Partially ordered sets in the analysis of alkanes fate in rivers

Dominance degree is introduced as a mathematical procedure to quantify the order relations between a pair of subsets contained in a partially ordered set obtained from the features of its elements. Dominance degree summarizes the partial order relations of the members of two subsets. If a member of one subset follows an order relation to a member of another subset, then the dominance degree informs how far this relation can be transferred to all elements of the two subsets. Dominance degree was applied to the study of 35 acyclic alkanes (from C5H12 to C8H,8)in two river-scenarios: hilly regions and lowland rivers. Each chemical was defined by three fate descriptors estimated by applying the module EXWAT from the E4CHEM package. It was found that CnH2n+2 dominates CmH2m+2 if n > m, which means that when considering the fate descriptors simultaneously, those of CnH2n+2 are higher than those of CmH2m+2. Finally, some particular results were found for the linear isomer of each subset.