Sentence examples for statement of uniqueness from inspiring English sources

Worn on sleeves, the patches are a fire company's statement of uniqueness.

But I also make this statement of uniqueness based on actual data.

It remains to prove the statement concerning uniqueness of.

We are now able to give the proof of the uniqueness statement of Theorem 5.2.

In view of this Remark and Corollaries 2.3 and 5.1, it is only the uniqueness statement of Theorem 5.2 that remains to be proved here.

As an application of Corollary 3.2 and Theorem 3.3, the result of Redjel's theorem (adding condition (U1) to the statement of Theorem 1.5, the uniqueness of the fixed point can be obtained.

Since Φ ∈ X S is the unique solution of functional equation (41) fulfilling (36), and every solution of (35) satisfies (41), we also obtain the statement concerning the uniqueness of Φ.

The statement of the lemma then follows by the uniqueness of the limit.

Clearly, (6) and (19) are equivalent, whence we derive the statement concerning the uniqueness of ψ. □.

Clearly (36) and (45) are equivalent, so we also obtain the statement on the uniqueness of Φ. □.

Remark 3 Note that from the above proof we can derive a much stronger statement on the uniqueness of T than the one formulated in Theorem 3. Namely, it is easy to see that T : = T m 0 is the unique additive mapping such that (19) holds with some L > 0.