The Fourier series of an 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 , 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.
To send voice and music, amplitude modulation had to be developed. And a key ingredient of this is the carrier wave.
The problem is, the carrier wave needs to have somewhat high frequencies, in the hundreds of kHz TODO why. But as you might imagine, that is hard to achieve by mechanical means such as a hand cranck like Hippolyte Pixiis alternator!
Interestingly, some of the first carrier wave generators were actually mechanical, e.g. the Alexanderson alternator.
But clearly such mechanical machines were not very scalable, and soon more electronic devices were introduced, notably the vacuum tube.
Our minimal definition of "electronic money" is the following.
Instead of creating legal tender such as Dollars as banknotes or transactions in some complex obscure banking system, the government offers an official simple centralized API that represents it instead.
Each citizen or legal entity has an account there, and transfers between registered users are just simple API calls.
Homepage: eli.thegreenplace.net/
Also has many great contributions on Stack Overflow: stackoverflow.com/users/8206/eli-bendersky
As of 2016, Eli worked at Google (reference). TODO before that, I had found his earlier info previously but lost it.
Eli focuses mostly on compiler toolchains.
He also has some mathematics stuff, so cute: eli.thegreenplace.net/2015/change-of-basis-in-linear-algebra/
- css/code-block.html
- css/img-table-vertical-center.html
- css/viewport-height.html: a div that is a tall as the viewport, and does not generate a toplevel scrollbar
- css/responsive-image-max-height.html: here we try to create an image that is never wider than the screen. If the screen is less wide than the image, then the image scales down proportionally. Otherwise, the image has a user determined fixed by the CSS or the HTML
heightproperty. Related:TODO I'm unable to do this....... stackoverflow.com/questions/69964332/how-to-set-the-default-height-of-responsive-images-when-screen-is-wide-and-have The objective was to implement: github.com/ourbigbook/ourbigbook/issues/168 - css/top-navigation.html
This is the most common home "ethernet cable" as of 2024. It is essentially ubiquitous. According to the existing Ethernet physical layer, the maximum speed supported is 2.5 Gbit/s.
sudo apt build-dep cataclysm-dda-curses cataclysm-dda-data cataclysm-dda-data
git clone https://github.com/CleverRaven/Cataclysm-DDA
cd Cataclysm-DDA
git checkout cdda-experimental-2022-01-27-0622
mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=Release -DTILES=ON -DSOUND=ON -DLOCALIZE=OFF ..
make -j`nproc`:part_index_’ may be used uninitialized [-Werror=maybe-uninitialized]
55 | return part_index_;-Werror check, they don't test GCC new enough regularly.Apparently, DC current comes in, and microwaves come out.
Constructs the quaternions from complex numbers, octonions from quaternions, and keeps doubling like this indefinitely.
Mnemonic is as follows: consider we have an initial basis . Now, we define the new basis in terms of the old basis, e.g.:which can be written in matrix form as:and so if we set:we have:
The usual question then is: given a vector in the new basis, how do we represent it in the old basis?
That is the matrix inverse.
There are unlisted articles, also show them or only show them.