ for all n\in\bn. In the present paper we generalize this result to multi-parameter contractions acting on $L^1$. As an application of that result we prove a generalization of the "zero-two" law.Comment: 10 page

Recent progress on univariate and multivariate polynomial and spline quasi-interpolants

Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform boundedness independently of the degree (polynomials) or of the partition (splines), good approximation order. We shall emphasize new results on various types of univariate and multivariate polynomial or spline QIs, depending on the nature of coefficient functionals, which can be differential, discrete or integral. We shall also present some applications of QIs to numerical methods

Low back pain around retirement age and physical occupational exposure during working life

<p>Abstract</p> <p>Background</p> <p>Physical occupational exposure is a risk factor for low back pain in workers but the long term effects of exposure remain unclear. As several countries consider increasing the retirement age, further information on this topic is relevant. This study aimed to describe the prevalence of low back pain among middle aged and aging individuals in the general French population according to physical occupational exposure and retirement status.</p> <p>Methods</p> <p>The study population originated from the French national survey 'Enquête décennale santé 2002'. Low back pain for more than 30 days within the previous twelve months (LBP) was assessed using a French version of the Nordic questionnaire. Occupational exposure was self assessed. Subjects were classified as "exposed" if they were currently or had previously been exposed to handling of heavy loads and/or to tiring postures. The weighted prevalence of LBP was computed separately for men and women, for active (aged 45-59) and retiree (aged 55-74), according to 5-year age group and past/present occupational exposure.</p> <p>Results</p> <p>For active men, the prevalence of LBP was significantly higher in those currently or previously exposed (n = 1051) compared with those never exposed (n = 1183), respectively over 20% versus less than 11%. Among retired men, the prevalence of LBP tended towards equivalence with increasing age among those previously exposed (n = 748) and those unexposed (n = 599).</p> <p>Patterns were quite similar for women with a higher prevalence in exposed active women (n = 741) compared to unexposed (n = 1260): around 25% versus 15%. Similarly, differences between previously exposed (n = 430) and unexposed (n = 489) retired women tended to reduce with age.</p> <p>Conclusion</p> <p>The prevalence of LBP in active workers was associated with occupational exposure. The link with past exposure among retirees decreased with age. These results should be considered for policies dealing with prevention at the workplace and retirement.</p

The costs of introducing artemisinin-based combination therapy: evidence from district-wide implementation in rural Tanzania

BACKGROUND\ud \ud The development of antimalarial drug resistance has led to increasing calls for the introduction of artemisinin-based combination therapy (ACT). However, little evidence is available on the full costs associated with changing national malaria treatment policy. This paper presents findings on the actual drug and non-drug costs associated with deploying ACT in one district in Tanzania, and uses these data to estimate the nationwide costs of implementation in a setting where identification of malaria cases is primarily dependant on clinical diagnosis.\ud \ud METHODS\ud \ud Detailed data were collected over a three year period on the financial costs of providing ACT in Rufiji District as part of a large scale effectiveness evaluation, including costs of drugs, distribution, training, treatment guidelines and other information, education and communication (IEC) materials and publicity. The district-level costs were scaled up to estimate the costs of nationwide implementation, using four scenarios to extrapolate variable costs.\ud \ud RESULTS\ud \ud The total district costs of implementing ACT over the three year period were slightly over one million USD, with drug purchases accounting for 72.8% of this total. The composite (best) estimate of nationwide costs for the first three years of ACT implementation was 48.3 million USD (1.29 USD per capita), which varied between 21 and 67.1 million USD in the sensitivity analysis (2003 USD). In all estimates drug costs constituted the majority of total costs. However, non-drug costs such as IEC materials, drug distribution, communication, and health worker training were also substantial, accounting for 31.4% of overall ACT implementation costs in the best estimate scenario. Annual implementation costs are equivalent to 9.5% of Tanzania's recurrent health sector budget, and 28.7% of annual expenditure on medical supplies, implying a 6-fold increase in the national budget for malaria treatment.\ud \ud CONCLUSION\ud \ud The costs of implementing ACT are substantial. Although drug purchases constituted a majority of total costs, non-drug costs were also considerable. It is clear that substantial external resources will be required to facilitate and sustain effective ACT delivery across Tanzania and other malaria-endemic countries