Average intensity differences

The number of structures solved using 3-D electron diffraction data sets is relatively small because of the experimental difficulties associated with the collection of 3-D diffraction data and dynamic scattering effects on diffraction intensities. A major development toward solving these difficulties is the precession electron diffraction technique, which allows a large number of reflections to be collected in a single orientation and averages over different beam directions to minimize dynamic effects. Progress is under way for more information see Refs. 40 and 41. 

Figure 10 The average width of the NMR spectrum (Mi) as a function of temperature and pH. Closed circles pH 5.2 open circles pH 6.2 closed triangles pH 7.4. Repetition time 50 sec at all temperatures where the sample contained some solid component, then 1 sec at higher temperatures. (In practice, the quadrupolar echo intensity was checked every few degrees at the 1-sec repetition time toward the completion of the solid-to-fluid transition, and when the echo intensity differed by < 1% between the short and long repetition times, a l-sec repetition time was used for all higher temperatures.)...

Fig. 9.15. Average intensities as a function of time after the laser pulse. Each sort of material is characterized by a different decay constant. Thus, each material has a different informative lifetime. (Reproduced with permission of the American Chemical Society.)...

FIGURE 7.9 In (a) and (b) are the resolution dependencies of two X-ray data sets recorded from two different but isomorphous crystals that show a clear difference in the rates at which average intensity declines with sin 9. The difference may be due to differences in crystal quality, decay rates, or many other factors. If the two data sets are scaled to one another using only a linear scale factor, the result in (c) is obtained, in which the crosshatched area represents the scaling mismatch, or residual. If a linear plus exponential scale factor is used, the falloff of the second data set is made to more closely approximate that of the first set, and the result in (d) is obtained in which the residual is substantially reduced. 

Upon taking an ensemble average, the first term, which contributes only at the origin, yields Ai2, where is the averaged intensity. The average value of the second term depends in an essential way on the correlation between positions of the different lines. On the assumptions that (1) the distributions of intensity and of positions are independent and (2) that the probability to find another line at a distance Aco from the first line depends... 

The average aroma intensity differences from the blanched reference are illustrated in Figures 2a,b,c. When the average aroma intensity was not different from the reference, the value on the y-axis would be 50, as shown by the horizontal line. The length of the vertical bar represents the degree of lesser or greater intensity difference from the reference. The cross-hatched bars indicate descriptors that were statistically different from the blanched reference. 

Figure 2. Average aroma intensity differences from the blanched reference of broccoli puree, a, Samples are control, added peroxidase, added lipase, and added lyase. Aroma descriptors designated with shaded bars are statistically different from the blanched reference sample at p < 0.05. Continued on next page.

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