## Notes: A family of ramp functions and the Beta function

Sometimes in a numerical method, you need to be able to continuously turn a calculation on or off in space or time.

Sometimes in a numerical method, you need to be able to continuously turn a calculation on or off in space or time.

Integrability conditions when trying to solve for a conformal factor

Here to save you some algebra and column-inches

An identity between vector commutation coefficients and coframe connection coefficients

These three objects form a superalgebra! Whoa!

When can you integrate-by-parts with Lie derivatives?

Special thanks to Ben Mares for coming up with this identity.

There is a nice 4-dimensional Weyl identity that I can never seem to remember off the top of my head; so I decided I need to write this note so I don’t have ...

The Weyl decomposition, further splitting into E/B, and computing in terms of 3+1 objects

In an effort to keep myself organized, I decided I should type up some notes I have laying around.