Axial points center point

This allocation of experiments has the effect of making the normalized uncertainty and normalized information contours more axially symmetric (the design isn t quite rotatable there are still only four mirror-image planes of reflection symmetry). However, because no experiments are now being carried out at the center point, the amount of uncertainty is greater there (and the amount of information is smaller there). The overall effect is to provide a normalized information surface that looks like a slightly square-shaped volcano. 

Three-Factor Central Composite Design with Axial Values a and Four Center Points... 

A five-level-five-factor CCRD was employed in this study, requiring 32 experiments (Cochran and Cox, 1992). The fractional factorial design consisted of 16 factorial points, 10 axial points (two axial points on the axis of each design variable at a distance of 2 from the design center), and 6 center points. The variables and their levels selected for the study of biodiesel synthesis were reaction time (4-20 h) temperature (25-65 °C) enzyme amount (10%-50% weight of canola oil, 0.1-0.5g) substrate molar ratio (2 1—5 1 methanol canola oil) and amount of added water (0-20%, by weight of canola oil). Table 9.5 shows the independent factors (X,), levels and experimental design coded and uncoded. Thirty-two runs were performed in a totally random order. 

Fig. 4 Central composite design for three factors. The factorial points are shaded, the axial points unshaded, and the center point(s) filled.

If a significant curvature is found, run the axial experiments and fit a quadratic model. Use the independent estimate of the experimental error from the replicated center point experiments to check the fit of model. 

Table 13 Axial Points with Center Point...

The 11-run design and resulting data are listed in Table 9. The first four runs are the imbedded 2 factorial points, the next four runs are the axial or star points, and the last three runs are the center points. The factor levels are listed in the actual units ( uncoded form) and in coded units. The value of a was set to 1 to minimize the number of factor levels required, instead of conducting a rotatable design... 

The central composite design (CCD) is based on the full quadratic polynomial. Hence it is composed of 2 factorial design, center points and 2k axial portion of design. 

There are two parameters in the design that must be specified the distance a of the axial runs from the design center and the number of center points. ... 

This design locates the star or axial points on the centers of the faces of the cube as shown in Figure A3. This variation of the central composite design requires only three levels of each factor, and in practice it is frequently difficult to change factor levels. 

The simulation values of correspond to a Kirkwood g factor equal to 2.7 again consistent %rith the general conclusion that centered point dipoles are not a good model for normal polar liquids. Brot et al have also examined the simulation consequences of assuming an off-center dipole at a distance r = 0.38 from the Lennard-Jones center and so approximately equivalent to a central dipole plus a central axial quadrupole. This results in a greatly reduced permittivity Cg > 11 1. With an approximate polarizability correction the permittivity of this model for CH p is about ten percent less than the experimental Cg = 22.5 at 206 K. 

Add an axial hydrogen atom to each carbon atom. The bonds to the axial hydrogen atoms point up when the carbon atom points upward, and down when the carbon atom points downward. They are parallel to an imaginary line that passes through the center of the cyclohexane ring. 

As we have indicated with our arrows, the mechanism of the uncatalyzed Cope rearrangement is a simple six-centered pericyclic process. Since the mechanism is so simple, it has been possible to study some rather subtle points, among them the question of whether the six-membered transition state is in the boat or the chair form. ° For the case of 3,4-dimethyl-l,5-hexadiene it was demonstrated conclusively that the transition state is in the chair form. This was shown by the stereospecific nature of the reaction The meso isomer gave the cis-trans product, while the ( ) compound gave the trans-trans diene. If the transition state is in the chair form (e.g., taking the meso isomer), one methyl must be axial and the other equatorial and the product must be the cis-trans alkene ... 

Although the number of actinides is the same as that of the lanthanides, their availability and chemical characteristics have so far largely restricted the study of their ligand substitution mechanisms to dioxouranium(VI), which is the ionic form of uranium most amenable to such studies in solution. In the solid state, the oxo ligands occupy axial sites above and below the U(VI) center, and four (328), five (329, 330), and six (331, 332) oxygen donor atoms have been reported to occupy equatorial positions. From a mechanistic point of view, this variability of the occupancy of the equatorial plane suggests the possibility of both d- and a-activated ligand substitution pro-... 

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