Sentence examples for Based on this proof from inspiring English sources

Based on this proof, we know that equality in (36) holds if and only if (P') is the midpoint of the closed straight line segment ([AA_]).

Based on this proof, we know that the equality in (12) holds if and only if Γ is a circle and P is the center of the circle.

Based on this proof, we see that the equality in (21) holds if and only if angle A_{i-1}A_{i}A_{i+1}=frac{N-2}{N}pi, quad i=1,2,ldots,N.

Based on this proof-of-concept preliminary study, we recommend long-term follow-up of patients enrolled in clinical trials to ascertain a more comprehensive assessment of the efficacy of experimental treatments.

Based on this proof-of principle experiment by MALDI-MS, we are currently performing a large-scale comparative quantitative glycomics experiment utilizing DRAG to identify glycan specific differences in the urinary glycome for various diseases.

Based on this preliminary proof-of-concept study, we recommend that long-term follow-up be incorporated into the study design of all clinical trials in nephrology that include pediatric and/or adult patients in order to enable more comprehensive assessment of the effect of the experimental treatments under evaluation (word count: 2301).

In Lemma 2.3, based on the proof line from [53], we make a generalization of this inequality.

Because the proposed algorithm has a similar strategy of backtracking which is used in ASP, the proofs are mainly based on the proof framework of ASP/ACoSaMP.

Based on the proof of Theorem 6.1, we can develop parallel results to Theorems 3.3-3.11 as follows.

Future studies, based on the proof of concept provided here, can explore that question productively for the entire first post-transplant year.

Based on the proof of Theorem 1, the base of the log must be greater then C in order to achieve the speed up.