as we know, kaehler-ricci flow can be reduced to solve a class of  parabolic   complex monge-amp\`ere equations for kaehler potentials and  the solutions usually depend on the kaehler class of initial metric.   thus there  gives a  degeneration of kaehler metrics arising from the kaehler-ricci flow.  for a class of $g$-spherical manifolds,   we can  use  the local estimate  of  monge-amp\`ere equations as well as  the h-invariant for $c^*$-degeneration  to determine the limit of  kaehler-ricci flow after resales.  in particular,  on such manifolds,  the flow will develop the singularities of  type ii.  

we discuss an analogue of the goldbach conjecture for polynomials with coefficients in semidomains (i.e., subsemirings of an integral domain).