Trimodal distribution measurements

TMPT activity in human erythrocytes is transmitted as an autosomic codominant trait [15] and is trimodally distributed, with 89-94% of the individuals having high, 6-11% intermediate, and 0.3% low activity [7, 15-17] (Figure 14.2). The measurement of TPMT activity in erythrocytes closely reflects the ability of bone marrow to inactivate 6-MP. TPMT activity is inversely related to erythrocyte 6-TGN levels [7, 13, 18, 19], and children with low TPMT activity and very high 6-TGN levels experienced profound myelotoxicity [20, 21]. Moreover, TPMT phenotype in erythrocyte reflects that in leukemic blasts [22]. Patients with intermediate TPMT activity had a 5-fold greater cumulative incidence of dose reductions than subjects with high activity [13], and TPMT activity has been inversely related to the time of treatment withdrawal due to cytopenia [21]. 

Figure 5. Trimodal distribution of a suspension containing 0.261, 1.09 and 2.99 pm latex spheres measured by PCS. For each nominal size, the input and measured mass fractions were as follows For 0.261 pm, input = 0.07, measured = 0.24 for 1.09 pm, input = 0.74, measured = 0.03 for 2.99 pm, input = 0.19, measured = 0.73.

The mode of distribution is simply the value of the most frequent size present. A distribution exhibiting a single maximum is referred to as a unimodal distribution. When two or more maxima are present, the distribution is caUed bimodal, trimodal, and so on. The mode representing a particle population may have different values depending on whether the measurement is carried out on the basis of particle length, surface area, mass, or volume, or whether the data are represented ia terms of the diameter or log (diameter). 

As noted above, the LUT algorithm assumes a unimodal lognormal functional form to describe stratospheric aerosols. This approximation is well suited for most non-volcanic stratospheric aerosols as shown by Pueschel et al. [7] and Yue et al. [8]. Volcanic size distributions, however, are typically bi- or trimodal. This raises the question of whether the assumption of unimodality in the LUT can introduce bias into retrieved values of Rt//, S and V. Russell et al. [1] have shown that retrieved unimodal distributions accurately describe the second, larger mode of several measured bimodal size distributions, but fail to account for the smaller particles in the first mode. The smaller particles, which contribute little to the measured extinction spectra, are not accounted for in the LUT retrievals. Unless this bias is accounted for, the values of Rtff retrieved under the assumption of a unimodal distribution will be overestimated. 

Figure 9 shows the molar mass distribution of a styrene/MMA block copolymer as measured using R1 and UV detection. The R1 responds to the styrene and MM A units, whereas the UV tuned to 260 nm predominantly picks up the presence of styrene in the copolymer. After detector calibration, the styrene and MMA content in each fraction can be measured. The MMA content distribution (black solid line) is superimposed on the MWD of the product in Fig. 9. It is obvious that the MMA content is not constant throughout the MWD, but continuously increases with the molar mass. The trimodal MWD itself shows only the presence of three different species. The MMA content information clearly reveals that the copolymerization process did not produce the block structure, but that the MMA was added to styrene chains of different molar mass.

Mode n The value of the data or observation in a set that has the highest frequency of occurrence. For a continuous distribution, the mode is the point on the density function with the greatest magnitude. In some situations there may be more than one mode. This occurs when there are multiple values that have the same and highest fi equency of occurrence. A set with a single mode is referred to as unimodal and a set with more than one mode is referred to as multimodal The terms bimodal and trimodal are commonly used for sets with two and three modes respectively. The mode is one of the common measures of central tendency. 

In agreement with the DRS measurements of Wettonetol. (154,155], the distribution of correlation times from NMR was found to be broader in the blend compared to the pure polymers. The 2D patterns could not be described by either a single-exponential correlation function or a single stretched exponential a multimodal distribution (bimodal or trimodal) was found more appropriate where the relative weighting of the components was correlated with local concentration fluctuations. 

Figure 3 A trimodal number-size distribution of an Arctic aerosol measured during the International Arctic Ocean Expedition 1991 (1). The solid squares represent the measurement, and the solid line the sum of log-normal distributions (dotted lines) of the ultrafine, the Aitken, and the accumulation mode.

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