Sentence examples for result asserted from inspiring English sources

end{aligned} We thus arrive at the desired result asserted by Lemma 3.

end{aligned} (5.12) The result asserted by Theorem 5 follows by applying Lemma 1.

we find from (2.3) and (2.4) the result asserted by Theorem 2.1.

Our eleven main identities are given here in the form of a single unified result asserted in the following theorem.

The proof of our main result asserted by Theorem 2 of the preceding section has made use of some familiar fixed point theorems.

Also in line with these works, we cite paper [12], employed in this present investigation to prove the main result asserted in Theorem 3.1 of Section 3.2 and, in particular, to construct the claimed explicit solution σ to system (1).

Our main result asserts that the following four assertions are equivalent:.

Our main result asserts that in this context, the wave maps system is locally wellposed at almost critical regularity.

Our main result asserts that in this variable-coefficient context, the wave maps system is wellposed at almost-critical regularity.

Our main result asserts that, when α is locally unitary in this sense and  is a locally trivial G-space, (A × G)$̂is a locally trivial Ĝ-space.

Our main result asserts that for G/K of rank at least two, a bounded real-valued function is annihilated by the system L⊕Hc if and only if it is the real part of a holomorphic function.