Sentence examples for view of assumptions from inspiring English sources

For, a direct calculation yields (3.30). in view of assumptions,,.

In view of assumptions and (3.7), (3.8), and by Lemma 3.2, we obtain (39).

In view of assumptions that g is a Lipschitz function and α ≤ β on ( 0, 1 ), it follows that α ( 1 ) ≤ β ( 1 ).

This conception keeps two of the three basic ingredients of Prawitz-style proof-theoretic semantics (see section 2.2.2): the role of proof reduction and the substitutional view of assumptions.

In view of assumptions (F1 - F3), it readily follows that the multivalued function (Sigma(cdot,cdot):[0,1]times C [-tau,0];H)rightarrow P(L_{2}^{0})) satisfies (H2).

Therefore, in view of assumptions (2) and (3), Theorem 3.1 (see also Remark 3.1) guarantees that the elements K ij, i, j = 1,..., n - 1, of Green's matrix K t, s) of the periodic problem (3.1), (3.2) are positive and satisfy inequalities (3.14).

In view of assumption (H5), we have (3.11).

In view of assumption (H2), we see that this contradicts (2.3).

In view of assumption (v), without loss of generality, let the pair ( f, T ) be absorbing and reciprocal continuous.

end{aligned} In view of assumption (3.19), the last inequality implies that (mathcal{H}_{2}) is a contraction.

In view of assumption (e′1), firstly we assume that g ( X ) is complete, then there exists u ∈ X such that lim n → ∞ g ( x n ) = g ( u ).