Gross-substitutes condition

A technical condition, gross substitutes [55] (or simply substitutes) on agent valuations is sufficient for integrality. Unit demand preferences, in which each agent wants at most one item (but can have different values for different items), is a special case. With this substitutes condition, LPi is integral... 

The reduction of aromatic carboxylic acids to the corresponding aldehydes under aerobic conditions is of interest in biotechnology, since the oxidoreductase from Nocardia sp. is able to accept a range of substituted benzoic acids, naphthoic acids, and a few heterocyclic carboxylic acids (Li and Rosazza 1997). The reaction involves formation of an acyl-AMP intermediate by reaction of the carboxylic acid with ATP NADPH then reduces this to the aldehyde (Li and Rosazza 1998 He et al. 2004). A comparable reaction for aromatic carboxylates has been demonstrated in Neurospora crassa (Gross 1972). 

Using Corey and Gross s internal quench method48 with TMSC1, silylenol ethers have been generated upon deprotonation of 4-substituted cyclohexanone with chiral lithium amides as shown in Scheme 20. It has been noted that the internal quench condition is crucial for achieving high level of enantioselectivity. 

From Table XI, note that the tt optimum for both 3- and 4-substituted TFMS series members acting on Foxtail grass in the presence of surfactant is 7t0 = —0.77. Examination of Figures 2c and 2d indicates, however, that gross differences in the herbicidal activity surfaces for the meta- and para-TFMS series exist. On this basis, it would appear that coincidence of tt0 values for 3- and 4-substituted series is not a sufficient condition for assuming that modes of herbicidal action for the two series are also identical. 

Entry 4 presents an early result on the gross stereochemistry of acetolysis of 2-octyl tosylate. We have seen earlier that after correction for racemization of the substrate and the product and addition of acetic acid to octenes under the reaction conditions, the displacement step occurs stereospecifically with inversion. The results cited in entry 5 are important and illustrate the importance of solvation of the ion-pair intermediates in nucleophilic substitution reactions of secondary substrates. In aqueous dioxane, the ion-pair intermediate may be solvated by water molecules or by dioxane. Inverted product results from solvation by water, but solvation by dioxane cannot collapse to a stable product. Subsequent solvation steps can lead to symmetrical solvation or attack by water from the front side, displacing dioxane. The observed result is the formation of partially racemic 2-octanol ... 

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