Approximation effects

Table 8.2 Approximate Effective Ionic Radii in Aqueous Solutions at 25°C 8.4...

These temperatures, partial pressures, and dimensions were used in Example 6 to determine gas emissivity and absorptivity, .q = 0.145 OCci = 0.210. The approximate effective emissivity of the boundary is (0.8 -I-1)72 = 0.9. Then from Eq. (5-155), modified to allow for sink emissivity and for the presence of a small amount of refractory boundary,... 

Equation (9-113) shows that Eq. (9-114) is only approximately true and should be used, if at all, solely for low interest rates. Let us consider the case of a nominal (DCFRR) of 5 percent and an inflation rate of 3 percent. Equation (9-14) yields an approximate effective return rate of 2 percent, compared with the real effective rate of 1.94 percent given by Eq. (9-113) i.e., there is an error of 3.1 percent. Now let us consider the case of a nominal (DCFRR) of 2.5 percent and an inflation rate of 23 percent. Equation (9-114) yields an approximate effective return rate of 2 percent, compared with 1.63 percent from Eq. (9-113) in this case, the error that results is 22.7 percent. 

Table 1.6 Approximate effects of voltage and frequency variations on motor performance...

Figure 7-6A. Diagram of approximate effects of backpressure on safety reiief vaive operation. Adapted by permission, Teledyne Farris Engineering Co.

The collective set of energetic advantages that result from productive substrate binding to the enzyme active site is known as the approximation effect. In concert, these effects can provide an important means of at least partially lowering the activation energy for transition state formation. 

Let the effective loss coefficient now include, in addition to intrinsic loss, a contribution due to absorption (and scattering) by the analyte contained in the evanescent fraction/of the WGM y = yx +/xa. The effect of the analyte on the resonant (single-frequency) drop signal D0a, when analyte absorption is a small fraction of the total loss, can be written in terms of an approximate effective absorption path length Leff as defined below ... 

Triamterene is a pyrazine derivative that inhibits reabsorption of sodium ions without increasing excretion of potassium ions. It exhibits the same approximate effect as spironolactone however, it does not competitively bind with aldosterone receptors. Its action does not have an effect on secretion of aldosterone or its antagonists, which are a result of direct action on renal tubules. 

Screening 6-40 Identify important variables. Estimate approximate effects. Plackett-Burman (PB) 2 Fractional feaorial (FF)... 

For the nearly symmetric copolymers studied by Hashimoto et al. (1994), the mismatch in composition was small. Thus, the approximate effective Flory-Huggins interaction parameter... 

Fig. 2.47 The approximate effect on the Curie point of the substitution of either strontium or...

For consistency with the quadratic approximation used in the potential expansion, the above expression for H has been tmncated at the quadratic term the higher-order and off-diagonal terms in the expansion can be treated as perturbations. Then, the approximate effective Hamiltonian for the reaction dynamics can be written in the form... 

The expansion, Eq. (6-2), was extended to higher order in 0 by a simple, though approximate, effective medium argument of Arrhenius (1917). According to this argument, we suppose that we increase hy d4> the particle concentration in a suspension of viscosity... 

Because we are working to linear order in iAL, we have used the fact that uUo,s) can contribute only higher powers of iL = ILq + iAL. Fligher powers of linear approximation. Effectively, it can be seen that the operator Ur(0, s) = e ° + 0(/AL), where O(iAL) indicates terms of order /AL and where we have used Eq. [99] and the time independence of /Lq. We also note that by definition, iLo/eq = 0. Thus only the first term in the Taylor series expansion of 17 (0, s) survives, yielding = /eq and we obtain Eq. [103]. 

The term e lKf>sV elKf>s in Eq. (88) is equal to the inverse time evolution that the operator Vi would have in the Heisenberg picture for the dynamics generated by Kq. Thus D, which is the term that is added to constitute the approximate effective Hamiltonian Kn = Kq + D, can be interpreted as the average of the perturbation with respect to the dynamics generated by Kq. 

The usual RWA consists in neglecting the 0-dependent operator V. The first term of V) (319) contains the counterrotating terms of the pump laser on the 1-2 transition and of the Stokes laser on the 2-3 transition. The next two terms correspond to the interactions of the pump laser on the 2-3 transition and of the Stokes laser on the 1-2 transition. Following the hypothesis (316), we neglect the first two terms and keep the last term, which becomes large (see Ref. 38 for details) when maxJ Oi(t), fi2(t) ] approaches or overcomes 8. The (approximate) effective one-mode Floquet Hamiltonian is thus... 

FIGURE 3.1 Plot of the approximate effect of various air to fuel ratios on the composition of automotive exhaust gas. Compiled from the data of Acres [I] and Stoker and Seager [7]. 

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