Cross-product array

As has been noted in this chapter, any restriction on the randomization of the experiment will lead the investigator to conduct one of the split-plot designs that were described in Section 2.4. In that section it was shown that the split-plot type designs can be a more efficient way to run robust design experiments than the cross-product arrays of Taguchi. Furthermore, the standard methods of analysis of split-plot experiments, that seek to... 

AN EXAMPLE OF A CROSS-PRODUCT ARRAY FACTORS A, B AND C FORM THE CONTROL ARRAY (AN L4), FACTORS X, Y AND Z FORM THE (ROTATED) NOISE ARRAY (ALSO AN L4). EACH OF THE ARRAYS HAS SETTINGS I - IV. NUMBERS 15 THROUGH 22 ARE FICTIVE RESPONSE VALUES... 

One of the rationales for the noise arrays and cross-product designs advocated by Taguchi and discussed in Section 2.1 is to deliberately... 

From these two orthogonal arrays a cross-product design is constructed (see Table 4.2 for an example), for each setting of the control factors in the inner array the complete noise factor (outer) array has to be executed to determine the effect of the environmental factors. 

Figure 11.7 shows a diagram of the process in which the format of the data is assembled and the resulting information is obtained. The pure component data matrix is a two-dimensional structure in which the pure array response patterns in each dimension are resolved. The resolution of the original matrix is based on the fact that this matrix is a cross-product of two vectors (the two arrays). 

On comparison with similar factors for period 2 hydrides, periodic scaling with respect to F is seen to be such that the cross products between these factors as they appear, moving towards C and I, respectively, are simple multiples of 3, as in the following array ... 

Palmisano and Santagostino first reported Stille reactions of indole-ring stannylindoles with their detailed studies of 1V-SEM stannane 159 [170], Thus 159, which is readily prepared by C-2 lithiation of A-SEM indole and quenching with Bu3SnCl (88%), couples under optimized Pd(0)-catalyzed conditions to give an array of cross-coupled products 160. Some other examples and... 

Cross-reactive sensing arrays were developed to detect odors and vapors in an artificial nose manner. Solvatochromic dyes such as Nile Red are adsorbed on the surface or embedded into various polymeric or porous silica beads. The beads respond to analyte vapor by a change in fluorescence maxima or/and intensity due to changes of polarity inside the bead. A portable instrument and preliminary field test for the detection of petroleum products was recently described [106]. 

Wire mini-grid OTEs. A mini-grid" is constructed with an array (or mesh ) of microscopically thin wires criss-crossing the face of a sheet of glass, silica or quartz. The wires are themselves too thin to see, but as soon as product is formed, it diffuses away from the wire. Since diffusion is entropy-driven (i.e. random), electrogenerated material does not diffuse in straight lines, but moves in all directions at once. In practice, as soon as material is formed, it is seen between the wires, and hence can be detected by the light beam of a spectrometer. 

Fig. 8. Generation of the form of the helical diffraction pattern. (A) shows that a continuous helical wire can be considered as a convolution of one turn of the helix and a set of points (actually three-dimensional delta-functions) aligned along the helix axis and separated axially by the pitch P. (B) shows that a discontinuous helix (i.e., a helical array of subunits) can be thought of as a product of the continuous helix in (A) and a set of horizontal density planes spaced h apart, where h is the subunit axial translation as in Fig. 7. This discontinuous set of points can then be convoluted with an atom (or a more complicated motif) to give a helical polymer. (C)-(F) represent helical objects and their computed diffraction patterns. (C) is half a turn of a helical wire. Its transform is a cross of intensity (high intensity is shown as white). (D) A full turn gives a similar cross with some substructure. A continuous helical wire has the transform of a complete helical turn, multiplied by the transform of the array of points in the middle of (A), namely, a set of planes of intensity a distance n/P apart (see Fig. 7). This means that in the transform in (E) the helix cross in (D) is only seen on the intensity planes, which are n/P apart. (F) shows the effect of making the helix in (E) discontinuous. The broken helix cross in (E) is now convoluted with the transform of the set of planes in (B), which are h apart. This transform is a set of points along the meridian of the diffraction pattern and separated by m/h. The resulting transform in (F) is therefore a series of helix crosses as in (E) but placed with their centers at the positions m/h from the pattern center. (Transforms calculated using MusLabel or FIELIX.)...

In an analogous approach, a second library of sulfonamides was prepared. N-Boc protected sulfonamides (11) were ionized by a column of PS-TBD heated to 80 °C, and the alkylation was performed as before the exit stream passed onto a column of PS-SO3H heated to 85 °C, which deprotected the Boc group and afforded the secondary sulfonamide products (Scheme 4.54). This method was applied to the synthesis of two collections of compounds, a 24-membered array and the second comprising a 48-compound set, in both high purities and yields. No cross-contamination was... 

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