A geometric characterization of inner product spaces

A normed linear spaceE is an inner product space if (and only if) there is a nontrivial closed bounded setD inE such that each translate ofD which misses the origin is taken by the inversion ofE to a convex set. Research supported in part by NSF Grant No. MCS 79-02734.     

PHOTOALLERGIC CONTACT DERMATITIS TO MUSK AMBRETTE: ACTION SPECTRA IN GUINEA PIGS AND MAN*

Abstract— Positive photopatch tests to musk ambrette were elicited using narrow band radiation in two patients with photoallergic contact dermatitis to musk ambrette and in photosensitized guinea pigs. The most effective wavelength range in the two patients was between 334 and 394 nm. Control subjects did not respond to the same light doses either in the presence or absence of musk ambrette. One patient exhibited maximum sensitivity at 346 nm. The action spectrum in guinea pigs extended from 322 to 406 nm with maximum response at 322 nm. Below 322 nm, erythema was observed at the same or higher doses than those required for evoking a minimal erythema response in non-sensitized animals. Morphologically and histologically the response below 322 nm appeared to be normal delayed erythema. No erythema was elicited by radiation between 322 and 430 nm in non-photosensitized animals which had received musk ambrette.     

Kinetics of urethane cleavage in crosslinked polyurethanes

A series of clean, well-defined polyurethane networks was synthesized from polyester glycols, 2,4-tolylene diisocyanate, and 1,1′,1″-trimethylolpropane by means that afforded precise control over the content of urethane groups per network chain. The thermal cleavage of these networks was studied using the technique of stress relaxation. Analysis of the stress-relaxation data on each network structure revealed two exponential decay processes differing in rate by about an order of magnitude. The rate of the slower process, which dominates the overall stress decay, was shown to be directly dependent on the content of urethane groups per network chain. Positive identification of this process with urethane cleavage was thereby established. The kinetic and thermodynamic constants associated with urethane cleavage were then calculated from data on this process at different temperatures. The more transient stress-decay process was not uniquely definable, but probably originated from the cleavage of one or more types of weak linkages found in small but variable proportions in the different polyurethane networks. The nature and origin of these weak linkages was discussed.     

Radical reactions of highly polar molecules. Chlorination of halopropanes

In polychloro-2,2-difluoropropanes, where a large inductive effect results in relatively low reactivity to chlorination, the presence of additional chlorine causes an increased reactivity of the hydrogens geminal to the chlorine and a reduced reactivity of the remote (third carbon) hydrogens. The ways in which resonance, inductive effect, and steric crowding interact in the rates of chlorination of polar molecules are discussed.