Non-linear reversible reactions with all aj

A procedure for determination of the transition probabilities is demonstrated by a detailed treatment of the following non-linear irreversible reactions  

1st step Transformation of Eqs.(3-ll) into the following set of irreversible reactions which best demonstrate the transition between the states  

2nd step Determination of the reaction rates for Eqs.(3-13) on the basis of Eqs.(3-12). The definition in Eq.(3-2) yields for species j = 1 reacting in the first reaction, i = 1, that  

3rd step Determination of the probabilities pjj. Applying Eqs.(3-6) and (3-14a) yields for species j = 1 where i = 1 that  

4th step Determination of the probabilities pjk- As observed in the reactions given by Eqs.(3-13)  

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