A typical left-invariant optimal control problem on the rotation group SO (3) is investigated. The reduced Hamilton equations associated with an extremal curve are derived in a simple and elegant manner. These equations are then explicitly integrated by Jacobi elliptic functions.

We show that if an inclusion of finite groups H ≤ G of index prime to p induces a homeomorphism of mod p cohomology varieties, or equivalently an F–isomorphism in mod p cohomology, then H controls p–fusion in G, if p is odd. This generalizes classical results of Quillen who proved this when H is a Sylow p–subgroup, and furthermore implies a hitherto difficult result of Mislin about cohomology i...

To provide good transportation services for passengers in the modern buildings, a good elevator group control system (EGCS) is inevitably necessary. The viewpoint of designing the EGCS is very important. Passenger-based vieypoint proposed here provides a new way to think about this system. The capacity constraint following the thoughtfulness consideration for the passengers is utilized to make ...