Extensible polycycle

We will use this curvature only for non-extensible polycycles in Section 8.2, and it will be only a counting, i.e. combinatorial, argument However, the above curvature, concentrated on points, can be made geometric. This is the subject of Alexandrov theory (see, for example, [Ale50]). 

Now we consider another natural notion of maximality for polycycles. An (r, q)-polycycle is called rum-extensible if it is not a partial subgraph of any other (r, [Pg.116]

Four exceptional non-extensible polycycles, depicted on Figure 8.3 are vertex-split Octahedron, vertex-split Icosahedron, and two infinite ones Pi x Pi = Prism<, and Tr% = APrismoo (see Section 4.2). 

The positivity of the right-hand side of Inequality (8.4) implies the positivity of the left-hand side. Thus, in view of Equation (8.1), the curvature 2 of the geodesic -gon is positive. The resulting inequality 2(r + q) — qr > 0 contradicts the assumption made. Hence, a finite non-extensible polycycle cannot have parabolic or hyperbolic parameters (r, q) these parameters are elliptic. ... 

It has been demonstrated that liposomes, micelles, certain oil emulsions, and macromolecules (e.g., serum albumin) will keep the sensitizer molecules in a monomeric form (Jori, 1992 Hoebeke, 1995). The fact that most sensitizers are heavily charged and in many cases present as zwitterions, combined with their extensive polycyclic nature, makes some of these compounds particularly difficult to incorporate in a simple emulsion or liposome preparation. The zwitterions, in particular, can be almost insoluble in hydrophilic and lipophilic media. Alternative formulation approaches may therefore be required for this group of sensitizers. 

The extension to polycycles with three or more rings is straightforward prefixes tricyclo-, tetracyclo-, etc. are used and the positions of the additional bridges are specified by superscripts (examples 59-61). 

Extension and revision of the von Baeyer system for naming polycyclic compounds (including bicyclic compounds), lUPAC recommendations for naming heterocycles 99PAC513. 

Among other reactions proceeding with the retention of the heterocyclic nucleus may be noted the synthesis of amino acids of the isoxazole series from isoxazole-5-aldehydes/ the successful extension of the Schmidt reaction to 3-acylisoxazoles, and the synthesis of various polycyclic heterocycles, e.g. 101 102, involving the isoxa-... 

Morishima et al. [30, 50-54, 73-76] have made extensive investigations on photoinduced ET, using polycyclic aromatic chromophores covalently attached to polyelectrolytes. They were the first to show that the polyeletrolyte molecular surface provides an unusual microenvironment which greatly changes the rate of photoinduced ET and the fate of the charged photoproducts. 

Dihydro-1-vinylnaphthalene (67) as well as 3,4-dihydro-2-vinylnaphtha-lene (68) are more reactive than the corresponding aromatic dienes. Therefore they may also undergo cycloaddition reactions with low reactive dienophiles, thus showing a wider range of applications in organic synthesis. The cycloadditions of dienes 67 and 68 and of the 6-methoxy-2,4-dihydro-1-vinylnaphthalene 69 have been used extensively in the synthesis of steroids, heterocyclic compounds and polycyclic aromatic compounds. Some of the reactions of dienes 67-69 are summarized in Schemes 2.24, 2.25 and 2.26. In order to synthesize indeno[c]phenanthrenones, the cycloaddition of diene 67 with 3-bromoindan-l-one, which is a precursor of inden-l-one, was studied. Bromoindanone was prepared by treating commercially available indanone with NBS [64]. 

In fused ring systems, the positions are not equivalent and there is usually a preferred orientation even in the unsubstituted hydrocarbon. The preferred positions may often by predicted as for benzene rings. Thus it is possible to draw more canonical forms for the arenium ion when naphthalene is attacked at the a position than when it is attacked at the p position, and the a position is the preferred site of attack,though, as previously mentioned (p. 682), the isomer formed by substitution at the p position is thermodynamically more stable and is the product if the reaction is reversible and equilibrium is reached. Because of the more extensive delocalization of charges in the corresponding arenium ions, naphthalene is more reactive than benzene and substitution is faster at both positions. Similarly, anthracene, phenanthrene, and other fused polycyclic aromatic hydrocarbons are also substituted faster than benzene. 

Mineral oils also known as extender oils comprise of a wide range of minimum 1000 different chemical components (Figure 32.6) and are used extensively for reduction of compound costs and improved processing behaviors.They are also used as plastisizers for improved low temperature properties and improved rubber elasticity. Basically they are a mixture of aromatic, naphthanic, paraffinic, and polycyclic aromatic (PCA) materials. Mostly, 75% of extender oils are used in the tread, subtread, and shoulder 10%-15% in the sidewall approximately 5% in the inner Uner and less than 10% in the remaining parts for a typical PCR tire. In total, one passanger tire can contain up to 700 g of oil. 

The cross-dimerization reaction is very commonly employed for the manufacture of intermediates for synthetic musks, which have become an important class of perfumery chemicals. Synthetic musks have been the target of extensive research over the years due to a conservation order placed on the musk deer. Nitro musks are being steadily replaced by non-nitro polycyclic musks becau.se of technical drawbacks and health aspects of the former, which are explosive, sensitive, and virtually nonbiodegradable. Non-nitro musks, on the other hand exhibit better stability to light and alkali, and more nearly duplicate the odour of the macrocyclic musks occurring in nature. Indian musk odorants are easily soluble in alcohol and perfume compositions. They have the added advantage of non-discoloration in soap and domestic products. In view of the low price, their future in the perfume industry appears very promising. 

An interesting extension of the above reactions in the achiral series is the facile, regioselective, one-pot bicyclization of aminodialkenes leading to a variety of polycyclic heteroatom-containing skeletons (Eq. 4.25) [137]. 

The search for an alternative reactive metabolite for the polycyclic hydrocarbon carcinogens was soon successful. Also in 1973, Borgen et al. (54) reported that, in the presence of a microsomal system from hamster liver, trans 7,8-dihydro-7,8-dihydroxybenzola]-pyrene (a metabolite of benzo[aJpyrene) was bound to DNA in vitro some ten times more extensively than was benzo[a]pyrene itself. 

In the past, general chapters and reviews have been published, related to the characteristics of CL as analytical technique [7-9], mainly in the liquid phase [10-14], and its use as detection mode in flowing streams and immunoassay [15-17]. Two extensive reviews reported on the specific application of CL reactions according to the nature of the analyte (inorganic species, enzymes and nucleotides, acids and amines, carbohydrates, steroids, polycyclic aromatic compounds, and drugs) and covering the literature from 1983 to 1991 [18] and from 1991 to mid-1995 [19]. 

Extensively developed by Ojima and co-workers, SiCaT and carbonylative silylcarbocyclization (CO-SiCaC) represent a rapid entry into polycyclic molecules of interest.271 For instance, the rhodium-catalyzed intramolecular SiCaT of triyne 441 afforded tricyclic compound 442 in high yield, accompanied by a small amount of cycloadduct 443 (Scheme 111).270... 

In Holton s and Wender s work, the total synthesis was achieved by sequentially forming the AB ring through the fragmentation of epoxy alcohols derived from (—)-camphor and a-pinene. Nicolau s, Danishefsky s, and Kuwa-jima s total syntheses involved B ring closure connecting the A and C rings, whereas in Mukaiyama s synthesis, the aldol reaction was extensively applied to construct the polycyclic system. 

The structures of taxol and its polycyclic part baccatin III are shown in Figure 7-2, and the numbering of these two compounds is extensively used throughout the rest of this chapter. Because connecting the side chain to baccatin HI is just routine chemistry, we introduce only the synthesis of baccatin III and the taxol side chain. 

An extensive range of compounds with homonuclear or heteronuclear single or double bonds between As, Sb, or Bi is known. They include the simple tetraorganodimetallic species, R2MMR2, double bonded species RM=MR, linear tri- and tetra-metallated species, and mono- or polycyclic compounds. In addition, adducts with coordinative metal-metal bonds are known.44-46 463 Examples for cationic species with Sb-Sb bonds are Me2SbSbMe2+ and... 

Since then, the photocycloaddition reaction has been extensively studied and has become a powerful tool for the construction of complex polycyclic molecules. High stereoselectivities are observed in some cases. The configuration of the diradical intermediate determines the stereochemistry of the adduct [33], Typical examples... 

Another isomerization reaction of arene oxides is equilibrium with oxe-pins [5], Here, the fused six-membered carbocycle and three-membered oxirane merge to form a seven-membered heterocycle, as shown in Fig. 10.2. An extensive computational and experimental study involving 75 epoxides of monocyclic, bicyclic, and polycyclic aromatic hydrocarbons has revealed much information on the structural factors that influence the reaction rate and position of equilibrium [11], Thus, some compounds were stable as oxepins (e.g., naphthalene 2,3-oxide), while others exhibited a balanced equilibrium... 

Anodic conversion of aromatics proceeds in most cases by le-transfer to the anode to form a radical cation (34) (Scheme 9). Oxidation is facilitated by extension of the 7T-system ( 1/2 vs. Ag/Ag+ benzene 2.08 V, pyrene 0.86 V) and by electron donating substituents ( 1/2 vs. Ag/Ag+p-phenylenediamine —0.15 V). Oxidation potentials of polycyclic aromatics and substituted benzenes are collected in Ref [140-142]. 

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