Log area ratios

Hence it is possible to find the ratio of two adjoining tubes from the reflection coefficients. It is not however possible to find the absolute values of the areas of the tubes (this is independent, just as the gain is independent of the filter coefficients). A common way of representing 12.36 is in terms of log area ratios, which are defined as ... 

The direct linear prediction, HR, coefficients are inherently unrobust with regard to quantisation and interpolation. A set of derived representations, including reflection coefficients, log area ratios and line spectral frequencies avoid these problems. 

Such log area ratios come in useful in a variety of ways, for example as a means of smoothing across joins in a manner that reflects physical reality. 

Transform die representation into a space that has more desirable properties log magnitude spectra follow the ear s dynamic range mel-scaled cepstra scale according to the frequency sensitivity to the ear log area ratios are amenable to simple interpolation and line-spectral frequencies show the formant patterns robustly. 

As already pointed out, the area ratio between flie metals in a galvanie eouple plays a crucial role for the galvanie eorrosion rate. The importanee is best illustrated in a potential-log current diagram, where flie area of the less noble metal eonveniently can be set equal to 1 cm. In Figure 7.8 this is shown by an example where iron or unalloyed steel in one case is alone = 1 cm ) and in other eases is eonneeted to stainless steel so that the total eafliodic area is 10 and 100 em, respeetively. For the sake of simplieity it has been assumed that flie cathodic overvoltage eurves are equal on stainless and unalloyed steel. Two different environments are eonsidered ... 

Kt = notch acuity factor n = slope of og da/drh) vs. log R ratio = minimum load/maximum load R.A. = reduction in area... 

Maximum /err occurs at d log I oJdAc = 0—that is, when the numerator of (5.16) equals zero. This occurs when A = Pc/(Pc + P ). If, as is frequently observed, Pc = Pa, then the maximum corrosion rate occurs at Ac = that is, at an anode-cathode area ratio of unity. At any other anode-cathode area ratio, the corrosion rate is less, reaching zero at a ratio equal to either zero or infinity. 

In two recent reports Rosas-Romero and co-workers (Rosas-Romero, Herrera and Muccini, 1996 Rosa-Romero et al, 1994) contributed to new TLC-FID procedures for the quantitative analysis of lipid classes of interest to the fat and oil industries. Concerned with the lack of linearity (particularly noticeable at high loads in the older latroscan systems), they suggested there is a need to establish an arithmetic transformation of the data. In order to improve quantitation of lipid classes, they proposed the data be transformed by establishing a regression of the log of the peak-area ratios against the log of the weight ratio (1996). Improvements in the design of the ion collector and the FID itself introduced for the Mark V will certainly improve the linearity of the untransformed data. 

The effect of anode-cathode area ratios has an important bearing on the rate of corrosion. This can be explained by a plot of log J vs . In the plot (Fig. 3.13) current I is plotted vs E and not i (current density) to establish the effect of area ratio. To define the conditions, the reversible potential ° of Zn (—0.760 V) and hydrogen (0.00 V) are located in the diagram. The values for hydrogen reduction on zinc, io (H) on zinc (—1 cm ). 

Figures 8 and 9 show the first order kinetic plots for the isomerization and crosslinking reactions, respectively. In the data analysis the area of the isoimide peak was measured between consistent limits chosen to exclude any contribution from the 1775 cm imide band. These data were generated by measuring the area of the appropriate peak in a baseline corrected spectrum and ratioing this area to that of a reference peak (which was invarient during the experiment) in the same spectrum. This concentration indicative number was then ratioed to the concentration ratio observed on the initial scan. Plots of the log of the ratio of the concentration of the functionality at time "t" to the concentration of the functionality at t = 0 were then constructed. In order to insure that the trends in the data were not artifacts of this procedure or of the baseline correction routine, we also plotted the data in terms of peak intensity in absorbance units and observed the same trends but with more scatter in the data.

We have first explored the Li line region (670.7nm) for faint stars (bottom of the RGB, the RGB Bump area and the HB, see Fig.l). Data reduction has been done with the GIRAFFE DRS on 123 spectra (signal to noise ratio around 70). The log g have been estimated with a fit of the mean RGB and HB sequences of 47 TUC to a theoretical isochrone (Bertelli et al. 1994), and Teff have been estimated from the (V-I) color-temperature relations (Houdashelt et al., 2000). With [Fe/H]= - 0.65 for 47 TUC, synthetic spectra have been computed from MARCS models (log g= 3.0 TejJ= 4800 K to 5100 K). Li abundances (A Li>0 dex, Li dots in Fig.l) have been derived for 41 stars (with uncertainties of about 0.2dex). 

As the carbon load of a particular type of stationary phase increases we expect both the phase ratio and the contact surface area for a given eluite probe to reach a plateau so that the dependence of k or log k on the carbon load is likely to be hyperbolic over a sufficiently wide range. A key point in this treatment is the accessible hydrocarbonaceous surface area, which is difficult to quantify and may strongly depend on the molecular architecture of the eluite used as a probe. Furthermore, the involvement of the... 

Eq. 1 log A, logarithm of the percentage increase in ethylmorphine N-demethylase activity alcP, ratio of molecular area to depth-square AE, EL - Eu, difference between the energy of the lowest unoccupied to the highest occupied molecular orbital log P, logarithm of the octanol/water partition coefficient. 

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