Iterative cyclic approaches

Another type of carbohydrate complex is the cyclic ester formed between a glycitol and a polyanion such as borate or molybdate (4). The possible species present at equilibrium have not previously been evaluated by iteration. The system mannitol-borate has been so analyzed, and it was possible to use the same approach as that for the metal chelates. 

In former editions of this expert report, I have used the equations determined in chapter 6.7.4. to calculate the relative saturation of masonry cyclically exposed to hydrogen cyanide. However, after using several approaches on exactly how to do it, which lead to sometimes quite different results,482 1 decided to refer to this equation only in order to establish the time it takes for masonry to reach its maximum saturation or a quasi-constant concentration (20 days and 20 daily cycles, respectively). In this edition, the quasi-stationary concentration in masonry were calculated iteratively using Fick s law of diffusion 483... 

Sulfone diene (277) was employed in an interesting approach towards linear chains of l,2 4,5-fused cyclohexa-1,4-diene rings, both linear and cyclic (beltenes) [1]. A Diels-Alder reaction between sulfone (277) and benzoquinone provided sulfolene (278), which is potentially poised for addition of another sulfone diene, followed by desulfurization to reveal a bifunctional diene. Unfortunately, the bifunctional approach has not proved fruitful so far, but (278) has been extended by an iterative, linear procedure to provide linear fused systems such as (280) (Scheme 6.80). 

Fig. 11. The three limit cycles found for the cyclic attractors in Fig. 10, by numerically integrating the piecewise linear equation for each cyclic attractor with all thresholds equal to 0.5. Only the values at the thresholds were computed. The concentration of each chemical at each iteration for one cycle are shown. Tlie cycles appear to be stable so that all points in any of the eight volumes on each of the cycles approach the cycle.

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