This is an extremely widely used technique as of 2020 and much earlier.
If allows you to amplify "any" sequence of choice (TODO length limitations) between a start and end sequences of interest which you synthesize.
If the sequence of interest is present, it gets amplified exponentially, and you end up with a bunch of DNA at the end.
You can then measure the DNA concentration based on simple light refraction methods to see if there is a lot of DNA or not in the post-processed sample.
Even Ciro Santilli had some contact with it at: Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it", see: PCR!
One common problem that happens with PCR if you don't design your primers right is: en.wikipedia.org/wiki/Primer_dimer
In this solution of the Schrödinger equation, by the uncertainty principle, position is completely unknown (the particle could be anywhere in space), and momentum (and therefore, energy) is perfectly known.
The plane wave function appears for example in the solution of the Schrödinger equation for a free one dimensional particle. This makes sense, because when solving with the time-independent Schrödinger equation, we do separation of variable on fixed energy levels explicitly, and the plane wave solutions are exactly fixed energy level ones.
Formal name: "plantae".
Polytechnic School of the University of São Paulo by 
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01On one hand, yes, we need knowledge at all levels, and it is fine to start top-to-bottom with an overview.
The problem is, however, that there is a huge knowledge gap between the one liner "this is the truth" and the much more important "this is how we know it, these are the experiments" as mentioned at how to teach and learn physics.
Therefore, if you have that extremely rare knowledge, you should be writing that in addition to the dumbed down version with an open knowledge license. It takes time, but that's what really changes the world.
Ciro Santilli has always felt that there is a huge gap between "the very basic" and "the very advanced", as mentioned at: Section "The missing link between basic and advanced", which existing scientific vulgarization is not doing enough to address. In a sense, filling out this "middle path" is the main goal of OurBigBook.com.
Ciro really enjoyed the description of the "Arindam Kumar Chatterjee" youTube channel:
Theoretical/mathematical physics at the graduate level and above. This is NOT a popular science channel. Here you find real theoretical physicists doing real theoretical physics. We think it is important for people to get a taste of the real deal, and for aspiring theoretical physicists to see what they are working towards, i.e., to provide the public with something beyond the ubiquitous Michio Kaku and Brian Cox.
One thing must be said however: there seems to be an actual bias against researchers tho try to create vulgarization material: How To Get Tenure at a Major Research University by Sean Carroll (2011), and that is terrible.
There is often more value in a tutorial by a beginner who is trying to fully learn and explain a subject, than by an expert who is trying to "dumb it down" too much.
2003 Nobel Prize in Physiology and Medicine by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01 Positrons are electrons travelling back in time by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01The highly underdocumented built-in module, that supports SQL spatial index and a lot more.
Quite horrendous as it only seems to work on geometric types and not existing columns. But why.
And it uses custom operatores, where standard operators would have been just fine for points...
Minimal runnable example with points:The index creation unfortunately took 100s, so it will not scale to 1B points very well whic his a shame.
set -x
time psql -c 'drop table if exists t'
time psql -c 'create table t(p point)'
time psql -c "insert into t select (point ('(' || generate_series || ',' || generate_series || ')')) from generate_series(1, 10000000)"
time psql -c 'create index on t using gist(p)'
time psql -c "select count(*) from t where p <@ box '(1000000,1000000),(9000000,2000000)'"Has the property of visiting all descendants before the parent.
This was so hot (no pun intended) and reproducible that the prize was awarded one year after discovery. Quite rare in those days already.
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