Rational approximation and arithmetic progressions

A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a metrical and a non-metrical point of view and, on the other hand, from an asymptotic and also a uniform point of view. The principal novelty is a Khintchine type theorem for uniform approximation in this context. Some applications of this theory are also discussed

Effectiveness and Safety of rhIGF-1 Therapy in Children: The European Increlex® Growth Forum Database Experience.

BACKGROUND/AIMS: We report data from the EU Increlex® Growth Forum Database (IGFD) Registry, an ongoing, open-label, observational study monitoring clinical practice use of recombinant human insulin-like growth factor-1 (rhIGF-1) therapy in children. METHODS: Safety and effectiveness data on rhIGF-1 treatment of 195 enrolled children with growth failure were collected from December 2008 to September 2013. RESULTS: Mean ± SD (95% CI) height velocity during first year of rhIGF-1 treatment was 6.9 ± 2.2 cm/year (6.5; 7.2) (n = 144); in prepubertal patients naïve to treatment, this was 7.3 ± 2.0 cm/year (6.8; 7.7) (n = 81). Female sex, younger age at start of rhIGF-1 therapy, and lower baseline height SDS predicted first-year change in height SDS. The most frequent targeted treatment-emergent adverse events (% patients) were hypoglycemia (17.6%, predictors: young age, diagnosis of Laron syndrome, but not rhIGF-1 dose), lipohypertrophy (10.6%), tonsillar hypertrophy (7.4%), injection site reactions (6.4%), and headache (5.9%). Sixty-one serious adverse events (37 related to rhIGF-1 therapy) were reported in 31 patients (16.5%). CONCLUSION: Safety and effectiveness data on use of rhIGF-1 in a 'real-world' setting were similar to those from controlled randomized trials. Severe growth phenotype and early start of rhIGF-1 improved height response and predicted risk of hypoglycemia