Nominal contrast factor

As explained in Section 9.4.3, the observed scattering intensity will depend on the orientation of the applied magnetic field. For Q perpendicular to H, the scattering intensity is proportional to the nuclear plus magnetic contrast factor whereas for Q parallel to H the scattering intensity only depends on the nuclear contrast factor. The ratio of these is known as the A-ratio. Equivalently, this ratio can be defined as the ratio of the relative precipitate volume fractions (V/ ) determined for Q 1 (perpendicular) to H and Q II (parallel) to H. Here V/ is the volume fraction determined using a nominal contrast factor ... 

Note that this relationship is in conPadiction to the well known equation for the calculation of the thickness resolving power given by Halmshaw in 111. The relationship in 111 requires explicit knowledge about built-up factors for scatter correction and the film contrast factory (depending on D) and is only valid for very small wall thickness changes compared to the nominal wall thickness. 

In the present context only the factor b/K) is of further interest. Since it contains the asymptotic phase shift Ae and the nominal wavenumber k which also is defined by its asymptotic value, the expression for b/K) holds everywhere even though it has been derived in the asymptotic limit (in contrast, the scattering function can be defined only in the asymptotic limit). Hence, the correct wavefunction P[Pg.288]

The processes for manufacturing methanol by synthesis gas reduction and ethanol by ethylene hydration and fermentation are very dissimilar and contribute to their cost differentials. The embedded raw-material cost per unit volume of alcohol has been a major cost factor. For example, assuming feedstock costs for the manufacture of methanol, synthetic ethanol, and fermentation ethanol are natural gas at 3.32/GJ ( 3.50/10 Btu), ethylene at 0.485/kg ( 0.22/lb), and corn at 0.098/kg ( 2.50/bu), respectively, the corresponding cost of the feedstock at an overall yield of 60% or 100% of the theoretical alcohol yields can be estimated as shown in Table 11.12. In nominal dollars, these feedstock costs are realistic for the mid-1990s and, with the exception of corn, have held up reasonably well for several years. The selling prices of the alcohols correlate with the embedded feedstock costs. This simple analysis ignores the value of by-products, processing differences, and the economies of scale, but it emphasizes one of the major reasons why the cost of methanol is low relative to the cost of synthetic and fermentation ethanol. The embedded feedstock cost has always been low for methanol because of the low cost of natural gas. The data in Table 11.12 also indicate that fermentation ethanol for fuel applications was quite competitive with synthetic ethanol when the data in this table were tabulated in contrast to the market years ago when synthetic ethanol had lower market prices than fermentation ethanol. Other factors also... 

In summary, the Type I error rate from using the LRT to test for the inclusion of a covariate in a model was inflated when the data were heteroscedastic and an inappropriate estimation method was used. Type I error rates with FOCE-I were in general near nominal values under most conditions studied and suggest that in most cases FOCE-I should be the estimation method of choice. In contrast, Type I error rates with FO-approximation and FOCE were very dependent on and sensitive to many factors, including number of samples per subject, number of subjects, and how the residual error was defined. The combination of high residual variability with sparse sampling was a particularly disastrous combination using... 

The small load carried by the asperities Is a direct consequence of the non-conformal geometry of the cam and follower contact. It Is Interesting to contrast the predicted small percentage of the total load carried by the asperities with the significant Increase In nominal minimum film thickness from the smooth surface case, which for the reference case (o = 0.2 Urn) was about 65%. This Is as a result of the small value of the pressure flow factor (x) at the low values of film thickness ratio (Hv. Physically this implies a considerable restriction to the lubricant flow (which is only In the direction of surface motion for the analysis here) and a consequent enhancement of nominal minimum film thickness for the same applied load. 

In contrast to the calculation of the nominal point, during off-design operation, the given value is the current drawn from the cell instead of the fuel utilization factor. The correlation between current density and the fuel utilization factor is given by the following relationship ... 

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