Perfect Occurrences

The Moderate, no. 59 (21-28 August), and probably Perfect Occurrences (17-24 August). 

The perfection of the geometrical structure. This is confirmed by a great number of x-ray reflexes, including, and in particular, the occurrence of layer reflexes and reflexes of a higher order than the first one (Fig. 5 and Table 3). 

Fig. 2e), virtually absent in perfect siUcalite-1 and immediately identified as a fingerprint of TS-1 material [37,52-55,63,70,71]. A qualitative correlation between the intensity of the infrared band at 960 cm and Ti content has been observed since the first synthesis of TS-1. Indeed, the occurrence of that band is one of the distinctive features of the material cited in the original patent [7]. However, the quantitative correlation has been reported only very recently by Ricchiardi et al. [52], owing to very serious experimental problems related to the saturation of the IR framework modes, hi the same work, the nature of the 960 cm band has been discussed in terms of theoretical calculations based on both cluster and periodical approaches. 

But for ordinary data, we would not expect such a sequence to happen. This is the reason most statistics work as general indicators of data performance the special cases that cause them to fail are themselves low-probability occurrences. In this case the problem is not whether or not the data are nonlinear, the problem is that they are nonrandom. This is a perfect example of the data failing to meet a criterion other than the one you are concerned with. Therefore the Durbin-Watson test fails, as would any statistical test fail for such data they are simply not amenable to meaningful statistical calculations. Nevertheless, a blind computation of the Durbin-Watson statistic would give an apparently satisfactory value. But this is a warning that other characteristics of the data can cause it to appear to meet the criteria. 

Progress in understanding stellar evolution and nucleosynthesis, and the discovery by Merrill (1952) of the unstable element technetium in the S star R Andromedae, demonstrating the occurrence of stellar nucleosynthesis within a few half-lives of Tc (i.e. < about 1 Myr see Fig. 1.8), has led to acceptance of the idea that abundance variations among stars are perfectly natural as a consequence of three main effects (see Fig. 3.37) ... 

The hydrogenation of 5 was carried out in an experimental manner similar to that of 2 (Scheme 8). No observation of the aromatic peak in the NMR spectra of the product indicated the occurrence of the perfect deben-zylation, giving rise to polysaccharide 7. The molecular weight determined by GPC with water eluent was 5,600, which is in good agreement with the calculated value (6,200). The solubility of 7 in water, DMSO, and DMF is higher than that of 3. 

It is shown that model, end-linked networks cannot be perfect networks. Simply from the mechanism of formation, post-gel intramolecular reaction must occur and some of this leads to the formation of inelastic loops. Data on the small-strain, shear moduli of trifunctional and tetrafunctional polyurethane networks from polyols of various molar masses, and the extents of reaction at gelation occurring during their formation are considered in more detail than hitherto. The networks, prepared in bulk and at various dilutions in solvent, show extents of reaction at gelation which indicate pre-gel intramolecular reaction and small-strain moduli which are lower than those expected for perfect network structures. From the systematic variations of moduli and gel points with dilution of preparation, it is deduced that the networks follow affine behaviour at small strains and that even in the limit of no pre-gel intramolecular reaction, the occurrence of post-gel intramolecular reaction means that network defects still occur. In addition, from the variation of defects with polyol molar mass it is demonstrated that defects will still persist in the limit of infinite molar mass. In this limit, theoretical arguments are used to define the minimal significant structures which must be considered for the definition of the properties and structures of real networks. 

The general character of Neumann s chemistry is practical rather than theoretical. It describes plainly and in considerable detail the occurrences, properties and preparations of a large number of mineral, animal, and vegetable products, and the value which it must have possessed at that time as a condensed encyclopedia of chemical facts is manifest. Neumann apparently accepts the phlogiston hypothesis without reservation. In the discussion of metals, which he divides into perfect metals—gold and silver imperfect metals—lead, copper, iron and tin and semimetals (not malleable)—mercury, bismuth, zinc, antimony, arsenic, he has this to say under the head of imperfect metals 7... 

The ever-increasing interest in the catenanes and knots of DNA stems not only from their widespread occurrence or from their topological novelty determination of their structures provides precious information about the biological processes which generate them. A whole class of enzymes - topoisomerases - effects these topological transformations perfectly [30, 31]. Their possible role in a large vari-... 

---