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Plotting Z against x gives a straight line that yields r2 =a and r1 as intercepts on extrapolation to x 0 and x 1, respectively The value of a, chosen as a Fm FM 1=2 where Fm and FM are the lowest and highest F values, respectively, distributes the experimental data symmetrically on the plot Even with the Kelen Tudos re nement there are statistical limitations inherent in the linearization method The independent variable in any form of the linear equation is not really independent, while the dependent variable does not have a constant variance [O Driscoll and Reilly, 1987] The most statistically sound method of analyzing composition data is the nonlinear method, which involves plotting the instantaneous copolymer composition versus comonomer feed composition for various feeds and then determining which theoretical plot best ts the data by trial-and-error selection of r1 and r2 values.

FIGURE 13.6. Comparison between measurements (continuous curves) and theoretical prediction (dashed curves) for time delay distributions for three position of vehicle antenna denoted by 1, 2 and 3, which correspond the antenna height of 2, 5 and 12 m, respectively.

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The pros and cons of the two methods have been discussed in detail, along with approaches for the best choice of feed compositions to maximize the accuracy of the r1 and r2 values [Bataille and Bourassa, 1989; Habibi et al, 2003; Hautus et al, 1984; Kelen and Tudos, 1990; Leicht and Fuhrmann, 1983; Monett et al, 2002; Tudos and Kelen, 1981] The use of a differential form of the copolymerization equation assumes that the feed composition does not change during the experiment, but this is not true One holds the conversion as low as possible, but there are limitations since one must be able to isolate a sample of the copolymer for direct analysis (or, if copolymer analysis is via the change in feed composition, there must be a signi cantly measurable change in the feed composition).

surrounding the moving vehicle are observed. The impulse (wideband) signal power distribution over the time delay is quasi-homogeneous and uni ed. A different picture is observed for the high BS antenna ($12 m) with respect to building roofs. In fact, as follows from the results of the normalized power spectrum distribution measurements in the time delay domain (presented in Figures 13.6a,b), for this case the shape of the spectrum has an obvious maximum

The use of an integrated form of the copolymerization equation does not have this limitation [Hamielec et al, 1989; O Driscoll and Reilly, 1987; Plaumann and Branston, 1989] The change in copolymer composition or feed composition with conversion is measured and the results curve tted to an integrated form of the copolymerization equation For example, one method uses the previously described Eq 6-34 [Meyer, 1966] Experimental data on the variation of feed composition with conversion are plotted as f1 or f2 versus 1-M/M0 to yield curves like those in Fig 6-3 Using computational procedures, one then determines the best values of r1 and r2 that must be used with Eq 6-34 to yield the same plot..

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that corresponds to the direct pulse arriving from the BS at the moving vehicle receiving antenna Only a few arriving pulses as multipath components due to multiple re ection and scattering are distributed close to the initial pulse and their power is less than that of the main pulse Here, three different positions of antennas, denoted by 1, 2, 3 near each curve, are presented We also present by dashed curves in Figures 136a,b the results of calculations according to theoretical results for different situations of the experiment (denoted by 1 in 136a and 2, 3 in Fig 136b, respectively) Again, as seen for the spectrum distribution in the azimuth domain, the theoretical predictions are in agreement with the experimental data Signal Distribution in Doppler Domain.

The copolymerization equation describes the copolymer composition on a macroscopic scale, that is, the overall composition of a copolymer sample produced from a comonomer feed. This leaves unanswered two details concerning composition copolymer. The rst concerns the exact arrangement of the two monomers along the polymer chain. Although the

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