Sentence examples for foregoing result from inspiring English sources

The foregoing result is applicable for the case where the algebra interior of the system (3.1) is empty.

The foregoing result analysis indicates that the FDE algorithm can efficiently reduce unnecessary DE computation time while maintaining nearly similar coding efficiency as the original 3D-HEVC encoder.

Interchanging the roles of the operators (mathcal{G}_{1}) and (mathcal {G}_{2}) in the foregoing result, we can obtain a second result by requiring the condition: frac{ell}{kappaGamma(beta+1)} zeta-xi)^{beta} zeta-xi^{beta}bigl 1-e^{-kappa zeta instead of (2.5).

Through the foregoing results, the mechanisms of substitution, as proposed in a previous work, have been confirmed to be independent of the type of solvent utilized.

The foregoing results suggest that an intensive phenome-wide analysis approach has the potential to uncover new aspects of brain function and its relation to metabolism that could provide important insights into these disorders.

Most recently, Alam et al. [16] extended the foregoing results for generalized φ-contractions due to Boyd and Wong [17].

The foregoing results prompt us to investigate the synthetic potentiality of pyrazolone 1 toward a variety of electrophilic reagents.

From the foregoing results, quicklime is adjudged to have exhibited somewhat superior engineering properties and therefore creates a more effective stabilization alternative for the soil.

The foregoing results have great potential to be useful for further study in this area, such as linear neutral systems and nonlinear systems.

Thus, the foregoing results would be helpful for profoundly understanding the morphologic properties and functional foundation of both immature and mature BMDCs.

Although the site density is by no means perfect in many parts of the Central Andes, we believe that the foregoing results are a significant improvement over the older 2-D models.