Sigmoidal manner

A typical grade efficiency curve, shown in Figure 1.10, rises from some minimum value, at small particle size, in a sigmoidal manner to a value of 1, at a size usually defined as dm. ) and G(d) = 1. 

The solubilizing power of a supercritical fluid depends on its density and capacity for specific intermolecular interactions. The density is related to the experimental parameters of pressure and temperature in a non-linear manner, Figure 7.2, described by an equation of state. Close to the critical point the density changes markedly in a sigmoidal manner with small changes in pressure. At temperatures further removed from the critical point the isobars are flatter and the change in density with pressure is... 

Repeat of the same land of experiments at other pHs shows that the rate constant 3 varies with pH in a sigmoid manner, as shown in Fig. 5 (whereas k2 and red practically insensitive to this factor). Figure 5 also displays the pH-dependent values ofks obtained with other cosubstrates than ferrocene methanol [35, 36], The dependency of k upon pH is due to the fact that, as with many redox enzymes, the prosthetic group of glucose oxidase does not merely exchange electrons with the cosubstrate but both electrons and protons. Analysis of the... 

The intensity of the scattering peak increased with time in a sigmoidal manner to plateau at a value Lo, corresponding to a limiting PCL crystallisation after about 1200 s for both pure PCL and for the blend at temperatures of about 40 °C. From values of times Xy2 required to reach 1, 2 were calculated. Values of Xj/2 showed that PCL crystallisation in the blend was slower than in pure PCL and that the rates of crystallisation, as might be expected, decreased as T was approached [95]. 

With a constant gas velocity, the mass transfer coefficient kg does not greatly depend on temperature, so that NA will be practically constant for a certain value of Ca and at high temperatures. Accordingly, the left-hand term of Equation 4.10, i.e. the chemical heat production rate per unit external area depends on Tt in the manner indicated in Figure 4.3, curves la and lb. The equation of these sigmoid curves is given by... 

For a typical CE process, the peak current may vary with scan rate in a complex manner. TTie peak current initially increases with scan rate (varying linearly with when the C step is reversible. However, as the scan-rate time-scale becomes faster than the kinetic time-scale associated with the C step, the peak current will start to decrease with scan rate as the kinetics of the chemical step are outrun and when the amount of electroactive product that can be oxidized/reduced at the electrode surface becomes limited. Eventually at scan rates that are much faster than the kinetic time-scale associated with the C step, a sigmoidal shaped response is observed when the current is no longer diffusion controlled, and is limited by the kinetics of the C step. Under these conditions the rate constant for the C step may be determined by a simple analytical expression (Saveant and Vianello, 1963,1967a,b Nicholson and Shain, 1964). 

Most uptake curves reported in Table 4.1 for cations (in absence of complexing anions) have a typical sigmoidal shape (Fig. 4.5(A)), and there are rather few exceptions. In contrast, the shapes of uptake(pH) curves reported for anions are very diverse, thus, it is rather difficult to compare the results from multiple sources in a quantitative manner as it was done for cations in Figs. 4.28-4.59. For example, the pHso as the criterion for such comparison is... 

E. Quantal Dose-Response Relationships When the minimum dose required to produce a specified response is determined in each member of a population, the quantal dose-response relationship is defined (Figure 2-2). When plotted as the fraction of the population that responds at each dose versus the log of the dose administered, a cumulative quantal dose-response curve, usually sigmoid in shape, is obtained. The median effective (ED j,), median toxic (TD, ), and median lethal doses (LD j,) are extracted from experiments carried out in this manner. 

All results established in chapter 2 for the analysis of eqns (2.7) in the phase plane therefore also apply to the two-variable system (5.4b,c). In particular, the two nullclines of the system remain defined by eqns (2.21). When parameter A exceeds a critical value, the product nullcline y= 4> takes the form of a sigmoid possessing a region in which the slope (da/dy) is negative in the phase plane (a, y). When the substrate nullcline v = a intersects the product nullcline in that region, in such a manner that condition (2.26) is satisfied, the steady state, which lies at the intersection of the two nullclines, is unstable and the system evolves towards a limit cycle corresponding to sustained oscillations (fig. 2.13). Such behaviour translates here into oscillations of ATP and extracellular cAMP, to which are associated oscillations in intracellular cAMP because of relation (5.4a), which links to the slower variables a and y. 

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