Sentence examples for unbounded exists from inspiring English sources

Otherwise, if x t) is unbounded, ( exists {left{{t}_nright}}_{n=1}^{infty } ), such that ( underset{nto infty }{lim }{t}_n=infty ), let ( xleft {t}_nright)=underset{sin left[T,{x}_nright]}{max}left{x s)right} ); thus, t n  ≥ τ(t n ) ≥ T. ( xleft tau left({t}_nright)right)le underset{sin left[T,{x}_nright]}{max}kern0.5em left{x s)right}=xleft {t}_nright) ).

Consider Algorithm 3.7, if positive definite matrices and are bounded, then one of the following situations occurs: (i the sequence is unbounded, in which case is also unbounded; (ii there exists an index such that for any, and one of the following situations occurs: (a).

Since is unbounded, there exists such that (2.1).

Since is unbounded, there exists a sequence such that.

In fact, if is unbounded, there exists a subsequence, still called, such that as.

Case i. Suppose that is unbounded; there exists such that for.

In fact, if { x n } is unbounded, there exists a subsequence, still called { x n }, such that ∥ x n ∥ → ∞ as n → ∞.

Since (mathcal{C}) is unbounded, there exists ({(lambda_{n},u_{n})}) such that ((lambda _{n},u_{n})inmathcal{C}) and (vert lambda_{n} vert + Vert u_{n} Vert rightarrowinfty).

If is unbounded, then there exists such that.

If the sequence is unbounded, then there exists such that is an escape solution.

First, we suppose that the sequence is unbounded and there exists a constant such that (3.11).