Parameter ratio

Parameter CeU system Li—Mn02 Ni-Cd Parameter ratio Li-Mn02/Ni-Cd... 

The dependence of birefringence on the temperature seems to be correlated to the temperature dependence of the lattice parameters ratio c/a shown in Fig. 102. 

The structure was refined with block diagonal least squares. In cases of pseudo-symmetry, least squares refinement is usually troublesome due to the high correlations between atoms related by false symmetry operations. Because of the poor quality of the data, only those reflections not suffering from the effects of decomposition were used in the refinement. With all non-hydrogen atoms refined with isotropic thermal parameters and hydrogen atoms included at fixed positions, the final R and R values were 0.142 and 0.190, respectively. Refinement with anisotropic thermal parameters resulted in slightly more attractive R values, but the much lower data to parameter ratio did not justify it. 

The dotted contour in Fig. 19 shows that a second form of touching condition can also occur, for sufficiently large values of the parameter ratio b/a. Simple analytical manipulations show that touching conditions of this second type, with real K, give rise to relative equilibria described by... 

The drop in current that occurs in coulometric experiments may arise not only from the decrease in bulk concentration of the substance being analyzed, but also from a decrease in its surface concentration caused by the development of concentration gradients (see Section 11.2.1). Low values of current density and strong solution stirring are used to avoid the interference of such effects. Thin-layer cells where the electrodes are very close together (tens of micrometers) and the parameter ratio SIV is high, are often used to shorten the experiments. 

Eq. (53) provides the variance-covariance matrix for the parameter ratios. Letting by, b2, and b3 denote the respective ratios of Eq. (59), then Eq. (37) may be applied to find... 

Macromolecular diffraction data are rarely of sufficient quality and quantity to allow construction of atomic models that would obey basic stereochemistry just based on this optimization of parameters to data. The observation-to-parameter ratio is a key factor in optimization procedures. For the optimization of a crystallographic model. 

Refinement is thus the optimization of the model parameters to simultaneously fit both the experimental diffraction observations and a set of a priori known stereochemical information. It should become clear from the formula above, that solvent content crucially affects the observation-to-parameter ratio. Since crystals that diffract to lower resolution typically have higher solvent content, refinement can often be carried out decently well even at nominally low resolution. 

Prediction of DDI from in vitro inactivation data has also been accomplished. However, unlike the aforementioned simple cutoff that can be applied to inhibition data, no such simple cutoff criterion has been well established for mechanism-based inactivation kinetic parameters. Ratios of k act/kdeg and [ ] vivolKi have been shown to be related to the magnitude of DDI [50]. The early screens previously discussed rely upon abbreviated approaches to identify mechanism-based inactivation as an issue rather than provide quantitative data for predictions of DDI. 

The same data collection and reduction techniques are commonly used by the same workers for many different polymers. Therefore, data for these other polymers may contain errors on a similar scale, but that the errors have usually, but not always, gone undetected (8). If more than 500 reflections are observed, from single crystals of simple molecules, recognizable electron-density distributions have been derived from visually estimated data classified only a "weak", "medium" or "strong". The calculation of the structure becomes more sensitive to the accuracy of the intensity data as the number of data points approaches the number of variables in the structure. One problem encountered in crystal structure analyses of fibrous polymers is that of a very limited number of reflections (low data to parameter ratio). In addition, fibrous polymers usually scatter x-rays too weakly to be accurately measured by ionization or scintillation counter techniques. Therefore, the need for a critical study of the photographic techniques of obtaining accurate diffraction intensities is paramount. 

Digital filter coefficient Temperature coefficient of resistance Resistance thermometer parameter Ratio of specific heats... 

Reid et al. (2002) have shown that parametrizations of gaseous lanthanide ions have much larger reductions in the F2(fd) and C] (fd) parameters from Hartree-Fock values than the other parameters. This would suggest that future calculations might examine specific reductions in these two parameters, rather than the current practice of keeping parameter ratios fixed. However, as of this time, such calculations have not been performed. 

Number of 3d electrons Cation Racah B parameter Racah C parameter Ratio C/B... 

Unusual parameter ratios, for example, Ca/Mg or Na/Cl. For example, groups of analyses where all magnesium concentrations are similar but calcium concentrations have a wide range may indicate that calcium and bicarbonate were lost during sampling or storage. 

Fig. 60. Lattice-parameter ratio c/y/2a for orthorhombic perovskitea in the systems La(MniixM )C>3+y, where M = Co111 + Mn4f, Ni111 + Mn4+, and Ga3+. (After Goodenough, Wold, Arnott, and Menyuk (225).)...

As the use of low-temperature techniques becomes more routine, the quality of the analyses in this regard should improve, but this will be affected by a trend toward the study of more complex molecules where the diffraction quality of the crystals and the observation-to-parameter ratio becomes less favorable for locating the hydrogen atoms. 

For comparable observation/parameter ratio, need more observations. Number of variables 9N +10, where N is number of all atoms and nine anisotropic extinction parameters are used... 

However, these refinements are made at a heavy cost in the observation-to-parameter ratio. The third-order terms, Cyk, of the Gram Charlier expansion add ten more parameters per atom to the nine Uy terms. These expressions are therefore only used when the experimental data are of exceptionally high quality, as in the neutron diffraction analysis of ice, Ih, discussed in Part IV, Chapter 21. They may also be necessary in experimental deformation density analysis, where a very precise description of the atomic thermal motion is required. 

A deficiency in all the protein crystal structures investigated thus far at high resolution < 1.8 A is that the data/parameter ratio is insufficient to permit least-squares... 

What are the parameter ratios that make the stationary process rate hmited by step 2 By step 3 What are the apparent activation energies of this reaction under conditions of large and minor coverage of the active center by the catalytic intermediates ... 

Table III gives the change in various mixing parameter ratios for 4 different scaleup calculations. What this shows is that we cannot control the ratio of every individual fluid mechanics parameter. It also indicates that it is better to use correlating parameters to find out how they change on scaleup, rather than searching for a constant scaleup parameter for every conceivable mixing process. There is no assurance that there is a constant scaleup parameter for any given process job we are studying. Therefore, pilot plant studies should be directed toward establishing a controlling factor in the process, so that its control on scaleup can be more closely monitored.

In theory single crystal methods can be effectively used for structure solution from powder diffraction X-ray data. However, in powder diffraction the number of peaks involved are limited, and hence the data-to-parameter ratio is very small, due to the transfer of the three-dimensional data to one dimension, namely, 29. In spite of the inherent shortcomings, conventional crystallographic methods such as Direct, Patterson and maximum entropy methods have been successfully applied to powder diffraction data. The most popular program, which uses reciprocal space methods for stmcture solution is EXPO. ... 

Little support for the large range in alkenone parameters (ratios of C37 to C38 ketones, alkenones to alkenoates, etc.) observed in culture experiments comes from the sediment realm. As one example, I compared (Herbert, 2000) the frequency distribution of the ratio of total C37... 

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