Is there a mathematical operator to truncate negative values to zero?
I have seen the notation $z^+$ to denote $\max\{z,0\}$ in many papers and books. Analogously, $z^-$ to denote $-\min\{z,0\}$. Wikipedia uses that notation too.
EDIT (thanks to @rzippo) : Note that $z^-$ denotes the so-called negative part, which is non-negative. If we want a function that simply truncates positive values to zero, then we would need the function $f(z)=\min\{z,0\}$ (without the minus sign), for which I do not know any particular notation.
How about adding the absolute value of the number to the number, and then dividing by 2. If the number is negative, the total will be zero, which divided by 2 is still zero. If the number is positive or zero, the result will be the number you began with.