Paul Colby's latest activity

It depends what you mean by "expressed". Do you mean for every z2 near the given one, there is a unique z1 near the given one such that...

Strange? All my Hilbert spaces look like a corridor lined with doorways leading to death.

This video experiments with local AI running on a modest PC with no internet connection. Although is it hardware limited, the results...

The PDP-8 I used to collect photon counting data had a bunch to display registers.

Or the advanced civilization they stumble upon can't imagine taking the risks or making the personal sacrifices needed to make such a...

I would think so, right? Shine a frosted and unfrosted LED on a white sheet of paper. You’ll note the paper isn’t uniformly illuminated...

Isn’t detecting a saddle point straightforward?

It says more than that. It says that the criterion for stability is being a minimum of the energy functional.

Doesn't this answer the question you posed in the OP of this thread?

Yes, there are several well-established examples in nonlinear field theory where stationary solutions exist mathematically but are...

Are there known examples of unstable solutions that yield stationary numerical configurations?

Lithium-ion batteries represent one of the greatest advances in energy storage. However, the transportation system is demanding more...

Never let best be the enemy of good enough. You have closed-form expressions for both methods. You could do an error analysis using the...

To a good approximation when light interacts with transparent plastic it’s either scattered or absorbed. Frosting is a roughening of the...

I was able to solve the problem, but my solution feels lengthy so i was curious if there was a mathematicallly simplier way to approach...