Skewness ratio

Zero Coverage. The peaks at Infinite dilution were slightly skewed (skew ratio 0.8), with virtually no dependence of retention volume on Injection size. Instead of the peak maximum method, retention volumes were measured by the method proposed by Conder and Young (32). To ensure that the adsorption of n-alkanes on carbon fibers was taking place under equilibrium conditions, the flow rate was varied In the range 20 to 32 cm3 min-1. The net retention volumes were essentially Independent of flow rate. 

There is an increase in the skew ratio parameter to a value of about 0.08 gg of water vapor, beyond which there is no further influence. An immediate explanation is that water molecules are adsorbed preferentially on any surface oxygen complexes which may be present and this could be effective in reducing the number of adsorption sites which exhibit a maximum in retentivity. Once all of these adsorption sites are occupied by water molecules, then increasing the water content of the incoming gas mixture has no further adverse effect on the skew ratio. 

Fig. 16.6 Chromatogram presenting the Conder and Young method to obtain the skewness ratio (a/b) and retention time, tg...

In the case of perfect symmetric peaks, the retention time can be determined directly from the peak maximum method, which is the simplest and most common. The peak maximum method is useful for determination of retention time if the skewness ratio is 0.7-1.3 [15]. The skewness ratio is defined as the ratio of tangent slope to the peak leading part and tangent slope to the peak tailing part whereas both tangents are drawn in the inflexion points. In such cases the skewness ratio is our of this interval, Ir is obtained from the first-order moment method or the Conder and Young method. Between these two methods, Conder and Young is recommended [16] ... 

In the most common production method, the semibatch process, about 10% of the preemulsified monomer is added to the deionised water in the reactor. A shot of initiator is added to the reactor to create the seed. Some manufacturers use master batches of seed to avoid variation in this step. Having set the number of particles in the pot, the remaining monomer and, in some cases, additional initiator are added over time. Typical feed times ate 1—4 h. Lengthening the feeds tempers heat generation and provides for uniform comonomer sequence distributions (67). Sometimes skewed monomer feeds are used to offset differences in monomer reactivity ratios. In some cases a second monomer charge is made to produce core—shell latices. At the end of the process pH adjustments are often made. The product is then pumped to a prefilter tank, filtered, and pumped to a post-filter tank where additional processing can occur. When the feed rate of monomer during semibatch production is very low, the reactor is said to be monomer starved. Under these... 

Resolution in TLC is defined in a similar manner to that in GC and LC, as the ratio of the mean spot width (peak width at the base) to the separation distance between the centers of the two spots (see figure 4). However, this will only be acceptable if the spots are not skewed under which circumstances the point of highest concentration within the spot is used. 

Peak asymmetry or skewing is a well-documented (4,6,7) characteristic of chromatographic peaks and is measured easily by ratioing the peak half widths at 10% height as shown ... 

Figure 22 shows the area ratio and average film thickness as a function of skewness. Similar trends to those shown in Fig. 21 are observed. When a smooth surface normally approaches a rough surface, a surface with positive skewness will be much more engaged in contact than the one with negative skewness. Since the average film thickness remains almost the constant, as demonstrated in Fig. 22(b), the real contact area will increase with skewness. 

Fig. 21 —The changes of lubrication properties with the kurtosis, simulated at cr=0.1 /xm and different values of skewness, (a) Contact area ratio versus skewness, (b) Load ratio versus skewness, (c) Maximum pressure versus kurtosis. (d) Maximum temperature versus kurtosis. (e) Average film thickness versus kurtosis.

Fig. 22—The change of contact area ratio and average film thickness with skewness, simulated at o-=0.1 /u.m and for different kurtosis. (a) Area ratio versus skewness and (b) average film thickness versus skewness.

The Knoop test is a microhardness test. In microhardness testing the indentation dimensions are comparable to microstructural ones. Thus, this testing method becomes useful for assessing the relative hardnesses of various phases or microconstituents in two phase or multiphase alloys. It can also be used to monitor hardness gradients that may exist in a solid, e.g., in a surface hardened part. The Knoop test employs a skewed diamond indentor shaped so that the long and short diagonals of the indentation are approximately in the ratio 7 1. The Knoop hardness number (KHN) is calculated as the force divided by the projected indentation area. The test uses low loads to provide small indentations required for microhardness studies. Since the indentations are very small their dimensions have to be measured under an optical microscope. This implies that the surface of the material is prepared approximately. For those reasons, microhardness assessments are not as often used industrially as are other hardness tests. However, the use of microhardness testing is undisputed in research and development situations. 

The monitoring uncertainty and operational transient margin is to ensure that the minimum DNB ratio is calculated at the worst operating condition. The assumed worst operating condition consists of a power surge of 12% in a worst power distribution (power skew at top), accompanied by an inlet coolant temperature elevation of 4°F (2°C) and a pressure swing of 30 psi (0.2 MPa). A set of worst hot channel factors in core life should also be used in evaluation of the worst power distribution. Such an assumed worst operating condition is obviously overly... 

For EMG peaks, peak skew increases with the ratio xG/oG. Figure 16-32 illustrates the characteristics of such a peak calculated for xG/aG = 1.5. In general, with xG/aG > 1 (peak skew > 0.7), a direct calculation of the moments is required to obtain a good approximation of the true value of N , since other methods give a large error (Yau et al., Modems Size-Exclusion Liquid Chromatography, Wiley, New York, 1979). Alternatively, Eq. (16-165) can be fitted to experimental peaks to determine the optimum values of fG, aG, and xG. 

Furthermore, it is sometimes questionable to use literature data for modeling purposes, as small variations in process parameters, reactor hydrodynamics, and analytical equipment limitations could skew selectivity results. To obtain a full product spectrum from an FT process, a few analyses need to be added together to form a complete picture. This normally involves analysis of the tail gas, water, oil, and wax fractions, which need to be combined in the correct ratio (calculated from the drainings of the respective phases) to construct a true product spectrum. Reducing the number of analyses to completely describe the product spectrum is one obvious way to minimize small errors compounding into large variations in... 

Mendal et al. (1993) compared eight tests of normality to detect a mixture consisting of two normally distributed components with different means but equal variances. Fisher s skewness statistic was preferable when one component comprised less than 15% of the total distribution. When the two components comprised more nearly equal proportions (35-65%) of the total distribution, the Engelman and Hartigan test (1969) was preferable. For other mixing proportions, the maximum likelihood ratio test was best. Thus, the maximum likelihood ratio test appears to perform very well, with only small loss from optimality, even when it is not the best procedure. 

Butene exists as an equilibrium mixture of two conformations, Me-skew and Me-syn (21). The most reliable composition to date is 83 17% according to combined ED, microwave (MW), and ab initio MO analysis (133). This study includes the MM (CFF)-ED-MW analysis of this molecule for comparison, which gave a final skew/syn ratio of 80 20. The molecular orbital constrained electron diffraction (MOCED) results appear to agree better with the observed data than does the MM constrained analysis, the R value of the least-squares analysis of the latter being 20% higher than that of MOCED. However, one may ask whether such a small difference in R values justifies the enormous difference in computer time between the ab initio (about 200 hr on an IBM 370/155) and MM (less than a minute) methods used in this work. 

Unfortunateiy, K z cannot be easily determined analytically, and is often either estimated using methods from the fieid of soil mechanics (from the normal stress ratio, K ), or simpiy adjusted to a vaiue which produces good fits for experimental data. The same can be said for the skew angie, a. 

Studies of the host rocks to giant porphyry copper deposits in Central and Northern Chile have shown that there are recognizable changes in the geochemistry of the volcanic rocks prior to mineralizing events (Skewes Stern 1995 Kay et al. 1999 Hollings et al. 2005). These include abrupt increases in the LaA b ratios of volcanic rocks associated with... 

It has been shown recently [25] that concentrations of NOj, tend to reduce with increase in the amplitude of discrete-frequency oscillations. The mechanisms remain uncertain, but may be associated with the imposition of a near-sine wave on a skewed Gaussian distribution with consequent reduction in the residence time at the adiabatic flame temperature. Profiles of NO, concentrations in the exit plane of the burner are shown in Fig. 19.6 as a function of the amplitude of oscillations with active control used to regulate the amplitude of pressure oscillations. At an overall equivalence ratio of 0.7, the reduction in the antinodal RMS pressure fluctuation by 12 dB, from around 4 kPa to 1 kPa by the oscillation of fuel in the pilot stream, led to an increase of around 5% in the spatial mean value of NO, compared with a difference of the order of 20% with control by the oscillation of the pressure field in the experiments of [25]. The smaller net increase in NO, emissions in the present flow may be attributed to an increase in NOj due to the reduction in pressure fluctuations that is partly offset by a decrease in NOj, due to the oscillation of fuel on either side of stoichiometry at the centre of the duct. 

Fry D.M., C.K. Toone, S.M. Speich, and R.J. Peard (1987). Sex ratio skew and breeding patterns of gulls Demographic and toxicological considerations. Studies in Avian Biology 10 26-43. 

The reason why ratios of geometric means are used in this context is as discussed in Section 11.4 the distributions of AUC and tend to be positively skewed and the log transformation is applied to recover normality. 

The degree of skewness is measured by the dimensionless third moment, fi3/fll12, where the normalized moment fip = npfot0 so that fio—l. The ratio gives a measure of unimodal versus bimodal behaviour in the eigenspectrum, as we will show later. 

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