  The main result of this paper is: Given any constant C, there is
$(\epsilon,k,L)$ such that if a complete, orientable, noncompact
odd-dimensional manifold with bounded positive sectional curvature contains a
$(\epsilon,k,L)$-neck, then the asymptotic scalar curvature ratio is bigger or
equal to C. As a application we proved that the asymptotic scalar curvature
ratio of a complete noncompact ancient Type I-like solution to the Ricci flow
with bounded positive sectional curvature on an orientable 3-manifold, is
infinity.
