Sentence examples for same hypothesis as from inspiring English sources

Theorem 3 Let us assume the same hypothesis as in Theorem  2.

Under the same hypothesis as Theorem 3 in [2], there exists a smooth bifurcation branch from ((d_{j}, (0,0))).

However, under the same hypothesis as proposed above for ERVFRDE1, this methylation pattern could correlate with the faint or absent ERV3 env expression in the first trimester highly proliferative CTs.

The rationale for this trial is based on the same hypothesis as the single-fraction radiosurgical studies: to improve pain control and local tumor control via dose intensified radiotherapy for vertebral metastases.

This may be explained by the same hypothesis as for C. cancapae in the Atlantic Ocean, because C. urceolaris also occurs in the warmest waters with lowest viscosities in the Indo-Pacific.

The German physicist Ludwig Prandtl, commonly regarded as the father of modern aerodynamics, arrived independently at the same hypotheses as Lanchester and developed the mathematical treatment.

With the same hypotheses as in Lemma 4.1, the following equality holds: (4.58).

Under the same hypotheses as in Lemma 4.1 one has that the corresponding solution of the system (1.1)–(1.11) satisfies (4.11).

This model is compared to GISTEL, which is another model governed by the same hypotheses as SICIC but differing by the invariability of its parameters in time.

Just notice that if we consider the weak topology in place of τ on X, then we have the same hypotheses as in Theorem 3.2 above.

Theorem 9 Under the same hypotheses as Theorem  8, without the continuity assumption of f, assume that whenever { x n } is a nondecreasing sequence in X such that x n → u ∈ X, x n ⪯ u for all n ∈ N. Then f has a fixed point.