attempts have been made to study the thermodynamic behavior of 1,3 butadiene purification columns with the aim of retrofitting those columns to more energy efficient separation schemes. 1,3 butadiene is purified in two columns in series through being separated from methyl acetylene and 1,2 butadiene in the first and second column respectively. comparisons have been made among different therm...

in this thesis we will present three topics. we define approximate fixed points in fuzzy normed spaces. also we obtain some necessary and sufficient conditions on the existence of? -fixed points for ? > 0. at the continue some results about approximate fixed points for a class of non-expansive maps on g-metric spaces are obtained and we define approximate fixed points in partial metric spa...

introduction acetic acid bacteria are large group of obligate aerobic gram negative bacteria with the ability to oxidize ethanol to acetic acid (1). they are widely distributed in natural habitats and classified in family acetobacteraceae. members of this family are useful in industrial production of vinegar(2). acetic acid bacteria (aab) can use substrates as glucose, ethanol, lactate or glyc...