Sentence examples for applying the conclusion from inspiring English sources

Applying the conclusion of the first part to the function on, we obtain such that (4.10).

Applying the conclusion of Step 2 and the excision property of fixed point index, we find that i ( T ˜ μ, S ∩ K, K ) = i ( T ˜ μ, B R 1 ∩ K, K ) = 1.

Then applying the conclusion of Lemma 2.1 in [18] and the comparison theorem, there are constants (M_{1}=max{(frac{Lambda}{d})^{u}, 1}) and (T_{1}>0) satisfying S t)+I t)leq M_{1}, quadmbox{for all }tgeq T_{1}.

Thus u < v on ∂ Ω 3 and consequently there is an ε > 0 such that u < v − ε on ∂ Ω 3. Noting that ∇ ( v − ε ) = ∇ v and applying the conclusion (1) to u and v − ε on Ω 3, we obtain u ≤ v − ε in Ω 3, which contradicts u = v on S. □  .

Applying the conclusion in Theorem 1 and Lemma 3, we obtain the following proposition, which converts the finite state sub-channel into a memoryless one: The sub-channel capacity is independent of the initial state and is given by begin{array}rcl@C=max_{Delta}sumlimits_{xiin mathbf{Xi}} sumlimits_{n=1}^{N}left(H(Y_{n}|xi -H(Y_{n}|xi -H,xi)right)Delta(xi), end{arraY_{n35).

Thus, clinicians must use discretion when applying the conclusions derived from both these techniques to the individual patient.

Priti Patel, a Conservative MP, says (with many others) that they are straining public services to breaking point.Politicians are now applying the conclusions they have drawn from the Polish surge to a new group of migrants.

No strong inferences should be drawn from the results of the analysis, and readers should take caution when interpreting and applying the conclusions of the review.

Both studies had used a validation test with high reliability and validity in assessing knowledge and skill in all the usual domains of evidence based medicine by asking focused questions, by searching for good answers, by critiquing literature, and by applying the conclusions to practice[ 36, 43].

so we can apply the conclusion in the previous paragraph to to get the same conclusion.

We may apply the conclusion of Case 3 to deduce our assertion.