Sentence examples for proved above from inspiring English sources

As we proved above, u defined by (20) is an optimal control of Problem (LQ SOC).

Since     for     and     for  ,  then  ,  and we  are finished (note that we proved above that   ).

In this section, as an application of our results proved above, we deduce certain Suzuki-Wardowski type fixed point theorems.

As an application of Lemma 3.2 and the results proved above, we deduce the following new fixed point theorems in triangular fuzzy metric spaces.

Note that from the case when (n=0) proved above, it follows that for all (K>0), (varphi_{r,f}^{K}(infty )

In virtue of property (19) proved above, the limit (lim_{M_{k}toinfty} vert G^{ k)}_{r,n,f,M_{k}}(0) vert ) does not depend on the choice of the sequence ({M_{k}}_{k=1}^{infty}).

The changes in the shallow ground water level were calculated in 16 shallow wells of the local people around Kamojang Geothermal Field to prove above assumption.

"At this point, with barely any funds, compromised integrity and low trust, Chairman Perez needs to prove above and beyond that he's willing to reform this party," Konst said in a text message to HuffPost.

Once again, Murdoch was to prove above the law.

"Charles Aránguiz has proven above all for the Chile national team what an extraordinary footballer he is," Völler said.

Author now has not enough time to prove above conjecture.