Complementary fraction

Cumulate control lines vs liquid lines of descent. In a study of the 1931-1986 basaltic eruptions from the Reunion Island (Indian Ocean), Albarede and Tamagnan (1988) found the Ni and Cr concentrations (in ppm) listed in Table 3.1 and shown in Figure 3.2. Samples with Ni>100ppm were found to contain large amounts of cumulus olivine. The last five samples of Table 3.1 are picrites. The smooth trend observed for all the rocks is suggestive of a complementary fractionation-accumulation relationship out of a single magma batch. Therefore, it is asked whether the trend observed for Ni and Cr in basalts with less than 100 ppm Ni may be ascribed to the removal of the olivine found in the cumulates. 

An old technology that is regaining popularity for peptide cation separation is ion mobility (19). This analyzer provides a complementary fractionation of the peptide ions as they are passed through a carrier buffer gas prior to mass analysis. Separation is achieved through the differential mobility of the ions due to their charge, size, and conformation. Application of ion mobility configurations at the inlet of MSs has proved very effective at separating peptides... 

When a fractional factorial design has been employed, there is always a possibility to run complementary fractions to resolve confounded effects. 

Full factorial designs Such designs are the best choice when the number of variables is four, or less. A full four-variable factorial design gives estimates of all main effects and two-variable interaction effects, and also an estimate of the experimental enor variance. This is obtained firom the residual sum of squares after a least squares fit of a second-order interaction model, see (Example Catalytic hydrogenation, p. 112). A full factoral design should be used if individual estimates of the interaction effects are desired. Otherwise, it is recommended first to run a half fraction 2 " (I = 1234), and then run the complementary fraction, if necessary, (see Example Synthesis of a semicarbazide, p. 135). 

With more than eight variables it is probably more practical to use a Resolution III design first, and run a complementary fraction by fold-over. 

Product separation and purification the first distillation column is designed to produce a cut enriched with acetic acid by the removal of the lighter and heavier components (methyl iodide, methyl acetate, etc.. This-cut is then dehydrated by heteroazeotropic distillation. The aqueous fraction recovered at the top is refractionated to remove excess water. The heavy stream is treated in a finishing column which produces glads acetic add in the distillate, while the residual acetic add at the bottom is also recovered in a complementary fractionation that separates the heavy products such as propionic add. These high-alloy steel columns each have between 35 and 45 actual trays. 

A quantUe divides a set of observations in two groups, such that one fraction falls above and the complementary fraction below, the value specified by the quantile. The most frequently appUed quantiles are quartiles and percentiles. 

By the time a total charge of 2F is transferred from the anode to the cathode, one mole of Cu has dissolved at the anode and an identical quantity of Cu has deposited at the cathode. And yet, only a fraction of the Cu ions liberated at the anode cross the junction because, in the electrolyte, both cations and anions contribute to the ionic current. The Cu ions carry a fraction t+ of the total current, with the SOl" ions providing the complementary fraction of the current t =l -t+ (we assume that there... 

The complementary fraction in the L.E. is 1 - s. s(X,t ), which may also be written s(X,a), is known as the "segregation function". This term is somewhat confusing as the process above is concerned with segregation of ages (mixing earliness). However, s(X,a) also describes the decay of segregation in the physical sense under the additional (and often made) assumption that E.E. = macrofluid and L.E. = microfluid. In the particular tube considered above, the... 

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