Sentence examples for completed by utilizing from inspiring English sources

and Ω 11 1, Ω 11 2, λ 1, λ 2 are given in Theorem 1. Remark 1 The proofs of Theorem 1 and Corollary 2 are completed by utilizing the technique involved in [19], so that the mode-transformation technique and the bounding technique are not employed.

With the help of (2.4), we can complete the proof by utilizing Banach's fixed-point theorem and an argument used frequently to prove the well-posedness of Cauchy problems for ordinary differential equations.

"Armed with a consumer's name and ZIP code, Michaels is capable of obtaining its customers' complete mailing address by utilizing a 'reverse phone book' that matches names and ZIP code, which it does in order to increase profits through direct marketing, or it could sell its customers' mailing addresses to third parties," the plaintiff argued in a legal brief filed with the state court.

Plasmodium completes their life cycles by utilizing different host cells as the carrier.

Finally, several projects completed by the FDOT will be utilized to illustrate the validity of this model.

Quantitative data were collected throughout the school year, as indicated by the implementation plan, and utilized measures completed by the student group members, their primary caretakers, and their teachers.

The starting model was completed by iterative rounds of model building utilizing COOT followed by refinement using PHENIX.

It allows organizations to identify opportunities for program / organizational development by utilizing the outcome from the work completed by the volunteers as necessary for the organization.

This study addresses the weak support in previous research for deep nodes in the PACMAD clade by utilizing complete plastomes.

The southern end of this project was completed by 1981, and the roadway directly angled northwesterly instead of utilizing a long sweeping curve between the road to the south and the new road to the north.

A cross-sectional design was utilized by means of the self-report technique through an online questionnaire completed by selected subjects who had provided informed consent.