Homogeneous catalysis heterogeneous catalysis is the petrochemical alkylation process, where the liquid reactants are immiscible with a solution containing the catalyst. Heterogeneous catalysis offers the advantage that products are readily separated from the catalyst, and heterogeneous catalysts are often more stable and degrade much slower than homogeneous catalysts. However, heterogeneous catalysts are difficult to study, so their reaction mechanisms are often unknown. Enzymes possess properties of both homogeneous and heterogeneous catalysts. As such, they are usually regarded as a third, separate category of catalyst. Homogeneous catalysis In chemistry, homogeneous catalysis is catalysis in a solution by a soluble catalyst. Homogeneous catalysis refers
Fair division of a single homogeneous resource Fair division of a single homogeneous resource Fair division of a single homogeneous resource is one of the simplest settings in fair division problems. There is a single resource that should be divided between several people. The challenge is that each person derives a different utility from each amount of the resource. Hence, there are several conflicting principles for deciding how the resource should be divided. A primary conflict is between efficiency and equality. Efficiency is represented by the "utilitarian" rule, which maximizes the sum of utilities; equality is represented by the "egalitarian" rule, which maximizes the minimum utility. In