Correlation with fractional number

The same Pt/SiC catalysts were poisoned by CS2 the hydrogenation of (+)-apopinene was used as an indicator reaction (ref. 14). The amount of CS2 necessary to eliminate the hydrogenation activity permits calculation of the fraction of metal sites active in olefin hydrogenation. This fraction correlates with the number of step sites. Similarly, a good correlation is found between this fraction and the rate of methyloxirane transformation (Table 1). These results reveal that the structure-sensitivity is caused by the variation in the number of active sites, and the steps appear to be the active sites for the regioselective hydrogenation of methyloxirane. 

When a system is operating at the limiting current, rather than at an appreciable fraction of the limiting current, the problem is very much simplified. Such problems can be classified as mass-transport limited. Usually, the limiting current density is correlated with dimensionless numbers. Most forced-convection correlations take the form... 

The surface of cells is constantly renewed the new plasma membraiK is synthraized in the cell and translocated to the surface while parts of the existing membrane are internalized in the endocytotic process, illustrated in Fig. 4. During the endocytotic process the polymer that was adsorbed on the cell surface and a small portion of the polymer in the surrounding medium enter into cells these polymers are enclosed in endocytotic vesicles. The internalized polymers stay firmly assodated with the cells. When the internalized poly-9-vinyladenine was followed for three cell divisions, the amount correlated with the number of viable cells within experimental error. Thus,no degradation or excretion of polynucleotide analogs from cells occurred. The cells containing radioactive polymer were also fractionated and (fistribution of radioactivity in aU these fractions was measured. Results confirm that a substantial amount of the polymer was in an enveloped form, probably in endocytotic vesides and lyM)somes ... 

The o-Ps intensity I3 is the fraction of positrons that formed Ps and are trapped in the holes. From many evidences it appears to be correlated with the number of the holes, but no quantitative relationship between them is derived yet. One will easily understand the difficulty considering the complicated processes of Ps formation and trapping into holes. In a most crude case, however, it is assumed that I3 is proportional to the number of holes. In such a case the free volume fi action Vf is equated to a product of the size of the o-Ps hole, vp , and I3 as V a vp I3, where a is the proportionality factor (14). In some reports it is claimed that this simple treatment works well. This is probably because all the complicated factors related to Ps formation and trapping processes and the digging and seeking nature are rounded off in the proportionality factor. However it is not mature to generalize this kind of treatment since we do not know the details of the processes leading to I3. 

It may be that hardness correlates with fractional charge on the central atom rather than its oxidation number. This rationalization receives support from observations of ligand effects. Despite a formal core possessed by both BF3 and BH3, the former compound is a hard Lewis acid, and the latter is a soft one. This occurs because hydride ions effectively reduce the charge of the boron atom in borane. This phenomenon is particularly evident with soft donor ligands from which the negative charge is easily transferred. 

Based on PPLB s work, Perdew [6] generalized the sum rule for the exchange-correlation hole to the fractional number of electrons, and Perdew and Levy [7] reached the conclusion that the local density approximation (LDA) and the generalized gradient approximation (GGA) energies were too low for systems with fractional numbers of electrons by analyzing this generalized sum rule. 

The resonating-valence-bond theory of metals discussed in this paper differs from the older theory in making use of all nine stable outer orbitals of the transition metals, for occupancy by unshared electrons and for use in bond formation the number of valency electrons is consequently considered to be much larger for these metals than has been hitherto accepted. The metallic orbital, an extra orbital necessary for unsynchronized resonance of valence bonds, is considered to be the characteristic structural feature of a metal. It has been found possible to develop a system of metallic radii that permits a detailed discussion to be given of the observed interatomic distances of a metal in terms of its electronic structure. Some peculiar metallic structures can be understood by use of the postulate that the most simple fractional bond orders correspond to the most stable modes of resonance of bonds. The existence of Brillouin zones is compatible with the resonating-valence-bond theory, and the new metallic valencies for metals and alloys with filled-zone properties can be correlated with the electron numbers for important Brillouin polyhedra. 

In MDR cells, a significant fraction of P-gp is found associated with caveolin-rich membranes, and there is a substantial increase in the number of caveolae and caveolin-1 protein level. For example, both multidrug resistant human colon adenocarcinoma HT-29 cells and adriamycin-resistant breast adenocarcinoma MCF-7 cells display about a 12-fold increase in caveolin expression, which correlates with an approximate fivefold increase in morphologically identifiable caveolae [55], In addition, these cells exhibit increased amounts of phospholipase D and lipids such as cholesterol, glucosylceramide, and sphingomyelin [56, 57], Similarly, taxol-resistant A549 cells display both increased caveolin expression and caveolae numbers [58], While these correlations track with MDR, they do not suggest a simple mechanism for the role of... 

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