Sentence examples for valid for a b from inspiring English sources

Scale bar in (c) = 50 μm, and is valid for (a), (b) and (c).

Calibration bar in b (valid for a, b) = 27.5 μm.

The following lemma shows that Lemma 2.3 is also valid for all A, B ∈ P ( E ) and γ = 0. Lemma 3.1 Let E be a metric space.

valid for all a, b > 0 and p ≠ 0. We begin by regarding bounds of l p in a convex-geometric form B p α G 1 - α as well: Theorem 4.1.

Let be a positive solution of (1.1) which is not eventually equal to 1, then the following conclusions are valid: (a) for   (b) for   (c) for   (d) for   (e) for  .

Therefore, the SIT model performs better than the B dot equation does even in the ionic strength range valid for the B dot equation, although the B dot equation does have the general applicability as it does not require any specific interaction coefficients.

The same sequence is valid for b, c and d.

However, if (17) is valid for B given by (15), then it is possible that (17) is not valid for (widetilde{B}(t)=B t)+tilde {c}), where (0<tilde{c}<c).

Remark 1.1 Here we remark that the above estimate is also valid for T Σ b.

end{aligned} This gives us a Banach space (B={fin L^{2}(G):|f|<infty}), which is contained in (L^{2}(M n))) and the space (mathcal{S}(M n))) of (C^{infty} -functions which are rapidly decreasing on (M(n)) can be shown to be dense in B. It suffices to prove the inequality of Theorem 3.2 for functions in (mathcal{S} -functions is automatically valid for any (fin B).

The same conclusion may be valid for the cluster B I, which also exclusively comprised Turkish isolates.