Substitution rate heterogeneity

Figure 2 Maximum likelihood tree. Distance analysis was performed using PUZZLE 4.0.2 (Strimmer and von Haeseler, 1996). Because of the unequal rate of nucleotide substitution among the positions, the matrix of maximum likelihood distances was computed using the model of Tamura and Nei (1993) with gamma distance corrections for substitution rate heterogeneity.

Models of Among-Site Substitution Rate Heterogeneity... 

In addition to variation in substitution patterns, variation in substitution rates among different sites in a sequence has been shown to profoimdly affect the results of tree building (Swofford et al., 1996). The most obvious example of among-site rate variation, or heterogeneity, is that evident among the three codon positions in a coding... 

The substitution model should be optimized to fit the observed data. Lor example, if there is a transition bias, evident by an inordinate number of sites that include only purines or pyrimidines, the likelihood of the data under a model that assumes no bias will never be as good as one that does. Likewise, if a substantial proportion of the sites are occupied by a single base and another substantial proportion have equal base frequencies, the likelihood of the data under a model that assumes that all sites evolve equally will be less than that of a model that allows rate heterogeneity. Modifying the substitution parameters, however, modifies the likelihood of the data associated with particular trees. Thus, the tree yielding the highest likelihood under one substitution model might yield much lower likelihood under another. 

When /(v) = 1, nueleation is said to be homogeneous, and when /(v) < 1, heterogeneous nueleation oeeurs. If a steady-state nueleation rate oeeurs in the system, substitution of equation 5.18 into equation 5.19 and subsequent rearrangement gives... 

If the flow is accompanied with CBA decomposition, the G value in Eq. (5) should be substituted with its time function, G(t). In the general case, thermal decomposition of a solid substance with gas emission is a heterogeneous topochemical reaction [22]. Kinetic curves of such reactions are S -shaped the curves representing reaction rate changes in time pass a maximum. At unchanging temperature, the G(t) function for any CBA is easily described with the Kolrauch exponential function [20, 23, 24] ... 

Substituting the reaction rate, Q, into Eq. 2 and after Laplace transformation, the equations obtained can be solved again by standard methods. The mass transfer rate for the heterogeneous part of the interface can be given as follows ... 

Fig. 14 Typical potential dependencies of the heterogeneous rate constant for the electroreduction of pora-substituted diaryl disulfides in DMF/O.IM TBAP. The dashed lines represent the parabolic fitting to the experimental data. The extrapolated standard potential and rate constant values (see text) are indicated.

Homogeneous molecular catalysts, which have far greater connol over selectivity than heterogeneous solid catalysts, are now being tested in SCFs, and early results show that high rates, improved selectivity, and elimination of mass-transfer problems can be achieved. Supercritical carbon dioxide may be an ideal replacement medium for nonpolar or weakly polar chemical processes. More than simply substitutes for nonpolar solvents, SCFs can radically change the observed chemistry (Jessop et al., 1995). 

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