Eddy diffusion is a process that describes the transport and mixing of particles, heat, or other substances in a medium, such as air or water, due to turbulent eddies or vortices. This phenomenon is particularly important in the fields of fluid dynamics, meteorology, oceanography, and environmental science. In turbulent flows, eddies of varying sizes are created as a result of chaotic fluid motion.
The Emerson Cavitation Tunnel is a specialized facility used for testing and studying cavitation phenomena in fluid dynamics, particularly in relation to marine and hydraulic applications. Cavitation occurs when a liquid is subjected to rapid changes in pressure, leading to the formation of vapor bubbles. These bubbles can collapse violently, causing damage to surfaces and affecting the performance of propellers, pumps, and other fluid machinery. Emerson's facility typically includes a long, submerged tunnel where water is circulated at controlled velocities.
If there is one thing that makes Ciro Santilli learn German, this is it (the Romance language are all the same, so reading them is basically covered for Ciro already).
The proper precise definition of mathematics can be found at: Section "Formalization of mathematics".
The most beautiful things in mathematics are described at: Section "The beauty of mathematics".
If Ciro Santilli ever becomes rich, he's going to solve this with: website front-end for a mathematical formal proof system, promise.
Source code:
- github.com/leanprover/lean4 why a separate repo per version... but it is what it is.
- github.com/leanprover/lean
The way Lean and Coq mix programming and mathematics is a thing of great beauty. This is especially notable in lean as you start to play with with things such as:
partialenv lean functions, and usingterminates_byto prove that certain functions terminate. Lean requires explicitly known if functions terminate or not to be able to use them in proofs.noncomputablefunctions. Lean allows you to define mathematical functions which you can't actually execute, and it tracks that explicitly
They are huge fans of Unicode characters! Check this out from a formal proof of the prime number theorem: github.com/AlexKontorovich/PrimeNumberTheoremAnd/blob/fbdbb5310d036d33b9797b35f3b04b08f2447a6e/PrimeNumberTheoremAnd/ZetaBounds.lean Here's map to Ascii: proofassistants.stackexchange.com/questions/954/does-lean-have-a-standard-ascii-representation/5289#5289
Their dependency graph thingy is just beautiful however: alexkontorovich.github.io/PrimeNumberTheoremAnd/web/dep_graph_document.html
A proof in some system for the formalization of mathematics.
The only cases where formal proof of theorems seem to have had actual mathematical value is for theorems that require checking a very large number of case, so much so that no human can be fully certain that no mistakes were made. Some examples:
A conjecture is an open problem in mathematics for which some famous dude gave heuristic arguments which indicate if the theorem is true or false.
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