Feasible point, selection

Therefore, after defining the model, the number of experiments one is willing to perform is selected, e.g. eight (the minimal number for Eq. (6.2) is six). The D-optimal design is the one that for all possible combinations of eight experiments from the total number of feasible points (grid points) yields a maximal value of the determinant of the matrix X, with... 

A single feasible point is selected initially and the corresponding objective function, I, is evaluated. A new point is then generated randomly. The objective function is evaluated at the new point again. The change in the objective function, A/ (= - fid), is computed. For a... 

The solution of the system (10.17) allows the search direction d (depending on the selected vector h) to be calculated. By using this direction, it is possible to obtain both a new feasible point and the new inequality constraint (passive or satisfied)... 

Initial attempts at developing precipitation titration methods were limited by a poor end point signal. Finding the end point by looking for the first addition of titrant that does not yield additional precipitate is cumbersome at best. The feasibility of precipitation titrimetry improved with the development of visual indicators and potentiometric ion-selective electrodes. 

Potcntiomctric Titrations In Chapter 9 we noted that one method for determining the equivalence point of an acid-base titration is to follow the change in pH with a pH electrode. The potentiometric determination of equivalence points is feasible for acid-base, complexation, redox, and precipitation titrations, as well as for titrations in aqueous and nonaqueous solvents. Acid-base, complexation, and precipitation potentiometric titrations are usually monitored with an ion-selective electrode that is selective for the analyte, although an electrode that is selective for the titrant or a reaction product also can be used. A redox electrode, such as a Pt wire, and a reference electrode are used for potentiometric redox titrations. More details about potentiometric titrations are found in Chapter 9. 

The majority of successful processes are those in which the entrainer and one of the components separate into two Hquid phases on cooling if direct recovery by distillation is not feasible. A further restriction in the selection of an azeotropic entrainer is that the boiling point of the entrainer is 10—40°C below that of the components. 

Feasibility Analysis Phase The point in a pollution prevention program at which waste reduction options are evaluated technically, economically and environmentally. The results are used to select options to be recommended for implementation. 

For comparison purposes we first determine the best grid point in the operability region using the same final time and constant sampling rate for all feasible experiments. In Table 1 the best experimental conditions are shown chosen by the volume criterion when as final time 20. 40 or 80 h is used. A total of 20 data points is used in all experiments. As seen, the selected conditions depend on our choice of the final time. 

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