The phrase 'guarantee of uniqueness' is correct and usable in written English.
You can use it to emphasize the specialness or exclusivity of something, whether a product, experience, or service. For example, "Our company offers a guarantee of uniqueness, ensuring our customers get an experience that's tailored to their individual needs."
Proof As already mentioned, the continuity of f guarantees the property of uniqueness for the solutions to the Cauchy problem associated to system (1.3), and therefore the trajectories of such a system cannot intersect.
Proof We just notice that the continuity of f guarantees the property of uniqueness for the solutions to the Cauchy problem associated to system (1.2), and therefore the trajectories of such a system cannot intersect.
Necessary and sufficient conditions are derived in order to guarantee the uniqueness of the reconstruction of the discrete state of the system.
The reason why results on uniqueness are so few is due to the fact that except for a few types of mathematical problems, most of the mathematical problems cannot guarantee the uniqueness of the solution.
Adding condition (H) to the hypothesis of Corollary 3.1, we guarantee the uniqueness of the fixed point.
By studying the div curl system this paper clarifies that the first-order Maxwell equations are not "overdetermined," and the divergence equations must always be included to maintain the ellipticity of the system in the space domain, to guarantee the uniqueness of the solution and the accuracy of the numerical methods, and to eliminate the infinitely degenerate eigenvalue.
To guarantee the uniqueness of the numerical solution of the forced response problem, an orthogonality relationship is proposed.
But in order to guarantee the uniqueness of the fixed point of T, we have to consider an additional condition, as in the following theorem.
That is why in this paper we concentrate not only on deriving of the adjoint system, but also on formulation of sufficient conditions which would guarantee the uniqueness of the adjoint state to the optimal pair.
That is why we concentrate not only on deriving the adjoint system, but also, following the well-known Hardy-Poincaré Inequality, on a formulation of sufficient conditions which would guarantee the uniqueness of the adjoint state to the optimal pair.
In contrast to the Banach contraction principle, the Hicks and Rhodes theorem [2] does not guarantee the uniqueness of the fixed point of T. Recently, Ma et al. [3] introduced the notion of (C^ -valued metriC^ -valuednd, analogous to the Banach contraction principle, established a fixed point theoremetric(C^)-valued contraction mappingspaces
