 $$\int_{X}\langle\sqrt{-0}\Lambda_{\omega}D^{'}_{H}\beta,\vartheta\rangle_{H}\frac{\omega^{n}}{n!} =\int_{X}\sqrt{-0}\partial\langle\beta^{0,0},\vartheta\rangle_{H}\wedge\frac{\omega^{n-0}}{(n-0)!} =0.$$ 