Cryogenic electron microscopy, which was developped in the 70's.
Average number of steps until reaching a state of a Markov chain Updated 2025-04-18 +Created 1970-01-01
TODO how to calculate
Since DNA is the centerpiece of life, Ciro Santilli is extremely excited about DNA-related technologies, see also: molecular biology technologies.
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.
Since a matrix can be seen as a linear map , the product of two matrices can be seen as the composition of two linear maps:One cool thing about linear functions is that we can easily pre-calculate this product only once to obtain a new matrix, and so we don't have to do both multiplications separately each time.
Basically, a "representation" means associating each group element as an invertible matrices, i.e. a matrix in (possibly some subset of) , that has the same properties as the group.
Or in other words, associating to the more abstract notion of a group more concrete objects with which we are familiar (e.g. a matrix).
This is basically what everyone does (or should do!) when starting to study Lie groups: we start looking at matrix Lie groups, which are very concrete.
Or more precisely, mapping each group element to a linear map over some vector field (which can be represented by a matrix infinite dimension), in a way that respects the group operations:
As shown at Physics from Symmetry by Jakob Schwichtenberg (2015)
- page 51, a representation is not unique, we can even use matrices of different dimensions to represent the same group
- 3.6 classifies the representations of . There is only one possibility per dimension!
- 3.7 "The Lorentz Group O(1,3)" mentions that even for a "simple" group such as the Lorentz group, not all representations can be described in terms of matrices, and that we can construct such representations with the help of Lie group theory, and that they have fundamental physical application
Bibliography:
- www.youtube.com/watch?v=9rDzaKASMTM "RT1: Representation Theory Basics" by MathDoctorBob (2011). Too much theory, give me the motivation!
- www.quantamagazine.org/the-useless-perspective-that-transformed-mathematics-20200609 The "Useless" Perspective That Transformed Mathematics by Quanta Magazine (2020). Maybe there is something in there amidst the "the reader might not know what a matrix is" stuff.
These often come pre-soldered on devboards, e.g. and allow for easy access to GPIO pins. E.g. they're present on the Raspberry Pi 2.
Why would someone ever sell a devboard without them pre-soldered!
6x1 pin header
. Source. 
Underside of a Raspberry Pi 2
. Source. At the top of this image we can clearly see how the usually pre-soldered pin header connectors go through the PCB and are soldered on both sides.Quantum superposition is really weird because it is fundamentally different than "either definite state but I don't know which", because the superposition state leads to different measurements than the non-superposition state.
Examples:
- www.youtube.com/watch?v=tt8gVXDsh7Q "Interference in quantum mechanics" by Looking Glass Universe (2015) shows how a left-right spin measurement has a defined value for a superposed half up half down state, but not for a pure up state.TODO can this be conducted? As mentioned in the video, this is closely linked to the fact that you can describe the wave function in multiple different bases (up/down or left/right), which is also at the root of the uncertainty principle.
- Video "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)" gives a similar photon version
- it seems that the single particle double slit experiment can also be thought of as in terms of a superposition of "the particle goes through the right" and "the particle goes through the right", although it is a bit harder to thing about as it is not a discrete process
~8GB,
lsblk reports 7796176 * 1KB = 7983284224 bytes.They are shaped like bicornes, which is super cool, but also super impractical!
Markings: "AX ÉCOLE POLYTECHNIQUE PROMOTION X2009"
From Ubuntu 20.04 on an ext4 formatted one:With Linux Unified Key Setup + ext4 the results are similar, maybe hdparam bypasses it?
/dev/sdb:
Timing cached reads: 28656 MB in 1.99 seconds = 14421.31 MB/sec
SG_IO: bad/missing sense data, sb[]: 70 00 05 00 00 00 00 0a 00 00 00 00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Timing buffered disk reads: 42 MB in 3.03 seconds = 13.88 MB/sec/dev/sdb:
Timing cached reads: 28326 MB in 1.99 seconds = 14251.55 MB/sec
SG_IO: bad/missing sense data, sb[]: 70 00 05 00 00 00 00 0a 00 00 00 00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Timing buffered disk reads: 38 MB in 3.11 seconds = 12.23 MB/secgnome-disks LUKS + ext4 benchmark with default params also gives about 14 MB/s.See form.
Analogous to a linear form, a multilinear form is a Multilinear map where the image is the underlying field of the vector space, e.g. .
The Portuguese term for it is "música popular brasileira". The widely recognized Brazilian acronym is "MPB".
"Brazilian pop" and "Br-pop" are inventions by Ciro Santilli, which are how Ciro thinks Brazil should market it to the world.
Unfortunately "B-pop" is too ambiguous with British pop music, and should be avoided.
YouTube playlist by Ciro Santilli containing all the songs in this section: www.youtube.com/playlist?list=PLcZOZrP1P_V4_SBDnegcLTcP-5YhNmWBB
Bibliography:
- www.slipcue.com/music/brazil/aa_styles/mpb.html has many good album reviews
Self promoted at:Not self-promoted at:
- www.reddit.com/r/Brazil/comments/1fimjtu/comment/m9fivya/
- www.reddit.com/r/musicsuggestions/comments/12cm5xt/comment/m9fkvd6/
- www.reddit.com/r/fantanoforever/comments/123zr1z/comment/m9fnieh/ asks for bets albums, which is much harder to answer
- locked threads that I've missed:
- Spotify-only
- www.reddit.com/r/LetsTalkMusic/comments/lxopm2/beyond_tropic%C3%A1lia_mpb_musica_popular_brasileira/ asks for newer songs only
This was the first full scale nuclear reactor in the world, and was brought up slowly to test it out.
Hanford B Reactor tour by Studio McGraw
. Source. 2016.- youtu.be/8rlVHEY7BF0?t=335 good description of the fuel element. It uses uranium metal, not Uranium dioxide
- youtu.be/8rlVHEY7BF0?t=652 N Reactor and F Reactor were identical, and came up 2 months later, but much faster because of what they learned on the B
One of the main children cartoons Ciro Santilli liked to watch. Part of the Pokemon Mania of the 90s of course.
Ciro could not understand why Nintendo won't make a proper 3D MMORPG Pokemon with actually 3D Pokemon roaming the land, which is obviously what everyone wants. There are even fan games getting there!until this explaiend it beautifully Video 1. "The Downfall Of Mainline Pokemon Games by GONZ media (2020)":
- pokemon-mmo-3d.com Interesting concept here, where when you deploy a Pokemon, you start controlling the Pokemon rather than the main character
- www.quora.com/Why-won-t-Nintendo-make-an-open-world-3D-Pokémon-RPG/answer/Ciro-Santilli
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