1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Confusing expression in a paper

  1. Mar 19, 2007 #1
    Hi all,

    Whilst reading http://www.jhuapl.edu/techdigest/td1703/thomas.pdf [Broken] 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!
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Mar 19, 2007 #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).
     
  4. Mar 19, 2007 #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.
     
  5. Mar 19, 2007 #4
    The only true occurence of z'' is in the denominator, just supress n(z'') to n.
     
  6. Mar 19, 2007 #5
    What do you mean suppress? n(z'') is quite a complex function of z''.
     
  7. Mar 19, 2007 #6
    What I meant was to differentiate implicitly.
     
  8. Mar 19, 2007 #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!
     
  9. Mar 29, 2007 #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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Confusing expression in a paper
  1. Looking for a paper (Replies: 28)

  2. Papers and Journals? (Replies: 1)

  3. Paper on Matrices (Replies: 10)

  4. Mathematical papers (Replies: 2)

  5. Need This Paper (Replies: 4)

Loading...