I'm confused how to express the following expressions in math equations for publication:

* $x =$ integer part of $y$
* $x =$ fraction part of $y$
* image $x =$ shifted version of image $y$ left with $z$ pixels.
* image $x =$ shifted version of image $y$ up with $z$ pixels.

I thought about this: $x =$ intPart$(y)$ and image$\_x =$ shiftLeft$(y, z)$.
But they are programming style more than math equations. Any hints ?