Parameter collinearity

At the time the experiments were perfomied (1984), this discrepancy between theory and experiment was attributed to quantum mechanical resonances drat led to enhanced reaction probability in the FlF(u = 3) chaimel for high impact parameter collisions. Flowever, since 1984, several new potential energy surfaces using a combination of ab initio calculations and empirical corrections were developed in which the bend potential near the barrier was found to be very flat or even non-collinear [49, M], in contrast to the Muckennan V surface. In 1988, Sato [ ] showed that classical trajectory calculations on a surface with a bent transition-state geometry produced angular distributions in which the FIF(u = 3) product was peaked at 0 = 0°, while the FIF(u = 2) product was predominantly scattered into the backward hemisphere (0 > 90°), thereby qualitatively reproducing the most important features in figure A3.7.5. 

In view of the central role that a magnetisation density plays for magnetic neutron scattering, it is useful to define a parameter for each reflection, called a canting angle, which gives a quantitative estimate of the deviation from the collinear approximation. The idea is as follows. 

Although these parameters represent the shape of substituents as a set, there is some collinearity among Bx, B2 and B3 for a number of substituents. Thus, Bx, B4 and L, as the most independent variables, are usually used in QSAR analysis 33). More recently, Verloop proposed the maximum width parameter, B5, and showed that, in most cases, B5 works well in place of B4 35). Since they are defined mechanically as the length or width, the background of their utilization along with other free-energy related parameters is not necessarily clear. 

More important is to avoid a collinearity with the hydrophobicity parameter which could be quite high when the selection of substituents is inadequate. For this purpose, we have quite often put such substituents as —S02CH3 and —S02N(CH3)2 into the correlation because of their high bulkiness as well as their low hydrophobicity. 

An additional advantage of PCR is that the score vectors are orthogonal (PCA provides orthogonal scores), so that the collinearity problems found in ILS are avoided and the resulting parameter estimates a are stable. Note also that this model also maintains the form described in eqn (3.3). This can be seen by starting with the original ILS model [eqn (3.26)] and multiplying by... 

Multilayered superconductor/ferromagnet S/F) structures are under an intensive study now (for a recent review see e.g. [1]). The interest in such systems originates from a possibility to find new physical phenomena as well from the hope to construct new devices based on these structures. Although a ferromagnet F attached to a superconductor S is expected to suppress the order parameter in S, under certain conditions superconductivity and ferromagnetism may coexist and exhibit interesting phenomena. In most papers on S/F structures the case of collinear (parallel or antiparallel) orientations... 

Here Hint is the anharmonic interaction in the collinear-configurational approximation (see Refs. [5,7]), Vmk = v/n,7i/2displacement operators of the host atoms with respect to the atom(s)of the mode (Y.i eimeim = M- We take into account that the strongly excited mode can be considered classically, and replace its coordinate operator by Q(t) = A cos( )/f), where A is the initial amplitude of the mode. Then... 

A simplified theory of FRET is sufficient to describe affinity sensors used in fluorescence transduction of glucose concentrations. A key quantity that describes the potential FRET interaction between a donor-acceptor pair is the Forster distance, Ro, the distance at which half the donor molecules are quenched by the acceptor molecules. Ro is proportional to several parameters of the fluorophores, in accordance with Ro = K6 Jx2n 4 cf>DJ l], where K is a constant. The variable k2 refers to the relative spatial orientation of the dipoles of D and A, taking on values from 0 to 4 for completely orthogonal dipoles and collinear and parallel transitional dipoles k2 = 4,... 

Because the correlations between the various factors influencing plant lead content are relatively low and of a similar magnitude (Tab. 9-8), the multiple linear model is not distorted by the existing collinearities in respect of the linear functions of the individual parameters. 

The goodness of fit is in accord with the experimental error in the data. Both equations 42 and 43 are significant at the 99.9% confidence level. Though 07 is significantly collinear in a dependence on both parameters is fairly certain. Electrical effects are the predominant factor in the structural effect with the localized effect making the greater contribution. 

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