Comparative Series

At this stage, the standard series for the variables is generated by determining the optimal level of all three variables for the events in the FMEA. The difference between the standard and comparative series is obtained and the results are used to determine the grey relation coefhcient. 

Chen and Klien have proposed an easy defuzzification method for obtaining the crisp number of a fuzzy set as shown here in Equation (7.9) (Chen and Klien (1997)). 

The values of c and d will remain the same for the defuzzification of all linguistic terms. The values ao and bo are rating values at the extreme limits of each linguistic term where the membership function is 0 and ay and hy are the rating values when the membership function is 1 (for a triangular membership function). 

For the application of this matrix in an FMEA study, the value of x,(fc) represents the defuzzified crisp number describing each linguistic variable considered for the identilled failure modes. For example, consider three failure events. A, B and C, where the linguistic terms have been assigned for the three variables considered as seen in Table 7.5 and assume that the values in brackets represent the defuzzified value for the associated linguistic term. The information in Table 7.5 can be represented in a matrix form to reflect the comparative series. 

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Table 1.8 although it should be emphasized that this technique is only used by the author as a means of comparing series of experimental products with known standards since different values are obtained for different batches of cement. 

A value of rA greater than 1 shows that AH is more reactive toward A02 than BH, and the reverse is true for rB. In a comparative series with the same AH compound, the increasing values of rB or decreasing values of rA indicate the presence of BH compounds which are more and more reactive toward R02. ... 

In a comparative series of experiments, Amouyal et al.142 studied the relationship between °(R/RT) and kq for compounds (2), (3) and (4) and others related to and including (12) and (13). They found that a correlation indeed existed, with fcq increasing as E° became less negative. However, this correlation did not extend to hydrogen production or turnover numbers of the viologen in a sacrificial hydrogen generation system.120 143 In fact, these two quantities were found to be maximized when — 0.41 V> E°>—0.50V. 

In a comparable series of reactions with acrylonitrile (Table II) the results... 

The base-catalyzed hydrolyses of phosphetanium ions 27, 25, and 28 offer an interesting comparative series, which further illustrates the proceeding considerations and supports the suggestion of the intervention of steric-bulk effects in determining the conformational mobility of the intermediates formed during nucleophilic displacement reactions in these systems 3). 

Lin, T. C., Pavlik, P. A., Martin, Y. C. Use of molecular fields to compare series of potentially bioactive molecules designed by scientists or by computer. Tetrahedron Comput. Methodol. 1990, 3, 723—738. 

As the optimization activities proceed, pharamceutical prohling provides feedback for property optimization. As the project moves ahead, a deeper understanding of individual compoimds becomes more important. Pharmaceutical prohling data can then be used to compare series analogs for selection. Often this informahon can be used for decisions to narrow the selection held from thousands to hundreds or tens of compounds for in-depth study. 

An indication of the role of electrostatic effects follows. The net charge on a -casein molecule at pH 7 is (— )13 (11), but Att and r are only slightly affected when, under given conditions, egg lecithin is replaced by lipids (e.g. phosphatidylserine, dicetyl phosphate, and arachidic acid) with a net negative charge. Electrostatic effects play a minor role in the interaction of /3-casein with insoluble lipid monolayers. A comparative series of experiments with lysozyme show some major effects. The results are summarized in Figure 6 where Att and r for lysozyme adsorbing to a variety of lipid monolayers at Cp1 = 5.6 X 10"5 % and... 

To explain the higher yields of cystine when neutron-irradiated sulfide is being used (compare Series A with B) we assume that among various products derivating from the sodium sulfide also colloidal sulfur is formed as a recoil product following the nuclear process. The colloidal sulfur could react rapidly with H atoms as well as with e m, forming SH radicals and S" radical ions, respectively ... 

A comparable series of bridged structure types is found in rhenium 6-8 clusters, e.g., Ba2(Re0S0S3-3g 2) (Bronger Miessen, 1982). Further versatility develops with the use of both chalcogenide and halide which provide the novel layered Re0Se0Cl2 (Re0Se 4Se " 4/2Se 4/2Cp2)... 

Isorhodanine (362) is convertible, by way of 5-anilinomethylene-isorhodanine, into a variety of quinomerocyanine dyes, e.g. (380) and (381). 4-Phenyliminothiazolidin-2-one, obtainable from isorhodanine by the action of aniline, gives rise to a comparable series of dyes. Their electronic spectra and solvatochromic properties were recorded and discussed. ... 

Figure 7.21. High-magnification electron micrographs of ionized IPNs PS/P(4-VP) = 76/24, 58/42,50/50,20/80. Series I (CsF stain) shows sulfonated PS as the dark phase, while series II (Lil stain) shows quaternized P(4-VP) as the dark phase. Comparing series I and II suggests a complementary staining. Domain sizes decrease as the P(4-VP) content increases, with a phase inversion occurring between 50 and 80% P(4-VP). ...

Comparative series of linear mPE oligomers and macrocycles were also studied and, depending on the solvent and the side chain, some aromatic systems have a greater propensity than others toward n-n stacking interactions, with at least a qnalitative correlation between the inter-molecular association of macrocycles and the stability of the helical conformation of the corresponding oligomers. 

In studies with a high prevalence for colorectal polyps or cancer, primary 2D reviewing performed well (PiNEAU et al. 2003 Johnson et al. 2003b Iannaccone et al. 2004a) and in comparative studies (primary 2D vs primary 3D) (McFarland et al. 2001 Macari et al. 2004 Iannaccone et al. 2004a) no difference in sensitivity was detected between primary 2D and primary 3D review methods. It is noteworthy that in these comparative series most likely conventional 3D methods with suboptimal surface visualization were used. This may have underestimated the diagnostic value of 3D. 

Principal component analysis (PCA) and multidimensional scaling (MDS) algorithms are mathematically elegant means of visualizing and discerning trends within multivariable data sets, and these techniques for comparing series can be exceptionally powerful and useful. An example of visualizing the diversity... 

The values for the methacrylate series show the effect of side chain length already observed. The other polymers do not fit irtto any comparative series. They show that a low Tg is generally associated with a high frequency for the transition zone, but this is not the only controlling parameter as evidenced by a comparison of polyisobutylene and unvulcanized Hevea rubber at 298°K. Although Tg is nearly the same for these two, the transition lies at higher frequencies by nearly three logarithmic decades in the rubber. Such differences will be discussed in more detail in terms of the monomeric friction coefficient in Section B below. 

Lateral validation of 3D-QSARs is a meta-analytical technique allowing the user to design molecules that would have specificity for one, but not other receptors, revealing differences and similarities between the targeted receptors or between the compared series as systems, not as individual compounds. Because of the underlying assumption that the compared QSAR models are correct, this technique cannot guarantee robustness or predictive and explanatory power. 

C. T. Lin, P. A. Pavlik, and Y. C. Martin, Tetrahedron Comput. Methodol., 3, 723 (1990). Use of Molecular Fields to Compare Series of Potentially Bioactive Molecules Designed by Scientists or by Computer. 

Edwards, 1943. Bureau of the Census, Sixteenth Census of the United States 1940, Population. Comparative Occupation Statistics for the United States, 1870 to 1940 A Comparison of the 1930 and the 1940 Census Occupation and Industry Classifications and Statistics A Comparable Series of Occupation Statistics, 1870 to 1930 and a Social-Economic Grouping of the Labor Force, 1910 to 1940. By Alba M. Edwards. 

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