Some characteristic features of optimal control problems in economic theory

This paper formulates the system equations, state and control space constraints, and a criterion functional for an elementary example of a problem in economic growth, and discusses some further interpretation of the underlying economic structure. Several examples are presented to illustrate particular features of control problems in economics; references to futher examples, and to more general work in mathematical economics, are cited.     

Management of uremic pericarditis: a report of 11 patients with cardiac tamponade and a review of the literature

Uremic pericarditis remains a significant cause of morbidity and mortality in most hemodialysis programs. A review of the literature and out own experience show that uremic pericarditis should be vigorously treated when detected. Usually an increase in the dialysis program with regional heparinization is sufficient to control the pericarditis. When signs of pericardial effusion are manifested, patients often progress rapidly to cardiac tamponade. A surgical anterolateral pericardiectomy is the most satisfactory measure in controlling pericardial effusion and preventing fatal cardiac tamponade. Although these patients have severely impaired renal function, the operation can be performed safely with a low morbidity and mortality.     

Optimal investment policy: An example of a control problem in economic theory

A problem in mathematical economics concerning the optimal investment of resources is solved via the techniques of optimal control theory. Interesting theoretical complications include the simultaneous presence of interdependent control variable inequality constraints, state variable inequality constraints, and singularity conditions. Economic implications of the results are briefly discussed.     

One-stage midline unifocalization and complete repair in infancy versus multiple-stage unifocalization followed by repair for complex heart disease with major aortopulmonary collaterals

BACKGROUND: Patients with pulmonary atresia, ventricular septal defect, and major aortopulmonary collateral arteries have traditionally required multiple unifocalization staging operations before undergoing complete repair. Recently, the feasibility of a single-stage unifocalization and repair was demonstrated by Hanley. In this report, we describe our experience with each approach. METHODS AND RESULTS: Since 1989, 11 of 12 patients with pulmonary atresia, ventricular septal defect, and major aortopulmonary collateral arteries have undergone complete surgical correction. The first seven patients were subjected to staged bilateral unifocalizations, with repair being achieved in six (group I). The last five patients have undergone a single-stage midline unifocalization and repair via a sternotomy (group II). Four of these were infants (2 weeks to 9 months) and one was 13 years old. All patients in group I had tetralogy of Fallot, whereas in group II three patients had tetralogy of Fallot, one patient had double-outlet right ventricle, and one patient had complete atrioventricular canal and transposition. In group I, the median age at the first operation was 43 weeks. Complete repair was performed at a median age of 3.5 years, with a mean number of 3.3 operations required. In group II, only one operation was required to achieve complete repair at a median age of 28 weeks. The postoperative right ventricular/left ventricular pressure ratio was 0.49 in group I and 0.45 in group II. One intraoperative death and one late death occurred in group I and no early or late deaths in group II. Currently, four patients in group I and all five patients in group II are alive and well. CONCLUSIONS: Early intervention with both surgical approaches can lead to complete biventricular repair in most patients. Because the single-stage midline unifocalization and repair can achieve a completely repaired heart in infancy with one operation, it is currently our approach of choice.     

The ductus and the coarctation

After Robert E. Gross' historic ligation of a persistent ductus arteriosus in August 1938, it took 6 years before the first coarctation was operated on. Gross initiated experimental procedures directed at repair of coarctation even before the ductal operation had been performed. He had the desire, the drive, and the determination. Why the delay that allowed Clarence Crafoord to perform the first coarctation repair in October 1944?