Separator program limitations/notes

It should be noted that computer programs written to calculate y(x) = sinxfx will usually fail at the point x = 0. The computer will display a division by zero error message. The point x = 0 must be treated separately and die value of the limit (y = 1) inserted. However, intelligent programs such as Maihematica avoid this problem. 

Remark 1 Assumption (i) (i.e., Y C V) eliminates the possibility of step 3b, and there are many applications in which Y C V holds (e.g., variable factor programming). If, however, Y V, then we may need to solve step 3b infinitely many successive times. In such a case, to preserve finite e-convergence, we can modify the procedure so as to finitely truncate any excessively long sequence of successive executions of step 3b and return to step 3a with y equal to the extrapolated limit point which is assumed to belong to Y fl V. If we do not make the assumption Y C V, then the key property to seek is that V has a representation in terms of a finite collection of constraints because if this is the case then step 3b can occur at most a finite number of times. Note that if in addition to Cl, we have that A represents bounds on thex-variables otX is given by linear constraints, and h,g satisfy the separability condition, then V can be represented in terms of a finite collection of constraints. 

The recommendations given in the preceding sections are summarized in Table 33. It should be taken into consideration that in many cases the listed rate coefficient parameters give expressions that are valid only for a limited temperature range ( 1000-2500 K). It should also be noted that reverse reactions are listed separately for all cases where both directions may be important in combustion modeling. For computer programs that automatically take reverse reactions into account, only one of each pair should be included. Using both directions independently may lead to small numerical... 

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