There's a bit of both sides in the 2016 race:
- tx 3aaae4adc68b3768e1a6029987f2aca2479818495c9aee6a86067710806e9c4f: "bEW Trump 2016! Stop the TPP!"
- tx 202ceac7b3e7b990d1961fd2eab18ba5c80c99f10eacc783f14c53ebfdcaee00 "oEW Fuck Obama&Clinton Go Trump!!!!"
- tx 53fcddaa69e79c0fdc4e2cd139bffef341a38d46bb653721d9adf42460b1afae "EW Trump will fail America, like all his businesses"
- data/out/0433.txt:1752:EW FUCK Trump and his supporters. You ppl are the dumbest scum ever.
- data/out/0435.txt:1904:EW TRUMP 2016 !!!!!!!!!!!!!!
- data/out/0437.txt:1150:bjEW FuCk OfF TrUmP!
- data/out/0439.txt:1017:EW trump will trample regulations justly
- data/out/0443.txt:1281:L9,GOD EMPEROR TRUMP WINS THIRD TERM`7
- data/out/0444.txt:2102:L99,TRUMPPPPPPPPPPPPPPP
- data/out/0445.txt:311:L127,TRUMP WILL SAVE THE WORLD.
- data/out/0445.txt:1257:EW Howard not Trump is the actual 45th president.
- tx 2fb07a8f358d690d8717734a48e5daf0ef70ea2d0e3b7c88dace8a5818fcb168 "L299,Trump touched my no-no"
- data/out/0457.txt:8677:EW All of the sheep think Donald Trump is literally Hitler.
- data/out/0481.txt:11481:I kill donald trump!!!!!!
- data/out/0545.txt:1239:}fEW fuck donald trump
- tx 05fce37228c732f4635f79e6f36d028be677404beab497ddace9024fe8e4b517 "EW Heil Trump!He's the true white leader our race need so much since Adolf"
- data/out/0552.txt:14:Trump needs to get impeached and locked up!
- data/out/0666.txt:56:(Trump was impeached for the second time in office.
The Einstein summation convention works will with partial derivatives and it is widely used in particle physics.
In particular, the divergence and the Laplacian can be succinctly expressed in this notation:
In order to express partial derivatives, we must use what Ciro Santilli calls the "partial index partial derivative notation", which refers to variables with indices such as , , , , and instead of the usual letters , and .
Directly modelled by group.
For continuous symmetries, see: Lie group.
Some sources say that this is just the part that says that the norm of a function is the same as the norm of its Fourier transform.
The comment at math.stackexchange.com/questions/446870/bijectiveness-injectiveness-and-surjectiveness-of-fourier-transformation-define/1235725#1235725 may be of interest, it says that the bijection statement is an easy consequence from the norm one, thus the confusion.
TODO does it require it to be in as well? Wikipedia en.wikipedia.org/w/index.php?title=Plancherel_theorem&oldid=987110841 says yes, but courses.maths.ox.ac.uk/node/view_material/53981 does not mention it.
More precisely, each generator of the corresponding Lie algebra leads to one separate conserved current, such that a single symmetry can lead to multiple conserved currents.
This is basically the local symmetry version of Noether's theorem.
Then to maintain charge conservation, we have to maintain local symmetry, which in turn means we have to add a gauge field as shown at Video "Deriving the qED Lagrangian by Dietterich Labs (2018)".
Bibliography:
- photonics101.com/relativistic-electrodynamics/gauge-invariance-action-charge-conservation#show-solution has a good explanation of the Gauge transformation. TODO how does that relate to symmetry?
- physics.stackexchange.com/questions/57901/noether-theorem-gauge-symmetry-and-conservation-of-charge
Visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016) by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Good ultra quick visual non-mathematical introduction to the Riemann hypothesis and analytic continuation.
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