Rationality in Differential Algebraic Geometry

Parametric Cartan theory of exterior differential systems, and explicit cohomology of projective manifolds reveal united rationality features of differential algebraic geometry.Comment: Abel Symposium 201

A standardized photographic method for evaluating enamel opacities including fluorosis

Objectives: The objective of this study was to demonstrate the reproducibility of a standardized photographic technique for recording fluorosis when used by a group of epidemiologists as part of a large multicentred European study. Methods: Studies were first carried out to develop the equipment specification and photographic method. The author (JAC) was then trained and calibrated in this method. She was then responsible for the training and calibration of examiners from a further six European study sites. The method involved taking two transparencies of the permanent maxillary central incisors of 8-year-old children, the first after 8 s while the teeth were still wet and the second after 105 s when the teeth had been allowed to dry out naturally. Data were collected at a central location during a training/calibration exercise and subsequently, during the conduct of a large study to measure fluorosis prevalence, at the seven sites. Intra-and interexaminer reproducibility of the photographic method were measured by grading the transparencies produced by all the examiners according to the DDE and TF indices. Results: The time period in which the transparencies were taken was to within 4 s among the examiners. Transparencies scored according to the TF index gave a range of Kappa values of 0.45-0.66 for intraexaminer reliability and 0.32-0.55 for interexaminer reliability. When using the DDE index Kappa values ranged from 0.43 to 0.70 for intraexaminer reliability and from 0.34 to 0.69 for interexaminer reliability. Conclusion: The photographic method was mostly robust and reproducible when used by epidemiologists from seven European study sites. © Blackwell Munksgaard, 2004