Trapezoid areas

Thus, the area under the spectrum would be a better measure of the overall efficiency of the extraction procedure than the absorbance at a single wavelength. The area was integrated by the trapezoidal area rule over the wavelength range 210-280 nm. This integration avoided the low transmittance at wavelengths below 200 nm. 

Calculate the trapezoidal area between all adjacent time points... 

There is an extra oscillation module, based on direct measurements of the capillary pressure, which operates from 1 to 150 Hz. There is also an additional accessory for the PAT1 for low-frequency oscillations. The range of surface and interfacial tension is 1 to 1000 mN/m with a resolution of 0.1 mN/m. The instrument allows for transient relaxation measurements, using perturbations such as ramp, square pulse, or trapezoidal area changes. 

It was shown by Loglio et al. (1991a) that the most useful disturbance for interfacial relaxation experiments is the trapezoidal area change. For time regimes realised in most of the transient relaxation experiments the trapezoidal area change can be approximated adequately by a square pulse. For the square pulse area change we obtain ... 

More convenient for relaxation studies are the square pulse (cf. Fig. 6.1, (c)) or its practical equivalence the trapezoidal area change (cf Fig. 6.1, (d)). The F-transforms of the respective area changes are as follows (cf Miller et al. 1991) ... 

The result for the trapezoidal area change is given in Chapter 6. 

The whole theoretical treatment of the derivation of interfacial response functions was discussed recently by Miller et al. [160]. It was shown by Loglio et al. [144, 161, 162] that exchange of matter functions derived for harmonic disturbances can be applied to transient ones. As the result for a diffusion-controlled exchange of matter, using the theory of Lucassen and van den Tempel [157], the following functions result for a trapezoidal area change [162]... 

The calculation of the expanded integral curve is based on the approximation of the concentration represented by the trapezoidal area in the low F rate half of each standard interval by... 

In Fig. 17 some typieal interfacial tension changes are shown which have been obtained for a trapezoidal area change of an aqueous protein solution drop in tetradecane. The elasticity can be calculated from the initial jump of the y t) dependence immediately following an expansion or compression. 

Here (0 is the oscillation frequency, and the parameter cOb is the characteristic frequency, which is inverse proportinal to the diffusion relaxation time Xd given in Eq. (35). This characteristic frequency exists also for any transient relaxation processes. The interfacial response functions for a number of transient relaxations were discussed recently by Loglio et al. (2001). Among these, the trapezoidal area change is the most general perturbation which contains area changes such as the step or ramp type and the square pulse as particular cases. 

Viscosity is directly related to structural levels. Comparing available values of viscosity rj with the density of the active faults of the Cenozoic era within the trapezoid area 5x5° and making an evaluation, it is not difficult for us to notice the inverse nonlinear tendency of mutual change between them (Fig. 1 (a)). 

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