A solid angle is a measure of how large an object appears to an observer from a particular point of view, and it indicates the two-dimensional angle in three-dimensional space. Solid angles are measured in steradians (sr), where one steradian corresponds to the solid angle subtended at the center of a sphere by an area on its surface equal to the square of the sphere's radius.
A homogeneous variety is a type of algebraic variety that exhibits a particular structure of symmetry. More precisely, it is a variety that can be expressed as the quotient of a given projective space by a group action of a linear algebraic group.
Non-anomalous: number of splits matches predictions of the Schrödinger equation about the number of possible states with a given angular momentum. TODO does it make numerical predictions?
www.pas.rochester.edu/~blackman/ast104/zeeman-split.html contains the hello world that everyone should know: 2p splits into 3 energy levels, so you see 3 spectral lines from 1s to 2p rather than just one.
It also mentions that polarization effects become visible from this: each line is polarized in a different way. TODO more details as in an experiment to observe this.
Well explained at: Video "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)".
Experimental physics - IV: 22 - Zeeman effect by Lehrportal Uni Gottingen (2020)
Source. This one is decent. Uses a cadmium lamp and an etalon on an optical table. They see a more or less clear 3-split in a circular interference pattern,
They filter out all but the transition of interest.
- youtu.be/ZmObNFAqkBE?t=165 passes the lines through a polarizer, which shows how orbital angular momentum is carried by photon polarization
- youtu.be/ZmObNFAqkBE?t=370 says they are looking at 1D2 to 1P1 changes.
In biology, "blot" typically refers to a molecular biology technique used to detect and analyze the presence of specific molecules, such as DNA, RNA, or proteins, in a sample. The term "blotting" is associated with several specific techniques: 1. **Southern Blot**: A method used to detect specific DNA sequences in DNA samples.
Eccentric nerdy slow speaking physicist mostly based in University of Cambridge.
Created the Dirac equation, what else do you need to know?!
QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) chapter 1.3 "P.A.M. Dirac and the Birth of Quantum Electrodynamics" quotes Dirac saying how being at high school during World War I was an advantage, since all slightly older boys were being sent to war, and so the younger kids were made advance as fast as they could through subjects. Exactly the type of thing Ciro Santilli wants to achieve with OurBigBook.com, but without the need for a world war hopefully.
Dirac was a staunch atheist having said during the Fifth Solvay Conference (1927)[ref]:
If we are honest - and scientists have to be - we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can't for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as why God allows so much misery and injustice, the exploitation of the poor by the rich and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards - in heaven if not on earth - all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins.
Paul Dirac and the religion of mathematical beauty by Royal Society (2013)
Source. From The Reuters websites and others we've found, we can establish see some clear stylistic trends across the websites which would allow us to find other likely candidates upon inspection:The most notable dissonance from the rest of the web is that there are no commercial looking website of companies, presumably because it was felt that it would be possible to verify the existence of such companies.
- natural sounding, sometimes long-ish, domain names generally with 2 or 3 full words. Most in English language, but a few in Spanish, and very few in other languages like French.
- shallow websites with a few tabs, many external links, sometimes many images, and few internal pages
- common themes include:
- .com and .net top-level domains, plus a few other very rare non .com .net TLDs, notably .info and .org
- each one has one "communication mechanism file": communication mechanisms
- narrow page width like in the days of old, lots of images
- split header images
- some common pattern they follow in their news lists:
ul.rss-items > li.rss-item
, e.g.: web.archive.org/web/20110202092126/http://beamingnews.com/- links with class
a.newslink
anda.newslinkalt
e.g. web.archive.org/web/20110128181622/http://profile-news.com/
Most domains are the only domain for its IP, i.e. the websites are mostly private hosted. However we have later found many exceptions to this general indicator, so it should not be used as a strong exclusion rule.
Count: 0.
The knowledge that light is polarized precedes the knowledge of the existence of the photon, see polarization of light for the classical point of view.
The polarization state and how it can be decomposed into different modes can be well visualized with the Poincaré sphere.
One key idea about photon polarization is that it carries angular momentum. Therefore, when an electron changes orbitals in the Schrödinger equation solution for the hydrogen atom, the angular momentum (as well as energy) change is carried out by the polarization of the photon!
- clear animations showing how two circular polarizations can make a vertical polarization
- a polarizer can be modelled bra operator.
- light polarization experiments are extremely direct evidence of quantum superposition. Individual photons must be on both L and R states at the same time because a V filter passes half of either L or R single photons, but it passes all L + R photons
Filter graphs are a thing of great beauty. What an amazingly obscure domain-specific language, but which can produce striking results with very little!!!
A quick example from stackoverflow.com/questions/59551013/how-to-generate-stereo-sine-wave-using-ffmpeg-with-different-frequencies-for-eac/77730492#77730492 illustrates some of the fundamentals:
ffplay -autoexit -nodisp -f lavfi -i '
sine=frequency=500[a];
sine=frequency=1000[b];
[a][b]amerge, atrim=end=2
'
+--------+
[sine=frequency=500]--->[a]-->| |
| amerge |-->[atrim]-->[output]
[sine=frequency=1000]-->[b]-->| |
+--------+
So we see the following syntax patterns:
sine
,amerge
andatrim
are filterssine=frequency=500
: the first=
says "araguments follow";
: separates statements[a]
,[b]
: sets the name of an edge,
: creates unnamed edge between filters that have one input and one output
A list of all filters can be obtained ith:and parameters for a single filter can be obtained with:Related question: stackoverflow.com/questions/69251087/in-ffmpeg-command-line-how-to-show-all-filter-settings-and-their-parameters-bef
ffmpeg -filters
ffmpeg --help filter=sine
TODO dump graph to ASCII art? trac.ffmpeg.org/wiki/FilteringGuide#Visualizingfilters mentions a
-dumpgraph
option, but haven't managed to use it yet.Bibliography:
- ffmpeg.org/ffmpeg-filters.html official documentation
- trac.ffmpeg.org/wiki/FilteringGuide some handy tips from the FFMpeg Wiki
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