Sentence examples for a implies that from inspiring English sources

The ellipticity of Q x, D) and the positivity of the operator A, implies that the factor G t (x, ξ) never vanishes and as in the proof of Theorem 3.1 we get that G t - 1 ε x, ξ B H ≤ C 1 + | w 1 - 1 a ε x, ξ | | 1 2 + | t + w 1 - 1 ξ 1 | - 1, (37) x ∈ B ε, ξ ∈ R n, i.e., the operator function G t (εx, ξ) has uniformly bounded inverse for (x, ξ) ∈ B ε ×R n.

Theorem 2.3(a) implies that (1.1) has a nonoscillatory solution.

Now, lim t → 0 t 4 − α x ( t ) = a implies that c 4 = a.

Theorem A implies that the Picard exception value of cannot be nonzero constant.

This inequality, together with Definition 1.3(a), implies that the expression (3.3).

The definition of A implies that there is z ∈ F ( x ∗ ) such that x ∗ ⪯ z.

As CENP-A is an essential protein required for chromosome segregation during mitosis, the association between UDG and CENP-A implies that UDG may be involved in cell proliferation.

The definition of and Lemma 2.2(a) imply that (2.10).

This implies that is a subset of.

This implies that is a singleton.

This implies that is a nonexpansive mapping.