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.
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  , PM6 3 , or PPM5 15 , et al.