Fermat-linked relations for the Boubaker polynomial sequences via Riordan matrices analysis

The Boubaker polynomials are investigated in this paper. Using Riordan matrices analysis, a sequence of relations outlining the relations with Chebyshev and Fermat polynomials have been obtained. The obtained expressions are a meaningful supply to recent applied physics studies using the Boubaker polynomials expansion scheme (BPES).Comment: 12 pages, LaTe

Air pollution exposure during pregnancy and symptoms of attention deficit and hyperactivity disorder in children in Europe.

BACKGROUND: Exposure to air pollution during pregnancy may increase attention-deficit/hyperactivity disorder (ADHD) symptoms in children, but findings have been inconsistent. We aimed to study this association in a collaborative study of eight European population-based birth/child cohorts, including 29,127 mother-child pairs. METHODS: Air pollution concentrations (nitrogen dioxide [NO2] and particulate matter [PM]) were estimated at the birth address by land-use regression models based on monitoring campaigns performed between 2008 and 2011. We extrapolated concentrations back in time to exact pregnancy periods. Teachers or parents assessed ADHD symptoms at 3-10 years of age. We classified children as having ADHD symptoms within the borderline/clinical range and within the clinical range using validated cutoffs. We combined all adjusted area-specific effect estimates using random-effects meta-analysis and multiple imputations and applied inverse probability-weighting methods to correct for loss to follow-up. RESULTS: We classified a total of 2,801 children as having ADHD symptoms within the borderline/clinical range, and 1,590 within the clinical range. Exposure to air pollution during pregnancy was not associated with a higher odds of ADHD symptoms within the borderline/clinical range (e.g., adjusted odds ratio [OR] for ADHD symptoms of 0.95, 95% confidence interval [CI] = 0.89, 1.01 per 10 µg/m increase in NO2 and 0.98, 95% CI = 0.80, 1.19 per 5 µg/m increase in PM2.5). We observed similar associations for ADHD within the clinical range. CONCLUSIONS: There was no evidence for an increase in risk of ADHD symptoms with increasing prenatal air pollution levels in children aged 3-10 years. See video abstract at, http://links.lww.com/EDE/B379