A quesion about class E PA

In Raab's classical paper 'idealized operation of the class E tuned power amplifier', a conclusion is that the normalized Pmax=0.0981 (Pmax @ClassA= 0.125). That means the PUF=Prf/Plin < 1

While in Steve Cripps's book <RF Power Amplifier for Wireless Communications>, the PUF of class E is -4sin(beta)/(1-sin(beta)), where beta is in fourth quadrant, so that the PUF can be larger than 1.

Is there anyone can explain the difference for me?

What is PUF? Also are you referring Pmax as the normalised power output capacity of the PA?