Sentence examples similar to assuming that hypothesis from inspiring English sources

Assume that Hypothesis 3.1(i - iii) holds and the process (X(cdot,x)) i - iiild solution of (3.1) witholdstiandvalue (xin {matheal{C}}).

Theorem 1 Let us assume that hypotheses (H1) and (H2) are fulfilled and that functions φ, ε, S X → Y Y satisfy the conditions | ( J φ ) ( t ) − φ ( t ) | ≤ ε ( t ), t ∈ X, (4).

Theorem 3.1 Assume that hypotheses (A 1) and (A 2) hold.

Theorem 3.3 Assume that hypotheses (A 2), (A 3), and (A 5) hold.

Assume that Hypothesis 3.1 holds.

Assume that hypothesis (A) holds.

Assume that hypothesis (iii) of Theorem 2.1 holds.

Assume that hypothesis (H0) holds and a, b, c are real constants with (a+b neq0 ).

Assume that hypothesis (H0) holds and a, b, c are real constants with (a+bneq0).

Assume that hypothesis (H1) in Theorem  3.1 holds and begin{aligned} liminf_{xirightarrow+infty}frac{Q xi)}{xi ^{2}}leqfrac{p_{0}M_{2sqrT,M }cdot|p|_{limsup_{xirightarrow+infty}frac{ightarrow+infty}frac{Q xi)}{xi^{2}}.

In our results, we assume that hypothesis (H1) is stronger than f ′ ( x ) ≥ 0. But our results do not depend on signs of the functions b ( t ) and q ( t ).