HI,
This statement is quite confusing:
"1/TUF SIGNIFIES THAT INPUT TRANSFORMER IF PRESENT MUST BE 1/TUF TIMES LARGER THAN THAT WHEN IT IS USED TO DELIVER POWER FROM A PURE AC SINUSOIDAL VOLTAGE."
Basically, as I understand it, the goal is to avoid saturation of the core by taking into account the details of how the transformer is utilized (such as center-tapped full-wave versus half-wave) or with loads/sources that deviate strongly from sinusoidal, such as switched mode supplies, since these have larger peak currents (and hence fields) relative to the powers involved.
I doubt the OP will return, but presumably the question relates to comparison of equivalent power delivery to the same (resistive) load under two conditions - for example: directly through the transformer as a simple AC secondary load or "indirectly" [say] for the case of a half-wave rectifier utilizing a single rectifier diode.
The Transformer Utilization Factor in the latter simple half-wave rectifier case would be notionally 0.286, meaning one would be over-sizing the transformer by a factor of approximately 3.5 when comparing with the case of a purely AC secondary connection to deliver the same effective load power.