Neo classification

The neo classification takes into account all benzenoids they can be either normal (n), essentially disconnected (e) or non-Kekulean (o). 

The neo classification divides all benzenoids into normal (n), essentially disconnected (e) and non-Kekuleans (o), where the n and e systems cover all the Kekuleans. Cyvin and Gutman [26] have advocated for this classification by saying From the point of view of the enumeration of Kekule structures the classification. . . [neo]. . . seems to be a rather appropriate one [94,87] . However, the distinction between Kekulean (closed-shell, non-radicalic) and non-Kekulean (radicalic) benzenoid hydrocarbons was made long before the explicit definition of the neo classification. This practice started with the first (substantial) enumeration of benzenoids in the chemical context by Balaban and Harary [13]. 

Together with the non-Kekul ans (o), the total number of single coronoids is accounted for. This classification, referred to as the neo classification, applies to benzenoids as well as (single) coronoids. 

Table 2 shows the numbers of single coronoid isomers according to the neo classification (n normal e essentially disconnected o non—Kekulean). Furthermore, the non—Kekulean systems, o, are classified according to their color excess (A). The table is arranged in a way which was found suitable for benzenoid isomers (Brunvoll, Cyvin BN and Cyvin 1992b). All the numbers in this table, although they have not been given before explicitly, can be deduced firom the data of Volume I, Tables 1-9.1 to 1-9.8. 

Notice that the neo classification for the single coronoids with h = 15 is known 142388n + 29824e + 281734o. On the other hand, the corresponding rio and rheo classifications are not known. 

From the conceptual descriptions as well as algorithmic details iven above, it is clear that NLP solvers are complex algorithms that ave required considerable research and development to turn them into reliable and efficient software tools. Practitioners who are confronted with engineering optimization problems should therefore leverage these efforts, rather than write their own codes. Table 3-4 presents a sampling of available NLP codes that represent the above classifications. Much more information on these and other codes can be found on the NEOS server (www-neos.mcs.anl.gov) and the NEOS Software Guide http /Avww-fp.mcs.anl.gov/otc/Guide2SoftwareGuide. 

Sotiriou C, Neo SY, McShane LM et al. Breast cancer classification and prognosis based on gene expression profiles from a population-based study. Proc Natl Acad Sci USA 2003 100 10393-10398. van de Vijver MJ, He YD, van t Veer LJ et al. A gene-expression signature as a predictor of survival in breast cancer. NEnglJMed2002 347 1999-2009. 

The classification referred to as neo takes into account all benzenoids. They are either normal (n), essentially disconnected (e) or non-Kekulean (o) cf., e.g., the multi-author report of Balaban et al. [30] and references cited therein. Among the Kekulean systems (n + e) the Kekule structures possess fixed bonds in the case of essentially disconnected benzenoid, while those of the normal benzenoids do not. 

Classification of Silicates On the basis of corners (0 1,2, 3 or 4) of the Si04 tetrahedra shared with other neo-silicate. 

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