Sentence examples for utilized the same as from inspiring English sources

In metric spaces, Jungck [15] introduced the notion of compatible mappings and utilized the same (as a tool) to improve commutativity conditions in common fixed point theorems.

In 1986, Jungck [17] introduced the notion of compatible mappings in metric spaces and utilized the same (as a tool) to improve commutativity conditions in common fixed point theorems.

Five new metal free organic dyes festooned with fluorene and fused thiazine structural units such as FPAA1, FPAA2 and FPTAA1 FPTAA3 have been synthesized by adopting multistep synthetic strategy and investigated nanocrystalline TiO2 based dye-sensitized solar cell performance by utilizing the same as sensitizers.

The new sub-routine utilized parameters whose values are known to the user; the other sub-routines utilized the same parameters as in the first paper.

The second trial, which utilized the same design as the first trial, evaluated formulations of QS-21 in various excipients.

Someone on Twitter also pointed out that The Capri Sun commercial utilized the same technology as the T1000 and Jason Waterfalls in the TLC video for "Waterfalls," and I thought that joke was very funny.

Study 2 utilized the same algorithm as Study 1.

For in vitro biofilm formation under anaerobic conditions, we utilized the same protocol as described above with the following exceptions.

Specifically, we utilized the same approach as that reported by Ref. [ 22] to solve the objective function with L1 regularization.

Both analyses utilized the same covariates as all other models (when controlling for youth reported events, we controlled for youth reported dependent and independent life events, respectively).

The pilot project conducted by us in New Delhi, India, utilized the same methodology as a previous study that monitored antibiotic use in the community through patient exit interviews at private retail pharmacies [ 8].