Rigid generation

Extremely high stereoselectivity in the metathesis of c/s-pent-2-ene catalyzed by the [W]=CHCMej complex (see Table 6.3) is maintained up to near-equilibrium conversion (Fig. 6.5). This can be explained either in terms of additional stabilization of the 1,3-ee structure of the tungstacyclobutane intermediate by the bulky ligands on tungsten, or by the rigidity generated by the cyclometallated ligand, or both (Couturier 1992). 

Remark. Theorem 11.1 was proven by Andronov and Leontovich via constructing and studying the mapping without using explicitly the theory of normal forms. Figures 11.5.1 and 11.5.2 are copied from the book Theory of Oscillations by Andronov, Vitt and Khaikin where they illustrated the phenomena of the soft and the rigid generation of self-oscillations (see Chap. 14). 

In most common chiral molecules, chirality arises from chiral tetravalent atoms. A conformation-independent chirality code (CICC) was developed that encodes the molecular chirality originating from a chiral tetravalent atom [42], For more generality, a conformation-dependent chirality code (CDCC) is used [43]. CDCC ti cats a molecule as a rigid set of points (atoms) linked by bonds, and it accounts for chirality generated by chirality centers, chirality axes, or chirality planes. 

A drawback of this approach is that it typically generates enormous and imwieldy synthesis trees which contain a large number of dead-end branches which are not worth further consideration. Furthermore, the chemist is forced to follow a rigid scheme during the planning process, alternating between the application of transforms, the derivation of new precursors, and again the application of further transforms to these precursors. 

There are two problems to consider when calculating 3D pharmacophores. First, unless the molecules are all completely rigid, one must take account of their conformational properties The second problem is to determine which combinations of pharmacophoric groups are common to the molecules and can be positioned in a similar orientation in space. More than one pharmacophore may be possible indeed, some algorithms can generate hundreds of possible pharmacophores, which must then be evaluated to determine which best fits the data. It is important to realise that all of these approaches to finding 3D pharmacophores assume that all of the molecules bind in a common manner to the macromolecule. 

Miscellaneous chemicals are used to modify the final properties of rigid polyurethane foams. Eor example, halogenated materials are used for flammabihty reduction, diols may be added for toughness or flexibiUty, and terephthalate-based polyester polyols may be used for decreased flammabiUty and smoke generation. Measurements of flammabihty and smoke characteristics are made with laboratory tests and do not necessarily reflect the effects of foams in actual fire situations. 

Adamantylamine is prepared from the corresponding alcohol or bromide by bridgehead cation generation in the presence of acetonitrile (49). Selective hydrolysis of the resultant acetamide to the rigid cycloahphatic amine by acid or base is difficult. 

Selection of a name for a specific compound is heavily influenced by the purpose at hand communication to a general audience, communication with specialists, or storage/retrieval through archival indexes. The first requires the simplest rules possible the second requires the shortest names possible and the third requires rigid adherence to a set of rules that will reliably generate a unique name. The name chosen may be different for each situation, although that is not necessarily so. 

Flexible rotors are designed to operate at speeds above those corresponding to their first natural frequencies of transverse vibrations. The phase relation of the maximum amplitude of vibration experiences a significant shift as the rotor operates above a different critical speed. Hence, the unbalance in a flexible rotor cannot simply be considered in terms of a force and moment when the response of the vibration system is in-line (or in-phase) with the generating force (the unbalance). Consequently, the two-plane dynamic balancing usually applied to a rigid rotor is inadequate to assure the rotor is balanced in its flexible mode. 

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