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This paper characterizes, in terms of thinness, compact sets K in a suitable harmonic space Ω \Omega which have the following property: functions which are harmonic (resp. continuous and superharmonic) on a neighbourhood of K can be uniformly approximated on K by functions which are harmonic (resp. continuous and superharmonic) on Ω \Omega . The corresponding problems of approximating functions which are continuous on K and harmonic (resp. superharmonic) on the interior K ˚ \mathring {K} are also solved.

Contents: Differentials on a Riemann surface Principal function The capacity function Harmonic differentials Analytic differentials Meromorphic functions

Aortic cross-clamping may produce ischemic damage due to a discrepancy between supply and demand. Supply is determined by noncoronary collateral flow and substrate stores, and demand by electromechanical activity, wall tension, and temperature. The effects of 60 minutes of conventional hypothermic ischemic arrest were compared to those of pharmacological arrest. Noncoronary collateral blood supply was comparable in both groups during cross-clamping. With ischemic arest, mechanical activity and endocardial electrical activity persisted and wall tension fell progressively. With pharmacological arrest, electromechanical activity stopped in less than 1 minute but returned (with increased wall tension) nearly 1 hour. Thirty minutes following reperfusion, coronary flow was redistributed away from subendocardium after ischemic arrest and toward endocardium after pharmacological arrest. Myocardial performance was depressed severely after conventional arrest and only mildy after pharmacological arrest. We conclude that aortic cross-clamping is safer with pharmacological arrest than with ischemic arrest. The cardioplegic solution modifies the supply/demand balance favorably, but it is washed out by noncoronary collateral blood supply.

Etude de la propriete de la moyenne des fonctions harmoniques. Existence, unicite et caracterisation de la meilleure approximation L 1 harmonique des fonctions strictement sous harmoniques