A remark on embedded bipartite graphs
Abstract A use of Euler's formula in Zaks ( J. Combin. Theory Ser. B 32 (1982) , 95–98) is replaced by an elementary argument on permutations.
Extending an extension of Grinberg's theorem
Abstract Grinberg's well-known necessary condition for a planar graph to be Hamiltonian was extended by Shimamoto to a condition for having a 2-factor. We derive a necessary condition for a planar graph to contain a collection of n disjoint circuits, none of which separates any other two. All is done in terms of the numbers p k which denote the numbers of k -gonal faces.
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.