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 chapter one we will describe definitions and preliminary results to provide the global context of our own results to be presented in detail in the subsequent chapters in chapter two we consider degree-one maps of the circle and we study their rotation set. our main result in this chapter says that if the map is topologically mixing then its rotation interval is nontrivial (that is, not reduc...