On the inverse problem of generalised compartmental systems

A necessary and sufficient condition has been given for the existence of an inducing generalised compartmental system to the system of differential equations (4.23). However, certain generalised compartmental systems (and differential equations) are to be considered as identical, as they are essentially not different. This will be done below and thus a problem of the type (3) formulated in Subsection 4.7.1.2 will be solved here. 

obviously equals the number of zero column vectors of the matrix K, R2 equals the number of positive elements in the zeroth row of the matrix K, while R3 equals the number of positive elements in the zeroth column of the matrix K. 

Let us consider the following strictly open generalised compartmental 

The core of a generalised compartmental system is obtained through substituting all first-order endpoints by the zero complex. Thus the core of our example is  

The core of a system of differential equations of the form (4.23) is the differential equation where the variables having the same index as the zero column vectors of the matrix (a,y) have been deleted. The induced kinetic differential equation of our generalised compartmental system is  

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