Ciro Santilli @cirosantilli 37

Types:

A Ring can be seen as a generalization of a field where:

Addition however has to be commutative and have inverses, i.e. it is an Abelian group.

The simplest example of a ring which is not a full fledged field and with commutative multiplication are the integers. Notably, no inverses exist except for the identity itself and -1. E.g. the inverse of 2 would be 1/2 which is not in the set. More specifically, the integers are a commutative ring.

A polynomial ring is another example with the same properties as the integers.

The simplest non-commutative, non-division is is the set of all 2x2 matrices of real numbers:Note that $GL(n)$ is not a ring because you can by addition reach the zero matrix.

Linear combination of a Dirichlet boundary condition and Neumann boundary condition at each point of the boundary.

Examples:

White papers are a form of advertisement. They are not peer reviewed papers and are generally not reproducible; their value lies entirely in trust of their publisher rather than being able to verify their claims.

A wiki that gathers mathematical proofs.

URL: proofwiki.org/wiki/Main_Page

MediaWiki-based.

This appears to be the creator: github.com/externl "Joe George".

www.cns.gatech.edu/~predrag/courses/PHYS-6124-12/StGoChap6.pdf 6.1 "Classification of PDE's" clarifies which boundary conditions are needed for existence and uniqueness of each type of second order of PDE:

Ciro Santilli started taking some notes at: github.com/cirosantilli/awesome-whole-cell-simulation. but they are going to be all migrated here.

It is interesting to note how one talks about single cell analysis, in contrast to whole cell simulation: experimentally it is hard to analyse a single cell. But theoretically, it is hard to simulate a single cell. This mismatch is perhaps the ultimate frontier of molecular biology.