Ciro Santilli @cirosantilli 40

The inaugural that predicted the Josephson effect.

Published on Physics Letters, then a new journal, before they split into Physics Letters A and Physics Letters B. True Genius: The Life and Science of John Bardeen mentions that this choice was made rather than the more prestigious Physical Review Letters because they were not yet so confident about the results.

Paywalled by Elsevier as of 2023 at: www.sciencedirect.com/science/article/abs/pii/0031916362913690

The usual definition of a polynomial is over a field as shown at polynomial over a field.

However, there is nothing in the immediate definition that prevents us from having a ring instead, i.e. a field but without the commutative property and inverse elements.

The only thing is that then we would need to differentiate between different orderings of the terms of multivariate polynomial, e.g. the following would all be potentially different terms:while for a field they would all go into a single term:so when considering a polynomial over a ring we end up with a lot more more possible terms.

If the ring is a commutative ring however, polynomials do look like proper polynomials: Section "Polynomial over a commutative ring".

Amazing talk by Richard Feynman that describes his experiences at Los Alamos National Laboratory while developing the first nuclear weapons.

Transcript: calteches.library.caltech.edu/34/3/FeynmanLosAlamos.htm Also included full text into Surely You're Joking, Mr. Feynman.

There are 3: real numbers, complex numbers and quaternions.

Notably, the octonions are not associative.

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

Sometime it fails: www.reddit.com/r/molecularbiology/comments/1kouomw/when_your_pcr_fails_again_and_you_start/and a comment:

A more photon-specific version of the Bloch sphere.

In it, each of the six sides has a clear and simple to understand photon polarization state, either of:

The sphere clearly suggests for example that a rotational or diagonal polarizations are the combination of left/right with the correct phase. This is clearly explained at: Video "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)".

This is the standard model.