On closed almost complex four manifolds

In this paper, by using weakly \widetilde{$\mathcal{D}$}^+_J (resp. $\mathcal{D}$^+_J )-closed technique firstly introduced by Tan, Wang, Zhou and Zhu, we will give a characterization of tamed and weakened tamed four-manifolds, and an almost Kaehler version of Nakai-Moishezon criterion for almost complex four-manifolds.