Continuity of singular perturbations in the graph topology

AbstractFor a certain model for singular perturbations in control systems, which we motivate by a simple example, we show that under weak assumptions continuity in the graph topology holds as the perturbation parameter tends to zero. This may be contrasted with a result by Cobb, who considered a different model for singular perturbations and who found a strong condition to be necessary for continuity in that model. Our proof techniques are based on the characterization (due to Qiu and Davison) of the graph topology as a topology of uniform convergence

Acute coronary events in general practice: the Imminent Myocardial Infarction Rotterdam Study

With the advent of coronary care units in the early sixties, the first concentrated effort was made to reduce mortality from myocardial infarction. Subsequent experience has demonstrated that in-hospital deaths, particularly those from arrhythmias, have decreased from some thirty-five per cent to below ten per cent. However, several studies had indicated that up to 60% of the total mortality from acu· te coronary events, i.e. sudden cardiac death and acute myocardial infarction, took place in pre-hospital phase 1-6 and as early as the late sixties, both clinicians and epidemiologists began to realize that the greatest further gains had to be achieved by decreasing mortality in that particular phase. In 1969, Bondurant7 stated: "the pre-hospital mortality due to ischaemic heart disease is greater than the total mortality due to any other single cause of death" and also: "the pre-hospital phase of acute myocardial infarction poses the greatest single medical problem of our nation in terms of loss of potential salvageable life". This seems to apply to the U.S.A. as well to the entire western world of today. Fulton et al. from Edinburgh, Scotland, concluded also in 1969: "The majority of deaths occur before patients with acute myocardial infarction reach hospital. Most of these are sudden and unattended medically. In many, symptoms of ischaemic heart disease have been present, but often they have passed unnoticed or at least undeclared. It is difficult to conceive of any system which would allow effective treatment of these patients. Therefore, reliable identification of those prone to sudden death and the development of prophylactlcmeasures would do as much or more to combat the problem of acute coronary attacks as any other approach. Thus, the emphasis began to swing away from further intra-hospital efforts at reducing death from coronary atherosclerotic heart disease (C.A.H.D.) to the out-of-hospital pre-coronary phase. For instance, Lown and Wolf stated in 1971: "Coronary care units, while effective in lowering hospital mortality, can not significantly reduce sudden cardiac death, which occurs primarily out-of-hospital and accounts for the majority of deaths from coronary heart disease