Frequency distribution curves comparison

Figure 14-15 Cumulative frequency distribution of relative differences for the comparison of drug assays example.The lighter curve indicates the Gaussian cumulative frequency distribution curve. In accordance with the test for normality, a good agreement is observed.

Graphical overlay of distribution curves can serve for comparison of a set of samples and finding even subtle differences among them. Note Instead using the weight fraction it is possible to use the mole fraction. The frequency functions are then called the number distribution functions and subscripts w and n can be used in order to differentiate between the weight distribution and number distribution, respectively. 

Frequency-dispersion curves are useful for analysing infrared and Raman spectra of polymer chains of Gnite length where chain vibrations associated with various phase different are observed. From the frequency-dispersion curves, the frequency distribution of the optical branches may be calculated, for studying the contributions of chain vibrations to heat capacities and the zero-point energy. The intrachain force field is also used in treating the elastic modulus along the chain axis, for comparison with the experimental data. 

Fig. 8.1. Dynamic viscosity t] (a>) and steady state viscosity f](y) for undiluted narrow distribution polystyrenes. The data are plotted in reduced form to facilitate comparison. The dimensionless shear rate or frequency is t]0Mwy/gRT >r r/ M co/gRT. [See Eq.(8.3)]. The dynamic viscosities are for Mw = 215000 (O) and Mw = 581000 ( ) at 160° C (312). The steady shear viscosity is for Mw = 411000 (A) at 176° C (313). The shapes in the onset region are similar for the three curves, but the apparent limiting slope for the dynamic...

Fig. 2 Comparison between normalized, frequency functions of size (F %) of silica particles for HPLC packing (5 gm LiChrospher, Merck, Darmstad) nominal distribution percentiles dig = 3.7 gm, J50 = 5.0 gm, dgg = 6.8 gm) curve 1 (full line) Fm % curve 2 (dashed line) Fcum % curve 3 (dashed line) 100 - %. (a) GrFFF/PSD Sample load 100 gg channel ...

Plotted for comparison on Figure 1 are two cumulative distributions in which the frequency is distributed normally. Note that the normal curves cannot satisfactorily fit the long tails of the log-normal distributions. While the normal curves have been chosen somewhat arbitrarily to fit the observed distributions at frequencies of 1 and 22, there is no consistent way in which to force a logarithmic curve to fit a linear one. 

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