Linear slope

Figure C2.8.4. The solid line shows a typical semilogaritlimic polarization curve (logy against U) for an active electrode. Different stages of reaction control are shown in tlie anodic and catliodic regimes tlie linear slope according to an exponential law indicates activation control at high anodic and catliodic potentials tlie current becomes independent of applied voltage, indicating diffusion control.

Current-mode control is best used in topologies where the linear slopes within the eurrent waveforms are higher. This would be the boost-mode topologies sueh as boost, buek-boost, and flybaek. 

FIGURE 6.6 Schilcl regression for pirenzepine antagonism of rat tracheal responses to carbachol. (a) Dose-response curves to carbachol in the absence (open circles, n = 20) and presence of pirenzepine 300 nM (filled squares, n = 4), 1 jjM (open diamonds, n=4), 3j.lM (filled inverted triangles, n = 6), and 10j.iM (open triangles, n = 6). Data fit to functions of constant maximum and slope, (b) Schild plot for antagonism shown in panel A. Ordinates Log (DR-1) values. Abscissae logarithms of molar concentrations of pirenzepine. Dotted line shows best line linear plot. Slope = 1.1 + 0.2 95% confidence limits = 0.9 to 1.15. Solid line is the best fit line with linear slope. pKB = 6.92. Redrawn from [5],... 

Figure 11.14 shows the original MQH data fit and Figures 11.15 and 11.16 show results for compartment lining material fires. Various lining materials were used and the firepower was measured by oxygen calorimetry. Departure from the linear slope behavior marks the onset of the ventilation-limited fires where the correlation based on the total firepower, within and outside the compartment, does not hold. The results for the lining fires also show the importance of the factor omitted from the simple MQH correlation. 

A plot of rj(o) versus the log of reduced stress shows a linear slope between the high and low shear limits. We can use this feature with our master curve to define another value of b. This slope is given by... 

The k2 term must be included since a k ), has a positive intercept ( j) at = is plot of A (if, -t- hf) h vs although linear (slope 0. A simple mechanism consistent with this rate law ... 

The plot of ogk vs p /l + p for the second-order reaction between Co(edta)" and Fe(CN)g- (Sec. 1.6.3) showed an initial linear slope at low p of 3.8, reached a maximum at p 0.1 M and then decreased. The ionic strength was supplied by NaC104. Give a reasonable explanation for this behavior. 

The viscosity of some polymers at constant temperature is essentially Newtonian over a wide shear rate range. At low enough shear rates all polymers approach a Newtonian response that is, the shear stress is essentially proportional to the shear rate, and the linear slope is the viscosity. Generally, the deviation of the viscosity response to a pseudoplastic is a function of molecular weight, molecular weight distribution, polymer structure, and temperature. A model was developed by Adams and Campbell [18] that predicts the non-Newtonian shear viscosity behavior for linear polymers using four parameters. The Adams-Campbell model is as follows ... 

The distribution of M depends on both the free amine salt in the organic phase and the concentration of free 17 in the aqueous phase until all metal in the aqueous phase is bound in the ML7 complex. At constant amine concentration, Eq. (4.64) indicates that a plot of Du vs. [L ] would have a linear slope p if the denominator of Eq. (4.64) is 1 i.e., the metal species in the aqueous phase are dominated by the uncomplexed metal ion At higher [L ] concentrations, where the ML7 complex begins to dominate in the aqneons phase, the >m valne becomes equal to [RNHL]. Equations (4.64) and (4.4) show that 5-shaped curves result for metals with large values. In a plot of Dm vs. [RNHL] ,j a straight line of slope p is obtained only at constant [L ]. From such measurements both p, and Pp can be evalnated. The following example illustrates this. 

Addition of a cosolvent is an alternative mechanism to increase contaminant solubility in an aqueous solution. When a contaminant with low solubility enters an aqueous solution containing a cosolvent (e.g., acetone), the logarithm of its solubility is nearly a linear function of the mole fraction composition of the cosolvent (Hartley and Graham-Bryce 1980). The amount of contaminant that can dissolve in a mixture of two equal amounts of different solvents, within an aqueous phase, is much smaller than the amount that can dissolve solely by the more powerful solvent. In the case of a powerful organic solvent miscible with water, a more nearly linear slope for the log solubility versus solvent composition relationship is obtained if the composition is plotted as volume fraction rather than mole fraction. 

Currents were obtained under a series of voltages, ranging usually from +100 to -100 mV and a constant conductance was always obtained from the linear slope of the current-voltage plot 97 pS in the example shown in Figure 4. In spite of the appearance of such a stable conductance level, the very next run usually gave a different conductance level. These observations are reconciled only by assuming... 

The absorption edge is determined from the intersection point of the energy axis and the extrapolated line of the linear slope of the transmission spectra. The ruby red colour of the (Na Se) and (K Se), and the orange red colour of (Na S) and (K S) correspond with their absorption edges. 

Carstensen directly relates the level at which degradation slows to the amount of water present in the matrix and utilizes this equilibrium level, denoted A, in further kinetic analysis. Kinetic treatment of the data reveals a first order decay character to the degradation, with a linear slope of the log of the thiamine hydrochloride concentration at a specific point (A) in relation to the observed equilibrium level (A ), with respect to time in days. 

A and B are model parameters representing the high-temperature linear slope (du>/8T t oo) and effective phonon-mode temperature (l>hui(Q) jfc >), respectively. w(0) is the phonon-mode frequency at T = OK. Table 3.5 summarizes the best-model parameters reported in [43]. In [127], a linear temperature-dependence with dw[E2 ]/ T = —1.85 x 10 2cm 1 K 1 was reported for temperatures above RT. 

Calcium-aluminum-rich inclusions The CAIs reveal a lot of isotopic action in calcium. But 4°Ca itself is taken as a reference for other isotopes because it is the most abundant. What is measured is the ratio of the other Ca isotope abundances to that of 4°Ca therefore attribution of an anomalous isotopic ratio to an anomaly in 4°Ca abundance is seldom made. Because of systematic linear variations with isotopic mass of the measured isotopic abundances, moreover, it is common to remove that effect by defining the ratio 44Ca/4°Ca as normal, a doubtful procedure, but common. Anomalies in other Ca isotopes thus appear as deviations from the linear slope set by the 44Ca/4°Ca ratio. All this is to say that a self-consistent analysis of the entire Ca suite is required. 

Oleic acid was increased to 48% of total milk fatty acids by feeding oleamide as a rumen-protected source of oleic acid (Jenkins, 1998). The response was nearly linear up to 5% of supplement in the diet dry matter. Proportions of all de uovo-synthesized milk fatty acids, except butyric, were reduced (Jenkins, 1999). LaCount et al. (1994) abomasally infused fatty acids from canola or high oleic acid sunflower oil into lactating cows. The transfer of oleic acid to milk fat was linear (slope = 0.541 0 350 g infused/ day) the proportion of oleic acid in milk fat increased and proportions of all de novo-synthesized fatty acids, except C4 and C6 decreased. The proportion of Ci8 o also was unchanged. Linoleic acid from canola also was transferred linearly (slope = 0.527 0-90 g infused/day). These transfers from the intestine are nearly identical to that reported by Banks et al. (1976). Hagemeister et al. (1991) reported 42 to 57% transfer of abomasally-infused linolenic acid to milk fat. 

VPj = gram solids of ingredient 1 S j = linear slope of ingredient 1 awl = initial aw of ingredient 1... 

Similarly, each of the lines at constant 0 are extrapolated to c = 0, i.e., to sin2(0/2) and the limiting points obtained extrapolated to 0 = 0. In this case the initial linear slope gives z in terms of A/,and n0... 

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