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bunje

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I did software engineering for 3 years after graduation. Now I teach mathematics in a high school since '20. Software engineering was very stressful for me and I also wanted to sync holidays with my kids. Parents seem to value my background. Pay is low but I have a reasonable amount of extra time to tinker.

Solutions to differential equations belong to infinite dimensional function spaces unless discretized.

I would guess that it is much more dangerous to modify a modern car because they utilize nontrivial shell geometry to improve the rigidity or to reduce weight. When I was attending driving lessons, my teacher claimed that the specific shape of the windscreen or rear window was a very important safety feature in the scenario that the car rolls over.

I think variational problems are more naturally understood through energy minimization. You start with the energy of the system and try to minimize it via derivatives. Then you arrive at a variational problem. The differential equation is then more of an afterthought.

Finite differences are simple in cubes and domains that can be mapped to one. Not so much in an arbitrary tetrahedral mesh.

I've analyzed performance data from air lubrication vessels with some retrofits included. Frankly, never witnessed over 5% gain. At specific velocity range the gain could be 5% on average if the installation has been really successful. They might be better nowadays.

Currently my greatest concern is the inability of Julia to provide stability even after they've reached 1.0. On paper 1.0 is a LTS release and still supported, but how many packages actually support it anymore? There seems to be no guidelines either, the official stance is that "we move on and drop LTS when the package developers move on."

You can accept a gift. It's also possible for someone to give a grant. But I'm not sure how they would work out in case of open source. I know that people write books using a grant.

Again, I'm not questioning that. Mathematically, does "tell people to use masks" imply "less new cases"? E.g., what if people decide to spend 5x more time with other people on average due to a mask requirement making them feel safe? That could easily cause more cases.

I once did an experiment with a rock containing uranium and a Geiger counter. The noise stopped immediately after putting printing paper between them and resumed after taking it off.

I have not so far heard any compelling arguments for using other than tetrahedral or hexahedral meshes in finite element computations. I know that there is a lot of research going on but the motivation is not clear to me.

Error estimates are dependent on the polynomial degree and the average cell size, and not the "amount of corners per cell" or anything like that.