Fractional correction method

Refractive Index. The refractometric value of sugar solutions is used as a rapid method for the approximate determination of the soHds content (also known as dry substance), because it is assumed that the nonsugars present have a similar influence on the refractive index as sucrose. Measurement is usually carried out on a Brix refractometer, which is graduated in percentage of sucrose on a wt/wt basis (g sucrose/100 g solution) according to ICUMSA tables of refractive index at 20.0°C and 589 nm. Tables are available that give mass fraction corrections to refractometric values at temperatures different from 20°C. 

Accuracy for all thorium measurements by TIMS is limited by the absence of an appropriate normalization isotope ratio for internal correction of instrumental mass fractionation. However, external mass fractionation correction factors may be obtained via analysis of suitable thorium standards, such as the UC-Santa Cruz and IRMM standards (Raptis et al. 1998) for °Th/ Th, and these corrections are usually small but significant (< few %o/amu). For very high precision analysis, the inability to perform an internal mass fractionation correction is probably the major limitation of all of the methods for thorium isotope analysis discussed above. For this reason, MC-ICPMS techniques where various methods for external mass fractionation correction are available, provide improved accuracy and precision for Th isotope determinations (Luo et al. 1997 Pietruszka et al. 2002). 

Multi-collection mass spectrometers can analyze isotope ratios in a static mode to eliminate the errors from beam instability. However, the static multi-collection method depends on the extent to which the collectors (e.g., Faraday cups) are identical and to the extent to which the gain of each collector is stable. An alternative approach is to use the so-called dynamic multi-collector mode, to cancel out beam instability, detector bias, and performing a power-law mass fractionation correction. The following descriptions are modified from the Finnigan MAT 262 Operating manual (Finnigan, 1992). 

The area A can be determined, e.g., by drawing a baseline and vertical lines at 141 and 159ppm and then cutting out and weighing the areas enclosed. Area A must then be corrected for SSB strengths and converted from mole fraction to weight fraction. The method summarized here follows procedures described in more detail by Hemmingson and Newman (1985) and Leary et al. (1986). 

Sample analysis by thermal ionization mass spectrometry (TIMS) results in measurement of isotopic ratios of minerals. Total mineral content of samples is then determined by one of two methods. One approach is to use flame atomic absorption spectrophotometry (AAS) to determine total mineral content of samples. Since AAS does not have the same level of precision as TIMS a sufficient number of replicates is analyzed for a mineral content determination with a CV of within 1%. Alternatively if a mineral has 3 or more isotopes and fractionation corrections are not made the following procedure may be used. An individual is fed one isotope and another isotope is added to the sample prior to analysis to determine the total mineral content of the sample by dilution of the second isotope. In this way both the amount of the isotope fed which is recovered in the feces and the total mineral content of the sample can be determined simultaneously. If fractionation corrections are to be made a mineral must have at least four isotopes. Details of these procedures will be reported separately. 

The pressure-based method was introduced by Harlow and Welch [67] and Chorin [30] for the calculation of unsteady incompressible viscous flows (parabolic equations). In Chorines fractional step method, an incomplete form of the momentum equations is integrated at each time step to 3ueld an approximate velocity field, which will in general not be divergence free, then a correction is applied to that velocity field to produce a divergence free velocity field. The correction to the velocity field is an orthogonal projection in the sense that it projects the initial velocity field into the divergence free... 

Our general conclusion is that it is probably possible to determine ra structures from NMR that are of comparable accuracy to those obtained from other methods. However, the required fractional corrections of observed interactions for vibrational effects will be larger. 

Dukhin et al. [83-85] have performed the direct calculation of the CVI in the situation of concentrated systems. In fact, it must be mentioned here that one of the most promising potential applicabilities of these methods is their usefiilness with concentrated systems (high volume fractions of solids, 4>) because the effect to be measured is also in this case a collective one. The first generalizations of the dynamic mobility theory to concentrated suspensions made use of the Levine and Neale cell model [86,87] to account for particle-particle interactions. An alternative method estimated the first-order volume fraction corrections to the mobility by detailed consideration of pair interactions between particles at all possible different orientations [88-90]. A comparison between these approaches and calculations based on the cell model of Zharkikh and Shilov [91] has been carried out in Refs. [92,93],... 

Thermal ionization mass spectrometry (TIMS) suffers from time-dependent mass bias, referred to as mass fractionation, as a result of the finite amount of sample on the source filament and the more efficient thermal ionization of the lighter isotope. Mass bias correction is more crucial with multi-collector (MC)-ICP-MS as the latter suffers significantly larger bias and, as noted earher, it may not necessarily be constant over extended periods of time. Therefore, rigorous correction methods are required. Over the last few decades, several different mass bias correction methods have been successfully used for the determination of isotope amount ratios, as illustrated by Albarede et al. [16]. 

Chu, Z.-Y., Yang, Y.-H., Guo, J.H., and Qiao, G.-S. (2011) Calculation methods for direct internal mass fractionation correction of spiked isotopic ratios from multi-collector mass spectrometric measurements. Int. J. Mass Spectrom., 299, 87-93. 

Although the raw efficiency, or number of true coincidences acquired, is a basic determinant of the quality of a PET scanner, the complicating factors of scattered and random events and dead time have to be brought into the analysis. Details of the distribution of scattered events and correction methods can be found elsewhere, but for the present purposes it can be stated that scattered radiation (or scatter for short) produces a relatively flat background on the projection and image data, impairing contrast and reducing quantitative accuracy. The quantity of scatter detected, the scatter fraction (SF), is expressed simply in terms of the total true (unscattered -i- scattered) events (Tj j) and the scattered events S) by... 

Recent advances in multi-collector inductively-coupled plasma mass spectrometry (MC-ICPMS) techniques show promise, as this method allows bracketing of samples by standards, thus providing a means for near-simultaneous fractionation correction. Problems with this technique include memory effects (boron from previously analyzed samples or standards remobihzed during subsequent analyses), and extreme sensitivity to the solution matrix, requiring samples and standards to have identical matrices. 

Group the component in a petroleum fraction, which is possible if the normal boiling temperature and the standard specific gravity are known. This method gives correct results when the chemical structure is simple as in the case of a paraffin or naphthene. 

Table 4.16 shows the results of this new method for an example. They differ significantly from those obtained with the method proposed by Riazi for the initial and 10% volume distilled points. The accuracy is improved and the deviations observed at small distilled fractions are corrected. 

The Monte Carlo approach, although much slower than the Hybrid method, makes it possible to address very large systems quite efficiently. It should be noted that the Monte Carlo approach gives a correct estimation of thermodynamic properties even though the number of production steps is a tiny fraction of the total number of possible ionization states. 

As in the case of the free bases, the substitution of a nuclear hydrogen atom by a methyl group induces a bathochromic shift that decreases in the order of the position substituted 4->5->2- Ferre et al. (187) have proposed a theoretical model based on the PPP (tt) method using the fractional core charge approximation that reproduces quite correctly this Order of decreasing perturbation. 

Feed analyses in terms of component concentrations are usually not available for complex hydrocarbon mixtures with a final normal boihng point above about 38°C (100°F) (/i-pentane). One method of haudhug such a feed is to break it down into pseudo components (narrow-boihng fractions) and then estimate the mole fraction and value for each such component. Edmister [2nd. Eng. Chem., 47,1685 (1955)] and Maxwell (Data Book on Hydrocarbons, Van Nostrand, Princeton, N.J., 1958) give charts that are useful for this estimation. Once values are available, the calculation proceeds as described above for multicomponent mixtures. Another approach to complex mixtures is to obtain an American Society for Testing and Materials (ASTM) or true-boihng point (TBP) cui ve for the mixture and then use empirical correlations to con-strucl the atmospheric-pressure eqiiihbrium-flash cui ve (EF 0, which can then be corrected to the desired operating pressure. A discussion of this method and the necessary charts are presented in a later subsection entitled Tetroleum and Complex-Mixture Distillation. ... 

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