Sentence examples for and the proof process from inspiring English sources

This extension can be achieved without any mathematical difficulties, and the proof process is the same as in [32].

For the proof of the form invariance for Ũ, Ṽ and U, V, we refer to [12, 19, 20] and references therein, where the proof process is similar.

The proof of Theorem 1.4 is based on the ideas from [10, 11] and we put some new ingredients in the proof process.

By the proof process of Lemma 2.3 and Theorem 2.1, we can also prove that ((X,g,Delta)) and ((Omega^,g,Delta)) are Menger PM-spaces.

The proof of the form invariance for U ˜ n, V ˜ n and U n, V n can refer to the context in [34], the proof process is similar (for proof details, see the Appendix).

From the proof process of Theorem 2.6, the operator, (3.10). is compact and strongly positive.

We neither construct a specific Lyapunov function for ISS in the proof process of the stability criteria nor design a specific structure of the control inputs.

But what of the axioms that are brought in at the beginning of the proof process?

For the sake of completeness, we give the proof process.

The proof process could be applied to similar problems.

However, the proof process in [2] is three pages.