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Notation Question

  1. Feb 21, 2016 #1
    1. The problem statement, all variables and given/known data

    I have these two equations from this paper: https://www.scribd.com/doc/299960566/Spiral [Broken]

    2. Relevant equations
    What are the vertical bars next to the drawn red starts supposed to indicate in this context?

    I'm trying to implement these equations into a program but I'm totally lost. I have no idea what's up with those vertical bars next to the red stars that I drew. Is it supposed to be the terms evaluated at (j+1-rtheta)? If so, then what variable is it even being plugged into (r or theta)?

    3. The attempt at a solution
    Googling and asking my professor.
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Feb 21, 2016 #2


    Staff: Mentor

    Vertical bars like that usually mean at what value the quantity to the left is evaluated at. The summation looks screwy to me, though, as the sum runs from j = 1 to j - 1, which doesn't make sense. If it had been written like what's below, that would make more sense to me.
    $$\sum_{j = 1}^{J - 1} \dots$$
    I.e., not reusing j (lower case) as both the index of the sum and the ending point.

    The author of the paper you're citing is an MD, so I suspect that he is not as able as he could be to communicate mathematical equations.
    Last edited by a moderator: May 7, 2017
  4. Feb 21, 2016 #3
    I just looked up zero crossing function in general and I think I figured it out. From what I can understand, the summation should actually be from j=1 to J-1. Furthermore, inside the sign functions, the average slope is subtracted from the slope at points j+1 and j respectively. Doing this will allow me to determine how many times the slope crosses its mean during data collection.
  5. Feb 21, 2016 #4


    Staff: Mentor

    That makes much more sense.
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