Patterns in rational base number systems

Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\'ele ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums

Relationship between the serum thyrotropin level, the prevalence of goiter and the pattern of iodine metabolism in Idjwi Island.

Radioimmunoassay of serum thyrotropin was performed in 185 patients, 4-30 yr old, living in Brussels (control group), in the nongoitrous (southwest) and in the goitrous (north) areas of Idjwi Island (Dem. Rep. of the Congo). Both these regions in Idjwi Island have a severe and quite similar iodine deficiency. The serum TSH level was higher in the inhabitants of Idjwi Island than in the Belgian controls; it was still higher in the goitrous area (in both goitrous and nongoitrous subjects) than in the nongoitrous area. No difference was observed in the 3 areas as a function of age, size of the thyroid, or its nodularity. There was a significant correlation between the TSH level and the plasma [l27I]PBI in the goitrous area. There was no correlation between the TSH level, the 6-hr thyroidal radioiodine uptake, the [125I]PBI estimated at the time of equilibrium in isotopic distribution and the organic exchangeable iodine pool of the thyroid in all 3 areas. The results observed in southwest Idjwi show that the human thyroid is capable of adapting itself adequately to a very severe iodine deficiency under the influence of an increased thyrotropic stimulation without clinical evidence of thyroidal hyperplasia. The higher serum TSH level observed in north Idjwi suggests that thyrotropic hyperstimulation is responsible for endemic goiter in Idjwi Island. In this island, the serum TSH level seems to be more closely related to the geographic environment than to the age of the subjects or the individual size of the thyroid. © 1971 by The Endocrine Society.SCOPUS: ar.jSCOPUS: ar.jinfo:eu-repo/semantics/publishe

Blood TSH Level in Idjwi Island: Modifications related to regional prevalence of goitre and not to individual thyroidal size and function

info:eu-repo/semantics/publishe

Informatics in the French Secondary Curricula: Recent Moves and Perspectives

International audienceIn France, since 2010, the situation regarding informatics education in secondary school has changed: Algorithmic was introduced in mathematics curricula at grade 11 and an elective Computer Science course (called ISN) has been introduced at grade 12 (Fall 2012). These changes have encouraged some initiatives for the promotion of informatics education, among them the French 2012-Bebras contest. However, the 'informatics as a tool approach' continues to guide decision makers in education. This context renews the issue of informatics education (including Computer Science) for all students at the different levels of secondary school. We submit some ideas to re-open the debat

Serum thyrotrophin determination on day 5 of life as screening procedure for congenital hypothyroidism.

In 327 newborns cord blood thyroxine (T4) was 11.8 +/- 0.4 mug/100 ml (SEM) (151.9 +/- 5.1 nmol/l), and serum thyrotrophin (TSH) 6.7+/-1.0 muU/ml. Variability was marked for both T4 and TSH. Remeasured in the same patients on the fifth day of life, the TSH level was 3.7 +/- 1.0 muU/ml, lower than at birth (P less than 0.001), while scattering of TSH values was much smaller, with 99.4 % of values less than 12 muU/ml..