It is proved that the solution to the initial value problem , u(0,x) = 1/(1+x²), does not belong to the Gevrey class in time for 0 ≤ s < 1. The proof is based on an estimation of a double sum of products of binomial coefficients.
The paper brings explicit formula for enumeration of vertex-labeled split graphs with given number of vertices. The authors derive this formula combinatorially using an auxiliary assertion concerning number of split graphs with given clique number. In conclusion authors discuss enumeration of vertex-labeled bipartite graphs, i.e., a graphical class defined in a similar manner to the class of split graphs.