Riesz-Fischer theorem is a norm version of it, and Carleson's theorem is stronger pointwise almost everywhere version.
Note that the Riesz-Fischer theorem is weaker because the pointwise limit could not exist just according to it: norm sequence convergence does not imply pointwise convergence.
How can you make a translation of the Bible and not put it in the public domain???? You tell me, you tell me.
With Falun Gong it's even more fun: the words of God Himself are will be copyrighted for a while after Li Hongzhi dies!!!
Ciro Santilli's admiration for Dyson goes beyond his "unify all the things approach", which Ciro loves, but also extends to the way he talks and the things he says. Dyson is one of Ciro's favorite physicist.
Besides this, he was also very idealistic compassionate, and supported a peaceful resolution until World War II with United Kingdom was basically inevitable. Note that this was a strategic mistake.
Dyson is "hawk nosed" as mentioned in Genius: Richard Feynman and Modern Physics by James Gleick (1994) chapter "Dyson". But he wasn't when he was young, see e.g. i2.wp.com/www.brainpickings.org/wp-content/uploads/2016/03/freemandyson_child-1.jpg?resize=768%2C1064&ssl=1 It sems that his nose just never stopped growing after puberty.
He also has some fun stories, like him practicing night climbing while at Cambridge University, and having walked from Cambridge to London (~86km!) in a day with his wheelchair bound friend.
Ciro Santilli feels that the label child prodigy applies even more so to him than to Feynman and Julian Schwinger.
Bibliography:
- QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) chapter 9 Freeman Dyson and the Structure of Quantum Field Theory
You need those because it is hard to do the following:
- client JavaScript sends a request to server
- server sends back data
- client updates what the user sees
This is hard to do notably because when the update happens, several things might need to change on the webpage at the same time.
Notably, new elements might need to be added to the webpage, which in turn means that new bindings such as button clicks have to be added to those, in a way that keeps the page working.
The only way to do this basically is to have a functional dependency graph that keeps everything in the page in working state as updates come.
Buckyballs (C60) by Periodic Videos (2010)
Source. Actually shows them in a lab!- youtu.be/ljF5QhD5hnI?t=167 has a photo of the first effective production method, which passes a large current between two carbon rods
- youtu.be/ljF5QhD5hnI?t=245 and forward cuts (their editing is very annoying) shows how fullerene dissolves in an organic solvent TODO name, sounds like thodium? and produces a violet solution, while graphite doesn't. A Ultrasonic bath is needed for the solution to form however.
- youtu.be/ljF5QhD5hnI?t=501 fullerene is not a good lubricant despite being a little ball, because it is reactive and polymerises under pressure
Functional Analysis I course of the University of Oxford 2023-2024 Updated 2025-07-11 +Created 1970-01-01
Open access with solutions: courses.maths.ox.ac.uk/course/view.php?id=4988
Lecturer: Luc Nguyen
This is about functions that take functions as input or output.
Set of ordered pairs. That's it! This is illustrated at: math.stackexchange.com/questions/1480651/is-fx-x-1-x-2-a-function/1481099#1481099
You don't learn the Harvard experience, you absorb it.
- This one does have bias danger though. But detecting greatness, is as type of bias arguably.
Being amongst excellent people makes you learn what excelent people are like, just like only by tasting many different types of wine can you know what good wine is like.
Most promising approaches as of 2020:
Why Private Billions Are Flowing Into Fusion by Bloomberg (2022)
Source. - Joint European Torus
- General Fusion: compress with liquid metal. Intends to demo in JET site.
- Helion Energy: direct fusion to electricity conversion without steam, direct from magnetic field movements
- First Light: shoot microscopic objct at a target to crush it so much that fusion happens
Main section: fusion power.
This is apparently the most important III-V semiconductor, it seems to actually have some applications, see also: gallium arsenide vs silicon.
Trying to use gallium arsenide was Seymour Cray's fatal last flaw as mentioned at The Supermen: The Story of Seymour Cray by Charles J. Murray (1997).
The Supermen: The Story of Seymour Cray by Charles J. Murray (1997) page 4 mentions:
Cray wanted his new machine to employ circuits made from a material called gallium arsenide. Gallium arsenide had achieved limited success, particularly in satellite communications and military electronics. But no one had succeeded with it in anything so complicated as a computer. In the computer industry, engineers had developed a saying: "Gallium arsenide is the technology of the future," they would say. "And it always will be."
The definition is not very precise, as in many games with random elements there is a mixture of both skill and luck.
So we just use the precise Non-deterministic game term instead for any game that has any random element beyond the control of the players.
He is extremely despicable and petty, enjoys only useless things, and is vengeful and disloyal. Rooting for sport teams is stupid.
Highlighted at the Origins of Precision by Machine Thinking (2017).
Saves preprocessor output and generated assembly to separate files.
- preprocessor:
- assembly:
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