The study of the complexity of logical problems has provided a very fruitful field of research since many decades. On the one hand researchers have tried to classify exactly in terms of complexity classes and upper and lower bounds the complexity of decision and other logical problems. Although in general such problems are of high complexity, efforts have been made to develop efficient algorith...

A framework for modelling memory consistency is presented. The framework is used to specify the operation of a total-store-order write buffer multiprocessor machine. The framework is used again to specify a more abstract “programmer-centric” model that does not refer to the write-buffer architecture. Finally, we prove that the abstract model correctly captures the computations of the operationa...

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...