Final slope

When carbon (S) spins are locked following a CP 90° pulse, the HB term becomes nonsecular and, after these oscillations vanish, the S spin-lock magnetization is fractionally reduced. Thus, the observed decay is generally a sum of two Weibull functions, usually exponentials (Equation 20 p = 1) the initial slope reflects a Tle dominated by a spin-lattice process and the final slope yields a Tt dominated... 

The rate of reduction of cupric ion is illustrated in Fig. 3 (1). Curve 21 represents the hydrogen pressure drop observed in a typical experiment. Curve 23 is a repetition of this reduction, starting, however, with the reduced solution of experiment 21, which was oxidized by molecular oxygen from a red reduced solution to a green oxidized one. The final slopes (reduction rate) are the same for 21 and 23, the only difference being that 23 has a much longer induction period. If the reaction is stopped just before the flat portion of the curve (21 and 23) is reached and the solution filtered through a fine filter paper, no precipitate is found. 

Schaefer et al. performed kinetic studies with radioiodinated apoA-I and apoA-II in two patients with homozygous Tangier disease (S5). ApoA-I was removed from the circulation faster than apoA-II, but both were catabolized much faster than in normal subjects. After the plasma HDL concentration was increased by HDL infusion in one of the Tangier patients, a repeat kinetic study showed that increasing HDL concentration may have influenced the initial removal of HDL tracer from the circulation, but not the final slope of the plasma radioactivity removal curve (S5). 

Additional relations are obtained from the initial and final slopes of 0 vs. [74], which are useful as internal criteria of the method. 

From the neutralization curve (Fig. 22.2), the initial and final slopes are drawn (Fig. 22.3) and a parallel line is drawn such that the mid-point is on the curve. This is the equivalence point, producing a titration value of xmL. 

The derivation of this relation will be treated in a future publication dealing more extensively with heating corrections to diffusion data, finally, it was found that values of D obtained from the final rate of sorption using (8) with n replacing Xj, were very close to the half-time or JA values, which varied in a more systematic manner with concentration. Therefore, the final slope was computed from these values of D. 

When analysing the data in the range of short adsorption times, a y(Vt)-plot is useful (Van Himsel Joos 1987a, Fainerman et al. 1994a). The results from Fig. 5.31 are shown in this form in Fig. 5.32. Only at low concentrations can a reasonable diffusion coefficient be calculated. For higher concentrations, the final slope of y(Vt) is located outside the experimental range, so that D cannot be determined from the plot. 

Eq. (2.76) requires a summation from 1 to s. The final slope in eq. (2.76) becomes indefinite at the limit Assuming r, is the smallest eigen-... 

In this case the sums have to be taken from 2 to s. Then all the exponents are negative. Consequently at the limit r —> <>o all the exponential functions become zero therefore the final slope is given by... 

The determination of these final slopes is demonstrated using the mechanism of a multi-step consecutive reaction... 

The final slopes are given in Table 2.7 for a variety of cases. In the first column the concentrations are listed which are graphed versus each other to form the K-diagram The next three columns repre-... 

In these equations, the symbols represents the degree of advancement reduced with respect to the initial concentration. In consequence in the -diagrams (reduced X-diagrams) the initial o and the final slopes are given according to eq. (2.87) as... 

In any case the final slope for this type of reaction in an X-diagram amounts to... 

These mechanisms given in this section are again compared in Table 3.4 with respect to mechanism, resulting in degrees of advancement and final slopes. 

The constant x was defined by eq. (3.40). Since this x does not contain any initial concentrations, the final slope in an ED-diagram will... 

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