Threshold separation

Shown in Figure 5 are the calculated response surfaces for both the threshold separation (CRF-4) and time-corrected normalized resolution product (CRF-5). As expected, the threshold response surface is discontinuous, with 3 local optima in contrast, the response surface for CRF-5 is smooth, with no apparent local optima. 

Figure 5. Comparison of the threshold separation and time-corrected, normalized, resolution-product response surfaces for the eight component sample (Table ID). Response surfaces calculated via equations 9 and 10 using the isothermal retention surfaces of Figure 4.

Criterion threshold separation factor (CRF-4, equation 9) Preselected condition temperature, 80 °C Optimized condition(s) density, 0.204 g/mL... 

Figure 8. Threshold separation factor response surface (equation 9) for the optimization of density and temperature in the SFC separation of the eight component sample.

The peak-valley ratios vary from zero for separations where no valley can be detected, to unity for complete separation. It ought to be noticed that a P value equal to zero does not necessarily imply that two solutes elute with exactly the same retention time (or k value). There is a threshold separation below which the presence of two individual bands in one peak only leads to peak broadening or deformation, without the occurrence of a valley. In these cases Rs values are indeed not equal to zero, because by definition (eqn.1.14) Rs is proportional to the difference in retention times. 

All product criteria will be zero if any single pair of peaks is completely unresolved. For FO, Rs and S this situation theoretically only occurs if the retention times of two peaks are equal. For peak-valley ratios a value of zero is estimated from the chromatogram below a certain threshold separation, which for Gaussian peaks corresponds to Rs < 0.59... 

Each of the subbands has its own defined masking threshold. The output data from each of the filtered subbands is requantized with just enough bit resolution to maintain adequate headroom between the quantization noise and the masking threshold for each band. In more complex coders, for example, ISO/MPEG layer 3, any spare bit capacity is utilized by those subbands with the greater need for increased masking threshold separation. 

It is useful to treat the atomic absorption below the ionization (discrete line spectrum) and the continuum absorption above the ionization threshold separately. The arctan expression in eq. (1), experimentally confirmed through the K spectra, is a good approximation for the continuum absorption. The atomic absorption lines may be interpreted through optical multiplets using the Z + 1 approximation. The validity of this approximation has been successfully demonstrated in numerous cases of K and L spectra, first by Parrat (1939) in the K absorption of gaseous Ar. Here the optically determined wp Rydberg series ( > 4) of K (Z = 19 Z + 1 ) nicely fits the atomic absorption lines of 2s - 4p (K) X-ray excitation of Ar ( Z ). The Z -I-1 potential accounts for the creation of the deep core hole. The inflection point of the arctan shaped continuum absorption is located at the series limit, i.e. the first ionization potential. 

For the third accident type, a new calibration of threshold separating low and high densities is necessary. 

A quite different application of the RRPA equag ons is illustrated in Fig. 7 where we compare experimental and theoretical Beutler-Fano resonances in the xenon photoabsorbtion cross section. These resonances occur for photon energies just above the 5p3/2 threshold and are a result of the coupling between nd and ns states converging to the 5pi/2 threshold and the continuum. Since the RRPA automatically provides for the 5p3/2 Pl/2 threshold separation, and includes couplings between the relevant open and closed channels, it is a theory Ideally suited to study such resonances. The comparison in Fig. 7 illustrates how well the theory works in such applications. 

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