To formulate the principle of semi-detailed balance, it is convenient to count the direct and inverse elementary reactions separately. In this case, the kinetic equations have the form: d N i d t = V ∑ ∑ r γ γ r i w r = V ∑ ∑ r ( β β r i − − α α r i ) w r Let us use the notations α α r = α α r i , β β r = β β r i for the input and the output vectors of the stoichiometric coefficients of the r th elementary reaction. Let Y be the set of all these vectors α α r , β β r .