Intonation development from five to thirteen

Research undertaken to date suggests that important developments in the understanding and use of intonation may take place after the age of 5;0. The present study aims to provide a more comprehensive account of these developments. A specially designed battery of prosodic tasks was administered to four groups of thirty children, from London (U.K.), with mean ages of 5;6, 8;7, 10;10 and 13;9. The tasks tap comprehension and production of functional aspects of intonation, in four communicative areas: CHUNKING (i.e. prosodic phrasing), AFFECT, INTERACTION and FOCUS. Results indicate that there is considerable variability among children within each age band on most tasks. The ability to produce intonation functionally is largely established in five-year-olds, though some specific functional contrasts are not mastered until C.A. 8;7. Aspects of intonation comprehension continue to develop up to C.A. 10;10, correlating with measures of expressive and receptive language development

The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

Thirteen Poems

Književno prevođenj