Sentence examples for prove by using from inspiring English sources

Proof It is easy to prove by using Definition 3.2 and 3.3.

This lemma is easy to prove by using the definition of ((-Delta)^{alpha}u) and inequalities of Strook and Varopoulos, so we omit it.

It is easy to prove by using mathematical induction that E q k n F ( t ) = E q k ( E q k n − 1 F ) ( t ) = F ( q k n t + ( 1 − q k n ) t k ), where n ∈ N and E q k 0 F ( t ) = F ( t ).

We will prove by using the linearization method and Lyapunov function that if (mathcal{R}_{0}leq1), then disease-free equilibrium is globally attractive, and as a result, the disease is also extinct, and by using the theory of persistence for dynamical systems that if (mathcal {R}_{0}>1), then the disease is permanent.

Moreover, we could prove by using the ITS-FAIR ASL approach that a high brain tumor perfusion is related to a short arterial transit time, as previously hypothesized [ 3].

The independence of the axioms is usually proved by using more than two truth values.

It can be proved by using contraction.

Stability and robustness are proved by using Lyapunov's method.

Thus the theorem is proved by using Theorem 5.2.

This lemma can be easily proved by using (6).

This can be proved by using (1.2) and (3.1).