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
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