Before revision: Next , we propose the  implementation of obtaining the new mappings satisfying the OP criterion from those of the existing mapped WENO-X schemes  where the notation "X" is used to identify the version of the existing mapped WENO scheme , e. g., X = M 11 , PM6 3 , or PPM5 15 , et al. Then we build the resultant mapped WENO schemes and denote them as MOP-WENO-X .
After revision: Next , we propose the implementation of obtaining the new mappings satisfying the OP criterion from those of the existing mapped WENO-X schemes where the notation "X" is used to identify the version of the existing mapped WENO scheme , e. g., X = M 11 , PM6 3 , or PPM5 15 . Finally, extensive numerical experiments and comparisons with competing schemes are conducted to demonstrate the enhanced performances of the MOP-WENO-X .