Gaussian peak, near

Resolution The chromatographic separation of two components, A and B, under trace conditions with small feed injections can be characterized in terms of the resolution, R,. For nearly Gaussian peaks ... 

Figure 5.1.7 shows the propagator of the motion measured for a clean and a biofilm impacted capillary [14,15] and the residence time distributions calculated for each from these velocity distributions. The clean capillary gives an experimental propagator equal to the theoretical velocity distribution convolved with a Gaussian diffusion curve [14], as shown in Figure 5.1.2. For the flow around the biofilm structure note the appearance of a high velocity tail indicating higher probability of large displacements relative to the clean capillary. The slow flow peak near zero displacement results from the protons trapped within the EPS gel matrix where the...

As noted earlier, the diffraction of X-rays, unlike the diffraction of neutrons, is primarily sensitive to the distribution of 00 separations. Although many of the early studies 9> of amorphous solid water included electron or X-ray diffraction measurements, the nature of the samples prepared and the restricted angular range of the measurements reported combine to prevent extraction of detailed structural information. The most complete of the early X-ray studies is by Bon-dot 26>. Only scanty description is given of the conditions of deposition but it appears likely his sample of amorphous solid water had little or no contamination with crystalline ice. He found a liquid-like distribution of 00 separations at 83 K, with the first neighbor peak centered at 2.77 A. If the pair correlation function is decomposed into a superposition of Gaussian peaks, the area of the near neighbor peak is found to correspond to 4.23 molecules, and to have a root mean square width of 0.50 A. 

Fig. 13. The strategy used for the construction of contoured scatterplots. Positions of metal ions near a carboxyl group are plotted for different crystal structures. The result is a scatterplot. Gaussian peaks are put on each scatterplot point. The resulting density is contoured as for an electron density. The result is a plot of the orientational preferences for binding.

Figure 2 - Left IF analysis, using a 100 cm 1 Gaussian filter (solid) (other filter widths gave similar results). The sliding window FFT results are shown for comparison (squares). The inset illustrates the exponential decay of the v7 mode. Right FFT of the IF showing a large peak near 50 cm 1. The resolution of this plot is fundamentally limited by the decay of the v7 mode.

As was discussed in Chapter 1 resolution, R, is a measure of the distance between two adjacent peaks in terms of the number of average peak widths than can fit between the band (zone) centers. Assuming symmetrical (Gaussian) peaks, when R = 1, peak separation is nearly complete with only about 2% overlap. This case was shown in Chapter 1, Figure 1-4. Resolution results from the physical and chemical interactions that occur as the sample travels through the column. It should, therefore, be no surprise that resolution may also be expressed in terms of the contribution of the individual column characteristics separation factor (selectivity, a), efficiency (narrowness of peak, N), and capacity factor (residence time, k ) of the first component. The equation that describes this interrelationship is... 

Equation (10) is the basic elution curve equation it is a Poisson function, but when n is large, the function approximates to a normal error function or Gaussian function. In practical chromatography systems, n is always greater than 100 and, thus, all chromatographic peaks will be Gaussian or nearly Gaussian in shape. 

The detected radiation is displayed to show near-Gaussian peaks (see Fig. 2.14) in a 1024-, 2048-, or 4096-channel spectrometer. The spectrometer is calibrated for energy by matching the channel at the midpoint of the peak to the known energy of gamma radiation emitted by a set of radioactivity sources. Typically, the channel width is set to approximately one-fourth of the detector peak resolution, but some compromise is needed because the resolution changes with energy. 

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