Ciro Santilli @cirosantilli 40

Capoeira music is amazing. And some Brazilian pop adaptations of it have also been awesome.

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.

Some interesting analysis by Parth Shukla twitter.com/pparth | www.linkedin.com/in/parth-shukla-59583b20/:Apparently most of the routers were Chinese. No surprise there.

Specifies the derivative in a direction normal to the boundary.

Can be used for elliptic partial differential equations and parabolic partial differential equations.

As of 2019, the more formal name for particle physics, which is notably missing general relativity to achieve the theory of everything.

cds.cern.ch/record/799984/files/0401010.pdf The Making of the Standard Model by Steven Weinberg mentions three crucial elements that made up the standard model post earlier less generalized quantum electrodynamics understandings

Complexity: NP-intermediate as of 2020:

The basis of RSA: RSA. But not proved NP-complete, which leads to:

archive.org/details/quantumstoryhist0000bagg on the Internet Archive Open Library.

The problem with a single-level paging scheme is that it would take up too much RAM: 4G / 4K = 1M entries per process.

If each entry is 4 bytes long, that would make 4M per process, which is too much even for a desktop computer: ps -A | wc -l says that I am running 244 processes right now, so that would take around 1GB of my RAM!

For this reason, x86 developers decided to use a multi-level scheme that reduces RAM usage.

The downside of this system is that is has a slightly higher access time, as we need to access RAM more times for each translation.