Dice throwing is used to illustrate relevant concepts of the statistical theory of uncertainties, in particular the meaning of a limiting distribution, the standard deviation, and the standard deviation of the mean. It is an important part in a sequence of especially programmed laboratory activities, developed for freshmen, at the Institute of Physics of the University of São Paulo. It is shown how this activity is employed within a constructive teaching approach, which aims at a growing understanding of the measuring processes and of the fundamentals of correct statistical handling of experimental data. †
It was proved by H. Whitney in 1933 that a Serre fibration of compact metric spaces admits a global section provided every fiber is homeomorphic to the unit interval [0,1]. Results of this paper extend Whitney theorem to the case when all fibers are homeomorphic to a given compact two-dimensional manifold.1991 Mathematics Subject Classification. Primary: 57N05, 57N10; Secondary: 54C65.
In general, the deposition of a given target dose requires a longer radiation time for intensity-modulated photon beams (IMBs) than for unmodulated beams. Hence, the routine use of intensity-modulated radiotherapy (IMRT) has repercussions both on the exposure of the patient to scatter and institutional radiation safety. A rule of thumb is presented to assess the maximum prolongation of radiation time for a case class in an idealized setting using static superimposed field segments. The method considers only the degree to which risk structures have to be blocked to meet specified dose restrictions.
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