We have analyzed a five-level $wedge$-configuration Four-Wave Mixing (FWM) scheme for obtaining a high-efficiency FWM based on the two electromagnetically induced transparency. We find that the maximum FWM efficiency is nearly 30%, which is orders of
magnitude larger than previous schemes based on the two electromagnetically induced transparency. Our scheme may provide a new possibility for technological applications such as nonlinear spectroscopy at very low light intensity, quantum single-photon nonlinear optics and quantum information science.
In this paper, the problem of pattern avoidance in generalized non-crossing trees is studied. The generating functions for generalized non-crossing trees avoiding patterns of length one and two are obtained. Lagrange inversion formula is used to obta
in the explicit formulas for some special cases. Bijection is also established between generalized non-crossing trees with special pattern avoidance and the little Schr{o}der paths.
