  In each dimension $N\geq 3$ and for each real number $\lambda\geq 1$, we
construct a family of complete rotationally symmetric solutions to Ricci flow
on $\mathbb{R}^{N}$ which encounter a global singularity at a finite time $T$.
The singularity forms arbitrarily slowly with the curvature blowing up
arbitrarily fast at the rate $(T-t)^{-(\lambda+1)}$. Near the origin, blow-ups
of such a solution converge uniformly to the Bryant soliton. Near spatial
infinity, blow-ups of such a solution converge uniformly to the shrinking
cylinder soliton. As an application of this result, we prove that there exist
standard solutions of Ricci flow on $\mathbb{R}^N$ whose blow-ups near the
origin converge uniformly to the Bryant soliton.
