Higher Order Indexes

Another important consideration is that all results reported here are based on the calculation of zero- and first-order connectivity indexes only. It is possible that die inclusion of higher-order indexes, which in turn means more detailed... 

We are able to apply successively the relation in Eq. (13-66) and thereby we determine the higher-order index transformed integrals, e.g.,... 

When the disperse phase has a slightly higher refractive index the compound tends to be blue when it is lower than that of the PVC the compound tends to be yellow and hazy. In order to overcome this a carefully determined quantity of a second MBS additive, with an appropriate refractive index and whieh is compatible with the PVC compound and hence forms a continuous phase with it, may be added to match the refractive indices. Such a matching operation should be evaluated at the proposed serviee temperature range of the product since the temperature coefficients of the two phases are usually different and a film which is blue at proeessing temperature may become yellow at 20°C. 

At lower molecular weights (higher melt index), the degree of conversion improvement is much larger. In order to utilize the improvement in heat transfer for a given product, therefore, an initiator system must be selected to provide a maximum conversion spread with increasing heat transfer. 

Profound line profile analysis is possible if a set of reflections is observed, i.e., peaks from several crystallographic orders indexed by (h) are accessible. With respect to a principal reflection found at the position, V(, the positions of the higher orders are... 

The situation is dramatically different for the RW configuration (ns = 1.2, nP = 1.575), for which the cover penetration depth can be varied between 100 nm and infinity for all the modes, with significantly improved cover index sensitivities (see Fig. 15.6b)9 15. For the CW configuration, the maximum obtainable sensitivity decreases with increasing mode orders compared to the zeroth-order modes. Con-trarily, the RW configuration offers the possibility to use higher order modes for... 

For molecular connectivity indices with orders higher than 2, it is also necessary to specify the subclass of index. There are four subclasses of higher order indices path, cluster, path/cluster, and chain. These subclasses are defined by the type of structural subunits they are describing, a subunit over which the summation is to be taken when the respective indices are calculated. Naturally, the valence counterparts of all four subclasses of higher order indices can be easily defined by analogy, described above for the first-order valence molecular connectivity index. 

The inclusion of higher order indices, such as the sixth order index used here, indicates that a critical dimension or number of atoms in a chain is influential... 

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