Sentence examples for be essential for proving from inspiring English sources

The next result will be essential for proving the convergence theorems for iterative process.

The estimates are essential for proving the existence of solutions.

The following basic results are essential for proving the main results in Section 3.

This is essential for proving the existence of a weak solution to problem (1.1) using the compactness method.

Also, SynFind was essential for proving that the genome of Utricularia gibba, despite is small size (82 MB), is derived from three sequential WGD events (Ibarra-Laclette et al. 2013).

Extras like WiFi service and guided walks are proving to be essential for second-home owners in Europe who want to attract guests -- and the money that their rentals produce.

This significant improvement in women's education levels has proven to be essential for children's health and well-being.

The quantitative distributions of marker concentrations in target and nontarget samples proved to be essential for the assessment of assay performance and were used to establish a new metric for quantitative source-specificity.

It proved to be essential for Wong's survival, as Farrell lost the seat.

His work ethic, boundless enthusiasm and energy were astonishing, and proved to be essential for accomplishing a week of work in three days without sacrificing quality.

The formation of a C/W emulsion with a continuous aqueous phase proved to be essential for the electroplating reaction.