Asymmetry, defined

Following Ref. [29] we introduce the quark chemical potential for the color c, fiqc and the chemical potential of the isospin asymmetry, //,/, defined as... 

Asymmetry in a similarity measure is the result of asymmetrical weighing of a dissimilarity component - multiplication is commutative by definition, difference is not. By weighing a and h, one obtains asymmetric similarity measures, including the Tversky similarity measure c j aa 4- fih + c), where a and fi are user-defined constants. The Tversky measure can be regarded as a generalization of the Tanimoto and Dice similarity measures like them, it does not consider the absence matches d. A particular case is c(a + c), which measures the number of common features relative to all the features present in A, and gives zero weight to h. 

Band Asymmetry. The peak asymmetry factor AF is often defined as the ratio of peak half-widths at 10% of peak height, that is, the ratio b/a, as shown in Fig. 11.2. When the asymmetry ratio lies outside the range 0.95-1.15 for a peak of k =2, the effective plate number should be calculated from the expression... 

Three Parameter Models. Most fluids deviate from the predicted corresponding states values. Thus the acentric factor, CO, was introduced to account for asymmetry in molecular stmcture (79). The acentric factor is defined as the deviation of reduced vapor pressure from 0.1, measured at a reduced temperature of 0.7. In equation form this becomes ... 

Figure 8-38 shows the residenee time distributions of some eom-mereial and fixed bed reaetors. These shapes ean be eompared with some statistieal distributions, namely the Gamma (or Erlang) and the Gaussian distribution funetions. However, these distributions are represented by limited parameters that define the asymmetry, the peak. 

The peak measured for a plate number determination contains additional information about the packing quality of a column. The same peak may also be used to quantify information about the shape as well. The peak width on both sides of the perpendicular through the peak maximum is measured at a height of 10% of the maximum height (see Fig. 14.2). The quotient of the back by the front part of the peak is defined as the asymmetry factor (AF) ... 

Fig. 7. Data of Parsonage et al. [77] on the adsorption of a series of block copolymers of polystyrene-poly-2-vinylpyridine. The ordinate is the measured surface density ( d 2) reduced by the density required for the nonadsorbing chains to overlap the abscissa is the solvent-enhanced size asymmetry of the block copolymer defined under Eq. 26. The form of this plot is that suggested by Eq. 28...

It would seem that, in practice, the inequality defined in (3) can frequently occur but the converse does not appear to be true. Thus, peak asymmetry (in part or whole) resulting from inequality in mass transfer between the two phases manifests itself in the form shown in figure 1. 

When only a few measurements of a given property are available, and especially if an asymmetry is involved, the median is often more appropriate than the mean. The median, x , is defined as the value that bisects the set of n ordered observations, that is,... 

Ever since Pasteur s work with enantiomers of sodium ammonium tartrate, the interaction of polarized light has provided a powerful, physical probe of molecular chirality [18]. What we may consider to be conventional circular dichroism (CD) arises from the different absorption of left- and right-circularly polarized light by target molecules of a specific handedness [19, 20]. However, absorption measurements made with randomly oriented samples provide a dichroism difference signal that is typically rather small. The chirally induced asymmetry or dichroism can be expressed as a Kuhn g-factor [21] defined as ... 

Circular dichroism convention. In this chapter, dichroism and asymmetry factors are defined as /icp hep or / =... 

An asymmetry or skewness parameter, f, ranging between 0 and 1 may be defined as... 

This case is shown schematically in Fig. 5c. In Eq. (50), qj. are generalized y-photon asymmetry parameters, defined, by analogy to the single-photon q parameter of Fano s formalism [68], in terms of the ratio of the resonance-mediated and direct transition matrix elements [31], j. is a reduced energy variable, and <7/ y, is proportional to the line strength of the spectroscopic transition. The structure predicted by Eq. (50) was observed in studies of HI and DI ionization in the vicinity of the 5<78 resonance [30, 33], In the case of a... 

In another study, Yamakazi and Elliott [73] measured the interference within a single angular momentum state arising from coupling to different continua. They defined an asymmetry parameter,... 

The permeability coefficients, PD and PR, are influenced by hydrodynamics. Depending upon the geometric symmetry or asymmetry of stirring in the donor and receiver chambers, their values may be equal or unequal. To analyze these situations, let us define PAm, as the effective permeability coefficient of the ABLs therefore, the geometric average of the mass transfer resistance of the ABLs is... 

In the general case, when the shielding tensor is not of axial symmetry, in place of its diagonal elements axx, ayy and kyyl > axx i the following parameters are generally used asymmetry parameter V = <3xx — ayy)/Gzz = (3/2)(cTj.j. — oyy)/h.o. The second form of rj arises from the fact that, as far as relaxation is concerned, the shielding tensor can be defined with respect to any time-independent reference (which therefore will not act as a relaxation mechanism). [Pg.96]

Asymmetry ratio, defined as (Vd/VaXP /Pc0 )) where Vd and Va are donor and acceptor solution volumes, respectively, and the superscripts refer to the two possible directions of transport... 

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