The aim of this retrospective study was to investigate cephalometrically the skeletal, dental, and soft tissue modifications induced by activator treatment in patients with Class II malocclusions caused by mandibular retrognathism. The subjects, all in the mixed dentition, were selected from a single centre and were divided into two groups: 40 patients treated with an incisor double capping act...

We show that there are constants k,K > 0 such that for all N, s ∈ N, s ≤ N , the point set consisting of N points chosen uniformly at random in the s-dimensional unit cube [0, 1]s with probability at least 1− e−ks admits an axis-parallel rectangle [0, x] ⊆ [0, 1]s containing K √ sN points more than expected. Consequently, the expected star discrepancy of a random point set is of order √

The extreme or unanchored discrepancy is the geometric discrepancy of point sets in the d-dimensional unit cube with respect to the set system of axis-parallel boxes. For 2 ≤ p < ∞ we provide upper bounds for the average Lp-extreme discrepancy. With these bounds we are able to derive upper bounds for the inverse of the L∞-extreme discrepancy with optimal dependence on the dimension d and explic...

Tractability properties of various notions of discrepancy have been intensively studied in the last decade. In this paper we consider the so-called weighted star discrepancy which was introduced by Sloan and Woźniakowski. We show that under a very mild condition on the weights one can obtain tractability with s-exponent zero (s is the dimension of the point set). In the case of product weights ...