Asymmetry coefficient

Figures 9.11 (a), (b) show the experimental results of the electric field dependency of the asymmetry coefficient ms...

Figure 9.11 Results of the scattering hysteresis experiment with an external electric field E0 a) asymmetrie coefficient ms versus E0 b) total scattering intensity f Is normalized on the scattering intensity at zero field versus E0. The direction of the arrows denote the sequence of the field changes.

Ultracentrifuge data can also be interpreted to give information about the effective shape of the dissolved polymer molecules. The actual frictional coefficient (f) can be calculated from the sedimentation constant, and this compared with the theoretical figure (f0) calculated from Stokes law (assuming a spherical molecule). The frictional ratio (f/fo) has been called the asymmetry coefficient. It expresses the deviation of the molecule in solution from a spherical shape, and can be interpreted in terms of the axial ratio of idealized particles. 

Second, we will consider that the degree of correlation between the fluctuating bilayers depends on their separation distance, with total correlation as z — - 0 and no correlation as z - °o. This provides an asymmetric distribution (Figure lb), which will be described using an asymmetry coefficient a in a truncated Gaussian distribution... 

And finally, studies of the phase function, P ( ), of StA, undertaken by G. Grams within the framework of IWLAAP [24], have made it possible to estimate the asymmetry coefficient g = < cos 6 > =... 

The moments of the highest orders [65] are used for more descriptive characterization of distribution. The asymmetry coefficient Yj = ju a, where ju is the central... 

The normal type of distribution, among all other distributions used in practice, has taken a special place because owing to the hmiting theorem, the vast majority of distributions asymptotically approaches the normal distribution with the growth of the extract volume [65]. The asymmetry coefficient Yi and excess Y2 are compared with the dispersions of these parameters D(Yi) and D(Y2> for verification of the correspondence of the distribution character of the incidental values Ri to the normal distribution. The dispersion functions can be expressed as follows ... 

In accordance with consent criterion, the asymmetry coefficient Yi and excess Y2 must comply with the following inequalities ... 

In some cases in HPLC, the IP agent can be added to the mobile phase to reduce the retention times of the solutes and to obtain an acceptable asymmetry coefficient. For example, the retention times of enoxacin and its 4-oxo metabolite and of pefloxacin decrease as the concentration of tetrabutylammoni-um hydroxide in the mobile phase increases and the peak sharpens as a consequence of this decrease in retention time. 

With the consideration of new forces and the asymmetry coefficients, the phenomenological equations given by Eqns (11.82)-( 11.84) reduce to... 

We note that the asymmetry coefficients a, b, and C3 affect the critical amplitudes but not the amplitude ratios which continue to have the same universal values listed in Table 10.3. Substitution of the parametric expressions for the scaling fields, sealing densities, and scaling susceptibilities from Table 10.4 into eqs 10.39 to 10.44 yields a linear-model equation of state consistent with complete scaling. 

Classical theories satisfy complete scaling in the mean-field approximation. Classical equations of state are analytic at the critical point, so that the d, jl, and P can be expanded in terms of powers of AT and Ap. The classical power series are recovered when the relations of the scaling fields and densities with the physical fields and densities, in accordance with complete scaling, are introduced in the classical Landau expansion of eq 10.6 with appropriate values for the coefficient Qq and uq and for the asymmetry coefficients b2, and in the scaling fields. Wang and Anisimov have collected values for ao and Uq and for the asymmetry coefficients and Z eff, associated with several classical equations of state. 

Just as eq 10.52b for Apmole fraction of a liquid mixture depends on the asymptotic behaviour of the specific heat capacity and on two asymmetry coefficients, namely eff= - Xcai/(l-Xcai) and h = b -xJ 2)lxJ -b2Sc). 

Equations 10.65a and 10.65b yield an excellent description of the mole fractions of the coexisting liquid phases as a function of temperature. As an example we show in Figure 10.3 Axcxc and Ax of four hydrocarbon solutions in nitrobenzene. Wang et al have found empirical evidence that the asymmetry coefficients aefr and efr are related to the ratio of the molecular volumes of the two components. 

If stray currents are random in character and have an alternate polarization, then from this relation the asymmetry coefficient yean be determined of changes of the structure potential E in relation to the stationary potential. The value of this coefficient is the measure of hazard. It determines the probability P that the potential value will be more positive than the stationary potential. In other words, it is the percentage share of time Te>Es of anodic polarization of the structure in the observation time T. The above dependencies can be given in the following way... 

A characteristic feature of these modified coefficients is that their values are included always in the strictly determined intervals the value of modified asymmetry coefficient K2m is always in the interval <-l, 1>, while the value of the modified flattening coefficient Kim is always in the interval <0,1>. 

Examples of the results of screen analysis for one of the grinding series are given in Table 4 which contains also calculated values of coefficients Ki Eq. (2) and K2 Eq. (3) and modified forms of these coefficients, i.e. Kjm and K2m- It was presumed preliminarily that the relationship between the values of flattening and asymmetry coefficients Kjm and K2m and the... 

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