Zero Sum Games for Nonhomogeneous Markov Chains with an Expected Average Payo Criterion

A solar heating system including an energy absorbent collector dish for receiving solar heat, a supply tube for distributing a heat transfer fluid over the collector dish, a drain pipe for removing the heat transfer liquid from the collector dish and an optical director including an array of converging lenses oriented to receive radiant energy from the sun and to direct the energy onto the collector dish. The array of converging lenses comprises a matrix of double convex lenses that form one half of a hemispherical optical dome, the other half of which possesses an inner reflective surface for reflecting radiant energy onto the collector dish and the optical dome is oriented such that some portion of the lens array faces the sun during an entire day's movement.