Activated complex asymptotics

It can be seen from this equation that maximal constitutive activity need not reach a maximal asymptote of unity. Submaximal constitutive activity has been observed with some receptors with maximal receptor expression [28]. While there is scattered evidence that the cubic ternary complex is operative in some receptor systems, and while it is thermodynamically more complete, it also is heuristic... 

Traditionally, iron-based catalysts have been used for FT synthesis when the syngas is coal derived, because of their activity in both FTS and WGS reactions. Complex mixtures of straight-chain paraffins, olefins, and oxygenate (in substantial proportions) compounds are known to be formed during iron-based FTS. Olefin selectivity of iron catalysts is typically greater than 50% of the hydrocarbon products at low carbon numbers, and more than 60% of the produced olefins are a-olefins.13 For iron-based catalysts, the olefin selectivity decreases asymptotically with increasing carbon number. 

A schematic representation of receptor systems in terms of the cubic ternary complex model is shown in Figure 3.13. The amount of signaling species (as a fraction of total receptor) as defined by the cubic ternary complex model (see Section 3.13.8) is expressed as predicts that the constitutive activity of receptor systems can reach a maximal asymptote that is below the system maximum (partial constitutive activity). This is because the cubic ternary complex model predicts the maximal constitutive activity, as given by Equation 3.24 ... 

Figure 11. Kinetic energy release distribution for metastable loss of CH4 from nascent Co(C3Hg)+ collision complexes. The "unrestricted" phase space theory curve assumes the entrance channel contains only an orbiting transition state, the exit channel has only an orbiting transition state (no reverse activation barrier), and there are no intermediate tight transition states that affect the dynamics. The "restricted" phase space theory calculation includes a tight transition state for insertion into a C-H bond located 0.08 eV below the asymptotic energy of the reactants.

Every dynamic adaptronic system must be checked for stability in the case of disturbances. For linear elastic adaptronic structures, asymptotic stability as defined in Sect. 5.2.4 is guaranteed if the poles (or eigenvalues) of the closed-loop active system lie in the left complex half-plane, i.e. if they have negative real parts. More stringent stability criteria, such as the generalized Nyquist criterion [7], also consider the zeros of the adaptronic system. 

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