In recent years, olefin cross metathesis (CM) has emerged as a powerful and convenient synthetic technique in organic chemistry; however, as a general synthetic method, CM has been limited by the lack of predictability in product selectivity and stereoselectivity. Investigations into olefin cross metathesis with several classes of olefins, including substituted and functionalized styrenes, secondary allylic alcohols, tertiary allylic alcohols, and olefins with alpha-quaternary centers, have led to a general model useful for the prediction of product selectivity and stereoselectivity in cross metathesis. As a general ranking of olefin reactivity in CM, olefins can be categorized by their relative abilities to undergo homodimerization via cross metathesis and the susceptibility of their homodimers toward secondary metathesis reactions. When an olefin of high reactivity is reacted with an olefin of lower reactivity (sterically bulky, electron-deficient, etc.), selective cross metathesis can be achieved using feedstock stoichiometries as low as 1:1. By employing a metathesis catalyst with the appropriate activity, selective cross metathesis reactions can be achieved with a wide variety of electron-rich, electron-deficient, and sterically bulky olefins. Application of this model has allowed for the prediction and development of selective cross metathesis reactions, culminating in unprecedented three-component intermolecular cross metathesis reactions.

General Considerations.Manipulation of organometallic compounds was performed using

dedicated to professor w. t. tutte on the occasion of his eightieth birthdayThe four-colour theorem, that every loopless planar graph admits a vertexcolouring with at most four different colours, was proved in 1976 by Appel and Haken, using a computer. Here we give another proof, still using a computer, but simpler than Appel and Haken's in several respects.

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Photoinduced force microscopy resolves nanometer-scale topology with chemical recognition based on material absorption.