It's great right? You can't link to your other answer alone: Stack Overflow link-only answer policy, but you can't copy the other answer either.
And because not all duplicate close votes succeed, see e.g. stackoverflow.com/questions/59649238/how-to-use-the-m5ops-in-gem5-such-m5-exit-and-m5-dump-stats-in-se-mode/63955139#63955139 the result is that someone else will come and answer the same thing in a different wording.
And some answers answer two questions that are not duplicates, e.g. superset/subset questions.
So just do a slight variation wording yourself and get all the reputation.
Capacitor Updated 2025-07-16
The fundamental intuition about capacitors is that they never let electrons through.
They can only absorb electrons up to a certain point, but then the pushback becomes too strong, and current stops.
Therefore, they cannot conduct direct current long term.
For alternating current however, things are different, because in alternating current, electrons are just jiggling back and forward a little bit around a center point. So you can send alternating current power across a capacitor.
The key equation that relates Voltage to electric current in the capacitor is:
So if a voltage Heavyside step function is applied what happens is:
  • the capacitor fills up instantly with an infinite current
  • the current then stops instantly
More realistically, one may consider the behavior or the series RC circuit to see what happens without infinities when a capacitor is involved as in the step response of the series RC circuit.
Figure 1.
Electronic symbol of a capacitor
. Source.
Video 1.
Finding capacitance with an oscilloscope by Jacob Watts (2020)
Source. Good experiment.
Video 2.
Capacitors Explained by The Engineering Mindset
. Source. 2019.
Capoeira music Updated 2025-07-16
Capoeira music is amazing. And some Brazilian pop adaptations of it have also been awesome.
Video 2.
Triste Bahia by Caetano Veloso
. Source.
Video 3.
Na Roda de Capoeira by Nara Leão
. Source. From the 1964 album "Opinião De Nara"
Base pair Updated 2025-07-16
Carleson's theorem Updated 2025-07-16
The Fourier series of an function (i.e. the function generated from the infinite sum of weighted sines) converges to the function pointwise almost everywhere.
The theorem also seems to hold (maybe trivially given the transform result) for the Fourier series (TODO if trivially, why trivially).
Only proved in 1966, and known to be a hard result without any known simple proof.
This theorem of course implies that Fourier basis is complete for , as it explicitly constructs a decomposition into the Fourier basis for every single function.
TODO vs Riesz-Fischer theorem. Is this just a stronger pointwise result, while Riesz-Fischer is about norms only?
Neuroscience Updated 2025-07-16
Standard Model Updated 2025-07-16
As of 2019, the more formal name for particle physics, which is notably missing general relativity to achieve the theory of everything.
cds.cern.ch/record/799984/files/0401010.pdf The Making of the Standard Model by Steven Weinberg mentions three crucial elements that made up the standard model post earlier less generalized quantum electrodynamics understandings
Carrier wave Updated 2025-07-16
Early transmitters such as the spark-gap transmitter could only send noises to send Morse code.
To send voice and music, amplitude modulation had to be developed. And a key ingredient of this is the carrier wave.
The problem is, the carrier wave needs to have somewhat high frequencies, in the hundreds of kHz TODO why. But as you might imagine, that is hard to achieve by mechanical means such as a hand cranck like Hippolyte Pixiis alternator!
Interestingly, some of the first carrier wave generators were actually mechanical, e.g. the Alexanderson alternator.
But clearly such mechanical machines were not very scalable, and soon more electronic devices were introduced, notably the vacuum tube.
Cascading Style Sheets Updated 2025-07-16
Star system Updated 2025-07-16

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