Correlative relationship

When correlation relationships imply a deep physical context, they become a good basis for the development of new, more common concepts or for the systematization of compounds, their properties, reactions, and even phenomena. Such relationships characterizing dihydrogen bonds are the focus of the chapter. 

CORRELATION RELATIONSHIPS ENERGY OF FORMATION VERSUS H-. H DISTANCE ESTABLISHED FOR EMTERMOLECULAR DIHYDROGEN BONDS... 

CORRELATION RELATIONSHIPS AMONG ENERGETIC, STRUCTURAL, AND ELECTRON DENSITY PARAMETERS OF INTERMOLECULAR DIHYDROGEN-BONDED COMPLEXES... 

Wang, Y.H., Wong, P.K. (2003) Correlation relationships between physico-chemical properties and gas chromatographic retention index of polychlorinated-dibenzofurans. Chemosphere 50, 499-505. 

IVIVC (In-Vitro, In-Vivo Correlation) module to correlate relationships between the in vitro dissolution of tablets and capsules and the in vivo dissolution in human and animal systems. 

FIGURE 3.57 The vicinal Karplus correlation. Relationship between dihedral angle (cj>) and coupling constant for vicinal protons. 

Dimensionality reduction or data compression is possible with principal component analysis because of correlations between measurement variables. Consider Figure 9.1, which shows a plot of 15 samples in a two-dimensional space. The coordinate axes of this measurement space are defined by the variables xr and x2. Both x, and x2 are correlated, since fixing the value of x, limits the range of values possible for x2. If x, and x2 were uncorrelated, the enclosed rectangle shown in Figure 9.1 would be completely filled by the data points. Because of this correlative relationship, the data points occupy only a fraction of the measurement space. 

A comprehensive research of a large number of benzofurazan nitro derivatives using UV spectroscopy and other physical-chemical methods has been carried out [777, 1006, 1007, 1106, 1107, 1229-1241], The frequencies of long-wave absorption bands of hydroxy- and aminosubstituted of nitrobenzofurazans greatly depend on the solvent nature [1106, 1107, 1230-1233, 1235, 1236], They are assigned to the bands of intramolecular charge transfer [1007, 1232], Correlation relationships between the wave number (v) and the Kamlet-Taft solvatochromic parameter (it ) are presented in the works cited ... 

A further advantage of an SCM approach is that thermodynamic parameters for adsorption reactions can be compared with the thermodynamic properties of other types of reactions, to assess correlative relations that may be used to predict the behaviour of chemical species for which experimental data are currently lacking. In Fein et al. (1997) the authors compared model results for equilibrium constants of metal-bacteria adsorption reactions, and found a strong correlative relationship between these values and corresponding equilibrium constants for metal-oxalate and metal-tiron (4,5-dihydroxy-m-benzenedisulphonic acid) aqueous... 

As was true for statistically significant linear relationship between (Tmeta and x was found. Quadratic relationships for o-meta similar in form to the relationships of Equations 4a and 4b are presented in Equations 5a and 5b for the meta-substituted TFMS derivatives. Both X2 and x terms are again necessary for optimum correlation although the final correlation relationship in Equation 5b for o-meta is not nearly as statistically significant (r2 = 0.44) as the final relationship for [Pg.263]

Other examples have been reported for Ln(III)-3d and Ln(III)-radical systems [69-71]. No general magneto-structure correlation relationship has been deduced from the reported compounds for a limited number of studies. These were also restricted by the difficulties of theoretical modeling and calculation for the spin-orbit coupling. 

High-temperature superconducting oxides are of interest for electrocatalysis since they represent materials that are comprehensively characterized by various physical methods. They therefore hold promise for obtaining new correlative relationships between catalytic activity and the bulk properties of materials. 

Referring once more to the effect of the aqueous medium composition upon the relative hydrophobicity of biological solutes, the correlation relationship establish-ecj io3,u6) between the effects of the medium ionic composition on the relative hydrophobicity of serum albumins of various origin and on that of erythrocytes from the same species should be noted. The ionic strength value of the medium in the aqueous ficoll-dextran biphasic system has been used as a quantitative index of the ionic composition of the system, and the ionic composition was varied from 0.11 M phosphate buffer to 0.15 M NaCl in 0.01 M buffer at pH 7.4 116). Partition coefficients of cells in an aqueous polymeric biphasic system are determined as the ratio of a number of the cells in the phase to that of the cells present at the interphase 90). Specific features of the partition behavior of cells in aqueous biphasic systems are discussed in detail elsewhere (see, e.g., Ref. 90 91). It has been established 116) that erythrocytes of different species are distributed in the aqueous ficoll-dextran biphasic system according to the following equation ... 

Patton S (1970) Correlative relationship of cholesterol and sphingomyelin in cell membranes. J Theor Biol 29 489 91... 

The distillation tests give an indication of the types of products and the quality of the products that can be obtained from petroleum, and the tests are used to compare different petroleum types through the yield and quality of the 300°C (572°F) residuum fraction. For example, the waxiness or viscosity of this fraction gives an indication of the amount, types, and quality of the residual fuel that can be obtained from the petroleum. In this respect, the determination of the aniline point (ASTM D-6II, IP 2) can be used to determine the aromatic or aliphatic character of petroleum. Although not necessarily the same as the wax content, correlative relationships can be derived from the data. 

MDF follows specific rules based on the relative atomic mass differences between the fractionating isotopes, and as a result produces highly correlated relationships between isotope ratios for that element (Chapter 2, Section 2.3.3.2 Chapater 5, Section 5.3.1.3). MDF is expressed as a deviation from the appropriate standard as a lower-case delta-value in parts per thousand, for example, <5180 %o, del oxygen eighteen - which is computed from the expression... 

Four major categories of LFERs have been developed over the past 60 years or so (Table 2). These relationships apply to a wide variety of classes of organic and inorganic compounds and a wide range of reactions—coordinative reactions (dissociation-association) of acids and metal complexes, hydrolysis, hydration, substitution, substituent group oxidations, electron exchange between metal ions, and so on. This section describes the basis for these categories of correlative relationships and the types of reactions to which they apply. 

Figure 2. Correlated relationship between the adipic acid degradation rate, the liquid phase adipic acid concentration, and the percent solids oxidation for the baseline data set. 

Some other kinds of models have shown parameters that seem to follow useful correlation relationships. Among these are the virial coefficient model of Bums (2), the interaction coefficient model of Helgeson, Kirkham, and Flowers (4), and the hydration theory model of Stokes and Robinson (1). The problem shared by all three of these models is that they employ individual ion size parameters in the Debye-Hiickel submodel. This led to restricted applicability to solutions of pure aqueous electrolytes, or thermodynamic inconsistencies in applications to electrolyte mixtures. Wolery and Jackson (in prep.) discuss empirical modification of the Debye-Huckel model to allow ion-size mixing without introducing thermodynamic inconsistencies. It appears worthwhile to examine what might be gained by modifying these other models. This paper looks at the hydration tlieory approach. 

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