First-move advantage in chess Updated 2025-07-16
First-order logic Updated 2025-07-16
Builds on top of propositional logic, adding notably existential quantification.
Fish subclade Updated 2025-07-16
Floating-point arithmetic Updated 2025-07-16
FluidSynth Updated 2025-07-16
Synthesizes MIDI input. vmpk +
aconnect + Advanced Linux Sound Architecture hello world: askubuntu.com/questions/34391/virtual-midi-piano-keyboard-setup/1298026#1298026Supports only very basic effects it seems: chorus effect and reverberation. The main way to add instruments to it is via SoundFont files.
Fluorescence microscope Updated 2025-07-16
Fourier-Bessel series Updated 2025-07-16
Completeness: math.stackexchange.com/questions/2192665/is-this-set-of-bessel-functions-a-basis-for-all-c10-a-functions TODO
This is the Bessel function analogue to Fourier basis is complete for .
Fourier inversion theorem Updated 2025-07-16
A set of theorems that prove under different conditions that the Fourier transform has an inverse for a given space, examples:
Georgism Updated 2025-07-16
Flux qubit Updated 2025-07-16
In Ciro's ASCII art circuit diagram notation, it is a loop with three Josephson junctions:
+----X-----+
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| |
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+--X----X--+
Superconducting Qubit by NTT SCL (2015)
Source. Offers an interesting interpretation of superposition in that type of device (TODO precise name, seems to be a flux qubit): current going clockwise or current going counter clockwise at the same time. youtu.be/xjlGL4Mvq7A?t=1348 clarifies that this is just one of the types of qubits, and that it was developed by Hans Mooij et. al., with a proposal in 1999 and experiments in 2000. The other type is dual to this one, and the superposition of the other type is between N and N + 1 copper pairs stored in a box.
Their circuit is a loop with three Josephson junctions, in Ciro's ASCII art circuit diagram notation:
+----X-----+
| |
| |
| |
+--X----X--+When half the magnetic flux quantum is applied as microwaves, this produces the ground state:where and cancel each other out. And the first excited state is:Then he mentions that:
- to go from 0 to 1, they apply the difference in energy
- if the duration is reduced by half, it creates a superposition of .
Fog computing Updated 2025-07-16
Our definition of fog computing: a system that uses the computational resources of individuals who volunteer their own devices, in which you give each of the volunteers part of a computational problem that you want to solve.
Forbidden mechanism Updated 2025-07-16
Formal language theory Updated 2025-07-16
Formal proof Updated 2025-07-16
A proof in some system for the formalization of mathematics.
Form of government Updated 2025-07-16
Rasselas Prince of Abyssinia CHAPTER VIII www.gutenberg.org/cache/epub/652/pg652-images.html:
Oppression is, in the Abyssinian dominions, neither frequent nor tolerated; but no form of government has been yet discovered by which cruelty can be wholly prevented. Subordination supposes power on one part and subjection on the other; and if power be in the hands of men it will sometimes be abused. The vigilance of the supreme magistrate may do much, but much will still remain undone. He can never know all the crimes that are committed, and can seldom punish all that he knows.
Forsyth-Edwards Notation Updated 2025-07-16
The cool thing about this notation is that is showed to Ciro Santilli that there is more state to a chess game than just the board itself! Notably:plus some other boring draw rules counters.
- whose move it is next
- castling availability
- en passant availability
German company Updated 2025-07-16
Fourier series Updated 2025-07-16
Approximates an original function by sines. If the function is "well behaved enough", the approximation is to arbitrary precision.
Fourier's original motivation, and a key application, is solving partial differential equations with the Fourier series.
Can only be used to approximate for periodic functions (obviously from its definition!). The Fourier transform however overcomes that restriction:
The Fourier series behaves really nicely in , where it always exists and converges pointwise to the function: Carleson's theorem.
Fourier transform Updated 2025-07-16
Continuous version of the Fourier series.
Can be used to represent functions that are not periodic: math.stackexchange.com/questions/221137/what-is-the-difference-between-fourier-series-and-fourier-transformation while the Fourier series is only for periodic functions.
Therefore, the Fourier transform can be seen as a generalization of the Fourier series that can also decompose functions defined on the entire real line.
As a more concrete example, just like the Fourier series is how you solve the heat equation on a line segment with Dirichlet boundary conditions as shown at: Section "Solving partial differential equations with the Fourier series", the Fourier transform is what you need to solve the problem when the domain is the entire real line.
Four-level laser Updated 2025-07-16
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