Sentence examples for use the result in from inspiring English sources

In order to obtain such an estimate we will use the result in Lemma 3. Indeed, we introduce two auxiliary problems: - Δ u ε = f in Ω ε, u ε = 0 on T μ ε, ∂ u ε ∂ ν = 0 on ∂ Ω (16).

When the spectrum of the infinitesimal generator does not only contain eigenvalues, we can use the result in [27], Chapter 4, Theorem 3.10 and Corollary 3.12] for eventually norm continuous semigroups (see Definition A.4 in Appendix A) which links the growth bound of the semigroup to the spectrum of A: (5).

The main difference with the previous design scheme is that we can use the result in the following lemma: The uniform solutions of the non-zero transition probabilities and for the stationary probability vector are p 0, 0 = γ ; p t − 1, t = 1 − γ, for t = 1, 2, … ; P t = γ ( 1 − γ ) t. (63).

We can then use the result in Theorem 1 to obtain begin{aligned} sum _{i=2}^{infty }kappa _ilambda _i^{3/2}&le frac{3}{16}inTr}left}mathrm {Tr}left[ left( Psi ^{-1}QPsi -2F'right) _-^2right] mathrm {d}x end{aligned} (3.13) begin{aligned}&le frac{3}{16}int _0^{1}maTr}leftr}left[ left( Psi ^{-1}QPsi -2F'right) ^2right] mathrm {d}x.

The inequality (a) is from the fact that Pr z max ≤ log M, g ≥ g T, z max ≥ Λ ∗ t − 1 ( S ∗ ) ≤ Pr g ≥ g T, z max ≥ Λ ∗ t − 1 ( S ∗ ), Pr z max ≥ i log M, g ≥ g T, z max ≥ Λ ∗ t − 1 ( S ∗ ) ≤ Pr z max ≥ i log M. For (b), we use the result in [38] (see proof of Theorem 1 in [38]), i.e. Pr ( z max ≥ i log M ) ≤ O ( e O ( i ) M i O ( i ) ) because zmax grows as logM when M→∞.

Physicians could then access test results through the Electronic Patient Record (EPR) and use the result in medical consultations with patients.

It may be possible to construct various useful discrete models by using the result in this paper.

Also, thank them for allowing us to access the data and use the results in this paper.

Use the results in maths to create tables, charts and graphs.

The government will use the results in deciding whether Medicare will cover the operation for those age 65 and over.

He hopes governments may be able to use the results in order to influence behaviour – for example by making more effective use of health education messages.