Many LED lighting applications involve the design of multiple optical surfaces. A prime example is a single lens with two refractive In this paper, we consider an light source approximated as point and far-field target intensity. Using Hamilton’s characteristic functions, problem converted into generalized Monge–Ampère equations by deriving generating function for each surface. The generalizati...

The Appell-type polynomial family corresponding to the simplest non-commutative derivative operator turns out to be connected with the Boolean probability theory, the simplest of the three universal non-commutative probability theories (the other two being free and tensor/classical probability). The basic properties of the Boolean Appell polynomials are described. In particular, their generatin...