Dominique Schmitt

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Given a set S of line segments in the plane, we introduce a new family of partitions of the convex hull of S called segment triangulations of S. The set of faces of such a triangulation is a maximal set of disjoint triangles that cut S at, and only at, their vertices. Surprisingly, several properties of point set triangulations extend to segment(More)
OBJECTIVES This study assesses the cognitive and emotional empathic competence in groups of children and adolescents with psychiatric disorders compared to a nonclinical control group. Subjective and objective diagnostic measures were employed. METHODS A total of 96 boys were tested: 20 with attention-deficit/hyperactivity disorder (ADHD) predominantly(More)
Let S be a finite set of n points in the plane in general position. We prove that every inclusion-maximal family of subsets of S separable by convex pseudo-circles has the same cardinal (n 0)+(n 1)+(n 2)+(n 3). This number does not depend on the configuration of S and is the same as the number of subsets of S separable by true circles. Buzaglo, Holzman, and(More)
Given a set V of n points in the plane, no three of them being collinear, a convex inclusion chain of V is an ordering of the points of V such that no point belongs to the convex hull of the points preceding it in the ordering. We call k-set of the convex inclusion chain, every k-set of an initial subsequence of at least k points of the ordering. We show(More)