Exponential map (Lie theory) Updated 2025-07-16
Like everything else in Lie group theory, you should first look at the matrix version of this operation: the matrix exponential.
The exponential map links small transformations around the origin (infinitely small) back to larger finite transformations, and small transformations around the origin are something we can deal with a Lie algebra, so this map links the two worlds.
The idea is that we can decompose a finite transformation into infinitely arbitrarily small around the origin, and proceed just like the product definition of the exponential function.
The definition of the exponential map is simply the same as that of the regular exponential function as given at Taylor expansion definition of the exponential function, except that the argument can now be an operator instead of just a number.
Fabrice Bellard Updated 2025-07-16
Creator of QEMU and FFmpeg, both of which Ciro Santilli deeply respects. And a bunch other random stuff.
What is shocking about Fabrice this is that both are insanely important software that Ciro Santilli really likes, and both seem to be completely unrelated subjects!
Google made billions on top of this dude:
- FFmpeg is the backend of YouTube
- QEMU is the default emulator for Android Studio as of 2019, which Android developers use by default under the hood to develop Android Apps on their desktop without the need for a real device.
At last but not least, Fabrice also studied in the same school that Ciro Santilli studied in France, École Polytechnique.
It is a shame that he keeps such a low profile, there are no videos of him on the web, and he declines interviews.
Another surprising fact is that Fabrice has not worked for the "Big Tech Companies" as far as can be publicly seen, but rather mostly on smaller companies that he co-founded: www.quora.com/Computer-Programmers/Computer-Programmers-Where-is-Fabrice-Bellard-employed
And he's also into some completely random projcts unsurprisingly:
- www.computerhistory.org/tdih/january/6/ Computer Scientist Fabrice Bellard Announces Computing Pi to Record Number of Digits
Bibliography:
- smartbear.com/de/blog/2011/fabrice-bellard-portrait-of-a-super-productive-pro/ contains a list of his projects as of 2011
Factorio Updated 2025-07-16
Falun Gong Updated 2025-07-16
Expectation value Updated 2025-07-16
Fashion MNIST Updated 2025-07-16
feathers-chat-react Updated 2025-07-16
Last updated 2018 as of 2021, but still just worked.
Gotta run github.com/feathersjs/feathers-chat first: github.com/feathersjs-ecosystem/feathers-chat-react/issues/5, then it worked:and on the other terminal:then visit localhost:3000/ and you can create an account and login, tested on Ubuntu 20.10. Data is stored on persistently.
git clone https://github.com/feathersjs/feathers-chat
cd feathers-chat
git checkout fd729a47c57f9e6170cc1fa23cee0c84a004feb5
npm install
npm startgit clone https://github.com/feathersjs-ecosystem/feathers-chat-react
cd feathers-chat-react
git checkout 36d56cbe80bbd5596f6a108b1de9db343b33dac3
npm install
npm startIf you disable JavaScript on Chromium, it stops working completely. There is a section on how to solve that at: docs.feathersjs.com/cookbook/express/view-engine.html but it does not cover React specifically. Codaisseur/feathersjs-react-redux-ssr might be good to look into.
FEniCS Project Updated 2025-07-16
One big advantage over FreeFem is that it uses plain old Python to describe the problems instead of a domain-specific language. Matplotlib is used for plotting by default, so we get full Python power out of the box!
One downside is that its documentation is a Springer published PDF link.springer.com/content/pdf/10.1007%2F978-3-319-52462-7.pdf which is several years out-of-date (tested with FEnics 2016.2. Newbs. This causes problems e.g.: stackoverflow.com/questions/53730427/fenics-did-not-show-figure-nameerror-name-interactive-is-not-defined/57390687#57390687
system of partial differential equations are mentioned at: link.springer.com/content/pdf/10.1007%2F978-3-319-52462-7.pdf 3.5 "A system of advection–diffusion–reaction equations". You don't need to manually iterate between the equations.
On Ubuntu 20.04 as per fenicsproject.org/download/Before 2020-06, it was failing with:but they seem to have created the Ubuntu 20.04 package as of 2020-06, so it now worked! askubuntu.com/questions/866901/what-can-i-do-if-a-repository-ppa-does-not-have-a-release-file
sudo apt-get install software-properties-common
sudo add-apt-repository ppa:fenics-packages/fenics
sudo apt-get update
sudo apt-get install --no-install-recommends fenics
sudo apt install fenics
python3 -m pip install -u matplotlibE: The repository 'http://ppa.launchpad.net/fenics-packages/fenics/ubuntu focal Release' does not have a Release file. Brewster's angle Updated 2025-07-16
Cis-trans isomerism Updated 2025-07-16
Exist because double bonds don't rotate freely. Have different properties of course, unlike enantiomer.
Condensed matter physics course of the University of Oxford Updated 2025-07-16
Enantiomer Updated 2025-07-16
Key exmaple: d and L amino acids. Enantiomers have identical physico-chemical properties. But their biological roles can be very different, because an enzyme might only be able to act on one of them.
Hund's first rule Updated 2025-07-16
Polymorphism (materials science) Updated 2025-07-16
Example:
- the three most table polymorphs of calcium carbonate polymorphs are:
Symmetry in Condensed Matter Physics course of the University of Oxford Updated 2025-07-16
www2.physics.ox.ac.uk/students/course-materials/symmetry-in-condensed-matter-physics# Archive: web.archive.org/web/20230804204137/https://www2.physics.ox.ac.uk/students/course-materials/symmetry-in-condensed-matter-physics Lecture notes from 2019.
Professor: Radu Coldea
Atmospheric science Updated 2025-07-16
Binary search tree Updated 2025-07-16
Geologic time scale Updated 2025-07-16
Hash table Updated 2025-07-16
Learning rate Updated 2025-07-16
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