Abundance estimation

The first of these difficulties arises primarily because of uncertainty in the temperature structure of the stars whose spectra are observed, measured, and interpreted to obtain Li abundance estimates. The problem can in turn be divided into three aspects ... 

At lower column densities, one is looking at systems where only a small fraction of the hydrogen is neutral metal lines (e.g. C il-iv, Si Il-iv) are weak and quantitative abundance estimates require an understanding of the ionizing radiation field, which may involve uncertainties of a factor of 3 or more the O VI doublet at AA 1032,1037 A, an important diagnostic, suffers from obscuration by the Ly-a forest. Existing results show a correlation with column density, with < [O/H] > — 1.5 for JV(H I) > 1015 cm-2 and-----2.5 for 10145 < /V(H I) < 1015 cm-2, perhaps reflect-... 

H.W. Higgins and DJ. Mackey, Algal class abundances, estimated from chlorophyll and carotenoid pigments, in the western Equatorial Pacific under El Nino and non-El Nino conditions. Deep Sea Res. 47 (2000) 1461-1483. 

In addition, taking the ratio of pixels calculated to belong to each component to the total number of pixels yields the following abundance estimates 41% for acetaminophen, 42% for aspirin and 12% for caffeine. 

There are other components in the tablet, composing the remaining 16% of the tablet. These excipients were not included in the initial model, so the results for the three API components need to be normalized to then-expected contribution to the whole tablet. When normalized to a total contribution of 84%, the abundance estimations are 36% for acetaminophen, 37% for aspirin and 11% for caffeine. These valnes compare favorably with the manufacturers label claim of 37% for acetaminophen, 37% for aspirin, and 10 % for caffeine. 

There is, however, a constraint on the types of samples that will give reasonable results for this abundance estimation approach. For example, in this particular analysis, there is no presumption of spatial organization or sample orientation. A measurement along any axis is assumed to be equivalent, resulting in an equivalent random component distribution. For example, this analysis would not deliver sensible results for samples that may have drug cores, coatings or other time-release mechanisms and other approaches would be required. Even with a randomly... 

Figure 2.6 The figure shows the different types of analyses that can be performed on chemical imaging data. The types of analyses that are performed can be grouped into three categories component abundance estimation, statistical analysis of component distribution, and morphological analysis of discrete particles. All three analyses are used to make inter- and intrasample comparisons, generating abundance and content uniformity estimates, sample heterogeneity and blend uniformity characterization, as well as domain statistics and domain size uniformity data.

The results show that group A abundance estimates more closely track the values reported on the label, whereas the group B estimations are further from reported values. Because the individual tablets comprise a single dataset, this difference is not due to experimental or data processing anomalies, as the data were... 

Table 2.2 Percent abundance estimations for group A and B samples...

Mustard, J. F. Pieters, C. M. (1987) Quantitative abundance estimates from bidirectional reflectance measurements. J. Geophys. Res., 92, E617-26. 

Uncertainties in phenocryst abundance estimates are a significant source of error, particularly for major and highly compatible elements in the main phenocryst phases. In most cases related to ocean drilling samples, phenocryst abundances in a particular sample are rarely known to better than about 5 vol.%. The most abundant phenocrysts are olivine and plagioclase, which contain the elements magnesium, silicon, calcium, aluminum, and nickel. 

D.L. Eskew, P.M. Gresshoff, M. Doty, C. Mora C (1992) Sealed-tube combustion for natural abundance estimation of Nj fixation and application to supemodulating soybean mutants. Canad. J. Microbiol. 38, 598-603... 

Figure 13. The diagonal band is the SBBN-predicted helium-4 mass fraction versus the SBBN-predicted deuterium abundance (by number relative to hydrogen). The width of the band accounts for the theoretical uncertainties in the SBBN predictions. Also shown by the filled circle and error bars are the primordial 4He and D abundance estimates adopted here.

Lack of an abundance estimate for a trace element like boron has no effect on the accuracy of the abundance analysis for other elements but merely restricts astrophysical interpretations involving B. On the other hand, helium is an abundant elements with effects on the atmospheric structure and through this on the derived abundances of other elements. Although rarely stated explicitly, abundance analyses of cool stars are dependent on an assumption about the He/H ratio the assumption enters both into the model atmosphere and synthetic spectrum calculations. For normal stars, ignorance about the He/H ratio is mitigated by the fact that the He/H ratio is surely constrained within tight limits (Y = 0.24 to 0.26, see above). 

The purpose of this paper is to present and support the argument that abundance estimates of the minerals in coal based upon x-ray diffraction (XRD) data can only be considered semi-quantitative with expected errors of determination of 10 percent or more of the reported values. The compositional and physical characteristics of the low temperature ash components of coal relative to the preparation and mounting of ash for XRD analysis also affect the precision of analyses. 

A major limitation to the capacity of 2-DE to display complete proteomes is the veiy high dynamic range of protein abundance, estimated at 10 for cells and tissues (Corthals et al., 2000) and 10 for plasma (Anderson and Anderson, 2002). This is beyond the dynamic range of 2-DE, with an estimated maximum dynamic range of 10" (Rabilloud, 2002). Clearly, the development of reliable and reproducible prefractionation strategies will be essential to access and retrieve quantitative data for the less abundant proteins present in biological samples such as the heart. 

A number of polycondensation systems have been investigated by FAB-MS. Table 7.1 reports the relative abundances, estimated from FAB, for the cycles formed in the polycondensation of bis(2-hydroxyethylene)terephtha-late with truxylloyl chloride. These appear to follow a distribution law of the type n indicating a kinetic control in the ring formation. ... 

Yet, 6 months later, the FSEIS contained two interesting claims. First, whereas the final, empirically derived relative abundance estimate for the percentage of juvenile striped bass that used the Westway interpier project area had been reported to Griffis office in July 1984 as 44%, in... 

Percentage Elative Abundance Estimates Based on Two-Group Cross-Validation... 

One of the key issues surrounding rare earths is their availability which is, in part, a result of the unfortunate name rare earth, which implies they are not common although a number of rare earths are quite abundant. Estimates of the abundances of elements are reported at the cosmic level,solar level and in the Earth s crast. Typical abundances for La, Ce, Pr, Nd, V, Mo, Ti, Cu and Cr in the Earth s crast are provided in Table 10.1. Ce, at60-70ppm, has a similar abundance to (2u. Of course, the actual availability of these rare earth elements relates to their mineralogy, as having rich ore bodies means that these elements can be mined and processed more easily than if they are distributed evenly within the Earth s crust. 

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