Sentence examples for applying the fact from inspiring English sources

Applying the fact that and, it is easy to check that and.

By equations (3.3), (3.4), and applying the fact that F is nondecreasing, equation (3.7), we deduce that V n + 1 ( t ) ≤ W n + 1 ( t ), t ∈ [ 0, T ].

Applying the fact that the Gaussian distribution maximizes the entropy over all distributions with the same variance [33, Theorem ], we obtain (8).

Applying the fact that ({|nabla u_{n}|^{p-2}nabla u_{n}}) is bounded in (L^{frac{p}{p-1}}(Omega)) and choosing the subsequence, one obtains that |nabla u_{n}|^{p-2}nabla u_{n} rightharpoonup |nabla u|^{p-2}nabla u quadmbox{in } L^{frac{p}{p-1}}( Omega).

Let ( x, y ) is comparable to ( x ∗, y ∗ ) with respect to the ordering in A × A. Applying the fact that F is a proximally coupled weak contraction on A to d ( x, F ( x, y ) ) = d ( A, B ) and d ( x ∗, F ( x ∗, y ∗ ) ) = d ( A, B ), we get ϕ ( d ( x, x ∗ ) ) ≤ 1 2 ϕ ( d ( x, x ∗ ) + d ( y, y ∗ ) ) − ψ ( d ( x, x ∗ ) + d ( y, y ∗ ) 2 ).

And the composition of the court changed around him, moving increasingly to the right, less hospitable to the arduous task of applying the facts of each case.

As a lawyer, I believe the jury did do a superb job of applying the facts to the law.

Reinforce your memorization by applying the facts in real life situations or problem solving.

where we apply the fact that is nondecreasing in.

But a skeptic might ask, "Why ought I apply that fact that I ought to be instrumentally coherent to my actions?" The realist might answer, "Because and here's another normative fact it just is the case that you ought to apply the fact that you ought to be instrumentally coherent to your actions".

Assuming that R h [0] and {A p } are known, we can apply the fact that R h [n] = R h [−n], and recursively find {R h [n]} for n = 1,2,…,P.