Similarity correlation measures

The phase-dependent directionality of photocurrents produced by such a detector entails advantageous properties of the photocurrents cross correlations in nonoverlapping time intervals or spatial regions (considered in Section 4.2.2). These directional time-dependent correlations are measured with one detector only. They involve solely terms dependent on LO phases, in contrast to similar correlations measured by conventional photocounters, which inevitably contain terms depending on photon fluxes such as the LO excess noise. Owing to these properties, the mean autocorrelation function of the SL quadrature is shown in the schemes considered here to be measurable without terms related to the LO noise. LO shot noise, which affects the degree of accuracy to which this autocorrelation is measured (i.e., its variance) is easily obtainable from zero time delay correlations because the LO excess noise is suppressed. The combined measurements of cross correlations and zero time delay correlations yield complete information on the SL in these schemes. 

There are a number of additional local structures and properties that appear even in elementary CA systems. Grassberger [grass84b, for example, has observed that rule R22 actually harbors very complex long-range effects, similar to a critical phenomenon (see section 3.1.4). Since the majority of these findings require the use of more general and sophisticated correlation measures than we have defined thus far, we will pick up our discussion of them in chapter 4. 

In the cost analysis, EPA stated that there was a correlation between SVE unit costs and the volume of soil treated. SVE was demonstrated to have a measurable economy of scale. Unit costs for the treatment of less than 10,000 yd of soil ranged from 60 to 350/yd. Unit costs for applications treating more than 10,000 yd of soil were as low as 5/yd treated. A similar correlation was noted for unit costs versus mass of contaminants removed. Unit costs for projects with less than 3000 lb of contaminants requiring removal ranged from 300 to 900/lb. Unit costs for larger projects were less than 15/lb, and costs for treating over 500,000 lb of contaminants were less than 2/lb (D22449H, pp. 4-1, p. 4-4). 

Similar to the correlation measurements discussed in the previous sections, we can define the doorway and window wavepackets and write the signal as their overlap in phase space. The derivation is presented in Appendix E, and we have... 

In this connection there arises a natural question, whether there exists a similar correlation for the parameters ve, ae, and a characterizing the rate of tunneling reactions. The question is answered by Fig. 23(a) and (b) presenting the data of Table 2. As can be seen from the figures, for the reactions of etr in water-alkaline glasses the dependences between log i e, a,., and a in a number of the reactions studied have the form of a field of points, i.e. the compensation effect is missing. This fact, in particular, allows one to conclude that the differences observed in the values of the parameters ve, ae, and a for various reactions reflect the real situation rather than that they are the consequence of systematic errors in measurements or data treatments. 

Consideration of the relative donor abilities of nitrosyl, carbonyl, and phosphine groups as measured by their ionization potentials, provides an explanation for variations in the molecular ionization potentials of these complexes (103, 194). As shown in Table III (Section IX) the ionization potentials decrease on introduction of the phosphine ligand, and parallel the corresponding decrease in ionization potentials of the phosphine ligands. Similar correlations were made for vco and vNO in the infrared spectra. 

Oxidation potentials measure the energy required to remove an electron from a molecule. To check whether in a partial electron transfer in charge transfer complex formation, a similar correlation would hold, the equilibrium constant... 

Figure 7.1 Dendrogram showing the association between 70 computed descriptors for a set of 13 pyrethroid insecticides. Distance on the vertical axis is a measure of similarity (correlation) between the variables. (From Ford, M.G. and Livingstone, D.J., Quant. Struct.-Act. Relat., 9, 107-114, 1990. With permission.)...

Similarly, intensity measurements utilizing a pulsed XeCl excimer laser (308 nm, 15 ns, and 150 mJ/pulse) have been carried out using a dye laser unit as flow-through cell for a lO M azobenzene solution (18). A linear correlation was found between the increase in absorbance at 358nm and the number of laser pulses (Ap), and the energy (E ) per laser pulse can be calculated using Eq. (21), i.e.. 

In some cases the error limits quoted are based solely on the reproducibility (precision) of the measurements and, in others, an attempt has been made to allow for other sources of error. However, it is clear from the differences in the values of k that in estimating the limits not all errors have been accounted for. The differences do not correlate with the various pressures used, which is sometimes a source of such discrepancies, but appear to be related to errors in the values of the optical absorption coefficient used in measuring the concentration of the CHO radical. In most of the studies optical detection methods were used and, in these cases, very similar experimentally measured values of k/e were obtained, where e is the optical absorption coefficient of CHO at the wavelength used. Differences in the values used for e account for the differences in the quoted values of k [16]. In this case the likely source of error can be identified fairly readily other cases are far less transparent and the reasons for scatter outside the quoted error limits can often not be identified. 

Sund et al. 101) and also Wallace et al. 20) reported retention characteristics of poly(vinyl chloride) powders of differing specific surface areas. It was shown that, once a calibration curve was established, gas chromatography could provide a rapid determination of surface areas of poly(vinyl chloride) powders. At temperatures below Tg the measured retention volume should be proportional to the surface partition coefficient and to the surface area of the stationary phase as expressed in Eq. (28). From the known airface areas of several samples the partition coefficient can be obtained, in turn allowing for the determination of the surface area of any sample from the measured retention volume. A similar correlation between BET surface areas and retention volumes was reported by Salovey et al. 102) for poly(vinyl chloride) powders. 

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