Is the solution to a system of linear ordinary differential equations, the exponential function is just a 1-dimensional subcase.
Note that more generally, the matrix exponential can be defined on any ring.
The matrix exponential is of particular interest in the study of Lie groups, because in the case of the Lie algebra of a matrix Lie group, it provides the correct exponential map.
Yet another awk-like domain-specific language to do things from the CLI in a ridiculously short humber of character? Oh yes.
There's a billion simple looking expressions which are not known to be transcendental numbers or not. It's cute simple to state but hard to prove at its best.
Open as of 2020:
Bibliography:
- www.quantamagazine.org/recounting-the-history-of-maths-transcendental-numbers-20230627/ How Math Achieved Transcendence by David S. Richeson (2023).
SGML predecessor.
This one strikes the right balance between restriction and permissions. NC and ND are simply too restrictive.
TODO where does the SA boundary end? E.g.:
- software: opensource.stackexchange.com/questions/173/what-do-i-need-to-share-if-i-include-cc-by-sa-artwork-in-my-software/11323#11323
- video game:
- website: graphicdesign.stackexchange.com/questions/68805/using-cc-by-sa-3-0-images-in-website-does-share-alike-affect-my-websites-lice/145124#145124
- book: academia.stackexchange.com/questions/48375/using-images-with-cc-by-sa-license-in-slides-or-a-thesis
- music in a podcast: opensource.stackexchange.com/questions/7022/using-cc-by-sa-music-in-a-podcast
White papers are a form of advertisement. They are not peer reviewed papers and are generally not reproducible; their value lies entirely in trust of their publisher rather than being able to verify their claims.
If a product of a big company has a catchy name it came from an acquisition by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Bibliography:Monday, January 29, 2024
- bitcoin.stackexchange.com/questions/5883/is-there-a-listing-of-strange-or-unusual-scripts-found-in-transactions/105392#105392
- bitcoin.stackexchange.com/questions/547/useful-alternative-bitcoin-transaction-scripts
- bitcoin.stackexchange.com/questions/35956/non-standard-tx-with-obscure-op-codes-examples/36037#36037 notably provides the amazing www.quantabytes.com/articles/a-survey-of-bitcoin-transaction-types
As usual, it is useful to think about how a bilinear form looks like in terms of vectors and matrices.
Unlike a linear form, which was a vector, because it has two inputs, the bilinear form is represented by a matrix which encodes the value for each possible pair of basis vectors.
Bitcoin script that terminates with multiple values on the stack by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16 3ad6677303fb6f700a4f2f977fe86e5324e0ddb0d3b33a649e513d7e88904e85 by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16This contains various outputs that seem trivially spendable in a made up of two non-zero constants, e.g.:Or are we missing something? The values are quite small and wouldn't be worth it the miner fees most likely. But is there a fundamental reason why this couldn't be spent by a non-standard miner?
{
"value": 0.00002000,
"n": 9,
"scriptPubKey": {
"asm": "1 8fe61f026c7545a99c6e0f37a5a7eceee5fdf6723c1994ccbfb740556632e9fe",
"desc": "rawtr(8fe61f026c7545a99c6e0f37a5a7eceee5fdf6723c1994ccbfb740556632e9fe)#lxgt8lak",
"hex": "51208fe61f026c7545a99c6e0f37a5a7eceee5fdf6723c1994ccbfb740556632e9fe",
"address": "bc1p3lnp7qnvw4z6n8rwpum6tflvamjlmanj8svefn9lkaq92e3ja8lqcc8mcx",
"type": "witness_v1_taproot"
}
}, Pinned article: 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 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. 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.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- 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