What is the partial derivative of a domain ?

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Discussion Overview

The discussion revolves around the concept of the partial derivative of a domain, particularly in the context of mathematical notation and its interpretation in academic papers. Participants explore the meaning of the notation and its implications for understanding boundaries in mathematical domains.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about the term "partial derivative of a domain," suggesting it may refer to a curve but is uncertain about which curve it is.
  • Another participant questions the notation, proposing that it might simply denote the boundary of a domain.
  • A participant provides a definition of the boundary of a domain using the notation \(\partial U\), explaining it in terms of closure and interior of the set.
  • There is acknowledgment of the possibility that the notation does not refer to a partial derivative, indicating a potential misunderstanding.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the term "partial derivative of a domain." There are competing views regarding whether it refers to a curve or simply the boundary of a domain.

Contextual Notes

The discussion includes references to specific mathematical notation and definitions, which may depend on the context of the papers being read. There are unresolved aspects regarding the interpretation of the notation and its application.

Navy King
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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!
 
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Can you tell me which papers you're looking at? (I hope it's not in chinese...)
 
What do you mean? Could it just be the notation that means the boundary of a domain?
 
Last edited:
micromass said:
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
 
yenchin said:
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
 
Do you mean the notation [tex]\partial R_i - \partial D[/tex]. That [tex]\partial[/tex] symbol there simply denotes the boundary of the domain. This is defined as

[tex]\partial U=\overline{U}\setminus U^\circ=\overline{U}\cap \overline{X\setminus U}[/tex]

where [tex]\overline{U}[/tex] is the closure of U, and [tex]U^\circ[/tex] is the interior of U.
 
micromass said:
Do you mean the notation [tex]\partial R_i - \partial D[/tex]. That [tex]\partial[/tex] symbol there simply denotes the boundary of the domain. This is defined as

[tex]\partial U=\overline{U}\setminus U^\circ=\overline{U}\cap \overline{X\setminus U}[/tex]

where [tex]\overline{U}[/tex] is the closure of U, and [tex]U^\circ[/tex] is the interior of U.

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

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