Sentence examples for in view of the assumption from inspiring English sources

Hence, in view of the assumption,.

In view of the assumption made, we thus have (6.3).

In view of the assumption and (3.40), we see that (3.42).

In view of the assumption for every it follows that (3.27).

In view of the assumption (3.2), the exponential term can be approximated as follows: (3.4).

In view of the assumption on and (2.19), we see that (2.21).

In view of the assumptions on the function ψ, it is clear that (psiinPsi_{0}).

(ii) For (0< p<1), by the reverse Hölder inequality [21], in view of the assumptions and with the same way, we obtain the reverse of (11).

Note that λ 1 [ F u ] ≥ 0, λ 2 [ F u ] ≥ 0 in view of the assumptions H1, H2, H4 and the positivity of Green's function G.

In view of the assumptions (1 - 3), Theorem 2.2 yields that Green's matrix K t, s) of the periodic problem for auxiliary system (3.1) exists and its elements K i,j (t, s), i, j = 1,..., n- 1, are non-negative and satisfy the inequalities (3.4).

In view of the assumptions in Theorem 3.1, it is easy to see that deg { J Q N, Ω ∩ Ker L, 0 } = sgn det W - c ¯ g ( exp { u } )  exp { v - u } ē g ′ ( exp { u } ) u  exp { u } 0  =  sgn - c e ¯ g ′ ( exp { u } ) u g ( exp { u } )  exp { v } ≠ 0, where deg is the Brouwer degree and W = − b ¯ exp { u } − c ¯ g ′ ( exp { u } ) u exp { v } + c ¯ g ( exp { u } ) exp { v − u }.