  We construct a uniform local bound of curvature operator from local bounds of
Ricci curvature and injectivity radius among all $n$-dimensional Ricci flows.
Thus new compactness theorems for the Ricci flow and Ricci solitons are
derived. In particular, we show that every Ricci flow with $|Ric|\leq K$ must
satisfy $|Rm|\leq Ct^{-1}$ for all $t\in (0,T]$, where $C$ depends only on the
dimension $n$ and $T$ depends on $K$ and the injectivity radius $inj_{g(t)}$.
  In the second part of this paper, we discuss the behavior of Ricci curvature
and its derivative when the injectivity radius is thoroughly unknown. In
particular, another Shi-type estimate for Ricci curvature is derived when the
derivative of Ricci curvature is controlled by the derivative of scalar
curvature.
