Partial vs. Total Relations
If ni >= 1 for all xi then each xi has exactly one related yij = R(xi), and the relation R(x,y) is, by definition, total (I.e., totally defined).
If ni = 0 for at least one xi, then that xi has no related yij and the relation is, by definition, partial (i.e., its value is not defined for some x in its domain).
The same reasoning applies symmetrically for the inverse relation Rinv(y,x).