Ciro Santilli @cirosantilli 40

TODO find a concrete numerical example of doing calculus on a differentiable manifold and visualizing it. Likely start with a boring circle. That would be sweet...

Based on the fact that we don't have a P algorithm for the discrete logarithm of the cyclic group as of 2020, but we do have an efficient algorithm for modular exponentiation. But nor do we have proof that one does not exist! Living on the edge as usual for public-key cryptography.

Polynomial (possibly a multivariate polynomial) with integer coefficients.

Sometimes systems of Diophantine equations are considered.

Problems generally involve finding integer solutions to the equations, notably determining if any solution exists, and if infinitely solutions exist.

The general problem is known to be undecidable: Hilbert's tenth problem.

The Pythagorean triples, and its generalization Fermat's last theorem, are the quintessential examples.

NCBI online tool to find and view all open reading frames in a given FASTA: www.ncbi.nlm.nih.gov/orffinder/

Previously known as "Food From Electricity", "NeoCarbonFood" sounds like a more commercializable version of it.

Uses electricity to electrolyse water into hydrogen and oxygen molecules, and then use bacteria that do hydrogen chemosynthesis to convert it into food.

Some coverage:

where:

Remember that $\psi$ is a 4-vetor, gamma matrices are 4x4 matrices, so the whole thing comes down to a dot product of two 4-vectors, with a modified $\psi$ by matrix multiplication/derivatives, and the result is a scalar, as expected for a Lagrangian.

Like any other Lagrangian, you can then recover the Dirac equation, which is the corresponding equations of motion, by applying the Euler-Lagrange equation to the Lagrangian.

Specifies fixed values.

Can be used for elliptic partial differential equations and parabolic partial differential equations.

Numerical examples:

Discord is useless if you want to participate in more than one large group because of this. It is impossible to get email notification for selected threads you care about.

No way to get email notifications for missed activity? support.discord.com/hc/en-us/community/posts/360041806392-Can-we-get-an-email-notification-option-for-messages-

Can we do better than "wrong password implies random bytes"?

Can the last disk access times be checked via forensic methods?

First we write a vector field as:Note how we are denoting each component of $F$ as $F^i$ with a raised index.

Then, the divergence can be written in Einstein notation as:

It is common to just omit the variables of the function, so we tend to just say:or equivalently when referring just to the operator:

Publishes through the Fermilab YouTube channel under the playlist "Fermilab - Videos by Don Lincoln"

Some insights, but too much on the popular science side of things.

Is this exact sentence really from UNIX philosophy? en.wikipedia.org/wiki/Unix_philosophy#Do_One_Thing_and_Do_It_Well

Of course, it has precedents, e.g. jack of all trades, master of none

Amazingly confirms the wave particle duality of quantum mechanics.

The effect is even more remarkable when done with individual particles such individual photons or electrons.

Richard Feynman liked to stress how this experiment can illustrate the core ideas of quantum mechanics. Notably, he night have created the infinitely many slits thought experiment which illustrates the path integral formulation.