In this paper, we compare some deterministic and probabilistic techniques in the study of upper bounds in problems related to certain mean square discrepancie with respect to balls in the d-dimensional unit torus, and show that the quality of these techniques depends in an intricate way on the dimension d under consideration.

background and aims. the correct relationship of the total mesiodistal width of the mandibular teeth to that of the maxillary teeth (bolton’s ratios) is among the main factors considered in obtaining an optimal occlusion. the present study was conducted to determining the bolton’s ratios before and after treatment in skeletal class i patients. materials and methods. in this descriptive analytic...