Multiple Collinearity

The units of k are cm molecule-1 s-1 for the collinear calculations and cm3 molecule-1 s-1 for the three dimensional calculations, the figures in parentheses denote multiplicative powers of ten. 

The interference process in this collinear approach is, however, different from the interference realized by mixing the local oscillator and the CARS field on a beam splitter. Interference takes place in the sample, which, in the presence of multiple frequencies, mediates the transfer of energy between the beams that participate in the nonlinear process. The local oscillator mixes with the anti-Stokes polarization in the focal volume, and is thus coherently coupled with the pump and Stokes beams in the sample through the third-order polarization of the material. In other words, the material s polarization, and its ability to radiate, is directly controlled in this collinear interferometric scheme. Under these conditions, energy from the local oscillator may flow to the pump and Stokes fields, and vice versa. For instance, when the local oscillator field is rout of phase with the pump/Stokes-induced anti-Stokes polarization in the focal interaction volume, complete depletion of the local oscillator may occur. The energy of the local oscillator field is not redistributed in terms... 

To a first approximation, the composition of the distillate and bottoms of a single-feed continuous distillation column lies on the same residue curve. Therefore, for systems having separatrices and multiple regions, distillation composition profiles are also constrained to lie in specific regions. The precise boundaries of these distillation regions are a function of reflux ratio, but they are closely approximated by the RCM separatrices. If a separatrix exists in a system, a corresponding distillation boundary also exists. Also, mass balance constraints require that the distillate composition, the bottoms composition, and the net feed composition plotted on an RCM for any feasible distillation be collinear and spaced in relation to distillate and bottoms flows according to the well-known lever rule. 

In prokaryotes there is only one copy of DNA per cell, and in nearly all cases there is only a single copy of a gene. Apart from regulatory DNA and signalling sequences, there are very few silent, or non-translated DNA sequences, in prokaryotes. Moreover, each gene is typically collinear with the amino-acid sequence for which it codes. This is in contrast to the organisation of eukaryotic DNA which is structurally and functionally far more complex the structural parts of genes are split by silent DNA and there are multiple copies of the chromosomes. 

Several groups at ISOLDE are planning further improvements of their techniques. For each element the most appropriate experimental scheme has to be found. Today, collinear laser spectroscopy is the most general high-resolution and sensitive method for optical spectroscopy on radioactive beams delivered by on-line mass separators. Its sensitivity ranges from 10 - 10 atoms/s depending on the strength and multiplicity of the optical transitions. 

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. 

Assumes collinear spins. Multiple-axis structures may also be possible. 

We noted earlier that two collinear bonds to metal atoms are formed by 0 in some finite ions and molecules. Examples include compounds of both transition and non-transition metals (Table 11.5). In all cases the short M-0 bonds indicate multiple-bond character though there are still shorter bonds to terminal 0 atoms in some of the molybdenum complexes. Details of some of these complexes are given at (a)-(c). Note the trigonal bipyramidal coordination of A1 in (a). 

PLS Able to model multiple target properties simultaneously Able to use collinear descriptors Difficulty in interpreting scores for the molecular descriptors Assumes a linear relationship between target property and molecular descriptors... 

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