Redundancy index

In reality this third index is not needed. However, it does help to bring out the relationship between the planes. Because it is a redundant index, the value of i is sometimes replaced by a dot, to give indices (hkl). This nomenclature emphasizes that the hexagonal system is under discussion without actually including a value for i. 

Notice that, for reasons of symmetry, in the hexagonal system a somewhat redundant index type may be used for plane identification. It is customary to define an auxiliary axis u at 120° to x and y and 90° to z (and with the same unit length of the x and y axes). As a consequence instead of indices (hid) for a face, indices (h, k, i, l) are used, where the index / is related to the axis u in the same way... 

The chromatographic capacity factor (AT ) for ester and amide derivatives of 6,6a, 7,8,9,10,10a, 11-octahydro-ll-oxodibenzo[ /]thiepine propionic acid 44, potent antiinflammatory agents, has been studied, since the parameter was widely used for the interpretation of the activity of drugs <2003RRC795>. K, was modeled topologically using molecular redundancy index (MRI), equalized electronegativity (xeq), and van der Waals volume (fw)-... 

Agrawal et al. have studied the anti-histaminic activity of these 2,3-disubstituted thiazolidin-4-one analogues (Table 9) with graph theoretical indices and discovered the following equation for the activity in terms of the rooted Wiener index (Ww), rooted Szeged index (Szw), molecular redundancy index (MRI), and an indicator variable Ipi (for the p-alkyl of the aryl... 

From the mean information content, Brillouin [Brillouin, 1962] defined a complementary quantity, called Brilloiiiii redundancy index R (or redundancy index), to measure the information redundancy of the system ... 

The K correlation index is a - redundancy index, taking the value of 1 when all of the variables are correlated and 0 when they are imcorrelated. From a geometrical point of view, K = 0 corresponds to a spherical p-dimensional space and K = l corresponds to a straight line in a p-dimensional space. In the case where p, the number of variables, is greater than n, the number of objects, the rank of the correlation matrix is n, this rank being less than or equal to min( , p). 

It was proposed with the aim of measuring molecular symmetry in terms of atom topological uniquenes, the lower the °k value the greater being the topological symmetry. The same index with the opposite trend can also be calculated as the - redundancy index. 

Figure 11.27 A graphical representation of the highly redundant index of the...

A probabilistic measure of robustness is the redundancy index RI, defined by (Fu Frangopol 1990) ... 

The redundancy index Rl and the redundancy factor Pr are nonlinearly related, since ... 

Since the rehabihty index of the undamaged and the damaged system are not precisely known, also the redundancy index, as defined by (16), is not precisely known. Hence, the random variable Br = Pr(Pj(0), Pg(0)) is introduced. As a random variable, Br has a PDF fgRlBg) and characteristics such as a mean pgR and a standard deviation OgR. 

The mean and standard deviation of the redundancy index can be derived by means of Taylor approximations. This yields the following ... 

Common practice in indexing documents that discuss chemical reactions is to index each reaction in its own link. When role indicators are added, this technique simulates a reaction database. Roles are used for every chemical, but experience has shown that an elaborate set of roles leads to redundant indexing . This database uses reactant, product, special agent, medium, and other (used when the aforementioned do not apply). A typical record is illustrated by Figure 8. 

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