Cube plots

Three-factor two-level factorial designs like that shown in Figure 14.2 can be shown on the printed page as cube plots ... 

Table 14.2 gives a traditional tabular presentation of the information in this cube plot. This type of table is often used before and during the experiments - it provides instructions on how the experiments should be carried out, and provides a column where the responses can be recorded. 

The cube plots for this experiment confirm the mathematical results. In the diagram... 

It is possible to selectively choose a subset of 4 of the original 8 factor combinations and use these to fit the reduced model with 100% efficiency. The resulting design is called a fractional factorial design . A full 2 factorial design has two half-replicates as shown in Figures 14.4 and 14.5, or in cube plot form as ... 

Calculate the grand average (MEAN), the three classical main effects (A, B, and C), the three two-factor interactions (AB, AC, and AD), and the single three-factor interaction (ABC) for the 2 full factorial design shown in the cube plot in Section 14.1. (Assume coded factor levels of -1 and +1). 

The results obtained are shown in Fig. 1 as a cube-plot representation. The zeolite FAU was obtained only in four runs and in the case of the three central points (yield 0.4/0.43/0.45 not presented in the figure). 

Figure 2. Cube-plot representation of experimental results for the second set of experiments.

Fig. 2. Parameter plot for NaZn13, showing the line corresponding to a regular icosahedron, the point corresponding to a regular snub cube, and the parameters actually obtained in the previous and present investigations.

In Fig. 2 conditions (11) and (12) are plotted on a parameter map together with the parameter values reported for NaZn13 by Zintl Hauke, those reported for KCd13 by Ketelaar, and those determined for NaZn13 in the present investigation. The uncertainties are indicated by the radii of circles drawn around the points determined by the parameter values since Zintl Hauke reported no uncertainty value, the uncertainty reported by Ketelaar (0-003) was assumed. It is seen that the parameter values obtained in the present work lie between those of Zintl Hauke and those of Ketelaar, and that they differ considerably from the values required either by a regular icosahedron or by a regular snub cube. 

Figure A. Relative luminescence flux versus the cube of the radius for Tb - and Eu -doped microspheres. Similar plots are obtained for (U02) - and Mn -doped microspheres.

Figure 8. Rate of carbon monoxide oxidation on calcined Pt cube monolayer as a function of temperature [27]. The square root of the SFG intensity as a function of time was fit with a first-order decay function to determine the rate of CO oxidation. Inset is an Arrhenius plot for the determination of the apparent activation energy by both SFG and gas chromatography. Reaction conditions were preadsorbed and 76 Torr O2 (flowing). (Reprinted from Ref. [27], 2006, with permission from American Chemical Society.)...

At the critical time, there is a change in slope in the cube root law plot [37,39]. 

For small amounts of powder, dissolution of the particulate material can often be assessed (and compared with that of other compounds) by placing the powder in a calorimeter [68] and measuring the heat evolved as a function of time. The surface area must be assessed microscopically (or by image analyzer), and the data must be plotted by a cube root equation [39] ... 

A more direct link with molecular volumes holds for alkali halides, because the lattice energy (IT) is inversely proportional to interatomic distance or the cube root of molecular volume (MV). The latter has been approximated by a logarithmic function which gives a superior data fit. Plots of AH against log(MV) are linear for alkali halides 37a). Presumably, U and AH can be equated because AH M, ) is a constant in a series, and AH (halide )) is approximately constant when the anion is referred to the dihalogen as the standard state. 

Fig. 7.18 The radiative recombination time r as a function of the blue shift of the photon energy AE from the bulk silicon band edge zero-phonon transitions (dots) TO phonon-assisted transitions (line). This scatter plot shows the radiative time for each member of an ensemble uniformly distributed around a cubic geometry. The top scale indicates the equivalent cube size. Redrawn from [Hy2],...

Equation (19.19) is consistent with the empirical observation that a nonzero initial slope is obtained when the activity of a ternary electrolyte such as BaCl2 is plotted against the cube of m2/m°). As the activity in the standard state is equal to 1, by definition, the standard state of a ternary electrolyte is that hypothetical state of unit molality ratio with an activity one-fourth of the activity obtained by extrapolation of dilute solution behavior to m2/m° equal to 1, as shown in Eigure 19.4. 

The soil in the chinampa was prepared in the traditional way of peasants at Xochimilco, by making a seed bed with mud from the bottom of the channels that surround the chinampa. When the mud was dry, it was cut in small cubes where the seeds were planted. The seedbed was then covered with soil and twigs. Once the seedlings reached 10-15 cm they were transplanted to a plot previously weeded and plowed. Treatments were placed randomly and covered with mud. These were 1. control (without fertilizer) 2. inorganic fertilizer (10 10 15), 250 g/m ... 

Instead, optical measurement was applied to clarify the formation mechanism of Agl nanoparticles in diluted suspensions. Figure 4.4.10A shows the absorption spectra of the 1-day aged suspension containing 3.33 X 10-4 M Ag+ and 6.67 X 10-4 M I- as a function of RSH concentration. When the content of RSH increased from 0 to 6.67 X I0-3 M (curves a-d), the absorption spectra of Agl particles blue-shifted, suggesting the quantum size effect. The relationship between the particle diameter, d (A), and the concentration of RSH, c (A/), was plotted in the inset, which shows the double-logarithmic linear line of d versus c. The aggregation number is found to be proportional to the cube of the size. The same relationship was reported on the formation of CdS nanoparticles (37). These correlations indicate that Agl and CdS have the same ionic nature and have the same reaction modules of thiols. 

Plot the ratio of a -dimensional hypersphere s volume to the -dimensional cube s volume that encloses the hypersphere. Plot this as a function of k. (Note that a box with an two-inch-long edge will contain a ball of radius one inch. Therefore, for this case, the box s hypervolume is simply iK) Here s a hint It turns out that an -dimensional ball fits better in an w-dimensional cube than an -cube fits in an -ball, if and only if n is eight or less. In nine-space (or higher) the volume ratio of an -ball to an -cube is smaller than the ratio of an -cube to an -ball. 

Figure 5 The value of //r is plotted against the cube root of rotation rate, showing a linear relationship.

Figure 3.12. Inelastic scattering of Ar from Pt(lll) at the various input energies listed in the figure and for an initial angle of incidence 0, = 45° and Ts = 800 K. Results are plotted as EfIE vs. the final scattered angle . Points are the experimental results and the lines marked adjacently in the label are results of molecular dynamics simulations on an empirical PES. The long dot-dashed curve is the prediction of a cube model of energy transfer, while the dashed curve is the prediction from hard sphere scattering. From Ref. [135].

Fig. 5.10 Plot of (Tq versus a 3 = N0—NAf the reciprocal of the cube of distance between occupied donors, in InP and InSb (Biskupski 1982),...

Figure 14.8 The 7-plot for a material with a Wulff shape corresponding to a cube...

For relatively large Lewis numbers and with appropriate feedback, we observe that convergence to the system s unique stable steady state is quite swift and straightforward from any initial value. To illustrate, we now plot the 3D trajectories that emanate from the eight corners of the (xa, xi>, y) unit cube... 

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