Sentence examples for establish the uniqueness from inspiring English sources

We classify the solutions and establish the uniqueness of radially symmetric solutions.

We establish the uniqueness for the nonsmooth dissipation coefficient and prove the convergence property of the minimizer of the regularizing cost functional for the inverse problem theoretically.

We establish the uniqueness of this solution for a given choice of the relevant parameters, the radius of the circle to be traced out and the location on the rolling circle of the tracing point.

In Section 4, we establish the uniqueness of the solution.

Now we establish the uniqueness of Suppose there exists such that for some.

We also establish the uniqueness of the solution if the reaction terms satisfy the Lipschitz condition.

Hölder's inequality, Gronwall's inequality, the Burkholder-Davis-Gundy (in short BDG) inequalities, Bihari's inequality and the Picard approximation scheme are used to establish the uniqueness-and-existence theorem.

Based on a conceptual and methodological framework proposed by Robert Rosen we elaborate such an anticipatory view that establishes the uniqueness of design compared to these paradigms.

Establishing the uniqueness of ({x_{k}}).

Furthermore we introduce a criteria establishing the uniqueness of fixed points for the mentioned operators.

Before establishing the uniqueness of NE in the power allocation game, we need the following definition.