Networks first-order, general solution

It is necessary to repeat our study for nonlinear networks. We discuss this problem and perspective of its solution in the concluding Section 8. Here we again use the experience summarized in the lUPAC Compendium (Ratecontrolling step, 2007) where the notion of controlling step is generalized onto nonlinear elementary reaction by inclusion of some concentration into "pseudo-first-order rate constant". 

An elegant, general solution for first-order networks has been provided in a classic publication by Wei and Prater [22]. In essence, the mathematics are developed for a reaction system with any number of participants that are all connected with one another by direct first-order pathways. For example, in a system with five participants, each of these can undergo four reactions, for a total of twenty first-order steps. Matrix methods are used to obtain concentration histories in constant-volume batch reactions, and a procedure is described for determination of all rate coefficients from such batch... 

A brief overview of the Wei-Prater general mathematical solution for arbitrary networks consisting entirely of reversible first-order steps is provided. 

Complex kinetic schemes cannot be handled easily, and, in general, a multidimensional search problem must be solved, which can be difficult in practice. This general problem has been considered for first-order reaction networks by Wei and Prater [13] in their now-classical treatment. As described in Ex. 1.4-1, their method defines fictitious components, B , that are special linear combinations of the real ones, Aj, such that the rate equations for their decay are uncoupled, and have solutions ... 

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