Как правильно переводятся предложения?

1. Then for any x>0, in the proportional-growth asymptotic U(k,n)->0 exponentially in n.

2.The term H(x) in (2.10), from the union bound over all matrices, results in an overly pessimistic bound in the vicinity of py=0.5. As we are seeking the least upper bound on U(k,n) we note that any upper bound for U(j,n) for j>k is also an upper U(k,n) bound for, and replace the bound with the minimum of U for x(p, 1] .