Sentence examples for proved together from inspiring English sources

In 2010, Avila learned that Mirzakhani had proved, together with the University of Chicago's Alex Eskin, the so-called magic-wand theorem.

An index theorem for higher Chern characters of odd Fredholm modules over crossed product algebras is proved, together with a local formula for the associated cyclic cocycle.

Starting from a heat semigroup, we develop a functional calculus and introduce a paraproduct based on the semigroup, for which commutator estimates and Schauder estimates are proved, together with their paracontrolled extensions.

In Section 3, our main result will be stated and proved, together with examples of application.

The facts that lim n → ∞ v n = u and the point u is unique are proved together.

"Today we proved together that we uphold democracy," President Ashraf Ghani tweeted Saturday.

I'd like to thank them for being a part of our love story, who knows where we would be right now without their help in proving together we are stronger and that #LoveWins!

In addition, Jeannin et al. proved that together with IL-4 or IL-13 and CD40L, CD86 was conducive to CD23-CD21 pasring, as the potential stimulating factor for human IgE and IgG4 synthesis [ 37].

We prove that together with the required generic properties a fair sharing of risks and benefits cannot be guaranteed.

We'd not be asking what our country can do for us, but proving what, together, we can do for our country.

While each of these problems is likely to prove surmountable, together they are clues to a question that will take much longer to answer: Can China make it as a fully modern economy and society?