Data-based error estimators

Numbers in the first 4 rows (apart from the error estimates) are taken from Raiteri, Gallino and Busso (1992). The others are based on data for individual isotopes given by Kappeler, Beer and Wisshak (1989). 

Fig. 5 Effect of varying relaxation delays between on- and off-resonance experiments in STD NMR experiments, a Experimental setnp for interleaved measnrements in STD NMR spectroscopy, n represents the nnmber of scans. The inter-scan delay Adi is varied while keeping on- and off-resonance freqnencies constant at -4 and -t300 ppm, respectively, b The resulting STD effects for the 0-methyl group of a-L-Fuc-O-methyl in the presence of RHDV VLPs. The equation that was used for non-linear least squares data fitting is based on the saturation recovery experiment [98], With Ti(iig) = 0.91 s as measured independently (unpublished results) and a Monte Carlo error estimation yields Ti(virus) = 10.06 0.41 s. This value does not directly correspond to a Tl relaxation time of the virus protons, because other factors also influence the observed relaxation [99]. According to these findings a relaxation delay Adi = 25 s was employed in all STD experiments. This results in a recovery of 92% of the virus resonance, and thereby reduces errors in epitope mapping that are introduced otherwise by non-homogeneous recovery of the binding site.

In a first step the scaling of intrinsic clearances determined in rat hepatocytes was compared to in vivo clearance. When taking account of non-linearity, the estimated hepatic metabolic clearance values were in reasonable agreement with observed total clearances, which ranged from 7 to 35 mL/min/kg, and it was considered reasonable to estimate the expected clearances in human by a similar scaling of human hepatocyte data. The error around the mean predicted human clearance was based on the variability seen in different batches of human hepatocytes. 

Statistical analysis of the results was performed using the software Statistica 5.5 (Stat Soft). Maximum lipase activities and time to reach the maximum were calculated through fitting of kinetic curves. The maximum was estimated by derivation of the fits. Empirical models were built to fit maximum lipase activity in the function of incubation temperature (T), moisture of the cake (%M), and supplementation (%00). The experimental error estimated from the duplicates was considered in the parameter estimation. The choice of the best model to describe the influence of the variables on lipase activity was based on the correlation coefficient (r2) and on the x2 test. The model that best fits the experimental data is presented in Table 2. 

Absolute error estimates for these data are based on the recommendations of the data bank compiler (25) and (for one standard deviation) are 0.1% for normalized triple-filament, silica-gel, and lead tetramethyl methods and 0.3% (for the 206/204 ratio) and 0.5% (for the 207/204... 

A quantitative analysis is not always required. In particular, when searching for the source of poisoning of a catalyst, a qualitative analysis, followed by a semi-quantitative estimate is sometimes sufficient. If the data base from which the semi-quantitative program takes its standards includes many standards of a composition similar to that of the sample, the accuracy of the measurement may be of the order of a percent. On the other hand, if the library does not contain standards of a similar composition, the error may be around 50% or even more. As the problem of catalyst poisoning is frequently encountered, the accuracy of the measurements is generally fairly good. The table below is a comparison of the results of semi-quantitative and quantitative analyses conducted on an used post-combustion catalyst. 

Table 7 Top 10 recent stratospheric releases of SO2, based on TOMS data. T3fpical errors on TOMS estimates are 30%. See Bluth et al. (1993, 1997) and Krueger et al. (1995) for details of methods.

The study of elementary reactions for a specific requirement such as hydrocarbon oxidation occupies an interesting position in the overall process. At a simplistic level, it could be argued that it lies at one extreme. Once the basic mechanism has been formulated as in Chapter 1, then the rate data are measured, evaluated and incorporated in a data base (Chapter 3), embedded in numerical models (Chapter 4) and finally used in the study of hydrocarbon oxidation from a range of viewpoints (Chapters 5-7). Such a mode of operation would fail to benefit from what is ideally an intensely cooperative and collaborative activity. Feedback is as central to research as it is to hydrocarbon oxidation Laboratory measurements must be informed by the sensitivity analysis performed on numerical models (Chapter 4), so that the key reactions to be studied in the laboratory can be identified, together with the appropriate conditions. A realistic assessment of the error associated with a particular rate parameter should be supplied to enable the overall uncertainty to be estimated in the simulation of a combustion process. Finally, the model must be validated against data for real systems. Such a validation, especially if combined with sensitivity analysis, provides a test of both the chemical mechanism and the rate parameters on which it is based. Therefore, it is important that laboratory determinations of rate parameters are performed collaboratively with both modelling and validation experiments. 

The adopted value is based upon a 3rd law analysis of effusion mass spectrometric data by Farber (1 ) who obtained (298.15 K) = 27.1 kcal mol" for Si(g) + SiCl2(g) 2 SiCl(g). With auxiliary JANAF data (2) this yields AjH (298.15 K) = 47.4 1.6 kcal mol". The error estimate is somewhat higher than that given by Farber and should more accurately reflect the uncertainties in... 

In surface tension measurements using the maximum bubble pressure method several sources of error may occur. As mentioned above, the exact machining of the capillary orifice is very important. A deviation from a circular orifice may cause an error of 0.3%. The determination of the immersion depth with an accuracy of 0.01 mm introduces an error of 0.3%. The accuracy of 1 Pa in the pressure measurement causes an additional error of 0.4%. The sum of all these errors gives an estimated total error of approximately 1%. Using the above-described apparatus, the standard deviations of the experimental data based on the least-squares statistical analysis were in the range 0.5% < sd > 1%. 

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