Sentence examples for hence we only need from inspiring English sources

Hence, we only need to focus on the heated half of the pipe.

Hence, we only need to prove (3.22).

Hence, we only need to prove (ii).

and hence, we only need to calculate (overline {Omega }).

Hence we only need to show (k_{9}

Hence we only need to prove the following result.

Hence, here we only need to prove that (chi (overline {mathcal {G}}_{s})leqslant chi (overline {mathcal {G}}_{g})).

Hence, further we only need to consider the stability of the null solution of Cohen-Grossberg neural networks.

Hence, by Proposition 3.1, we only need to prove (i).

Hence, to prove (2.2), we only need to show that (2.5) and (2.6) hold true.

Hence, by Theorem 1, we only need a positive definite matrix P such that | α ˜ k − 1 | < 1, ∀ k ∈ Z, where α ˜ k − 1 = a e α Δ k, i = 1, 2, …, N, are the same as in Theorem 1.