Optimizing Designs-II

The foregoing results illustrate four simple, practical applications of Second-Law costing methods (i) costing, (ii) optimal design, (iii) preliminary design, and (iv) operation and mainte-... 

Araujo P. W. Brereton R. G., Experimental design II. Optimization, Trends Anal. Chem. 1996,15, 63-77... 

Substrate specificity is also controlled by the oxidizing power of compounds I and II. Using a series of substituted aromatic amines and phenols, Dunford and co-workers have shown that the rate constants for the reduction of HRP compounds I and II by these substrates increased with the electron-donating power of the substituents (131-133). Correlation of the rate constants with Hammett cr parameters, rather than a- parameters, revealed concerted electron and proton transfer from the substrate in the rate-determining step. A similar study showed that CCP is a much less efficient oxidant of aromatic substrates than HRP, and the rate constants are better correlated with a than with cr, indicating the development of positive charge on the substrate in the transition state (134). Hence, it appears that the heme cavity of CCP, unlike that of HRP, is not optimally designed to promote rapid oxidation of small aromatic substrates. 

The advantages of using D-optimal designs instead of fractional factorial designs in principal properties can be summarized as follows. It is possible to (i) reduce the number of required structures (ii) exclude molecules too difficult to synthesize (iii) include molecules already available or tested and (iv) reduce polysubstitution even controlling several sites. 

I. S. Dubova and V. V. Federov, Tables of optimum designs II (Saturated D-optimal designs on a cube). Preprint n° 40, issued by Interfaculty Laboratory of Statistical Methods, Moscow University. 

We have shown the principle of the exchange algorithm in paragraph II.D, for a fixed number of experiments. The next question to be answered is how do we decide on the number of experiments Subject to possible external constraints, this depends on the statistical properties of the design. We demonstrate this by determining D-optimal designs for different values of N, in the above process study, and examine trends in their properties. 

Comparison of the different designs at II and 12 experiments Table 8.1 shows the characteristics of the different designs constructed. The D-optimal design for 11 factors is not given, as it is identical to the Rechtschaffner design (which is thus D-optimal). 

An adsorption isotherm depicts the relation between the quantity adsorbed (as defined in Section II.A) and the bulk phase pressure (or density) at equilibrium for a constant temperature. It is a dataset of specified adsorption equilibrimn. Such equilibrium data are required for optimal design of processes relying on adsorption and are considered ftmdamental information for theoretical studies. Adsorption isotherms can be obtained either experimentally or by molecular simulation on computers. However, it shordd be noted that only the excess adsorption can be... 

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