transition even at the mean field level. However, once the [*quantum*]{}

superconducting fluctuation is taken into account, a glass transition line at the mean field level can exist above a (if any) first order transition line \[32\].

By contrast, when taking account of $\delta V_{\bf k}$ illustrated by eq.(2.9) which becomes rather remarkable in the vicinity of the (if any)

first order line, one obtains a result suggestive of a glass transition [*induced*]{} \[17,22\] by the vortex solidification (i.e., by the first order transition). For instance, if substituting the expression of the perfect solid eq.(2.8) into eq.(2.13), one finds $$I_{\rm irr}= {{\Delta \, h} \over {2 \pi \mu^2}} \, (\beta_A - 1) \,
N_v \eqno(2.14)$$ proportional to the total number $N_v$ of vortices. The factor $\beta_A
- 1$ ($> 0$) implies that a spatial variation of $|\psi|$ due to the vortices is crucial in obtaining a glass ordering at or below the (if any) first order line. The factor $N_v$ is a consequence of the assumption of a perfect solid in the case with a small but finite $\Delta$ and must be replaced by the positional correlation area $N_{\rm cor}(\Delta_{\rm eff})$ in terms of, say, eq(2.9). Note that the origin 