Sentence examples for in the proof process from inspiring English sources

Mathematical induction will be exploited in the proof process, which incorporates three steps.

However, there exists a gap in the proof process of above Theorem CC.

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.

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

In the proof process of Theorem 3.1, we do not use Suzuki's Lemma (see [27]), which was used by many others for obtaining as (see [4, 5, 28]).

end{aligned} In the proof process, we can easily know that for (i=0) equality of inequality (1.10) holds if and only if K is an ellipsoid, and for (0< ileq n-1) if and only if all ((n-i -dimensional sub-con-i -dimensionalin-i -dimensionali))-ball centered at the origin.

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).

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

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

Assuming that the mathematical form of the 6-year harmonic signal to be analyzed can be expressed as the final complex formula f(t) = A exp(iω(t − t 0)), where i is the imaginary unit and ( omega =frac{2pi }{T} ), then, the two important properties of NMWT are as follows (In this article, it is unnecessary to repeat the proof process, which is shown in detailed by Liu et al. 2007).

Using the same techniques in proving Lemma 1, we omit the proof process.