Mutual correlations

When JUNGLE2.dat and JUNGLE3.dat are analyzed with program CORREL, a plausible pattern turns up Impurities A, B, and C and the pH are mutually correlated impurity D is correlated with Titr and HPLC. The artifacts in JUNGLE3.dat cause a reduction in the strengths of correlation in four bins (three of them over two to four classes), and an increase in three bins over one class each. 

CMR represents the overall calculated molar refractivity. Its negative sign bring out a steric effect. It is interesting to note here that there is a high mutual correlation between ClogF and CMR (r= 0.966). Thus, it is very hard to predict for this data set if it is a negative hydrophobic or a polarizability effect. 

We measured many properties of the soil, the growing trees and the apples after harvest and after storage. The results were studied in relation to the management factors and mutual correlations were computed. This procedure enabled us to contribute to the validation of the IQC (step 3, Table 5.3), the validation of new parameters (steps 5 and 6) and the evaluation of orchard management. Details of the methods and results of the apple series are described elsewhere (Bloksma et al., 2001, 2004). Here, we mention only some of the results that are relevant to the IQC. 

In addition to the influence of neighbors on 29Si chemical shifts, the geometrical effects (such as Si-O-T angles) already described above are also evident of mixed frameworks with elements other than Si on tetrahedral positions. This is reflected by the broadness of the bars shown in Fig. 1. Multinuclear NMR investigations on a large set of sodalite structures with various framework compositions show that T-O-T bond angle (T = Si, Al, Ga) and dTT distance chemical shift dependences exist, and mutual correlations between chemical shift of these NMR nuclei can be observed [68],... 

Standardizing the spectral response is mathematically more complex than standardizing the calibration models but provides better results as it allows slight spectral differences - the most common between very similar instruments - to be corrected via simple calculations. More marked differences can be accommodated with more complex and specific algorithms. This approach compares spectra recorded on different instruments, which are used to derive a mathematical equation, allowing their spectral response to be mutually correlated. The equation is then used to correct the new spectra recorded on the slave, which are thus made more similar to those obtained with the master. The simplest methods used in this context are of the univariate type, which correlate each wavelength in two spectra in a direct, simple manner. These methods, however, are only effective with very simple spectral differences. On the other hand, multivariate methods allow the construction of matrices correlating bodies of spectra recorded on different instruments for the above-described purpose. The most frequent choice in this context is piecewise direct standardization... 

The only difference to the simple diastereoselection lies in the fact that the olefmic components now have two reactive sites each, namely the two olefmic sp1 centers, which are all converted into sp3, and hence potentially stereogenic centers. However, the configurations of these stereogenic centers are not independent, but mutually correlated by the principle of suprafacial addition (see Section 2.3.1). Thus, although a maximum of 24 stereoisomers could be formed, this number must be divided in half for each olefmic reactant with a defined (E)) Z) configuration. This results in only four stereoisomers in the form of two enantiomeric pairs of ejeo/enrfo-diastereomers. 

Therefore the ideal structure of Y7O6F9 can be depicted as a stacking of. .. AjBiAjBj. .. along [100], as shown in Fig. 2.36. In the real crystal, shown in Fig. 2.35, mutual correlations among these atomic planes exist. These result in structural modulation, i.e. the movement of not only anions but also cations from the ideal positions, although the dimensions of the subcells of each plane (Aj., Bj, Aj, B2) are assumed to be constant in the ideal structure, and, moreover, the site occupancy of anions is differentiated. 

Examination of the Egyptian material led to a further discovery. The general Nile pattern, produced by Nile muds and the ceramics made from it, is on first glance very close to that of the Palestinian red field clay. When the plots of three clays and six sherds were matched by the scandium—iron points, cobalt, chromium, and europium also matched exactly. Thus in the Nile samples, concentrations of the five elements are highly mutually correlated. This observation then allowed detection of subtle differences between Palestinian and Egyptian materials. The... 

Coffander-iype Relationships Collander has studied partition coefficients in different alcohol-water systems [16]. He found that these partition coefficients are mutually correlated. For certain compounds containing one hydrophilic group, such as alkanols, alkanoic acids, alkanoates, dialkyl ethers, and alkylamines and selected compounds containing two, three, or four such groups, he reports the following equation ... 

Geostatistical methods are also termed random field sampling as opposed to random sampling [BORGMAN and QUIMBY, 1988], The spatial dependence of data and their mutual correlation can be analyzed by use of semivariograms. Statements on the anisotropy of the spatial distribution are also possible. Kriging, a geostatistical method of... 

The active electrons are thus explicitly correlated, while the inactive electrons are not. One expects that the lack of correlation in the inactive subsystem will result in a constant error throughout the potential surface and therefore just uniformly shift the calculated energies relative to fully correlated surfaces. Note that in this model the inactive electrons are still affected by the progress of the reaction, since their orbitals rearrange and optimize at all points of the reaction coordinate. It is simply their mutual correlation that is considered as constant. 

Table II shows the linear correlation coefficients of the species from Table I. For 95 observations a correlation greater than 0.26 is significant at the 1% level. Thus, the correlations involving lead are not significant (consistent with expectation), while the mutual correlations of fine particle sulfur, selenium and mass are impressively large. Correlations involving gaseous sulfur are only slightly less large.

An obvious connection between states that possess the same electronic configuration would be the one indicated by dashed lines in Figure 7-13. This does not occur, however, because states of the same symmetry cannot cross. This is, again, a realization of the noncrossing rule, which applies to electronic states as well as to orbitals. Instead of crossing, when two states are coming too close to each other they will turn away, and so the two ground states, both of Ag symmetry and also two Ag symmetry excited states will each mutually correlate. 

Therefore, irrespective of the beautiful algebraic form of Cioslowski s UDA one must conclude that its predictions are not in complete agreement with empirical findings [115, 116]. Furthermore, it was shown [117] that a hidden assumption behind Eq. (78) is that the coefficients b(B, k) of the characteristic polynomial are not mutually correlated. Empirical testing [118] revealed that, on the contrary, a high degree of correlation exists between these coefficients. 

The parameters of the out-of-plane deformation, namely t and Xn> for the molecular fragment considered by Gilli and coworkers4 are mutually correlated in a similar manner as for the enamines described by Dunitz1. The correlation curve, shown in Figure 3a,... 

The Buckingham Eq. (6-10) takes into account the fact that the infiuence of solvent dipolarity [characterized by /(cr) = (cr — l)/(2er- -1)] and solvent polarizability [characterized by f n ) = n — l)j 2n + 1)] on the solute IR vibrations are two independent effects. Based on the assumption that solute/solvent collision complexes are formed in solution, which should lead to a mutual correlation in dipolarity/ polarizability changes, Bekarek et al. have added a third cross-term f ef) f n ) to the two terms of Eq. (6-10) [379]. Indeed, using the modified three-term Eq. (6-12),... 

This matrix does not have the state of a diagonal matrix and consequently, all the regression coefficients are in mutual correlation. So we carmot develop a different significance test for each of the coefficients. From this point of view it is not possible to use the tj values given by relation (5.95) as the base of a procedure for the process factor arrangement ... 

On the basis of this model, it has been concluded that more hydrophobic compounds having ortho and para substituents with an electron-withdrawing property and less bulky meta-position substituents would lead to better activity. In these compounds octopamine agonistic activity in terms of K, the concentration of the agonist necessary for half-maximal activation of adenylate cyclase, and its log Vmax are mutually correlated. This has prompted us to suggest that the larger the V"max value, the greater would be the activity of the compounds [202]. 

Calcium channel blockers bind specifically to receptor sites associated with the voltage-dependent calcium channels [31,32]. These blockers inhibit calcium uptake [33,34] and block smooth muscle contraction [35,36]. All these three activities of calcium channel blockers have been found to be mutually correlated. For ten known calciiun channel blockers (Table 4), Papaionnou et al. [37] derived the correlations ... 

Statistical Molecular Distribution Functions in a Static and in an Alter-natii Electric Field.— We now shall apply the statistical distribution function expansion (100) to a molecular gas (or dilute solution of polar molecules in a non-polar solvent) immersed in an external electric field E. Not taking into consideration the mutual correlations of molecules but solely their interaction with the field E, we are justified by equation (81) in writing the potential energy to within the square of the field as follows ... 

Various grid region seiection methods have recently been proposed with the aim of significantly reducing the number of field variables and their mutual correlation. 

Table 5 The correlations matrix of (a), of data from Table 4 and clustering objects with highest mutual correlation, (b)...

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