Homogeneous catalysis Homogeneous catalysis In chemistry, homogeneous catalysis is catalysis in a solution by a soluble catalyst. Homogeneous catalysis refers to catalytic reactions where the catalyst is in the same phase as the reactants. Homogeneous catalysis applies to reactions in the gas phase and even in solids. Heterogeneous catalysis is the alternative to homogeneous catalysis, where the catalysis occurs at the interface of two phases, typically gas-solid. The term is used almost exclusively to describe solutions and often implies catalysis by organometallic compounds. The area is one of intense research and many practical applications, e.g., the production of acetic acid. Enzymes are
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