The discussion centers on the concept of the partial derivative of a domain, specifically in the context of the paper "The 2.1-D Sketch" by Mark Nitzberg and David Mumford. Participants clarify that the notation \(\partial R_i - \partial D\) refers to the boundary of a domain, denoted as \(\partial U\), which is defined mathematically as \(\partial U=\overline{U}\setminus U^\circ=\overline{U}\cap \overline{X\setminus U}\). This notation indicates the boundary rather than a partial derivative in the traditional sense, resolving the initial confusion regarding its interpretation.
PREREQUISITESMathematicians, students of calculus and topology, and researchers analyzing mathematical papers who seek clarity on the interpretation of domain boundaries and related notations.
micromass said:Can you tell me which papers you're looking at? (I hope it's not in chinese...)
yenchin said:What do you mean? Could it just be the notation that means the boundary of a domain?
micromass said: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.