We prove that an iterated function system of similarities on $\mathbb{R}$ satisfies the weak separation condition and has interval as its self-similar set stronger generalized finite type condition. It is unknown if assumption necessary.

The Kuo condition and the second are known as criteria for an r-jet to be V-sufficient in Cr mappings Cr+1 mappings, respectively. In [2] we considered notions of V-sufficiency jets these conditions relative case a given closed set ?, showed that is criterion ?-V-sufficient sufficient mappings. this paper discuss several equivalent or condition.

Recently we proposed a model in which when a scientist writes a manuscript, he picks up several random papers, cites them and also copies a fraction of their references (cond-mat/0305150). The model was stimulated by our discovery that a majority of scientific citations are copied from the lists of references used in other papers (cond-mat/0212043). It accounted quantitatively for several prope...

3 4 Cassie Wilson, Mark A. King and Maurice R. Yeadon 5 6 1 Department for Health, University of Bath, Bath, BA2 7AY, UK. 7 2 School of Sport, Exercise and Health Sciences, Loughborough University, 8 Loughborough LE11 3TU, UK. 9 10 11 12