Difference equations stability behaviour

The curve obtained from these equations is shown in fig. 6 together with that obtained for semiregenerative Pt-Re/Al203 CR catalysts. It is clear the difference in deactivation behaviour for both catalysts. Pt-Sn catalysts show a monotonic decrease in activity, whereas Pt-Re catalysts have a fast initial deactivation but then it stabilizes out from around 11 to 45 Blls/lbcat (aproximately 50 to 200 days) followed by a slow deactivation process. 

The consideration of the heat transfer condition (2.253) detonates the stability behaviour of the explicit difference formula. As the coefficients of the explicit difference equations (2.256) and (2.258) must be positive in order to guarantee stability, we obtain the stability condition... 

Stability relates to the behaviour of a system when it is subjected to a small perturbation away from a given stationary state (or if fluctuations occur naturally). If the perturbation decays to zero, the system has some in-built tendency to return back to the same state. In this case it is described as locally stable. (The qualification local means that very large perturbations may have different consequences.) We will introduce the relatively simple mathematical techniques required to determine this local stability of a given state in Chapter 3. It will also be useful before then to reduce the reaction rate equations (2.1)—(2.3) to their simplest possible form by introducing dimensionless variables and quantities. 

CR represent different conformations of the crown ether. T1+ is closer to Ag+ than to K+ or Rb+ in its behaviour. In studies of the aquation of [RhCl,] " by Hg +, Tl +, Cd +, and In + and of the equation of [RhBre] " by Tl + there is a general correlation between the rate and the stability constant of the monohalogeno-complex of the catalytic cation. The decomposition of [MeTl(OAc)2] to TlOAc and MeCOaOMe has been studied in a variety of solvents. Usually simple first-order kinetics are observed, but in deuteuriochloroform and in THE there is an initial induction period in which the solution becomes saturated with TlOAc. The authors propose a rate-determining 5n2 reaction of [AcO] with the methyl group bonded to thallium. 

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