  We propose a family of one-dimensional mosaic models inlaid with a slowly
varying potential $V_n=\lambda\cos(\pi\alpha n^\nu)$, where $n$ is the lattice
site index and $0<\nu<1$. Combinating the asymptotic heuristic argument with
the theory of trace map of transfer matrix, mobility edges (MEs) and
pseudo-mobility edges (PMEs) in their energy spectra are solved
semi-analytically, where ME separates extended states from weakly localized
ones and PME separates weakly localized states from strongly localized ones.
The nature of eigenstates in extended, critical, weakly localized and strongly
localized is diagnosed by the local density of states, the Lyapunov exponent,
and the localization tensor. Numerical calculation results are in excellent
quantitative agreement with theoretical predictions.
