Comparison with results of other methods

A control chart can be used to determine whether a method is under control over time it is not, however, able to detect a systematic error which is present from the moment of introduction of the method in a laboratory. Results should hence be verified by other methods. As stressed later in this chapter, all methods have their own particular sources of error which are related to one or several analytical steps (Quevauviller et al., 1996a). An independent method should be used to verify the results of routine analysis. If the results of both methods are in good agreement, it can be concluded that the results of the routine analysis are unlikely to be affected by a contribution of a systematic nature (e.g. insufficient extraction). This conclusion is stronger when the two methods differ widely. If the methods have similarities, such as an extraction step, a comparison of the results would probably lead to conclusions concerning the accuracy of the method of final determination, and not as regards the analytical result as a whole. 

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As mentioned, the data obtained by this method are expressed as cumulative size distribution curves. Since the computations assume Stokes law for spherical particles, the plotted curves give the distribution of spherical particles which would behave like the actual sample with respect to this experiment. For this reason, the sizes on the distribution curves should be labelled Stokes Equivalent Diameter . Because of the underlying assumptions and the above interpretation of the results, it is clear that the repeatability of this method has more meaning than accuracy of comparison with results of other methods... 

In this section we discuss the types of calculations made and sources of error in the results, and we make comparisons with results of other methods for the H + H2 and F + H2 reactions. In general, the integration over E -02. equation (1) requires that one both extrapolate a(m->n E g ) to energies at which actual scattering calculations were not made and interpolate, since calculations were made at a finite number of energies. This introduces error apart from that inherent in the fact that the approximate lOS method was used in the dynamical calculations. In order to obtain some estimate... 

It is also possible to compute various mathematical indices or to flag the results on reports using convenient symbols. When using such presentation methods, the original observed value should also be reported to allow comparison with results of other laboratory tests and metabolic calculations. 

The results of this study are somewhat atypical in the sense that the inferred re and tq structures of Sis are nearly the same. This is a somewhat fortuitous circumstance, which cannot be attributed entirely to the fact that Sis appears to be only weakly anharmonic (see cubic constants in Table I), since it has a relatively low-frequency bending mode that is potentially problematic. Nonetheless, it can be stated with some certainty that the structure obtained in the present research is accurate to within 0.002A and 0.2 . Hence, this structure can be used as a reference for benchmarking quantum chemical methods intended for high accuracy calculations on silicon clusters, as well as for comparison with structures of other silicon-containing molecules. 

The strength of glass is relatively low in comparison with that of other inorganic materials (ceramics, metals). This is why the strength of glass has been paid a great deal of attention, resulting in a number of methods for substantial improvement. 

All methods for the determination of tensile strength described above are too complicated and time consuming to be suitable for routine industrial quality control applications. In those cases it is the task of the test procedure to determine a specific characteristic of the agglomerate easily, quickly, and reliably. The results must only be reproducible and comparable within the own organization and a relation to theoretical predictions is normally not required comparisons with results from other plants are often not necessary or, in case of competing products, not desired. 

Chloride is often determined as AgCl by the simple turbidimetric method, but spectrophotometric methods are more accurate, and more sensitive. Many such methods are based on the oxidation of chloride to chlorine, which undergoes subsequent redox reaction resulting in either the appearance or disappearance of colour (e.g., the Methyl Red method described below). In direct methods involving chloride ions, advantage is taken of the higher stability of the colourless Hg(II) chloride complex in comparison with that of other coloured Hg(n) complexes. 

We review the Douglas-Kroll-Hess (DKH) approach to relativistic density functional calculations for molecular systems, also in comparison with other two-component approaches and four-component relativistic quantum chemistry methods. The scalar relativistic variant of the DKH method of solving the Dirac-Kohn-Sham problem is an efficient procedure for treating compounds of heavy elements including such complex systems as transition metal clusters, adsorption complexes, and solvated actinide compounds. This method allows routine ad-electron density functional calculations on heavy-element compounds and provides a reliable alternative to the popular approximate strategy based on relativistic effective core potentials. We discuss recent method development aimed at an efficient treatment of spin-orbit interaction in the DKH approach as well as calculations of g tensors. Comparison with results of four-component methods for small molecules reveals that, for many application problems, a two-component treatment of spin-orbit interaction can be competitive with these more precise procedures. 

In fact, in the method described here and applied to lithium, it is not necessary to go through surface energies in order to predict the shape of a cluster. It is sufficient to compute for several homothetic clusters of greater and greater size, so as to deduce by interpolation the most stable arrangement for a given number of atoms The computation of surface energies presented here is but a test of the method, for it permits comparison of the results with those of other methods. 

If values of cos 0p and cos 0p are required, the relationship between the two distributions of orientations niust be known. This can only be established initially by comparison of the fluorescence results with those of other methods which give direct information about cos 0p and cos 0p, such as infra-red and Raman spectroscopy, and studies along these lines are in progress (see Section 5.3.2). If the relationship can be satisfactorily established the fluorescence method could become a much simpler method of quantitatively characterising molecular orientation in amorphous polymers than any of the other methods that offer information about both cos 0p and cos 0p. 

It turns out that for some systems the GPM yields the pair interactions, particularly those between first neighbors, which do not correspond to experimental phase diagrams. It is the purpose of the present work to show some of these cases and make a comparison with results obtained by other methods, particularly by the CWIS. 

Comparison of the pore size distribution determined by the present method with that from the classical methods such as the BJH, the Broekhoff-de Boer and the Saito-Foley methods is shown in Figure 4. Figure 5 shows a close resemblance of the results of our method with those from the recent NLDFT of Niemark et al. [16], and XRD pore diameter for their sample AMI. The results clearly indicate the utility of our method and accuracy comparable to the much more computationally demanding density functional theory. There are several other methods published recently (e. g. [21]), however space limitations do not permit comparison with these results here. It is hoped to discuss these in a future publication. 

The approximations of the superposition-type like equation (2.3.54), are used in those problems of theoreticals physics when other-kind expansions (e.g., in powers of a small parameter) cannot be employed. First of all, we mean physics of phase transitions and critical phenomena [4, 13-15] where there are no small parameters at all. Neglect of the higher correlation forms a(ml in (2.3.54) introduces into solution errors which cannot be, in fact, estimated within the framework of the method used. That is, accuracy of the superposition-like approximations could be obtained by a comparison with either simplest explicitly solvable models (like the Ising model in the theory of phase transitions) or with results of direct computer simulations. Note, first of all, several distinctive features of the superposition approximations. 

A good example of application is given by the protein structural changes of bovine ribonuclease A in the course of its denaturation by pressure. The UV spectrum of RNase is dominated by the absorbance of tyrosine - this RNase does not contain tryptophan. As shown in Figure 6, an increase of pressure from 1 to 500 MPa results in a blue-shift of the 4th derivative maximum from 285.7 0.05 to 283.5 0.05 nm. This shift of 2.2 nm corresponds to an increase of the mean dielectric constant from 25 to 59. It is characteristic of the exposure to the aqueous solvent of part of the 6 tyrosines, as it is expected for a partly denaturation. The transition is fully reversible with clear isosbestic points. The pressure effect can therefore be described by a simple two-state model between the native (e,. = 25) and the partially denatured (e,. = 59) state. A simulation on the basis of this model permitted us to determine the thermodynamic parameters of this transition AG° = 10.3 kJ/mol and AV = - 52 ml/mol. A comparison with results obtained by other methods indicates that the (e,. = 59) state corresponds to an intermediate in the defolding process which has molten globule like characteristics [12]. It thus appears that fourth derivative... 

The comparison of results per technique did not allow us to detect any bias which could be attributed to one particular technique. As shown in Table 8.26, the CVs within one method are systematically larger, or of the same order of magnitude (Ni) than those between different techniques. Consequently, it cannot be inferred that the results of one technique do not agree with those of other techniques for the elements mentioned. 

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