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The Fall of The Simpsons: How it Happened by Super Eyepatch Wolf (2017)
Source. This interesting video essay makes the main point that the Simpsons used to be good because they mocked mainstream. But then they became mainstream, which basically defeated their purpose. Think different from Apple comes to mind.Surprisingly, it can also become a superfluid even though each atom is a fermion! This is because of Cooper pair formation, just like in superconductors, but the transition happens at lower temperatures than superfluid helium-4, which is a boson.
aps.org/publications/apsnews/202110/history.cfm: October 1972: Publication of Discovery of Superfluid Helium-3 contains comments on the seminal paper and a graph which we must steal.
Also sometimes called helium II, in contrast to helium I, which is the non-superfluid liquid helium phase.
This is true. The level of competition in university entry exams in Asia in insane in the early 21st century compared to the West.
This is actually both good and bad. Good because it selects some very good exam passers. And bad because it selects some very good exam passers.
Lie Groups, Physics, and Geometry by Robert Gilmore (2008) 7.2 "The covering problem" gives some amazing intuition on the subject as usual.
The most important example is perhaps and , both of which have the same Lie algebra, but are not isomorphic.
Show up when solving the Laplace's equation on spherical coordinates by separation of variables, which leads to the differential equation shown at: en.wikipedia.org/w/index.php?title=Legendre_polynomials&oldid=1018881414#Definition_via_differential_equation.
Generalization of Laplace's equation where the value is not necessarily 0.
A solution to Laplace's equation.
Basically: S.
The variables of the Lagrangian, e.g. the angles of a double pendulum. From that example it is clear that these variables don't need to be simple things like cartesian coordinates or polar coordinates (although these tend to be the overwhelming majority of simple case encountered): any way to describe the system is perfectly valid.
In quantum field theory, those variables are actually fields.
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 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