Arithmetic for closed balls

Inspired by circular complex interval arithmetic, an arithmetic for closed balls in Rn is pursued. In this sense, the properties of certain operations on closed balls in Rn, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n є {3, 7}, are studied. In particular, known results for operations on closed balls in C, which can be identified with R2, are extended to closed balls in Rn

The European Smoking Prevention Framework Approach (ESFA): Effects after 24 and 30 months.

The European Smoking Prevention Framework Approach (ESFA) study in six countries tested the effects of a comprehensive smoking prevention approach after 24 (T3; N = 10,751) and 30 months (T4; N = 9,282). The programme targeted four levels, i.e. adolescents in schools, school policies, parents and the community. In Portugal, 12.4% of the T1 non-smokers in the control group had started smoking at T4 compared to 7.9% of the experimental group. Smoking onset in the experimental group was thus 36% lower. In Finland, 32.4% of the T1 non-smokers started smoking compared to 27.6% of the experimental group, implying a 15% lower onset in the experimental group. In Spain, 33.0% of the T1 non-smokers in the control group had started smoking, compared to 29.1% of the experimental group, implying a 12% lower onset. In The Netherlands, the ESFA programme was effective for non-native adolescents with 11.4% new weekly smokers compared to 19.9% in the control group. An opposite effect was found in native Dutch adolescents with 19.0% new weekly smokers in the comparison group compared to 24.0% new smokers in the experimental group. Future programmes should use more standardized ways to assess process evaluations and should assess which elements are responsible for behavioral effect