Pontryagin's Minimum Principle states informally that this must be minimized over the set U, the set of all permissible controls for every u-star in U. The Bondy-Chvatal theorem claims that a graph is this if and only if its 
Pontryagin's Minimum Principle states informally that this must be minimized over the set U, the set of all permissible controls for every u-star in U. The Bondy-Chvatal theorem claims that a graph is this if and only if its closure also has this property. This type of vector field defines a flow on a symplectic manifold. A non-abelian group in which all subgroups are normal is known as this kind of group. As a quantum mechanical operator, it is self- adjoint and it is the observable corresponding to the total energy of the system. For 10 points, this is also the ring of the non-commutative extensions of complex numbers, developed by an Irish mathematician also known as quaternions.
Pontryagin's Minimum Principle states informally that this must be minimized over the set U, the set of all permissible controls for every u-star in U.
Hamiltonian