Cyclic derivatives definition

Purinophanes are, by definition, cyclic derivatives incorporating one or more purine moieties in the ring structure. Synthesis of this type of compound, containing two purine units has been undertaken with a view to using the products as model compounds for the study of the three-dimensional base pairing present in the DNA helix. 

Two atypical triterpenes were isolated from cultures of the species Euplotes vannus collected in Indonesia. These cyclical derivatives of squalene have an irregular carbon skeleton previously unknown in Nature. The relative percentages for varmusals A and B vary with the strain grown, and it has been shown that these derivatives are absent from Dunaliella salina, which is symbiotic with Euplotes vannus. The definitive structures of varmusals A and B were deduced from intense spectroscopic and synthetic researches (Nicolaou, Zhang, and Ortiz, 2009 Nicolaou, Ortiz, and Zhang, 2009 Nicolaou et al., 2010a, 2010b). 

The present Recommendations deal with the acyclic and cyclic forms of monosaccharides and their simple derivatives, as well as with the nomenclature of oligosaccharides and polysaccharides. They are additional to the Definitive Rules for the Nomenclature of Organic Chemistry [13,14] and are intended to govern those aspects of the nomenclature of carbohydrates not covered by those rules. 

The chemical and physical properties of the polymers obtained by these alternate methods are identical, except insofar as they are affected by differences in molecular weight. In order to avoid the confusion which would result if classification of the products were to be based on the method of synthesis actually employed in each case, it has been proposed that the substance be referred to as a condensation polymer in such instances, irrespective of whether a condensation or an addition polymerization process was used in its preparation. The cyclic compound is after all a condensation product of one or more bifunctional compounds, and in this sense the linear polymer obtained from the cyclic intermediate can be regarded as the polymeric derivative of the bifunctional monomer(s). Furthermore, each of the polymers listed in Table III may be degraded to bifunctional monomers differing in composition from the structural unit, although such degradation of polyethylene oxide and the polythioether may be difficult. Apart from the demands of any particular definition, it is clearly desirable to include all of these substances among the condensation... 

The governing dimensionless partial derivative equations are similar to those derived for cyclic voltammetry in Section 6.2.2 for the various dimerization mechanisms and in Section 6.2.1 for the EC mechanism. They are summarized in Table 6.6. The definition of the dimensionless variables is different, however, the normalizing time now being the time tR at which the potential is reversed. Definitions of the new time and space variables and of the kinetic parameter are thus changed (see Table 6.6). The equation systems are then solved numerically according to a finite difference method after discretization of the time and space variables (see Section 2.2.8). Computation of the... 

The classical definition for the graph centre is not helpful for cyclic graphs where often a large number of vertices (most of them topologically non-equivalent) appear as central. Recently, Bonchev, Balaban and Mekenyan 67) proposed a generalized concept for the graph centre, and several centric indices were derived on this basis. The new definition consists of four hierarchically ordered criteria based on the distance matrix 1) the smallest maximum distance in the row or column of the vertex ... 

When X = C2, X can be identified with the set of GLJl(C)-orbits of (Hi, B2, i) where Bi, B2 are commuting n x n-matrices and i is a cyclic vector (Theorem 1.14). Many properties of (C2) are derived from this description. In Chapter 3, we shall regard the description as a geometric invariant theory quotient and a hyper-Kahler quotient. This description is very similar to the definition of quiver varieties which were studied in [62]. 

Another equilibrium partner of the form 102a is the cyclic Schiff base 101a, formed by dehydration. The C=N chromophore in 101a exhibits a weakly positive Cotton effect at 250 nm, by which the proportion of 101a present can be demonstrated. The Cotton effect disappears at pH values below 6. By comparison with 5-amino-5-deoxy-D-xylopyranose (17), 102a is definitely the more stable toward acids. Neither an Amadori rearrangement product, nor aromatization to a p)nTole derivative, is observed down to pH 1.0. 

Apparently the first definite assignment of a chair form to a six-membered, cyclic-acetal ring was made in order to explain the occurrence of only one stable isomer of methyl 4,6-0-benzylidene-,8-D-glucopyranoside, which will have the conformation L. The stable forms of 4,6-0-benzyli-dene derivatives of methyl /3-D-mannopyranoside, methyl 8-D-allopyrano-side, and methyl S-D-altropyranoside will differ from L only in the configurations at C2 and 03. "... 

For a monosubstituted oxane, the excess free enthalpy of the conformation with an axial substituent over the conformation with an equatorial substituent is, as we know by definition, the conformational free energy (CFE) of the substituent in oxane at this position. These values, possibly measured indirectly by utilizing intennediate compounds, are shown in Table 2.2. Equatorial conformations correspond to anti conformations in butane and methoxyethane, and the axial conformations (not represented) to gauche conformations. We can observe that the environment of derivative 2.20 is closest to that of the cyclohexane and that the CFE is of the same order. On the other hand, the presence of the cyclic oxygen lowers notably the CFE of derivative 2.19. The important point is the noteworthy increase in the CFE of compound 2.18, where the methyl group is close to the cyclic oxygen and possesses, on one side, an environment similar to that of methoxyethane. Let us look at the equilibrium (2.4) of the dimethylated derivative 2.21. 

The total Hamiltonian of the system will be the same as in equation (65) and for its periodic part one can use the procedure given in equations (59)-(62). As before one can derive the system of equations (78) with the definitions (79)—(81) for the LCAO case. Finally taking into account that for a periodic polymer all matrices occurring in equation (78) are cyclic hypermatrices, one arrives after block-diagonalization again to equations (86) (in this case without the field ). 

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