Meta-distribution

Specify the number of inner and outer loop simulations for the 2nd-order Monte Carlo analysis. In the 1st outer loop simulation, values for the parameters with uncertainty (either constants or random variables) are randomly selected from the outer loop distributions. These values are then used to specify the inner loop constants and random variable distributions. The analysis then proceeds for the number of simulations specified by the analyst for the inner loop. This is analogous to a Ist-order Monte Carlo analysis. The analysis then proceeds to the 2nd outer loop simulation and the process is repeated. When the number of outer loop simulations reaches the value specified by the analyst, the analysis is complete. The result is a distribution of distributions, a meta-distribution that expresses uncertainty both from uncertainty and from variability (Figure 7.1). 

In the case of lithium orthoniobate, Li3Nb04, no meta-stable phase was found that had a rock-salt crystal structure with disordered cation distribution [268]. Nevertheless, solid solutions Li2+xTii-4xNb3x03, where 0 < x < 0.22, have a monoclinic structure at low temperatures and undergo transformation to a disordered NaCl type structure at high temperatures [274]. 

The isomer distribution is normal even when the low relative reactivity of substrates is observed. If reaction occurred at every collision then the statistical isomer distribution (40 % ortho, 40 % meta, and 20 % para for monoalkylbenzenes for example) would be expected, but this is not the case. 

The photographs obtained for pyridine and py-razine are so closely similar to those of benzene as to leave no doubt that the three molecules have nearly identical structures. The radial distribution curve for pyridine (Fig. 1) calculated from the data given in Table II has well-defined peaks at 1.38, 2.39 (= V3 X 1.38), and 2.76 (= 2 X 1.38) A. The sharpness of the 2.39 peak indicates that the six meta distances in the ring are nearly equal. The calculated intensity curve for the model with C-C = 1.39 A., C-N = 1.33 A., C-H = 1.08 A., the angle C-N-C = 119° and the angles C-C-C = 121°, and having nearly equal meta and para distances, is shown in Fig. 3. The comparison of s0 and s values for this model (Table II) leads to the values C-H =... 

The thermodynamic product distribution in the Friedel-Crafts methylation (Scheme 20) is in contrast to the kinetic distribution. The reaction kinetically shows the ortho and para orientations. Thermodynamic stabilities of the products prefer the meta isomer as a major product. 

The observed distribution can be readily explained upon assuming that the only part of polymer framework accessible to the metal precursor was the layer of swollen polymer beneath the pore surface. UCP 118 was meta-lated with a solution of [Pd(AcO)2] in THF/water (2/1) and palladium(II) was subsequently reduced with a solution of NaBH4 in ethanol. In the chemisorption experiment, saturation of the metal surface was achieved at a CO/Pd molar ratio as low as 0.02. For sake of comparison, a Pd/Si02 material (1.2% w/w) was exposed to CO under the same conditions and saturation was achieved at a CO/Pd molar ratio around 0.5. These observations clearly demonstrate that whereas palladium(II) is accessible to the reactant under solid-liquid conditions, when a swollen polymer layer forms beneath the pore surface, this is not true for palladium metal under gas-solid conditions, when swelling of the pore walls does not occur. In spite of this, it was reported that the treatment of dry resins containing immobilized metal precursors [92,85] with dihydrogen gas is an effective way to produce pol-5mer-supported metal nanoclusters. This could be the consequence of the small size of H2 molecules, which... 

Distribution of ortho-, meta-, and para-isomers in the divinyl benzene copolymer... 

The ambiphilic reactivity of aromatic cation radicals, as described in Schemes 12 and 13, is particularly subtle in the charge-transfer nitration of toluene and anisole, which afford uniformly high (>95%) yields of only isomeric nitrotoluenes and nitroanisoles, respectively, without the admixture of other types of aromatic byproducts. Accordingly, let us consider how the variations in the isomeric (ortho meta para) product distributions with... 

Observation (iii) above, taken in the context of the triad annihilation in Scheme 12, indicates that the more or less statistical o/p pattern is diagnostic of the homolytic pathway (66) since it will clearly dominate the competition for TOL+- at the high concentrations of added N02 (Scheme 16). Indeed this conclusion is supported by observation (i), in which essentially the same isomeric product distribution (i.e. ortho meta para 70 2 28%) is achieved when the pyridine competition is thwarted for the sterically hindered 2,6-lutidine, an ineffective nucleophile (Schlesener et al., 1984). According to the formulation in Scheme 16, the isomeric product distribution is established from the sterically hindered Me2PyNOj during the homolytic annihilation of TOL+- by N02, most favourably at the ortho and para... 

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