I have been working with Java a couple of years, but up until recently I haven\'t run across this construct:
int count = isHere ? getHereCount(index) : getAw
Others have answered this to reasonable extent, but often with the name "ternary operator".
Being the pedant that I am, I'd like to make it clear that the name of the operator is the conditional operator or "conditional operator ?:". It's a ternary operator (in that it has three operands) and it happens to be the only ternary operator in Java at the moment.
However, the spec is pretty clear that its name is the conditional operator or "conditional operator ?:" to be absolutely unambiguous. I think it's clearer to call it by that name, as it indicates the behaviour of the operator to some extent (evaluating a condition) rather than just how many operands it has.