The beta family at the prime two and modular forms of level three

We use the orientation underlying the Hirzebruch genus of level three to map the beta family at the prime p=2 into the ring of divided congruences. This procedure, which may be thought of as the elliptic greek letter beta construction, yields the f-invariants of this family.Comment: 13 page

Effects of dental probing on occlusal surfaces - A scanning electron microscopy evaluation

The aim of this clinical-morphological study was to investigate the effects of dental probing on occlusal surfaces by scanning electron microscopy (SEM). Twenty sound occlusal surfaces of third molars and 20 teeth with initial carious lesions of 17- to 26-year-old patients (n = 18) were involved. Ten molars of each group were probed with a sharp dental probe (No. 23) before extraction; the other molars served as negative controls. After extraction of the teeth, the crowns were separated and prepared for the SEM study. Probing-related surface defects, enlargements and break-offs of occlusal pits and fissures were observed on all occlusal surfaces with initial carious lesions and on 2 sound surfaces, respectively. No traumatic defects whatsoever were visible on unprobed occlusal surfaces. This investigation confirms findings of light-microscopic studies that using a sharp dental probe for occlusal caries detection causes enamel defects. Therefore, dental probing should be considered as an inappropriate procedure and should be replaced by a meticulous visual inspection. Critical views of tactile caries detection methods with a sharp dental probe as a diagnostic tool seem to be inevitable in undergraduate and postgraduate dental education programmes. Copyright (c) 2007 S. Karger AG, Basel

Fracture

Ope

Still Dance

Ope

Forest Falls

Ope