The Observer-Conditioned-Observable (OCO) combines digitizing and transcoding of numeric change events. During the processing of numeric events, the transcoder converts the number from one range into another while preserving the mathematical integrity of the value. Numeric controllers that generate such events can be based in floating point numbers or integer numbers. For example, the JSpinners...

Our purpose here is to announce results in harmonic analysis related to a large class of hypoelliptic operators on arbitrary simply-connected nilpotent Lie groups. We find the asymptotic development of their fundamental solutions, both locally and at infinity, and study corresponding Riesz transforms and analogues of the Hardy-Littlewood-Sobolev theorem for fractional integration. Details will ...