Sentence examples for proceed to extend from inspiring English sources

We now proceed to extend the local bifurcation curves obtained in Theorem 1.1 by the global bifurcation theory of Rabinowitz [16] and its developed version in [17].

We proceed to extend the fractional integral operator I z α to the space L 2 ( U ; H ). Define the fractional integral operator I z α : L 2 ( U ; H ) → L 2 ( U ; H ) by I z α u ( z ) : = ∫ 0 z ( z − ζ ) α − 1 Γ u d ζ, α > 0, where u ∈ L 2 ( U ; H ). We have the following property.

We now proceed to extend this model to accommodate fitness data.

Dip slightly as the flyer jumps in and proceed to extend your arms upward and unbend your legs.

He then proceeded to extend his power over an area corresponding to modern Cheshire, Shropshire, and Hereford and Worcester.

The new rulers of China quickly proceeded to extend their power into the Mongolian steppe, where they encountered agents of the Russian tsar.

Sharapova's racket provider Head never wavered in its support of her, citing her as a "role model and woman of integrity" at the time of her failed test and proceeding to extend her deal.

Since the integral inequalities are considered to be important, therefore the research has been proceeded to extend the investigation for such type of inequalities.

He proceeded to extend the simple tower house, in around 1550, by the addition of a large west range, incorporating a new entrance gate and hall.

We are now proceeding to extend this analysis more broadly to 2011 Ecuador census data which provides sufficient data to construct INSOC variables.

Having established differential protein expression between normal and diseased groups in the pilot study we then proceeded to extend the sample group numbers with the aim of consolidating the results.