On convex bodies of constant width
Abstract We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in R n is a contractible Hilbert cube manifold. The proof also works for certain subspaces of compact convex sets of constant width as well as for the pairs of compact convex sets of constant relative width. Besides, it is proved that the projection map of compact closed subsets of constant width is not 0-soft in the sense of Shchepin, in particular, is not open.
Topology of the hyperspace of convex bodies of constant width
The hyperspace of all convex bodies of constant width in Euclidean spaceRn,n≥2, is proved to be homeomorphic to a contractibleQ-manifold (Q denotes the Hilbert cube). The proof makes use of an explicitly constructed retraction of the entire hyperspace of convex bodies on the hyperspace of convex bodies of constant width.
Frequency distributions of the mixing height over an urban area from SODAR data
The height of the mixing-layer (MLH) is an important parameter in the assessment of the dilution of primarily emitted or secondarily formed air pollutants in the atmospheric boundary-layer. A continuous measurement of MLH is possible only by remote sensing. Here, 17 months of SODAR data have been analysed automatically to derive the MLH over the city of Hannover in Northern Germany. In contrast to earlier studies the MLH has been determined from vertical profiles of the acoustic backscatter intensity and from the variance of the vertical velocity component. The results are presented in form of monthly frequency distributions and mean daily courses of MLH. These statistical evaluations of MLH show a clear annual course and interannual variability. The study shows the possibility to derive meaningful climatological information from long-term SODAR measurements for air quality issues.