Ciro Santilli @cirosantilli 37

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Sauropsida subclade Updated 2025-07-16

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Google infrastructure Updated 2025-07-16

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Ivy League Updated 2025-07-16

Columbia University

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Neutron Updated 2025-07-16

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x

belongs to the elliptic curve over a non quadratically closed field Updated 2025-07-16

One major difference between the elliptic curve over a finite field or the elliptic curve over the rational numbers the elliptic curve over the real numbers is that not every possible

x

generates a member of the curve.

This is because on the Equation "Definition of the elliptic curves" we see that given an

x

, we calculate

x^{3} + a x + b

, which always produces an element

y^{2}

.

But then we are not necessarily able to find an

y

for the

y^{2}

, because not all fields are not quadratically closed fields.

For example: with

a = 1

and

b = 1

, taking

x = 1

gives:

y^{2} = 1^{3} + 1 \times 1 + 1 = 3

and therefore there is no

y \in Q

that satisfies the equation. So

x = 1

is not on the curve if we consider this elliptic curve over the rational numbers.

That

x

would also not belong to Elliptic curve over the finite field

F_{4}

, because doing everything

mod 4

we have:

0 * 0 1 * 1 2 * 2 3 * 3 = 0 = 1 = 4 = 9 = 0 = 1 mod 4 mod 4 mod 4 mod 4

Therefore, there is no element

y \in F_{4}

such that

y \times y = 2

or

y \times y = 3

, i.e.

2

and

3

don't have a multiplicative inverse.

For the real numbers, it would work however, because the real numbers are a quadratically closed field, and

3 \in R

.

For this reason, it is not necessarily trivial to determine the number of elements of an elliptic curve.

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Quantum dot single photon source Updated 2025-07-16

Mentioned at: Video "Quantum Computing with Light by Quantum Light University of Sheffield (2015)" youtu.be/nyK-vhoOBpE?t=185.

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Sinologist Updated 2025-07-16

en.wikipedia.org/wiki/List_of_sinologists

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CSS flex Updated 2025-07-16

css/flex.html: illustrates basic flex usage, including:
flex-grow: if there's space left, this determines how much extra space will be given to each.
flex-basis: the size the items want to be. But if there isnt' enough space, this can be cut up.
Note that the minimal space required by children of the flex children cannot be necessarily cut up, and might lead things to overflow out of the container.
flex-shrink: if there's space missing, this determines how much extra space will be removed from each flex-basis

Other examples include:

css/flex-fill-vertical.html: minimal setup for a editor: docs.ourbigbook.com/editor

That example calculates and displays the final widths via JavaScript, making it easier to understand the calculations being done.

Answers: stackoverflow.com/questions/28473807/how-does-flex-grow0-get-interpreted/69995712#69995712

Bibliography:

developer.mozilla.org/en-US/docs/Web/CSS/CSS_Flexible_Box_Layout

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Annalen der Physik Updated 2025-07-16

This was the God OG physics journal of the early 20th century, before the Nazis fucked German science back to the Middle Ages!

Notable papers:

Annus Mirabilis papers

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Bacterial outer membrane Updated 2025-07-16

Only present in Gram-negative bacteria.

Figure 1.
Structure of a Gram-negative bacteria
. Source.

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Baryon Updated 2025-07-16

composite particle made up of an odd number of elementary particles.

The most important examples by far are the proton and the neutron.

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Color charge Updated 2025-07-16

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Experiments that measure the gravitational constant Updated 2025-07-16

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Git tips Updated 2025-07-16

This is a quick presentation that goes over some of the most common difficulties people find with Git.

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Gluon Updated 2025-07-16

Force carrier of quantum chromodynamics, like the photon is the force carrier of quantum electrodynamics.

One big difference is that it carrier itself color charge.

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Google product Updated 2025-07-16

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Google subsidiary Updated 2025-07-16

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Proton decay Updated 2025-07-16

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Rio de Janeiro (state) Updated 2025-07-16

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Strong interaction Updated 2025-07-16

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