It is shown that there is no digraph F which could decompose the complete digraph on 5 vertices minus any 2-arc remainder into three parts isomorphic to F for each choice of the remainder. On the other hand, for each n ≥ 3 there is a universal third part F of the complete 2-graph 2Kn on n vertices, i.e., for each edge subset R of size [formula] mod 3, there is an F-decomposition of 2Kn−R. Using an exhaustive computer-aided search, we find all, exactly six, mutually nonisomorphic universal third parts of the 5-vertex 2-graph. Nevertheless, none of their orientations is a universal third part of the corresponding complete digraph.
A numerical method for solving axisymmetric transient nonNewtonian free surface flows is presented. The methodology employed is an extension of the twodimensional GENSMAC code, employing a markerandcell technique and solving the governing equations using finite differences approximations on a staggered grid. Marker particles are used which provide both the location and the visualization of the free surface. Several simulations demonstrating the differences between Newtonian and nonNewtonian flow are presented.
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