Sentence examples for proof the hypothesis from inspiring English sources

Proof The hypothesis on F gives an ℛ-decomposable vector measure ν 1 on a δ-ring ℛ and an order isometry φ : F → L w 1 ( ν 1 ) (see Theorem 10 in [27] and Section 6 in [13]).

Proof The hypothesis R commutes with M C implies R commutes with M 0, R 1 C = C R 2 and δ ( M C + R ) ( M 0 + R ) n ( I ) = δ M C M n ( I ).

Proof The hypothesis (2.6) clearly implies that there exists a constant R > 0 such that if | x | ≥ R, then A 2 | x | σ ≤ u 0 ( x ) ≤ 2 A | x | σ.

The aim of the present study was to proof the hypothesis that mean urine [TIMP-2]*[IGFBP7] levels in patients with AKI differ significantly to patients without AKI within the first 24 h after surgery.

Proof: The hypotheses imposed on f, c and d imply that the following conditions are valid.

Proof: The hypotheses imposed above ensure by (2.3) and (3.7) that g is an increasing mapping from L l o c 1 ( a, b ] to the order interval [g-, g+] of A R [ a, b ], where r ∫ a t g − = ∑ i = 1 n H i ( t ) K ∫ a t f ¯ i + H 0 ( t ), r ∫ a t g + = ∑ i = 1 n H i ( t ) K ∫ a t f ¯ i + H 0 ( t ), t ∈ [ a, b ].

The proof of the hypothesis is presented through a statistical evaluation of the experiment.

DDT's effectiveness against mosquitoes may actually be proof that the hypothesis works.

The proof of the hypothesis is obtained by performing diffusion bonding of ZrC with Ti/Zr/Ti interlayer under different temperature and time conditions, notably at 1400 °C/1 h/20 MPa.

This study also provided an experimental proof for the hypothesis that moderately supersaturated formulations are valuable alternative to high supersaturation formulations, resulting in optimal in vivo performance, and the degree of supersaturation should be carefully controlled to optimize drug absorption.

Proof By the hypothesis, { x n } ⇀ w.