Sentence examples for contributed to the proof from inspiring English sources

D.K. and J.M. contributed to the proof.

He also contributed to the proof of the prime number theorem, a formula for determining the number of primes below a given number.

RM and MK contributed to the proof reading.

YF taught the students as student tutor and contributed to the manuscript including proof reading as native speaker.

Both SP and JR contributed to the discussion and proofing and approved the final manuscript.

YMB, TPS, YSC, JWH, and KLH contributed to the preparation and proof-reading of the manuscript.

According to the Wald criterion, seeing the thermal image significantly contributed to the householder draught proofing their home (p =.02), with the odds ratio of 6.53, which equates to a probability ratio (relative risk) of 4.85 (Osborne, 2006).

All authors contributed to the manuscript preparation, read, and proofed the final manuscript.

ÅMS contributed to the design of the study and performed proof-reading of the recorded data.

Although not presenting the formalism of an experimental study, the use of proof of concept also contributed to the preliminary evaluation of the questions about the evaluation instrument, the mitigation of specific technical difficulties and the refinement of the steps that were, subsequently applied in the case study.

MSZ contributed to the writing of the discussion, final amendments, and proof reading of the manuscript.