Circles through two points that always enclose many points

This paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams and a lower bound on the minimum number of semispaces of size at most k.Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by the National Science Foundation under Grant CCR-8714565, by the second author has been partially supported by the Digital Equipment Corporation, by the fourth author has been partially supported by the Office of Naval Research under Grant N00014-86K-0416.     

Infrared study of co adsorbed species on ru/silicalite catalyst

Carbon monoxide adsorbed species on Ru/silicalite and their reactivity towards oxygen have been studied using in situ diffuse reflectance infrared spectroscopy (DRIFT). Four species were detected: a bridge bonded CO on metallic Ru (1980 cm ^-1), a linearly adsorbed CO on metallic Ru (2040 cm^-1), a linearly adsorbed CO on partially oxidized Ru (2081 cm^-1), and a multicarbonyl on oxidized Ru (2081 and 2133 cm^-1). Among the four CO species the most strongly held species was the bridge bonded CO on metallic Ru while the multicarbonyl was the most weakly held species. These four species have different reactivities towards oxygen. Only the linearly adsorbed CO on metallic Ru can be oxidized at room temperature.     

Coriatone and corianlactone, two novel sesquiterpenes from Coriaria nepalensis

Both coriatone (1). a novel highly oxygenated picrotoxane-type sesquiterpene, and corianlactone (2). with an unprecedented sesquiterpene basic skeleton, named coriane, were isolated from Coriaria nepalensis Wall. The structures of 1 and 2 were determined by analysis of their two-dimensional NMR data, and the structure of 2 was confirmed by X-ray analysis. Compounds 1 and 2 showed no remarkable inhibitory activity toward K(562) cells. They are cytotoxic with IC(50) > 50 microg/mL (cis-platinim: IC(50) = 0.49 microg/mL).