# Notation Question

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1. Feb 21, 2016

### Aaerion

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

Last edited by a moderator: May 7, 2017
2. Feb 21, 2016

### 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
3. Feb 21, 2016

### Aaerion

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.

4. Feb 21, 2016

### Staff: Mentor

That makes much more sense.