The invention relates to a zoom optical system that can offer an effective tradeoff between size reductions and cost reductions and electronic equipment incorporating it. In accordance with the present invention, an e-commerce systems architecture can include an instantiable owning business logic component derived from an abstract business definition and one or more instantiable business element components configured for aggregation under the control of a business facility instance. The node is located proximal to the output terminal of the transmission gate. The manipulation system outputs two-dimensional affine transforms that contain rotation, scale, and translation information.