Sentence examples for achieving the existence from inspiring English sources

The concentration-compactness principle, which was built by Lions in [7, 8], plays an important role in achieving the existence of a nontrivial solution of the problems in them.

All the numerical examples reported through the paper have clearly highlighted the capability of the proposed approach in successfully achieving the co-existence of IS, AS, and IFSHPS between chaotic and hyperchaotic systems of different dimensions for both commensurate and incommensurate fractional-order systems.

We have tried to achieve the global existence, but it is still an open problem.

UKIP has made itself superfluous by achieving the key point of its existence: Brexit.

Previous research links successful clusters to heightened innovation capacity achieved through the existence of social ties linking individuals across companies.

We have shown through rigorous analysis that full diversity is achieved despite the existence of the eavesdropper.

Meanwhile, the direct kinematics analysis of the MMAMs is achieved automatically, the existence of dead point position in the mechanism within movement range is checked and the micro-displacement amplification ratio is calculated out.

To achieve proving the existence and uniqueness of solution of the given problem (1.5), we employ Banach's contraction mapping principle and Krasnoselskii's fixed point theorem in Section 3.

To achieve this, the existence of a centralised list of data collections (and their associated namespace) was required.

Applying Theorem 3.3, this achieves the proof of the existence of mild solutions of the system (4.1 - 4.3 4.1 - 4.3

Once union was achieved, the self and all existence were seen to be divine.