Existence and uniqueness of solutions of ordinary differential equations by
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Every Riemann integrable function is Lebesgue integrable by
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Every Lie algebra has a unique single corresponding simply connected Lie group by
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
This simply connected is called the universal covering group.
For the most part, a great pseudo-country to live in with lots of cultural diversity, art and safety.
However, Europe is in economic decline after all its Jewish and German geniuses fled in/after World War II and due to having more than one natural language is bad for the world.
Ciro Santilli moved to Europe in 2010.
Described at: arxiv.org/pdf/2107.12475.pdf where a relation to the Busy beaver scale is proven, and the intuitive relation to the Collatz conjecture described. Perhaps more directly: demonstrations.wolfram.com/CollatzSequenceComputedByATuringMachine/
Enrico Fermi: physicist by Emilio Segrè (1970) by
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Biography of Enrico Fermi by fellow physicist, free rent on the on the Internet Archive: archive.org/details/enricofermiphysi0000segr
Died of cancer at age 53. Ciro Santilli just can't help but speculate that it is linked to radioactivity exposure.
One of the things Ciro Santilli really likes, see: Linux Kernel Module Cheat.
Polynomial time for most inputs, but not for some very rare ones. TODO can they be determined?
But it is better in practice than the AKS primality test, which is always polynomial time.
It is called "AC effect" because when we apply a DC voltage, it produces an alternating current on the device.
By looking at the Josephson equations, we see that a positive constant, then just increases linearly without bound.
Wikipedia mentions that this frequency is , so it is very very high, so we are not able to view individual points of the sine curve separately with our instruments.
Also it is likely not going to be very useful for many practical applications in this mode.
An I-V curve can also be seen at: Figure "Electron microscope image of a Josephson junction its I-V curve".
I-V curve of the AC Josephson effect
. Source. Voltage is horizontal, current vertical. The vertical bar in the middle is the effect of interest: the current is going up and down very quickly between , the Josephson current of the device. Because it is too quick for the oscilloscope, we just see a solid vertical bar.
Superconducting Transition of Josephson junction by Christina Wicker (2016)
Source. Amazing video that presumably shows the screen of a digital oscilloscope doing a voltage sweep as temperature is reduced and superconductivity is reached.The elliptic curve group of an elliptic curve is a group in which the elements of the group are points on an elliptic curve.
The group operation is called elliptic curve point addition.
Created by Luke Dashjr.
Then come the most important symbols:
Num: Value Size Type Bind Vis Ndx Name
4: 0000000000000000 0 NOTYPE LOCAL DEFAULT 1 hello_world
5: 000000000000000d 0 NOTYPE LOCAL DEFAULT ABS hello_world_len
6: 0000000000000000 0 NOTYPE GLOBAL DEFAULT 2 _start
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