matrices have the same eigenvalues. Reversed, the matrix Z
which can be obtained spectroscopically leads to the eigen-
values of the Jacobian matrix which are searched for in
general.
mally controlled reaction systems (as well as of quasi-linear
photoreactions).
This work was kindly supported by the Deutsche Forschungs-
gemeinschaft (DFG, Bonn, Germany; project Po222/8-1). We
thank Dr. Ganzle, Institute of Technical Microbiology of the
Technical University Munchen (Freising-Weihenstephan,
Germany), for the construction of Figs. 1(a), 1(b), 3(a) and 3(b).
We thank Dipl. mat. Schleip (Lehrstuhl fur Fluidmechanik
und Prozeautomation, TU Munchen) for helpful discussions.
According to theorem 2 given in refs. 1 and 41 two strictly
linear reaction systems whose Jacobian matrices have the
same rank can not be distinguished from each other by purely
spectroscopic means. And according to theorem 31,41 ther-
mally controlled reaction systems that consist of s linearly
independent reaction stepsÈone step of which is at least a
reaction of second orderÈcan not be distinguished from each
other by purely spectroscopic means if their eigenvalues have
the same functional dependence on the initial concentrations.
Because of these two theorems evaluation of the n-
dimensional Mauser space using the method described here is
generally applicable to cases s \ 1 and s \ 2 for linear and
non-linear reaction systems. Thus, for example, the following
systems can be evaluated here,
References
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2
3
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7
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A ¢ B
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The characteristic equations developed here are also true for
these systems (compare eqns. (17a), (18a), (22a), (22b), (23a)
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Kinetic evaluation of Scheme 3 represents a procedure
which is applicable to many linear reactions such as, for
example, A ] B ] C (s \ 2). As well, system (7a) and (7b) is
representative of about 100 mechanisms including second
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Comparison of efficiency between the formal integration
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obtained earlier by formal integration. As shown here, the
results can even be improved when the n-dimensional Mauser
space is used in combination with formal integration. The cri-
teria for selecting appropriate wavelengths to establish the
Mauser space are essentially the same as those for the con-
struction of the Mauser diagrams.1,2
In the special case of linear reactions, a reduction of the
system is possible on the basis of the concept of parallel pro-
jection (s \ 2 ] s \ 1,5 s \ 3 ] s \ 2 ] s \ 14). The concept
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reaction systems with poor spectroscopic properties may be
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space with the concept of parallel projection.
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6
Conclusions
Mauser space is a powerful tool in the kinetic analysis of ther-
Phys. Chem. Chem. Phys., 2001, 3, 993È999
999