Sentence examples for uniquely exists from inspiring English sources

We show the time-local well-posedness for a system of nonlinear dispersive equations for the water wave interaction[formula]It is shown that for any initial data (u0, v0)∈Hs(R)×Hs−1/2(R) (s⩾0), the solution for the above equation uniquely exists in a subset ofC((−T, T);Hs)×C((−T, T);Hs−1/2) and depends continuously on the data.

The solution of (1.6) uniquely exists.

τ* ∈ (0,T) uniquely exists under Assumption 3.2 and (11).

That is, there uniquely exists trivial solution satisfying (3.8).

Hence, we know that (v_{1}) uniquely exists and is positive.

Then there uniquely exists p ∈ Ω such that Q p 2 x = s [25, 26].

(i if, weak entropy solution of(3.1 is S and has a form as (3.3); (ii)if, weak entropy solution of (3.1) is and has a form as (3.5); (iii) weak entropy solutions formed as (3.3) and (3.5) uniquely exist.

Thirteen of these genes uniquely exist in pKF3-70 but not in R100 or F, and among them only ORF62 contains a trans-membrane domain.

In the second step, distinct subgraphs that uniquely exist in single networks were identified from the modules discovered in the first step.

Moreover, if a geodesic exists uniquely for each (x, y in X), then we call X a uniquely geodesic space.

(tau^ in [ 0, T ]) exists uniquely.