Ring counting

We need to define what is meant by a double bond equivalent any element-element double bond (C = C, C = 0, C=N) count as 1, while triple bonds count as 2. A saturated ring counts as 1, and any double bond present in the ring also counts as 1 thus a benzene ring corresponds to 4 double bond equivalents. 

Table 2 Table of mean aromatic ring count in the Glaxo-SmithKline pipeline... 

As pointed out by Muller (1978), there are well-documented differences between the ages of materials determined by dating with radioisotopes and the ages determined by other means, such as tree-ring counting. In addition to systematic effects, there are statistical errors due to the limited number of atoms observed. Both types of errors can be considered to be fluctuations in n, the number of atoms observed. A relationship can be derived between the magnitude of these fluctuations and the resulting error in the estimation of age of the sample ... 

Tree-ring counting as a measure of age is described under Pine Trees. However, it is of note to mention an August 1990 report on how tree rings were used to reveal the age of the oldest road." which was found m a peat bog in 1970. The road is located in southwestern England. It dates back 4000 years. 

The pi bonding structure of pyrrole. The pyrrole nitrogen atom is sp2 hybridized, with a lone pair of electrons in the p orbital. This p orbital overlaps with the p orbitals of the carbon atoms to form a continuous ring. Counting the four electrons of the double bonds and the two electrons in the nitrogen p orbital, there are six pi electrons. 

All treatments to be used in initial field tests were done with standard test coupons provided by the Forest Products Laboratory. These wood specimens are cut from Southern Yellow Pine trees harvested from U.S. Forest Service timber stands and cut into precision 1.5 x 6 x 0.25 inch (3.81 x 15.24 x 0.635 cm) sauries with the grain running lengthwise and a ring count of 6 to 10 per inch. By design, each sample therefore has a standard volume of 36.87 cm. ... 

Simple presence or counts of individual atoms, bonds, or features, such as rings, have been included in many descriptor sets used for substructure search. The CAS ONLINE dictionary [6], for instance, contains a variety of simple descriptors to represent individual atom counts, degree of connectivity, bond composition, unusual mass, valence, ring count, and type of ring (size and ring connectivity). 

Ritchie, T.J. and Macdonald, S.J.F. (2009) The impact of aromatic ring count on compound developability are too many aromatic rings a liability in drug design Drug Discovery Today, 14, 1011-1020. 

A recent study has shown that aromatic ring count is a significant factor in compound developability [53]. 

Note that carbons 3 and 6 of the ring count as substituents on the double bond. 

Besides the walk counts there are, of course, the path counts and the ring counts. The smallest length of a cycle, if there is one, gives another interesting pareimeter ... 

We saw in Equation (2.2) that walk counts are obtained by summing the entries in suitable powers of the bond matrix of y or of y. Further, there are the purely topological indices such as path counts and ring counts, denoted as follows ... 

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