Sentence examples for by using the assumption from inspiring English sources
Both Bürgi and Kepler were astronomical observers, and Kepler included logarithmic tables in his famous Tabulae Rudolphinae (1627; "Rudolphine Tables"), astronomical tabulations of planetary motion derived by using the assumption of elliptical orbits about the Sun.
By using the assumption that Δ ⊆ E ( G ), we immediately obtain X f ≠ ∅.
By using the assumption of, we can get following equality: (3.5).
By using the assumption, we have α ( x n, x ∗ ) ≥ 1 for all n.
The present work proposes achieving this goal by using the assumption of simple scaling invariance.
These higher response moments should enable better reliability predictions than those obtained by using the assumption of Gaussian responses.
By using the assumptions of the theorem, we conclude the proof.
Proof By using the assumptions of this lemma, we have G 1 ( t, s ) ≥ 0 for all ( t, s ) ∈ [ 0, 1 ] × [ 0, 1 ], and so u ( t ) ≥ 0 for all t ∈ [ 0, 1 ].
On the other hand, by using the assumptions of the theorem we easily get vert x_{n}vert lefrac{Vert fVert _{infty}}{sqrt{vert qvert } (sqrt{vert qvert }-1)}< infty, quad nin mathbb{N}_{0}, from which the boundedness of ((x_{n})_{ninmathbb{N}_{0}}), follows.
Then, by using the key assumption, we establish that the condition ( H h ( γ 0, μ 0 ) ) is a sufficient and necessary condition for the lower semicontinuity, the Hausdorff lower semicontinuity, the continuity and Hausdorff continuity of solutions for (MQVIP).
As shown in Figure 3, we first extrapolated cell C by assuming that cell B was the mean of cells A and C. Then we proceeded to calculate cells D, G, and H by using the same assumption.
