What is the partial derivative of a domain ?

[Navy King]

hello,everyone,I'm from Shanghai, china.I got a problem when i was reading papers.I can't understand what is the partial derivative of a domain.I suppose it may be a curve,but exactly which curve it is? thank you very much!

 

[micromass]

Can you tell me which papers you're looking at? (I hope it's not in chinese...)

 

[yenchin]

What do you mean? Could it just be the notation that means the boundary of a domain?

 

[Navy King]

Can you tell me which papers you're looking at? (I hope it's not in chinese...)

the paper is The 2.1-D Sketch,Mark Nitzberg David Mumford

 

[Navy King]

What do you mean? Could it just be the notation that means the boundary of a domain?

may be you are right.may be the notation dose not mean partial derivative. thanks a lot.and i need your help

 

[micromass]

Do you mean the notation $$\partial R_i - \partial D$$. That $$\partial$$ symbol there simply denotes the boundary of the domain. This is defined as

$$\partial U=\overline{U}\setminus U^\circ=\overline{U}\cap \overline{X\setminus U}$$

where $$\overline{U}$$ is the closure of U, and $$U^\circ$$ is the interior of U.

 

[Navy King]

Do you mean the notation $$\partial R_i - \partial D$$. That $$\partial$$ symbol there simply denotes the boundary of the domain. This is defined as

$$\partial U=\overline{U}\setminus U^\circ=\overline{U}\cap \overline{X\setminus U}$$

where $$\overline{U}$$ is the closure of U, and $$U^\circ$$ is the interior of U.

wow,you're so kind,thank you very very much.my english is so poor.