Cauchy's Hypothesis or Noll's theorem states that $\vec{t}(\vec{X},t;\partial \Omega) = \vec{t}(\vec{X},t;\vec{N})$ where $\vec{N}$ is the outward unity normal to the positively oriented surface $\partial \Omega$. This translates to words as the dependence of the surface interaction vector on the surface on which it acts is only through the normal $\vec{N}$. My question is what is the significance of the semicolon (;)? How does it differ from the comma (,) used to separated the function's first two arguments?

up vote 13 down vote accepted

There is no hard mathematical difference between the comma (,) and the semicolon(;).

The semicolon is used sometimes to optically separate some variable group. So the semicolon is not more than a reading aid.

The situation can be compared to the usage of different kind of parentheses, to make complex nestings more readable.

A semicolon is used to separate variables from parameters. Quite often, the terms variables and parameters are used interchangeably, but with a semicolon the meaning is that we are defining a function of the parameters that returns a function of the variables.

For example, if I write $f(x1,x2,\ldots;p1,p2,\ldots)$ then I mean that by supplying the parameters $(p1, p2,\ldots)$, I create a new function whose arguments are $(x1, x2,\ldots)$.

So the general syntax is $functionname(variables;parameters)$.

In Noll's theorem it says that the function created by supplying $\partial \Omega$ is the same as that created by supplying $\vec{N}$. That's rather a nice way of saying that the function created only depends on $\vec{N}$.

Your Answer

 

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.