Establishing in a sentence

All methods of establishing uniqueness can be thought of as establishing that each equilibrium has the same positive local index, in which case by the index theorem there can be but one such equilibrium.

Given the importance in Jewish ritual of establishing the accurate timing of monthly and annual times, some futurist writers and researchers have considered whether a "corrected" system of establishing the Hebrew date is required.

He spent several years establishing his authority there but found some difficulty in establishing his family as successors to the rule of those provinces.

Rudolph I and primogeniture (1278–1358) Rudolf I spent several years establishing his authority in Austria, finding some difficulty in establishing his family as successors to the rule of the province.

Ten years after independence, Slovenia has made tremendous progress establishing democratic institutions, enshrining respect for human rights, establishing a market economy and adapting its military to Western norms and standards.

The initial pioneers were charged with establishing farms, growing crops, building fences and herds, and establishing preliminary settlements to feed and support the many thousands of emigrants expected in the coming years.

About 56 years ago, fans saw the actor establishing the now-iconic rogues gallery in that series.

Accepting Taiwan into international organisations and establishing a stronger Pacific defence alliance are also expected to be on Ms Truss’s wish list.

According to him, establishing such a fund will be the party’s way of showing appreciation for the dedication and services of these personalities to the party.

According to Hon. Offiono, It is alleged that the current Chief of Air Staff, Air Marshal Hassan Abubakar is considering de-establishing the FOB Ogoja for reasons still unknown.

According to Tomlin, practicing in pads is crucial to establishing that competitive demeanor and the physicality you need on the football field and that Pittsburgh lacked against the Texans this past Sunday.

Additionally, our Reno facility continues to make significant progress in establishing base and injector manufacturing.

After establishing a career built in large part on his streams of various first-person shooter games, earlier this year TimTheTatman finally made his first appearance as a playable character in one.

After establishing herself as one of the greatest pop singers of all time, Spears appeared in a number of Pepsi commercials throughout the 2000s.

After establishing the property was unoccupied, the reporter observed the agents work with a locksmith to force their way in and install a prepayment meter.

After re-establishing the SEC as a new entity in the Latrobe Valley, D’Ambrosio says a first priority will be building the 4½ gigawatts of new renewable energy.

Alejandro Garnacho burst onto the scene last season, establishing himself as Man United's most attention-grabbing youngster.

Almost three months have passed since that meeting and Ampadu has wasted no time in establishing himself as one of the driving forces in United’s promotion push with his performances in midfield picking up plaudits from far and wide.

Although Hydra was unsuccessful in establishing its worldwide rule, Pierce managed to sustain a major victory nonetheless.

Although this may be seen as bad news, it actually represents a huge leap forward by establishing that in microbial communities, the whole is much more than the sum of its parts.