Convex -polycycle

Call a polycycle proper if it is apartial subgraph of r, q) and a helicene, otherwise (this term will be justified later by Theorem 4.3.1). Call a proper (r, )-polycycle induced (moreover, isometric) if this subgraph is, in addition, an induced (moreover, isometric) subgraph of r, q). Another interesting possible property of aptoper (r, q)-polycycle is being convex in r, q (see Section 4.4). 

Note, that for ft = 7, there are outerplanar (3,4)- and (3,5)-polycycles, which remain helicenes in 3, 5 and 3,6, respectively. A fan of (q - 1) r-gons with -valent common (boundary) vertex, is an example of outerplanar (r, )-polycycle, which is a proper non-convex (r, 2q — 3)-polycycle. 

Proof The (5,3)-polycycles 4 and D + E2 + D are non-2-embeddable. So, some of their alternating zones do not define convex cuts ... 

It remains to investigate the (3,5)-polycycles with elementary summands C4, d, e, e-i, e-j. We assume that c3 and d + ez+d o not appear as sub-polycycles and we will prove that their alternating zones define convex cuts. 

Two interesting features of these models include the presence of an acid/base pair for organization of a well-defined six-membered transition state, and the role of the asymmetry adjacent to the basic group (X), which determines the face selectivity of the reaction. Note that for some catalysts (i.e. 85 and 87) the least-hindered site of coordination is not necessarily the convex face of a polycyclic system. 

Polycyclic systems such as pentacyclic compound 13 are also hydrogenated in a diastereospecific manner with hydrogen transfer occurring from the sterically unencumbered convex face60. 

Table 6 gives a survey on the range of M-P distances. The upper limits are uncertain because the selected distances are only compared with atomic radii and take not into account the topology (convex polyhedra procedure). The M-P coordination in solid phosphides demonstrates both coordination and donor functions in isolated complex compounds (cf. the (E15) complexes, stabilized in the coordination sphere of transition metals). This is especially true with the polyphosphides. An extreme is CU2P3I2 (see Section 6.5.7), which is an adduct of Cul and elemental phosphorus (charge transfer complex). Chains of polycyclic... 

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