Ratio correlation

Some authors have sought to circumvent the problems of ratio correlation by txansforming their data into logarithmic form. Unfortunately this also does not solve any problems for the problems are preserved even as log-ratios (see Kenny, 1982 Rollinson and Roberts, 1986). 

A number of elemental plots of trace elements are presented as ratio plots of the form X lXi vs X- fXi X vs X Xi or Xi vs X2/X1 and are all subject to the constraints of ratio correlation discussed above. In some cases the trace element diagrams are designed only for classification purposes but, where linear trends are important for petrogenetic interpretation, then the problem of spurious correlation applies. In this case the plots should be considered carefully and ideas tested on alternative plots before any petrological conclusions are drawn from the data. 

A related problem in isotope geology is the correlation between the ratio Sr/ Sr and Sr concentrations. In this case (provided there is no analytical error) the correlation is most likely to result from the random mixing of two uniform sources of Sr with different isotopic compositions) although there is also the possibility that the observed correlations have arisen as a consequence of the common denominator effect resulting from ratio correlation. 

Geochemists are used to expressing the major element compositions of rocks and minerals as percentages, so that the sum of the major elements will always be about 100%. This has to be, simply because there is no other way of presenting a chemical analysis in a form which can be compared with other analyses. This stmdard universally used by geochemists rock and mineral 

A third consequence of percentage formation is that subcompositions, frequently used in variation diagrams such as the AFM diagram, do not reflect the variations present in the parent data-set. Aitchison (1986 — Table 3.1) shows that the correlation coefficient between pairs of variables varies substantially in subsets of a data-set and that there is no apparent pattern to the changes. In addition, subcompositions have variances which shqw different rank orderings from those in the parent data-set. For example, in the subset of data AFM (Na20+K20, MgO) the variances may be A F M, but in the parent data-set the variances may be F A M. 

---

AplP ratio. The Ap/ P ratio is calculated by dividing the numbers of carbon atoms in aliphatic chains in a plasticizer molecule by the number of ester groups present. The Ap/P ratio correlates well with several properties of the plasticizers such as melting point, density, modulus and water absorption. 

Figure 10-86. Heat transfer ratio correlations for steam and air system. (Used by permission Henderson, C. L, and Marchello, J. M. ASME Transactions Journal of Heat Transfer, V. 91, No. 8, p. 44, 1969. American Society of Mechanical Engineers. All rights reserved.)...

For fluids with viscosity greater than 500cp, no good general relationship is available. E jq)erimental work on one system allowed a swell ratio correlation of the following form ... 

Another recent study on historic, basaltic lava flows (1848 to 1977 AD) from Karthala volcano (Comores, Indian ocean) by Claude-Ivanad et al. (1998) reveals significant variations of the ( Ra)o/Ba ratios, correlated with Sr/ Sr ratios, which are explained by mantle source heterogeneities preserved by short transfer times of the magmas (a few centuries at most). 

EOS, LRC (loading ratio correlation), Dubinin-Radushkevich (D-R), and Dubinin-Astakhov (D-A) are more suitable. 

This three-parameter equation behaves linearly in the Henry s law region and reduces to the Langmuir isotherm for m = 1. Other well-known isotherms include the Langmuir-Freundlich isotherm or Sips isotherm [Sips,/. Chem. Phys., 16, 490 (1948) Koble and Corrigan, Ind. Eng. Chem., 44,383 (1952)] or loading ratio correlation with prescribed temperature dependence [Yon and Turnock, AlChE Symp. Sen, 67(117), 75 (1971)]... 

Loading, of fillers, 11 305-306 Loading amplitudes, fatigue and, 14 450 Loading cycles, 13 482 Loading Ratio Correlation (LRC) Method, 1 626, 628... 

The most widely used standard is a belemnite from the Peedee Formation in South Carolina (PDB) therefore, some ratios may be expressed as negative values. Most carbon isotope ratio correlations are made on the C15+ fraction of crude oil because it is less affected by degradation processes. Valid correlations using carbon isotopes can only be conducted on the same fractions of samples. 

Second, Kudo et al. (submitted) have shown that neocortex ratio correlates with with grooming clique size. This result suggests that species with larger neocortices can handle proportionately more relationships and keep them simultaneously functional. In this context, grooming cliques can be interpreted as alliances on which members rely in negotiat-... 

Typical values of the correlation coefficients are 0.5 for two isotopic ratios equal to unity and quickly tend to unity for large ratios. Correlations between errors due to counting statistics are clearly minimized by using ratios with values <1. 

The IR employs dedicated algorithms processed by a microprocessor analyzing radiation, ratios, correlations, threshold values, and flickering signals obtained from the three sensors. 

The most famous example of the crystal structure correlating with the average number of valence electrons per atom or band filling, N, is the Hume-Rothery alloy system of noble metals with sp-valent elements, such as Zn, Al, Si, Ge, and Sn. Assuming that Cu and Ag have a valence of 1, then the fee -phase is found to extend to a value of N around 1.38, the bcc / -phase to be stabilized around 1.48, the -phase around 1.62, and the hep e-phase around 1.75, as illustrated for the specific case of Cu-Zn alloys in Fig. 6.15. In 1936 Mott and Jones pointed out that the fee and bcc electron per atom ratios correlate with the number of electrons required for a free-electron Fermi sphere first to make contact with the fee and bcc Brillouin zone faces. The corresponding values of the Fermi vector, fcF, are given by... 

Fig. 11-1. Bubble-point pressure —solution gas-oil ratio correlation Copyright 1947 Chevron Oil Field Research Co., with permission.)...

We will discuss equilibrium-ratio correlations in some detail later. First, however, we will look at their use in gas-liquid equilibria calculations. 

Figure 9-3, page 252, Stock-Tank Gas-Oil Ratio Correlation... 

Isotherm Models for Adsorption of Matures. Of the following models, all but the ideal adsorbed solution dieory (IAST) and the related heterogeneous ideal adsorbed solution theory (H1AST) have been shown to contain some thermodynamic inconsistencies. They include Markham and Benton, die Leavitt loading ratio correlation (LRC) method, lire ideal adsorbed solution (IAS) model, the heterogeneous ideal adsorbed solution theory (HIAST), and the vacancy solution model (VSM). 

The loading ratio correlation (LRC) method for correlation of pure component sorption therms and prediction of multi-component sorption therms. 

The Loading Ratio Correlation. The equilibrium sorption therms for the pure components are correlated to the LRC model (1), which can be stated in the following manner ... 

Coefficients in loading ratio correlation (LRC), defined by equations (2) and (3)... 

The effects of raloxifene on the vascular endothelium have been studied in 19 subjects who underwent endothelial function testing at baseline and after treatment with placebo or raloxifene (60 mg/day for 6 weeks) (27). The findings in this small short-term study were entirely positive. Brachial artery diameter change (flow-mediated dilatation) increased 5.0% with placebo and 8.6% with raloxifene in response to a hyperemic stimulus. The ratio of AUC response to AUC reference with the use of laser Doppler measures was 1.18 for placebo and 1.28 for raloxifene. Flow-mediated dilatation and AUC ratio correlated significantly. The authors concluded that raloxifene enhanced endothelial-mediated dilatation in brachial arteries and digital vessels in these women, and they discussed the drug s possible cardioprotective effect. 

Baskin F, Rosenberg RN, Iyer L, Hynan L, Cullum CM. Platelet APP isoform ratios correlate with declining cognition in AD. Neurology 2000 54(10) 1907-1909. 

The problem of predicting multicomponent adsorption equilibria from single-component isotherm data has attracted considerable attention, and several more sophisticated approaches have been developed, including the ideal adsorbed solution theory and the vacancy solution theory. These theories provide useful quantitative correlations for a number of binary and ternary systems, although available experimental data are somewhat limited. A simpler but purely empirical approach is to use a modified form of isotherm expression based on Langmuir-Freundlich or loading ratio correlation equations ... 

In this section, the correlation in the heat flux ratio versus the pyrolyzed depth given by Equation 19.14 is incorporated into the numerical model to predict the pyrolysis process of the PA6 nanocomposite at different heat fluxes and thicknesses. The boundary conditions remain as those given by Equations 19.8 and 19.9. However, the MLR is now calculated from the heat flux ratio correlation in Equation 19.14 as... 

---