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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.

This study compares the effects of 60 minutes of ischemic arrest with profound topical hypothermia (10 dogs) on myocardial (1) blood flow and distribution (microspheres), (2) metabolism (oxygen and lactate), (3) water content (wet to dry weights), (4) compliance (intraventricular balloon), and (5) performance (isovolumetric function curves) with 180 minutes of cardiopulmonary bypass with the heart in the beating empty state (seven dogs). Studies performed before and 30 minutes after 1 hour of ischemic arrest with profound topical hypothermia showed: (1) total left ventricular blood flow increased 50 per cent but became redistributed away from the subendocardium (endocardial/epicardial flow ratio fell from 1.13 to 0.77,(2) left ventricular oxygen consumption fell 30 per cent while left ventricular oxygen extraction fell from 51 to 29 per cent; (3) lactate extraction fell from 15 to 4 per cent (two dogs produced lactate); (4) left ventricular endocardial (papillary muscle) water content rose 2.4 per cent; (5) left ventricular compliance decreased from 1.68 to 1.01 ml. H2O/mm. Hg (at 25 ml.); (6) left ventricular performance was depressed 49 per cent below control values. In contrast, 3 hours of cardiopulmonary bypass in the beating empty heart produced only minimal changes in these variables.

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