Feces by Ciro Santilli 35 Updated +Created
De Broglie-Bohm theory by Ciro Santilli 35 Updated +Created
Deterministic, but non-local.
Plausible deniability of email password handover by Ciro Santilli 35 Updated +Created
You need a secondary password that when used leads to an empty inbox with a setting set where message are deleted after 2 days.
This way, if the attacker sends a test email, it will still show up, but being empty is also plausible.
Of course, this means that any new emails received will be visible by the attacker, so you have to find a way to inform senders that the account has been compromised.
So you have to find a way to inform senders that the account has been compromised, e.g. a secret pre-agreed canary that must be checked each time as part of the contact protocol.
Model of elliptic geometry by Ciro Santilli 35 Updated +Created
Lepton by Ciro Santilli 35 Updated +Created
Can be contrasted with baryons as mentioned at baryon vs meson vs lepton.
Electromagnetic tensor by Ciro Santilli 35 Updated +Created
Frame of reference by Ciro Santilli 35 Updated +Created
Open Knowledge Foundation by Ciro Santilli 35 Updated +Created
Teach For All by Ciro Santilli 35 Updated +Created
Short-read DNA sequencing by Ciro Santilli 35 Updated +Created
Fog computing by Ciro Santilli 35 Updated +Created
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.
Folding@home and SETI@home are perfect example of that definition.
Antimatter by Ciro Santilli 35 Updated +Created
Predicted by the Dirac equation.
Can be easily seen from the solution of Equation "Expanded Dirac equation in Planck units" when the particle is at rest as shown at Video "Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)".
Klein-Gordon equation by Ciro Santilli 35 Updated +Created
A relativistic version of the Schrödinger equation.
Correctly describes spin 0 particles.
The most memorable version of the equation can be written as shown at Section "Klein-Gordon equation in Einstein notation" with Einstein notation and Planck units:
Has some issues which are solved by the Dirac equation:
Cryogen-free dilution refrigerator by Ciro Santilli 35 Updated +Created
Developmental genetics by Ciro Santilli 35 Updated +Created
How genes form bodies.
Video 1.
Developmental Genetics 1 by Joseph Ross (2020)
Source. Talks about homeobox genes.
When viewed as matrices, it is the group of all matrices that preserve the dot product, i.e.:
This implies that it also preserves important geometric notions such as norm (intuitively: distance between two points) and angles.
This is perhaps the best "default definition".
Product definition of the exponential function by Ciro Santilli 35 Updated +Created
The basic intuition for this is to start from the origin and make small changes to the function based on its known derivative at the origin.
More precisely, we know that for any base b, exponentiation satisfies:
  • .
  • .
And we also know that for in particular that we satisfy the exponential function differential equation and so:
One interesting fact is that the only thing we use from the exponential function differential equation is the value around , which is quite little information! This idea is basically what is behind the importance of the ralationship between Lie group-Lie algebra correspondence via the exponential map. In the more general settings of groups and manifolds, restricting ourselves to be near the origin is a huge advantage.
Now suppose that we want to calculate . The idea is to start from and then then to use the first order of the Taylor series to extend the known value of to .
E.g., if we split into 2 parts, we know that:
or in three parts:
so we can just use arbitrarily many parts that are arbitrarily close to :
and more generally for any we have:
Let's see what happens with the Taylor series. We have near in little-o notation:
Therefore, for , which is near for any fixed :
and therefore:
which is basically the formula tha we wanted. We just have to convince ourselves that at , the disappears, i.e.:
To do that, let's multiply by itself once:
and multiplying a third time:
TODO conclude.

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