Quantitative analysis, assumptions

In practice, it is probable that both of the effects discussed contribute to the overall peak asymmetry. Unfortunately, peak asymmetry varies in extent from the very obvious to the barely noticeable and because of this, peak asymmetry is often dismissed as the normal shape of a single solute peak. Such an assumption can cause serious errors in both qualitative and quantitative analysis. 

Quantitative analysis of emission spectra is difficult. As a first assumption the emission intensity from a species is proportional to its concentration, but the pro-... 

Equations (1) and (2) depend on some major assumptions, in particular that the cmc gives the concentration of monomeric surfacant and that rate and binding constants in the micellar pseudophase are unaffected by reactants and products. These equations have been used very extensively and provided the basis for quantitative analysis of micellar rate effects. Much of this work has been reviewed in a comprehensive monograph which gives extensive compilations of data up to 1974 (Fendler and Fendler, 1975). 

Screening assessments incorporate variability and uncertainty implicitly, by using worst-case assumptions and safety factors. As mentioned earlier, these have rarely been based on a quantitative analysis and may not take account of the full range of uncertainties, so in principle they should be reviewed to determine whether they provide adequate margins of safety. 

The approach to the quantitative analysis and mathematical modelling of the dipping process is based on the solution of the well-known problem of physicochemical hydrodynamics of the thickness of liquid layers retained on the surface of a body removed from the liquid (see, e.g., u,12>). Upon the assumption that the body (support, prototype, mould) is taken out of the plastisol liquid vertically, the general relationships may be written in the following form 2> 7 11"14> ... 

Serious problems with respect to a quantitative analysis can occur if the assumption of identical grain boundaries is violated. In sintering processes, inhomogeneities are the rule rather than the exception and grain boundary cores in one and the same polycrystal can easily differ in terms of structure and chemistry [109, 120, 242-246], Hence, core as well as space charge conductivities might also vary from boundary to... 

Inspection of the curves of the effectiveness factor versus the Weisz modulus for different values of Kp. s and E reveals two interesting phenomena when E > 0 (Fig. 20) [87, 88, 91]. At first, for large values of Ay i.s (10-100) effectiveness factors above unity may occur even though isothermal conditions prevail. This can be explained by the fact that the reaction rate given by eq 103 has a maximum for certain combinations of p and P2. This maximum results from the assumption that the rate is proportional to the concentration of the adsorbed reactants At and A2 which compete for adsorption sites on the active (inner) surface. When, for example, Ai is adsorbed more strongly than A2, then a raised partial pressure of Ai, at constant partial pressure of A2, will lead to a displacement of A2 from the surface, and hence to a lowered reaction rate. By a quantitative analysis, it can be shown that effectiveness factors above unity will appear whenever Kp, is greater than (E + 2)/E [91]. 

At T > Tg, a quantitative analysis using Eq. (46) is further complicated for the following reasons. Regarding the description of 4>p(f)> is not dear whether Eq. (43) still applies, since above Tg the assumption of a thermally activated process is no longer justified. Indeed, there are indications that the temperature-dependence of ip changes upon passing Tg [157,326-329]. In addition, it is not clear what function has to be used to interpolate Again, one may use the... 

With HPLC methods where individual anthocyanins are separated and the method of detection is DAD, individual anthocyanin standards are preferred for quantitation, but not always available. A standard mix of the glucoside form of the six aglycones of the anthocyanidins has been commercially available. However, obtaining a consistent purity has been a challenge at times. Because of the large numbers of anthocyanins present, it is not reasonable at this point in time to have a standard for every individual anthocyanin. Thus, some assumptions and compromises must be made in any quantitative analysis of anthocyanins. Calculation of the anthocyanins containing the same anthocyanidin based upon the glucoside equivalent has been a workable compromise. 

It is possible to obtain the exact but rather complex solution of this kinetic problem [200]. However, the number of the parameters in the final equations does not permit quantitative analysis without additional assumptions. Assuming that the excited state is produced mostly within the cip configuration at a rate kg and the ground state mostly within the ssip configuration at a rate kgi, one can simply obtain ... 

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