Numerical method to solve a partial differential equation by 
Ciro Santilli 35 Updated 2025-03-20 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-20 +Created 1970-01-01The finite element method is one of the most common ways to solve PDEs in practice.
The weird one, not directly coded in the genetic code.
A really good option to store educational media such as images and video!
Shame that like the rest of Wikimedia, their interface is so clunky and lacking obvious features.
System of linear equations algorithm by Ciro Santilli 35 Updated 2025-03-20 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-20 +Created 1970-01-01Same value if you swap any input arguments.
A common case is , and .
One thing that makes such functions particularly simple is that they can be fully specified by specifyin how they act on all possible combinations of input basis vectors: they are therefore specified by only a finite number of elements of .
Every linear map in finite dimension can be represented by a matrix, the points of the domain being represented as vectors.
As such, when we say "linear map", we can think of a generalization of matrix multiplication that makes sense in infinite dimensional spaces like Hilbert spaces, since calling such infinite dimensional maps "matrices" is stretching it a bit, since we would need to specify infinitely many rows and columns.
The prototypical building block of infinite dimensional linear map is the derivative. In that case, the vectors being operated upon are functions, which cannot therefore be specified by a finite number of parameters, e.g.
For example, the left side of the time-independent Schrödinger equation is a linear map. And the time-independent Schrödinger equation can be seen as a eigenvalue problem.
Cover up the entire sky in a compatible way with the traditional constellations. They are also very square, the boundaries consisting only of vertical and horizontal lines on the sphere.
One of the most beautiful molecular machines known!
The first one with such complexity that was uncovered.
The thing rotates like a water wheel for God's sake, except it uses protons instead of water.
The ATP synthase complex is so large that Power, Sex, Suicide by Nick Lane (2006) page 123 contains a cryoEM image of several ATP synthases on small membrane vesicles, this is the paper: pubs.acs.org/doi/abs/10.1021/bi00437a031# under a fucking paywall.
ATP synthase in action by HarvardX (2017)
Source. There are six, three in each sense, depending on where you start modulo-3.
It seems to implement Zermelo-Fraenkel set theory.
The China front was of course the Russia front this time: stackoverflow.com/users/895245 (web.archive.org/web/20220322230513/https://stackoverflow.com/users/895245/ciro-santilli-Путлер-Капут-六四事)
A generalization of the Pythagorean triple infinity question.
Some interesting usages:
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!
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/derivative - 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 4. Visual Studio Code extension tree navigation.
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.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Internal cross file references done right:
- Infinitely deep tables of contents:
Figure 6. Dynamic article tree with infinitely deep table of contents.Live URL: ourbigbook.com/cirosantilli/chordateDescendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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