For optimal control problems involving isoperimetric constraints, by using a two-norm approach, a new sufficiency theorem for a proper strong minimum is obtained. It is applicable to processes that satisfy the Legendre-Clebsch necessary condition but its strict version is not imposed, that is, the processes may be singular. The conditions are expressed explicitly in terms of the second variatio...

Food Policy, in much of Asia, has been slow to transition from its historic focus on staple grain self-sufficiency to a more integrated approach to nutrition security. Research and policy discussions continue to focus on hunger and calorie deficiency rather than on the need for a balanced diets to address chronic micronutrient malnutrition and the emerging problems of over weight and obesity. S...

The stability of arbitrary toroidal magnetohydrostatic equilibria is investigated near the limit of a vacuum magnetic field. Nonsingular expansions in powers of ß ~ p/B2 are considered to all orders. Order by order minimization of the energy variaiton shows that any orders are positive semidefinite in the nullspace of all lower orders if either the vacuum field has shear or (for an identically ...

This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated paralelly to the the measure theoretic case. It turns out that several classical examples and results have a non-commutative analogue. Some of the results are presented without proof (but with exact references) and the presentation is intended to be self-contained. The ...

In the wake of the 2007-08 food crisis that brought higher and more volatile food prices, many countries expressed increased interest in pursuing policies to bolster their levels of food self-sufficiency. At the same time, there has also been widespread critique of policies designed to support food self-sufficiency, on the grounds that they are inefficient and can disrupt trade. This debate has...

Companies, industries, and nations often consume resources supplied by unstable producers. Perturbations that affect the supplier propagate downstream to create volatility in resource prices. Consumers can invest to reduce this insecurity in two ways; invest in and impose security on the suppliers, or can invest in self-sufficiency so that shocks no longer present devastating consequences. We u...