Averages intrinsic average

The affinity and cross-reactivity of the whole serum and Fab fragments were determined using equilibrium dialysis for the affinity determination and RIA for the cross-reactivity studies. The average intrinsic affinity constant (Ko) of the antibody (Nisonoff and Pressman 1958) changed very little throughout the... 

For polydisperse samples, the weight average intrinsic viscosity [p])w is measured (Equation (8)) and the so-called viscosity averaged molar mass is obtained ... 

The AGq data may be compared with the average intrinsic barrier expected for a concerted dissociative process to the sulfides. A value of 15.7 kcal mol... 

As specific viscosities are additive in the limit of infinite dilution, the weight average intrinsic viscosity is obtained for a polydisperse polymer and My is defined as... 

It should be noted that, since the H/Br difference is opposite in sign to the H/Cl and Br/Cl differences, the average intrinsic shift difference is considerably smaller than the absolute values of the... 

Besides the phase average, it is also important to introduce the intrinsic average, which is defined by... 

Hence, the phase average can be related to the intrinsic average by the volume fraction of phase k, c, as... 

Usually, the intrinsic average reflects the real physical property or quantity such as density and velocity, while the phase average gives a pseudoproperty or quantity based on the selection of control volume. Phase averages are used to construct the continuum of each phase to which Eulerian description can be applied. 

Note that volume averaging can only be applied to quantities per unit volume, such as density, momentum per unit volume, and energy per unit volume. The intrinsic average of the velocity of phase k may thus be defined as... 

Furthermore, the intrinsic average of velocity correlation may be approximated by a product of intrinsic averages of velocities as... 

The approximation in the preceding equation is to circumvent any conflict with Eq. (5.100), which defines the intrinsic average of velocity. This approximate relation becomes an equivalent one under the isothermal condition of phase k with the expansion work estimated by... 

Assuming the material density or the intrinsic averaged density of phase k to be constant (as is true for the solids and almost true for the fluid when the effect of temperature variation on the material density can be neglected), we have... 

The relationship between regional average and intrinsic average is... 

To simplify the problem further, we adopt a concept similar to that for the intrinsic averaged velocity and intrinsic velocity tensor as in Eqs. (5.129) and (5.130). Thus, Eqs. (6.95) and (6.96), respectively, become... 

For subsequent discussions, the symbol () is removed with an understanding that the velocities and densities involved are intrinsically averaged. 

The dimensionless intrinsic average of the total mass density having been expanded in a Taylor series... 

Intrinsic averaging corresponds to calculating density, concentration, or other parameter directly obtainable from experiments. Comparison of (A-7) and (A-8) shows that... 

Figure 6. Intrinsic reaction rate in dependence of sulphur poisoning for a) normal catalysts ( ), b) gum deactivated catalysts (A). The dotted line represents the ideal relation for the average intrinsic activity of a normal shell poisoned catalyst, 0 = 0.9. Steam reforming of ethane, H2O/C = 4.0, P = 1 bar. Activities normalized with activity of unpoisoned catalyst.

Antigen Injected (mg) Average Intrinsic Association Constants for Binding of c-DNP-Lysine to Anti-DNP Antibodies ... 

The average of the spatial deviation V fc is computed applying the intrinsic average operator (3.118) on (3.208). The obvious result is ... 

If i( is a constant, then < /f )f = /<. The intrinsic average is useful in analysis of multiphase flow and in dealing with the energy equation. 

The results showed that K promotion resulted in almost 50 times the increase in the reaction rate. TOF based on the amount of hydrogen chemisorption increased by about two orders of magnitude with K-promotion. However, the intrinsic TOF based on SSITKA increased only by a factor of 16. The increase in activity with K promotion was actually due to both a significant increase by a factor of 3 in the surface concentration of intermediates, and an increase by a factor of 16 in the average intrinsic site activity. 

When dealing with porous catalysts, one generally does not work with the intrinsic average transport equation given by... 

In this notation for the volume averages, a Greek subscript is used to identify the particular phase under consideration, while a Greek superscript is used to identify an intrinsic average. Since the intrinsic and superficial averages differ by a factor of Sy, it is essential to make use of a notation that clearly distinguishes between the two averages. 

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