Number of rings

Find the minimum number of rings to describe a ring system. 

Figure 2-36. Identification of the number of rings in adamantane after graph reduction (the different ring systems are highlighted with bold lines). Note that a graph does not car 3D information thus, the two structures on the upper right-hand side are identical.

The second step, the so called generation, created only those structures which complied with the given constraints, and imposed additional restrictions on the compounds such as the number of rings or double bonds. The third and final phase, the tester phase, examined each proposed solution for each proposed compound a mass spectrum was predicted which was then compared with the actual data of the compound. The possible solutions were then ranked depending on the deviation between the observed and the predicted mass spectra. 

Number of atoms of various elements Number of bonds of various orders Number of rings... 

In general the most stable resonance structure for a polycyclic aromatic hydro carbon is the one with the greatest number of rings that correspond to Kekule formula tions of benzene Naphthalene provides a fairly typical example... 

Number of ring members Rings containing nitrogen Rings containing no nitrogen ... 

Number of Rings and Double Bonds. The total number of rings and double bonds can be determined from the empirical formula (C H O N ) by the relationship... 

In the matter of ring stability it is the number of atoms in the ring that is of central importance. In the following equations 1, m, and m represent the number of ring (1) and backbone (m, m )atoms in the species shown. Note that for linear species m and m are proportional to the degree of polymerization but are more suitable for present purposes than the latter. The following general reactions are pertinent to the present discussion ... 

Although the number of ring atoms is the structural feature upon which we focus attention, we shall use the criteria of thermodynamics and kinetics to assess the feasibility of the reactions listed above. 

Glycols may undergo intramolecular cyclization or cycHcaHy condense with other molecules to form a number of ring stmctures. Transesterification of carbonates with ethylene glycol produces ethylene carbonate [96-49-1] (eq. 4). Numerous materials catalyze carbonate transesterifications. 

In the case of l,4-ben2oquinone, the product is steam-distilled, chilled, and obtained in high yield and purity. Direct oxidation of the appropriate unoxygenated hydrocarbon has been described for a large number of ring systems, but is generally utilized only for the polynuclear quinones without side chains. A representative sample of quinone uses is given in Table 5. 

Ligand, L Complex formula Ring size Number of rings Number of coordinated donor atoms LogV ... 

The ease of oxidation varies considerably with the nature and number of ring substituents thus, although simple alkyl derivatives of pyrazine, quinoxaline and phenazine are easily oxidized by peracetic acid generated in situ from hydrogen peroxide and acetic acid, some difficulties are encountered. With unsymmetrical substrates there is inevitably the selectivity problem. Thus, methylpyrazine on oxidation with peracetic acid yields mixtures of the 1-and 4-oxides (42) and (43) (59YZ1275). In favourable circumstances, such product mixtures may be separated by fractional crystallization. Simple alkyl derivatives of quinoxalines are... 

D - shaft diameter, in h - radial clearance, in Pq = high side pressure, psia T(, = temperature, °R R -- specific gas constant n = number of rings in series a = parameter, function of p po (see Figure D-7)... 

Fig. 5.23. The shock-induced polarization of the indicated polymers containing benzene rings in their structure is shown to be strongly dependent on the number of rings (after Graham [82G02]).

It is the purpose of this chapter to describe a number of ring enlargement and simultaneous ring enlargement-ring contraction procedures which should be of general use. Recommended illustrative experimental procedures are given. 

Mention must also be made of the neat series of reactions carried out by Wieland and Neeb which led to a number of ring extended products. These are summarized by the conversion of 406 into 406a and 407. The structure of 406a was confirmed by a comparison of its... 

Out- side Diam. In. Out- side Length In. WaU Thick- ness In. Number of Rings per Ft Weight of Rings per Ft Percent Free Gas Space Ft of Surface Area per Ft of Packing Net Cross-Section Area of Packing in Ft2/Ft2 ... 

An important principle is that security must be built in depth - otherwise known as defense in depth. In this context, it may be helpful to think of security as a set of concentric rings, where the target is located at the center. Each ring represents a level of physical protection (perimeter fence, building shell, security case) but the number of rings and security resistance will vary relative to the risk. The spaces between the rings may represent other defensive measures such as closed-circuit television (CCTV), security lighting, intruder alarm systems, etc. 

---