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I was reading a parametrization and they used a peculiar way to write their equations which I am unfamiliar with as to how to properly interpret it. K refers to Kelvins in this case and what I am particularly struggling with is with the symbolic meaning of the $min[1, max[0,f(x)]$ structure.

$ Tscale_{i} = \min[1, \max[0, \frac{Tsurf_i-268.16 K}{Tmelt_i-268.16 K}]] $

Hope you guys can help me understand it. Regards.

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  • $\begingroup$ Sorry about that! I have corrected the question. $\endgroup$
    – RMS
    Jun 7, 2020 at 21:04

1 Answer 1

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  • $\min[a,b]$ is a function returning the smaller of $a$ and $b$.

  • $\max[b,c]$ is a function returning the larger of $b$ and $c$.

  • $\min[a,\max[b,c]]$ is a function returning the smaller of $a$ and (the larger of $b$ and $c$).

  • $i$ is an index.


speculation:

$T$ seems to refer to temperature, $K$ seems to be a unit (Kelvin), $T_{surf}$ might mean surface temperature, $T_{melt}$ may be melting point.


If our suppositions are true, the function is intended for application on a sequence of paired surface temperatures/melting points. It returns a measure called $T_{scale}$ with no units. This measure ranges from zero to one inclusive. More specifically, it equals either $0$, $1$, or $\frac{T_{surf}-268.16}{T_{melt}-268.16}$ when this value is between zero and one.

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  • $\begingroup$ Thank you so much for the great answer, I'll up vote it as soon I have enough exp. $\endgroup$
    – RMS
    Jun 7, 2020 at 21:05

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