In this article we study an optimal control problem subject to the Fokker-Planck equation ∂ t ρ − ν ∆ div( ρB [ u ]) = 0 The variable is time-dependent and possibly multidimensional, function B depends on space control. cost functional of tracking type includes a quadratic regularization term For problem, prove existence controls first order necessary conditions. Main emphasis placed second suf...

The map illustrates the geographic variation across counties and shows that counties with the highest prevalence of Medicare beneficiaries with 6 or more chronic conditions are located predominantly in southern states (eg, Texas, Florida, Kentucky) and northeastern states (eg, New York, Pennsylvania). Counties with the lowest prevalence are found mostly in western states (eg, Oregon, Montana, W...

The response of a soap film to the continuous deformation of its wire boundary is considered, with particular attention to the topological transitions that can occur at critical stages of the deformation process. Two well-known examples that have been studied by both theory and experiment are the catenoid suspended between circular wires in parallel planes, and the Möbius-strip soap film spanni...

The clinical management of intersex has undergone a significant change in values. Whereas in former times, benevolent medical paternalism was the rule, today, the patient's right to respect for dignity and self-determination is given priority. This paper discusses ethical considerations shaping the modern therapeutic management of intersex conditions that do not entail acute health risks. It co...