# Correct Interpretation of Notation

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.

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

## 1 Answer

• $$\min[a,b]$$ 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.

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