Convergent Procedures

The determination of the steam density, pj, therefore requires the simultaneous solution of two algebraic equations. This represents an IMPLICIT algebraic loop and cannot be solved within a simulation program without the incorporation of a trial and error convergence procedure. 

The method starts with an assumption of the column temperature and flow profiles. The stage equations are then solved to determine the stage component compositions and the results used to revise the temperature profiles for subsequent trial calculations. Efficient convergence procedures have been developed for the Thiele-Geddes method. The so-called theta method , described by Lyster et al. (1959) and Holland (1963), is recommended. The Thiele-Geddes method can be used for the solution of complex distillation problems,... 

Following the convergent procedure, dendrimers of type 58,59 and 60 have been prepared from the chiral core triol 54 and achiral Frechet-type [62] ben-zylic branch bromides. In the series of dendrimers with aromatic spacers (60) and without spacers (58), the optical activity [a]D decreased on going from the 1st (not shown in Fig. 21) to the 2nd generation, whereas with aliphatic spacers... 

Warga, J., 1963, A convergent procedure for solving the thermo-chemical equilibrium problem. Journal Society Industrial and Applied Mathematicians 11, 594-606. 

Japonilure R), the sex pheromone of the female Japanese beetle. Papilla japonica and its enantiomer, (5)-(+)-(5Z )-tetradecen-4-olide, which is the pheromone of the Osaka beetle, Anomala osakana have been synthesized using a highly convergent procedure and in satisfactory overall yields. 

This is a dramatic increase in the average polymer growth considering that for a 1 — 2 branching pattern and using a convergent procedure, the degree of polymerization follows Equation (5.2). 

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