Sentence examples for existed results from inspiring English sources

Moreover, our proof techniques are simpler than some existed results.

Using the existed results (Theorems 5, 6 and 7) relating to the general invexities, we deduce the similar results for G-generalized invexities; see Theorems 8, 10 and 11.

In sharp contrast to the existed results which can only finite-timely synchronize or stabilize the non-delayed systems, the theoretical results of this paper are more general and rigorous.

Whilst a degree of spatial variability existed, results showed that chlorophyll SOS lagged approximately 20 35 days behind LAI SOS, and the end of season (EOS) LAI dates were predominantly between 20 and 30 days later than chlorophyll EOS.

Compared with those existed results, the adaptive controllers presented in this paper can globally exponentially stabilize the chaotic systems and can globally exponentially synchronize the two chaotic systems under certain conditions, and therefore can improve the convergence rate of the control processes.

Follow-up inspections found that 845 properties had no new violations, while 312 of the hazardous conditions still existed, resulting in additional citations.

Note that we establish the result by applying the above Theorem 8, which is an existed result for semistrictly preinvex function.

Until now, however, little evidence or consensus regarding the optimum delivery of RRT has existed, resulting in wide variations in clinical practice [ 2].

The largest American firms are all keen on developing such vehicles.To the extent that aggregate records for private-equity returns exist, results in China are strong (see table).

Where baseline differences were found to exist, results were analysed using analysis of covariance with baseline values as a covariate.

Although a generalized idea about the accumulation of DNA damage with age exists, results found in the literature are inconsistent.