Ciro Santilli @cirosantilli 35

Haven't found the one yet:

Optional but really ideal:

The state of messaging is ridiculous as of 2020.

One is reminded of Nick Leeson.

Operated by a hand crank.

I think these are the ones where $\Delta H\times \Delta S>0$, i.e. enthalpy and entropy push the reaction in different directions. And so we can use temperature to move the Chemical equilibrium back and forward.

Logarithm of a discrete groups.

NP-intermediate as of 2020 for similar reasons as integer factorization.

An important case is the discrete logarithm of the cyclic group in which the group is a cyclic group.

1-dimensional heat equation example with Dirichlet boundary condition

The Fourier series of an $L^2$ function (i.e. the function generated from the infinite sum of weighted sines) converges to the function pointwise almost everywhere.

The theorem also seems to hold (maybe trivially given the transform result) for the Fourier series (TODO if trivially, why trivially).

Only proved in 1966, and known to be a hard result without any known simple proof.

This theorem of course implies that Fourier basis is complete for $L^2$, as it explicitly constructs a decomposition into the Fourier basis for every single function.

TODO vs Riesz-Fischer theorem. Is this just a stronger pointwise result, while Riesz-Fischer is about norms only?

One of the many fourier inversion theorems.