Solving quadratic equations using continued fractions is a method linked to the approximation of the solutions of these equations through the use of continued fractions. Quadratic equations typically take the form: \[ ax^2 + bx + c = 0 \] where \(a\), \(b\), and \(c\) are coefficients, and \(x\) is the variable we want to solve for.
Stronger version of the big O notation, basically means that ratio goes to zero. In big O notation, the ratio does not need to go to zero.
Example: llvm/hello.ll adapted from: llvm.org/docs/LangRef.html#module-structure but without double newline.
To execute it as mentioned at github.com/dfellis/llvm-hello-world we can either use their crazy assembly interpreter, tested on Ubuntu 22.10:This seems to use
sudo apt install llvm-runtime
lli hello.llputs from the C standard library.Or we can Lower it to assembly of the local machine:which produces:and then we can assemble link and run with gcc:or with clang:
sudo apt install llvm
llc hello.llhello.sgcc -o hello.out hello.s -no-pie
./hello.outclang -o hello.out hello.s -no-pie
./hello.outhello.s uses the GNU GAS format, which clang is highly compatible with, so both should work in general.Very easy to use and pretty powerful MIDI creator!!!
One of the rare audio applications actually works with PulseAudio on Ubuntu 20.04 out-of-the-box, so you don't have to turn off every other audio application!!!
Has lot's of plugins built-in just working out of the box, e.g. ZynAddSubFX out-of-the-box without doing a gazillion complex setup connections.
Most plugins are just simple toys however, ZynAddSubFX is the only super powerful one. The others are more LMMS integrate however, and seem to use a more dedicated LMMS GUI style.
Local symmetries of the Lagrangian imply conserved currents by 
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01More precisely, each generator of the corresponding Lie algebra leads to one separate conserved current, such that a single symmetry can lead to multiple conserved currents.
This is basically the local symmetry version of Noether's theorem.
Then to maintain charge conservation, we have to maintain local symmetry, which in turn means we have to add a gauge field as shown at Video "Deriving the qED Lagrangian by Dietterich Labs (2018)".
Bibliography:
- photonics101.com/relativistic-electrodynamics/gauge-invariance-action-charge-conservation#show-solution has a good explanation of the Gauge transformation. TODO how does that relate to symmetry?
- physics.stackexchange.com/questions/57901/noether-theorem-gauge-symmetry-and-conservation-of-charge
Step of electronic design automation that maps the register transfer level input (e.g. Verilog) to a standard cell library.
Yung Professional Move to London by Sans Beanstalk
. Source. The sad thing is that the same author also has another accurate video criticizing British suburbia, so there's no escape basically in the UK: www.youtube.com/watch?v=oIJuZbXLZeY.
Video "Being a Dickhead's Cool by Reuben Dangoor (2010)" also comes to mind.
Cute simple paper-cut stop motion animations videos by Mithuna Yoganathan, a PhD in theoretical physics at the University of Cambridge: www.damtp.cam.ac.uk/person/my332.
Loop-mediated isothermal amplification by Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01Like PCR, but does not require thermal cycling. Thus the "isothermal" in the name: iso means same, so "same temperature".
Not needing the thermo cycling means that the equipment needed is much smaller and cheaper it seems.
Lorentz transform consequence: everyone sees the same speed of light by Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01OK, so let's verify the main desired consequence of the Lorentz transformation: that everyone observes the same speed of light.
Observers will measure the speed of light by calculating how long it takes the light going towards cross a rod of length laid in the x axis at position .
Each observer will observe two events:
Supposing that the standing observer measures the speed of light as and that light hits the left side of the rod at time , then he observes the coordinates:
Now, if we transform for the moving observer:and so the moving observer measures the speed of light as:
Historian Alan B. Carr:
- www.youtube.com/@AlanBCarr. IMPORTANT NOTE: Although Alan B. Carr is a Los Alamos National Laboratory (LANL) employee, this page has absolutely no formal connection with LANL.
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact