Sentence examples for defined and proven from inspiring English sources

We need politicians to act on already defined and proven ways to get off fossil fuels.

In this paper the problem is mathematically defined and proven NP-complete.

Besides, a lack of defined and proven standards as well as transparency causes a decline of the learning system during the continuous operation.

In addition, the system properties of incremental composition, partial testability and global deadlock-free operation are formally defined and proven in the formalism.

Due to using a clearly defined and proven measurement protocol, abnormalities were mainly caused by transcription errors and could be identified in the plotting step.

Upper bounds on network utilization for any MAC protocol and for fixed linear and grid topologies are defined and proven by Xiao et al. in [53].

It is worth noting that in [33], all the definitions and results we have just mentioned are defined and proved for functions defined on the interval ([0,a]) instead of (A_{q,t}^).

First, based on the theoretical modeling and mathematical analysis, three frequency allocation schemes are proposed and key parameters affecting the capacity are defined and proved with closed-form solutions in different scenarios.

The borderline between flirtation and harassment is hard to define; and proving that someone has crossed it is harder still.

Since he joined "Kaun Banega Crorepati," the Indian version of "Who Wants to Be a Millionaire," in 2000, he has come to define, and prove indispensable to the quiz show that offers ordinary Indians a chance to win 50 million rupees ($911,000).

In the following, we define and prove the variational framework of the dynamic equation (1).