There are about 33, 6.5 and 1.0 pb$^{-1}$ of $e^+e^-$ annihilation data have been taken around the center-of-mass energies of $sqrt s=$ 3.773 GeV, at $sqrt s=$ 3.650 GeV and at $sqrt s=$ 3.6648 GeV, respectively, with the BES-II detector at the BEPC collider. By analyzing these data sets, we have measured the branching fraction for $psi(3770)to$ non-$Dbar D$ by several different methods; and have observed an anomalous line shape of $sigma^{e^+e^-to{rm hadrons}}$ in energy region from 3.65 to 3.87 GeV; and have measured the line shapes of the $D^+D^-$, $D^0bar D^0$ and $Dbar D$ production and together with the ratios of the production rates of $D^+D^-$ and $D^0bar D^0$ in $e^+e^-$ annihilation around the $psi(3770)$ resonance.
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