Sentence examples for assert that there exists from inspiring English sources

Thereby, condition allows to assert that there exists, such that for all (3.9).

First, we assert that there exists such that is completely continuous.

(7) We assert that there exists a positive constant (r_{1}) such that (I_{1} ( r_{1} ) >0).

Also, we can assert that there exists x ∈ ( Ω ¯ 2 ∖ Ω 1 ) ∩ K such that L x = N x.

Therefore, for all so large that, as is a weak solution to, by taking as the test function in(2.5), from (2.9), and, we can assert that there exists such that (2.11).

We assert that there exists a positive constant M such that begin{aligned}& uleq M delta)+bar{u}_{varepsilon},quad xin Omega_{rho}^, end{aligned} (4.3) begin{aligned}& underline{u}_{varepsilon}leq u+M delta),quad xinOmega_{rho}^.

Third, we assert that there exist such that if.

Then by Lemma 6, using (3.24) and (3.25), we assert that there exist ϵ > 0 and two sequences { m k } and { n k } of positive integers such that n k > m k > k and sequences given in (2.2) tends to ϵ as k → ∞.

Observing (3.9), (3.10), (3.11) and applying, respectively, Theorem 2.1 to A, Q r 5, η and Q η, R 4, we assert that there exist u 1 ∈ Q r 5, η and u 2 ∈ Q η, R 4 such that A u 1 = u 1 and A u 2 = u 2 and, by Lemma 2.3 and (3.11), S u 1, S u 2 are positive solutions of BVP (1.1).

The paper asserts that "there exists no appropriate judicial forum to evaluate these constitutional considerations".

Professor Ledenyov, of the Moscow Conservatory, the oldest composer present, serenely maintained the old Soviet line, asserting that "there exists a Russian school of composers" characterized by "a conglomerate of certain features peculiar to this national culture and its folk music".