the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

The C-C bond formation is an important reaction in organic synthesis to obtain value-added intermediates. Therefore, in this paper an attempt has been made to accelerate the Henry reaction (C-C bond formation) between aryl aldehydes and nitromethane using less expensive whole cell biocatalyst, baker’s yeast (BY). The scope of the methodology was also tested for the heteryl aldehyde i.e. 2-chlor...

The C-C bond formation is an important reaction in organic synthesis to obtain value-added intermediates. Therefore, in this paper an attempt has been made to accelerate the Henry reaction (C-C bond formation) between aryl aldehydes and nitromethane using less expensive whole cell biocatalyst, baker’s yeast (BY). The scope of the methodology was also tested for the heteryl aldehyde i.e. 2-chlor...