Confusing expression in a paper

In summary, the conversation revolves around interpreting a confusing expression in an equation on page 3 of the paper. The equation involves a function n that is only dependent on z'' and z'' is not a function of anything else. The discussion includes trying to rewrite the expression using a variable substitution and implicit differentiation, but it is ultimately concluded that the problem lies in replacing z'' with Z' and Zi'.
  • #1
natski
267
2
Hi all,

Whilst reading http://www.jhuapl.edu/techdigest/td1703/thomas.pdf I found one of the equations a little difficult to interpret. On page 3, there is a function defined as f. On the denominator there it appears that they have differentiated n(z''(Z')) as a function of z'' and then evaluated it for the case where Z' goes to Zi'.

As far as I can tell, n is only a function of z'' and z'' is not a function of anything else, so the n(z''(Z')) doesn't make much sense to me. I interpretted it as meaning that I write down the expression n(z'') then replace all my z'' s with Z' using an appropriate equation of the form:
Z'=some function of z''.

However, I cannot even write down a clean expression for this! The form of Z', as seen just below eqn 4, cannot be easily rewritten to express z'' as a function of a Z'.

Can anyone help me interpretting this confusing expression?

Thanks!
 
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  • #2
Reading the text above equation (4), it appears that Z'(z'') originates from a "simple variable substitution" which they then detail, below equation (4).
 
  • #3
Yes you are right but when I tried to rewrite Z'(z'') as z''(Z') I could not and it seemed to require solving in some kind of non-algebraic way.
 
  • #4
The only true occurence of z'' is in the denominator, just supress n(z'') to n.
 
  • #5
What do you mean suppress? n(z'') is quite a complex function of z''.
 
  • #6
What I meant was to differentiate implicitly.
 
  • #7
Umm ok, so I can write:

z''=[n(h) (R+h) Cos(Delta)]/(n(z'') Z') - R

Then are you thinking I should replace all my z''s in n(z'') with this equation? If I do this, I can't differentiate by z'' since now I have got Z' in there too.

I think I should differentiate first n(z'') by z'' first since that's not too hard. I then need to replace z'' with the equation above. However, when I then replace Z' with Zi' I still have z'' floating about which I can't get rid off!
 
  • #8
Differentiating implicity or using some kind of chain rule or anything will not make life any easier as far as I can tell. The differentation part is the one part that is easily done, it's the replacing z''->Z'->Zi' that's the problem.
 

1. What do you mean by "confusing expression" in a paper?

"Confusing expression" refers to any language or wording in a paper that is unclear, ambiguous, or difficult to understand. This can include complex sentence structures, jargon, or lack of clarity in the author's ideas.

2. How can I identify confusing expressions in my own writing?

One way to identify confusing expressions is to read your paper out loud and pay attention to any parts that feel unclear or difficult to understand. You can also ask a friend or colleague to read your paper and provide feedback on any confusing sections.

3. What impact can confusing expressions have on a paper?

Confusing expressions can have a negative impact on a paper by making it difficult for readers to understand the author's ideas. This can lead to confusion, frustration, and a lack of credibility for the author.

4. How can I improve confusing expressions in my paper?

To improve confusing expressions in your paper, try to simplify your language and use clear, concise sentences. You can also define any technical terms or jargon and provide examples to help clarify your ideas. It can also be helpful to have someone else read your paper and provide feedback on any confusing sections.

5. Are there any resources available to help with confusing expressions in a paper?

Yes, there are many resources available, such as writing centers, online writing guides, and style manuals, that can provide tips and strategies for improving confusing expressions in a paper. It can also be helpful to seek feedback and guidance from professors, colleagues, or writing tutors.

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