Formal lumping procedures

In mathematical terms lumping can be described as the reduction of the n-dimensional system described in equation (4.1) to an n-dimensional lumped set. 

What degree of lumping can be achieved while maintaining the accuracy of the reduced scheme, i.e., how small can the lower dimensional space be  

What is the optimal way of choosing lumping functions which give the smallest reduced model for any general system of equations and still satisfactorily represents the behaviour of the full scheme  

So far, the main aims of research into lumping have been to try and find mathematical procedures which apply to any general reaction system, and provide an automatic algorithm for reduction. It is not clear yet whether or not such a technique will ever exist which can be applied for any mechanism. Certainly if a method is to be developed it will have to be founded on rigorous mathematical principles. Quite a large amount of 

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The question of efficient techniques for performing these lumping analyses are a subject of current research. The successful applications to date, as above, have been based on heuristic reasoning, and more formal procedures are not available. Basic theoretical results for monomolecular reaction systems have been provided by Wei and Kuo [22] and Ozawa [23], and important other features are given by Luss et al. [24] (and other references provided there). 

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