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
Quasi-homogeneous polynomial Quasi-homogeneous polynomial In algebra, a multivariate polynomial is quasi-homogeneous or weighted homogeneous, if there exist "r" integers formula_2, called weights of the variables, such that the sum formula_3 is the same for all nonzero terms of "f". This sum "w" is the "weight" or the "degree" of the polynomial. The term "quasi-homogeneous" comes from the fact that a polynomial "f" is quasi-homogeneous if and only if for every formula_5 in any field containing the coefficients. A polynomial formula_6 is quasi-homogeneous with weights formula_2 if and only if is a homogeneous polynomial in the formula_9. In particular, a homogeneous polynomial is