I'll try to relay this from a different perspective...

You have an inductor, a piece of iron, or a ceramic semiconductor torroid, a pencil, whatever...

with no inducing field, all the atoms are randomly pointing in any direction, their magnetic moments are everywhere, canceling each other out
there is no detectable magnetic field outside the material.

when we bring a magnetic field close to the material, the field domains line up opposing that field.
mostly in the same direction.
Now, this takes time,... to turn them, so from a "neutral" point, it takes time X to orient the atoms against the inducing field.
(this is approx. 1/4 the self-resonant freq, but follow)

We now alternate the inducing field to the opposite direction, causing the atoms in the inductor to flip the other way.
  This takes time.
How much time? well, if you don't take a break between flipping one way to the other (because to do so would add +1/4 f)
It takes exactly 1/2 of the self-resonant freq.

So,. if you change the inducing magnetic field, at a frequency exactly twice that if the time it takes for the poles to flip from one direction to the other...
   you effectively flip poles at the maximum frequency the inductor can flip at.
Now, if we flip at a speed slower than that, the magnetic field domains revert to the "neutral state", and have to be brought back to the oriented state.
This causes a loss in energy, due to reluctance.
If you flip the field at a speed faster than that, you do not get full induction within the core, reluctive losses are much greater.

Now, some of you that have been paying attention have noticed by now that there is a difference in the self-resonant freq. and the max freq. posted on the data sheet.
 (good job if that's you!!)

There are some tiny differences in the inductor material, try as we may to perfect it, That causes the "perfect balance" in magnetic flux that we desire,
to vary slightly from the fastest possible that we can flip the field.

In a non-superconductor material, this frequency is less than the maximum.
In a true superconductor, the self-resonant frequency of an inductor is the same as its' maximum frequency.

::::For the language barrier --  those who don't understand what I mean when I talk about the frequency of the inductor
It is a factor of the response time of the inductor, meaning how many times the field domains flip from one pole to the other and back again, per second (Hz).
This corresponds exactly to both the input frequency and the output of any secondary coil(s).
This is affected by the diameter of the wire, length of the wire, number of coils, diameter(s) of coiling, and to some degree, distance from the inductor.

What it means for a system to be "resonant", is that the frequencies are coherent with one another.
They do not disrupt each others patterns.

This can be frequencies that are the same.
Frequencies that are divisible, or multiples of one another.
or frequencies that meet as certain corresponding "nodes",
      for instance 1/4th or 1/2 nodes, or nodes that may only meet once every 133 cycles.....
But what happens at these nodes is that the amplitudes of the signals are increased, not just for one, but both or all of the combining signals.
This is not just an additive quantity, but can be exponential at reoccurring intervals.

you notice the difference when you are operating in a resonant mode, because the coil and the inductor will "ring" at these resonant frequencies.
increase in amplitude. voltage /or current spikes depending on the situation. In electronics we generally treat this as a problem.
it blows out capacitors, burns resistors and diodes, fries traces on our circuit boards..
There are MANY MANY solutions to these problems. Look at the base of a radio broadcast antanae, theres a million dollar "solution" right there at the bottom.

If a resonant frequency is in the audible spectrum, you may actually hear an increase in the sound coming out of the inductor.
if you scope it, you see an increase in amplitudes

Here's your first piece of "garbage" for the day.

Take an inductor of your choice, and look at the manufacturers data sheet, find the self-resonant frequency
and engineer two coils around it to a coherent frequency of that.

Then send the self-resonant frequency though one of the coils, using a signal generator
 and take a scope image of the other.
Now compare this image to that of other frequencies NOT in the self-resonant mode.

Now you have a visual representation of the inductive losses that are present in ALL operating modes outside the resonance of the circuit.

Well thanks for the extra effort you put into the explanation. It makes sense this time around. Now what resonant frequency are you referring to?  The resonant frequency of the coils inductance and its windings capacitance or something else?

This is not just an additive quantity, but can be exponential at reoccurring intervals.

Yes, you are absolutely correct! Tesla proved this when he attached a small handheld oscillating device to a structural iron beam in his research facility in New York. The beam started to resonate and then the whole building started shaking. People in the area started freaking out... Tesla had to grab a hammer and smash the device!

Another point worth mentioning is that the inductor used could be a permanent magnet, which should be able to be harnessed across a range of different frequencies.... I recall that Steven Mark, in his later comments, spoke of very high outputs when ultilizing rare earth magnets....

Come on guys.... this cannot be that difficult... Mark's was working with 60 hertz! I do not have the technical background or the equipment to put this together... but I do grasp the concept. I think you engineers are all looking for something that is complicated in order to figure it out, when it is all really quite simple! I think Smoky is right on target!

Inductance... reluctance... reactance... capacitance... resonance...  how difficult can it be? Perhaps Floyd Sweet's setup did not at all require conditioned magnets... just proper tuning. He did after all, first notice the phenomena in a transformer that kept running after it was turned off! (Never forget that, a run of the mill transformer in self oscillation when the primary has been turned off!) Once again... 60 HZ! So we know the frequency! A primary, a secondary and an inductor!

A torroidal core or a H style core should not have much to do with it all. Sweet just used a magnet. While Sweet wound his coils across each other at a 90 degree angle on the barium magnet... the transformer he witnessed the phenomena in was no doubt just a conventional set up. Mark's favored toroidal cores, while more efficient may not at all necessary. It is doubtful he used a toroid when when working with the rare earths, but could have.

Like the saying goes.... just 'get er done' Forget about trying to figure out why it works, concentrate on how to get it working.

And for heavens sake if you do get it working....share it! Do not be a hero and try to patent it... the world is about to go over the cliff anyway and you would be wasting your time and maybe even get yourself killed. If you want to make some money... build them and sell them to people, the market would be insatiable.