Sentence examples for be proved by applying from inspiring English sources

The optimality can be proved by applying Bellman's equation [15].

This will be proved by applying an inequality due to Agarwal and Pang [30].

It can be proved by applying the method in [1, 12].

The lemma can easily be proved by applying the principle of mathematical induction.

It can be proved by applying Lemma 2.1 and stated as follows.

It can be proved by applying Lemma 2.1 with a similar reasoning as in [10] and stated as follows.

This statement can be proven by applying logarithmic operation at both sides of the objective function of (32), which becomes.

Note that this inequality can itself be proven by applying the Cauchy-Schwarz inequality to (langle mathbb {1}, vert x vert rangle ).

The capability of proposed scheme has been proved by applying it on two practical case studies.

The feasibility of this new method is proved by applying it to two examples.

The steady state motion for such a system is always in one direction, which is proved by applying the Hopf bifurcation theorem.